%------------------------------------------------------------------------------
% File : Z3---4.15.1
% Problem : GRA145-1 : TPTP v9.3.0. Released v9.3.0.
% Transfm : none
% Format : tptp
% Command : run_E %s %d THM
% Computer : n012.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Tue May 5 06:33:52 PM UTC 2026
% Result : Unsatisfiable 1.52s 1.74s
% Output : Proof 3.53s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.06 % Problem : GRA145-1 : TPTP v9.3.0. Released v9.3.0.
% 0.00/0.06 % Command : run_E %s %d THM
% 0.07/0.24 % Computer : n012.cluster.edu
% 0.07/0.24 % Model : x86_64 x86_64
% 0.07/0.24 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.07/0.24 % Memory : 8042.1875MB
% 0.07/0.24 % OS : Linux 3.10.0-693.el7.x86_64
% 0.07/0.24 % CPULimit : 300
% 0.07/0.24 % WCLimit : 300
% 0.07/0.24 % DateTime : Mon May 4 23:31:02 EDT 2026
% 0.07/0.24 % CPUTime :
% 1.52/1.74 % SZS status Unsatisfiable
% 1.52/1.74 % SZS output start Proof
% 1.52/1.74 tff(s_type, type, (
% 1.52/1.74 s: $i > $i)).
% 1.52/1.74 tff(elem_1_type, type, (
% 1.52/1.74 elem_1: $i)).
% 1.52/1.74 tff(z_type, type, (
% 1.52/1.74 z: $i)).
% 1.52/1.74 tff(inj_0_type, type, (
% 1.52/1.74 inj_0: $i > $i)).
% 1.52/1.74 tff(r_type, type, (
% 1.52/1.74 r: ( $i * $i ) > $o)).
% 1.52/1.74 tff(b_type, type, (
% 1.52/1.74 b: ( $i * $i ) > $o)).
% 1.52/1.74 tff(1,plain,
% 1.52/1.74 (![Xk!0: $i] : (inj_0(s(Xk!0)) = Xk!0) <=> ![Xk!0: $i] : (inj_0(s(Xk!0)) = Xk!0)),
% 1.52/1.74 inference(rewrite,[status(thm)],[])).
% 1.52/1.74 tff(2,plain,
% 1.52/1.74 (![Y: $i, X: $i] : ((~(s(X) = s(Y))) | (X = Y)) <=> ![Xk!0: $i] : (inj_0(s(Xk!0)) = Xk!0)),
% 1.52/1.74 inference(rewrite,[status(thm)],[])).
% 1.52/1.74 tff(3,plain,
% 1.52/1.74 (![Y: $i, X: $i] : ((~(s(X) = s(Y))) | (X = Y)) <=> ![Y: $i, X: $i] : ((~(s(X) = s(Y))) | (X = Y))),
% 1.52/1.74 inference(rewrite,[status(thm)],[])).
% 1.52/1.74 tff(4,axiom,(![Y: $i, X: $i] : ((~(s(X) = s(Y))) | (X = Y))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','sinj')).
% 1.52/1.74 tff(5,plain,
% 1.52/1.74 (![Y: $i, X: $i] : ((~(s(X) = s(Y))) | (X = Y))),
% 1.52/1.74 inference(modus_ponens,[status(thm)],[4, 3])).
% 1.52/1.74 tff(6,plain,(
% 1.52/1.74 ![Y: $i, X: $i] : ((~(s(X) = s(Y))) | (X = Y))),
% 1.52/1.74 inference(skolemize,[status(sab)],[5])).
% 1.52/1.74 tff(7,plain,
% 1.52/1.74 (![Xk!0: $i] : (inj_0(s(Xk!0)) = Xk!0)),
% 1.52/1.74 inference(modus_ponens,[status(thm)],[6, 2])).
% 1.52/1.74 tff(8,plain,
% 1.52/1.74 (![Xk!0: $i] : (inj_0(s(Xk!0)) = Xk!0)),
% 1.52/1.74 inference(modus_ponens,[status(thm)],[7, 1])).
% 1.52/1.74 tff(9,plain,
% 1.52/1.74 ((~![Xk!0: $i] : (inj_0(s(Xk!0)) = Xk!0)) | (inj_0(s(s(s(s(s(s(s(s(elem!1))))))))) = s(s(s(s(s(s(s(elem!1))))))))),
% 1.52/1.74 inference(quant_inst,[status(thm)],[])).
% 1.52/1.74 tff(10,plain,
% 1.52/1.74 (inj_0(s(s(s(s(s(s(s(s(elem!1))))))))) = s(s(s(s(s(s(s(elem!1)))))))),
% 1.52/1.74 inference(unit_resolution,[status(thm)],[9, 8])).
% 1.52/1.74 tff(11,assumption,(~(s(s(elem!1)) = s(s(z)))), introduced(assumption)).
% 1.52/1.74 tff(12,assumption,(z = elem!1), introduced(assumption)).
% 1.52/1.74 tff(13,plain,
% 1.52/1.74 (s(z) = s(elem!1)),
% 1.52/1.74 inference(monotonicity,[status(thm)],[12])).
% 1.52/1.74 tff(14,plain,
% 1.52/1.74 (s(s(z)) = s(s(elem!1))),
% 1.52/1.74 inference(monotonicity,[status(thm)],[13])).
% 1.52/1.74 tff(15,plain,
% 1.52/1.74 (s(s(elem!1)) = s(s(z))),
% 1.52/1.74 inference(symmetry,[status(thm)],[14])).
% 1.52/1.74 tff(16,plain,
% 1.52/1.74 ($false),
% 1.52/1.74 inference(unit_resolution,[status(thm)],[11, 15])).
% 1.52/1.74 tff(17,plain,((~(z = elem!1)) | (s(s(elem!1)) = s(s(z)))), inference(lemma,lemma(discharge,[]))).
% 1.52/1.74 tff(18,plain,
% 1.52/1.74 (~(z = elem!1)),
% 1.52/1.74 inference(unit_resolution,[status(thm)],[17, 11])).
% 1.52/1.74 tff(19,plain,
% 1.52/1.74 ((~![Xk!0: $i] : (inj_0(s(Xk!0)) = Xk!0)) | (inj_0(s(elem!1)) = elem!1)),
% 1.52/1.74 inference(quant_inst,[status(thm)],[])).
% 1.52/1.74 tff(20,plain,
% 1.52/1.74 (inj_0(s(elem!1)) = elem!1),
% 1.52/1.74 inference(unit_resolution,[status(thm)],[19, 8])).
% 1.52/1.74 tff(21,assumption,(s(elem!1) = s(z)), introduced(assumption)).
% 1.52/1.74 tff(22,plain,
% 1.52/1.74 (inj_0(s(elem!1)) = inj_0(s(z))),
% 1.52/1.74 inference(monotonicity,[status(thm)],[21])).
% 1.52/1.74 tff(23,plain,
% 1.52/1.74 (inj_0(s(z)) = inj_0(s(elem!1))),
% 1.52/1.74 inference(symmetry,[status(thm)],[22])).
% 1.52/1.74 tff(24,plain,
% 1.52/1.74 ((~![Xk!0: $i] : (inj_0(s(Xk!0)) = Xk!0)) | (inj_0(s(z)) = z)),
% 1.52/1.74 inference(quant_inst,[status(thm)],[])).
% 1.52/1.74 tff(25,plain,
% 1.52/1.74 (inj_0(s(z)) = z),
% 1.52/1.74 inference(unit_resolution,[status(thm)],[24, 8])).
% 1.52/1.74 tff(26,plain,
% 1.52/1.74 (z = inj_0(s(z))),
% 1.52/1.74 inference(symmetry,[status(thm)],[25])).
% 1.52/1.74 tff(27,plain,
% 1.52/1.74 (z = elem!1),
% 1.52/1.74 inference(transitivity,[status(thm)],[26, 23, 20])).
% 1.52/1.74 tff(28,assumption,(~(z = elem!1)), introduced(assumption)).
% 1.52/1.74 tff(29,plain,
% 1.52/1.74 ($false),
% 1.52/1.74 inference(unit_resolution,[status(thm)],[28, 27])).
% 1.52/1.74 tff(30,plain,((~(s(elem!1) = s(z))) | (z = elem!1)), inference(lemma,lemma(discharge,[]))).
% 1.52/1.74 tff(31,plain,
% 1.52/1.74 (~(s(elem!1) = s(z))),
% 1.52/1.74 inference(unit_resolution,[status(thm)],[30, 18])).
% 1.52/1.74 tff(32,plain,
% 1.52/1.74 ((~![Xk!0: $i] : (inj_0(s(Xk!0)) = Xk!0)) | (inj_0(s(s(z))) = s(z))),
% 1.52/1.74 inference(quant_inst,[status(thm)],[])).
% 1.52/1.74 tff(33,plain,
% 1.52/1.74 (inj_0(s(s(z))) = s(z)),
% 1.52/1.74 inference(unit_resolution,[status(thm)],[32, 8])).
% 1.52/1.74 tff(34,assumption,(s(s(z)) = s(s(elem!1))), introduced(assumption)).
% 1.52/1.74 tff(35,plain,
% 1.52/1.74 (inj_0(s(s(z))) = inj_0(s(s(elem!1)))),
% 1.52/1.74 inference(monotonicity,[status(thm)],[34])).
% 1.52/1.74 tff(36,plain,
% 1.52/1.74 (inj_0(s(s(elem!1))) = inj_0(s(s(z)))),
% 1.52/1.74 inference(symmetry,[status(thm)],[35])).
% 1.52/1.74 tff(37,plain,
% 1.52/1.74 ((~![Xk!0: $i] : (inj_0(s(Xk!0)) = Xk!0)) | (inj_0(s(s(elem!1))) = s(elem!1))),
% 1.52/1.75 inference(quant_inst,[status(thm)],[])).
% 1.52/1.75 tff(38,plain,
% 1.52/1.75 (inj_0(s(s(elem!1))) = s(elem!1)),
% 1.52/1.75 inference(unit_resolution,[status(thm)],[37, 8])).
% 1.52/1.75 tff(39,plain,
% 1.52/1.75 (s(elem!1) = inj_0(s(s(elem!1)))),
% 1.52/1.75 inference(symmetry,[status(thm)],[38])).
% 1.52/1.75 tff(40,plain,
% 1.52/1.75 (s(elem!1) = s(z)),
% 1.52/1.75 inference(transitivity,[status(thm)],[39, 36, 33])).
% 1.52/1.75 tff(41,assumption,(~(s(elem!1) = s(z))), introduced(assumption)).
% 1.52/1.75 tff(42,plain,
% 1.52/1.75 ($false),
% 1.52/1.75 inference(unit_resolution,[status(thm)],[41, 40])).
% 1.52/1.75 tff(43,plain,((~(s(s(z)) = s(s(elem!1)))) | (s(elem!1) = s(z))), inference(lemma,lemma(discharge,[]))).
% 1.52/1.75 tff(44,plain,
% 1.52/1.75 (~(s(s(z)) = s(s(elem!1)))),
% 1.52/1.75 inference(unit_resolution,[status(thm)],[43, 31])).
% 1.52/1.75 tff(45,assumption,(~(s(s(elem!1)) = s(s(s(elem!1))))), introduced(assumption)).
% 1.52/1.75 tff(46,plain,
% 1.52/1.75 ((s(s(s(elem!1))) = s(s(elem!1))) <=> (s(s(elem!1)) = s(s(s(elem!1))))),
% 1.52/1.75 inference(commutativity,[status(thm)],[])).
% 1.52/1.75 tff(47,assumption,(s(s(s(elem!1))) = s(s(elem!1))), introduced(assumption)).
% 1.52/1.75 tff(48,plain,
% 1.52/1.75 (s(s(elem!1)) = s(s(s(elem!1)))),
% 1.52/1.75 inference(modus_ponens,[status(thm)],[47, 46])).
% 1.52/1.75 tff(49,plain,
% 1.52/1.75 ($false),
% 1.52/1.75 inference(unit_resolution,[status(thm)],[45, 48])).
% 1.52/1.75 tff(50,plain,((~(s(s(s(elem!1))) = s(s(elem!1)))) | (s(s(elem!1)) = s(s(s(elem!1))))), inference(lemma,lemma(discharge,[]))).
% 1.52/1.75 tff(51,plain,
% 1.52/1.75 (~(s(s(s(elem!1))) = s(s(elem!1)))),
% 1.52/1.75 inference(unit_resolution,[status(thm)],[50, 45])).
% 1.52/1.75 tff(52,assumption,(~(s(s(z)) = s(s(elem!1)))), introduced(assumption)).
% 1.52/1.75 tff(53,assumption,(b(s(z), z)), introduced(assumption)).
% 1.52/1.75 tff(54,assumption,(~b(s(z), s(s(elem!1)))), introduced(assumption)).
% 1.52/1.75 tff(55,assumption,(s(z) = s(s(elem!1))), introduced(assumption)).
% 1.52/1.75 tff(56,plain,
% 1.52/1.75 (inj_0(s(z)) = inj_0(s(s(elem!1)))),
% 1.52/1.75 inference(monotonicity,[status(thm)],[55])).
% 1.52/1.75 tff(57,plain,
% 1.52/1.75 (inj_0(s(s(elem!1))) = inj_0(s(z))),
% 1.52/1.75 inference(symmetry,[status(thm)],[56])).
% 1.52/1.75 tff(58,plain,
% 1.52/1.75 (s(elem!1) = z),
% 1.52/1.75 inference(transitivity,[status(thm)],[39, 57, 25])).
% 1.52/1.75 tff(59,plain,
% 1.52/1.75 (^[X: $i] : refl((~(s(X) = z)) <=> (~(s(X) = z)))),
% 1.52/1.75 inference(bind,[status(th)],[])).
% 1.52/1.75 tff(60,plain,
% 1.52/1.75 (![X: $i] : (~(s(X) = z)) <=> ![X: $i] : (~(s(X) = z))),
% 1.52/1.75 inference(quant_intro,[status(thm)],[59])).
% 1.52/1.75 tff(61,plain,
% 1.52/1.75 (![X: $i] : (~(s(X) = z)) <=> ![X: $i] : (~(s(X) = z))),
% 1.52/1.75 inference(rewrite,[status(thm)],[])).
% 1.52/1.75 tff(62,axiom,(![X: $i] : (~(s(X) = z))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','snz')).
% 1.52/1.75 tff(63,plain,
% 1.52/1.75 (![X: $i] : (~(s(X) = z))),
% 1.52/1.75 inference(modus_ponens,[status(thm)],[62, 61])).
% 1.52/1.75 tff(64,plain,(
% 1.52/1.75 ![X: $i] : (~(s(X) = z))),
% 1.52/1.75 inference(skolemize,[status(sab)],[63])).
% 1.52/1.75 tff(65,plain,
% 1.52/1.75 (![X: $i] : (~(s(X) = z))),
% 1.52/1.75 inference(modus_ponens,[status(thm)],[64, 60])).
% 1.52/1.75 tff(66,plain,
% 1.52/1.75 ((~![X: $i] : (~(s(X) = z))) | (~(s(elem!1) = z))),
% 1.52/1.75 inference(quant_inst,[status(thm)],[])).
% 1.52/1.75 tff(67,plain,
% 1.52/1.75 (~(s(elem!1) = z)),
% 1.52/1.75 inference(unit_resolution,[status(thm)],[66, 65])).
% 1.52/1.75 tff(68,plain,
% 1.52/1.75 ($false),
% 1.52/1.75 inference(unit_resolution,[status(thm)],[67, 58])).
% 1.52/1.75 tff(69,plain,(~(s(z) = s(s(elem!1)))), inference(lemma,lemma(discharge,[]))).
% 1.52/1.75 tff(70,plain,
% 1.52/1.75 (^[Y: $i, X: $i] : refl(((X = Y) | b(X, Y) | r(X, Y)) <=> ((X = Y) | b(X, Y) | r(X, Y)))),
% 1.52/1.75 inference(bind,[status(th)],[])).
% 1.52/1.75 tff(71,plain,
% 1.52/1.75 (![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y)) <=> ![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))),
% 1.52/1.75 inference(quant_intro,[status(thm)],[70])).
% 1.52/1.75 tff(72,plain,
% 1.52/1.75 (![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y)) <=> ![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))),
% 1.52/1.75 inference(rewrite,[status(thm)],[])).
% 1.52/1.75 tff(73,plain,
% 1.52/1.75 (^[Y: $i, X: $i] : rewrite((((X = Y) | r(X, Y)) | b(X, Y)) <=> ((X = Y) | b(X, Y) | r(X, Y)))),
% 1.52/1.75 inference(bind,[status(th)],[])).
% 1.52/1.75 tff(74,plain,
% 1.52/1.75 (![Y: $i, X: $i] : (((X = Y) | r(X, Y)) | b(X, Y)) <=> ![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))),
% 1.52/1.75 inference(quant_intro,[status(thm)],[73])).
% 1.52/1.75 tff(75,axiom,(![Y: $i, X: $i] : (((X = Y) | r(X, Y)) | b(X, Y))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','rb')).
% 1.52/1.75 tff(76,plain,
% 1.52/1.75 (![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))),
% 1.52/1.75 inference(modus_ponens,[status(thm)],[75, 74])).
% 1.52/1.75 tff(77,plain,
% 1.52/1.75 (![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))),
% 1.52/1.75 inference(modus_ponens,[status(thm)],[76, 72])).
% 1.52/1.75 tff(78,plain,(
% 1.52/1.75 ![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))),
% 1.52/1.75 inference(skolemize,[status(sab)],[77])).
% 1.52/1.75 tff(79,plain,
% 1.52/1.75 (![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))),
% 1.52/1.75 inference(modus_ponens,[status(thm)],[78, 71])).
% 1.52/1.75 tff(80,plain,
% 1.52/1.75 (((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((s(z) = s(s(elem!1))) | b(s(z), s(s(elem!1))) | r(s(z), s(s(elem!1))))) <=> ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (s(z) = s(s(elem!1))) | b(s(z), s(s(elem!1))) | r(s(z), s(s(elem!1))))),
% 1.52/1.75 inference(rewrite,[status(thm)],[])).
% 1.52/1.75 tff(81,plain,
% 1.52/1.75 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((s(z) = s(s(elem!1))) | b(s(z), s(s(elem!1))) | r(s(z), s(s(elem!1))))),
% 1.52/1.75 inference(quant_inst,[status(thm)],[])).
% 1.52/1.75 tff(82,plain,
% 1.52/1.75 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (s(z) = s(s(elem!1))) | b(s(z), s(s(elem!1))) | r(s(z), s(s(elem!1)))),
% 1.52/1.75 inference(modus_ponens,[status(thm)],[81, 80])).
% 1.52/1.75 tff(83,plain,
% 1.52/1.75 ((s(z) = s(s(elem!1))) | b(s(z), s(s(elem!1))) | r(s(z), s(s(elem!1)))),
% 1.52/1.75 inference(unit_resolution,[status(thm)],[82, 79])).
% 1.52/1.75 tff(84,plain,
% 1.52/1.75 (b(s(z), s(s(elem!1))) | r(s(z), s(s(elem!1)))),
% 1.52/1.75 inference(unit_resolution,[status(thm)],[83, 69])).
% 1.52/1.75 tff(85,plain,
% 1.52/1.75 (r(s(z), s(s(elem!1)))),
% 1.52/1.75 inference(unit_resolution,[status(thm)],[84, 54])).
% 1.52/1.75 tff(86,assumption,(~r(s(s(s(elem!1))), z)), introduced(assumption)).
% 1.52/1.75 tff(87,assumption,(~b(s(s(s(elem!1))), z)), introduced(assumption)).
% 1.52/1.75 tff(88,plain,
% 1.52/1.75 ((~![X: $i] : (~(s(X) = z))) | (~(s(s(s(elem!1))) = z))),
% 1.52/1.75 inference(quant_inst,[status(thm)],[])).
% 1.52/1.75 tff(89,plain,
% 1.52/1.75 (~(s(s(s(elem!1))) = z)),
% 1.52/1.75 inference(unit_resolution,[status(thm)],[88, 65])).
% 1.52/1.75 tff(90,plain,
% 1.52/1.75 (((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((s(s(s(elem!1))) = z) | b(s(s(s(elem!1))), z) | r(s(s(s(elem!1))), z))) <=> ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (s(s(s(elem!1))) = z) | b(s(s(s(elem!1))), z) | r(s(s(s(elem!1))), z))),
% 1.52/1.75 inference(rewrite,[status(thm)],[])).
% 1.52/1.75 tff(91,plain,
% 1.52/1.75 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((s(s(s(elem!1))) = z) | b(s(s(s(elem!1))), z) | r(s(s(s(elem!1))), z))),
% 1.52/1.75 inference(quant_inst,[status(thm)],[])).
% 1.52/1.75 tff(92,plain,
% 1.52/1.75 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (s(s(s(elem!1))) = z) | b(s(s(s(elem!1))), z) | r(s(s(s(elem!1))), z)),
% 1.52/1.75 inference(modus_ponens,[status(thm)],[91, 90])).
% 1.52/1.75 tff(93,plain,
% 1.52/1.75 ($false),
% 1.52/1.75 inference(unit_resolution,[status(thm)],[92, 79, 89, 86, 87])).
% 1.52/1.75 tff(94,plain,(b(s(s(s(elem!1))), z) | r(s(s(s(elem!1))), z)), inference(lemma,lemma(discharge,[]))).
% 1.52/1.75 tff(95,plain,
% 1.52/1.75 (b(s(s(s(elem!1))), z)),
% 1.52/1.75 inference(unit_resolution,[status(thm)],[94, 86])).
% 1.52/1.75 tff(96,assumption,(b(s(s(s(elem!1))), s(z))), introduced(assumption)).
% 1.52/1.75 tff(97,assumption,(r(s(z), z)), introduced(assumption)).
% 1.52/1.75 tff(98,assumption,(~b(s(z), s(s(s(elem!1))))), introduced(assumption)).
% 1.52/1.75 tff(99,assumption,(s(z) = s(s(s(elem!1)))), introduced(assumption)).
% 1.52/1.75 tff(100,plain,
% 1.52/1.75 (s(s(s(elem!1))) = s(z)),
% 1.52/1.75 inference(symmetry,[status(thm)],[99])).
% 1.52/1.75 tff(101,assumption,(s(s(s(elem!1))) = s(z)), introduced(assumption)).
% 1.52/1.75 tff(102,plain,
% 1.52/1.75 (inj_0(s(s(s(elem!1)))) = inj_0(s(z))),
% 1.52/1.75 inference(monotonicity,[status(thm)],[101])).
% 1.52/1.75 tff(103,plain,
% 1.52/1.75 ((~![Xk!0: $i] : (inj_0(s(Xk!0)) = Xk!0)) | (inj_0(s(s(s(elem!1)))) = s(s(elem!1)))),
% 1.52/1.75 inference(quant_inst,[status(thm)],[])).
% 1.52/1.75 tff(104,plain,
% 1.52/1.75 (inj_0(s(s(s(elem!1)))) = s(s(elem!1))),
% 1.52/1.75 inference(unit_resolution,[status(thm)],[103, 8])).
% 1.52/1.75 tff(105,plain,
% 1.52/1.75 (s(s(elem!1)) = inj_0(s(s(s(elem!1))))),
% 1.52/1.75 inference(symmetry,[status(thm)],[104])).
% 1.52/1.75 tff(106,plain,
% 1.52/1.75 (s(s(elem!1)) = z),
% 1.52/1.75 inference(transitivity,[status(thm)],[105, 102, 25])).
% 1.52/1.75 tff(107,plain,
% 1.52/1.75 ((~![X: $i] : (~(s(X) = z))) | (~(s(s(elem!1)) = z))),
% 1.52/1.75 inference(quant_inst,[status(thm)],[])).
% 1.52/1.75 tff(108,plain,
% 1.52/1.75 (~(s(s(elem!1)) = z)),
% 1.52/1.75 inference(unit_resolution,[status(thm)],[107, 65])).
% 1.52/1.75 tff(109,plain,
% 1.52/1.75 ($false),
% 1.52/1.75 inference(unit_resolution,[status(thm)],[108, 106])).
% 1.52/1.75 tff(110,plain,(~(s(s(s(elem!1))) = s(z))), inference(lemma,lemma(discharge,[]))).
% 1.52/1.75 tff(111,plain,
% 1.52/1.75 ($false),
% 1.52/1.75 inference(unit_resolution,[status(thm)],[110, 100])).
% 1.52/1.75 tff(112,plain,(~(s(z) = s(s(s(elem!1))))), inference(lemma,lemma(discharge,[]))).
% 1.52/1.75 tff(113,plain,
% 1.52/1.75 (((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((s(z) = s(s(s(elem!1)))) | b(s(z), s(s(s(elem!1)))) | r(s(z), s(s(s(elem!1)))))) <=> ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (s(z) = s(s(s(elem!1)))) | b(s(z), s(s(s(elem!1)))) | r(s(z), s(s(s(elem!1)))))),
% 1.52/1.75 inference(rewrite,[status(thm)],[])).
% 1.52/1.75 tff(114,plain,
% 1.52/1.75 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((s(z) = s(s(s(elem!1)))) | b(s(z), s(s(s(elem!1)))) | r(s(z), s(s(s(elem!1)))))),
% 1.52/1.75 inference(quant_inst,[status(thm)],[])).
% 1.52/1.75 tff(115,plain,
% 1.52/1.75 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (s(z) = s(s(s(elem!1)))) | b(s(z), s(s(s(elem!1)))) | r(s(z), s(s(s(elem!1))))),
% 1.52/1.75 inference(modus_ponens,[status(thm)],[114, 113])).
% 1.52/1.75 tff(116,plain,
% 1.52/1.75 (b(s(z), s(s(s(elem!1)))) | r(s(z), s(s(s(elem!1))))),
% 1.52/1.75 inference(unit_resolution,[status(thm)],[115, 79, 112])).
% 1.52/1.75 tff(117,plain,
% 1.52/1.75 (r(s(z), s(s(s(elem!1))))),
% 1.52/1.75 inference(unit_resolution,[status(thm)],[116, 98])).
% 1.52/1.75 tff(118,assumption,(b(z, s(z))), introduced(assumption)).
% 1.52/1.75 tff(119,assumption,(r(s(z), s(s(s(elem!1))))), introduced(assumption)).
% 1.52/1.75 tff(120,assumption,(r(s(z), s(s(z)))), introduced(assumption)).
% 1.52/1.75 tff(121,assumption,(b(s(s(s(elem!1))), z)), introduced(assumption)).
% 1.52/1.75 tff(122,assumption,(b(s(s(z)), z)), introduced(assumption)).
% 1.52/1.75 tff(123,plain,
% 1.52/1.75 ((s(s(s(s(elem!1)))) = s(s(elem!1))) <=> (s(s(elem!1)) = s(s(s(s(elem!1)))))),
% 1.52/1.75 inference(commutativity,[status(thm)],[])).
% 1.52/1.75 tff(124,plain,
% 1.52/1.75 ((s(s(elem!1)) = s(s(s(s(elem!1))))) <=> (s(s(s(s(elem!1)))) = s(s(elem!1)))),
% 1.52/1.75 inference(symmetry,[status(thm)],[123])).
% 1.52/1.75 tff(125,assumption,(~b(z, s(s(z)))), introduced(assumption)).
% 1.52/1.75 tff(126,plain,
% 1.52/1.75 ((s(s(z)) = s(s(elem!1))) <=> (s(s(elem!1)) = s(s(z)))),
% 1.52/1.75 inference(commutativity,[status(thm)],[])).
% 1.52/1.75 tff(127,plain,
% 1.52/1.75 ((s(s(elem!1)) = s(s(z))) <=> (s(s(z)) = s(s(elem!1)))),
% 1.52/1.75 inference(symmetry,[status(thm)],[126])).
% 1.52/1.75 tff(128,assumption,(s(s(elem!1)) = s(s(z))), introduced(assumption)).
% 1.52/1.75 tff(129,plain,
% 1.52/1.75 (s(s(z)) = s(s(elem!1))),
% 1.52/1.75 inference(modus_ponens,[status(thm)],[128, 127])).
% 1.52/1.75 tff(130,plain,
% 1.52/1.75 ($false),
% 1.52/1.75 inference(unit_resolution,[status(thm)],[52, 129])).
% 1.52/1.75 tff(131,plain,((~(s(s(elem!1)) = s(s(z)))) | (s(s(z)) = s(s(elem!1)))), inference(lemma,lemma(discharge,[]))).
% 1.52/1.75 tff(132,plain,
% 1.52/1.75 (~(s(s(elem!1)) = s(s(z)))),
% 1.52/1.75 inference(unit_resolution,[status(thm)],[131, 52])).
% 1.52/1.75 tff(133,plain,
% 1.52/1.75 ((~![Xk!0: $i] : (inj_0(s(Xk!0)) = Xk!0)) | (inj_0(s(s(s(z)))) = s(s(z)))),
% 1.52/1.75 inference(quant_inst,[status(thm)],[])).
% 1.52/1.75 tff(134,plain,
% 1.52/1.75 (inj_0(s(s(s(z)))) = s(s(z))),
% 1.52/1.75 inference(unit_resolution,[status(thm)],[133, 8])).
% 1.52/1.75 tff(135,assumption,(s(s(s(elem!1))) = s(s(s(z)))), introduced(assumption)).
% 1.52/1.75 tff(136,plain,
% 1.52/1.75 (inj_0(s(s(s(elem!1)))) = inj_0(s(s(s(z))))),
% 1.52/1.75 inference(monotonicity,[status(thm)],[135])).
% 1.52/1.75 tff(137,plain,
% 1.52/1.75 (s(s(elem!1)) = s(s(z))),
% 1.52/1.75 inference(transitivity,[status(thm)],[105, 136, 134])).
% 1.52/1.75 tff(138,plain,
% 1.52/1.75 ($false),
% 1.52/1.75 inference(unit_resolution,[status(thm)],[11, 137])).
% 1.52/1.75 tff(139,plain,((~(s(s(s(elem!1))) = s(s(s(z))))) | (s(s(elem!1)) = s(s(z)))), inference(lemma,lemma(discharge,[]))).
% 1.52/1.75 tff(140,plain,
% 1.52/1.75 (~(s(s(s(elem!1))) = s(s(s(z))))),
% 1.52/1.75 inference(unit_resolution,[status(thm)],[139, 132])).
% 1.52/1.75 tff(141,plain,
% 1.52/1.75 ((z = s(s(z))) <=> (s(s(z)) = z)),
% 1.52/1.75 inference(commutativity,[status(thm)],[])).
% 1.52/1.75 tff(142,plain,
% 1.52/1.75 ((s(s(z)) = z) <=> (z = s(s(z)))),
% 1.52/1.75 inference(symmetry,[status(thm)],[141])).
% 1.52/1.75 tff(143,plain,
% 1.52/1.75 ((~(s(s(z)) = z)) <=> (~(z = s(s(z))))),
% 1.52/1.75 inference(monotonicity,[status(thm)],[142])).
% 1.52/1.75 tff(144,plain,
% 1.52/1.75 ((~![X: $i] : (~(s(X) = z))) | (~(s(s(z)) = z))),
% 1.52/1.75 inference(quant_inst,[status(thm)],[])).
% 1.52/1.75 tff(145,plain,
% 1.52/1.75 (~(s(s(z)) = z)),
% 1.52/1.75 inference(unit_resolution,[status(thm)],[144, 65])).
% 1.52/1.75 tff(146,plain,
% 1.52/1.75 (~(z = s(s(z)))),
% 1.52/1.75 inference(modus_ponens,[status(thm)],[145, 143])).
% 1.52/1.75 tff(147,plain,
% 1.52/1.75 (((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((z = s(s(z))) | b(z, s(s(z))) | r(z, s(s(z))))) <=> ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (z = s(s(z))) | b(z, s(s(z))) | r(z, s(s(z))))),
% 1.52/1.75 inference(rewrite,[status(thm)],[])).
% 1.52/1.75 tff(148,plain,
% 1.52/1.75 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((z = s(s(z))) | b(z, s(s(z))) | r(z, s(s(z))))),
% 1.52/1.75 inference(quant_inst,[status(thm)],[])).
% 1.52/1.75 tff(149,plain,
% 1.52/1.75 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (z = s(s(z))) | b(z, s(s(z))) | r(z, s(s(z)))),
% 1.52/1.75 inference(modus_ponens,[status(thm)],[148, 147])).
% 1.52/1.75 tff(150,plain,
% 1.52/1.75 ((z = s(s(z))) | b(z, s(s(z))) | r(z, s(s(z)))),
% 1.52/1.75 inference(unit_resolution,[status(thm)],[149, 79])).
% 1.52/1.75 tff(151,plain,
% 1.52/1.75 (b(z, s(s(z))) | r(z, s(s(z)))),
% 1.52/1.75 inference(unit_resolution,[status(thm)],[150, 146])).
% 1.52/1.75 tff(152,plain,
% 1.52/1.75 (r(z, s(s(z)))),
% 1.52/1.75 inference(unit_resolution,[status(thm)],[151, 125])).
% 1.52/1.75 tff(153,plain,
% 1.52/1.75 (r(s(s(s(elem!1))), z)),
% 1.52/1.75 inference(unit_resolution,[status(thm)],[94, 87])).
% 1.52/1.75 tff(154,assumption,(r(s(s(s(elem!1))), z)), introduced(assumption)).
% 1.52/1.75 tff(155,assumption,(r(z, s(s(z)))), introduced(assumption)).
% 1.52/1.75 tff(156,assumption,(b(s(s(z)), s(z))), introduced(assumption)).
% 1.52/1.75 tff(157,plain,
% 1.52/1.75 (^[X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : refl(((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1))) <=> ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1))))),
% 1.52/1.75 inference(bind,[status(th)],[])).
% 1.52/1.75 tff(158,plain,
% 1.52/1.75 (![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1))) <=> ![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))),
% 1.52/1.75 inference(quant_intro,[status(thm)],[157])).
% 1.52/1.75 tff(159,plain,
% 1.52/1.75 (![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1))) <=> ![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))),
% 1.52/1.75 inference(rewrite,[status(thm)],[])).
% 1.52/1.75 tff(160,plain,
% 1.52/1.75 (^[X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite((((~b(X0, X1)) | (~b(X0, X2))) | (~b(X1, X2))) <=> ((~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))), (((((~b(X0, X1)) | (~b(X0, X2))) | (~b(X1, X2))) | (~b(X2, X3))) <=> (((~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1))) | (~b(X2, X3))))), rewrite((((~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1))) | (~b(X2, X3))) <=> ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))), (((((~b(X0, X1)) | (~b(X0, X2))) | (~b(X1, X2))) | (~b(X2, X3))) <=> ((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1))))), ((((((~b(X0, X1)) | (~b(X0, X2))) | (~b(X1, X2))) | (~b(X2, X3))) | (~b(X0, X4))) <=> (((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1))) | (~b(X0, X4))))), rewrite((((~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1))) | (~b(X0, X4))) <=> ((~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))), ((((((~b(X0, X1)) | (~b(X0, X2))) | (~b(X1, X2))) | (~b(X2, X3))) | (~b(X0, X4))) <=> ((~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1))))), (((((((~b(X0, X1)) | (~b(X0, X2))) | (~b(X1, X2))) | (~b(X2, X3))) | (~b(X0, X4))) | (~b(X3, X4))) <=> (((~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1))) | (~b(X3, X4))))), rewrite((((~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1))) | (~b(X3, X4))) <=> ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))), (((((((~b(X0, X1)) | (~b(X0, X2))) | (~b(X1, X2))) | (~b(X2, X3))) | (~b(X0, X4))) | (~b(X3, X4))) <=> ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))))),
% 1.52/1.75 inference(bind,[status(th)],[])).
% 1.52/1.75 tff(161,plain,
% 1.52/1.75 (![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((((((~b(X0, X1)) | (~b(X0, X2))) | (~b(X1, X2))) | (~b(X2, X3))) | (~b(X0, X4))) | (~b(X3, X4))) <=> ![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))),
% 1.52/1.75 inference(quant_intro,[status(thm)],[160])).
% 1.52/1.75 tff(162,axiom,(![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((((((~b(X0, X1)) | (~b(X0, X2))) | (~b(X1, X2))) | (~b(X2, X3))) | (~b(X0, X4))) | (~b(X3, X4)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','axb')).
% 1.52/1.75 tff(163,plain,
% 1.52/1.75 (![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))),
% 1.52/1.75 inference(modus_ponens,[status(thm)],[162, 161])).
% 1.52/1.75 tff(164,plain,
% 1.52/1.75 (![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))),
% 1.52/1.75 inference(modus_ponens,[status(thm)],[163, 159])).
% 1.52/1.75 tff(165,plain,(
% 1.52/1.75 ![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))),
% 1.52/1.75 inference(skolemize,[status(sab)],[164])).
% 1.52/1.75 tff(166,plain,
% 1.52/1.75 (![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))),
% 1.52/1.75 inference(modus_ponens,[status(thm)],[165, 158])).
% 1.52/1.75 tff(167,plain,
% 1.52/1.75 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), z)) | (~b(s(s(s(elem!1))), s(s(z)))) | (~b(s(s(s(elem!1))), s(z))) | (~b(z, s(z))) | (~b(s(s(z)), s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), z)) | (~b(s(s(s(elem!1))), s(s(z)))) | (~b(s(s(s(elem!1))), s(z))) | (~b(z, s(z))) | (~b(s(s(z)), s(z))))),
% 1.52/1.75 inference(rewrite,[status(thm)],[])).
% 1.52/1.75 tff(168,plain,
% 1.52/1.75 (((~b(z, s(z))) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(z), z)) | (~b(s(s(z)), s(z))) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(s(s(elem!1))), s(s(z))))) <=> ((~b(s(z), z)) | (~b(s(s(s(elem!1))), s(s(z)))) | (~b(s(s(s(elem!1))), s(z))) | (~b(z, s(z))) | (~b(s(s(z)), s(z))))),
% 1.52/1.75 inference(rewrite,[status(thm)],[])).
% 1.52/1.75 tff(169,plain,
% 1.52/1.75 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(z))) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(z), z)) | (~b(s(s(z)), s(z))) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(s(s(elem!1))), s(s(z)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), z)) | (~b(s(s(s(elem!1))), s(s(z)))) | (~b(s(s(s(elem!1))), s(z))) | (~b(z, s(z))) | (~b(s(s(z)), s(z)))))),
% 1.52/1.75 inference(monotonicity,[status(thm)],[168])).
% 1.52/1.75 tff(170,plain,
% 1.52/1.75 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(z))) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(z), z)) | (~b(s(s(z)), s(z))) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(s(s(elem!1))), s(s(z)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), z)) | (~b(s(s(s(elem!1))), s(s(z)))) | (~b(s(s(s(elem!1))), s(z))) | (~b(z, s(z))) | (~b(s(s(z)), s(z))))),
% 1.52/1.75 inference(transitivity,[status(thm)],[169, 167])).
% 1.52/1.75 tff(171,plain,
% 1.52/1.75 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(z))) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(z), z)) | (~b(s(s(z)), s(z))) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(s(s(elem!1))), s(s(z)))))),
% 1.52/1.75 inference(quant_inst,[status(thm)],[])).
% 1.52/1.75 tff(172,plain,
% 1.52/1.75 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), z)) | (~b(s(s(s(elem!1))), s(s(z)))) | (~b(s(s(s(elem!1))), s(z))) | (~b(z, s(z))) | (~b(s(s(z)), s(z)))),
% 1.52/1.76 inference(modus_ponens,[status(thm)],[171, 170])).
% 1.52/1.76 tff(173,plain,
% 1.52/1.76 (~b(s(s(s(elem!1))), s(s(z)))),
% 1.52/1.76 inference(unit_resolution,[status(thm)],[172, 166, 53, 96, 118, 156])).
% 1.52/1.76 tff(174,plain,
% 1.52/1.76 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), z)) | (~b(z, s(z))) | (~b(s(s(z)), z)) | (~b(s(s(z)), s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), z)) | (~b(z, s(z))) | (~b(s(s(z)), z)) | (~b(s(s(z)), s(z))))),
% 1.52/1.76 inference(rewrite,[status(thm)],[])).
% 1.52/1.76 tff(175,plain,
% 1.52/1.76 (((~b(s(z), z)) | (~b(s(s(z)), z)) | (~b(z, s(z))) | (~b(s(z), z)) | (~b(s(s(z)), z)) | (~b(s(s(z)), s(z)))) <=> ((~b(s(z), z)) | (~b(z, s(z))) | (~b(s(s(z)), z)) | (~b(s(s(z)), s(z))))),
% 1.52/1.76 inference(rewrite,[status(thm)],[])).
% 1.52/1.76 tff(176,plain,
% 1.52/1.76 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), z)) | (~b(s(s(z)), z)) | (~b(z, s(z))) | (~b(s(z), z)) | (~b(s(s(z)), z)) | (~b(s(s(z)), s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), z)) | (~b(z, s(z))) | (~b(s(s(z)), z)) | (~b(s(s(z)), s(z)))))),
% 1.52/1.76 inference(monotonicity,[status(thm)],[175])).
% 1.52/1.76 tff(177,plain,
% 1.52/1.76 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), z)) | (~b(s(s(z)), z)) | (~b(z, s(z))) | (~b(s(z), z)) | (~b(s(s(z)), z)) | (~b(s(s(z)), s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), z)) | (~b(z, s(z))) | (~b(s(s(z)), z)) | (~b(s(s(z)), s(z))))),
% 1.52/1.76 inference(transitivity,[status(thm)],[176, 174])).
% 1.52/1.76 tff(178,plain,
% 1.52/1.76 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), z)) | (~b(s(s(z)), z)) | (~b(z, s(z))) | (~b(s(z), z)) | (~b(s(s(z)), z)) | (~b(s(s(z)), s(z))))),
% 1.52/1.76 inference(quant_inst,[status(thm)],[])).
% 1.52/1.76 tff(179,plain,
% 1.52/1.76 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), z)) | (~b(z, s(z))) | (~b(s(s(z)), z)) | (~b(s(s(z)), s(z)))),
% 1.52/1.76 inference(modus_ponens,[status(thm)],[178, 177])).
% 1.52/1.76 tff(180,plain,
% 1.52/1.76 ($false),
% 1.52/1.76 inference(unit_resolution,[status(thm)],[179, 166, 53, 118, 156, 122])).
% 1.52/1.76 tff(181,plain,((~b(s(z), z)) | (~b(z, s(z))) | (~b(s(s(z)), s(z))) | (~b(s(s(z)), z))), inference(lemma,lemma(discharge,[]))).
% 1.52/1.76 tff(182,plain,
% 1.52/1.76 (~b(s(s(z)), z)),
% 1.52/1.76 inference(unit_resolution,[status(thm)],[181, 53, 156, 118])).
% 1.52/1.76 tff(183,plain,
% 1.52/1.76 (((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((s(s(z)) = z) | b(s(s(z)), z) | r(s(s(z)), z))) <=> ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (s(s(z)) = z) | b(s(s(z)), z) | r(s(s(z)), z))),
% 1.52/1.76 inference(rewrite,[status(thm)],[])).
% 1.52/1.76 tff(184,plain,
% 1.52/1.76 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((s(s(z)) = z) | b(s(s(z)), z) | r(s(s(z)), z))),
% 1.52/1.76 inference(quant_inst,[status(thm)],[])).
% 1.52/1.76 tff(185,plain,
% 1.52/1.76 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (s(s(z)) = z) | b(s(s(z)), z) | r(s(s(z)), z)),
% 1.52/1.76 inference(modus_ponens,[status(thm)],[184, 183])).
% 1.52/1.76 tff(186,plain,
% 1.52/1.76 (b(s(s(z)), z) | r(s(s(z)), z)),
% 1.52/1.76 inference(unit_resolution,[status(thm)],[185, 79, 145])).
% 1.52/1.76 tff(187,plain,
% 1.52/1.76 (r(s(s(z)), z)),
% 1.52/1.76 inference(unit_resolution,[status(thm)],[186, 182])).
% 1.52/1.76 tff(188,plain,
% 1.52/1.76 (^[X0: $i, X3: $i, X2: $i, X1: $i] : refl(((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1))) <=> ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1))))),
% 1.52/1.76 inference(bind,[status(th)],[])).
% 1.52/1.76 tff(189,plain,
% 1.52/1.76 (![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1))) <=> ![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))),
% 1.52/1.76 inference(quant_intro,[status(thm)],[188])).
% 1.52/1.76 tff(190,plain,
% 1.52/1.76 (![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1))) <=> ![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))),
% 1.52/1.76 inference(rewrite,[status(thm)],[])).
% 1.52/1.76 tff(191,plain,
% 1.52/1.76 (^[X0: $i, X3: $i, X2: $i, X1: $i] : trans(monotonicity(rewrite((((~r(X0, X1)) | (~r(X0, X2))) | (~r(X1, X2))) <=> ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))), (((((~r(X0, X1)) | (~r(X0, X2))) | (~r(X1, X2))) | (~r(X2, X3))) <=> (((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1))) | (~r(X2, X3))))), rewrite((((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1))) | (~r(X2, X3))) <=> ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))), (((((~r(X0, X1)) | (~r(X0, X2))) | (~r(X1, X2))) | (~r(X2, X3))) <=> ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))))),
% 1.52/1.76 inference(bind,[status(th)],[])).
% 1.52/1.76 tff(192,plain,
% 1.52/1.76 (![X0: $i, X3: $i, X2: $i, X1: $i] : ((((~r(X0, X1)) | (~r(X0, X2))) | (~r(X1, X2))) | (~r(X2, X3))) <=> ![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))),
% 1.52/1.76 inference(quant_intro,[status(thm)],[191])).
% 1.52/1.76 tff(193,axiom,(![X0: $i, X3: $i, X2: $i, X1: $i] : ((((~r(X0, X1)) | (~r(X0, X2))) | (~r(X1, X2))) | (~r(X2, X3)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','axr')).
% 1.52/1.76 tff(194,plain,
% 1.52/1.76 (![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))),
% 1.52/1.76 inference(modus_ponens,[status(thm)],[193, 192])).
% 1.52/1.76 tff(195,plain,
% 1.52/1.76 (![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))),
% 1.52/1.76 inference(modus_ponens,[status(thm)],[194, 190])).
% 1.52/1.76 tff(196,plain,(
% 1.52/1.76 ![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))),
% 1.52/1.76 inference(skolemize,[status(sab)],[195])).
% 1.52/1.76 tff(197,plain,
% 1.52/1.76 (![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))),
% 1.52/1.76 inference(modus_ponens,[status(thm)],[196, 189])).
% 1.52/1.76 tff(198,plain,
% 1.52/1.76 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(z)))) | (~r(s(s(z)), z)) | (~r(s(s(s(elem!1))), z)) | (~r(s(s(s(elem!1))), s(s(z)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, s(s(z)))) | (~r(s(s(z)), z)) | (~r(s(s(s(elem!1))), z)) | (~r(s(s(s(elem!1))), s(s(z)))))),
% 1.52/1.76 inference(rewrite,[status(thm)],[])).
% 1.52/1.76 tff(199,plain,
% 1.52/1.76 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(z)))) | (~r(s(s(z)), z)) | (~r(s(s(s(elem!1))), z)) | (~r(s(s(s(elem!1))), s(s(z)))))),
% 1.52/1.76 inference(quant_inst,[status(thm)],[])).
% 1.52/1.76 tff(200,plain,
% 1.52/1.76 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, s(s(z)))) | (~r(s(s(z)), z)) | (~r(s(s(s(elem!1))), z)) | (~r(s(s(s(elem!1))), s(s(z))))),
% 1.52/1.76 inference(modus_ponens,[status(thm)],[199, 198])).
% 1.52/1.76 tff(201,plain,
% 1.52/1.76 (~r(s(s(s(elem!1))), s(s(z)))),
% 1.52/1.76 inference(unit_resolution,[status(thm)],[200, 197, 154, 155, 187])).
% 1.52/1.76 tff(202,assumption,(s(s(s(elem!1))) = s(s(z))), introduced(assumption)).
% 1.52/1.76 tff(203,plain,
% 1.52/1.76 (s(s(z)) = s(s(s(elem!1)))),
% 1.52/1.76 inference(symmetry,[status(thm)],[202])).
% 1.52/1.76 tff(204,assumption,(s(s(z)) = s(s(s(elem!1)))), introduced(assumption)).
% 1.52/1.76 tff(205,plain,
% 1.52/1.76 (inj_0(s(s(z))) = inj_0(s(s(s(elem!1))))),
% 1.52/1.76 inference(monotonicity,[status(thm)],[204])).
% 1.52/1.76 tff(206,plain,
% 1.52/1.76 (s(z) = inj_0(s(s(z)))),
% 1.52/1.76 inference(symmetry,[status(thm)],[33])).
% 1.52/1.76 tff(207,plain,
% 1.52/1.76 (s(z) = s(s(elem!1))),
% 1.52/1.76 inference(transitivity,[status(thm)],[206, 205, 104])).
% 1.52/1.76 tff(208,plain,
% 1.52/1.76 ($false),
% 1.52/1.76 inference(unit_resolution,[status(thm)],[69, 207])).
% 1.52/1.76 tff(209,plain,(~(s(s(z)) = s(s(s(elem!1))))), inference(lemma,lemma(discharge,[]))).
% 1.52/1.76 tff(210,plain,
% 1.52/1.76 ($false),
% 1.52/1.76 inference(unit_resolution,[status(thm)],[209, 203])).
% 1.52/1.76 tff(211,plain,(~(s(s(s(elem!1))) = s(s(z)))), inference(lemma,lemma(discharge,[]))).
% 1.52/1.76 tff(212,assumption,(~b(s(s(s(elem!1))), s(s(z)))), introduced(assumption)).
% 1.52/1.76 tff(213,assumption,(~r(s(s(s(elem!1))), s(s(z)))), introduced(assumption)).
% 1.52/1.76 tff(214,plain,
% 1.52/1.76 (((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((s(s(s(elem!1))) = s(s(z))) | b(s(s(s(elem!1))), s(s(z))) | r(s(s(s(elem!1))), s(s(z))))) <=> ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (s(s(s(elem!1))) = s(s(z))) | b(s(s(s(elem!1))), s(s(z))) | r(s(s(s(elem!1))), s(s(z))))),
% 1.52/1.76 inference(rewrite,[status(thm)],[])).
% 1.52/1.76 tff(215,plain,
% 1.52/1.76 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((s(s(s(elem!1))) = s(s(z))) | b(s(s(s(elem!1))), s(s(z))) | r(s(s(s(elem!1))), s(s(z))))),
% 1.52/1.76 inference(quant_inst,[status(thm)],[])).
% 1.52/1.76 tff(216,plain,
% 1.52/1.76 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (s(s(s(elem!1))) = s(s(z))) | b(s(s(s(elem!1))), s(s(z))) | r(s(s(s(elem!1))), s(s(z)))),
% 1.52/1.76 inference(modus_ponens,[status(thm)],[215, 214])).
% 1.52/1.76 tff(217,plain,
% 1.52/1.76 ($false),
% 1.52/1.76 inference(unit_resolution,[status(thm)],[216, 79, 213, 212, 211])).
% 1.52/1.76 tff(218,plain,(b(s(s(s(elem!1))), s(s(z))) | r(s(s(s(elem!1))), s(s(z)))), inference(lemma,lemma(discharge,[]))).
% 1.52/1.76 tff(219,plain,
% 1.52/1.76 ($false),
% 1.52/1.76 inference(unit_resolution,[status(thm)],[218, 201, 173])).
% 1.52/1.76 tff(220,plain,((~b(s(z), z)) | (~r(s(s(s(elem!1))), z)) | (~r(z, s(s(z)))) | (~b(s(s(s(elem!1))), s(z))) | (~b(z, s(z))) | (~b(s(s(z)), s(z)))), inference(lemma,lemma(discharge,[]))).
% 1.52/1.76 tff(221,plain,
% 1.52/1.76 (~b(s(z), z)),
% 1.52/1.76 inference(unit_resolution,[status(thm)],[220, 96, 155, 154, 118, 156])).
% 1.52/1.76 tff(222,assumption,(~r(s(z), z)), introduced(assumption)).
% 1.52/1.76 tff(223,assumption,(~b(s(z), z)), introduced(assumption)).
% 1.52/1.76 tff(224,plain,
% 1.52/1.76 ((~![X: $i] : (~(s(X) = z))) | (~(s(z) = z))),
% 1.52/1.76 inference(quant_inst,[status(thm)],[])).
% 1.52/1.76 tff(225,plain,
% 1.52/1.76 (~(s(z) = z)),
% 1.52/1.76 inference(unit_resolution,[status(thm)],[224, 65])).
% 1.52/1.76 tff(226,plain,
% 1.52/1.76 (((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((s(z) = z) | b(s(z), z) | r(s(z), z))) <=> ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (s(z) = z) | b(s(z), z) | r(s(z), z))),
% 1.52/1.76 inference(rewrite,[status(thm)],[])).
% 1.52/1.76 tff(227,plain,
% 1.52/1.76 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((s(z) = z) | b(s(z), z) | r(s(z), z))),
% 1.52/1.76 inference(quant_inst,[status(thm)],[])).
% 1.52/1.76 tff(228,plain,
% 1.52/1.76 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (s(z) = z) | b(s(z), z) | r(s(z), z)),
% 1.52/1.76 inference(modus_ponens,[status(thm)],[227, 226])).
% 1.52/1.76 tff(229,plain,
% 1.52/1.76 ($false),
% 1.52/1.76 inference(unit_resolution,[status(thm)],[228, 79, 225, 223, 222])).
% 1.52/1.76 tff(230,plain,(r(s(z), z) | b(s(z), z)), inference(lemma,lemma(discharge,[]))).
% 1.52/1.76 tff(231,plain,
% 1.52/1.76 (r(s(z), z)),
% 1.52/1.76 inference(unit_resolution,[status(thm)],[230, 221])).
% 1.52/1.76 tff(232,plain,
% 1.52/1.76 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), z)) | (~r(s(z), z)) | (~r(s(z), s(s(s(elem!1))))) | (~r(z, s(s(z)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(elem!1))), z)) | (~r(s(z), z)) | (~r(s(z), s(s(s(elem!1))))) | (~r(z, s(s(z)))))),
% 1.52/1.76 inference(rewrite,[status(thm)],[])).
% 1.52/1.76 tff(233,plain,
% 1.52/1.76 (((~r(z, s(s(z)))) | (~r(s(s(s(elem!1))), z)) | (~r(s(z), z)) | (~r(s(z), s(s(s(elem!1)))))) <=> ((~r(s(s(s(elem!1))), z)) | (~r(s(z), z)) | (~r(s(z), s(s(s(elem!1))))) | (~r(z, s(s(z)))))),
% 1.52/1.76 inference(rewrite,[status(thm)],[])).
% 1.52/1.76 tff(234,plain,
% 1.52/1.76 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(z)))) | (~r(s(s(s(elem!1))), z)) | (~r(s(z), z)) | (~r(s(z), s(s(s(elem!1))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), z)) | (~r(s(z), z)) | (~r(s(z), s(s(s(elem!1))))) | (~r(z, s(s(z))))))),
% 1.52/1.76 inference(monotonicity,[status(thm)],[233])).
% 1.52/1.76 tff(235,plain,
% 1.52/1.76 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(z)))) | (~r(s(s(s(elem!1))), z)) | (~r(s(z), z)) | (~r(s(z), s(s(s(elem!1))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(elem!1))), z)) | (~r(s(z), z)) | (~r(s(z), s(s(s(elem!1))))) | (~r(z, s(s(z)))))),
% 1.52/1.76 inference(transitivity,[status(thm)],[234, 232])).
% 1.52/1.76 tff(236,plain,
% 1.52/1.76 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(z)))) | (~r(s(s(s(elem!1))), z)) | (~r(s(z), z)) | (~r(s(z), s(s(s(elem!1))))))),
% 1.52/1.76 inference(quant_inst,[status(thm)],[])).
% 1.52/1.76 tff(237,plain,
% 1.52/1.76 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(elem!1))), z)) | (~r(s(z), z)) | (~r(s(z), s(s(s(elem!1))))) | (~r(z, s(s(z))))),
% 1.52/1.76 inference(modus_ponens,[status(thm)],[236, 235])).
% 1.52/1.76 tff(238,plain,
% 1.52/1.76 (~r(s(z), s(s(s(elem!1))))),
% 1.52/1.76 inference(unit_resolution,[status(thm)],[237, 197, 154, 155, 231])).
% 1.52/1.76 tff(239,plain,
% 1.52/1.76 (b(s(z), s(s(s(elem!1))))),
% 1.52/1.76 inference(unit_resolution,[status(thm)],[116, 238])).
% 1.52/1.76 tff(240,assumption,(b(z, s(s(s(elem!1))))), introduced(assumption)).
% 1.52/1.76 tff(241,assumption,(b(s(z), s(s(s(elem!1))))), introduced(assumption)).
% 1.52/1.76 tff(242,plain,
% 1.52/1.76 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(s(elem!1))))) | (~b(s(z), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(z))) | (~b(z, s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(s(s(elem!1))))) | (~b(s(z), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(z))) | (~b(z, s(z))))),
% 1.52/1.76 inference(rewrite,[status(thm)],[])).
% 1.52/1.76 tff(243,plain,
% 1.52/1.76 (((~b(s(z), s(s(s(elem!1))))) | (~b(z, s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(z), s(s(s(elem!1))))) | (~b(z, s(s(s(elem!1))))) | (~b(z, s(z)))) <=> ((~b(z, s(s(s(elem!1))))) | (~b(s(z), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(z))) | (~b(z, s(z))))),
% 1.52/1.76 inference(rewrite,[status(thm)],[])).
% 1.52/1.76 tff(244,plain,
% 1.52/1.76 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(s(elem!1))))) | (~b(z, s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(z), s(s(s(elem!1))))) | (~b(z, s(s(s(elem!1))))) | (~b(z, s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(s(elem!1))))) | (~b(s(z), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(z))) | (~b(z, s(z)))))),
% 1.52/1.76 inference(monotonicity,[status(thm)],[243])).
% 1.52/1.76 tff(245,plain,
% 1.52/1.76 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(s(elem!1))))) | (~b(z, s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(z), s(s(s(elem!1))))) | (~b(z, s(s(s(elem!1))))) | (~b(z, s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(s(s(elem!1))))) | (~b(s(z), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(z))) | (~b(z, s(z))))),
% 1.52/1.76 inference(transitivity,[status(thm)],[244, 242])).
% 1.52/1.76 tff(246,plain,
% 1.52/1.76 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(s(elem!1))))) | (~b(z, s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(z), s(s(s(elem!1))))) | (~b(z, s(s(s(elem!1))))) | (~b(z, s(z))))),
% 1.52/1.76 inference(quant_inst,[status(thm)],[])).
% 1.52/1.76 tff(247,plain,
% 1.52/1.76 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(s(s(elem!1))))) | (~b(s(z), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(z))) | (~b(z, s(z)))),
% 1.52/1.76 inference(modus_ponens,[status(thm)],[246, 245])).
% 1.52/1.76 tff(248,plain,
% 1.52/1.76 ($false),
% 1.52/1.76 inference(unit_resolution,[status(thm)],[247, 166, 241, 240, 96, 118])).
% 1.52/1.76 tff(249,plain,((~b(s(z), s(s(s(elem!1))))) | (~b(z, s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(z))) | (~b(z, s(z)))), inference(lemma,lemma(discharge,[]))).
% 1.52/1.76 tff(250,plain,
% 1.52/1.76 (~b(z, s(s(s(elem!1))))),
% 1.52/1.76 inference(unit_resolution,[status(thm)],[249, 239, 118, 96])).
% 1.52/1.76 tff(251,assumption,(z = s(s(s(elem!1)))), introduced(assumption)).
% 1.52/1.76 tff(252,plain,
% 1.52/1.76 (s(s(s(elem!1))) = z),
% 1.52/1.76 inference(symmetry,[status(thm)],[251])).
% 1.52/1.76 tff(253,plain,
% 1.52/1.76 ($false),
% 1.52/1.76 inference(unit_resolution,[status(thm)],[89, 252])).
% 1.52/1.76 tff(254,plain,(~(z = s(s(s(elem!1))))), inference(lemma,lemma(discharge,[]))).
% 1.52/1.76 tff(255,assumption,(~r(z, s(s(s(elem!1))))), introduced(assumption)).
% 1.52/1.76 tff(256,assumption,(~b(z, s(s(s(elem!1))))), introduced(assumption)).
% 1.52/1.76 tff(257,plain,
% 1.52/1.76 (((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((z = s(s(s(elem!1)))) | b(z, s(s(s(elem!1)))) | r(z, s(s(s(elem!1)))))) <=> ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (z = s(s(s(elem!1)))) | b(z, s(s(s(elem!1)))) | r(z, s(s(s(elem!1)))))),
% 1.52/1.76 inference(rewrite,[status(thm)],[])).
% 1.52/1.76 tff(258,plain,
% 1.52/1.76 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((z = s(s(s(elem!1)))) | b(z, s(s(s(elem!1)))) | r(z, s(s(s(elem!1)))))),
% 1.52/1.76 inference(quant_inst,[status(thm)],[])).
% 1.52/1.76 tff(259,plain,
% 1.52/1.76 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (z = s(s(s(elem!1)))) | b(z, s(s(s(elem!1)))) | r(z, s(s(s(elem!1))))),
% 1.52/1.76 inference(modus_ponens,[status(thm)],[258, 257])).
% 1.52/1.76 tff(260,plain,
% 1.52/1.76 ($false),
% 1.52/1.76 inference(unit_resolution,[status(thm)],[259, 79, 256, 255, 254])).
% 1.52/1.76 tff(261,plain,(r(z, s(s(s(elem!1)))) | b(z, s(s(s(elem!1))))), inference(lemma,lemma(discharge,[]))).
% 1.52/1.76 tff(262,plain,
% 1.52/1.76 (r(z, s(s(s(elem!1))))),
% 1.52/1.76 inference(unit_resolution,[status(thm)],[261, 250])).
% 1.52/1.76 tff(263,assumption,(b(s(s(z)), s(s(s(elem!1))))), introduced(assumption)).
% 1.52/1.76 tff(264,plain,
% 1.52/1.76 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(s(z)), s(z))) | (~b(s(s(z)), s(s(s(elem!1))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(s(z)), s(z))) | (~b(s(s(z)), s(s(s(elem!1))))))),
% 1.52/1.76 inference(rewrite,[status(thm)],[])).
% 1.52/1.76 tff(265,plain,
% 1.52/1.76 (((~b(s(s(s(elem!1))), s(z))) | (~b(s(s(z)), s(z))) | (~b(s(z), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(s(z)), s(z))) | (~b(s(s(z)), s(s(s(elem!1)))))) <=> ((~b(s(z), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(s(z)), s(z))) | (~b(s(s(z)), s(s(s(elem!1))))))),
% 1.52/1.76 inference(rewrite,[status(thm)],[])).
% 1.52/1.76 tff(266,plain,
% 1.52/1.76 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), s(z))) | (~b(s(s(z)), s(z))) | (~b(s(z), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(s(z)), s(z))) | (~b(s(s(z)), s(s(s(elem!1))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(s(z)), s(z))) | (~b(s(s(z)), s(s(s(elem!1)))))))),
% 1.52/1.76 inference(monotonicity,[status(thm)],[265])).
% 1.52/1.76 tff(267,plain,
% 1.52/1.76 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), s(z))) | (~b(s(s(z)), s(z))) | (~b(s(z), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(s(z)), s(z))) | (~b(s(s(z)), s(s(s(elem!1))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(s(z)), s(z))) | (~b(s(s(z)), s(s(s(elem!1))))))),
% 1.52/1.77 inference(transitivity,[status(thm)],[266, 264])).
% 1.52/1.77 tff(268,plain,
% 1.52/1.77 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), s(z))) | (~b(s(s(z)), s(z))) | (~b(s(z), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(s(z)), s(z))) | (~b(s(s(z)), s(s(s(elem!1))))))),
% 1.52/1.77 inference(quant_inst,[status(thm)],[])).
% 1.52/1.77 tff(269,plain,
% 1.52/1.77 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(s(z)), s(z))) | (~b(s(s(z)), s(s(s(elem!1)))))),
% 1.52/1.77 inference(modus_ponens,[status(thm)],[268, 267])).
% 1.52/1.77 tff(270,plain,
% 1.52/1.77 ($false),
% 1.52/1.77 inference(unit_resolution,[status(thm)],[269, 166, 241, 96, 156, 263])).
% 1.52/1.77 tff(271,plain,((~b(s(z), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(s(z)), s(z))) | (~b(s(s(z)), s(s(s(elem!1)))))), inference(lemma,lemma(discharge,[]))).
% 1.52/1.77 tff(272,plain,
% 1.52/1.77 (~b(s(s(z)), s(s(s(elem!1))))),
% 1.52/1.77 inference(unit_resolution,[status(thm)],[271, 239, 156, 96])).
% 1.52/1.77 tff(273,assumption,(~r(s(s(z)), s(s(s(elem!1))))), introduced(assumption)).
% 1.52/1.77 tff(274,assumption,(~b(s(s(z)), s(s(s(elem!1))))), introduced(assumption)).
% 1.52/1.77 tff(275,plain,
% 1.52/1.77 (((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((s(s(z)) = s(s(s(elem!1)))) | b(s(s(z)), s(s(s(elem!1)))) | r(s(s(z)), s(s(s(elem!1)))))) <=> ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (s(s(z)) = s(s(s(elem!1)))) | b(s(s(z)), s(s(s(elem!1)))) | r(s(s(z)), s(s(s(elem!1)))))),
% 1.52/1.77 inference(rewrite,[status(thm)],[])).
% 1.52/1.77 tff(276,plain,
% 1.52/1.77 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((s(s(z)) = s(s(s(elem!1)))) | b(s(s(z)), s(s(s(elem!1)))) | r(s(s(z)), s(s(s(elem!1)))))),
% 1.52/1.77 inference(quant_inst,[status(thm)],[])).
% 1.52/1.77 tff(277,plain,
% 1.52/1.77 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (s(s(z)) = s(s(s(elem!1)))) | b(s(s(z)), s(s(s(elem!1)))) | r(s(s(z)), s(s(s(elem!1))))),
% 1.52/1.77 inference(modus_ponens,[status(thm)],[276, 275])).
% 1.52/1.77 tff(278,plain,
% 1.52/1.77 ($false),
% 1.52/1.77 inference(unit_resolution,[status(thm)],[277, 79, 274, 273, 209])).
% 1.52/1.77 tff(279,plain,(b(s(s(z)), s(s(s(elem!1)))) | r(s(s(z)), s(s(s(elem!1))))), inference(lemma,lemma(discharge,[]))).
% 1.52/1.77 tff(280,plain,
% 1.52/1.77 (r(s(s(z)), s(s(s(elem!1))))),
% 1.52/1.77 inference(unit_resolution,[status(thm)],[279, 272])).
% 1.52/1.77 tff(281,assumption,(r(s(s(z)), s(s(s(elem!1))))), introduced(assumption)).
% 1.52/1.77 tff(282,assumption,(r(z, s(s(s(elem!1))))), introduced(assumption)).
% 1.52/1.77 tff(283,plain,
% 1.52/1.77 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), z)) | (~r(z, s(s(s(elem!1))))) | (~r(s(s(z)), s(s(s(elem!1))))) | (~r(z, s(s(z)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(elem!1))), z)) | (~r(z, s(s(s(elem!1))))) | (~r(s(s(z)), s(s(s(elem!1))))) | (~r(z, s(s(z)))))),
% 1.52/1.77 inference(rewrite,[status(thm)],[])).
% 1.52/1.77 tff(284,plain,
% 1.52/1.77 (((~r(s(s(s(elem!1))), z)) | (~r(s(s(z)), s(s(s(elem!1))))) | (~r(z, s(s(s(elem!1))))) | (~r(z, s(s(z))))) <=> ((~r(s(s(s(elem!1))), z)) | (~r(z, s(s(s(elem!1))))) | (~r(s(s(z)), s(s(s(elem!1))))) | (~r(z, s(s(z)))))),
% 1.52/1.77 inference(rewrite,[status(thm)],[])).
% 1.52/1.77 tff(285,plain,
% 1.52/1.77 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), z)) | (~r(s(s(z)), s(s(s(elem!1))))) | (~r(z, s(s(s(elem!1))))) | (~r(z, s(s(z)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), z)) | (~r(z, s(s(s(elem!1))))) | (~r(s(s(z)), s(s(s(elem!1))))) | (~r(z, s(s(z))))))),
% 1.52/1.77 inference(monotonicity,[status(thm)],[284])).
% 1.52/1.77 tff(286,plain,
% 1.52/1.77 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), z)) | (~r(s(s(z)), s(s(s(elem!1))))) | (~r(z, s(s(s(elem!1))))) | (~r(z, s(s(z)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(elem!1))), z)) | (~r(z, s(s(s(elem!1))))) | (~r(s(s(z)), s(s(s(elem!1))))) | (~r(z, s(s(z)))))),
% 1.52/1.77 inference(transitivity,[status(thm)],[285, 283])).
% 1.52/1.77 tff(287,plain,
% 1.52/1.77 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), z)) | (~r(s(s(z)), s(s(s(elem!1))))) | (~r(z, s(s(s(elem!1))))) | (~r(z, s(s(z)))))),
% 1.52/1.77 inference(quant_inst,[status(thm)],[])).
% 1.52/1.77 tff(288,plain,
% 1.52/1.77 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(elem!1))), z)) | (~r(z, s(s(s(elem!1))))) | (~r(s(s(z)), s(s(s(elem!1))))) | (~r(z, s(s(z))))),
% 1.52/1.77 inference(modus_ponens,[status(thm)],[287, 286])).
% 1.52/1.77 tff(289,plain,
% 1.52/1.77 ($false),
% 1.52/1.77 inference(unit_resolution,[status(thm)],[288, 197, 154, 155, 282, 281])).
% 1.52/1.77 tff(290,plain,((~r(s(s(z)), s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), z)) | (~r(z, s(s(z)))) | (~r(z, s(s(s(elem!1)))))), inference(lemma,lemma(discharge,[]))).
% 1.52/1.77 tff(291,plain,
% 1.52/1.77 ($false),
% 1.52/1.77 inference(unit_resolution,[status(thm)],[290, 280, 262, 155, 154])).
% 1.52/1.77 tff(292,plain,((~b(s(s(s(elem!1))), s(z))) | (~r(z, s(s(z)))) | (~r(s(s(s(elem!1))), z)) | (~b(s(s(z)), s(z))) | (~b(z, s(z)))), inference(lemma,lemma(discharge,[]))).
% 1.52/1.77 tff(293,plain,
% 1.52/1.77 (~b(s(s(z)), s(z))),
% 1.52/1.77 inference(unit_resolution,[status(thm)],[292, 96, 152, 118, 153])).
% 1.52/1.77 tff(294,plain,
% 1.52/1.77 ((s(s(z)) = s(z)) <=> (s(z) = s(s(z)))),
% 1.52/1.77 inference(commutativity,[status(thm)],[])).
% 1.52/1.77 tff(295,plain,
% 1.52/1.77 ((s(z) = s(s(z))) <=> (s(s(z)) = s(z))),
% 1.52/1.77 inference(symmetry,[status(thm)],[294])).
% 1.52/1.77 tff(296,plain,
% 1.52/1.77 ((~(s(z) = s(s(z)))) <=> (~(s(s(z)) = s(z)))),
% 1.52/1.77 inference(monotonicity,[status(thm)],[295])).
% 1.52/1.77 tff(297,assumption,(s(z) = s(s(z))), introduced(assumption)).
% 1.52/1.77 tff(298,plain,
% 1.52/1.77 (inj_0(s(z)) = inj_0(s(s(z)))),
% 1.52/1.77 inference(monotonicity,[status(thm)],[297])).
% 1.52/1.77 tff(299,plain,
% 1.52/1.77 (inj_0(s(s(z))) = inj_0(s(z))),
% 1.52/1.77 inference(symmetry,[status(thm)],[298])).
% 1.52/1.77 tff(300,plain,
% 1.52/1.77 (s(z) = z),
% 1.52/1.77 inference(transitivity,[status(thm)],[206, 299, 25])).
% 1.52/1.77 tff(301,plain,
% 1.52/1.77 ($false),
% 1.52/1.77 inference(unit_resolution,[status(thm)],[225, 300])).
% 1.52/1.77 tff(302,plain,(~(s(z) = s(s(z)))), inference(lemma,lemma(discharge,[]))).
% 1.52/1.77 tff(303,plain,
% 1.52/1.77 (~(s(s(z)) = s(z))),
% 1.52/1.77 inference(modus_ponens,[status(thm)],[302, 296])).
% 1.52/1.77 tff(304,plain,
% 1.52/1.77 (((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((s(s(z)) = s(z)) | b(s(s(z)), s(z)) | r(s(s(z)), s(z)))) <=> ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (s(s(z)) = s(z)) | b(s(s(z)), s(z)) | r(s(s(z)), s(z)))),
% 1.52/1.77 inference(rewrite,[status(thm)],[])).
% 1.52/1.77 tff(305,plain,
% 1.52/1.77 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((s(s(z)) = s(z)) | b(s(s(z)), s(z)) | r(s(s(z)), s(z)))),
% 1.52/1.77 inference(quant_inst,[status(thm)],[])).
% 1.52/1.77 tff(306,plain,
% 1.52/1.77 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (s(s(z)) = s(z)) | b(s(s(z)), s(z)) | r(s(s(z)), s(z))),
% 1.52/1.77 inference(modus_ponens,[status(thm)],[305, 304])).
% 1.52/1.77 tff(307,plain,
% 1.52/1.77 ((s(s(z)) = s(z)) | b(s(s(z)), s(z)) | r(s(s(z)), s(z))),
% 1.52/1.77 inference(unit_resolution,[status(thm)],[306, 79])).
% 1.52/1.77 tff(308,plain,
% 1.52/1.77 (b(s(s(z)), s(z)) | r(s(s(z)), s(z))),
% 1.52/1.77 inference(unit_resolution,[status(thm)],[307, 303])).
% 1.52/1.77 tff(309,plain,
% 1.52/1.77 (r(s(s(z)), s(z))),
% 1.52/1.77 inference(unit_resolution,[status(thm)],[308, 293])).
% 1.52/1.77 tff(310,assumption,(b(s(s(elem!1)), s(z))), introduced(assumption)).
% 1.52/1.77 tff(311,assumption,(r(s(z), s(s(elem!1)))), introduced(assumption)).
% 1.52/1.77 tff(312,assumption,(~b(z, s(z))), introduced(assumption)).
% 1.52/1.77 tff(313,plain,
% 1.52/1.77 ((z = s(z)) <=> (s(z) = z)),
% 1.52/1.77 inference(commutativity,[status(thm)],[])).
% 1.52/1.77 tff(314,plain,
% 1.52/1.77 ((s(z) = z) <=> (z = s(z))),
% 1.52/1.77 inference(symmetry,[status(thm)],[313])).
% 1.52/1.77 tff(315,plain,
% 1.52/1.77 ((~(s(z) = z)) <=> (~(z = s(z)))),
% 1.52/1.77 inference(monotonicity,[status(thm)],[314])).
% 1.52/1.77 tff(316,plain,
% 1.52/1.77 (~(z = s(z))),
% 1.52/1.77 inference(modus_ponens,[status(thm)],[225, 315])).
% 1.52/1.77 tff(317,plain,
% 1.52/1.77 (((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((z = s(z)) | b(z, s(z)) | r(z, s(z)))) <=> ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (z = s(z)) | b(z, s(z)) | r(z, s(z)))),
% 1.52/1.77 inference(rewrite,[status(thm)],[])).
% 1.52/1.77 tff(318,plain,
% 1.52/1.77 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((z = s(z)) | b(z, s(z)) | r(z, s(z)))),
% 1.52/1.77 inference(quant_inst,[status(thm)],[])).
% 1.52/1.77 tff(319,plain,
% 1.52/1.77 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (z = s(z)) | b(z, s(z)) | r(z, s(z))),
% 1.52/1.77 inference(modus_ponens,[status(thm)],[318, 317])).
% 1.52/1.77 tff(320,plain,
% 1.52/1.77 ((z = s(z)) | b(z, s(z)) | r(z, s(z))),
% 1.52/1.77 inference(unit_resolution,[status(thm)],[319, 79])).
% 1.52/1.77 tff(321,plain,
% 1.52/1.77 (b(z, s(z)) | r(z, s(z))),
% 1.52/1.77 inference(unit_resolution,[status(thm)],[320, 316])).
% 1.52/1.77 tff(322,plain,
% 1.52/1.77 (r(z, s(z))),
% 1.52/1.77 inference(unit_resolution,[status(thm)],[321, 312])).
% 1.52/1.77 tff(323,assumption,(r(z, s(z))), introduced(assumption)).
% 1.52/1.77 tff(324,plain,
% 1.52/1.77 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(z))) | (~r(s(z), s(s(z)))) | (~r(s(s(z)), s(s(s(elem!1))))) | (~r(z, s(s(z)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, s(z))) | (~r(s(z), s(s(z)))) | (~r(s(s(z)), s(s(s(elem!1))))) | (~r(z, s(s(z)))))),
% 1.52/1.77 inference(rewrite,[status(thm)],[])).
% 1.52/1.77 tff(325,plain,
% 1.52/1.77 (((~r(s(s(z)), s(s(s(elem!1))))) | (~r(s(z), s(s(z)))) | (~r(z, s(s(z)))) | (~r(z, s(z)))) <=> ((~r(z, s(z))) | (~r(s(z), s(s(z)))) | (~r(s(s(z)), s(s(s(elem!1))))) | (~r(z, s(s(z)))))),
% 1.52/1.77 inference(rewrite,[status(thm)],[])).
% 1.52/1.77 tff(326,plain,
% 1.52/1.77 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(z)), s(s(s(elem!1))))) | (~r(s(z), s(s(z)))) | (~r(z, s(s(z)))) | (~r(z, s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(z))) | (~r(s(z), s(s(z)))) | (~r(s(s(z)), s(s(s(elem!1))))) | (~r(z, s(s(z))))))),
% 1.52/1.77 inference(monotonicity,[status(thm)],[325])).
% 1.52/1.77 tff(327,plain,
% 1.52/1.77 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(z)), s(s(s(elem!1))))) | (~r(s(z), s(s(z)))) | (~r(z, s(s(z)))) | (~r(z, s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, s(z))) | (~r(s(z), s(s(z)))) | (~r(s(s(z)), s(s(s(elem!1))))) | (~r(z, s(s(z)))))),
% 1.52/1.77 inference(transitivity,[status(thm)],[326, 324])).
% 1.52/1.77 tff(328,plain,
% 1.52/1.77 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(z)), s(s(s(elem!1))))) | (~r(s(z), s(s(z)))) | (~r(z, s(s(z)))) | (~r(z, s(z))))),
% 1.52/1.77 inference(quant_inst,[status(thm)],[])).
% 1.52/1.77 tff(329,plain,
% 1.52/1.77 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, s(z))) | (~r(s(z), s(s(z)))) | (~r(s(s(z)), s(s(s(elem!1))))) | (~r(z, s(s(z))))),
% 1.52/1.77 inference(modus_ponens,[status(thm)],[328, 327])).
% 1.52/1.77 tff(330,plain,
% 1.52/1.77 ($false),
% 1.52/1.77 inference(unit_resolution,[status(thm)],[329, 197, 120, 155, 323, 281])).
% 1.52/1.77 tff(331,plain,((~r(s(s(z)), s(s(s(elem!1))))) | (~r(s(z), s(s(z)))) | (~r(z, s(s(z)))) | (~r(z, s(z)))), inference(lemma,lemma(discharge,[]))).
% 1.52/1.77 tff(332,plain,
% 1.52/1.77 (~r(s(s(z)), s(s(s(elem!1))))),
% 1.52/1.77 inference(unit_resolution,[status(thm)],[331, 323, 155, 120])).
% 1.52/1.77 tff(333,assumption,(r(s(s(z)), s(s(elem!1)))), introduced(assumption)).
% 1.52/1.77 tff(334,assumption,(s(s(elem!1)) = s(s(s(elem!1)))), introduced(assumption)).
% 1.52/1.77 tff(335,plain,
% 1.52/1.77 (r(s(s(z)), s(s(elem!1))) <=> r(s(s(z)), s(s(s(elem!1))))),
% 1.52/1.77 inference(monotonicity,[status(thm)],[334])).
% 1.52/1.77 tff(336,plain,
% 1.52/1.77 (r(s(s(z)), s(s(s(elem!1))))),
% 1.52/1.77 inference(modus_ponens,[status(thm)],[333, 335])).
% 1.52/1.77 tff(337,plain,
% 1.52/1.77 ($false),
% 1.52/1.77 inference(unit_resolution,[status(thm)],[273, 336])).
% 1.52/1.77 tff(338,plain,((~r(s(s(z)), s(s(elem!1)))) | r(s(s(z)), s(s(s(elem!1)))) | (~(s(s(elem!1)) = s(s(s(elem!1)))))), inference(lemma,lemma(discharge,[]))).
% 1.52/1.77 tff(339,plain,
% 1.52/1.77 (~(s(s(elem!1)) = s(s(s(elem!1))))),
% 1.52/1.77 inference(unit_resolution,[status(thm)],[338, 333, 332])).
% 1.52/1.77 tff(340,plain,
% 1.52/1.77 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), z)) | (~r(s(s(z)), s(s(elem!1)))) | (~r(s(z), s(s(z)))) | (~r(z, s(s(z)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(z), z)) | (~r(s(s(z)), s(s(elem!1)))) | (~r(s(z), s(s(z)))) | (~r(z, s(s(z)))))),
% 1.52/1.77 inference(rewrite,[status(thm)],[])).
% 1.52/1.77 tff(341,plain,
% 1.52/1.77 (((~r(s(s(z)), s(s(elem!1)))) | (~r(z, s(s(z)))) | (~r(s(z), s(s(z)))) | (~r(s(z), z))) <=> ((~r(s(z), z)) | (~r(s(s(z)), s(s(elem!1)))) | (~r(s(z), s(s(z)))) | (~r(z, s(s(z)))))),
% 1.52/1.77 inference(rewrite,[status(thm)],[])).
% 1.52/1.77 tff(342,plain,
% 1.52/1.77 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(z)), s(s(elem!1)))) | (~r(z, s(s(z)))) | (~r(s(z), s(s(z)))) | (~r(s(z), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), z)) | (~r(s(s(z)), s(s(elem!1)))) | (~r(s(z), s(s(z)))) | (~r(z, s(s(z))))))),
% 1.52/1.77 inference(monotonicity,[status(thm)],[341])).
% 1.52/1.77 tff(343,plain,
% 1.52/1.77 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(z)), s(s(elem!1)))) | (~r(z, s(s(z)))) | (~r(s(z), s(s(z)))) | (~r(s(z), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(z), z)) | (~r(s(s(z)), s(s(elem!1)))) | (~r(s(z), s(s(z)))) | (~r(z, s(s(z)))))),
% 1.52/1.77 inference(transitivity,[status(thm)],[342, 340])).
% 1.52/1.77 tff(344,plain,
% 1.52/1.77 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(z)), s(s(elem!1)))) | (~r(z, s(s(z)))) | (~r(s(z), s(s(z)))) | (~r(s(z), z)))),
% 1.52/1.77 inference(quant_inst,[status(thm)],[])).
% 1.52/1.77 tff(345,plain,
% 1.52/1.77 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(z), z)) | (~r(s(s(z)), s(s(elem!1)))) | (~r(s(z), s(s(z)))) | (~r(z, s(s(z))))),
% 1.52/1.77 inference(modus_ponens,[status(thm)],[344, 343])).
% 1.52/1.77 tff(346,plain,
% 1.52/1.77 ($false),
% 1.52/1.77 inference(unit_resolution,[status(thm)],[345, 197, 120, 155, 97, 333])).
% 1.52/1.77 tff(347,plain,((~r(s(z), s(s(z)))) | (~r(z, s(s(z)))) | (~r(s(z), z)) | (~r(s(s(z)), s(s(elem!1))))), inference(lemma,lemma(discharge,[]))).
% 1.52/1.77 tff(348,plain,
% 1.52/1.77 (~r(s(z), z)),
% 1.52/1.77 inference(unit_resolution,[status(thm)],[347, 333, 155, 120])).
% 1.52/1.77 tff(349,plain,
% 1.52/1.77 (b(s(z), z)),
% 1.52/1.77 inference(unit_resolution,[status(thm)],[230, 348])).
% 1.52/1.77 tff(350,assumption,(r(s(s(s(elem!1))), s(z))), introduced(assumption)).
% 1.52/1.77 tff(351,plain,
% 1.52/1.77 ((~![Xk!0: $i] : (inj_0(s(Xk!0)) = Xk!0)) | (inj_0(s(s(s(s(elem!1))))) = s(s(s(elem!1))))),
% 1.52/1.77 inference(quant_inst,[status(thm)],[])).
% 1.52/1.77 tff(352,plain,
% 1.52/1.77 (inj_0(s(s(s(s(elem!1))))) = s(s(s(elem!1)))),
% 1.52/1.77 inference(unit_resolution,[status(thm)],[351, 8])).
% 1.52/1.77 tff(353,assumption,(s(s(s(elem!1))) = s(s(s(s(elem!1))))), introduced(assumption)).
% 1.52/1.77 tff(354,plain,
% 1.52/1.77 (inj_0(s(s(s(elem!1)))) = inj_0(s(s(s(s(elem!1)))))),
% 1.52/1.77 inference(monotonicity,[status(thm)],[353])).
% 1.52/1.77 tff(355,plain,
% 1.52/1.77 (s(s(elem!1)) = s(s(s(elem!1)))),
% 1.52/1.77 inference(transitivity,[status(thm)],[105, 354, 352])).
% 1.52/1.77 tff(356,plain,
% 1.52/1.77 ($false),
% 1.52/1.77 inference(unit_resolution,[status(thm)],[45, 355])).
% 1.52/1.77 tff(357,plain,((~(s(s(s(elem!1))) = s(s(s(s(elem!1)))))) | (s(s(elem!1)) = s(s(s(elem!1))))), inference(lemma,lemma(discharge,[]))).
% 1.52/1.77 tff(358,plain,
% 1.52/1.77 (~(s(s(s(elem!1))) = s(s(s(s(elem!1)))))),
% 1.52/1.77 inference(unit_resolution,[status(thm)],[357, 45])).
% 1.52/1.77 tff(359,assumption,(s(s(s(s(elem!1)))) = s(s(s(elem!1)))), introduced(assumption)).
% 1.52/1.77 tff(360,plain,
% 1.52/1.77 (s(s(s(elem!1))) = s(s(s(s(elem!1))))),
% 1.52/1.77 inference(symmetry,[status(thm)],[359])).
% 1.52/1.77 tff(361,assumption,(~(s(s(s(elem!1))) = s(s(s(s(elem!1)))))), introduced(assumption)).
% 1.52/1.77 tff(362,plain,
% 1.52/1.77 ($false),
% 1.52/1.77 inference(unit_resolution,[status(thm)],[361, 360])).
% 1.52/1.77 tff(363,plain,((~(s(s(s(s(elem!1)))) = s(s(s(elem!1))))) | (s(s(s(elem!1))) = s(s(s(s(elem!1)))))), inference(lemma,lemma(discharge,[]))).
% 1.52/1.77 tff(364,plain,
% 1.52/1.77 (~(s(s(s(s(elem!1)))) = s(s(s(elem!1))))),
% 1.52/1.77 inference(unit_resolution,[status(thm)],[363, 358])).
% 1.52/1.77 tff(365,assumption,(r(z, s(s(elem!1)))), introduced(assumption)).
% 1.52/1.77 tff(366,plain,
% 1.52/1.77 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), z)) | (~r(s(z), s(s(elem!1)))) | (~r(s(s(s(elem!1))), s(z))) | (~r(z, s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(elem!1))), z)) | (~r(s(z), s(s(elem!1)))) | (~r(s(s(s(elem!1))), s(z))) | (~r(z, s(z))))),
% 1.52/1.77 inference(rewrite,[status(thm)],[])).
% 1.52/1.77 tff(367,plain,
% 1.52/1.77 (((~r(s(z), s(s(elem!1)))) | (~r(z, s(z))) | (~r(s(s(s(elem!1))), s(z))) | (~r(s(s(s(elem!1))), z))) <=> ((~r(s(s(s(elem!1))), z)) | (~r(s(z), s(s(elem!1)))) | (~r(s(s(s(elem!1))), s(z))) | (~r(z, s(z))))),
% 1.52/1.77 inference(rewrite,[status(thm)],[])).
% 1.52/1.77 tff(368,plain,
% 1.52/1.77 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(s(elem!1)))) | (~r(z, s(z))) | (~r(s(s(s(elem!1))), s(z))) | (~r(s(s(s(elem!1))), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), z)) | (~r(s(z), s(s(elem!1)))) | (~r(s(s(s(elem!1))), s(z))) | (~r(z, s(z)))))),
% 1.52/1.77 inference(monotonicity,[status(thm)],[367])).
% 1.52/1.77 tff(369,plain,
% 1.52/1.77 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(s(elem!1)))) | (~r(z, s(z))) | (~r(s(s(s(elem!1))), s(z))) | (~r(s(s(s(elem!1))), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(elem!1))), z)) | (~r(s(z), s(s(elem!1)))) | (~r(s(s(s(elem!1))), s(z))) | (~r(z, s(z))))),
% 1.52/1.77 inference(transitivity,[status(thm)],[368, 366])).
% 1.52/1.77 tff(370,plain,
% 1.52/1.77 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(s(elem!1)))) | (~r(z, s(z))) | (~r(s(s(s(elem!1))), s(z))) | (~r(s(s(s(elem!1))), z)))),
% 1.52/1.77 inference(quant_inst,[status(thm)],[])).
% 1.52/1.77 tff(371,plain,
% 1.52/1.77 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(elem!1))), z)) | (~r(s(z), s(s(elem!1)))) | (~r(s(s(s(elem!1))), s(z))) | (~r(z, s(z)))),
% 1.52/1.77 inference(modus_ponens,[status(thm)],[370, 369])).
% 1.52/1.77 tff(372,plain,
% 1.52/1.77 ($false),
% 1.52/1.77 inference(unit_resolution,[status(thm)],[371, 197, 311, 154, 350, 323])).
% 1.52/1.77 tff(373,plain,((~r(s(s(s(elem!1))), s(z))) | (~r(s(z), s(s(elem!1)))) | (~r(s(s(s(elem!1))), z)) | (~r(z, s(z)))), inference(lemma,lemma(discharge,[]))).
% 1.52/1.77 tff(374,plain,
% 1.52/1.77 (~r(s(z), s(s(elem!1)))),
% 1.52/1.77 inference(unit_resolution,[status(thm)],[373, 154, 323, 350])).
% 1.52/1.77 tff(375,plain,
% 1.52/1.77 (b(s(z), s(s(elem!1)))),
% 1.52/1.77 inference(unit_resolution,[status(thm)],[84, 374])).
% 1.52/1.77 tff(376,assumption,(b(s(z), s(s(elem!1)))), introduced(assumption)).
% 1.52/1.77 tff(377,assumption,(r(s(s(elem!1)), s(s(s(elem!1))))), introduced(assumption)).
% 1.52/1.77 tff(378,plain,
% 1.52/1.77 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(elem!1)))) | (~r(s(s(elem!1)), s(s(s(elem!1))))) | (~r(s(s(z)), s(s(elem!1)))) | (~r(z, s(s(z)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, s(s(elem!1)))) | (~r(s(s(elem!1)), s(s(s(elem!1))))) | (~r(s(s(z)), s(s(elem!1)))) | (~r(z, s(s(z)))))),
% 1.52/1.77 inference(rewrite,[status(thm)],[])).
% 1.52/1.77 tff(379,plain,
% 1.52/1.77 (((~r(s(s(elem!1)), s(s(s(elem!1))))) | (~r(s(s(z)), s(s(elem!1)))) | (~r(z, s(s(elem!1)))) | (~r(z, s(s(z))))) <=> ((~r(z, s(s(elem!1)))) | (~r(s(s(elem!1)), s(s(s(elem!1))))) | (~r(s(s(z)), s(s(elem!1)))) | (~r(z, s(s(z)))))),
% 1.52/1.77 inference(rewrite,[status(thm)],[])).
% 1.52/1.77 tff(380,plain,
% 1.52/1.77 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(elem!1)), s(s(s(elem!1))))) | (~r(s(s(z)), s(s(elem!1)))) | (~r(z, s(s(elem!1)))) | (~r(z, s(s(z)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(elem!1)))) | (~r(s(s(elem!1)), s(s(s(elem!1))))) | (~r(s(s(z)), s(s(elem!1)))) | (~r(z, s(s(z))))))),
% 1.52/1.78 inference(monotonicity,[status(thm)],[379])).
% 1.52/1.78 tff(381,plain,
% 1.52/1.78 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(elem!1)), s(s(s(elem!1))))) | (~r(s(s(z)), s(s(elem!1)))) | (~r(z, s(s(elem!1)))) | (~r(z, s(s(z)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, s(s(elem!1)))) | (~r(s(s(elem!1)), s(s(s(elem!1))))) | (~r(s(s(z)), s(s(elem!1)))) | (~r(z, s(s(z)))))),
% 1.52/1.78 inference(transitivity,[status(thm)],[380, 378])).
% 1.52/1.78 tff(382,plain,
% 1.52/1.78 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(elem!1)), s(s(s(elem!1))))) | (~r(s(s(z)), s(s(elem!1)))) | (~r(z, s(s(elem!1)))) | (~r(z, s(s(z)))))),
% 1.52/1.78 inference(quant_inst,[status(thm)],[])).
% 1.52/1.78 tff(383,plain,
% 1.52/1.78 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, s(s(elem!1)))) | (~r(s(s(elem!1)), s(s(s(elem!1))))) | (~r(s(s(z)), s(s(elem!1)))) | (~r(z, s(s(z))))),
% 1.52/1.78 inference(modus_ponens,[status(thm)],[382, 381])).
% 1.52/1.78 tff(384,plain,
% 1.52/1.78 ($false),
% 1.52/1.78 inference(unit_resolution,[status(thm)],[383, 197, 155, 377, 333, 365])).
% 1.52/1.78 tff(385,plain,((~r(s(s(z)), s(s(elem!1)))) | (~r(z, s(s(z)))) | (~r(s(s(elem!1)), s(s(s(elem!1))))) | (~r(z, s(s(elem!1))))), inference(lemma,lemma(discharge,[]))).
% 1.52/1.78 tff(386,plain,
% 1.52/1.78 (~r(s(s(z)), s(s(elem!1)))),
% 1.52/1.78 inference(unit_resolution,[status(thm)],[385, 377, 155, 365])).
% 1.52/1.78 tff(387,plain,
% 1.52/1.78 (((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((s(s(z)) = s(s(elem!1))) | b(s(s(z)), s(s(elem!1))) | r(s(s(z)), s(s(elem!1))))) <=> ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (s(s(z)) = s(s(elem!1))) | b(s(s(z)), s(s(elem!1))) | r(s(s(z)), s(s(elem!1))))),
% 1.52/1.78 inference(rewrite,[status(thm)],[])).
% 1.52/1.78 tff(388,plain,
% 1.52/1.78 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((s(s(z)) = s(s(elem!1))) | b(s(s(z)), s(s(elem!1))) | r(s(s(z)), s(s(elem!1))))),
% 1.52/1.78 inference(quant_inst,[status(thm)],[])).
% 1.52/1.78 tff(389,plain,
% 1.52/1.78 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (s(s(z)) = s(s(elem!1))) | b(s(s(z)), s(s(elem!1))) | r(s(s(z)), s(s(elem!1)))),
% 1.52/1.78 inference(modus_ponens,[status(thm)],[388, 387])).
% 1.52/1.78 tff(390,plain,
% 1.52/1.78 ((s(s(z)) = s(s(elem!1))) | b(s(s(z)), s(s(elem!1))) | r(s(s(z)), s(s(elem!1)))),
% 1.52/1.78 inference(unit_resolution,[status(thm)],[389, 79])).
% 1.52/1.78 tff(391,plain,
% 1.52/1.78 (b(s(s(z)), s(s(elem!1)))),
% 1.52/1.78 inference(unit_resolution,[status(thm)],[390, 386, 52])).
% 1.52/1.78 tff(392,assumption,(r(s(s(z)), s(z))), introduced(assumption)).
% 1.52/1.78 tff(393,assumption,(r(s(s(elem!1)), s(s(z)))), introduced(assumption)).
% 1.52/1.78 tff(394,plain,
% 1.52/1.78 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(elem!1)))) | (~r(s(s(z)), s(z))) | (~r(s(s(elem!1)), s(s(z)))) | (~r(z, s(s(z)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, s(s(elem!1)))) | (~r(s(s(z)), s(z))) | (~r(s(s(elem!1)), s(s(z)))) | (~r(z, s(s(z)))))),
% 1.52/1.78 inference(rewrite,[status(thm)],[])).
% 1.52/1.78 tff(395,plain,
% 1.52/1.78 (((~r(s(s(z)), s(z))) | (~r(s(s(elem!1)), s(s(z)))) | (~r(z, s(s(z)))) | (~r(z, s(s(elem!1))))) <=> ((~r(z, s(s(elem!1)))) | (~r(s(s(z)), s(z))) | (~r(s(s(elem!1)), s(s(z)))) | (~r(z, s(s(z)))))),
% 1.52/1.78 inference(rewrite,[status(thm)],[])).
% 1.52/1.78 tff(396,plain,
% 1.52/1.78 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(z)), s(z))) | (~r(s(s(elem!1)), s(s(z)))) | (~r(z, s(s(z)))) | (~r(z, s(s(elem!1)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(elem!1)))) | (~r(s(s(z)), s(z))) | (~r(s(s(elem!1)), s(s(z)))) | (~r(z, s(s(z))))))),
% 1.52/1.78 inference(monotonicity,[status(thm)],[395])).
% 1.52/1.78 tff(397,plain,
% 1.52/1.78 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(z)), s(z))) | (~r(s(s(elem!1)), s(s(z)))) | (~r(z, s(s(z)))) | (~r(z, s(s(elem!1)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, s(s(elem!1)))) | (~r(s(s(z)), s(z))) | (~r(s(s(elem!1)), s(s(z)))) | (~r(z, s(s(z)))))),
% 1.52/1.78 inference(transitivity,[status(thm)],[396, 394])).
% 1.52/1.78 tff(398,plain,
% 1.52/1.78 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(z)), s(z))) | (~r(s(s(elem!1)), s(s(z)))) | (~r(z, s(s(z)))) | (~r(z, s(s(elem!1)))))),
% 1.52/1.78 inference(quant_inst,[status(thm)],[])).
% 1.52/1.78 tff(399,plain,
% 1.52/1.78 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, s(s(elem!1)))) | (~r(s(s(z)), s(z))) | (~r(s(s(elem!1)), s(s(z)))) | (~r(z, s(s(z))))),
% 1.52/1.78 inference(modus_ponens,[status(thm)],[398, 397])).
% 1.52/1.78 tff(400,plain,
% 1.52/1.78 ($false),
% 1.52/1.78 inference(unit_resolution,[status(thm)],[399, 197, 393, 155, 392, 365])).
% 1.52/1.78 tff(401,plain,((~r(s(s(elem!1)), s(s(z)))) | (~r(z, s(s(z)))) | (~r(s(s(z)), s(z))) | (~r(z, s(s(elem!1))))), inference(lemma,lemma(discharge,[]))).
% 1.52/1.78 tff(402,plain,
% 1.52/1.78 (~r(s(s(elem!1)), s(s(z)))),
% 1.52/1.78 inference(unit_resolution,[status(thm)],[401, 155, 392, 365])).
% 1.52/1.78 tff(403,plain,
% 1.52/1.78 (~r(s(s(z)), s(s(elem!1)))),
% 1.52/1.78 inference(unit_resolution,[status(thm)],[385, 155, 377, 365])).
% 1.52/1.78 tff(404,plain,
% 1.52/1.78 (b(s(s(z)), s(s(elem!1)))),
% 1.52/1.78 inference(unit_resolution,[status(thm)],[390, 403, 52])).
% 1.52/1.78 tff(405,assumption,(b(s(s(elem!1)), s(s(z)))), introduced(assumption)).
% 1.52/1.78 tff(406,plain,
% 1.52/1.78 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(s(elem!1)))) | (~r(z, s(s(elem!1)))) | (~r(z, s(z))) | (~r(s(s(elem!1)), s(s(s(elem!1))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(z), s(s(elem!1)))) | (~r(z, s(s(elem!1)))) | (~r(z, s(z))) | (~r(s(s(elem!1)), s(s(s(elem!1))))))),
% 1.52/1.78 inference(rewrite,[status(thm)],[])).
% 1.52/1.78 tff(407,plain,
% 1.52/1.78 (((~r(s(s(elem!1)), s(s(s(elem!1))))) | (~r(s(z), s(s(elem!1)))) | (~r(z, s(s(elem!1)))) | (~r(z, s(z)))) <=> ((~r(s(z), s(s(elem!1)))) | (~r(z, s(s(elem!1)))) | (~r(z, s(z))) | (~r(s(s(elem!1)), s(s(s(elem!1))))))),
% 1.52/1.78 inference(rewrite,[status(thm)],[])).
% 1.52/1.78 tff(408,plain,
% 1.52/1.78 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(elem!1)), s(s(s(elem!1))))) | (~r(s(z), s(s(elem!1)))) | (~r(z, s(s(elem!1)))) | (~r(z, s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(s(elem!1)))) | (~r(z, s(s(elem!1)))) | (~r(z, s(z))) | (~r(s(s(elem!1)), s(s(s(elem!1)))))))),
% 1.52/1.78 inference(monotonicity,[status(thm)],[407])).
% 1.52/1.78 tff(409,plain,
% 1.52/1.78 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(elem!1)), s(s(s(elem!1))))) | (~r(s(z), s(s(elem!1)))) | (~r(z, s(s(elem!1)))) | (~r(z, s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(z), s(s(elem!1)))) | (~r(z, s(s(elem!1)))) | (~r(z, s(z))) | (~r(s(s(elem!1)), s(s(s(elem!1))))))),
% 1.52/1.78 inference(transitivity,[status(thm)],[408, 406])).
% 1.52/1.78 tff(410,plain,
% 1.52/1.78 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(elem!1)), s(s(s(elem!1))))) | (~r(s(z), s(s(elem!1)))) | (~r(z, s(s(elem!1)))) | (~r(z, s(z))))),
% 1.52/1.78 inference(quant_inst,[status(thm)],[])).
% 1.52/1.78 tff(411,plain,
% 1.52/1.78 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(z), s(s(elem!1)))) | (~r(z, s(s(elem!1)))) | (~r(z, s(z))) | (~r(s(s(elem!1)), s(s(s(elem!1)))))),
% 1.52/1.78 inference(modus_ponens,[status(thm)],[410, 409])).
% 1.52/1.78 tff(412,plain,
% 1.52/1.78 ($false),
% 1.52/1.78 inference(unit_resolution,[status(thm)],[411, 197, 311, 323, 377, 365])).
% 1.52/1.78 tff(413,plain,((~r(s(s(elem!1)), s(s(s(elem!1))))) | (~r(s(z), s(s(elem!1)))) | (~r(z, s(z))) | (~r(z, s(s(elem!1))))), inference(lemma,lemma(discharge,[]))).
% 1.52/1.78 tff(414,plain,
% 1.52/1.78 (~r(s(z), s(s(elem!1)))),
% 1.52/1.78 inference(unit_resolution,[status(thm)],[413, 377, 365, 323])).
% 1.52/1.78 tff(415,plain,
% 1.52/1.78 (b(s(z), s(s(elem!1)))),
% 1.52/1.78 inference(unit_resolution,[status(thm)],[84, 414])).
% 1.52/1.78 tff(416,plain,
% 1.52/1.78 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(elem!1)))) | (~b(s(s(elem!1)), s(s(z)))) | (~b(s(z), s(s(z)))) | (~b(s(s(z)), s(s(elem!1)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), s(s(elem!1)))) | (~b(s(s(elem!1)), s(s(z)))) | (~b(s(z), s(s(z)))) | (~b(s(s(z)), s(s(elem!1)))))),
% 1.52/1.78 inference(rewrite,[status(thm)],[])).
% 1.52/1.78 tff(417,plain,
% 1.52/1.78 (((~b(s(s(z)), s(s(elem!1)))) | (~b(s(z), s(s(elem!1)))) | (~b(s(s(elem!1)), s(s(z)))) | (~b(s(s(z)), s(s(elem!1)))) | (~b(s(z), s(s(elem!1)))) | (~b(s(z), s(s(z))))) <=> ((~b(s(z), s(s(elem!1)))) | (~b(s(s(elem!1)), s(s(z)))) | (~b(s(z), s(s(z)))) | (~b(s(s(z)), s(s(elem!1)))))),
% 1.52/1.78 inference(rewrite,[status(thm)],[])).
% 1.52/1.78 tff(418,plain,
% 1.52/1.78 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), s(s(elem!1)))) | (~b(s(z), s(s(elem!1)))) | (~b(s(s(elem!1)), s(s(z)))) | (~b(s(s(z)), s(s(elem!1)))) | (~b(s(z), s(s(elem!1)))) | (~b(s(z), s(s(z)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(elem!1)))) | (~b(s(s(elem!1)), s(s(z)))) | (~b(s(z), s(s(z)))) | (~b(s(s(z)), s(s(elem!1))))))),
% 1.52/1.78 inference(monotonicity,[status(thm)],[417])).
% 1.52/1.78 tff(419,plain,
% 1.52/1.78 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), s(s(elem!1)))) | (~b(s(z), s(s(elem!1)))) | (~b(s(s(elem!1)), s(s(z)))) | (~b(s(s(z)), s(s(elem!1)))) | (~b(s(z), s(s(elem!1)))) | (~b(s(z), s(s(z)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), s(s(elem!1)))) | (~b(s(s(elem!1)), s(s(z)))) | (~b(s(z), s(s(z)))) | (~b(s(s(z)), s(s(elem!1)))))),
% 1.52/1.78 inference(transitivity,[status(thm)],[418, 416])).
% 1.52/1.78 tff(420,plain,
% 1.52/1.78 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), s(s(elem!1)))) | (~b(s(z), s(s(elem!1)))) | (~b(s(s(elem!1)), s(s(z)))) | (~b(s(s(z)), s(s(elem!1)))) | (~b(s(z), s(s(elem!1)))) | (~b(s(z), s(s(z)))))),
% 1.52/1.78 inference(quant_inst,[status(thm)],[])).
% 1.52/1.78 tff(421,plain,
% 1.52/1.78 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), s(s(elem!1)))) | (~b(s(s(elem!1)), s(s(z)))) | (~b(s(z), s(s(z)))) | (~b(s(s(z)), s(s(elem!1))))),
% 1.52/1.78 inference(modus_ponens,[status(thm)],[420, 419])).
% 1.52/1.78 tff(422,plain,
% 1.52/1.78 (~b(s(z), s(s(z)))),
% 1.52/1.78 inference(unit_resolution,[status(thm)],[421, 166, 415, 405, 404])).
% 1.52/1.78 tff(423,plain,
% 1.52/1.78 (((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((s(z) = s(s(z))) | b(s(z), s(s(z))) | r(s(z), s(s(z))))) <=> ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (s(z) = s(s(z))) | b(s(z), s(s(z))) | r(s(z), s(s(z))))),
% 1.52/1.78 inference(rewrite,[status(thm)],[])).
% 1.52/1.78 tff(424,plain,
% 1.52/1.78 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((s(z) = s(s(z))) | b(s(z), s(s(z))) | r(s(z), s(s(z))))),
% 1.52/1.78 inference(quant_inst,[status(thm)],[])).
% 1.52/1.78 tff(425,plain,
% 1.52/1.78 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (s(z) = s(s(z))) | b(s(z), s(s(z))) | r(s(z), s(s(z)))),
% 1.52/1.78 inference(modus_ponens,[status(thm)],[424, 423])).
% 1.52/1.78 tff(426,plain,
% 1.52/1.78 ((s(z) = s(s(z))) | b(s(z), s(s(z))) | r(s(z), s(s(z)))),
% 1.52/1.78 inference(unit_resolution,[status(thm)],[425, 79])).
% 1.52/1.78 tff(427,plain,
% 1.52/1.78 (b(s(z), s(s(z))) | r(s(z), s(s(z)))),
% 1.52/1.78 inference(unit_resolution,[status(thm)],[426, 302])).
% 1.52/1.78 tff(428,plain,
% 1.52/1.78 (r(s(z), s(s(z)))),
% 1.52/1.78 inference(unit_resolution,[status(thm)],[427, 422])).
% 1.52/1.78 tff(429,plain,
% 1.52/1.78 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(z))) | (~r(s(s(z)), s(z))) | (~r(s(z), s(s(z)))) | (~r(z, s(s(z)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, s(z))) | (~r(s(s(z)), s(z))) | (~r(s(z), s(s(z)))) | (~r(z, s(s(z)))))),
% 1.52/1.78 inference(rewrite,[status(thm)],[])).
% 1.52/1.78 tff(430,plain,
% 1.52/1.78 (((~r(s(s(z)), s(z))) | (~r(s(z), s(s(z)))) | (~r(z, s(s(z)))) | (~r(z, s(z)))) <=> ((~r(z, s(z))) | (~r(s(s(z)), s(z))) | (~r(s(z), s(s(z)))) | (~r(z, s(s(z)))))),
% 1.52/1.78 inference(rewrite,[status(thm)],[])).
% 1.52/1.78 tff(431,plain,
% 1.52/1.78 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(z)), s(z))) | (~r(s(z), s(s(z)))) | (~r(z, s(s(z)))) | (~r(z, s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(z))) | (~r(s(s(z)), s(z))) | (~r(s(z), s(s(z)))) | (~r(z, s(s(z))))))),
% 1.52/1.78 inference(monotonicity,[status(thm)],[430])).
% 1.52/1.78 tff(432,plain,
% 1.52/1.78 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(z)), s(z))) | (~r(s(z), s(s(z)))) | (~r(z, s(s(z)))) | (~r(z, s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, s(z))) | (~r(s(s(z)), s(z))) | (~r(s(z), s(s(z)))) | (~r(z, s(s(z)))))),
% 1.52/1.78 inference(transitivity,[status(thm)],[431, 429])).
% 1.52/1.78 tff(433,plain,
% 1.52/1.78 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(z)), s(z))) | (~r(s(z), s(s(z)))) | (~r(z, s(s(z)))) | (~r(z, s(z))))),
% 1.52/1.78 inference(quant_inst,[status(thm)],[])).
% 1.52/1.78 tff(434,plain,
% 1.52/1.78 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, s(z))) | (~r(s(s(z)), s(z))) | (~r(s(z), s(s(z)))) | (~r(z, s(s(z))))),
% 1.52/1.78 inference(modus_ponens,[status(thm)],[433, 432])).
% 1.52/1.78 tff(435,plain,
% 1.52/1.78 ($false),
% 1.52/1.78 inference(unit_resolution,[status(thm)],[434, 197, 428, 155, 323, 392])).
% 1.52/1.78 tff(436,plain,((~r(z, s(s(z)))) | (~r(z, s(z))) | (~r(s(s(z)), s(z))) | (~b(s(s(elem!1)), s(s(z)))) | (s(s(z)) = s(s(elem!1))) | (~r(s(s(elem!1)), s(s(s(elem!1))))) | (~r(z, s(s(elem!1))))), inference(lemma,lemma(discharge,[]))).
% 1.52/1.78 tff(437,plain,
% 1.52/1.78 (~b(s(s(elem!1)), s(s(z)))),
% 1.52/1.78 inference(unit_resolution,[status(thm)],[436, 155, 392, 323, 44, 377, 365])).
% 1.52/1.78 tff(438,plain,
% 1.52/1.78 (((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((s(s(elem!1)) = s(s(z))) | b(s(s(elem!1)), s(s(z))) | r(s(s(elem!1)), s(s(z))))) <=> ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (s(s(elem!1)) = s(s(z))) | b(s(s(elem!1)), s(s(z))) | r(s(s(elem!1)), s(s(z))))),
% 1.52/1.78 inference(rewrite,[status(thm)],[])).
% 1.52/1.78 tff(439,plain,
% 1.52/1.78 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((s(s(elem!1)) = s(s(z))) | b(s(s(elem!1)), s(s(z))) | r(s(s(elem!1)), s(s(z))))),
% 1.52/1.78 inference(quant_inst,[status(thm)],[])).
% 1.52/1.78 tff(440,plain,
% 1.52/1.78 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (s(s(elem!1)) = s(s(z))) | b(s(s(elem!1)), s(s(z))) | r(s(s(elem!1)), s(s(z)))),
% 1.52/1.78 inference(modus_ponens,[status(thm)],[439, 438])).
% 1.52/1.78 tff(441,plain,
% 1.52/1.78 ((s(s(elem!1)) = s(s(z))) | b(s(s(elem!1)), s(s(z))) | r(s(s(elem!1)), s(s(z)))),
% 1.52/1.78 inference(unit_resolution,[status(thm)],[440, 79])).
% 1.52/1.78 tff(442,plain,
% 1.52/1.78 ($false),
% 1.52/1.78 inference(unit_resolution,[status(thm)],[441, 437, 402, 11])).
% 1.52/1.78 tff(443,plain,((~r(z, s(s(z)))) | (s(s(elem!1)) = s(s(z))) | (~r(s(s(z)), s(z))) | (~r(z, s(z))) | (~r(s(s(elem!1)), s(s(s(elem!1))))) | (~r(z, s(s(elem!1))))), inference(lemma,lemma(discharge,[]))).
% 1.52/1.78 tff(444,plain,
% 1.52/1.78 (~r(s(s(z)), s(z))),
% 1.52/1.78 inference(unit_resolution,[status(thm)],[443, 377, 155, 323, 132, 365])).
% 1.52/1.78 tff(445,plain,
% 1.52/1.78 (b(s(s(z)), s(z))),
% 1.52/1.78 inference(unit_resolution,[status(thm)],[308, 444])).
% 1.52/1.78 tff(446,assumption,(b(s(s(z)), s(s(elem!1)))), introduced(assumption)).
% 1.52/1.78 tff(447,plain,
% 1.52/1.78 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(elem!1)))) | (~b(s(s(elem!1)), s(z))) | (~b(s(s(z)), s(s(elem!1)))) | (~b(s(s(z)), s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), s(s(elem!1)))) | (~b(s(s(elem!1)), s(z))) | (~b(s(s(z)), s(s(elem!1)))) | (~b(s(s(z)), s(z))))),
% 1.52/1.78 inference(rewrite,[status(thm)],[])).
% 1.52/1.78 tff(448,plain,
% 1.52/1.78 (((~b(s(s(elem!1)), s(z))) | (~b(s(s(z)), s(z))) | (~b(s(z), s(s(elem!1)))) | (~b(s(s(elem!1)), s(z))) | (~b(s(s(z)), s(z))) | (~b(s(s(z)), s(s(elem!1))))) <=> ((~b(s(z), s(s(elem!1)))) | (~b(s(s(elem!1)), s(z))) | (~b(s(s(z)), s(s(elem!1)))) | (~b(s(s(z)), s(z))))),
% 1.52/1.78 inference(rewrite,[status(thm)],[])).
% 1.52/1.78 tff(449,plain,
% 1.52/1.78 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), s(z))) | (~b(s(s(z)), s(z))) | (~b(s(z), s(s(elem!1)))) | (~b(s(s(elem!1)), s(z))) | (~b(s(s(z)), s(z))) | (~b(s(s(z)), s(s(elem!1)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(elem!1)))) | (~b(s(s(elem!1)), s(z))) | (~b(s(s(z)), s(s(elem!1)))) | (~b(s(s(z)), s(z)))))),
% 1.52/1.78 inference(monotonicity,[status(thm)],[448])).
% 1.52/1.78 tff(450,plain,
% 1.52/1.78 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), s(z))) | (~b(s(s(z)), s(z))) | (~b(s(z), s(s(elem!1)))) | (~b(s(s(elem!1)), s(z))) | (~b(s(s(z)), s(z))) | (~b(s(s(z)), s(s(elem!1)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), s(s(elem!1)))) | (~b(s(s(elem!1)), s(z))) | (~b(s(s(z)), s(s(elem!1)))) | (~b(s(s(z)), s(z))))),
% 1.52/1.78 inference(transitivity,[status(thm)],[449, 447])).
% 1.52/1.78 tff(451,plain,
% 1.52/1.78 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), s(z))) | (~b(s(s(z)), s(z))) | (~b(s(z), s(s(elem!1)))) | (~b(s(s(elem!1)), s(z))) | (~b(s(s(z)), s(z))) | (~b(s(s(z)), s(s(elem!1)))))),
% 1.52/1.78 inference(quant_inst,[status(thm)],[])).
% 1.52/1.78 tff(452,plain,
% 1.52/1.78 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), s(s(elem!1)))) | (~b(s(s(elem!1)), s(z))) | (~b(s(s(z)), s(s(elem!1)))) | (~b(s(s(z)), s(z)))),
% 1.52/1.78 inference(modus_ponens,[status(thm)],[451, 450])).
% 1.52/1.78 tff(453,plain,
% 1.52/1.78 ($false),
% 1.52/1.78 inference(unit_resolution,[status(thm)],[452, 166, 376, 310, 446, 156])).
% 1.52/1.78 tff(454,plain,((~b(s(s(elem!1)), s(z))) | (~b(s(z), s(s(elem!1)))) | (~b(s(s(z)), s(s(elem!1)))) | (~b(s(s(z)), s(z)))), inference(lemma,lemma(discharge,[]))).
% 1.52/1.78 tff(455,plain,
% 1.52/1.78 ($false),
% 1.52/1.78 inference(unit_resolution,[status(thm)],[454, 445, 391, 310, 376])).
% 1.52/1.78 tff(456,plain,((~r(s(s(elem!1)), s(s(s(elem!1))))) | (~b(s(s(elem!1)), s(z))) | (~b(s(z), s(s(elem!1)))) | (s(s(z)) = s(s(elem!1))) | (~r(z, s(s(z)))) | (~r(z, s(z))) | (~r(z, s(s(elem!1))))), inference(lemma,lemma(discharge,[]))).
% 1.52/1.78 tff(457,plain,
% 1.52/1.78 (~r(s(s(elem!1)), s(s(s(elem!1))))),
% 1.52/1.78 inference(unit_resolution,[status(thm)],[456, 52, 375, 310, 155, 323, 365])).
% 1.52/1.78 tff(458,plain,
% 1.52/1.78 (((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((s(s(elem!1)) = s(s(s(elem!1)))) | b(s(s(elem!1)), s(s(s(elem!1)))) | r(s(s(elem!1)), s(s(s(elem!1)))))) <=> ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (s(s(elem!1)) = s(s(s(elem!1)))) | b(s(s(elem!1)), s(s(s(elem!1)))) | r(s(s(elem!1)), s(s(s(elem!1)))))),
% 1.52/1.78 inference(rewrite,[status(thm)],[])).
% 1.52/1.78 tff(459,plain,
% 1.52/1.78 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((s(s(elem!1)) = s(s(s(elem!1)))) | b(s(s(elem!1)), s(s(s(elem!1)))) | r(s(s(elem!1)), s(s(s(elem!1)))))),
% 1.52/1.79 inference(quant_inst,[status(thm)],[])).
% 1.52/1.79 tff(460,plain,
% 1.52/1.79 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (s(s(elem!1)) = s(s(s(elem!1)))) | b(s(s(elem!1)), s(s(s(elem!1)))) | r(s(s(elem!1)), s(s(s(elem!1))))),
% 1.52/1.79 inference(modus_ponens,[status(thm)],[459, 458])).
% 1.52/1.79 tff(461,plain,
% 1.52/1.79 ((s(s(elem!1)) = s(s(s(elem!1)))) | b(s(s(elem!1)), s(s(s(elem!1)))) | r(s(s(elem!1)), s(s(s(elem!1))))),
% 1.52/1.79 inference(unit_resolution,[status(thm)],[460, 79])).
% 1.52/1.79 tff(462,plain,
% 1.52/1.79 (b(s(s(elem!1)), s(s(s(elem!1))))),
% 1.52/1.79 inference(unit_resolution,[status(thm)],[461, 457, 45])).
% 1.52/1.79 tff(463,assumption,(b(s(s(elem!1)), s(s(s(elem!1))))), introduced(assumption)).
% 1.52/1.79 tff(464,assumption,(r(s(s(s(elem!1))), s(s(z)))), introduced(assumption)).
% 1.52/1.79 tff(465,plain,
% 1.52/1.79 (~b(s(s(z)), s(z))),
% 1.52/1.79 inference(unit_resolution,[status(thm)],[454, 376, 310, 446])).
% 1.52/1.79 tff(466,plain,
% 1.52/1.79 (r(s(s(z)), s(z))),
% 1.52/1.79 inference(unit_resolution,[status(thm)],[308, 465])).
% 1.52/1.79 tff(467,plain,
% 1.52/1.79 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), z)) | (~b(s(z), s(s(elem!1)))) | (~b(s(s(elem!1)), s(z))) | (~b(s(z), s(s(z)))) | (~b(s(s(z)), s(s(elem!1)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), z)) | (~b(s(z), s(s(elem!1)))) | (~b(s(s(elem!1)), s(z))) | (~b(s(z), s(s(z)))) | (~b(s(s(z)), s(s(elem!1)))))),
% 1.52/1.79 inference(rewrite,[status(thm)],[])).
% 1.52/1.79 tff(468,plain,
% 1.52/1.79 (((~b(s(z), z)) | (~b(s(z), z)) | (~b(s(s(elem!1)), s(z))) | (~b(s(s(z)), s(s(elem!1)))) | (~b(s(z), s(s(elem!1)))) | (~b(s(z), s(s(z))))) <=> ((~b(s(z), z)) | (~b(s(z), s(s(elem!1)))) | (~b(s(s(elem!1)), s(z))) | (~b(s(z), s(s(z)))) | (~b(s(s(z)), s(s(elem!1)))))),
% 1.52/1.79 inference(rewrite,[status(thm)],[])).
% 1.52/1.79 tff(469,plain,
% 1.52/1.79 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), z)) | (~b(s(z), z)) | (~b(s(s(elem!1)), s(z))) | (~b(s(s(z)), s(s(elem!1)))) | (~b(s(z), s(s(elem!1)))) | (~b(s(z), s(s(z)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), z)) | (~b(s(z), s(s(elem!1)))) | (~b(s(s(elem!1)), s(z))) | (~b(s(z), s(s(z)))) | (~b(s(s(z)), s(s(elem!1))))))),
% 1.52/1.79 inference(monotonicity,[status(thm)],[468])).
% 1.52/1.79 tff(470,plain,
% 1.52/1.79 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), z)) | (~b(s(z), z)) | (~b(s(s(elem!1)), s(z))) | (~b(s(s(z)), s(s(elem!1)))) | (~b(s(z), s(s(elem!1)))) | (~b(s(z), s(s(z)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), z)) | (~b(s(z), s(s(elem!1)))) | (~b(s(s(elem!1)), s(z))) | (~b(s(z), s(s(z)))) | (~b(s(s(z)), s(s(elem!1)))))),
% 1.52/1.79 inference(transitivity,[status(thm)],[469, 467])).
% 1.52/1.79 tff(471,plain,
% 1.52/1.79 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), z)) | (~b(s(z), z)) | (~b(s(s(elem!1)), s(z))) | (~b(s(s(z)), s(s(elem!1)))) | (~b(s(z), s(s(elem!1)))) | (~b(s(z), s(s(z)))))),
% 1.52/1.79 inference(quant_inst,[status(thm)],[])).
% 1.52/1.79 tff(472,plain,
% 1.52/1.79 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), z)) | (~b(s(z), s(s(elem!1)))) | (~b(s(s(elem!1)), s(z))) | (~b(s(z), s(s(z)))) | (~b(s(s(z)), s(s(elem!1))))),
% 1.52/1.79 inference(modus_ponens,[status(thm)],[471, 470])).
% 1.52/1.79 tff(473,plain,
% 1.52/1.79 ((~b(s(z), s(s(elem!1)))) | (~b(s(z), s(s(z))))),
% 1.52/1.79 inference(unit_resolution,[status(thm)],[472, 166, 53, 310, 446])).
% 1.52/1.79 tff(474,plain,
% 1.52/1.79 (~b(s(z), s(s(z)))),
% 1.52/1.79 inference(unit_resolution,[status(thm)],[473, 376])).
% 1.52/1.79 tff(475,plain,
% 1.52/1.79 (r(s(z), s(s(z)))),
% 1.52/1.79 inference(unit_resolution,[status(thm)],[427, 474])).
% 1.52/1.79 tff(476,plain,
% 1.52/1.79 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), s(z))) | (~r(s(s(z)), s(z))) | (~r(s(z), s(s(z)))) | (~r(s(s(s(elem!1))), s(s(z)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(elem!1))), s(z))) | (~r(s(s(z)), s(z))) | (~r(s(z), s(s(z)))) | (~r(s(s(s(elem!1))), s(s(z)))))),
% 1.52/1.79 inference(rewrite,[status(thm)],[])).
% 1.52/1.79 tff(477,plain,
% 1.52/1.79 (((~r(s(s(z)), s(z))) | (~r(s(z), s(s(z)))) | (~r(s(s(s(elem!1))), s(s(z)))) | (~r(s(s(s(elem!1))), s(z)))) <=> ((~r(s(s(s(elem!1))), s(z))) | (~r(s(s(z)), s(z))) | (~r(s(z), s(s(z)))) | (~r(s(s(s(elem!1))), s(s(z)))))),
% 1.52/1.79 inference(rewrite,[status(thm)],[])).
% 1.52/1.79 tff(478,plain,
% 1.52/1.79 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(z)), s(z))) | (~r(s(z), s(s(z)))) | (~r(s(s(s(elem!1))), s(s(z)))) | (~r(s(s(s(elem!1))), s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), s(z))) | (~r(s(s(z)), s(z))) | (~r(s(z), s(s(z)))) | (~r(s(s(s(elem!1))), s(s(z))))))),
% 1.52/1.79 inference(monotonicity,[status(thm)],[477])).
% 1.52/1.79 tff(479,plain,
% 1.52/1.79 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(z)), s(z))) | (~r(s(z), s(s(z)))) | (~r(s(s(s(elem!1))), s(s(z)))) | (~r(s(s(s(elem!1))), s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(elem!1))), s(z))) | (~r(s(s(z)), s(z))) | (~r(s(z), s(s(z)))) | (~r(s(s(s(elem!1))), s(s(z)))))),
% 1.52/1.79 inference(transitivity,[status(thm)],[478, 476])).
% 1.52/1.79 tff(480,plain,
% 1.52/1.79 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(z)), s(z))) | (~r(s(z), s(s(z)))) | (~r(s(s(s(elem!1))), s(s(z)))) | (~r(s(s(s(elem!1))), s(z))))),
% 1.52/1.79 inference(quant_inst,[status(thm)],[])).
% 1.52/1.79 tff(481,plain,
% 1.52/1.79 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(elem!1))), s(z))) | (~r(s(s(z)), s(z))) | (~r(s(z), s(s(z)))) | (~r(s(s(s(elem!1))), s(s(z))))),
% 1.52/1.79 inference(modus_ponens,[status(thm)],[480, 479])).
% 1.52/1.79 tff(482,plain,
% 1.52/1.79 ($false),
% 1.52/1.79 inference(unit_resolution,[status(thm)],[481, 197, 120, 350, 392, 464])).
% 1.52/1.79 tff(483,plain,((~r(s(z), s(s(z)))) | (~r(s(s(s(elem!1))), s(z))) | (~r(s(s(z)), s(z))) | (~r(s(s(s(elem!1))), s(s(z))))), inference(lemma,lemma(discharge,[]))).
% 1.52/1.79 tff(484,plain,
% 1.52/1.79 ($false),
% 1.52/1.79 inference(unit_resolution,[status(thm)],[483, 475, 466, 350, 464])).
% 1.52/1.79 tff(485,plain,((~b(s(z), s(s(elem!1)))) | (~r(s(s(s(elem!1))), s(z))) | (~r(s(s(s(elem!1))), s(s(z)))) | (~b(s(z), z)) | (~b(s(s(elem!1)), s(z))) | (~b(s(s(z)), s(s(elem!1))))), inference(lemma,lemma(discharge,[]))).
% 1.52/1.79 tff(486,plain,
% 1.52/1.79 (~r(s(s(s(elem!1))), s(s(z)))),
% 1.52/1.79 inference(unit_resolution,[status(thm)],[485, 446, 350, 53, 310, 376])).
% 1.52/1.79 tff(487,plain,
% 1.52/1.79 ((s(s(s(elem!1))) = s(s(z))) <=> (s(s(z)) = s(s(s(elem!1))))),
% 1.52/1.79 inference(commutativity,[status(thm)],[])).
% 1.52/1.79 tff(488,plain,
% 1.52/1.79 ((s(s(z)) = s(s(s(elem!1)))) <=> (s(s(s(elem!1))) = s(s(z)))),
% 1.52/1.79 inference(symmetry,[status(thm)],[487])).
% 1.52/1.79 tff(489,plain,
% 1.52/1.79 ((~(s(s(z)) = s(s(s(elem!1))))) <=> (~(s(s(s(elem!1))) = s(s(z))))),
% 1.52/1.79 inference(monotonicity,[status(thm)],[488])).
% 1.52/1.79 tff(490,plain,
% 1.52/1.79 (~(s(s(s(elem!1))) = s(s(z)))),
% 1.52/1.79 inference(modus_ponens,[status(thm)],[209, 489])).
% 1.52/1.79 tff(491,plain,
% 1.52/1.79 ((s(s(s(elem!1))) = s(s(z))) | b(s(s(s(elem!1))), s(s(z)))),
% 1.52/1.79 inference(unit_resolution,[status(thm)],[216, 79, 213])).
% 1.52/1.79 tff(492,plain,
% 1.52/1.79 (b(s(s(s(elem!1))), s(s(z)))),
% 1.52/1.79 inference(unit_resolution,[status(thm)],[491, 490])).
% 1.52/1.79 tff(493,plain,
% 1.52/1.79 (b(s(s(z)), s(s(s(elem!1))))),
% 1.52/1.79 inference(unit_resolution,[status(thm)],[277, 79, 273, 209])).
% 1.52/1.79 tff(494,plain,
% 1.52/1.79 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(s(z)))) | (~b(s(s(elem!1)), s(s(z)))) | (~b(s(s(z)), s(s(s(elem!1))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(s(z)))) | (~b(s(s(elem!1)), s(s(z)))) | (~b(s(s(z)), s(s(s(elem!1))))))),
% 1.52/1.79 inference(rewrite,[status(thm)],[])).
% 1.52/1.79 tff(495,plain,
% 1.52/1.79 (((~b(s(s(s(elem!1))), s(s(z)))) | (~b(s(s(elem!1)), s(s(z)))) | (~b(s(s(z)), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(s(z)))) | (~b(s(s(elem!1)), s(s(z)))) | (~b(s(s(elem!1)), s(s(s(elem!1)))))) <=> ((~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(s(z)))) | (~b(s(s(elem!1)), s(s(z)))) | (~b(s(s(z)), s(s(s(elem!1))))))),
% 1.52/1.79 inference(rewrite,[status(thm)],[])).
% 1.52/1.79 tff(496,plain,
% 1.52/1.79 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), s(s(z)))) | (~b(s(s(elem!1)), s(s(z)))) | (~b(s(s(z)), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(s(z)))) | (~b(s(s(elem!1)), s(s(z)))) | (~b(s(s(elem!1)), s(s(s(elem!1))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(s(z)))) | (~b(s(s(elem!1)), s(s(z)))) | (~b(s(s(z)), s(s(s(elem!1)))))))),
% 1.52/1.79 inference(monotonicity,[status(thm)],[495])).
% 1.52/1.79 tff(497,plain,
% 1.52/1.79 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), s(s(z)))) | (~b(s(s(elem!1)), s(s(z)))) | (~b(s(s(z)), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(s(z)))) | (~b(s(s(elem!1)), s(s(z)))) | (~b(s(s(elem!1)), s(s(s(elem!1))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(s(z)))) | (~b(s(s(elem!1)), s(s(z)))) | (~b(s(s(z)), s(s(s(elem!1))))))),
% 1.52/1.79 inference(transitivity,[status(thm)],[496, 494])).
% 1.52/1.79 tff(498,plain,
% 1.52/1.79 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), s(s(z)))) | (~b(s(s(elem!1)), s(s(z)))) | (~b(s(s(z)), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(s(z)))) | (~b(s(s(elem!1)), s(s(z)))) | (~b(s(s(elem!1)), s(s(s(elem!1))))))),
% 1.52/1.79 inference(quant_inst,[status(thm)],[])).
% 1.52/1.79 tff(499,plain,
% 1.52/1.79 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(s(z)))) | (~b(s(s(elem!1)), s(s(z)))) | (~b(s(s(z)), s(s(s(elem!1)))))),
% 1.52/1.79 inference(modus_ponens,[status(thm)],[498, 497])).
% 1.52/1.79 tff(500,plain,
% 1.52/1.79 ($false),
% 1.52/1.79 inference(unit_resolution,[status(thm)],[499, 166, 463, 405, 493, 492])).
% 1.52/1.79 tff(501,plain,(r(s(s(s(elem!1))), s(s(z))) | (~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(s(s(elem!1)), s(s(z)))) | r(s(s(z)), s(s(s(elem!1))))), inference(lemma,lemma(discharge,[]))).
% 1.52/1.79 tff(502,plain,
% 1.52/1.79 (~b(s(s(elem!1)), s(s(z)))),
% 1.52/1.79 inference(unit_resolution,[status(thm)],[501, 486, 463, 273])).
% 1.52/1.79 tff(503,plain,
% 1.52/1.79 (~b(s(s(z)), s(z))),
% 1.52/1.79 inference(unit_resolution,[status(thm)],[454, 446, 310, 376])).
% 1.52/1.79 tff(504,plain,
% 1.52/1.79 (r(s(s(z)), s(z))),
% 1.52/1.79 inference(unit_resolution,[status(thm)],[308, 503])).
% 1.52/1.79 tff(505,plain,
% 1.52/1.79 (~r(s(s(elem!1)), s(s(z)))),
% 1.52/1.79 inference(unit_resolution,[status(thm)],[401, 504, 155, 365])).
% 1.52/1.79 tff(506,plain,
% 1.52/1.79 ($false),
% 1.52/1.79 inference(unit_resolution,[status(thm)],[441, 505, 502, 11])).
% 1.52/1.79 tff(507,plain,((~b(s(s(z)), s(s(elem!1)))) | (s(s(elem!1)) = s(s(z))) | (~r(z, s(s(z)))) | (~r(z, s(s(elem!1)))) | (~b(s(s(elem!1)), s(s(s(elem!1))))) | r(s(s(z)), s(s(s(elem!1)))) | (~r(s(s(s(elem!1))), s(z))) | (~b(s(z), z)) | (~b(s(s(elem!1)), s(z))) | (~b(s(z), s(s(elem!1))))), inference(lemma,lemma(discharge,[]))).
% 1.52/1.79 tff(508,plain,
% 1.52/1.79 (~b(s(s(z)), s(s(elem!1)))),
% 1.52/1.79 inference(unit_resolution,[status(thm)],[507, 132, 155, 365, 463, 273, 350, 53, 310, 376])).
% 1.52/1.79 tff(509,plain,
% 1.52/1.79 (r(s(s(z)), s(s(elem!1)))),
% 1.52/1.79 inference(unit_resolution,[status(thm)],[390, 508, 52])).
% 1.52/1.79 tff(510,plain,
% 1.52/1.79 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(elem!1)))) | (~r(s(s(z)), s(s(elem!1)))) | (~r(s(s(elem!1)), s(s(z)))) | (~r(z, s(s(z)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, s(s(elem!1)))) | (~r(s(s(z)), s(s(elem!1)))) | (~r(s(s(elem!1)), s(s(z)))) | (~r(z, s(s(z)))))),
% 1.52/1.79 inference(rewrite,[status(thm)],[])).
% 1.52/1.79 tff(511,plain,
% 1.52/1.79 (((~r(s(s(z)), s(s(elem!1)))) | (~r(s(s(elem!1)), s(s(z)))) | (~r(z, s(s(z)))) | (~r(z, s(s(elem!1))))) <=> ((~r(z, s(s(elem!1)))) | (~r(s(s(z)), s(s(elem!1)))) | (~r(s(s(elem!1)), s(s(z)))) | (~r(z, s(s(z)))))),
% 1.52/1.79 inference(rewrite,[status(thm)],[])).
% 1.52/1.79 tff(512,plain,
% 1.52/1.79 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(z)), s(s(elem!1)))) | (~r(s(s(elem!1)), s(s(z)))) | (~r(z, s(s(z)))) | (~r(z, s(s(elem!1)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(elem!1)))) | (~r(s(s(z)), s(s(elem!1)))) | (~r(s(s(elem!1)), s(s(z)))) | (~r(z, s(s(z))))))),
% 1.52/1.79 inference(monotonicity,[status(thm)],[511])).
% 1.52/1.79 tff(513,plain,
% 1.52/1.79 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(z)), s(s(elem!1)))) | (~r(s(s(elem!1)), s(s(z)))) | (~r(z, s(s(z)))) | (~r(z, s(s(elem!1)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, s(s(elem!1)))) | (~r(s(s(z)), s(s(elem!1)))) | (~r(s(s(elem!1)), s(s(z)))) | (~r(z, s(s(z)))))),
% 1.52/1.79 inference(transitivity,[status(thm)],[512, 510])).
% 1.52/1.79 tff(514,plain,
% 1.52/1.79 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(z)), s(s(elem!1)))) | (~r(s(s(elem!1)), s(s(z)))) | (~r(z, s(s(z)))) | (~r(z, s(s(elem!1)))))),
% 1.52/1.79 inference(quant_inst,[status(thm)],[])).
% 1.52/1.79 tff(515,plain,
% 1.52/1.79 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, s(s(elem!1)))) | (~r(s(s(z)), s(s(elem!1)))) | (~r(s(s(elem!1)), s(s(z)))) | (~r(z, s(s(z))))),
% 1.52/1.79 inference(modus_ponens,[status(thm)],[514, 513])).
% 1.52/1.79 tff(516,plain,
% 1.52/1.79 ($false),
% 1.52/1.79 inference(unit_resolution,[status(thm)],[515, 197, 393, 155, 333, 365])).
% 1.52/1.79 tff(517,plain,((~r(s(s(elem!1)), s(s(z)))) | (~r(z, s(s(z)))) | (~r(s(s(z)), s(s(elem!1)))) | (~r(z, s(s(elem!1))))), inference(lemma,lemma(discharge,[]))).
% 1.52/1.79 tff(518,plain,
% 1.52/1.79 (~r(s(s(elem!1)), s(s(z)))),
% 1.52/1.79 inference(unit_resolution,[status(thm)],[517, 509, 155, 365])).
% 1.52/1.79 tff(519,plain,
% 1.52/1.79 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), z)) | (~r(s(s(z)), s(s(elem!1)))) | (~r(s(s(s(elem!1))), s(s(z)))) | (~r(z, s(s(z)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(elem!1))), z)) | (~r(s(s(z)), s(s(elem!1)))) | (~r(s(s(s(elem!1))), s(s(z)))) | (~r(z, s(s(z)))))),
% 1.52/1.79 inference(rewrite,[status(thm)],[])).
% 1.52/1.79 tff(520,plain,
% 1.52/1.79 (((~r(s(s(z)), s(s(elem!1)))) | (~r(z, s(s(z)))) | (~r(s(s(s(elem!1))), s(s(z)))) | (~r(s(s(s(elem!1))), z))) <=> ((~r(s(s(s(elem!1))), z)) | (~r(s(s(z)), s(s(elem!1)))) | (~r(s(s(s(elem!1))), s(s(z)))) | (~r(z, s(s(z)))))),
% 1.52/1.79 inference(rewrite,[status(thm)],[])).
% 1.52/1.79 tff(521,plain,
% 1.52/1.79 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(z)), s(s(elem!1)))) | (~r(z, s(s(z)))) | (~r(s(s(s(elem!1))), s(s(z)))) | (~r(s(s(s(elem!1))), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), z)) | (~r(s(s(z)), s(s(elem!1)))) | (~r(s(s(s(elem!1))), s(s(z)))) | (~r(z, s(s(z))))))),
% 1.62/1.80 inference(monotonicity,[status(thm)],[520])).
% 1.62/1.80 tff(522,plain,
% 1.62/1.80 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(z)), s(s(elem!1)))) | (~r(z, s(s(z)))) | (~r(s(s(s(elem!1))), s(s(z)))) | (~r(s(s(s(elem!1))), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(elem!1))), z)) | (~r(s(s(z)), s(s(elem!1)))) | (~r(s(s(s(elem!1))), s(s(z)))) | (~r(z, s(s(z)))))),
% 1.62/1.80 inference(transitivity,[status(thm)],[521, 519])).
% 1.62/1.80 tff(523,plain,
% 1.62/1.80 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(z)), s(s(elem!1)))) | (~r(z, s(s(z)))) | (~r(s(s(s(elem!1))), s(s(z)))) | (~r(s(s(s(elem!1))), z)))),
% 1.62/1.80 inference(quant_inst,[status(thm)],[])).
% 1.62/1.80 tff(524,plain,
% 1.62/1.80 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(elem!1))), z)) | (~r(s(s(z)), s(s(elem!1)))) | (~r(s(s(s(elem!1))), s(s(z)))) | (~r(z, s(s(z))))),
% 1.62/1.80 inference(modus_ponens,[status(thm)],[523, 522])).
% 1.62/1.80 tff(525,plain,
% 1.62/1.80 ($false),
% 1.62/1.80 inference(unit_resolution,[status(thm)],[524, 197, 154, 155, 333, 464])).
% 1.62/1.80 tff(526,plain,((~r(s(s(s(elem!1))), s(s(z)))) | (~r(s(s(s(elem!1))), z)) | (~r(z, s(s(z)))) | (~r(s(s(z)), s(s(elem!1))))), inference(lemma,lemma(discharge,[]))).
% 1.62/1.80 tff(527,plain,
% 1.62/1.80 (~r(s(s(s(elem!1))), s(s(z)))),
% 1.62/1.80 inference(unit_resolution,[status(thm)],[526, 509, 155, 154])).
% 1.62/1.80 tff(528,plain,
% 1.62/1.80 (~b(s(s(elem!1)), s(s(z)))),
% 1.62/1.80 inference(unit_resolution,[status(thm)],[501, 527, 463, 273])).
% 1.62/1.80 tff(529,plain,
% 1.62/1.80 ($false),
% 1.62/1.80 inference(unit_resolution,[status(thm)],[441, 528, 518, 132])).
% 1.62/1.80 tff(530,plain,((s(s(z)) = s(s(elem!1))) | (~b(s(s(elem!1)), s(s(s(elem!1))))) | r(s(s(z)), s(s(s(elem!1)))) | (~r(z, s(s(z)))) | (~r(z, s(s(elem!1)))) | (~r(s(s(s(elem!1))), z)) | (~r(s(s(s(elem!1))), s(z))) | (~b(s(z), z)) | (~b(s(s(elem!1)), s(z))) | (~b(s(z), s(s(elem!1))))), inference(lemma,lemma(discharge,[]))).
% 1.62/1.80 tff(531,plain,
% 1.62/1.80 (r(s(s(z)), s(s(s(elem!1))))),
% 1.62/1.80 inference(unit_resolution,[status(thm)],[530, 462, 52, 155, 365, 154, 350, 53, 310, 375])).
% 1.62/1.80 tff(532,plain,
% 1.62/1.80 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(elem!1)))) | (~r(s(s(elem!1)), s(s(z)))) | (~r(s(s(z)), s(s(s(elem!1))))) | (~r(z, s(s(z)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, s(s(elem!1)))) | (~r(s(s(elem!1)), s(s(z)))) | (~r(s(s(z)), s(s(s(elem!1))))) | (~r(z, s(s(z)))))),
% 1.62/1.80 inference(rewrite,[status(thm)],[])).
% 1.62/1.80 tff(533,plain,
% 1.62/1.80 (((~r(s(s(z)), s(s(s(elem!1))))) | (~r(s(s(elem!1)), s(s(z)))) | (~r(z, s(s(z)))) | (~r(z, s(s(elem!1))))) <=> ((~r(z, s(s(elem!1)))) | (~r(s(s(elem!1)), s(s(z)))) | (~r(s(s(z)), s(s(s(elem!1))))) | (~r(z, s(s(z)))))),
% 1.62/1.80 inference(rewrite,[status(thm)],[])).
% 1.62/1.80 tff(534,plain,
% 1.62/1.80 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(z)), s(s(s(elem!1))))) | (~r(s(s(elem!1)), s(s(z)))) | (~r(z, s(s(z)))) | (~r(z, s(s(elem!1)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(elem!1)))) | (~r(s(s(elem!1)), s(s(z)))) | (~r(s(s(z)), s(s(s(elem!1))))) | (~r(z, s(s(z))))))),
% 1.62/1.80 inference(monotonicity,[status(thm)],[533])).
% 1.62/1.80 tff(535,plain,
% 1.62/1.80 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(z)), s(s(s(elem!1))))) | (~r(s(s(elem!1)), s(s(z)))) | (~r(z, s(s(z)))) | (~r(z, s(s(elem!1)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, s(s(elem!1)))) | (~r(s(s(elem!1)), s(s(z)))) | (~r(s(s(z)), s(s(s(elem!1))))) | (~r(z, s(s(z)))))),
% 1.62/1.80 inference(transitivity,[status(thm)],[534, 532])).
% 1.62/1.80 tff(536,plain,
% 1.62/1.80 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(z)), s(s(s(elem!1))))) | (~r(s(s(elem!1)), s(s(z)))) | (~r(z, s(s(z)))) | (~r(z, s(s(elem!1)))))),
% 1.62/1.80 inference(quant_inst,[status(thm)],[])).
% 1.62/1.80 tff(537,plain,
% 1.62/1.80 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, s(s(elem!1)))) | (~r(s(s(elem!1)), s(s(z)))) | (~r(s(s(z)), s(s(s(elem!1))))) | (~r(z, s(s(z))))),
% 1.62/1.80 inference(modus_ponens,[status(thm)],[536, 535])).
% 1.62/1.80 tff(538,plain,
% 1.62/1.80 ($false),
% 1.62/1.80 inference(unit_resolution,[status(thm)],[537, 197, 393, 155, 365, 281])).
% 1.62/1.80 tff(539,plain,((~r(s(s(z)), s(s(s(elem!1))))) | (~r(s(s(elem!1)), s(s(z)))) | (~r(z, s(s(z)))) | (~r(z, s(s(elem!1))))), inference(lemma,lemma(discharge,[]))).
% 1.62/1.80 tff(540,plain,
% 1.62/1.80 (~r(s(s(elem!1)), s(s(z)))),
% 1.62/1.80 inference(unit_resolution,[status(thm)],[539, 531, 155, 365])).
% 1.62/1.80 tff(541,plain,
% 1.62/1.80 (b(s(s(elem!1)), s(s(z)))),
% 1.62/1.80 inference(unit_resolution,[status(thm)],[441, 540, 132])).
% 1.62/1.80 tff(542,plain,
% 1.62/1.80 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(s(z), s(s(elem!1)))) | (~b(s(s(elem!1)), s(s(z)))) | (~b(s(s(elem!1)), s(z))) | (~b(s(s(z)), s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(s(z), s(s(elem!1)))) | (~b(s(s(elem!1)), s(s(z)))) | (~b(s(s(elem!1)), s(z))) | (~b(s(s(z)), s(z))))),
% 1.62/1.80 inference(rewrite,[status(thm)],[])).
% 1.62/1.80 tff(543,plain,
% 1.62/1.80 (((~b(s(s(elem!1)), 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(z)), s(z))) | (~b(s(s(elem!1)), s(z))) | (~b(s(s(elem!1)), s(s(z))))) <=> ((~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(s(z), s(s(elem!1)))) | (~b(s(s(elem!1)), s(s(z)))) | (~b(s(s(elem!1)), s(z))) | (~b(s(s(z)), s(z))))),
% 1.62/1.80 inference(rewrite,[status(thm)],[])).
% 1.62/1.80 tff(544,plain,
% 1.62/1.80 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(s(z), s(s(elem!1)))) | (~b(s(s(z)), s(z))) | (~b(s(s(elem!1)), s(z))) | (~b(s(s(elem!1)), s(s(z)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(s(z), s(s(elem!1)))) | (~b(s(s(elem!1)), s(s(z)))) | (~b(s(s(elem!1)), s(z))) | (~b(s(s(z)), s(z)))))),
% 1.62/1.80 inference(monotonicity,[status(thm)],[543])).
% 1.62/1.80 tff(545,plain,
% 1.62/1.80 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(s(z), s(s(elem!1)))) | (~b(s(s(z)), s(z))) | (~b(s(s(elem!1)), s(z))) | (~b(s(s(elem!1)), s(s(z)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(s(z), s(s(elem!1)))) | (~b(s(s(elem!1)), s(s(z)))) | (~b(s(s(elem!1)), s(z))) | (~b(s(s(z)), s(z))))),
% 1.62/1.80 inference(transitivity,[status(thm)],[544, 542])).
% 1.62/1.80 tff(546,plain,
% 1.62/1.80 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(s(z), s(s(elem!1)))) | (~b(s(s(z)), s(z))) | (~b(s(s(elem!1)), s(z))) | (~b(s(s(elem!1)), s(s(z)))))),
% 1.62/1.80 inference(quant_inst,[status(thm)],[])).
% 1.62/1.80 tff(547,plain,
% 1.62/1.80 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(s(z), s(s(elem!1)))) | (~b(s(s(elem!1)), s(s(z)))) | (~b(s(s(elem!1)), s(z))) | (~b(s(s(z)), s(z)))),
% 1.62/1.80 inference(modus_ponens,[status(thm)],[546, 545])).
% 1.62/1.80 tff(548,plain,
% 1.62/1.80 ($false),
% 1.62/1.80 inference(unit_resolution,[status(thm)],[547, 166, 376, 463, 405, 310, 156])).
% 1.62/1.80 tff(549,plain,((~b(s(s(z)), s(z))) | (~b(s(z), s(s(elem!1)))) | (~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(s(s(elem!1)), s(s(z)))) | (~b(s(s(elem!1)), s(z)))), inference(lemma,lemma(discharge,[]))).
% 1.62/1.80 tff(550,plain,
% 1.62/1.80 (~b(s(s(z)), s(z))),
% 1.62/1.80 inference(unit_resolution,[status(thm)],[549, 541, 462, 375, 310])).
% 1.62/1.80 tff(551,plain,
% 1.62/1.80 (r(s(s(z)), s(z))),
% 1.62/1.80 inference(unit_resolution,[status(thm)],[308, 550])).
% 1.62/1.80 tff(552,plain,
% 1.62/1.80 ($false),
% 1.62/1.80 inference(unit_resolution,[status(thm)],[434, 197, 120, 155, 323, 392])).
% 1.62/1.80 tff(553,plain,((~r(s(z), s(s(z)))) | (~r(z, s(s(z)))) | (~r(z, s(z))) | (~r(s(s(z)), s(z)))), inference(lemma,lemma(discharge,[]))).
% 1.62/1.80 tff(554,plain,
% 1.62/1.80 (~r(s(z), s(s(z)))),
% 1.62/1.80 inference(unit_resolution,[status(thm)],[553, 551, 323, 155])).
% 1.62/1.80 tff(555,plain,
% 1.62/1.80 (b(s(z), s(s(z)))),
% 1.62/1.80 inference(unit_resolution,[status(thm)],[427, 554])).
% 1.62/1.80 tff(556,assumption,(b(s(z), s(s(z)))), introduced(assumption)).
% 1.62/1.80 tff(557,plain,
% 1.62/1.80 ($false),
% 1.62/1.80 inference(unit_resolution,[status(thm)],[421, 166, 376, 405, 556, 446])).
% 1.62/1.80 tff(558,plain,((~b(s(s(z)), s(s(elem!1)))) | (~b(s(z), s(s(elem!1)))) | (~b(s(s(elem!1)), s(s(z)))) | (~b(s(z), s(s(z))))), inference(lemma,lemma(discharge,[]))).
% 1.62/1.80 tff(559,plain,
% 1.62/1.80 (~b(s(s(z)), s(s(elem!1)))),
% 1.62/1.80 inference(unit_resolution,[status(thm)],[558, 541, 375, 555])).
% 1.62/1.80 tff(560,plain,
% 1.62/1.80 (r(s(s(z)), s(s(elem!1)))),
% 1.62/1.80 inference(unit_resolution,[status(thm)],[390, 559, 52])).
% 1.62/1.80 tff(561,assumption,(r(s(s(elem!1)), s(s(s(s(elem!1)))))), introduced(assumption)).
% 1.62/1.80 tff(562,plain,
% 1.62/1.80 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(elem!1)))) | (~r(s(s(z)), s(s(elem!1)))) | (~r(s(s(elem!1)), s(s(s(s(elem!1)))))) | (~r(z, s(s(z)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, s(s(elem!1)))) | (~r(s(s(z)), s(s(elem!1)))) | (~r(s(s(elem!1)), s(s(s(s(elem!1)))))) | (~r(z, s(s(z)))))),
% 1.62/1.80 inference(rewrite,[status(thm)],[])).
% 1.62/1.80 tff(563,plain,
% 1.62/1.80 (((~r(s(s(elem!1)), s(s(s(s(elem!1)))))) | (~r(s(s(z)), s(s(elem!1)))) | (~r(z, s(s(elem!1)))) | (~r(z, s(s(z))))) <=> ((~r(z, s(s(elem!1)))) | (~r(s(s(z)), s(s(elem!1)))) | (~r(s(s(elem!1)), s(s(s(s(elem!1)))))) | (~r(z, s(s(z)))))),
% 1.62/1.80 inference(rewrite,[status(thm)],[])).
% 1.62/1.80 tff(564,plain,
% 1.62/1.80 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(elem!1)), s(s(s(s(elem!1)))))) | (~r(s(s(z)), s(s(elem!1)))) | (~r(z, s(s(elem!1)))) | (~r(z, s(s(z)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(elem!1)))) | (~r(s(s(z)), s(s(elem!1)))) | (~r(s(s(elem!1)), s(s(s(s(elem!1)))))) | (~r(z, s(s(z))))))),
% 1.62/1.80 inference(monotonicity,[status(thm)],[563])).
% 1.62/1.80 tff(565,plain,
% 1.62/1.80 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(elem!1)), s(s(s(s(elem!1)))))) | (~r(s(s(z)), s(s(elem!1)))) | (~r(z, s(s(elem!1)))) | (~r(z, s(s(z)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, s(s(elem!1)))) | (~r(s(s(z)), s(s(elem!1)))) | (~r(s(s(elem!1)), s(s(s(s(elem!1)))))) | (~r(z, s(s(z)))))),
% 1.62/1.80 inference(transitivity,[status(thm)],[564, 562])).
% 1.62/1.80 tff(566,plain,
% 1.62/1.80 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(elem!1)), s(s(s(s(elem!1)))))) | (~r(s(s(z)), s(s(elem!1)))) | (~r(z, s(s(elem!1)))) | (~r(z, s(s(z)))))),
% 1.62/1.80 inference(quant_inst,[status(thm)],[])).
% 1.62/1.80 tff(567,plain,
% 1.62/1.80 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, s(s(elem!1)))) | (~r(s(s(z)), s(s(elem!1)))) | (~r(s(s(elem!1)), s(s(s(s(elem!1)))))) | (~r(z, s(s(z))))),
% 1.62/1.80 inference(modus_ponens,[status(thm)],[566, 565])).
% 1.62/1.80 tff(568,plain,
% 1.62/1.80 ($false),
% 1.62/1.80 inference(unit_resolution,[status(thm)],[567, 197, 155, 333, 365, 561])).
% 1.62/1.80 tff(569,plain,((~r(s(s(elem!1)), s(s(s(s(elem!1)))))) | (~r(z, s(s(z)))) | (~r(s(s(z)), s(s(elem!1)))) | (~r(z, s(s(elem!1))))), inference(lemma,lemma(discharge,[]))).
% 1.62/1.80 tff(570,plain,
% 1.62/1.80 (~r(s(s(elem!1)), s(s(s(s(elem!1)))))),
% 1.62/1.80 inference(unit_resolution,[status(thm)],[569, 560, 155, 365])).
% 1.62/1.80 tff(571,plain,
% 1.62/1.80 (~r(s(s(s(elem!1))), s(s(z)))),
% 1.62/1.80 inference(unit_resolution,[status(thm)],[526, 560, 155, 154])).
% 1.62/1.80 tff(572,plain,
% 1.62/1.80 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), z)) | (~r(s(s(s(elem!1))), s(z))) | (~r(z, s(z))) | (~r(s(z), s(s(s(elem!1))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(elem!1))), z)) | (~r(s(s(s(elem!1))), s(z))) | (~r(z, s(z))) | (~r(s(z), s(s(s(elem!1))))))),
% 1.62/1.80 inference(rewrite,[status(thm)],[])).
% 1.62/1.80 tff(573,plain,
% 1.62/1.80 (((~r(s(z), s(s(s(elem!1))))) | (~r(z, s(z))) | (~r(s(s(s(elem!1))), s(z))) | (~r(s(s(s(elem!1))), z))) <=> ((~r(s(s(s(elem!1))), z)) | (~r(s(s(s(elem!1))), s(z))) | (~r(z, s(z))) | (~r(s(z), s(s(s(elem!1))))))),
% 1.62/1.80 inference(rewrite,[status(thm)],[])).
% 1.62/1.80 tff(574,plain,
% 1.62/1.80 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(s(s(elem!1))))) | (~r(z, s(z))) | (~r(s(s(s(elem!1))), s(z))) | (~r(s(s(s(elem!1))), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), z)) | (~r(s(s(s(elem!1))), s(z))) | (~r(z, s(z))) | (~r(s(z), s(s(s(elem!1)))))))),
% 1.62/1.80 inference(monotonicity,[status(thm)],[573])).
% 1.62/1.80 tff(575,plain,
% 1.62/1.80 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(s(s(elem!1))))) | (~r(z, s(z))) | (~r(s(s(s(elem!1))), s(z))) | (~r(s(s(s(elem!1))), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(elem!1))), z)) | (~r(s(s(s(elem!1))), s(z))) | (~r(z, s(z))) | (~r(s(z), s(s(s(elem!1))))))),
% 1.62/1.80 inference(transitivity,[status(thm)],[574, 572])).
% 1.62/1.80 tff(576,plain,
% 1.62/1.80 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(s(s(elem!1))))) | (~r(z, s(z))) | (~r(s(s(s(elem!1))), s(z))) | (~r(s(s(s(elem!1))), z)))),
% 1.62/1.80 inference(quant_inst,[status(thm)],[])).
% 1.62/1.80 tff(577,plain,
% 1.62/1.80 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(elem!1))), z)) | (~r(s(s(s(elem!1))), s(z))) | (~r(z, s(z))) | (~r(s(z), s(s(s(elem!1)))))),
% 1.62/1.80 inference(modus_ponens,[status(thm)],[576, 575])).
% 1.62/1.80 tff(578,plain,
% 1.62/1.80 (~r(s(s(s(elem!1))), z)),
% 1.62/1.80 inference(unit_resolution,[status(thm)],[577, 197, 350, 323, 119])).
% 1.62/1.80 tff(579,plain,
% 1.62/1.80 (b(s(s(s(elem!1))), z)),
% 1.62/1.80 inference(unit_resolution,[status(thm)],[94, 578])).
% 1.62/1.80 tff(580,plain,
% 1.62/1.80 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), s(z))) | (~r(z, s(z))) | (~r(s(z), s(s(s(elem!1))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), s(z))) | (~r(z, s(z))) | (~r(s(z), s(s(s(elem!1))))))),
% 1.62/1.80 inference(rewrite,[status(thm)],[])).
% 1.62/1.80 tff(581,plain,
% 1.62/1.80 (((~r(s(z), s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), s(z))) | (~r(z, s(z))) | (~r(z, s(s(s(elem!1)))))) <=> ((~r(z, s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), s(z))) | (~r(z, s(z))) | (~r(s(z), s(s(s(elem!1))))))),
% 1.62/1.80 inference(rewrite,[status(thm)],[])).
% 1.62/1.80 tff(582,plain,
% 1.62/1.80 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), s(z))) | (~r(z, s(z))) | (~r(z, s(s(s(elem!1))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), s(z))) | (~r(z, s(z))) | (~r(s(z), s(s(s(elem!1)))))))),
% 1.62/1.80 inference(monotonicity,[status(thm)],[581])).
% 1.62/1.80 tff(583,plain,
% 1.62/1.80 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), s(z))) | (~r(z, s(z))) | (~r(z, s(s(s(elem!1))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), s(z))) | (~r(z, s(z))) | (~r(s(z), s(s(s(elem!1))))))),
% 1.62/1.80 inference(transitivity,[status(thm)],[582, 580])).
% 1.62/1.80 tff(584,plain,
% 1.62/1.80 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), s(z))) | (~r(z, s(z))) | (~r(z, s(s(s(elem!1))))))),
% 1.62/1.80 inference(quant_inst,[status(thm)],[])).
% 1.62/1.80 tff(585,plain,
% 1.62/1.80 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), s(z))) | (~r(z, s(z))) | (~r(s(z), s(s(s(elem!1)))))),
% 1.62/1.80 inference(modus_ponens,[status(thm)],[584, 583])).
% 1.62/1.80 tff(586,plain,
% 1.62/1.80 ($false),
% 1.62/1.80 inference(unit_resolution,[status(thm)],[585, 197, 350, 323, 119, 282])).
% 1.62/1.80 tff(587,plain,((~r(s(s(s(elem!1))), s(z))) | (~r(z, s(z))) | (~r(s(z), s(s(s(elem!1))))) | (~r(z, s(s(s(elem!1)))))), inference(lemma,lemma(discharge,[]))).
% 1.62/1.80 tff(588,plain,
% 1.62/1.80 (~r(z, s(s(s(elem!1))))),
% 1.62/1.80 inference(unit_resolution,[status(thm)],[587, 119, 323, 350])).
% 1.62/1.80 tff(589,plain,
% 1.62/1.80 (b(z, s(s(s(elem!1))))),
% 1.62/1.80 inference(unit_resolution,[status(thm)],[261, 588])).
% 1.62/1.80 tff(590,plain,
% 1.62/1.80 (~r(s(s(elem!1)), s(s(s(elem!1))))),
% 1.62/1.80 inference(unit_resolution,[status(thm)],[385, 333, 155, 365])).
% 1.62/1.80 tff(591,plain,
% 1.62/1.80 (b(s(s(elem!1)), s(s(s(elem!1))))),
% 1.62/1.80 inference(unit_resolution,[status(thm)],[461, 590, 45])).
% 1.62/1.80 tff(592,assumption,(b(s(s(elem!1)), z)), introduced(assumption)).
% 1.62/1.80 tff(593,plain,
% 1.62/1.80 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(z, s(s(s(elem!1))))) | (~b(s(s(elem!1)), z)) | (~b(s(s(s(elem!1))), z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(z, s(s(s(elem!1))))) | (~b(s(s(elem!1)), z)) | (~b(s(s(s(elem!1))), z)))),
% 1.62/1.80 inference(rewrite,[status(thm)],[])).
% 1.62/1.80 tff(594,plain,
% 1.62/1.80 (((~b(z, s(s(s(elem!1))))) | (~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), z)) | (~b(z, s(s(s(elem!1))))) | (~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(s(s(elem!1)), z))) <=> ((~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(z, s(s(s(elem!1))))) | (~b(s(s(elem!1)), z)) | (~b(s(s(s(elem!1))), z)))),
% 1.62/1.80 inference(rewrite,[status(thm)],[])).
% 1.62/1.80 tff(595,plain,
% 1.62/1.80 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(s(elem!1))))) | (~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), z)) | (~b(z, s(s(s(elem!1))))) | (~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(s(s(elem!1)), z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(z, s(s(s(elem!1))))) | (~b(s(s(elem!1)), z)) | (~b(s(s(s(elem!1))), z))))),
% 1.62/1.80 inference(monotonicity,[status(thm)],[594])).
% 1.62/1.80 tff(596,plain,
% 1.62/1.80 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(s(elem!1))))) | (~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), z)) | (~b(z, s(s(s(elem!1))))) | (~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(s(s(elem!1)), z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(z, s(s(s(elem!1))))) | (~b(s(s(elem!1)), z)) | (~b(s(s(s(elem!1))), z)))),
% 1.62/1.81 inference(transitivity,[status(thm)],[595, 593])).
% 1.62/1.81 tff(597,plain,
% 1.62/1.81 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(s(elem!1))))) | (~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), z)) | (~b(z, s(s(s(elem!1))))) | (~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(s(s(elem!1)), z)))),
% 1.62/1.81 inference(quant_inst,[status(thm)],[])).
% 1.62/1.81 tff(598,plain,
% 1.62/1.81 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(z, s(s(s(elem!1))))) | (~b(s(s(elem!1)), z)) | (~b(s(s(s(elem!1))), z))),
% 1.62/1.81 inference(modus_ponens,[status(thm)],[597, 596])).
% 1.62/1.81 tff(599,plain,
% 1.62/1.81 ($false),
% 1.62/1.81 inference(unit_resolution,[status(thm)],[598, 166, 463, 240, 121, 592])).
% 1.62/1.81 tff(600,plain,((~b(z, s(s(s(elem!1))))) | (~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), z)) | (~b(s(s(elem!1)), z))), inference(lemma,lemma(discharge,[]))).
% 1.62/1.81 tff(601,plain,
% 1.62/1.81 (~b(s(s(elem!1)), z)),
% 1.62/1.81 inference(unit_resolution,[status(thm)],[600, 591, 240, 121])).
% 1.62/1.81 tff(602,assumption,(~r(s(s(elem!1)), z)), introduced(assumption)).
% 1.62/1.81 tff(603,assumption,(~b(s(s(elem!1)), z)), introduced(assumption)).
% 1.62/1.81 tff(604,plain,
% 1.62/1.81 (((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((s(s(elem!1)) = z) | b(s(s(elem!1)), z) | r(s(s(elem!1)), z))) <=> ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (s(s(elem!1)) = z) | b(s(s(elem!1)), z) | r(s(s(elem!1)), z))),
% 1.62/1.81 inference(rewrite,[status(thm)],[])).
% 1.62/1.81 tff(605,plain,
% 1.62/1.81 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((s(s(elem!1)) = z) | b(s(s(elem!1)), z) | r(s(s(elem!1)), z))),
% 1.62/1.81 inference(quant_inst,[status(thm)],[])).
% 1.62/1.81 tff(606,plain,
% 1.62/1.81 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (s(s(elem!1)) = z) | b(s(s(elem!1)), z) | r(s(s(elem!1)), z)),
% 1.62/1.81 inference(modus_ponens,[status(thm)],[605, 604])).
% 1.62/1.81 tff(607,plain,
% 1.62/1.81 ($false),
% 1.62/1.81 inference(unit_resolution,[status(thm)],[606, 79, 108, 603, 602])).
% 1.62/1.81 tff(608,plain,(r(s(s(elem!1)), z) | b(s(s(elem!1)), z)), inference(lemma,lemma(discharge,[]))).
% 1.62/1.81 tff(609,plain,
% 1.62/1.81 (r(s(s(elem!1)), z)),
% 1.62/1.81 inference(unit_resolution,[status(thm)],[608, 601])).
% 1.62/1.81 tff(610,plain,
% 1.62/1.81 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(elem!1)))) | (~r(s(s(elem!1)), z)) | (~r(s(s(z)), s(s(elem!1)))) | (~r(z, s(s(z)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, s(s(elem!1)))) | (~r(s(s(elem!1)), z)) | (~r(s(s(z)), s(s(elem!1)))) | (~r(z, s(s(z)))))),
% 1.62/1.81 inference(rewrite,[status(thm)],[])).
% 1.62/1.81 tff(611,plain,
% 1.62/1.81 (((~r(s(s(elem!1)), z)) | (~r(s(s(z)), s(s(elem!1)))) | (~r(z, s(s(elem!1)))) | (~r(z, s(s(z))))) <=> ((~r(z, s(s(elem!1)))) | (~r(s(s(elem!1)), z)) | (~r(s(s(z)), s(s(elem!1)))) | (~r(z, s(s(z)))))),
% 1.62/1.81 inference(rewrite,[status(thm)],[])).
% 1.62/1.81 tff(612,plain,
% 1.62/1.81 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(elem!1)), z)) | (~r(s(s(z)), s(s(elem!1)))) | (~r(z, s(s(elem!1)))) | (~r(z, s(s(z)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(elem!1)))) | (~r(s(s(elem!1)), z)) | (~r(s(s(z)), s(s(elem!1)))) | (~r(z, s(s(z))))))),
% 1.62/1.81 inference(monotonicity,[status(thm)],[611])).
% 1.62/1.81 tff(613,plain,
% 1.62/1.81 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(elem!1)), z)) | (~r(s(s(z)), s(s(elem!1)))) | (~r(z, s(s(elem!1)))) | (~r(z, s(s(z)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, s(s(elem!1)))) | (~r(s(s(elem!1)), z)) | (~r(s(s(z)), s(s(elem!1)))) | (~r(z, s(s(z)))))),
% 1.62/1.81 inference(transitivity,[status(thm)],[612, 610])).
% 1.62/1.81 tff(614,plain,
% 1.62/1.81 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(elem!1)), z)) | (~r(s(s(z)), s(s(elem!1)))) | (~r(z, s(s(elem!1)))) | (~r(z, s(s(z)))))),
% 1.62/1.81 inference(quant_inst,[status(thm)],[])).
% 1.62/1.81 tff(615,plain,
% 1.62/1.81 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, s(s(elem!1)))) | (~r(s(s(elem!1)), z)) | (~r(s(s(z)), s(s(elem!1)))) | (~r(z, s(s(z))))),
% 1.62/1.81 inference(modus_ponens,[status(thm)],[614, 613])).
% 1.62/1.81 tff(616,plain,
% 1.62/1.81 ($false),
% 1.62/1.81 inference(unit_resolution,[status(thm)],[615, 197, 155, 333, 365, 609])).
% 1.62/1.81 tff(617,plain,((~r(s(s(z)), s(s(elem!1)))) | (~r(z, s(s(z)))) | (~r(z, s(s(elem!1)))) | (~b(z, s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), z)) | (s(s(elem!1)) = s(s(s(elem!1))))), inference(lemma,lemma(discharge,[]))).
% 1.62/1.81 tff(618,plain,
% 1.62/1.81 (~r(s(s(z)), s(s(elem!1)))),
% 1.62/1.81 inference(unit_resolution,[status(thm)],[617, 589, 365, 155, 579, 45])).
% 1.62/1.81 tff(619,plain,
% 1.62/1.81 (s(elem!1) = s(z)),
% 1.62/1.81 inference(unit_resolution,[status(thm)],[43, 34])).
% 1.62/1.81 tff(620,plain,
% 1.62/1.81 (z = elem!1),
% 1.62/1.81 inference(unit_resolution,[status(thm)],[30, 619])).
% 1.62/1.81 tff(621,plain,
% 1.62/1.81 (r(z, s(s(elem!1))) <=> r(elem!1, s(s(elem!1)))),
% 1.62/1.81 inference(monotonicity,[status(thm)],[620])).
% 1.62/1.81 tff(622,plain,
% 1.62/1.81 (r(elem!1, s(s(elem!1)))),
% 1.62/1.81 inference(modus_ponens,[status(thm)],[365, 621])).
% 1.62/1.81 tff(623,plain,
% 1.62/1.81 ((s(s(s(s(elem!1)))) = z) <=> (s(s(s(s(elem!1)))) = elem!1)),
% 1.62/1.81 inference(monotonicity,[status(thm)],[620])).
% 1.62/1.81 tff(624,plain,
% 1.62/1.81 ((~(s(s(s(s(elem!1)))) = z)) <=> (~(s(s(s(s(elem!1)))) = elem!1))),
% 1.62/1.81 inference(monotonicity,[status(thm)],[623])).
% 1.62/1.81 tff(625,plain,
% 1.62/1.81 ((~![X: $i] : (~(s(X) = z))) | (~(s(s(s(s(elem!1)))) = z))),
% 1.62/1.81 inference(quant_inst,[status(thm)],[])).
% 1.62/1.81 tff(626,plain,
% 1.62/1.81 (~(s(s(s(s(elem!1)))) = z)),
% 1.62/1.81 inference(unit_resolution,[status(thm)],[625, 65])).
% 1.62/1.81 tff(627,plain,
% 1.62/1.81 (~(s(s(s(s(elem!1)))) = elem!1)),
% 1.62/1.81 inference(modus_ponens,[status(thm)],[626, 624])).
% 1.62/1.81 tff(628,plain,
% 1.62/1.81 (b(s(s(s(elem!1))), z) <=> b(s(s(s(elem!1))), elem!1)),
% 1.62/1.81 inference(monotonicity,[status(thm)],[12])).
% 1.62/1.81 tff(629,plain,
% 1.62/1.81 (b(s(s(s(elem!1))), elem!1) <=> b(s(s(s(elem!1))), z)),
% 1.62/1.81 inference(symmetry,[status(thm)],[628])).
% 1.62/1.81 tff(630,plain,
% 1.62/1.81 ((~b(s(s(s(elem!1))), elem!1)) <=> (~b(s(s(s(elem!1))), z))),
% 1.62/1.81 inference(monotonicity,[status(thm)],[629])).
% 1.62/1.81 tff(631,assumption,(~b(s(s(s(elem!1))), elem!1)), introduced(assumption)).
% 1.62/1.81 tff(632,plain,
% 1.62/1.81 (~b(s(s(s(elem!1))), z)),
% 1.62/1.81 inference(modus_ponens,[status(thm)],[631, 630])).
% 1.62/1.81 tff(633,plain,
% 1.62/1.81 ($false),
% 1.62/1.81 inference(unit_resolution,[status(thm)],[121, 632])).
% 1.62/1.81 tff(634,plain,(b(s(s(s(elem!1))), elem!1) | (~b(s(s(s(elem!1))), z)) | (~(z = elem!1))), inference(lemma,lemma(discharge,[]))).
% 1.62/1.81 tff(635,plain,
% 1.62/1.81 (b(s(s(s(elem!1))), elem!1)),
% 1.62/1.81 inference(unit_resolution,[status(thm)],[634, 620, 579])).
% 1.62/1.81 tff(636,plain,
% 1.62/1.81 (b(s(z), z) <=> b(s(z), elem!1)),
% 1.62/1.81 inference(monotonicity,[status(thm)],[620])).
% 1.62/1.81 tff(637,plain,
% 1.62/1.81 (b(s(z), elem!1)),
% 1.62/1.81 inference(modus_ponens,[status(thm)],[53, 636])).
% 1.62/1.81 tff(638,plain,
% 1.62/1.81 (b(z, s(s(s(elem!1)))) <=> b(elem!1, s(s(s(elem!1))))),
% 1.62/1.81 inference(monotonicity,[status(thm)],[620])).
% 1.62/1.81 tff(639,plain,
% 1.62/1.81 (b(elem!1, s(s(s(elem!1))))),
% 1.62/1.81 inference(modus_ponens,[status(thm)],[589, 638])).
% 1.62/1.81 tff(640,assumption,(b(s(s(s(s(elem!1)))), elem!1)), introduced(assumption)).
% 1.62/1.81 tff(641,assumption,(b(s(s(s(elem!1))), elem!1)), introduced(assumption)).
% 1.62/1.81 tff(642,assumption,(b(s(z), elem!1)), introduced(assumption)).
% 1.62/1.81 tff(643,assumption,(b(elem!1, s(s(s(elem!1))))), introduced(assumption)).
% 1.62/1.81 tff(644,plain,
% 1.62/1.81 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(z), elem!1)) | (~b(s(s(s(s(elem!1)))), elem!1)) | (~b(s(s(s(s(elem!1)))), s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(z), elem!1)) | (~b(s(s(s(s(elem!1)))), elem!1)) | (~b(s(s(s(s(elem!1)))), s(z))))),
% 1.62/1.81 inference(rewrite,[status(thm)],[])).
% 1.62/1.81 tff(645,plain,
% 1.62/1.81 (((~b(s(s(s(elem!1))), elem!1)) | (~b(s(s(s(s(elem!1)))), elem!1)) | (~b(elem!1, s(s(s(elem!1))))) | (~b(s(z), elem!1)) | (~b(s(s(s(s(elem!1)))), elem!1)) | (~b(s(s(s(s(elem!1)))), s(z)))) <=> ((~b(elem!1, s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(z), elem!1)) | (~b(s(s(s(s(elem!1)))), elem!1)) | (~b(s(s(s(s(elem!1)))), s(z))))),
% 1.62/1.81 inference(rewrite,[status(thm)],[])).
% 1.62/1.81 tff(646,plain,
% 1.62/1.81 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), elem!1)) | (~b(s(s(s(s(elem!1)))), elem!1)) | (~b(elem!1, s(s(s(elem!1))))) | (~b(s(z), elem!1)) | (~b(s(s(s(s(elem!1)))), elem!1)) | (~b(s(s(s(s(elem!1)))), s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(z), elem!1)) | (~b(s(s(s(s(elem!1)))), elem!1)) | (~b(s(s(s(s(elem!1)))), s(z)))))),
% 1.62/1.81 inference(monotonicity,[status(thm)],[645])).
% 1.62/1.81 tff(647,plain,
% 1.62/1.81 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), elem!1)) | (~b(s(s(s(s(elem!1)))), elem!1)) | (~b(elem!1, s(s(s(elem!1))))) | (~b(s(z), elem!1)) | (~b(s(s(s(s(elem!1)))), elem!1)) | (~b(s(s(s(s(elem!1)))), s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(z), elem!1)) | (~b(s(s(s(s(elem!1)))), elem!1)) | (~b(s(s(s(s(elem!1)))), s(z))))),
% 1.62/1.81 inference(transitivity,[status(thm)],[646, 644])).
% 1.62/1.81 tff(648,plain,
% 1.62/1.81 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), elem!1)) | (~b(s(s(s(s(elem!1)))), elem!1)) | (~b(elem!1, s(s(s(elem!1))))) | (~b(s(z), elem!1)) | (~b(s(s(s(s(elem!1)))), elem!1)) | (~b(s(s(s(s(elem!1)))), s(z))))),
% 1.62/1.81 inference(quant_inst,[status(thm)],[])).
% 1.62/1.81 tff(649,plain,
% 1.62/1.81 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(z), elem!1)) | (~b(s(s(s(s(elem!1)))), elem!1)) | (~b(s(s(s(s(elem!1)))), s(z)))),
% 1.62/1.81 inference(modus_ponens,[status(thm)],[648, 647])).
% 1.62/1.81 tff(650,plain,
% 1.62/1.81 (~b(s(s(s(s(elem!1)))), s(z))),
% 1.62/1.81 inference(unit_resolution,[status(thm)],[649, 166, 643, 642, 641, 640])).
% 1.62/1.81 tff(651,assumption,(s(s(s(s(elem!1)))) = s(z)), introduced(assumption)).
% 1.62/1.81 tff(652,plain,
% 1.62/1.81 (inj_0(s(s(s(s(elem!1))))) = inj_0(s(z))),
% 1.62/1.81 inference(monotonicity,[status(thm)],[651])).
% 1.62/1.81 tff(653,plain,
% 1.62/1.81 (s(s(s(elem!1))) = inj_0(s(s(s(s(elem!1)))))),
% 1.62/1.81 inference(symmetry,[status(thm)],[352])).
% 1.62/1.81 tff(654,plain,
% 1.62/1.81 (s(s(s(elem!1))) = z),
% 1.62/1.81 inference(transitivity,[status(thm)],[653, 652, 25])).
% 1.62/1.81 tff(655,plain,
% 1.62/1.81 ($false),
% 1.62/1.81 inference(unit_resolution,[status(thm)],[89, 654])).
% 1.62/1.81 tff(656,plain,(~(s(s(s(s(elem!1)))) = s(z))), inference(lemma,lemma(discharge,[]))).
% 1.62/1.81 tff(657,plain,
% 1.62/1.81 (((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((s(s(s(s(elem!1)))) = s(z)) | b(s(s(s(s(elem!1)))), s(z)) | r(s(s(s(s(elem!1)))), s(z)))) <=> ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (s(s(s(s(elem!1)))) = s(z)) | b(s(s(s(s(elem!1)))), s(z)) | r(s(s(s(s(elem!1)))), s(z)))),
% 1.62/1.81 inference(rewrite,[status(thm)],[])).
% 1.62/1.81 tff(658,plain,
% 1.62/1.81 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((s(s(s(s(elem!1)))) = s(z)) | b(s(s(s(s(elem!1)))), s(z)) | r(s(s(s(s(elem!1)))), s(z)))),
% 1.62/1.81 inference(quant_inst,[status(thm)],[])).
% 1.62/1.81 tff(659,plain,
% 1.62/1.81 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (s(s(s(s(elem!1)))) = s(z)) | b(s(s(s(s(elem!1)))), s(z)) | r(s(s(s(s(elem!1)))), s(z))),
% 1.62/1.81 inference(modus_ponens,[status(thm)],[658, 657])).
% 1.62/1.81 tff(660,plain,
% 1.62/1.81 ((s(s(s(s(elem!1)))) = s(z)) | b(s(s(s(s(elem!1)))), s(z)) | r(s(s(s(s(elem!1)))), s(z))),
% 1.62/1.81 inference(unit_resolution,[status(thm)],[659, 79])).
% 1.62/1.81 tff(661,plain,
% 1.62/1.81 (b(s(s(s(s(elem!1)))), s(z)) | r(s(s(s(s(elem!1)))), s(z))),
% 1.62/1.81 inference(unit_resolution,[status(thm)],[660, 656])).
% 1.62/1.81 tff(662,plain,
% 1.62/1.81 (r(s(s(s(s(elem!1)))), s(z))),
% 1.62/1.81 inference(unit_resolution,[status(thm)],[661, 650])).
% 1.62/1.81 tff(663,plain,
% 1.62/1.81 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(z), elem!1)) | (~b(s(s(s(s(elem!1)))), elem!1)) | (~b(s(z), s(s(s(s(elem!1)))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(z), elem!1)) | (~b(s(s(s(s(elem!1)))), elem!1)) | (~b(s(z), s(s(s(s(elem!1)))))))),
% 1.62/1.81 inference(rewrite,[status(thm)],[])).
% 1.62/1.81 tff(664,plain,
% 1.62/1.81 (((~b(s(s(s(elem!1))), elem!1)) | (~b(s(z), elem!1)) | (~b(elem!1, s(s(s(elem!1))))) | (~b(s(s(s(s(elem!1)))), elem!1)) | (~b(s(z), elem!1)) | (~b(s(z), s(s(s(s(elem!1))))))) <=> ((~b(elem!1, s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(z), elem!1)) | (~b(s(s(s(s(elem!1)))), elem!1)) | (~b(s(z), s(s(s(s(elem!1)))))))),
% 1.62/1.81 inference(rewrite,[status(thm)],[])).
% 1.62/1.81 tff(665,plain,
% 1.62/1.81 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), elem!1)) | (~b(s(z), elem!1)) | (~b(elem!1, s(s(s(elem!1))))) | (~b(s(s(s(s(elem!1)))), elem!1)) | (~b(s(z), elem!1)) | (~b(s(z), s(s(s(s(elem!1)))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(z), elem!1)) | (~b(s(s(s(s(elem!1)))), elem!1)) | (~b(s(z), s(s(s(s(elem!1))))))))),
% 1.62/1.81 inference(monotonicity,[status(thm)],[664])).
% 1.62/1.81 tff(666,plain,
% 1.62/1.81 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), elem!1)) | (~b(s(z), elem!1)) | (~b(elem!1, s(s(s(elem!1))))) | (~b(s(s(s(s(elem!1)))), elem!1)) | (~b(s(z), elem!1)) | (~b(s(z), s(s(s(s(elem!1)))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(z), elem!1)) | (~b(s(s(s(s(elem!1)))), elem!1)) | (~b(s(z), s(s(s(s(elem!1)))))))),
% 1.62/1.81 inference(transitivity,[status(thm)],[665, 663])).
% 1.62/1.81 tff(667,plain,
% 1.62/1.81 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), elem!1)) | (~b(s(z), elem!1)) | (~b(elem!1, s(s(s(elem!1))))) | (~b(s(s(s(s(elem!1)))), elem!1)) | (~b(s(z), elem!1)) | (~b(s(z), s(s(s(s(elem!1)))))))),
% 1.62/1.81 inference(quant_inst,[status(thm)],[])).
% 1.62/1.81 tff(668,plain,
% 1.62/1.81 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(z), elem!1)) | (~b(s(s(s(s(elem!1)))), elem!1)) | (~b(s(z), s(s(s(s(elem!1))))))),
% 1.62/1.81 inference(modus_ponens,[status(thm)],[667, 666])).
% 1.62/1.81 tff(669,plain,
% 1.62/1.81 (~b(s(z), s(s(s(s(elem!1)))))),
% 1.62/1.81 inference(unit_resolution,[status(thm)],[668, 166, 643, 642, 641, 640])).
% 1.62/1.81 tff(670,plain,
% 1.62/1.81 ((s(z) = s(s(s(s(elem!1))))) <=> (s(s(s(s(elem!1)))) = s(z))),
% 1.62/1.81 inference(commutativity,[status(thm)],[])).
% 1.62/1.81 tff(671,assumption,(s(z) = s(s(s(s(elem!1))))), introduced(assumption)).
% 1.62/1.81 tff(672,plain,
% 1.62/1.81 (s(s(s(s(elem!1)))) = s(z)),
% 1.62/1.81 inference(modus_ponens,[status(thm)],[671, 670])).
% 1.62/1.81 tff(673,assumption,(~(s(s(s(s(elem!1)))) = s(z))), introduced(assumption)).
% 1.62/1.81 tff(674,plain,
% 1.62/1.81 ($false),
% 1.62/1.81 inference(unit_resolution,[status(thm)],[673, 672])).
% 1.62/1.81 tff(675,plain,((~(s(z) = s(s(s(s(elem!1)))))) | (s(s(s(s(elem!1)))) = s(z))), inference(lemma,lemma(discharge,[]))).
% 1.62/1.81 tff(676,plain,
% 1.62/1.81 (~(s(z) = s(s(s(s(elem!1)))))),
% 1.62/1.81 inference(unit_resolution,[status(thm)],[675, 656])).
% 1.62/1.81 tff(677,plain,
% 1.62/1.81 (((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((s(z) = s(s(s(s(elem!1))))) | b(s(z), s(s(s(s(elem!1))))) | r(s(z), s(s(s(s(elem!1))))))) <=> ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (s(z) = s(s(s(s(elem!1))))) | b(s(z), s(s(s(s(elem!1))))) | r(s(z), s(s(s(s(elem!1))))))),
% 1.62/1.81 inference(rewrite,[status(thm)],[])).
% 1.62/1.81 tff(678,plain,
% 1.62/1.81 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((s(z) = s(s(s(s(elem!1))))) | b(s(z), s(s(s(s(elem!1))))) | r(s(z), s(s(s(s(elem!1))))))),
% 1.62/1.81 inference(quant_inst,[status(thm)],[])).
% 1.62/1.81 tff(679,plain,
% 1.62/1.81 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (s(z) = s(s(s(s(elem!1))))) | b(s(z), s(s(s(s(elem!1))))) | r(s(z), s(s(s(s(elem!1)))))),
% 1.62/1.81 inference(modus_ponens,[status(thm)],[678, 677])).
% 1.62/1.81 tff(680,plain,
% 1.62/1.81 ((s(z) = s(s(s(s(elem!1))))) | b(s(z), s(s(s(s(elem!1))))) | r(s(z), s(s(s(s(elem!1)))))),
% 1.62/1.81 inference(unit_resolution,[status(thm)],[679, 79])).
% 1.62/1.81 tff(681,plain,
% 1.62/1.81 (b(s(z), s(s(s(s(elem!1))))) | r(s(z), s(s(s(s(elem!1)))))),
% 1.62/1.81 inference(unit_resolution,[status(thm)],[680, 676])).
% 1.62/1.81 tff(682,plain,
% 1.62/1.81 (r(s(z), s(s(s(s(elem!1)))))),
% 1.62/1.81 inference(unit_resolution,[status(thm)],[681, 669])).
% 1.62/1.81 tff(683,plain,
% 1.62/1.81 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(s(s(s(elem!1)))), elem!1)) | (~b(s(s(s(elem!1))), s(s(s(s(elem!1)))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(s(s(s(elem!1)))), elem!1)) | (~b(s(s(s(elem!1))), s(s(s(s(elem!1)))))))),
% 1.62/1.81 inference(rewrite,[status(thm)],[])).
% 1.62/1.81 tff(684,plain,
% 1.62/1.81 (((~b(s(s(s(elem!1))), elem!1)) | (~b(s(s(s(elem!1))), elem!1)) | (~b(elem!1, s(s(s(elem!1))))) | (~b(s(s(s(s(elem!1)))), elem!1)) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(s(s(elem!1))), s(s(s(s(elem!1))))))) <=> ((~b(elem!1, s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(s(s(s(elem!1)))), elem!1)) | (~b(s(s(s(elem!1))), s(s(s(s(elem!1)))))))),
% 1.62/1.81 inference(rewrite,[status(thm)],[])).
% 1.62/1.81 tff(685,plain,
% 1.62/1.81 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), elem!1)) | (~b(s(s(s(elem!1))), elem!1)) | (~b(elem!1, s(s(s(elem!1))))) | (~b(s(s(s(s(elem!1)))), elem!1)) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(s(s(elem!1))), s(s(s(s(elem!1)))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(s(s(s(elem!1)))), elem!1)) | (~b(s(s(s(elem!1))), s(s(s(s(elem!1))))))))),
% 1.62/1.81 inference(monotonicity,[status(thm)],[684])).
% 1.62/1.81 tff(686,plain,
% 1.62/1.81 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), elem!1)) | (~b(s(s(s(elem!1))), elem!1)) | (~b(elem!1, s(s(s(elem!1))))) | (~b(s(s(s(s(elem!1)))), elem!1)) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(s(s(elem!1))), s(s(s(s(elem!1)))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(s(s(s(elem!1)))), elem!1)) | (~b(s(s(s(elem!1))), s(s(s(s(elem!1)))))))),
% 1.62/1.81 inference(transitivity,[status(thm)],[685, 683])).
% 1.62/1.81 tff(687,plain,
% 1.62/1.82 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), elem!1)) | (~b(s(s(s(elem!1))), elem!1)) | (~b(elem!1, s(s(s(elem!1))))) | (~b(s(s(s(s(elem!1)))), elem!1)) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(s(s(elem!1))), s(s(s(s(elem!1)))))))),
% 1.62/1.82 inference(quant_inst,[status(thm)],[])).
% 1.62/1.82 tff(688,plain,
% 1.62/1.82 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(s(s(s(elem!1)))), elem!1)) | (~b(s(s(s(elem!1))), s(s(s(s(elem!1))))))),
% 1.62/1.82 inference(modus_ponens,[status(thm)],[687, 686])).
% 1.62/1.82 tff(689,plain,
% 1.62/1.82 (~b(s(s(s(elem!1))), s(s(s(s(elem!1)))))),
% 1.62/1.82 inference(unit_resolution,[status(thm)],[688, 166, 643, 641, 640])).
% 1.62/1.82 tff(690,assumption,(~r(s(s(s(elem!1))), s(s(s(s(elem!1)))))), introduced(assumption)).
% 1.62/1.82 tff(691,assumption,(~b(s(s(s(elem!1))), s(s(s(s(elem!1)))))), introduced(assumption)).
% 1.62/1.82 tff(692,plain,
% 1.62/1.82 (((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((s(s(s(elem!1))) = s(s(s(s(elem!1))))) | b(s(s(s(elem!1))), s(s(s(s(elem!1))))) | r(s(s(s(elem!1))), s(s(s(s(elem!1))))))) <=> ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (s(s(s(elem!1))) = s(s(s(s(elem!1))))) | b(s(s(s(elem!1))), s(s(s(s(elem!1))))) | r(s(s(s(elem!1))), s(s(s(s(elem!1))))))),
% 1.62/1.82 inference(rewrite,[status(thm)],[])).
% 1.62/1.82 tff(693,plain,
% 1.62/1.82 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((s(s(s(elem!1))) = s(s(s(s(elem!1))))) | b(s(s(s(elem!1))), s(s(s(s(elem!1))))) | r(s(s(s(elem!1))), s(s(s(s(elem!1))))))),
% 1.62/1.82 inference(quant_inst,[status(thm)],[])).
% 1.62/1.82 tff(694,plain,
% 1.62/1.82 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (s(s(s(elem!1))) = s(s(s(s(elem!1))))) | b(s(s(s(elem!1))), s(s(s(s(elem!1))))) | r(s(s(s(elem!1))), s(s(s(s(elem!1)))))),
% 1.62/1.82 inference(modus_ponens,[status(thm)],[693, 692])).
% 1.62/1.82 tff(695,plain,
% 1.62/1.82 ($false),
% 1.62/1.82 inference(unit_resolution,[status(thm)],[694, 79, 361, 691, 690])).
% 1.62/1.82 tff(696,plain,(r(s(s(s(elem!1))), s(s(s(s(elem!1))))) | (s(s(s(elem!1))) = s(s(s(s(elem!1))))) | b(s(s(s(elem!1))), s(s(s(s(elem!1)))))), inference(lemma,lemma(discharge,[]))).
% 1.62/1.82 tff(697,plain,
% 1.62/1.82 (r(s(s(s(elem!1))), s(s(s(s(elem!1)))))),
% 1.62/1.82 inference(unit_resolution,[status(thm)],[696, 689, 361])).
% 1.62/1.82 tff(698,assumption,(r(s(s(s(elem!1))), s(s(s(s(elem!1)))))), introduced(assumption)).
% 1.62/1.82 tff(699,assumption,(r(s(z), s(s(s(s(elem!1)))))), introduced(assumption)).
% 1.62/1.82 tff(700,assumption,(r(s(s(s(s(elem!1)))), s(z))), introduced(assumption)).
% 1.62/1.82 tff(701,plain,
% 1.62/1.82 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(s(s(elem!1))))) | (~r(s(z), s(s(s(s(elem!1)))))) | (~r(s(s(s(elem!1))), s(s(s(s(elem!1)))))) | (~r(s(s(s(s(elem!1)))), s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(z), s(s(s(elem!1))))) | (~r(s(z), s(s(s(s(elem!1)))))) | (~r(s(s(s(elem!1))), s(s(s(s(elem!1)))))) | (~r(s(s(s(s(elem!1)))), s(z))))),
% 1.62/1.82 inference(rewrite,[status(thm)],[])).
% 1.62/1.82 tff(702,plain,
% 1.62/1.82 (((~r(s(s(s(s(elem!1)))), s(z))) | (~r(s(s(s(elem!1))), s(s(s(s(elem!1)))))) | (~r(s(z), s(s(s(s(elem!1)))))) | (~r(s(z), s(s(s(elem!1)))))) <=> ((~r(s(z), s(s(s(elem!1))))) | (~r(s(z), s(s(s(s(elem!1)))))) | (~r(s(s(s(elem!1))), s(s(s(s(elem!1)))))) | (~r(s(s(s(s(elem!1)))), s(z))))),
% 1.62/1.82 inference(rewrite,[status(thm)],[])).
% 1.62/1.82 tff(703,plain,
% 1.62/1.82 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(elem!1)))), s(z))) | (~r(s(s(s(elem!1))), s(s(s(s(elem!1)))))) | (~r(s(z), s(s(s(s(elem!1)))))) | (~r(s(z), s(s(s(elem!1))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(s(s(elem!1))))) | (~r(s(z), s(s(s(s(elem!1)))))) | (~r(s(s(s(elem!1))), s(s(s(s(elem!1)))))) | (~r(s(s(s(s(elem!1)))), s(z)))))),
% 1.62/1.82 inference(monotonicity,[status(thm)],[702])).
% 1.62/1.82 tff(704,plain,
% 1.62/1.82 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(elem!1)))), s(z))) | (~r(s(s(s(elem!1))), s(s(s(s(elem!1)))))) | (~r(s(z), s(s(s(s(elem!1)))))) | (~r(s(z), s(s(s(elem!1))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(z), s(s(s(elem!1))))) | (~r(s(z), s(s(s(s(elem!1)))))) | (~r(s(s(s(elem!1))), s(s(s(s(elem!1)))))) | (~r(s(s(s(s(elem!1)))), s(z))))),
% 1.62/1.82 inference(transitivity,[status(thm)],[703, 701])).
% 1.62/1.82 tff(705,plain,
% 1.62/1.82 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(elem!1)))), s(z))) | (~r(s(s(s(elem!1))), s(s(s(s(elem!1)))))) | (~r(s(z), s(s(s(s(elem!1)))))) | (~r(s(z), s(s(s(elem!1))))))),
% 1.62/1.82 inference(quant_inst,[status(thm)],[])).
% 1.62/1.82 tff(706,plain,
% 1.62/1.82 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(z), s(s(s(elem!1))))) | (~r(s(z), s(s(s(s(elem!1)))))) | (~r(s(s(s(elem!1))), s(s(s(s(elem!1)))))) | (~r(s(s(s(s(elem!1)))), s(z)))),
% 1.62/1.82 inference(modus_ponens,[status(thm)],[705, 704])).
% 1.62/1.82 tff(707,plain,
% 1.62/1.82 ($false),
% 1.62/1.82 inference(unit_resolution,[status(thm)],[706, 197, 700, 699, 119, 698])).
% 1.62/1.82 tff(708,plain,((~r(s(z), s(s(s(s(elem!1)))))) | (~r(s(s(s(s(elem!1)))), s(z))) | (~r(s(z), s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), s(s(s(s(elem!1))))))), inference(lemma,lemma(discharge,[]))).
% 1.62/1.82 tff(709,plain,
% 1.62/1.82 ($false),
% 1.62/1.82 inference(unit_resolution,[status(thm)],[708, 697, 682, 119, 662])).
% 1.62/1.82 tff(710,plain,((~b(s(s(s(s(elem!1)))), elem!1)) | (~r(s(z), s(s(s(elem!1))))) | (s(s(s(elem!1))) = s(s(s(s(elem!1))))) | (~b(elem!1, s(s(s(elem!1))))) | (~b(s(z), elem!1)) | (~b(s(s(s(elem!1))), elem!1))), inference(lemma,lemma(discharge,[]))).
% 1.62/1.82 tff(711,plain,
% 1.62/1.82 (~b(s(s(s(s(elem!1)))), elem!1)),
% 1.62/1.82 inference(unit_resolution,[status(thm)],[710, 639, 358, 119, 637, 635])).
% 1.62/1.82 tff(712,assumption,(~(s(s(s(s(elem!1)))) = elem!1)), introduced(assumption)).
% 1.62/1.82 tff(713,assumption,(~r(s(s(s(s(elem!1)))), elem!1)), introduced(assumption)).
% 1.62/1.82 tff(714,assumption,(~b(s(s(s(s(elem!1)))), elem!1)), introduced(assumption)).
% 1.62/1.82 tff(715,plain,
% 1.62/1.82 (((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((s(s(s(s(elem!1)))) = elem!1) | b(s(s(s(s(elem!1)))), elem!1) | r(s(s(s(s(elem!1)))), elem!1))) <=> ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (s(s(s(s(elem!1)))) = elem!1) | b(s(s(s(s(elem!1)))), elem!1) | r(s(s(s(s(elem!1)))), elem!1))),
% 1.62/1.82 inference(rewrite,[status(thm)],[])).
% 1.62/1.82 tff(716,plain,
% 1.62/1.82 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((s(s(s(s(elem!1)))) = elem!1) | b(s(s(s(s(elem!1)))), elem!1) | r(s(s(s(s(elem!1)))), elem!1))),
% 1.62/1.82 inference(quant_inst,[status(thm)],[])).
% 1.62/1.82 tff(717,plain,
% 1.62/1.82 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (s(s(s(s(elem!1)))) = elem!1) | b(s(s(s(s(elem!1)))), elem!1) | r(s(s(s(s(elem!1)))), elem!1)),
% 1.62/1.82 inference(modus_ponens,[status(thm)],[716, 715])).
% 1.62/1.82 tff(718,plain,
% 1.62/1.82 ($false),
% 1.62/1.82 inference(unit_resolution,[status(thm)],[717, 79, 714, 713, 712])).
% 1.62/1.82 tff(719,plain,(r(s(s(s(s(elem!1)))), elem!1) | b(s(s(s(s(elem!1)))), elem!1) | (s(s(s(s(elem!1)))) = elem!1)), inference(lemma,lemma(discharge,[]))).
% 1.62/1.82 tff(720,plain,
% 1.62/1.82 (r(s(s(s(s(elem!1)))), elem!1)),
% 1.62/1.82 inference(unit_resolution,[status(thm)],[719, 711, 627])).
% 1.62/1.82 tff(721,plain,
% 1.62/1.82 ((s(s(s(s(elem!1)))) = s(s(z))) <=> (s(s(s(s(elem!1)))) = s(s(elem!1)))),
% 1.62/1.82 inference(monotonicity,[status(thm)],[34])).
% 1.62/1.82 tff(722,plain,
% 1.62/1.82 ((s(s(s(s(elem!1)))) = s(s(z))) <=> (s(s(elem!1)) = s(s(s(s(elem!1)))))),
% 1.62/1.82 inference(transitivity,[status(thm)],[721, 123])).
% 1.62/1.82 tff(723,plain,
% 1.62/1.82 ((s(s(s(s(elem!1)))) = s(s(z))) <=> (s(s(s(s(elem!1)))) = s(s(elem!1)))),
% 1.62/1.82 inference(transitivity,[status(thm)],[722, 124])).
% 1.62/1.82 tff(724,plain,
% 1.62/1.82 ((~(s(s(s(s(elem!1)))) = s(s(z)))) <=> (~(s(s(s(s(elem!1)))) = s(s(elem!1))))),
% 1.62/1.82 inference(monotonicity,[status(thm)],[723])).
% 1.62/1.82 tff(725,assumption,(s(s(s(s(elem!1)))) = s(s(z))), introduced(assumption)).
% 1.62/1.82 tff(726,plain,
% 1.62/1.82 (s(s(z)) = s(s(s(s(elem!1))))),
% 1.62/1.82 inference(symmetry,[status(thm)],[725])).
% 1.62/1.82 tff(727,plain,
% 1.62/1.82 (inj_0(s(s(z))) = inj_0(s(s(s(s(elem!1)))))),
% 1.62/1.82 inference(monotonicity,[status(thm)],[726])).
% 1.62/1.82 tff(728,plain,
% 1.62/1.82 (s(z) = s(s(s(elem!1)))),
% 1.62/1.82 inference(transitivity,[status(thm)],[206, 727, 352])).
% 1.62/1.82 tff(729,plain,
% 1.62/1.82 (inj_0(s(z)) = inj_0(s(s(s(elem!1))))),
% 1.62/1.82 inference(monotonicity,[status(thm)],[728])).
% 1.62/1.82 tff(730,plain,
% 1.62/1.82 (inj_0(s(s(s(elem!1)))) = inj_0(s(z))),
% 1.62/1.82 inference(symmetry,[status(thm)],[729])).
% 1.62/1.82 tff(731,plain,
% 1.62/1.82 (s(s(elem!1)) = z),
% 1.62/1.82 inference(transitivity,[status(thm)],[105, 730, 25])).
% 1.62/1.82 tff(732,plain,
% 1.62/1.82 ($false),
% 1.62/1.82 inference(unit_resolution,[status(thm)],[108, 731])).
% 1.62/1.82 tff(733,plain,(~(s(s(s(s(elem!1)))) = s(s(z)))), inference(lemma,lemma(discharge,[]))).
% 1.62/1.82 tff(734,plain,
% 1.62/1.82 (~(s(s(s(s(elem!1)))) = s(s(elem!1)))),
% 1.62/1.82 inference(modus_ponens,[status(thm)],[733, 724])).
% 1.62/1.82 tff(735,plain,
% 1.62/1.82 (r(z, s(z)) <=> r(elem!1, s(z))),
% 1.62/1.82 inference(monotonicity,[status(thm)],[12])).
% 1.62/1.82 tff(736,plain,
% 1.62/1.82 (r(elem!1, s(z)) <=> r(z, s(z))),
% 1.62/1.82 inference(symmetry,[status(thm)],[735])).
% 1.62/1.82 tff(737,plain,
% 1.62/1.82 ((~r(elem!1, s(z))) <=> (~r(z, s(z)))),
% 1.62/1.82 inference(monotonicity,[status(thm)],[736])).
% 1.62/1.82 tff(738,assumption,(~r(elem!1, s(z))), introduced(assumption)).
% 1.62/1.82 tff(739,plain,
% 1.62/1.82 (~r(z, s(z))),
% 1.62/1.82 inference(modus_ponens,[status(thm)],[738, 737])).
% 1.62/1.82 tff(740,plain,
% 1.62/1.82 ($false),
% 1.62/1.82 inference(unit_resolution,[status(thm)],[323, 739])).
% 1.62/1.82 tff(741,plain,((~(z = elem!1)) | (~r(z, s(z))) | r(elem!1, s(z))), inference(lemma,lemma(discharge,[]))).
% 1.62/1.82 tff(742,plain,
% 1.62/1.82 (r(elem!1, s(z))),
% 1.62/1.82 inference(unit_resolution,[status(thm)],[741, 620, 323])).
% 1.62/1.82 tff(743,assumption,(r(s(s(s(s(elem!1)))), elem!1)), introduced(assumption)).
% 1.62/1.82 tff(744,assumption,(r(elem!1, s(z))), introduced(assumption)).
% 1.62/1.82 tff(745,plain,
% 1.62/1.82 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(s(s(elem!1))))) | (~r(elem!1, s(z))) | (~r(s(s(s(s(elem!1)))), s(z))) | (~r(s(s(s(s(elem!1)))), elem!1)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(z), s(s(s(elem!1))))) | (~r(elem!1, s(z))) | (~r(s(s(s(s(elem!1)))), s(z))) | (~r(s(s(s(s(elem!1)))), elem!1)))),
% 1.62/1.82 inference(rewrite,[status(thm)],[])).
% 1.62/1.82 tff(746,plain,
% 1.62/1.82 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(s(s(elem!1))))) | (~r(elem!1, s(z))) | (~r(s(s(s(s(elem!1)))), s(z))) | (~r(s(s(s(s(elem!1)))), elem!1)))),
% 1.62/1.82 inference(quant_inst,[status(thm)],[])).
% 1.62/1.82 tff(747,plain,
% 1.62/1.82 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(z), s(s(s(elem!1))))) | (~r(elem!1, s(z))) | (~r(s(s(s(s(elem!1)))), s(z))) | (~r(s(s(s(s(elem!1)))), elem!1))),
% 1.62/1.82 inference(modus_ponens,[status(thm)],[746, 745])).
% 1.62/1.82 tff(748,plain,
% 1.62/1.82 ($false),
% 1.62/1.82 inference(unit_resolution,[status(thm)],[747, 197, 744, 700, 119, 743])).
% 1.62/1.82 tff(749,plain,((~r(s(s(s(s(elem!1)))), s(z))) | (~r(elem!1, s(z))) | (~r(s(z), s(s(s(elem!1))))) | (~r(s(s(s(s(elem!1)))), elem!1))), inference(lemma,lemma(discharge,[]))).
% 1.62/1.82 tff(750,plain,
% 1.62/1.82 (~r(s(s(s(s(elem!1)))), s(z))),
% 1.62/1.82 inference(unit_resolution,[status(thm)],[749, 742, 119, 720])).
% 1.62/1.82 tff(751,plain,
% 1.62/1.82 (b(s(s(s(s(elem!1)))), s(z))),
% 1.62/1.82 inference(unit_resolution,[status(thm)],[661, 750])).
% 1.62/1.82 tff(752,plain,
% 1.62/1.82 (elem!1 = z),
% 1.62/1.82 inference(symmetry,[status(thm)],[620])).
% 1.62/1.82 tff(753,plain,
% 1.62/1.82 ((s(s(elem!1)) = elem!1) <=> (s(s(elem!1)) = z)),
% 1.62/1.82 inference(monotonicity,[status(thm)],[752])).
% 1.62/1.82 tff(754,plain,
% 1.62/1.82 ((s(s(elem!1)) = z) <=> (s(s(elem!1)) = elem!1)),
% 1.62/1.82 inference(symmetry,[status(thm)],[753])).
% 1.62/1.82 tff(755,plain,
% 1.62/1.82 ((~(s(s(elem!1)) = z)) <=> (~(s(s(elem!1)) = elem!1))),
% 1.62/1.82 inference(monotonicity,[status(thm)],[754])).
% 1.62/1.82 tff(756,plain,
% 1.62/1.82 (~(s(s(elem!1)) = elem!1)),
% 1.62/1.82 inference(modus_ponens,[status(thm)],[108, 755])).
% 1.62/1.82 tff(757,plain,
% 1.62/1.82 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(s(elem!1)))) | (~r(s(s(s(elem!1))), s(z))) | (~r(s(z), s(s(s(elem!1))))) | (~r(s(s(elem!1)), s(s(s(elem!1))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(z), s(s(elem!1)))) | (~r(s(s(s(elem!1))), s(z))) | (~r(s(z), s(s(s(elem!1))))) | (~r(s(s(elem!1)), s(s(s(elem!1))))))),
% 1.62/1.82 inference(rewrite,[status(thm)],[])).
% 1.62/1.82 tff(758,plain,
% 1.62/1.82 (((~r(s(s(s(elem!1))), s(z))) | (~r(s(s(elem!1)), s(s(s(elem!1))))) | (~r(s(z), s(s(s(elem!1))))) | (~r(s(z), s(s(elem!1))))) <=> ((~r(s(z), s(s(elem!1)))) | (~r(s(s(s(elem!1))), s(z))) | (~r(s(z), s(s(s(elem!1))))) | (~r(s(s(elem!1)), s(s(s(elem!1))))))),
% 1.62/1.82 inference(rewrite,[status(thm)],[])).
% 1.62/1.82 tff(759,plain,
% 1.62/1.82 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), s(z))) | (~r(s(s(elem!1)), s(s(s(elem!1))))) | (~r(s(z), s(s(s(elem!1))))) | (~r(s(z), s(s(elem!1)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(s(elem!1)))) | (~r(s(s(s(elem!1))), s(z))) | (~r(s(z), s(s(s(elem!1))))) | (~r(s(s(elem!1)), s(s(s(elem!1)))))))),
% 1.62/1.82 inference(monotonicity,[status(thm)],[758])).
% 1.62/1.82 tff(760,plain,
% 1.62/1.82 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), s(z))) | (~r(s(s(elem!1)), s(s(s(elem!1))))) | (~r(s(z), s(s(s(elem!1))))) | (~r(s(z), s(s(elem!1)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(z), s(s(elem!1)))) | (~r(s(s(s(elem!1))), s(z))) | (~r(s(z), s(s(s(elem!1))))) | (~r(s(s(elem!1)), s(s(s(elem!1))))))),
% 1.62/1.82 inference(transitivity,[status(thm)],[759, 757])).
% 1.62/1.82 tff(761,plain,
% 1.62/1.82 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), s(z))) | (~r(s(s(elem!1)), s(s(s(elem!1))))) | (~r(s(z), s(s(s(elem!1))))) | (~r(s(z), s(s(elem!1)))))),
% 1.62/1.82 inference(quant_inst,[status(thm)],[])).
% 1.62/1.82 tff(762,plain,
% 1.62/1.82 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(z), s(s(elem!1)))) | (~r(s(s(s(elem!1))), s(z))) | (~r(s(z), s(s(s(elem!1))))) | (~r(s(s(elem!1)), s(s(s(elem!1)))))),
% 1.62/1.82 inference(modus_ponens,[status(thm)],[761, 760])).
% 1.62/1.82 tff(763,plain,
% 1.62/1.82 ($false),
% 1.62/1.82 inference(unit_resolution,[status(thm)],[762, 197, 311, 350, 377, 119])).
% 1.62/1.82 tff(764,plain,((~r(s(s(elem!1)), s(s(s(elem!1))))) | (~r(s(z), s(s(elem!1)))) | (~r(s(s(s(elem!1))), s(z))) | (~r(s(z), s(s(s(elem!1)))))), inference(lemma,lemma(discharge,[]))).
% 1.62/1.82 tff(765,plain,
% 1.62/1.82 (~r(s(s(elem!1)), s(s(s(elem!1))))),
% 1.62/1.82 inference(unit_resolution,[status(thm)],[764, 311, 350, 119])).
% 1.62/1.82 tff(766,plain,
% 1.62/1.82 (b(s(s(elem!1)), s(s(s(elem!1))))),
% 1.62/1.82 inference(unit_resolution,[status(thm)],[461, 765, 45])).
% 1.62/1.82 tff(767,assumption,(~(s(s(elem!1)) = elem!1)), introduced(assumption)).
% 1.62/1.82 tff(768,assumption,(r(s(s(elem!1)), elem!1)), introduced(assumption)).
% 1.62/1.82 tff(769,plain,
% 1.62/1.82 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(s(elem!1)))) | (~r(s(s(elem!1)), elem!1)) | (~r(z, s(s(elem!1)))) | (~r(z, s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(z), s(s(elem!1)))) | (~r(s(s(elem!1)), elem!1)) | (~r(z, s(s(elem!1)))) | (~r(z, s(z))))),
% 1.62/1.82 inference(rewrite,[status(thm)],[])).
% 1.62/1.82 tff(770,plain,
% 1.62/1.82 (((~r(s(s(elem!1)), elem!1)) | (~r(s(z), s(s(elem!1)))) | (~r(z, s(s(elem!1)))) | (~r(z, s(z)))) <=> ((~r(s(z), s(s(elem!1)))) | (~r(s(s(elem!1)), elem!1)) | (~r(z, s(s(elem!1)))) | (~r(z, s(z))))),
% 1.62/1.82 inference(rewrite,[status(thm)],[])).
% 1.62/1.82 tff(771,plain,
% 1.62/1.82 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(elem!1)), elem!1)) | (~r(s(z), s(s(elem!1)))) | (~r(z, s(s(elem!1)))) | (~r(z, s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(s(elem!1)))) | (~r(s(s(elem!1)), elem!1)) | (~r(z, s(s(elem!1)))) | (~r(z, s(z)))))),
% 1.62/1.82 inference(monotonicity,[status(thm)],[770])).
% 1.62/1.82 tff(772,plain,
% 1.62/1.82 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(elem!1)), elem!1)) | (~r(s(z), s(s(elem!1)))) | (~r(z, s(s(elem!1)))) | (~r(z, s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(z), s(s(elem!1)))) | (~r(s(s(elem!1)), elem!1)) | (~r(z, s(s(elem!1)))) | (~r(z, s(z))))),
% 1.62/1.82 inference(transitivity,[status(thm)],[771, 769])).
% 1.62/1.82 tff(773,plain,
% 1.62/1.82 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(elem!1)), elem!1)) | (~r(s(z), s(s(elem!1)))) | (~r(z, s(s(elem!1)))) | (~r(z, s(z))))),
% 1.62/1.82 inference(quant_inst,[status(thm)],[])).
% 1.62/1.82 tff(774,plain,
% 1.62/1.82 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(z), s(s(elem!1)))) | (~r(s(s(elem!1)), elem!1)) | (~r(z, s(s(elem!1)))) | (~r(z, s(z)))),
% 1.62/1.82 inference(modus_ponens,[status(thm)],[773, 772])).
% 1.62/1.82 tff(775,plain,
% 1.62/1.82 ($false),
% 1.62/1.82 inference(unit_resolution,[status(thm)],[774, 197, 311, 323, 768, 365])).
% 1.62/1.82 tff(776,plain,((~r(s(s(elem!1)), elem!1)) | (~r(s(z), s(s(elem!1)))) | (~r(z, s(z))) | (~r(z, s(s(elem!1))))), inference(lemma,lemma(discharge,[]))).
% 1.62/1.82 tff(777,plain,
% 1.62/1.82 (~r(s(s(elem!1)), elem!1)),
% 1.62/1.82 inference(unit_resolution,[status(thm)],[776, 311, 323, 365])).
% 1.62/1.82 tff(778,assumption,(~r(s(s(elem!1)), elem!1)), introduced(assumption)).
% 1.62/1.82 tff(779,assumption,(~b(s(s(elem!1)), elem!1)), introduced(assumption)).
% 1.62/1.82 tff(780,plain,
% 1.62/1.82 (((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((s(s(elem!1)) = elem!1) | b(s(s(elem!1)), elem!1) | r(s(s(elem!1)), elem!1))) <=> ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (s(s(elem!1)) = elem!1) | b(s(s(elem!1)), elem!1) | r(s(s(elem!1)), elem!1))),
% 1.62/1.82 inference(rewrite,[status(thm)],[])).
% 1.62/1.82 tff(781,plain,
% 1.62/1.82 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((s(s(elem!1)) = elem!1) | b(s(s(elem!1)), elem!1) | r(s(s(elem!1)), elem!1))),
% 1.62/1.82 inference(quant_inst,[status(thm)],[])).
% 1.62/1.82 tff(782,plain,
% 1.62/1.82 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (s(s(elem!1)) = elem!1) | b(s(s(elem!1)), elem!1) | r(s(s(elem!1)), elem!1)),
% 1.62/1.82 inference(modus_ponens,[status(thm)],[781, 780])).
% 1.62/1.82 tff(783,plain,
% 1.62/1.82 ($false),
% 1.62/1.82 inference(unit_resolution,[status(thm)],[782, 79, 779, 767, 778])).
% 1.62/1.82 tff(784,plain,(b(s(s(elem!1)), elem!1) | (s(s(elem!1)) = elem!1) | r(s(s(elem!1)), elem!1)), inference(lemma,lemma(discharge,[]))).
% 1.62/1.82 tff(785,plain,
% 1.62/1.82 (b(s(s(elem!1)), elem!1)),
% 1.62/1.82 inference(unit_resolution,[status(thm)],[784, 777, 767])).
% 1.62/1.82 tff(786,assumption,(b(s(s(elem!1)), elem!1)), introduced(assumption)).
% 1.62/1.82 tff(787,plain,
% 1.62/1.82 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(s(s(elem!1)), elem!1)) | (~b(elem!1, s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), elem!1)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(s(s(elem!1)), elem!1)) | (~b(elem!1, s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), elem!1)))),
% 1.62/1.82 inference(rewrite,[status(thm)],[])).
% 1.62/1.82 tff(788,plain,
% 1.62/1.82 (((~b(elem!1, s(s(s(elem!1))))) | (~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), elem!1)) | (~b(elem!1, s(s(s(elem!1))))) | (~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(s(s(elem!1)), elem!1))) <=> ((~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(s(s(elem!1)), elem!1)) | (~b(elem!1, s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), elem!1)))),
% 1.62/1.82 inference(rewrite,[status(thm)],[])).
% 1.62/1.82 tff(789,plain,
% 1.62/1.82 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(s(s(elem!1))))) | (~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), elem!1)) | (~b(elem!1, s(s(s(elem!1))))) | (~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(s(s(elem!1)), elem!1)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(s(s(elem!1)), elem!1)) | (~b(elem!1, s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), elem!1))))),
% 1.62/1.83 inference(monotonicity,[status(thm)],[788])).
% 1.62/1.83 tff(790,plain,
% 1.62/1.83 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(s(s(elem!1))))) | (~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), elem!1)) | (~b(elem!1, s(s(s(elem!1))))) | (~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(s(s(elem!1)), elem!1)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(s(s(elem!1)), elem!1)) | (~b(elem!1, s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), elem!1)))),
% 1.62/1.83 inference(transitivity,[status(thm)],[789, 787])).
% 1.62/1.83 tff(791,plain,
% 1.62/1.83 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(s(s(elem!1))))) | (~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), elem!1)) | (~b(elem!1, s(s(s(elem!1))))) | (~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(s(s(elem!1)), elem!1)))),
% 1.62/1.83 inference(quant_inst,[status(thm)],[])).
% 1.62/1.83 tff(792,plain,
% 1.62/1.83 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(s(s(elem!1)), elem!1)) | (~b(elem!1, s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), elem!1))),
% 1.62/1.83 inference(modus_ponens,[status(thm)],[791, 790])).
% 1.62/1.83 tff(793,plain,
% 1.62/1.83 ($false),
% 1.62/1.83 inference(unit_resolution,[status(thm)],[792, 166, 463, 786, 643, 641])).
% 1.62/1.83 tff(794,plain,((~b(s(s(s(elem!1))), elem!1)) | (~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(s(s(elem!1)), elem!1)) | (~b(elem!1, s(s(s(elem!1)))))), inference(lemma,lemma(discharge,[]))).
% 1.62/1.83 tff(795,plain,
% 1.62/1.83 ($false),
% 1.62/1.83 inference(unit_resolution,[status(thm)],[794, 785, 766, 641, 643])).
% 1.62/1.83 tff(796,plain,((~r(s(z), s(s(elem!1)))) | (~b(s(s(s(elem!1))), elem!1)) | (~b(elem!1, s(s(s(elem!1))))) | (s(s(elem!1)) = elem!1) | (s(s(elem!1)) = s(s(s(elem!1)))) | (~r(z, s(z))) | (~r(z, s(s(elem!1)))) | (~r(s(s(s(elem!1))), s(z))) | (~r(s(z), s(s(s(elem!1)))))), inference(lemma,lemma(discharge,[]))).
% 1.62/1.83 tff(797,plain,
% 1.62/1.83 (~r(s(z), s(s(elem!1)))),
% 1.62/1.83 inference(unit_resolution,[status(thm)],[796, 635, 639, 756, 45, 323, 365, 350, 119])).
% 1.62/1.83 tff(798,plain,
% 1.62/1.83 (b(s(z), s(s(elem!1)))),
% 1.62/1.83 inference(unit_resolution,[status(thm)],[84, 797])).
% 1.62/1.83 tff(799,plain,
% 1.62/1.83 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(elem!1)))), s(s(elem!1)))) | (~b(s(z), s(s(elem!1)))) | (~b(s(s(elem!1)), s(z))) | (~b(s(s(s(s(elem!1)))), s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(elem!1)))), s(s(elem!1)))) | (~b(s(z), s(s(elem!1)))) | (~b(s(s(elem!1)), s(z))) | (~b(s(s(s(s(elem!1)))), s(z))))),
% 1.62/1.83 inference(rewrite,[status(thm)],[])).
% 1.62/1.83 tff(800,plain,
% 1.62/1.83 (((~b(s(s(elem!1)), s(z))) | (~b(s(s(s(s(elem!1)))), s(z))) | (~b(s(z), s(s(elem!1)))) | (~b(s(s(elem!1)), s(z))) | (~b(s(s(s(s(elem!1)))), s(z))) | (~b(s(s(s(s(elem!1)))), s(s(elem!1))))) <=> ((~b(s(s(s(s(elem!1)))), s(s(elem!1)))) | (~b(s(z), s(s(elem!1)))) | (~b(s(s(elem!1)), s(z))) | (~b(s(s(s(s(elem!1)))), s(z))))),
% 1.62/1.83 inference(rewrite,[status(thm)],[])).
% 1.62/1.83 tff(801,plain,
% 1.62/1.83 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), s(z))) | (~b(s(s(s(s(elem!1)))), s(z))) | (~b(s(z), s(s(elem!1)))) | (~b(s(s(elem!1)), s(z))) | (~b(s(s(s(s(elem!1)))), s(z))) | (~b(s(s(s(s(elem!1)))), s(s(elem!1)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(elem!1)))), s(s(elem!1)))) | (~b(s(z), s(s(elem!1)))) | (~b(s(s(elem!1)), s(z))) | (~b(s(s(s(s(elem!1)))), s(z)))))),
% 1.62/1.83 inference(monotonicity,[status(thm)],[800])).
% 1.62/1.83 tff(802,plain,
% 1.62/1.83 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), s(z))) | (~b(s(s(s(s(elem!1)))), s(z))) | (~b(s(z), s(s(elem!1)))) | (~b(s(s(elem!1)), s(z))) | (~b(s(s(s(s(elem!1)))), s(z))) | (~b(s(s(s(s(elem!1)))), s(s(elem!1)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(elem!1)))), s(s(elem!1)))) | (~b(s(z), s(s(elem!1)))) | (~b(s(s(elem!1)), s(z))) | (~b(s(s(s(s(elem!1)))), s(z))))),
% 1.62/1.83 inference(transitivity,[status(thm)],[801, 799])).
% 1.62/1.83 tff(803,plain,
% 1.62/1.83 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), s(z))) | (~b(s(s(s(s(elem!1)))), s(z))) | (~b(s(z), s(s(elem!1)))) | (~b(s(s(elem!1)), s(z))) | (~b(s(s(s(s(elem!1)))), s(z))) | (~b(s(s(s(s(elem!1)))), s(s(elem!1)))))),
% 1.62/1.83 inference(quant_inst,[status(thm)],[])).
% 1.62/1.83 tff(804,plain,
% 1.62/1.83 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(elem!1)))), s(s(elem!1)))) | (~b(s(z), s(s(elem!1)))) | (~b(s(s(elem!1)), s(z))) | (~b(s(s(s(s(elem!1)))), s(z)))),
% 1.62/1.83 inference(modus_ponens,[status(thm)],[803, 802])).
% 1.62/1.83 tff(805,plain,
% 1.62/1.83 (~b(s(s(s(s(elem!1)))), s(s(elem!1)))),
% 1.62/1.83 inference(unit_resolution,[status(thm)],[804, 166, 798, 310, 751])).
% 1.62/1.83 tff(806,assumption,(~(s(s(s(s(elem!1)))) = s(s(elem!1)))), introduced(assumption)).
% 1.62/1.83 tff(807,assumption,(~b(s(s(s(s(elem!1)))), s(s(elem!1)))), introduced(assumption)).
% 1.62/1.83 tff(808,assumption,(~r(s(s(s(s(elem!1)))), s(s(elem!1)))), introduced(assumption)).
% 1.62/1.83 tff(809,plain,
% 1.62/1.83 (((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((s(s(s(s(elem!1)))) = s(s(elem!1))) | b(s(s(s(s(elem!1)))), s(s(elem!1))) | r(s(s(s(s(elem!1)))), s(s(elem!1))))) <=> ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (s(s(s(s(elem!1)))) = s(s(elem!1))) | b(s(s(s(s(elem!1)))), s(s(elem!1))) | r(s(s(s(s(elem!1)))), s(s(elem!1))))),
% 1.62/1.83 inference(rewrite,[status(thm)],[])).
% 1.62/1.83 tff(810,plain,
% 1.62/1.83 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((s(s(s(s(elem!1)))) = s(s(elem!1))) | b(s(s(s(s(elem!1)))), s(s(elem!1))) | r(s(s(s(s(elem!1)))), s(s(elem!1))))),
% 1.62/1.83 inference(quant_inst,[status(thm)],[])).
% 1.62/1.83 tff(811,plain,
% 1.62/1.83 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (s(s(s(s(elem!1)))) = s(s(elem!1))) | b(s(s(s(s(elem!1)))), s(s(elem!1))) | r(s(s(s(s(elem!1)))), s(s(elem!1)))),
% 1.62/1.83 inference(modus_ponens,[status(thm)],[810, 809])).
% 1.62/1.83 tff(812,plain,
% 1.62/1.83 ($false),
% 1.62/1.83 inference(unit_resolution,[status(thm)],[811, 79, 808, 807, 806])).
% 1.62/1.83 tff(813,plain,(b(s(s(s(s(elem!1)))), s(s(elem!1))) | r(s(s(s(s(elem!1)))), s(s(elem!1))) | (s(s(s(s(elem!1)))) = s(s(elem!1)))), inference(lemma,lemma(discharge,[]))).
% 1.62/1.83 tff(814,plain,
% 1.62/1.83 (r(s(s(s(s(elem!1)))), s(s(elem!1)))),
% 1.62/1.83 inference(unit_resolution,[status(thm)],[813, 805, 734])).
% 1.62/1.83 tff(815,plain,
% 1.62/1.83 ((~(s(s(s(s(elem!1)))) = s(s(z)))) <=> (~(s(s(elem!1)) = s(s(s(s(elem!1))))))),
% 1.62/1.83 inference(monotonicity,[status(thm)],[722])).
% 1.62/1.83 tff(816,plain,
% 1.62/1.83 (~(s(s(elem!1)) = s(s(s(s(elem!1)))))),
% 1.62/1.83 inference(modus_ponens,[status(thm)],[733, 815])).
% 1.62/1.83 tff(817,plain,
% 1.62/1.83 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(elem!1)))) | (~b(s(s(elem!1)), s(z))) | (~b(s(s(elem!1)), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), s(s(elem!1)))) | (~b(s(s(elem!1)), s(z))) | (~b(s(s(elem!1)), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), s(z))))),
% 1.62/1.83 inference(rewrite,[status(thm)],[])).
% 1.62/1.83 tff(818,plain,
% 1.62/1.83 (((~b(s(s(elem!1)), s(z))) | (~b(s(s(elem!1)), s(z))) | (~b(s(z), s(s(elem!1)))) | (~b(s(s(s(s(elem!1)))), s(z))) | (~b(s(s(elem!1)), s(z))) | (~b(s(s(elem!1)), s(s(s(s(elem!1))))))) <=> ((~b(s(z), s(s(elem!1)))) | (~b(s(s(elem!1)), s(z))) | (~b(s(s(elem!1)), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), s(z))))),
% 1.62/1.83 inference(rewrite,[status(thm)],[])).
% 1.62/1.83 tff(819,plain,
% 1.62/1.83 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), s(z))) | (~b(s(s(elem!1)), s(z))) | (~b(s(z), s(s(elem!1)))) | (~b(s(s(s(s(elem!1)))), s(z))) | (~b(s(s(elem!1)), s(z))) | (~b(s(s(elem!1)), s(s(s(s(elem!1)))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(elem!1)))) | (~b(s(s(elem!1)), s(z))) | (~b(s(s(elem!1)), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), s(z)))))),
% 1.62/1.83 inference(monotonicity,[status(thm)],[818])).
% 1.62/1.83 tff(820,plain,
% 1.62/1.83 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), s(z))) | (~b(s(s(elem!1)), s(z))) | (~b(s(z), s(s(elem!1)))) | (~b(s(s(s(s(elem!1)))), s(z))) | (~b(s(s(elem!1)), s(z))) | (~b(s(s(elem!1)), s(s(s(s(elem!1)))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), s(s(elem!1)))) | (~b(s(s(elem!1)), s(z))) | (~b(s(s(elem!1)), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), s(z))))),
% 1.62/1.83 inference(transitivity,[status(thm)],[819, 817])).
% 1.62/1.83 tff(821,plain,
% 1.62/1.83 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), s(z))) | (~b(s(s(elem!1)), s(z))) | (~b(s(z), s(s(elem!1)))) | (~b(s(s(s(s(elem!1)))), s(z))) | (~b(s(s(elem!1)), s(z))) | (~b(s(s(elem!1)), s(s(s(s(elem!1)))))))),
% 1.62/1.83 inference(quant_inst,[status(thm)],[])).
% 1.62/1.83 tff(822,plain,
% 1.62/1.83 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), s(s(elem!1)))) | (~b(s(s(elem!1)), s(z))) | (~b(s(s(elem!1)), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), s(z)))),
% 1.62/1.83 inference(modus_ponens,[status(thm)],[821, 820])).
% 1.62/1.83 tff(823,plain,
% 1.62/1.83 (~b(s(s(elem!1)), s(s(s(s(elem!1)))))),
% 1.62/1.83 inference(unit_resolution,[status(thm)],[822, 166, 798, 310, 751])).
% 1.62/1.83 tff(824,plain,
% 1.62/1.83 (((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((s(s(elem!1)) = s(s(s(s(elem!1))))) | b(s(s(elem!1)), s(s(s(s(elem!1))))) | r(s(s(elem!1)), s(s(s(s(elem!1))))))) <=> ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (s(s(elem!1)) = s(s(s(s(elem!1))))) | b(s(s(elem!1)), s(s(s(s(elem!1))))) | r(s(s(elem!1)), s(s(s(s(elem!1))))))),
% 1.62/1.83 inference(rewrite,[status(thm)],[])).
% 1.62/1.83 tff(825,plain,
% 1.62/1.83 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((s(s(elem!1)) = s(s(s(s(elem!1))))) | b(s(s(elem!1)), s(s(s(s(elem!1))))) | r(s(s(elem!1)), s(s(s(s(elem!1))))))),
% 1.62/1.83 inference(quant_inst,[status(thm)],[])).
% 1.62/1.83 tff(826,plain,
% 1.62/1.83 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (s(s(elem!1)) = s(s(s(s(elem!1))))) | b(s(s(elem!1)), s(s(s(s(elem!1))))) | r(s(s(elem!1)), s(s(s(s(elem!1)))))),
% 1.62/1.83 inference(modus_ponens,[status(thm)],[825, 824])).
% 1.62/1.83 tff(827,plain,
% 1.62/1.83 ((s(s(elem!1)) = s(s(s(s(elem!1))))) | b(s(s(elem!1)), s(s(s(s(elem!1))))) | r(s(s(elem!1)), s(s(s(s(elem!1)))))),
% 1.62/1.83 inference(unit_resolution,[status(thm)],[826, 79])).
% 1.62/1.83 tff(828,plain,
% 1.62/1.83 (r(s(s(elem!1)), s(s(s(s(elem!1)))))),
% 1.62/1.83 inference(unit_resolution,[status(thm)],[827, 823, 816])).
% 1.62/1.83 tff(829,plain,
% 1.62/1.83 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(s(elem!1)))) | (~r(s(s(s(s(elem!1)))), s(s(elem!1)))) | (~r(s(s(s(s(elem!1)))), elem!1)) | (~r(s(s(elem!1)), s(s(s(s(elem!1)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(elem!1, s(s(elem!1)))) | (~r(s(s(s(s(elem!1)))), s(s(elem!1)))) | (~r(s(s(s(s(elem!1)))), elem!1)) | (~r(s(s(elem!1)), s(s(s(s(elem!1)))))))),
% 1.62/1.83 inference(rewrite,[status(thm)],[])).
% 1.62/1.83 tff(830,plain,
% 1.62/1.83 (((~r(s(s(elem!1)), s(s(s(s(elem!1)))))) | (~r(elem!1, s(s(elem!1)))) | (~r(s(s(s(s(elem!1)))), s(s(elem!1)))) | (~r(s(s(s(s(elem!1)))), elem!1))) <=> ((~r(elem!1, s(s(elem!1)))) | (~r(s(s(s(s(elem!1)))), s(s(elem!1)))) | (~r(s(s(s(s(elem!1)))), elem!1)) | (~r(s(s(elem!1)), s(s(s(s(elem!1)))))))),
% 1.62/1.83 inference(rewrite,[status(thm)],[])).
% 1.62/1.83 tff(831,plain,
% 1.62/1.83 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(elem!1)), s(s(s(s(elem!1)))))) | (~r(elem!1, s(s(elem!1)))) | (~r(s(s(s(s(elem!1)))), s(s(elem!1)))) | (~r(s(s(s(s(elem!1)))), elem!1)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(s(elem!1)))) | (~r(s(s(s(s(elem!1)))), s(s(elem!1)))) | (~r(s(s(s(s(elem!1)))), elem!1)) | (~r(s(s(elem!1)), s(s(s(s(elem!1))))))))),
% 1.62/1.83 inference(monotonicity,[status(thm)],[830])).
% 1.62/1.83 tff(832,plain,
% 1.62/1.83 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(elem!1)), s(s(s(s(elem!1)))))) | (~r(elem!1, s(s(elem!1)))) | (~r(s(s(s(s(elem!1)))), s(s(elem!1)))) | (~r(s(s(s(s(elem!1)))), elem!1)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(elem!1, s(s(elem!1)))) | (~r(s(s(s(s(elem!1)))), s(s(elem!1)))) | (~r(s(s(s(s(elem!1)))), elem!1)) | (~r(s(s(elem!1)), s(s(s(s(elem!1)))))))),
% 1.62/1.83 inference(transitivity,[status(thm)],[831, 829])).
% 1.62/1.83 tff(833,plain,
% 1.62/1.83 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(elem!1)), s(s(s(s(elem!1)))))) | (~r(elem!1, s(s(elem!1)))) | (~r(s(s(s(s(elem!1)))), s(s(elem!1)))) | (~r(s(s(s(s(elem!1)))), elem!1)))),
% 1.62/1.83 inference(quant_inst,[status(thm)],[])).
% 1.62/1.83 tff(834,plain,
% 1.62/1.83 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(elem!1, s(s(elem!1)))) | (~r(s(s(s(s(elem!1)))), s(s(elem!1)))) | (~r(s(s(s(s(elem!1)))), elem!1)) | (~r(s(s(elem!1)), s(s(s(s(elem!1))))))),
% 1.62/1.83 inference(modus_ponens,[status(thm)],[833, 832])).
% 1.62/1.83 tff(835,plain,
% 1.62/1.83 ($false),
% 1.62/1.83 inference(unit_resolution,[status(thm)],[834, 197, 828, 814, 720, 622])).
% 1.62/1.83 tff(836,plain,((~(s(s(z)) = s(s(elem!1)))) | (~b(s(s(elem!1)), s(z))) | (~r(s(z), s(s(s(elem!1))))) | (s(s(elem!1)) = s(s(s(elem!1)))) | (~r(z, s(z))) | (~r(z, s(s(elem!1)))) | (~r(s(s(s(elem!1))), s(z))) | (~b(s(z), z))), inference(lemma,lemma(discharge,[]))).
% 1.62/1.83 tff(837,plain,
% 1.62/1.83 (~(s(s(z)) = s(s(elem!1)))),
% 1.62/1.83 inference(unit_resolution,[status(thm)],[836, 119, 310, 45, 323, 365, 350, 53])).
% 1.62/1.83 tff(838,plain,
% 1.62/1.83 (b(s(s(z)), s(s(elem!1)))),
% 1.62/1.83 inference(unit_resolution,[status(thm)],[390, 837, 618])).
% 1.62/1.83 tff(839,assumption,(b(s(s(s(elem!1))), s(s(elem!1)))), introduced(assumption)).
% 1.62/1.83 tff(840,plain,
% 1.62/1.83 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(z), z)) | (~b(s(s(s(elem!1))), s(s(z)))) | (~b(s(s(s(elem!1))), z)) | (~b(s(s(elem!1)), s(z))) | (~b(s(s(z)), s(s(elem!1)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(z), z)) | (~b(s(s(s(elem!1))), s(s(z)))) | (~b(s(s(s(elem!1))), z)) | (~b(s(s(elem!1)), s(z))) | (~b(s(s(z)), s(s(elem!1)))))),
% 1.62/1.83 inference(rewrite,[status(thm)],[])).
% 1.62/1.83 tff(841,plain,
% 1.62/1.83 (((~b(s(z), z)) | (~b(s(s(s(elem!1))), z)) | (~b(s(s(elem!1)), s(z))) | (~b(s(s(z)), s(s(elem!1)))) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(s(s(elem!1))), s(s(z))))) <=> ((~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(z), z)) | (~b(s(s(s(elem!1))), s(s(z)))) | (~b(s(s(s(elem!1))), z)) | (~b(s(s(elem!1)), s(z))) | (~b(s(s(z)), s(s(elem!1)))))),
% 1.62/1.83 inference(rewrite,[status(thm)],[])).
% 1.62/1.83 tff(842,plain,
% 1.62/1.83 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), z)) | (~b(s(s(s(elem!1))), z)) | (~b(s(s(elem!1)), s(z))) | (~b(s(s(z)), s(s(elem!1)))) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(s(s(elem!1))), s(s(z)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(z), z)) | (~b(s(s(s(elem!1))), s(s(z)))) | (~b(s(s(s(elem!1))), z)) | (~b(s(s(elem!1)), s(z))) | (~b(s(s(z)), s(s(elem!1))))))),
% 1.62/1.83 inference(monotonicity,[status(thm)],[841])).
% 1.62/1.83 tff(843,plain,
% 1.62/1.83 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), z)) | (~b(s(s(s(elem!1))), z)) | (~b(s(s(elem!1)), s(z))) | (~b(s(s(z)), s(s(elem!1)))) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(s(s(elem!1))), s(s(z)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(z), z)) | (~b(s(s(s(elem!1))), s(s(z)))) | (~b(s(s(s(elem!1))), z)) | (~b(s(s(elem!1)), s(z))) | (~b(s(s(z)), s(s(elem!1)))))),
% 1.62/1.83 inference(transitivity,[status(thm)],[842, 840])).
% 1.62/1.83 tff(844,plain,
% 1.62/1.83 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), z)) | (~b(s(s(s(elem!1))), z)) | (~b(s(s(elem!1)), s(z))) | (~b(s(s(z)), s(s(elem!1)))) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(s(s(elem!1))), s(s(z)))))),
% 1.62/1.83 inference(quant_inst,[status(thm)],[])).
% 1.62/1.83 tff(845,plain,
% 1.62/1.83 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(z), z)) | (~b(s(s(s(elem!1))), s(s(z)))) | (~b(s(s(s(elem!1))), z)) | (~b(s(s(elem!1)), s(z))) | (~b(s(s(z)), s(s(elem!1))))),
% 1.62/1.83 inference(modus_ponens,[status(thm)],[844, 843])).
% 1.62/1.83 tff(846,plain,
% 1.62/1.83 (~b(s(s(s(elem!1))), s(s(z)))),
% 1.62/1.83 inference(unit_resolution,[status(thm)],[845, 166, 839, 53, 310, 121, 446])).
% 1.62/1.83 tff(847,plain,
% 1.62/1.83 (r(s(s(s(elem!1))), s(s(z)))),
% 1.62/1.83 inference(unit_resolution,[status(thm)],[216, 79, 846, 211])).
% 1.62/1.83 tff(848,plain,
% 1.62/1.83 (~b(s(z), s(s(elem!1)))),
% 1.62/1.83 inference(unit_resolution,[status(thm)],[485, 847, 350, 53, 310, 446])).
% 1.62/1.83 tff(849,plain,
% 1.62/1.83 (r(s(z), s(s(elem!1)))),
% 1.62/1.83 inference(unit_resolution,[status(thm)],[84, 848])).
% 1.62/1.83 tff(850,plain,
% 1.62/1.83 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(s(elem!1)))) | (~r(s(s(z)), s(z))) | (~r(s(s(s(elem!1))), s(z))) | (~r(s(s(s(elem!1))), s(s(z)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(z), s(s(elem!1)))) | (~r(s(s(z)), s(z))) | (~r(s(s(s(elem!1))), s(z))) | (~r(s(s(s(elem!1))), s(s(z)))))),
% 1.62/1.83 inference(rewrite,[status(thm)],[])).
% 1.62/1.83 tff(851,plain,
% 1.62/1.83 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(s(elem!1)))) | (~r(s(s(z)), s(z))) | (~r(s(s(s(elem!1))), s(z))) | (~r(s(s(s(elem!1))), s(s(z)))))),
% 1.62/1.83 inference(quant_inst,[status(thm)],[])).
% 1.62/1.83 tff(852,plain,
% 1.62/1.83 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(z), s(s(elem!1)))) | (~r(s(s(z)), s(z))) | (~r(s(s(s(elem!1))), s(z))) | (~r(s(s(s(elem!1))), s(s(z))))),
% 1.62/1.83 inference(modus_ponens,[status(thm)],[851, 850])).
% 1.62/1.83 tff(853,plain,
% 1.62/1.83 ($false),
% 1.62/1.83 inference(unit_resolution,[status(thm)],[852, 197, 311, 350, 392, 464])).
% 1.62/1.83 tff(854,plain,((~r(s(s(z)), s(z))) | (~r(s(z), s(s(elem!1)))) | (~r(s(s(s(elem!1))), s(z))) | (~r(s(s(s(elem!1))), s(s(z))))), inference(lemma,lemma(discharge,[]))).
% 1.62/1.84 tff(855,plain,
% 1.62/1.84 (~r(s(s(z)), s(z))),
% 1.62/1.84 inference(unit_resolution,[status(thm)],[854, 849, 350, 847])).
% 1.62/1.84 tff(856,plain,
% 1.62/1.84 (b(s(s(z)), s(z))),
% 1.62/1.84 inference(unit_resolution,[status(thm)],[308, 855])).
% 1.62/1.84 tff(857,plain,
% 1.62/1.84 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(z, s(s(s(elem!1))))) | (~b(s(z), z)) | (~b(s(s(z)), s(s(elem!1)))) | (~b(s(s(z)), z)) | (~b(s(s(z)), s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(z, s(s(s(elem!1))))) | (~b(s(z), z)) | (~b(s(s(z)), s(s(elem!1)))) | (~b(s(s(z)), z)) | (~b(s(s(z)), s(z))))),
% 1.62/1.84 inference(rewrite,[status(thm)],[])).
% 1.62/1.84 tff(858,plain,
% 1.62/1.84 (((~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(s(z)), s(s(elem!1)))) | (~b(z, s(s(s(elem!1))))) | (~b(s(z), z)) | (~b(s(s(z)), z)) | (~b(s(s(z)), s(z)))) <=> ((~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(z, s(s(s(elem!1))))) | (~b(s(z), z)) | (~b(s(s(z)), s(s(elem!1)))) | (~b(s(s(z)), z)) | (~b(s(s(z)), s(z))))),
% 1.62/1.84 inference(rewrite,[status(thm)],[])).
% 1.62/1.84 tff(859,plain,
% 1.62/1.84 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(s(z)), s(s(elem!1)))) | (~b(z, s(s(s(elem!1))))) | (~b(s(z), z)) | (~b(s(s(z)), z)) | (~b(s(s(z)), s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(z, s(s(s(elem!1))))) | (~b(s(z), z)) | (~b(s(s(z)), s(s(elem!1)))) | (~b(s(s(z)), z)) | (~b(s(s(z)), s(z)))))),
% 1.62/1.84 inference(monotonicity,[status(thm)],[858])).
% 1.62/1.84 tff(860,plain,
% 1.62/1.84 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(s(z)), s(s(elem!1)))) | (~b(z, s(s(s(elem!1))))) | (~b(s(z), z)) | (~b(s(s(z)), z)) | (~b(s(s(z)), s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(z, s(s(s(elem!1))))) | (~b(s(z), z)) | (~b(s(s(z)), s(s(elem!1)))) | (~b(s(s(z)), z)) | (~b(s(s(z)), s(z))))),
% 1.62/1.84 inference(transitivity,[status(thm)],[859, 857])).
% 1.62/1.84 tff(861,plain,
% 1.62/1.84 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(s(z)), s(s(elem!1)))) | (~b(z, s(s(s(elem!1))))) | (~b(s(z), z)) | (~b(s(s(z)), z)) | (~b(s(s(z)), s(z))))),
% 1.62/1.84 inference(quant_inst,[status(thm)],[])).
% 1.62/1.84 tff(862,plain,
% 1.62/1.84 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(z, s(s(s(elem!1))))) | (~b(s(z), z)) | (~b(s(s(z)), s(s(elem!1)))) | (~b(s(s(z)), z)) | (~b(s(s(z)), s(z)))),
% 1.62/1.84 inference(modus_ponens,[status(thm)],[861, 860])).
% 1.62/1.84 tff(863,plain,
% 1.62/1.84 ((~b(s(s(z)), z)) | (~b(s(s(z)), s(z)))),
% 1.62/1.84 inference(unit_resolution,[status(thm)],[862, 166, 839, 240, 53, 446])).
% 1.62/1.84 tff(864,plain,
% 1.62/1.84 (~b(s(s(z)), z)),
% 1.62/1.84 inference(unit_resolution,[status(thm)],[863, 856])).
% 1.62/1.84 tff(865,plain,
% 1.62/1.84 (r(s(s(z)), z)),
% 1.62/1.84 inference(unit_resolution,[status(thm)],[186, 864])).
% 1.62/1.84 tff(866,assumption,(r(s(s(z)), z)), introduced(assumption)).
% 1.62/1.84 tff(867,plain,
% 1.62/1.84 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), s(z))) | (~r(s(z), s(s(z)))) | (~r(s(s(z)), z)) | (~r(s(s(s(elem!1))), s(s(z)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(elem!1))), s(z))) | (~r(s(z), s(s(z)))) | (~r(s(s(z)), z)) | (~r(s(s(s(elem!1))), s(s(z)))))),
% 1.62/1.84 inference(rewrite,[status(thm)],[])).
% 1.62/1.84 tff(868,plain,
% 1.62/1.84 (((~r(s(s(z)), z)) | (~r(s(z), s(s(z)))) | (~r(s(s(s(elem!1))), s(s(z)))) | (~r(s(s(s(elem!1))), s(z)))) <=> ((~r(s(s(s(elem!1))), s(z))) | (~r(s(z), s(s(z)))) | (~r(s(s(z)), z)) | (~r(s(s(s(elem!1))), s(s(z)))))),
% 1.62/1.84 inference(rewrite,[status(thm)],[])).
% 1.62/1.84 tff(869,plain,
% 1.62/1.84 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(z)), z)) | (~r(s(z), s(s(z)))) | (~r(s(s(s(elem!1))), s(s(z)))) | (~r(s(s(s(elem!1))), s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), s(z))) | (~r(s(z), s(s(z)))) | (~r(s(s(z)), z)) | (~r(s(s(s(elem!1))), s(s(z))))))),
% 1.62/1.84 inference(monotonicity,[status(thm)],[868])).
% 1.62/1.84 tff(870,plain,
% 1.62/1.84 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(z)), z)) | (~r(s(z), s(s(z)))) | (~r(s(s(s(elem!1))), s(s(z)))) | (~r(s(s(s(elem!1))), s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(elem!1))), s(z))) | (~r(s(z), s(s(z)))) | (~r(s(s(z)), z)) | (~r(s(s(s(elem!1))), s(s(z)))))),
% 1.62/1.84 inference(transitivity,[status(thm)],[869, 867])).
% 1.62/1.84 tff(871,plain,
% 1.62/1.84 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(z)), z)) | (~r(s(z), s(s(z)))) | (~r(s(s(s(elem!1))), s(s(z)))) | (~r(s(s(s(elem!1))), s(z))))),
% 1.62/1.84 inference(quant_inst,[status(thm)],[])).
% 1.62/1.84 tff(872,plain,
% 1.62/1.84 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(elem!1))), s(z))) | (~r(s(z), s(s(z)))) | (~r(s(s(z)), z)) | (~r(s(s(s(elem!1))), s(s(z))))),
% 1.62/1.84 inference(modus_ponens,[status(thm)],[871, 870])).
% 1.62/1.84 tff(873,plain,
% 1.62/1.84 ($false),
% 1.62/1.84 inference(unit_resolution,[status(thm)],[872, 197, 120, 350, 866, 464])).
% 1.62/1.84 tff(874,plain,((~r(s(s(s(elem!1))), s(s(z)))) | (~r(s(z), s(s(z)))) | (~r(s(s(s(elem!1))), s(z))) | (~r(s(s(z)), z))), inference(lemma,lemma(discharge,[]))).
% 1.62/1.84 tff(875,plain,
% 1.62/1.84 (~r(s(z), s(s(z)))),
% 1.62/1.84 inference(unit_resolution,[status(thm)],[874, 865, 847, 350])).
% 1.62/1.84 tff(876,plain,
% 1.62/1.84 (b(s(z), s(s(z)))),
% 1.62/1.84 inference(unit_resolution,[status(thm)],[427, 875])).
% 1.62/1.84 tff(877,plain,
% 1.62/1.84 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), s(z))) | (~b(s(z), s(s(z)))) | (~b(s(s(z)), s(s(elem!1)))) | (~b(s(s(z)), s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(elem!1)), s(z))) | (~b(s(z), s(s(z)))) | (~b(s(s(z)), s(s(elem!1)))) | (~b(s(s(z)), s(z))))),
% 1.62/1.84 inference(rewrite,[status(thm)],[])).
% 1.62/1.84 tff(878,plain,
% 1.62/1.84 (((~b(s(s(z)), s(z))) | (~b(s(s(z)), s(z))) | (~b(s(z), s(s(z)))) | (~b(s(s(elem!1)), s(z))) | (~b(s(s(z)), s(z))) | (~b(s(s(z)), s(s(elem!1))))) <=> ((~b(s(s(elem!1)), s(z))) | (~b(s(z), s(s(z)))) | (~b(s(s(z)), s(s(elem!1)))) | (~b(s(s(z)), s(z))))),
% 1.62/1.84 inference(rewrite,[status(thm)],[])).
% 1.62/1.84 tff(879,plain,
% 1.62/1.84 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), s(z))) | (~b(s(s(z)), s(z))) | (~b(s(z), s(s(z)))) | (~b(s(s(elem!1)), s(z))) | (~b(s(s(z)), s(z))) | (~b(s(s(z)), s(s(elem!1)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), s(z))) | (~b(s(z), s(s(z)))) | (~b(s(s(z)), s(s(elem!1)))) | (~b(s(s(z)), s(z)))))),
% 1.62/1.84 inference(monotonicity,[status(thm)],[878])).
% 1.62/1.84 tff(880,plain,
% 1.62/1.84 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), s(z))) | (~b(s(s(z)), s(z))) | (~b(s(z), s(s(z)))) | (~b(s(s(elem!1)), s(z))) | (~b(s(s(z)), s(z))) | (~b(s(s(z)), s(s(elem!1)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(elem!1)), s(z))) | (~b(s(z), s(s(z)))) | (~b(s(s(z)), s(s(elem!1)))) | (~b(s(s(z)), s(z))))),
% 1.62/1.84 inference(transitivity,[status(thm)],[879, 877])).
% 1.62/1.84 tff(881,plain,
% 1.62/1.84 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), s(z))) | (~b(s(s(z)), s(z))) | (~b(s(z), s(s(z)))) | (~b(s(s(elem!1)), s(z))) | (~b(s(s(z)), s(z))) | (~b(s(s(z)), s(s(elem!1)))))),
% 1.62/1.84 inference(quant_inst,[status(thm)],[])).
% 1.62/1.84 tff(882,plain,
% 1.62/1.84 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(elem!1)), s(z))) | (~b(s(z), s(s(z)))) | (~b(s(s(z)), s(s(elem!1)))) | (~b(s(s(z)), s(z)))),
% 1.62/1.84 inference(modus_ponens,[status(thm)],[881, 880])).
% 1.62/1.84 tff(883,plain,
% 1.62/1.84 ($false),
% 1.62/1.84 inference(unit_resolution,[status(thm)],[882, 166, 876, 310, 446, 856])).
% 1.62/1.84 tff(884,plain,((~b(s(s(z)), s(s(elem!1)))) | (~b(s(s(elem!1)), s(z))) | (~r(s(s(s(elem!1))), s(z))) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(z, s(s(s(elem!1))))) | (~b(s(z), z)) | (~b(s(s(s(elem!1))), z))), inference(lemma,lemma(discharge,[]))).
% 1.62/1.84 tff(885,plain,
% 1.62/1.84 (~b(s(s(s(elem!1))), s(s(elem!1)))),
% 1.62/1.84 inference(unit_resolution,[status(thm)],[884, 838, 350, 310, 589, 53, 579])).
% 1.62/1.84 tff(886,plain,
% 1.62/1.84 (((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((s(s(s(elem!1))) = s(s(elem!1))) | b(s(s(s(elem!1))), s(s(elem!1))) | r(s(s(s(elem!1))), s(s(elem!1))))) <=> ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (s(s(s(elem!1))) = s(s(elem!1))) | b(s(s(s(elem!1))), s(s(elem!1))) | r(s(s(s(elem!1))), s(s(elem!1))))),
% 1.62/1.84 inference(rewrite,[status(thm)],[])).
% 1.62/1.84 tff(887,plain,
% 1.62/1.84 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((s(s(s(elem!1))) = s(s(elem!1))) | b(s(s(s(elem!1))), s(s(elem!1))) | r(s(s(s(elem!1))), s(s(elem!1))))),
% 1.62/1.84 inference(quant_inst,[status(thm)],[])).
% 1.62/1.84 tff(888,plain,
% 1.62/1.84 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (s(s(s(elem!1))) = s(s(elem!1))) | b(s(s(s(elem!1))), s(s(elem!1))) | r(s(s(s(elem!1))), s(s(elem!1)))),
% 1.62/1.84 inference(modus_ponens,[status(thm)],[887, 886])).
% 1.62/1.84 tff(889,plain,
% 1.62/1.84 ((s(s(s(elem!1))) = s(s(elem!1))) | b(s(s(s(elem!1))), s(s(elem!1))) | r(s(s(s(elem!1))), s(s(elem!1)))),
% 1.62/1.84 inference(unit_resolution,[status(thm)],[888, 79])).
% 1.62/1.84 tff(890,plain,
% 1.62/1.84 (r(s(s(s(elem!1))), s(s(elem!1)))),
% 1.62/1.84 inference(unit_resolution,[status(thm)],[889, 885, 51])).
% 1.62/1.84 tff(891,plain,
% 1.62/1.84 (~b(s(s(elem!1)), z)),
% 1.62/1.84 inference(unit_resolution,[status(thm)],[600, 766, 589, 579])).
% 1.62/1.84 tff(892,plain,
% 1.62/1.84 (r(s(s(elem!1)), z)),
% 1.62/1.84 inference(unit_resolution,[status(thm)],[608, 891])).
% 1.62/1.84 tff(893,plain,
% 1.62/1.84 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(s(elem!1)))) | (~r(z, s(s(elem!1)))) | (~r(z, s(z))) | (~r(s(s(elem!1)), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(z), s(s(elem!1)))) | (~r(z, s(s(elem!1)))) | (~r(z, s(z))) | (~r(s(s(elem!1)), z)))),
% 1.62/1.84 inference(rewrite,[status(thm)],[])).
% 1.62/1.84 tff(894,plain,
% 1.62/1.84 (((~r(s(s(elem!1)), z)) | (~r(s(z), s(s(elem!1)))) | (~r(z, s(s(elem!1)))) | (~r(z, s(z)))) <=> ((~r(s(z), s(s(elem!1)))) | (~r(z, s(s(elem!1)))) | (~r(z, s(z))) | (~r(s(s(elem!1)), z)))),
% 1.62/1.84 inference(rewrite,[status(thm)],[])).
% 1.62/1.84 tff(895,plain,
% 1.62/1.84 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(elem!1)), z)) | (~r(s(z), s(s(elem!1)))) | (~r(z, s(s(elem!1)))) | (~r(z, s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(s(elem!1)))) | (~r(z, s(s(elem!1)))) | (~r(z, s(z))) | (~r(s(s(elem!1)), z))))),
% 1.62/1.84 inference(monotonicity,[status(thm)],[894])).
% 1.62/1.84 tff(896,plain,
% 1.62/1.84 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(elem!1)), z)) | (~r(s(z), s(s(elem!1)))) | (~r(z, s(s(elem!1)))) | (~r(z, s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(z), s(s(elem!1)))) | (~r(z, s(s(elem!1)))) | (~r(z, s(z))) | (~r(s(s(elem!1)), z)))),
% 1.62/1.84 inference(transitivity,[status(thm)],[895, 893])).
% 1.62/1.84 tff(897,plain,
% 1.62/1.84 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(elem!1)), z)) | (~r(s(z), s(s(elem!1)))) | (~r(z, s(s(elem!1)))) | (~r(z, s(z))))),
% 1.62/1.84 inference(quant_inst,[status(thm)],[])).
% 1.62/1.84 tff(898,plain,
% 1.62/1.84 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(z), s(s(elem!1)))) | (~r(z, s(s(elem!1)))) | (~r(z, s(z))) | (~r(s(s(elem!1)), z))),
% 1.62/1.84 inference(modus_ponens,[status(thm)],[897, 896])).
% 1.62/1.84 tff(899,plain,
% 1.62/1.84 ($false),
% 1.62/1.84 inference(unit_resolution,[status(thm)],[898, 197, 311, 323, 365, 892])).
% 1.62/1.84 tff(900,plain,((~r(s(z), s(s(elem!1)))) | (~r(z, s(z))) | (~r(z, s(s(elem!1)))) | (s(s(elem!1)) = s(s(s(elem!1)))) | (~r(s(s(s(elem!1))), s(z))) | (~r(s(z), s(s(s(elem!1)))))), inference(lemma,lemma(discharge,[]))).
% 1.62/1.84 tff(901,plain,
% 1.62/1.84 (~r(s(z), s(s(elem!1)))),
% 1.62/1.84 inference(unit_resolution,[status(thm)],[900, 119, 365, 45, 350, 323])).
% 1.62/1.84 tff(902,plain,
% 1.62/1.84 (b(s(z), s(s(elem!1)))),
% 1.62/1.84 inference(unit_resolution,[status(thm)],[84, 901])).
% 1.62/1.84 tff(903,plain,
% 1.62/1.84 (~b(s(s(z)), s(z))),
% 1.62/1.84 inference(unit_resolution,[status(thm)],[454, 902, 310, 838])).
% 1.62/1.84 tff(904,plain,
% 1.62/1.84 (r(s(s(z)), s(z))),
% 1.62/1.84 inference(unit_resolution,[status(thm)],[308, 903])).
% 1.62/1.84 tff(905,assumption,(r(s(s(s(elem!1))), s(s(elem!1)))), introduced(assumption)).
% 1.62/1.84 tff(906,plain,
% 1.62/1.84 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), s(s(elem!1)))) | (~r(s(z), s(s(s(elem!1))))) | (~r(s(s(z)), s(z))) | (~r(s(s(z)), s(s(s(elem!1))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(elem!1))), s(s(elem!1)))) | (~r(s(z), s(s(s(elem!1))))) | (~r(s(s(z)), s(z))) | (~r(s(s(z)), s(s(s(elem!1))))))),
% 1.62/1.84 inference(rewrite,[status(thm)],[])).
% 1.62/1.84 tff(907,plain,
% 1.62/1.84 (((~r(s(s(s(elem!1))), s(s(elem!1)))) | (~r(s(z), s(s(s(elem!1))))) | (~r(s(s(z)), s(s(s(elem!1))))) | (~r(s(s(z)), s(z)))) <=> ((~r(s(s(s(elem!1))), s(s(elem!1)))) | (~r(s(z), s(s(s(elem!1))))) | (~r(s(s(z)), s(z))) | (~r(s(s(z)), s(s(s(elem!1))))))),
% 1.62/1.84 inference(rewrite,[status(thm)],[])).
% 1.62/1.84 tff(908,plain,
% 1.62/1.84 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), s(s(elem!1)))) | (~r(s(z), s(s(s(elem!1))))) | (~r(s(s(z)), s(s(s(elem!1))))) | (~r(s(s(z)), s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), s(s(elem!1)))) | (~r(s(z), s(s(s(elem!1))))) | (~r(s(s(z)), s(z))) | (~r(s(s(z)), s(s(s(elem!1)))))))),
% 1.62/1.84 inference(monotonicity,[status(thm)],[907])).
% 1.62/1.84 tff(909,plain,
% 1.62/1.84 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), s(s(elem!1)))) | (~r(s(z), s(s(s(elem!1))))) | (~r(s(s(z)), s(s(s(elem!1))))) | (~r(s(s(z)), s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(elem!1))), s(s(elem!1)))) | (~r(s(z), s(s(s(elem!1))))) | (~r(s(s(z)), s(z))) | (~r(s(s(z)), s(s(s(elem!1))))))),
% 1.62/1.84 inference(transitivity,[status(thm)],[908, 906])).
% 1.62/1.84 tff(910,plain,
% 1.62/1.84 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), s(s(elem!1)))) | (~r(s(z), s(s(s(elem!1))))) | (~r(s(s(z)), s(s(s(elem!1))))) | (~r(s(s(z)), s(z))))),
% 1.62/1.84 inference(quant_inst,[status(thm)],[])).
% 1.62/1.84 tff(911,plain,
% 1.62/1.84 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(elem!1))), s(s(elem!1)))) | (~r(s(z), s(s(s(elem!1))))) | (~r(s(s(z)), s(z))) | (~r(s(s(z)), s(s(s(elem!1)))))),
% 1.62/1.84 inference(modus_ponens,[status(thm)],[910, 909])).
% 1.62/1.84 tff(912,plain,
% 1.62/1.84 ($false),
% 1.62/1.84 inference(unit_resolution,[status(thm)],[911, 197, 392, 905, 119, 281])).
% 1.62/1.84 tff(913,plain,((~r(s(z), s(s(s(elem!1))))) | (~r(s(s(z)), s(z))) | (~r(s(s(s(elem!1))), s(s(elem!1)))) | (~r(s(s(z)), s(s(s(elem!1)))))), inference(lemma,lemma(discharge,[]))).
% 1.62/1.84 tff(914,plain,
% 1.62/1.84 (~r(s(s(z)), s(s(s(elem!1))))),
% 1.62/1.84 inference(unit_resolution,[status(thm)],[913, 904, 119, 890])).
% 1.62/1.84 tff(915,plain,
% 1.62/1.84 (~r(s(s(s(elem!1))), s(s(z)))),
% 1.62/1.84 inference(unit_resolution,[status(thm)],[485, 902, 350, 53, 310, 838])).
% 1.62/1.84 tff(916,plain,
% 1.62/1.84 (~(s(s(elem!1)) = s(s(z)))),
% 1.62/1.84 inference(unit_resolution,[status(thm)],[131, 837])).
% 1.62/1.84 tff(917,plain,
% 1.62/1.84 (~r(s(s(elem!1)), s(s(s(elem!1))))),
% 1.62/1.84 inference(unit_resolution,[status(thm)],[443, 904, 155, 323, 916, 365])).
% 1.62/1.84 tff(918,plain,
% 1.62/1.84 (b(s(s(elem!1)), s(s(s(elem!1))))),
% 1.62/1.84 inference(unit_resolution,[status(thm)],[461, 917, 45])).
% 1.62/1.84 tff(919,plain,
% 1.62/1.84 (~r(s(s(elem!1)), s(s(z)))),
% 1.62/1.84 inference(unit_resolution,[status(thm)],[401, 904, 155, 365])).
% 1.62/1.84 tff(920,plain,
% 1.62/1.84 (b(s(s(elem!1)), s(s(z)))),
% 1.62/1.84 inference(unit_resolution,[status(thm)],[441, 919, 916])).
% 1.62/1.84 tff(921,plain,
% 1.62/1.84 ($false),
% 1.62/1.84 inference(unit_resolution,[status(thm)],[501, 920, 918, 915, 914])).
% 1.62/1.84 tff(922,plain,((~r(s(z), s(s(s(elem!1))))) | (s(s(elem!1)) = s(s(s(elem!1)))) | (~r(z, s(s(z)))) | (~r(z, s(s(elem!1)))) | (~r(z, s(z))) | (~r(s(s(s(elem!1))), s(z))) | (~b(s(z), z)) | (~b(s(s(elem!1)), s(z)))), inference(lemma,lemma(discharge,[]))).
% 1.62/1.84 tff(923,plain,
% 1.62/1.84 (~r(s(z), s(s(s(elem!1))))),
% 1.62/1.84 inference(unit_resolution,[status(thm)],[922, 365, 155, 45, 323, 350, 53, 310])).
% 1.62/1.84 tff(924,plain,
% 1.62/1.84 (b(s(z), s(s(s(elem!1))))),
% 1.62/1.84 inference(unit_resolution,[status(thm)],[116, 923])).
% 1.62/1.84 tff(925,plain,
% 1.62/1.84 (~r(s(s(z)), s(s(s(elem!1))))),
% 1.62/1.84 inference(unit_resolution,[status(thm)],[290, 282, 155, 154])).
% 1.62/1.84 tff(926,plain,
% 1.62/1.84 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), s(z))) | (~r(z, s(s(elem!1)))) | (~r(s(s(elem!1)), s(s(s(elem!1))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), s(z))) | (~r(z, s(s(elem!1)))) | (~r(s(s(elem!1)), s(s(s(elem!1))))))),
% 1.62/1.84 inference(rewrite,[status(thm)],[])).
% 1.62/1.84 tff(927,plain,
% 1.62/1.84 (((~r(s(s(s(elem!1))), s(z))) | (~r(s(s(elem!1)), s(s(s(elem!1))))) | (~r(z, s(s(s(elem!1))))) | (~r(z, s(s(elem!1))))) <=> ((~r(z, s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), s(z))) | (~r(z, s(s(elem!1)))) | (~r(s(s(elem!1)), s(s(s(elem!1))))))),
% 1.62/1.84 inference(rewrite,[status(thm)],[])).
% 1.62/1.84 tff(928,plain,
% 1.62/1.84 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), s(z))) | (~r(s(s(elem!1)), s(s(s(elem!1))))) | (~r(z, s(s(s(elem!1))))) | (~r(z, s(s(elem!1)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), s(z))) | (~r(z, s(s(elem!1)))) | (~r(s(s(elem!1)), s(s(s(elem!1)))))))),
% 1.62/1.84 inference(monotonicity,[status(thm)],[927])).
% 1.62/1.84 tff(929,plain,
% 1.62/1.84 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), s(z))) | (~r(s(s(elem!1)), s(s(s(elem!1))))) | (~r(z, s(s(s(elem!1))))) | (~r(z, s(s(elem!1)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), s(z))) | (~r(z, s(s(elem!1)))) | (~r(s(s(elem!1)), s(s(s(elem!1))))))),
% 1.62/1.84 inference(transitivity,[status(thm)],[928, 926])).
% 1.62/1.84 tff(930,plain,
% 1.62/1.84 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), s(z))) | (~r(s(s(elem!1)), s(s(s(elem!1))))) | (~r(z, s(s(s(elem!1))))) | (~r(z, s(s(elem!1)))))),
% 1.62/1.85 inference(quant_inst,[status(thm)],[])).
% 1.62/1.85 tff(931,plain,
% 1.62/1.85 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), s(z))) | (~r(z, s(s(elem!1)))) | (~r(s(s(elem!1)), s(s(s(elem!1)))))),
% 1.62/1.85 inference(modus_ponens,[status(thm)],[930, 929])).
% 1.62/1.85 tff(932,plain,
% 1.62/1.85 ($false),
% 1.62/1.85 inference(unit_resolution,[status(thm)],[931, 197, 350, 377, 365, 282])).
% 1.62/1.85 tff(933,plain,((~r(s(s(elem!1)), s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), s(z))) | (~r(z, s(s(elem!1)))) | (~r(z, s(s(s(elem!1)))))), inference(lemma,lemma(discharge,[]))).
% 1.62/1.85 tff(934,plain,
% 1.62/1.85 (~r(s(s(elem!1)), s(s(s(elem!1))))),
% 1.62/1.85 inference(unit_resolution,[status(thm)],[933, 282, 365, 350])).
% 1.62/1.85 tff(935,plain,
% 1.62/1.85 (b(s(s(elem!1)), s(s(s(elem!1))))),
% 1.62/1.85 inference(unit_resolution,[status(thm)],[461, 934, 45])).
% 1.62/1.85 tff(936,plain,
% 1.62/1.85 (s(s(z)) = s(s(elem!1))),
% 1.62/1.85 inference(unit_resolution,[status(thm)],[530, 935, 925, 155, 365, 154, 350, 53, 310, 375])).
% 1.62/1.85 tff(937,plain,
% 1.62/1.85 (s(elem!1) = s(z)),
% 1.62/1.85 inference(unit_resolution,[status(thm)],[43, 936])).
% 1.62/1.85 tff(938,plain,
% 1.62/1.85 (z = elem!1),
% 1.62/1.85 inference(unit_resolution,[status(thm)],[30, 937])).
% 1.62/1.85 tff(939,plain,
% 1.62/1.85 (r(z, s(s(s(elem!1)))) <=> r(elem!1, s(s(s(elem!1))))),
% 1.62/1.85 inference(monotonicity,[status(thm)],[938])).
% 1.62/1.85 tff(940,plain,
% 1.62/1.85 (r(elem!1, s(s(s(elem!1))))),
% 1.62/1.85 inference(modus_ponens,[status(thm)],[282, 939])).
% 1.62/1.85 tff(941,plain,
% 1.62/1.85 (r(elem!1, s(z))),
% 1.62/1.85 inference(unit_resolution,[status(thm)],[741, 938, 323])).
% 1.62/1.85 tff(942,assumption,(r(elem!1, s(s(s(elem!1))))), introduced(assumption)).
% 1.62/1.85 tff(943,plain,
% 1.62/1.85 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), s(z))) | (~r(elem!1, s(s(s(elem!1))))) | (~r(elem!1, s(z))) | (~r(s(z), s(s(s(s(elem!1)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(elem!1))), s(z))) | (~r(elem!1, s(s(s(elem!1))))) | (~r(elem!1, s(z))) | (~r(s(z), s(s(s(s(elem!1)))))))),
% 1.62/1.85 inference(rewrite,[status(thm)],[])).
% 1.62/1.85 tff(944,plain,
% 1.62/1.85 (((~r(s(z), s(s(s(s(elem!1)))))) | (~r(s(s(s(elem!1))), s(z))) | (~r(elem!1, s(z))) | (~r(elem!1, s(s(s(elem!1)))))) <=> ((~r(s(s(s(elem!1))), s(z))) | (~r(elem!1, s(s(s(elem!1))))) | (~r(elem!1, s(z))) | (~r(s(z), s(s(s(s(elem!1)))))))),
% 1.62/1.85 inference(rewrite,[status(thm)],[])).
% 1.62/1.85 tff(945,plain,
% 1.62/1.85 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(s(s(s(elem!1)))))) | (~r(s(s(s(elem!1))), s(z))) | (~r(elem!1, s(z))) | (~r(elem!1, s(s(s(elem!1))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), s(z))) | (~r(elem!1, s(s(s(elem!1))))) | (~r(elem!1, s(z))) | (~r(s(z), s(s(s(s(elem!1))))))))),
% 1.62/1.85 inference(monotonicity,[status(thm)],[944])).
% 1.62/1.85 tff(946,plain,
% 1.62/1.85 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(s(s(s(elem!1)))))) | (~r(s(s(s(elem!1))), s(z))) | (~r(elem!1, s(z))) | (~r(elem!1, s(s(s(elem!1))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(elem!1))), s(z))) | (~r(elem!1, s(s(s(elem!1))))) | (~r(elem!1, s(z))) | (~r(s(z), s(s(s(s(elem!1)))))))),
% 1.62/1.85 inference(transitivity,[status(thm)],[945, 943])).
% 1.62/1.85 tff(947,plain,
% 1.62/1.85 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(s(s(s(elem!1)))))) | (~r(s(s(s(elem!1))), s(z))) | (~r(elem!1, s(z))) | (~r(elem!1, s(s(s(elem!1))))))),
% 1.62/1.85 inference(quant_inst,[status(thm)],[])).
% 1.62/1.85 tff(948,plain,
% 1.62/1.85 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(elem!1))), s(z))) | (~r(elem!1, s(s(s(elem!1))))) | (~r(elem!1, s(z))) | (~r(s(z), s(s(s(s(elem!1))))))),
% 1.62/1.85 inference(modus_ponens,[status(thm)],[947, 946])).
% 1.62/1.85 tff(949,plain,
% 1.62/1.85 ($false),
% 1.62/1.85 inference(unit_resolution,[status(thm)],[948, 197, 350, 744, 942, 699])).
% 1.62/1.85 tff(950,plain,((~r(s(z), s(s(s(s(elem!1)))))) | (~r(s(s(s(elem!1))), s(z))) | (~r(elem!1, s(z))) | (~r(elem!1, s(s(s(elem!1)))))), inference(lemma,lemma(discharge,[]))).
% 1.62/1.85 tff(951,plain,
% 1.62/1.85 (~r(s(z), s(s(s(s(elem!1)))))),
% 1.62/1.85 inference(unit_resolution,[status(thm)],[950, 941, 350, 940])).
% 1.62/1.85 tff(952,plain,
% 1.62/1.85 (b(s(z), s(s(s(s(elem!1)))))),
% 1.62/1.85 inference(unit_resolution,[status(thm)],[681, 951])).
% 1.62/1.85 tff(953,plain,
% 1.62/1.85 (b(s(z), z) <=> b(s(z), elem!1)),
% 1.62/1.85 inference(monotonicity,[status(thm)],[938])).
% 1.62/1.85 tff(954,plain,
% 1.62/1.85 (b(s(z), elem!1)),
% 1.62/1.85 inference(modus_ponens,[status(thm)],[53, 953])).
% 1.62/1.85 tff(955,plain,
% 1.62/1.85 (elem!1 = z),
% 1.62/1.85 inference(symmetry,[status(thm)],[938])).
% 1.62/1.85 tff(956,plain,
% 1.62/1.85 ((s(s(elem!1)) = elem!1) <=> (s(s(elem!1)) = z)),
% 1.62/1.85 inference(monotonicity,[status(thm)],[955])).
% 1.62/1.85 tff(957,plain,
% 1.62/1.85 ((s(s(elem!1)) = z) <=> (s(s(elem!1)) = elem!1)),
% 1.62/1.85 inference(symmetry,[status(thm)],[956])).
% 1.62/1.85 tff(958,plain,
% 1.62/1.85 ((~(s(s(elem!1)) = z)) <=> (~(s(s(elem!1)) = elem!1))),
% 1.62/1.85 inference(monotonicity,[status(thm)],[957])).
% 1.62/1.85 tff(959,plain,
% 1.62/1.85 (~(s(s(elem!1)) = elem!1)),
% 1.62/1.85 inference(modus_ponens,[status(thm)],[108, 958])).
% 1.62/1.85 tff(960,plain,
% 1.62/1.85 (r(s(s(s(elem!1))), z) <=> r(s(s(s(elem!1))), elem!1)),
% 1.62/1.85 inference(monotonicity,[status(thm)],[12])).
% 1.62/1.85 tff(961,plain,
% 1.62/1.85 (r(s(s(s(elem!1))), elem!1) <=> r(s(s(s(elem!1))), z)),
% 1.62/1.85 inference(symmetry,[status(thm)],[960])).
% 1.62/1.85 tff(962,plain,
% 1.62/1.85 ((~r(s(s(s(elem!1))), elem!1)) <=> (~r(s(s(s(elem!1))), z))),
% 1.62/1.85 inference(monotonicity,[status(thm)],[961])).
% 1.62/1.85 tff(963,assumption,(~r(s(s(s(elem!1))), elem!1)), introduced(assumption)).
% 1.62/1.85 tff(964,plain,
% 1.62/1.85 (~r(s(s(s(elem!1))), z)),
% 1.62/1.85 inference(modus_ponens,[status(thm)],[963, 962])).
% 1.62/1.85 tff(965,plain,
% 1.62/1.85 ($false),
% 1.62/1.85 inference(unit_resolution,[status(thm)],[154, 964])).
% 1.62/1.85 tff(966,plain,(r(s(s(s(elem!1))), elem!1) | (~r(s(s(s(elem!1))), z)) | (~(z = elem!1))), inference(lemma,lemma(discharge,[]))).
% 1.62/1.85 tff(967,plain,
% 1.62/1.85 (r(s(s(s(elem!1))), elem!1)),
% 1.62/1.85 inference(unit_resolution,[status(thm)],[966, 938, 154])).
% 1.62/1.85 tff(968,plain,
% 1.62/1.85 (s(s(s(z))) = s(s(s(elem!1)))),
% 1.62/1.85 inference(monotonicity,[status(thm)],[936])).
% 1.62/1.85 tff(969,plain,
% 1.62/1.85 (r(s(s(s(z))), s(s(z))) <=> r(s(s(s(elem!1))), s(s(elem!1)))),
% 1.62/1.85 inference(monotonicity,[status(thm)],[968, 936])).
% 1.62/1.85 tff(970,plain,
% 1.62/1.85 (b(s(z), s(s(s(z)))) <=> b(s(z), s(s(s(elem!1))))),
% 1.62/1.85 inference(monotonicity,[status(thm)],[968])).
% 1.62/1.85 tff(971,plain,
% 1.62/1.85 (b(s(z), s(s(s(elem!1)))) <=> b(s(z), s(s(s(z))))),
% 1.62/1.85 inference(symmetry,[status(thm)],[970])).
% 1.62/1.85 tff(972,plain,
% 1.62/1.85 (b(s(z), s(s(s(z))))),
% 1.62/1.85 inference(modus_ponens,[status(thm)],[924, 971])).
% 1.62/1.85 tff(973,plain,
% 1.62/1.85 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), s(z))) | (~r(z, s(z))) | (~r(s(z), s(s(z)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), s(z))) | (~r(z, s(z))) | (~r(s(z), s(s(z)))))),
% 1.62/1.85 inference(rewrite,[status(thm)],[])).
% 1.62/1.85 tff(974,plain,
% 1.62/1.85 (((~r(s(z), s(s(z)))) | (~r(s(s(s(elem!1))), s(z))) | (~r(z, s(z))) | (~r(z, s(s(s(elem!1)))))) <=> ((~r(z, s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), s(z))) | (~r(z, s(z))) | (~r(s(z), s(s(z)))))),
% 1.62/1.85 inference(rewrite,[status(thm)],[])).
% 1.62/1.85 tff(975,plain,
% 1.62/1.85 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(s(z)))) | (~r(s(s(s(elem!1))), s(z))) | (~r(z, s(z))) | (~r(z, s(s(s(elem!1))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), s(z))) | (~r(z, s(z))) | (~r(s(z), s(s(z))))))),
% 1.62/1.85 inference(monotonicity,[status(thm)],[974])).
% 1.62/1.85 tff(976,plain,
% 1.62/1.85 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(s(z)))) | (~r(s(s(s(elem!1))), s(z))) | (~r(z, s(z))) | (~r(z, s(s(s(elem!1))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), s(z))) | (~r(z, s(z))) | (~r(s(z), s(s(z)))))),
% 1.62/1.85 inference(transitivity,[status(thm)],[975, 973])).
% 1.62/1.85 tff(977,plain,
% 1.62/1.85 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(s(z)))) | (~r(s(s(s(elem!1))), s(z))) | (~r(z, s(z))) | (~r(z, s(s(s(elem!1))))))),
% 1.62/1.85 inference(quant_inst,[status(thm)],[])).
% 1.62/1.85 tff(978,plain,
% 1.62/1.85 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), s(z))) | (~r(z, s(z))) | (~r(s(z), s(s(z))))),
% 1.62/1.85 inference(modus_ponens,[status(thm)],[977, 976])).
% 1.62/1.85 tff(979,plain,
% 1.62/1.85 ($false),
% 1.62/1.85 inference(unit_resolution,[status(thm)],[978, 197, 120, 350, 323, 282])).
% 1.62/1.85 tff(980,plain,((~r(s(z), s(s(z)))) | (~r(s(s(s(elem!1))), s(z))) | (~r(z, s(z))) | (~r(z, s(s(s(elem!1)))))), inference(lemma,lemma(discharge,[]))).
% 1.62/1.85 tff(981,plain,
% 1.62/1.85 (~r(s(z), s(s(z)))),
% 1.62/1.85 inference(unit_resolution,[status(thm)],[980, 282, 323, 350])).
% 1.62/1.85 tff(982,plain,
% 1.62/1.85 (b(s(z), s(s(z)))),
% 1.62/1.85 inference(unit_resolution,[status(thm)],[427, 981])).
% 1.62/1.85 tff(983,plain,
% 1.62/1.85 (b(s(s(z)), s(s(s(z)))) <=> b(s(s(elem!1)), s(s(s(elem!1))))),
% 1.62/1.85 inference(monotonicity,[status(thm)],[936, 968])).
% 1.62/1.85 tff(984,plain,
% 1.62/1.85 (b(s(s(elem!1)), s(s(s(elem!1)))) <=> b(s(s(z)), s(s(s(z))))),
% 1.62/1.85 inference(symmetry,[status(thm)],[983])).
% 1.62/1.85 tff(985,plain,
% 1.62/1.85 (b(s(s(z)), s(s(s(z))))),
% 1.62/1.85 inference(modus_ponens,[status(thm)],[935, 984])).
% 1.62/1.85 tff(986,assumption,(b(s(s(z)), s(s(s(z))))), introduced(assumption)).
% 1.62/1.85 tff(987,assumption,(b(s(s(s(z))), s(s(z)))), introduced(assumption)).
% 1.62/1.85 tff(988,assumption,(b(s(z), s(s(s(z))))), introduced(assumption)).
% 1.62/1.85 tff(989,plain,
% 1.62/1.85 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(z)))) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(z)), s(s(s(z))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), s(s(z)))) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(z)), s(s(s(z))))))),
% 1.62/1.85 inference(rewrite,[status(thm)],[])).
% 1.62/1.85 tff(990,plain,
% 1.62/1.85 (((~b(s(s(z)), s(s(s(z))))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(z), s(s(s(z))))) | (~b(s(z), s(s(z))))) <=> ((~b(s(z), s(s(z)))) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(z)), s(s(s(z))))))),
% 1.62/1.85 inference(rewrite,[status(thm)],[])).
% 1.62/1.85 tff(991,plain,
% 1.62/1.85 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), s(s(s(z))))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(z), s(s(s(z))))) | (~b(s(z), s(s(z)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(z)))) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(z)), s(s(s(z)))))))),
% 1.62/1.85 inference(monotonicity,[status(thm)],[990])).
% 1.62/1.85 tff(992,plain,
% 1.62/1.85 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), s(s(s(z))))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(z), s(s(s(z))))) | (~b(s(z), s(s(z)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), s(s(z)))) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(z)), s(s(s(z))))))),
% 1.62/1.85 inference(transitivity,[status(thm)],[991, 989])).
% 1.62/1.85 tff(993,plain,
% 1.62/1.85 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), s(s(s(z))))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(z), s(s(s(z))))) | (~b(s(z), s(s(z)))))),
% 1.62/1.85 inference(quant_inst,[status(thm)],[])).
% 1.62/1.85 tff(994,plain,
% 1.62/1.85 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), s(s(z)))) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(z)), s(s(s(z)))))),
% 1.62/1.85 inference(modus_ponens,[status(thm)],[993, 992])).
% 1.62/1.85 tff(995,plain,
% 1.62/1.85 ($false),
% 1.62/1.85 inference(unit_resolution,[status(thm)],[994, 166, 556, 988, 987, 986])).
% 1.62/1.85 tff(996,plain,((~b(s(s(z)), s(s(s(z))))) | (~b(s(z), s(s(z)))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(z))), s(s(z))))), inference(lemma,lemma(discharge,[]))).
% 1.62/1.85 tff(997,plain,
% 1.62/1.85 (~b(s(s(s(z))), s(s(z)))),
% 1.62/1.85 inference(unit_resolution,[status(thm)],[996, 985, 982, 972])).
% 1.62/1.85 tff(998,assumption,(s(s(s(z))) = s(s(z))), introduced(assumption)).
% 1.62/1.85 tff(999,plain,
% 1.62/1.85 (s(s(z)) = s(s(s(z)))),
% 1.62/1.85 inference(symmetry,[status(thm)],[998])).
% 1.62/1.85 tff(1000,plain,
% 1.62/1.85 (inj_0(s(s(z))) = inj_0(s(s(s(z))))),
% 1.62/1.85 inference(monotonicity,[status(thm)],[999])).
% 1.62/1.85 tff(1001,plain,
% 1.62/1.85 (s(z) = s(s(z))),
% 1.62/1.85 inference(transitivity,[status(thm)],[206, 1000, 134])).
% 1.62/1.85 tff(1002,plain,
% 1.62/1.85 ($false),
% 1.62/1.85 inference(unit_resolution,[status(thm)],[302, 1001])).
% 1.62/1.85 tff(1003,plain,(~(s(s(s(z))) = s(s(z)))), inference(lemma,lemma(discharge,[]))).
% 1.62/1.85 tff(1004,assumption,(~b(s(s(s(z))), s(s(z)))), introduced(assumption)).
% 1.62/1.85 tff(1005,assumption,(~r(s(s(s(z))), s(s(z)))), introduced(assumption)).
% 1.62/1.85 tff(1006,plain,
% 1.62/1.85 (((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((s(s(s(z))) = s(s(z))) | b(s(s(s(z))), s(s(z))) | r(s(s(s(z))), s(s(z))))) <=> ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (s(s(s(z))) = s(s(z))) | b(s(s(s(z))), s(s(z))) | r(s(s(s(z))), s(s(z))))),
% 1.62/1.85 inference(rewrite,[status(thm)],[])).
% 1.62/1.85 tff(1007,plain,
% 1.62/1.85 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((s(s(s(z))) = s(s(z))) | b(s(s(s(z))), s(s(z))) | r(s(s(s(z))), s(s(z))))),
% 1.62/1.85 inference(quant_inst,[status(thm)],[])).
% 1.62/1.85 tff(1008,plain,
% 1.62/1.85 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (s(s(s(z))) = s(s(z))) | b(s(s(s(z))), s(s(z))) | r(s(s(s(z))), s(s(z)))),
% 1.62/1.85 inference(modus_ponens,[status(thm)],[1007, 1006])).
% 1.62/1.85 tff(1009,plain,
% 1.62/1.85 ($false),
% 1.62/1.85 inference(unit_resolution,[status(thm)],[1008, 79, 1005, 1004, 1003])).
% 1.62/1.85 tff(1010,plain,(b(s(s(s(z))), s(s(z))) | r(s(s(s(z))), s(s(z)))), inference(lemma,lemma(discharge,[]))).
% 1.62/1.85 tff(1011,plain,
% 1.62/1.85 (r(s(s(s(z))), s(s(z)))),
% 1.62/1.85 inference(unit_resolution,[status(thm)],[1010, 997])).
% 1.62/1.85 tff(1012,plain,
% 1.62/1.85 (r(s(s(s(elem!1))), s(s(elem!1)))),
% 1.62/1.85 inference(modus_ponens,[status(thm)],[1011, 969])).
% 1.62/1.85 tff(1013,assumption,(r(s(s(s(elem!1))), elem!1)), introduced(assumption)).
% 1.62/1.85 tff(1014,plain,
% 1.62/1.85 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(z))) | (~r(s(s(elem!1)), elem!1)) | (~r(s(s(s(elem!1))), elem!1)) | (~r(s(s(s(elem!1))), s(s(elem!1)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(elem!1, s(z))) | (~r(s(s(elem!1)), elem!1)) | (~r(s(s(s(elem!1))), elem!1)) | (~r(s(s(s(elem!1))), s(s(elem!1)))))),
% 1.62/1.85 inference(rewrite,[status(thm)],[])).
% 1.62/1.85 tff(1015,plain,
% 1.62/1.85 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(z))) | (~r(s(s(elem!1)), elem!1)) | (~r(s(s(s(elem!1))), elem!1)) | (~r(s(s(s(elem!1))), s(s(elem!1)))))),
% 1.62/1.85 inference(quant_inst,[status(thm)],[])).
% 1.62/1.85 tff(1016,plain,
% 1.62/1.85 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(elem!1, s(z))) | (~r(s(s(elem!1)), elem!1)) | (~r(s(s(s(elem!1))), elem!1)) | (~r(s(s(s(elem!1))), s(s(elem!1))))),
% 1.62/1.85 inference(modus_ponens,[status(thm)],[1015, 1014])).
% 1.62/1.85 tff(1017,plain,
% 1.62/1.85 ($false),
% 1.62/1.85 inference(unit_resolution,[status(thm)],[1016, 197, 744, 768, 905, 1013])).
% 1.62/1.85 tff(1018,plain,((~r(s(s(elem!1)), elem!1)) | (~r(elem!1, s(z))) | (~r(s(s(s(elem!1))), s(s(elem!1)))) | (~r(s(s(s(elem!1))), elem!1))), inference(lemma,lemma(discharge,[]))).
% 1.62/1.85 tff(1019,plain,
% 1.62/1.85 (~r(s(s(elem!1)), elem!1)),
% 1.62/1.85 inference(unit_resolution,[status(thm)],[1018, 941, 1012, 967])).
% 1.62/1.85 tff(1020,plain,
% 1.62/1.85 (b(s(s(elem!1)), elem!1)),
% 1.62/1.85 inference(unit_resolution,[status(thm)],[784, 1019, 959])).
% 1.62/1.85 tff(1021,plain,
% 1.62/1.85 ((s(s(s(s(elem!1)))) = s(s(z))) <=> (s(s(s(s(elem!1)))) = s(s(elem!1)))),
% 1.62/1.85 inference(monotonicity,[status(thm)],[936])).
% 1.62/1.85 tff(1022,plain,
% 1.62/1.85 ((s(s(s(s(elem!1)))) = s(s(z))) <=> (s(s(elem!1)) = s(s(s(s(elem!1)))))),
% 1.62/1.85 inference(transitivity,[status(thm)],[1021, 123])).
% 1.62/1.85 tff(1023,plain,
% 1.62/1.85 ((~(s(s(s(s(elem!1)))) = s(s(z)))) <=> (~(s(s(elem!1)) = s(s(s(s(elem!1))))))),
% 1.62/1.85 inference(monotonicity,[status(thm)],[1022])).
% 1.62/1.85 tff(1024,plain,
% 1.62/1.85 (~(s(s(elem!1)) = s(s(s(s(elem!1)))))),
% 1.62/1.85 inference(modus_ponens,[status(thm)],[733, 1023])).
% 1.62/1.85 tff(1025,plain,
% 1.62/1.85 (r(z, s(s(elem!1))) <=> r(elem!1, s(s(elem!1)))),
% 1.62/1.85 inference(monotonicity,[status(thm)],[938])).
% 1.62/1.85 tff(1026,plain,
% 1.62/1.85 (r(elem!1, s(s(elem!1)))),
% 1.62/1.85 inference(modus_ponens,[status(thm)],[365, 1025])).
% 1.62/1.85 tff(1027,assumption,(r(elem!1, s(s(elem!1)))), introduced(assumption)).
% 1.62/1.85 tff(1028,plain,
% 1.62/1.85 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(s(elem!1)))) | (~r(s(s(s(elem!1))), s(s(elem!1)))) | (~r(elem!1, s(s(s(elem!1))))) | (~r(s(s(elem!1)), s(s(s(s(elem!1)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(elem!1, s(s(elem!1)))) | (~r(s(s(s(elem!1))), s(s(elem!1)))) | (~r(elem!1, s(s(s(elem!1))))) | (~r(s(s(elem!1)), s(s(s(s(elem!1)))))))),
% 1.62/1.85 inference(rewrite,[status(thm)],[])).
% 1.62/1.85 tff(1029,plain,
% 1.62/1.85 (((~r(s(s(elem!1)), s(s(s(s(elem!1)))))) | (~r(s(s(s(elem!1))), s(s(elem!1)))) | (~r(elem!1, s(s(elem!1)))) | (~r(elem!1, s(s(s(elem!1)))))) <=> ((~r(elem!1, s(s(elem!1)))) | (~r(s(s(s(elem!1))), s(s(elem!1)))) | (~r(elem!1, s(s(s(elem!1))))) | (~r(s(s(elem!1)), s(s(s(s(elem!1)))))))),
% 1.62/1.85 inference(rewrite,[status(thm)],[])).
% 1.62/1.85 tff(1030,plain,
% 1.62/1.85 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(elem!1)), s(s(s(s(elem!1)))))) | (~r(s(s(s(elem!1))), s(s(elem!1)))) | (~r(elem!1, s(s(elem!1)))) | (~r(elem!1, s(s(s(elem!1))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(s(elem!1)))) | (~r(s(s(s(elem!1))), s(s(elem!1)))) | (~r(elem!1, s(s(s(elem!1))))) | (~r(s(s(elem!1)), s(s(s(s(elem!1))))))))),
% 1.62/1.85 inference(monotonicity,[status(thm)],[1029])).
% 1.62/1.85 tff(1031,plain,
% 1.62/1.85 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(elem!1)), s(s(s(s(elem!1)))))) | (~r(s(s(s(elem!1))), s(s(elem!1)))) | (~r(elem!1, s(s(elem!1)))) | (~r(elem!1, s(s(s(elem!1))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(elem!1, s(s(elem!1)))) | (~r(s(s(s(elem!1))), s(s(elem!1)))) | (~r(elem!1, s(s(s(elem!1))))) | (~r(s(s(elem!1)), s(s(s(s(elem!1)))))))),
% 1.62/1.85 inference(transitivity,[status(thm)],[1030, 1028])).
% 1.62/1.85 tff(1032,plain,
% 1.62/1.85 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(elem!1)), s(s(s(s(elem!1)))))) | (~r(s(s(s(elem!1))), s(s(elem!1)))) | (~r(elem!1, s(s(elem!1)))) | (~r(elem!1, s(s(s(elem!1))))))),
% 1.62/1.85 inference(quant_inst,[status(thm)],[])).
% 1.62/1.85 tff(1033,plain,
% 1.62/1.85 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(elem!1, s(s(elem!1)))) | (~r(s(s(s(elem!1))), s(s(elem!1)))) | (~r(elem!1, s(s(s(elem!1))))) | (~r(s(s(elem!1)), s(s(s(s(elem!1))))))),
% 1.62/1.85 inference(modus_ponens,[status(thm)],[1032, 1031])).
% 1.62/1.85 tff(1034,plain,
% 1.62/1.85 ($false),
% 1.62/1.85 inference(unit_resolution,[status(thm)],[1033, 197, 942, 905, 561, 1027])).
% 1.62/1.85 tff(1035,plain,((~r(s(s(elem!1)), s(s(s(s(elem!1)))))) | (~r(elem!1, s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), s(s(elem!1)))) | (~r(elem!1, s(s(elem!1))))), inference(lemma,lemma(discharge,[]))).
% 1.62/1.85 tff(1036,plain,
% 1.62/1.86 (~r(s(s(elem!1)), s(s(s(s(elem!1)))))),
% 1.62/1.86 inference(unit_resolution,[status(thm)],[1035, 940, 1012, 1026])).
% 1.62/1.86 tff(1037,plain,
% 1.62/1.86 (b(s(s(elem!1)), s(s(s(s(elem!1)))))),
% 1.62/1.86 inference(unit_resolution,[status(thm)],[827, 1036, 1024])).
% 1.62/1.86 tff(1038,plain,
% 1.62/1.86 (~(s(s(s(s(elem!1)))) = s(s(s(elem!1))))),
% 1.62/1.86 inference(unit_resolution,[status(thm)],[363, 361])).
% 1.62/1.86 tff(1039,plain,
% 1.62/1.86 ((s(s(s(s(z)))) = elem!1) <=> (elem!1 = s(s(s(s(z)))))),
% 1.62/1.86 inference(commutativity,[status(thm)],[])).
% 1.62/1.86 tff(1040,plain,
% 1.62/1.86 ((s(s(s(s(z)))) = z) <=> (s(s(s(s(z)))) = elem!1)),
% 1.62/1.86 inference(monotonicity,[status(thm)],[620])).
% 1.62/1.86 tff(1041,plain,
% 1.62/1.86 ((s(s(s(s(z)))) = z) <=> (elem!1 = s(s(s(s(z)))))),
% 1.62/1.86 inference(transitivity,[status(thm)],[1040, 1039])).
% 1.62/1.86 tff(1042,plain,
% 1.62/1.86 ((~(s(s(s(s(z)))) = z)) <=> (~(elem!1 = s(s(s(s(z))))))),
% 1.62/1.86 inference(monotonicity,[status(thm)],[1041])).
% 1.62/1.86 tff(1043,plain,
% 1.62/1.86 ((~![X: $i] : (~(s(X) = z))) | (~(s(s(s(s(z)))) = z))),
% 1.62/1.86 inference(quant_inst,[status(thm)],[])).
% 1.62/1.86 tff(1044,plain,
% 1.62/1.86 (~(s(s(s(s(z)))) = z)),
% 1.62/1.86 inference(unit_resolution,[status(thm)],[1043, 65])).
% 1.62/1.86 tff(1045,plain,
% 1.62/1.86 (~(elem!1 = s(s(s(s(z)))))),
% 1.62/1.86 inference(modus_ponens,[status(thm)],[1044, 1042])).
% 1.62/1.86 tff(1046,assumption,(b(s(s(elem!1)), s(s(s(s(elem!1)))))), introduced(assumption)).
% 1.62/1.86 tff(1047,assumption,(r(elem!1, s(s(s(s(elem!1)))))), introduced(assumption)).
% 1.62/1.86 tff(1048,assumption,(r(s(s(s(s(elem!1)))), s(s(s(elem!1))))), introduced(assumption)).
% 1.62/1.86 tff(1049,plain,
% 1.62/1.86 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(s(s(s(elem!1)))))) | (~r(s(s(s(elem!1))), s(z))) | (~r(elem!1, s(s(s(elem!1))))) | (~r(s(s(s(s(elem!1)))), s(s(s(elem!1))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(elem!1, s(s(s(s(elem!1)))))) | (~r(s(s(s(elem!1))), s(z))) | (~r(elem!1, s(s(s(elem!1))))) | (~r(s(s(s(s(elem!1)))), s(s(s(elem!1))))))),
% 1.62/1.86 inference(rewrite,[status(thm)],[])).
% 1.62/1.86 tff(1050,plain,
% 1.62/1.86 (((~r(s(s(s(elem!1))), s(z))) | (~r(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(elem!1))))))) <=> ((~r(elem!1, s(s(s(s(elem!1)))))) | (~r(s(s(s(elem!1))), s(z))) | (~r(elem!1, s(s(s(elem!1))))) | (~r(s(s(s(s(elem!1)))), s(s(s(elem!1))))))),
% 1.62/1.86 inference(rewrite,[status(thm)],[])).
% 1.62/1.86 tff(1051,plain,
% 1.62/1.86 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), s(z))) | (~r(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(elem!1)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(s(s(s(elem!1)))))) | (~r(s(s(s(elem!1))), s(z))) | (~r(elem!1, s(s(s(elem!1))))) | (~r(s(s(s(s(elem!1)))), s(s(s(elem!1)))))))),
% 1.62/1.86 inference(monotonicity,[status(thm)],[1050])).
% 1.62/1.86 tff(1052,plain,
% 1.62/1.86 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), s(z))) | (~r(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(elem!1)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(elem!1, s(s(s(s(elem!1)))))) | (~r(s(s(s(elem!1))), s(z))) | (~r(elem!1, s(s(s(elem!1))))) | (~r(s(s(s(s(elem!1)))), s(s(s(elem!1))))))),
% 1.62/1.86 inference(transitivity,[status(thm)],[1051, 1049])).
% 1.62/1.86 tff(1053,plain,
% 1.62/1.86 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), s(z))) | (~r(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(elem!1)))))))),
% 1.62/1.86 inference(quant_inst,[status(thm)],[])).
% 1.62/1.86 tff(1054,plain,
% 1.62/1.86 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(elem!1, s(s(s(s(elem!1)))))) | (~r(s(s(s(elem!1))), s(z))) | (~r(elem!1, s(s(s(elem!1))))) | (~r(s(s(s(s(elem!1)))), s(s(s(elem!1)))))),
% 1.62/1.86 inference(modus_ponens,[status(thm)],[1053, 1052])).
% 1.62/1.86 tff(1055,plain,
% 1.62/1.86 ($false),
% 1.62/1.86 inference(unit_resolution,[status(thm)],[1054, 197, 350, 942, 1048, 1047])).
% 1.62/1.86 tff(1056,plain,((~r(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), s(z))) | (~r(elem!1, s(s(s(elem!1))))) | (~r(elem!1, s(s(s(s(elem!1))))))), inference(lemma,lemma(discharge,[]))).
% 1.62/1.86 tff(1057,plain,
% 1.62/1.86 (~r(s(s(s(s(elem!1)))), s(s(s(elem!1))))),
% 1.62/1.86 inference(unit_resolution,[status(thm)],[1056, 1047, 942, 350])).
% 1.62/1.86 tff(1058,assumption,(~(s(s(s(s(elem!1)))) = s(s(s(elem!1))))), introduced(assumption)).
% 1.62/1.86 tff(1059,assumption,(~r(s(s(s(s(elem!1)))), s(s(s(elem!1))))), introduced(assumption)).
% 1.62/1.86 tff(1060,assumption,(~b(s(s(s(s(elem!1)))), s(s(s(elem!1))))), introduced(assumption)).
% 1.62/1.86 tff(1061,plain,
% 1.62/1.86 (((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((s(s(s(s(elem!1)))) = s(s(s(elem!1)))) | b(s(s(s(s(elem!1)))), s(s(s(elem!1)))) | r(s(s(s(s(elem!1)))), s(s(s(elem!1)))))) <=> ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (s(s(s(s(elem!1)))) = s(s(s(elem!1)))) | b(s(s(s(s(elem!1)))), s(s(s(elem!1)))) | r(s(s(s(s(elem!1)))), s(s(s(elem!1)))))),
% 1.62/1.86 inference(rewrite,[status(thm)],[])).
% 1.62/1.86 tff(1062,plain,
% 1.62/1.86 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((s(s(s(s(elem!1)))) = s(s(s(elem!1)))) | b(s(s(s(s(elem!1)))), s(s(s(elem!1)))) | r(s(s(s(s(elem!1)))), s(s(s(elem!1)))))),
% 1.62/1.86 inference(quant_inst,[status(thm)],[])).
% 1.62/1.86 tff(1063,plain,
% 1.62/1.86 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (s(s(s(s(elem!1)))) = s(s(s(elem!1)))) | b(s(s(s(s(elem!1)))), s(s(s(elem!1)))) | r(s(s(s(s(elem!1)))), s(s(s(elem!1))))),
% 1.62/1.86 inference(modus_ponens,[status(thm)],[1062, 1061])).
% 1.62/1.86 tff(1064,plain,
% 1.62/1.86 ($false),
% 1.62/1.86 inference(unit_resolution,[status(thm)],[1063, 79, 1060, 1059, 1058])).
% 1.62/1.86 tff(1065,plain,(r(s(s(s(s(elem!1)))), s(s(s(elem!1)))) | b(s(s(s(s(elem!1)))), s(s(s(elem!1)))) | (s(s(s(s(elem!1)))) = s(s(s(elem!1))))), inference(lemma,lemma(discharge,[]))).
% 1.62/1.86 tff(1066,plain,
% 1.62/1.86 (b(s(s(s(s(elem!1)))), s(s(s(elem!1))))),
% 1.62/1.86 inference(unit_resolution,[status(thm)],[1065, 1057, 1038])).
% 1.62/1.86 tff(1067,plain,
% 1.62/1.86 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(s(s(s(elem!1)))))) | (~r(elem!1, s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), s(s(s(s(elem!1)))))) | (~r(s(s(s(s(elem!1)))), s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(elem!1, s(s(s(s(elem!1)))))) | (~r(elem!1, s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), s(s(s(s(elem!1)))))) | (~r(s(s(s(s(elem!1)))), s(z))))),
% 1.62/1.86 inference(rewrite,[status(thm)],[])).
% 1.62/1.86 tff(1068,plain,
% 1.62/1.86 (((~r(s(s(s(s(elem!1)))), s(z))) | (~r(s(s(s(elem!1))), s(s(s(s(elem!1)))))) | (~r(elem!1, s(s(s(s(elem!1)))))) | (~r(elem!1, s(s(s(elem!1)))))) <=> ((~r(elem!1, s(s(s(s(elem!1)))))) | (~r(elem!1, s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), s(s(s(s(elem!1)))))) | (~r(s(s(s(s(elem!1)))), s(z))))),
% 1.62/1.86 inference(rewrite,[status(thm)],[])).
% 1.62/1.86 tff(1069,plain,
% 1.62/1.86 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(elem!1)))), s(z))) | (~r(s(s(s(elem!1))), s(s(s(s(elem!1)))))) | (~r(elem!1, s(s(s(s(elem!1)))))) | (~r(elem!1, s(s(s(elem!1))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(s(s(s(elem!1)))))) | (~r(elem!1, s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), s(s(s(s(elem!1)))))) | (~r(s(s(s(s(elem!1)))), s(z)))))),
% 1.62/1.86 inference(monotonicity,[status(thm)],[1068])).
% 1.62/1.86 tff(1070,plain,
% 1.62/1.86 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(elem!1)))), s(z))) | (~r(s(s(s(elem!1))), s(s(s(s(elem!1)))))) | (~r(elem!1, s(s(s(s(elem!1)))))) | (~r(elem!1, s(s(s(elem!1))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(elem!1, s(s(s(s(elem!1)))))) | (~r(elem!1, s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), s(s(s(s(elem!1)))))) | (~r(s(s(s(s(elem!1)))), s(z))))),
% 1.62/1.86 inference(transitivity,[status(thm)],[1069, 1067])).
% 1.62/1.86 tff(1071,plain,
% 1.62/1.86 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(elem!1)))), s(z))) | (~r(s(s(s(elem!1))), s(s(s(s(elem!1)))))) | (~r(elem!1, s(s(s(s(elem!1)))))) | (~r(elem!1, s(s(s(elem!1))))))),
% 1.62/1.86 inference(quant_inst,[status(thm)],[])).
% 1.62/1.86 tff(1072,plain,
% 1.62/1.86 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(elem!1, s(s(s(s(elem!1)))))) | (~r(elem!1, s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), s(s(s(s(elem!1)))))) | (~r(s(s(s(s(elem!1)))), s(z)))),
% 1.62/1.86 inference(modus_ponens,[status(thm)],[1071, 1070])).
% 1.62/1.86 tff(1073,plain,
% 1.62/1.86 ($false),
% 1.62/1.86 inference(unit_resolution,[status(thm)],[1072, 197, 942, 700, 698, 1047])).
% 1.62/1.86 tff(1074,plain,((~r(s(s(s(elem!1))), s(s(s(s(elem!1)))))) | (~r(elem!1, s(s(s(elem!1))))) | (~r(s(s(s(s(elem!1)))), s(z))) | (~r(elem!1, s(s(s(s(elem!1))))))), inference(lemma,lemma(discharge,[]))).
% 1.62/1.86 tff(1075,plain,
% 1.62/1.86 (~r(s(s(s(elem!1))), s(s(s(s(elem!1)))))),
% 1.62/1.86 inference(unit_resolution,[status(thm)],[1074, 1047, 700, 942])).
% 1.62/1.86 tff(1076,plain,
% 1.62/1.86 (b(s(s(s(elem!1))), s(s(s(s(elem!1)))))),
% 1.62/1.86 inference(unit_resolution,[status(thm)],[696, 1075, 361])).
% 1.62/1.86 tff(1077,plain,
% 1.62/1.86 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(s(s(elem!1)), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(s(s(s(elem!1)))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(s(s(elem!1)), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(s(s(s(elem!1)))))))),
% 1.62/1.86 inference(rewrite,[status(thm)],[])).
% 1.62/1.86 tff(1078,plain,
% 1.62/1.86 (((~b(s(s(s(elem!1))), s(s(s(s(elem!1)))))) | (~b(s(s(elem!1)), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(s(s(s(elem!1)))))) | (~b(s(s(elem!1)), s(s(s(s(elem!1)))))) | (~b(s(s(elem!1)), s(s(s(elem!1)))))) <=> ((~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(s(s(elem!1)), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(s(s(s(elem!1)))))))),
% 1.62/1.86 inference(rewrite,[status(thm)],[])).
% 1.62/1.86 tff(1079,plain,
% 1.62/1.86 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), s(s(s(s(elem!1)))))) | (~b(s(s(elem!1)), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(s(s(s(elem!1)))))) | (~b(s(s(elem!1)), s(s(s(s(elem!1)))))) | (~b(s(s(elem!1)), s(s(s(elem!1))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(s(s(elem!1)), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(s(s(s(elem!1))))))))),
% 1.62/1.86 inference(monotonicity,[status(thm)],[1078])).
% 1.62/1.86 tff(1080,plain,
% 1.62/1.86 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), s(s(s(s(elem!1)))))) | (~b(s(s(elem!1)), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(s(s(s(elem!1)))))) | (~b(s(s(elem!1)), s(s(s(s(elem!1)))))) | (~b(s(s(elem!1)), s(s(s(elem!1))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(s(s(elem!1)), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(s(s(s(elem!1)))))))),
% 1.62/1.86 inference(transitivity,[status(thm)],[1079, 1077])).
% 1.62/1.86 tff(1081,plain,
% 1.62/1.86 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), s(s(s(s(elem!1)))))) | (~b(s(s(elem!1)), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(s(s(s(elem!1)))))) | (~b(s(s(elem!1)), s(s(s(s(elem!1)))))) | (~b(s(s(elem!1)), s(s(s(elem!1))))))),
% 1.62/1.86 inference(quant_inst,[status(thm)],[])).
% 1.62/1.86 tff(1082,plain,
% 1.62/1.86 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(s(s(elem!1)), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(s(s(s(elem!1))))))),
% 1.62/1.86 inference(modus_ponens,[status(thm)],[1081, 1080])).
% 1.62/1.86 tff(1083,plain,
% 1.62/1.86 ($false),
% 1.62/1.86 inference(unit_resolution,[status(thm)],[1082, 166, 463, 1046, 1076, 1066])).
% 1.62/1.86 tff(1084,plain,((~r(elem!1, 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(elem!1)))))) | (~r(elem!1, s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), s(z))) | (s(s(s(elem!1))) = s(s(s(s(elem!1))))) | (~r(s(s(s(s(elem!1)))), s(z)))), inference(lemma,lemma(discharge,[]))).
% 1.62/1.86 tff(1085,plain,
% 1.62/1.86 (~r(elem!1, s(s(s(s(elem!1)))))),
% 1.62/1.86 inference(unit_resolution,[status(thm)],[1084, 1046, 463, 942, 350, 361, 700])).
% 1.62/1.86 tff(1086,plain,
% 1.62/1.86 (s(s(s(z))) = s(s(s(elem!1)))),
% 1.62/1.86 inference(monotonicity,[status(thm)],[34])).
% 1.62/1.86 tff(1087,plain,
% 1.62/1.86 (s(s(s(s(z)))) = s(s(s(s(elem!1))))),
% 1.62/1.86 inference(monotonicity,[status(thm)],[1086])).
% 1.62/1.86 tff(1088,plain,
% 1.62/1.86 (r(elem!1, s(s(s(s(z))))) <=> r(elem!1, s(s(s(s(elem!1)))))),
% 1.62/1.86 inference(monotonicity,[status(thm)],[1087])).
% 1.62/1.86 tff(1089,assumption,(r(elem!1, s(s(s(s(z)))))), introduced(assumption)).
% 1.62/1.86 tff(1090,plain,
% 1.62/1.86 (r(elem!1, s(s(s(s(elem!1)))))),
% 1.62/1.86 inference(modus_ponens,[status(thm)],[1089, 1088])).
% 1.62/1.86 tff(1091,assumption,(~r(elem!1, s(s(s(s(elem!1)))))), introduced(assumption)).
% 1.62/1.86 tff(1092,plain,
% 1.62/1.86 ($false),
% 1.62/1.86 inference(unit_resolution,[status(thm)],[1091, 1090])).
% 1.62/1.86 tff(1093,plain,((~r(elem!1, s(s(s(s(z)))))) | r(elem!1, s(s(s(s(elem!1))))) | (~(s(s(z)) = s(s(elem!1))))), inference(lemma,lemma(discharge,[]))).
% 1.62/1.86 tff(1094,plain,
% 1.62/1.86 (~r(elem!1, s(s(s(s(z)))))),
% 1.62/1.86 inference(unit_resolution,[status(thm)],[1093, 1085, 34])).
% 1.62/1.86 tff(1095,plain,
% 1.62/1.86 (((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((elem!1 = s(s(s(s(z))))) | b(elem!1, s(s(s(s(z))))) | r(elem!1, s(s(s(s(z))))))) <=> ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (elem!1 = s(s(s(s(z))))) | b(elem!1, s(s(s(s(z))))) | r(elem!1, s(s(s(s(z))))))),
% 1.62/1.86 inference(rewrite,[status(thm)],[])).
% 1.62/1.86 tff(1096,plain,
% 1.62/1.86 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((elem!1 = s(s(s(s(z))))) | b(elem!1, s(s(s(s(z))))) | r(elem!1, s(s(s(s(z))))))),
% 1.62/1.86 inference(quant_inst,[status(thm)],[])).
% 1.62/1.86 tff(1097,plain,
% 1.62/1.86 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (elem!1 = s(s(s(s(z))))) | b(elem!1, s(s(s(s(z))))) | r(elem!1, s(s(s(s(z)))))),
% 1.62/1.86 inference(modus_ponens,[status(thm)],[1096, 1095])).
% 1.62/1.86 tff(1098,plain,
% 1.62/1.86 ((elem!1 = s(s(s(s(z))))) | b(elem!1, s(s(s(s(z))))) | r(elem!1, s(s(s(s(z)))))),
% 1.62/1.86 inference(unit_resolution,[status(thm)],[1097, 79])).
% 1.62/1.86 tff(1099,plain,
% 1.62/1.86 (b(elem!1, s(s(s(s(z)))))),
% 1.62/1.86 inference(unit_resolution,[status(thm)],[1098, 1094, 1045])).
% 1.62/1.86 tff(1100,plain,
% 1.62/1.86 (b(elem!1, s(s(s(s(z))))) <=> b(elem!1, s(s(s(s(elem!1)))))),
% 1.62/1.86 inference(monotonicity,[status(thm)],[1087])).
% 1.62/1.86 tff(1101,assumption,(b(elem!1, s(s(s(s(z)))))), introduced(assumption)).
% 1.62/1.86 tff(1102,plain,
% 1.62/1.86 (b(elem!1, s(s(s(s(elem!1)))))),
% 1.62/1.86 inference(modus_ponens,[status(thm)],[1101, 1100])).
% 1.62/1.86 tff(1103,assumption,(~b(elem!1, s(s(s(s(elem!1)))))), introduced(assumption)).
% 1.62/1.86 tff(1104,plain,
% 1.62/1.86 ($false),
% 1.62/1.86 inference(unit_resolution,[status(thm)],[1103, 1102])).
% 1.62/1.86 tff(1105,plain,((~b(elem!1, s(s(s(s(z)))))) | b(elem!1, s(s(s(s(elem!1))))) | (~(s(s(z)) = s(s(elem!1))))), inference(lemma,lemma(discharge,[]))).
% 1.62/1.86 tff(1106,plain,
% 1.62/1.86 (b(elem!1, s(s(s(s(elem!1)))))),
% 1.62/1.86 inference(unit_resolution,[status(thm)],[1105, 1099, 34])).
% 1.62/1.86 tff(1107,assumption,(b(s(s(s(s(elem!1)))), s(s(s(elem!1))))), introduced(assumption)).
% 1.62/1.86 tff(1108,assumption,(b(elem!1, s(s(s(s(elem!1)))))), introduced(assumption)).
% 1.62/1.86 tff(1109,plain,
% 1.62/1.86 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(s(s(elem!1)), elem!1)) | (~b(s(s(elem!1)), s(z))) | (~b(s(z), elem!1)) | (~b(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~b(elem!1, s(s(s(s(elem!1)))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(s(s(elem!1)), elem!1)) | (~b(s(s(elem!1)), s(z))) | (~b(s(z), elem!1)) | (~b(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~b(elem!1, s(s(s(s(elem!1)))))))),
% 1.62/1.86 inference(rewrite,[status(thm)],[])).
% 1.62/1.86 tff(1110,plain,
% 1.62/1.86 (((~b(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(elem!1, s(s(s(s(elem!1)))))) | (~b(s(z), elem!1)) | (~b(s(s(elem!1)), elem!1)) | (~b(s(s(elem!1)), s(z)))) <=> ((~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(s(s(elem!1)), elem!1)) | (~b(s(s(elem!1)), s(z))) | (~b(s(z), elem!1)) | (~b(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~b(elem!1, s(s(s(s(elem!1)))))))),
% 1.62/1.86 inference(rewrite,[status(thm)],[])).
% 1.62/1.86 tff(1111,plain,
% 1.62/1.86 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(elem!1, s(s(s(s(elem!1)))))) | (~b(s(z), elem!1)) | (~b(s(s(elem!1)), elem!1)) | (~b(s(s(elem!1)), s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(s(s(elem!1)), elem!1)) | (~b(s(s(elem!1)), s(z))) | (~b(s(z), elem!1)) | (~b(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~b(elem!1, s(s(s(s(elem!1))))))))),
% 1.62/1.86 inference(monotonicity,[status(thm)],[1110])).
% 1.62/1.86 tff(1112,plain,
% 1.62/1.86 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(elem!1, s(s(s(s(elem!1)))))) | (~b(s(z), elem!1)) | (~b(s(s(elem!1)), elem!1)) | (~b(s(s(elem!1)), s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(s(s(elem!1)), elem!1)) | (~b(s(s(elem!1)), s(z))) | (~b(s(z), elem!1)) | (~b(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~b(elem!1, s(s(s(s(elem!1)))))))),
% 1.62/1.86 inference(transitivity,[status(thm)],[1111, 1109])).
% 1.62/1.86 tff(1113,plain,
% 1.62/1.86 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(elem!1, s(s(s(s(elem!1)))))) | (~b(s(z), elem!1)) | (~b(s(s(elem!1)), elem!1)) | (~b(s(s(elem!1)), s(z))))),
% 1.62/1.86 inference(quant_inst,[status(thm)],[])).
% 1.62/1.86 tff(1114,plain,
% 1.62/1.86 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(s(s(elem!1)), elem!1)) | (~b(s(s(elem!1)), s(z))) | (~b(s(z), elem!1)) | (~b(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~b(elem!1, s(s(s(s(elem!1))))))),
% 1.62/1.86 inference(modus_ponens,[status(thm)],[1113, 1112])).
% 1.62/1.86 tff(1115,plain,
% 1.62/1.86 ($false),
% 1.62/1.86 inference(unit_resolution,[status(thm)],[1114, 166, 463, 786, 310, 642, 1108, 1107])).
% 1.62/1.86 tff(1116,plain,((~b(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(s(s(elem!1)), elem!1)) | (~b(s(s(elem!1)), s(z))) | (~b(s(z), elem!1)) | (~b(elem!1, s(s(s(s(elem!1))))))), inference(lemma,lemma(discharge,[]))).
% 1.62/1.86 tff(1117,plain,
% 1.62/1.86 (~b(s(s(s(s(elem!1)))), s(s(s(elem!1))))),
% 1.62/1.86 inference(unit_resolution,[status(thm)],[1116, 1106, 786, 310, 642, 463])).
% 1.62/1.87 tff(1118,plain,
% 1.62/1.87 (r(s(s(s(s(elem!1)))), s(s(s(elem!1))))),
% 1.62/1.87 inference(unit_resolution,[status(thm)],[1065, 1117, 1038])).
% 1.62/1.87 tff(1119,plain,
% 1.62/1.87 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), elem!1)) | (~b(s(s(elem!1)), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), elem!1)) | (~b(elem!1, s(s(s(s(elem!1)))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(elem!1)), elem!1)) | (~b(s(s(elem!1)), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), elem!1)) | (~b(elem!1, s(s(s(s(elem!1)))))))),
% 1.62/1.87 inference(rewrite,[status(thm)],[])).
% 1.62/1.87 tff(1120,plain,
% 1.62/1.87 (((~b(elem!1, s(s(s(s(elem!1)))))) | (~b(s(s(elem!1)), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), elem!1)) | (~b(elem!1, s(s(s(s(elem!1)))))) | (~b(s(s(elem!1)), s(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(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), elem!1)) | (~b(elem!1, s(s(s(s(elem!1)))))))),
% 1.62/1.87 inference(rewrite,[status(thm)],[])).
% 1.62/1.87 tff(1121,plain,
% 1.62/1.87 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(s(s(s(elem!1)))))) | (~b(s(s(elem!1)), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), elem!1)) | (~b(elem!1, s(s(s(s(elem!1)))))) | (~b(s(s(elem!1)), s(s(s(s(elem!1)))))) | (~b(s(s(elem!1)), elem!1)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), elem!1)) | (~b(s(s(elem!1)), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), elem!1)) | (~b(elem!1, s(s(s(s(elem!1))))))))),
% 1.62/1.87 inference(monotonicity,[status(thm)],[1120])).
% 1.62/1.87 tff(1122,plain,
% 1.62/1.87 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(s(s(s(elem!1)))))) | (~b(s(s(elem!1)), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), elem!1)) | (~b(elem!1, s(s(s(s(elem!1)))))) | (~b(s(s(elem!1)), s(s(s(s(elem!1)))))) | (~b(s(s(elem!1)), elem!1)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(elem!1)), elem!1)) | (~b(s(s(elem!1)), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), elem!1)) | (~b(elem!1, s(s(s(s(elem!1)))))))),
% 1.62/1.87 inference(transitivity,[status(thm)],[1121, 1119])).
% 1.62/1.87 tff(1123,plain,
% 1.62/1.87 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(s(s(s(elem!1)))))) | (~b(s(s(elem!1)), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), elem!1)) | (~b(elem!1, s(s(s(s(elem!1)))))) | (~b(s(s(elem!1)), s(s(s(s(elem!1)))))) | (~b(s(s(elem!1)), elem!1)))),
% 1.62/1.87 inference(quant_inst,[status(thm)],[])).
% 1.62/1.87 tff(1124,plain,
% 1.62/1.87 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(elem!1)), elem!1)) | (~b(s(s(elem!1)), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), elem!1)) | (~b(elem!1, s(s(s(s(elem!1))))))),
% 1.62/1.87 inference(modus_ponens,[status(thm)],[1123, 1122])).
% 1.62/1.87 tff(1125,plain,
% 1.62/1.87 ($false),
% 1.62/1.87 inference(unit_resolution,[status(thm)],[1124, 166, 786, 1046, 1108, 640])).
% 1.62/1.87 tff(1126,plain,((~b(elem!1, s(s(s(s(elem!1)))))) | (~b(s(s(elem!1)), elem!1)) | (~b(s(s(elem!1)), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), elem!1))), inference(lemma,lemma(discharge,[]))).
% 1.62/1.87 tff(1127,plain,
% 1.62/1.87 (~b(s(s(s(s(elem!1)))), elem!1)),
% 1.62/1.87 inference(unit_resolution,[status(thm)],[1126, 1106, 1046, 786])).
% 1.62/1.87 tff(1128,plain,
% 1.62/1.87 (r(s(s(s(s(elem!1)))), elem!1)),
% 1.62/1.87 inference(unit_resolution,[status(thm)],[719, 1127, 627])).
% 1.62/1.87 tff(1129,plain,
% 1.62/1.87 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), s(z))) | (~r(elem!1, s(s(s(elem!1))))) | (~r(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~r(s(s(s(s(elem!1)))), elem!1)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(elem!1))), s(z))) | (~r(elem!1, s(s(s(elem!1))))) | (~r(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~r(s(s(s(s(elem!1)))), elem!1)))),
% 1.62/1.87 inference(rewrite,[status(thm)],[])).
% 1.62/1.87 tff(1130,plain,
% 1.62/1.87 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), s(z))) | (~r(elem!1, s(s(s(elem!1))))) | (~r(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~r(s(s(s(s(elem!1)))), elem!1)))),
% 1.62/1.87 inference(quant_inst,[status(thm)],[])).
% 1.62/1.87 tff(1131,plain,
% 1.62/1.87 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(elem!1))), s(z))) | (~r(elem!1, s(s(s(elem!1))))) | (~r(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~r(s(s(s(s(elem!1)))), elem!1))),
% 1.62/1.87 inference(modus_ponens,[status(thm)],[1130, 1129])).
% 1.62/1.87 tff(1132,plain,
% 1.62/1.87 ($false),
% 1.62/1.87 inference(unit_resolution,[status(thm)],[1131, 197, 350, 942, 1128, 1118])).
% 1.62/1.87 tff(1133,plain,((~b(s(s(elem!1)), s(s(s(s(elem!1)))))) | (~r(s(s(s(elem!1))), s(z))) | (~r(elem!1, s(s(s(elem!1))))) | (~b(s(s(elem!1)), elem!1)) | (~b(s(s(elem!1)), s(z))) | (~b(s(z), elem!1)) | (~b(s(s(elem!1)), s(s(s(elem!1))))) | (~(s(s(z)) = s(s(elem!1)))) | (s(s(s(elem!1))) = s(s(s(s(elem!1))))) | (~r(s(s(s(s(elem!1)))), s(z)))), inference(lemma,lemma(discharge,[]))).
% 1.62/1.87 tff(1134,plain,
% 1.62/1.87 (~r(s(s(s(s(elem!1)))), s(z))),
% 1.62/1.87 inference(unit_resolution,[status(thm)],[1133, 1037, 940, 1020, 310, 954, 935, 936, 358, 350])).
% 1.62/1.87 tff(1135,plain,
% 1.62/1.87 (b(s(s(s(s(elem!1)))), s(z))),
% 1.62/1.87 inference(unit_resolution,[status(thm)],[661, 1134])).
% 1.62/1.87 tff(1136,plain,
% 1.62/1.87 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(elem!1)))) | (~b(s(s(elem!1)), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), s(z))) | (~b(s(z), s(s(s(s(elem!1)))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), s(s(elem!1)))) | (~b(s(s(elem!1)), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), s(z))) | (~b(s(z), s(s(s(s(elem!1)))))))),
% 1.62/1.87 inference(rewrite,[status(thm)],[])).
% 1.62/1.87 tff(1137,plain,
% 1.62/1.87 (((~b(s(z), s(s(elem!1)))) | (~b(s(z), s(s(elem!1)))) | (~b(s(s(s(s(elem!1)))), s(z))) | (~b(s(s(elem!1)), s(s(s(s(elem!1)))))) | (~b(s(z), s(s(s(s(elem!1)))))) | (~b(s(z), s(s(elem!1))))) <=> ((~b(s(z), s(s(elem!1)))) | (~b(s(s(elem!1)), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), s(z))) | (~b(s(z), s(s(s(s(elem!1)))))))),
% 1.62/1.87 inference(rewrite,[status(thm)],[])).
% 1.62/1.87 tff(1138,plain,
% 1.62/1.87 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(elem!1)))) | (~b(s(z), s(s(elem!1)))) | (~b(s(s(s(s(elem!1)))), s(z))) | (~b(s(s(elem!1)), s(s(s(s(elem!1)))))) | (~b(s(z), s(s(s(s(elem!1)))))) | (~b(s(z), s(s(elem!1)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(elem!1)))) | (~b(s(s(elem!1)), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), s(z))) | (~b(s(z), s(s(s(s(elem!1))))))))),
% 1.62/1.87 inference(monotonicity,[status(thm)],[1137])).
% 1.62/1.87 tff(1139,plain,
% 1.62/1.87 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(elem!1)))) | (~b(s(z), s(s(elem!1)))) | (~b(s(s(s(s(elem!1)))), s(z))) | (~b(s(s(elem!1)), s(s(s(s(elem!1)))))) | (~b(s(z), s(s(s(s(elem!1)))))) | (~b(s(z), s(s(elem!1)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), s(s(elem!1)))) | (~b(s(s(elem!1)), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), s(z))) | (~b(s(z), s(s(s(s(elem!1)))))))),
% 1.62/1.87 inference(transitivity,[status(thm)],[1138, 1136])).
% 1.62/1.87 tff(1140,plain,
% 1.62/1.87 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(elem!1)))) | (~b(s(z), s(s(elem!1)))) | (~b(s(s(s(s(elem!1)))), s(z))) | (~b(s(s(elem!1)), s(s(s(s(elem!1)))))) | (~b(s(z), s(s(s(s(elem!1)))))) | (~b(s(z), s(s(elem!1)))))),
% 1.62/1.87 inference(quant_inst,[status(thm)],[])).
% 1.62/1.87 tff(1141,plain,
% 1.62/1.87 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), s(s(elem!1)))) | (~b(s(s(elem!1)), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), s(z))) | (~b(s(z), s(s(s(s(elem!1))))))),
% 1.62/1.87 inference(modus_ponens,[status(thm)],[1140, 1139])).
% 1.62/1.87 tff(1142,plain,
% 1.62/1.87 ($false),
% 1.62/1.87 inference(unit_resolution,[status(thm)],[1141, 166, 375, 1037, 1135, 952])).
% 1.62/1.87 tff(1143,plain,((~r(z, s(s(s(elem!1))))) | (~b(s(s(elem!1)), s(z))) | (~r(s(s(s(elem!1))), s(z))) | (~r(z, s(s(elem!1)))) | (~b(s(z), z)) | (~r(s(s(s(elem!1))), z)) | (~r(z, s(z))) | (~r(z, s(s(z)))) | (s(s(elem!1)) = s(s(s(elem!1))))), inference(lemma,lemma(discharge,[]))).
% 1.62/1.87 tff(1144,plain,
% 1.62/1.87 (~r(z, s(s(s(elem!1))))),
% 1.62/1.87 inference(unit_resolution,[status(thm)],[1143, 154, 350, 365, 53, 310, 323, 155, 45])).
% 1.62/1.87 tff(1145,plain,
% 1.62/1.87 (b(z, s(s(s(elem!1))))),
% 1.62/1.87 inference(unit_resolution,[status(thm)],[261, 1144])).
% 1.62/1.87 tff(1146,plain,
% 1.62/1.87 (~(z = elem!1)),
% 1.62/1.87 inference(unit_resolution,[status(thm)],[17, 132])).
% 1.62/1.87 tff(1147,plain,
% 1.62/1.87 ((elem!1 = z) <=> (z = elem!1)),
% 1.62/1.87 inference(commutativity,[status(thm)],[])).
% 1.62/1.87 tff(1148,assumption,(elem!1 = z), introduced(assumption)).
% 1.62/1.87 tff(1149,plain,
% 1.62/1.87 (z = elem!1),
% 1.62/1.87 inference(modus_ponens,[status(thm)],[1148, 1147])).
% 1.62/1.87 tff(1150,plain,
% 1.62/1.87 ($false),
% 1.62/1.87 inference(unit_resolution,[status(thm)],[28, 1149])).
% 1.62/1.87 tff(1151,plain,((~(elem!1 = z)) | (z = elem!1)), inference(lemma,lemma(discharge,[]))).
% 1.62/1.87 tff(1152,plain,
% 1.62/1.87 (~(elem!1 = z)),
% 1.62/1.87 inference(unit_resolution,[status(thm)],[1151, 1146])).
% 1.62/1.87 tff(1153,assumption,(s(s(elem!1)) = s(s(s(s(elem!1))))), introduced(assumption)).
% 1.62/1.87 tff(1154,plain,
% 1.62/1.87 (s(s(s(s(elem!1)))) = s(s(elem!1))),
% 1.62/1.87 inference(symmetry,[status(thm)],[1153])).
% 1.62/1.87 tff(1155,plain,
% 1.62/1.87 (b(s(s(s(s(elem!1)))), z) <=> b(s(s(elem!1)), z)),
% 1.62/1.87 inference(monotonicity,[status(thm)],[1154])).
% 1.62/1.87 tff(1156,plain,
% 1.62/1.87 (b(s(s(elem!1)), z) <=> b(s(s(s(s(elem!1)))), z)),
% 1.62/1.87 inference(symmetry,[status(thm)],[1155])).
% 1.62/1.87 tff(1157,plain,
% 1.62/1.87 (s(s(s(s(elem!1)))) = s(s(elem!1))),
% 1.62/1.87 inference(modus_ponens,[status(thm)],[1153, 124])).
% 1.62/1.87 tff(1158,plain,
% 1.62/1.87 ($false),
% 1.62/1.87 inference(unit_resolution,[status(thm)],[806, 1157])).
% 1.62/1.87 tff(1159,plain,((~(s(s(elem!1)) = s(s(s(s(elem!1)))))) | (s(s(s(s(elem!1)))) = s(s(elem!1)))), inference(lemma,lemma(discharge,[]))).
% 1.62/1.87 tff(1160,plain,
% 1.62/1.87 (s(s(s(s(elem!1)))) = s(s(elem!1))),
% 1.62/1.87 inference(unit_resolution,[status(thm)],[1159, 1153])).
% 1.62/1.87 tff(1161,assumption,(s(s(s(s(elem!1)))) = s(s(elem!1))), introduced(assumption)).
% 1.62/1.87 tff(1162,plain,
% 1.62/1.87 (inj_0(s(s(s(s(elem!1))))) = inj_0(s(s(elem!1)))),
% 1.62/1.87 inference(monotonicity,[status(thm)],[1161])).
% 1.62/1.87 tff(1163,plain,
% 1.62/1.87 (s(s(s(elem!1))) = s(elem!1)),
% 1.62/1.87 inference(transitivity,[status(thm)],[653, 1162, 38])).
% 1.62/1.87 tff(1164,assumption,(~(s(s(s(elem!1))) = s(elem!1))), introduced(assumption)).
% 1.62/1.87 tff(1165,plain,
% 1.62/1.87 ($false),
% 1.62/1.87 inference(unit_resolution,[status(thm)],[1164, 1163])).
% 1.62/1.87 tff(1166,plain,((~(s(s(s(s(elem!1)))) = s(s(elem!1)))) | (s(s(s(elem!1))) = s(elem!1))), inference(lemma,lemma(discharge,[]))).
% 1.62/1.87 tff(1167,plain,
% 1.62/1.87 (s(s(s(elem!1))) = s(elem!1)),
% 1.62/1.87 inference(unit_resolution,[status(thm)],[1166, 1160])).
% 1.62/1.87 tff(1168,plain,
% 1.62/1.87 (s(elem!1) = s(s(s(elem!1)))),
% 1.62/1.87 inference(symmetry,[status(thm)],[1167])).
% 1.62/1.87 tff(1169,plain,
% 1.62/1.87 (inj_0(s(elem!1)) = inj_0(s(s(s(elem!1))))),
% 1.62/1.87 inference(monotonicity,[status(thm)],[1168])).
% 1.62/1.87 tff(1170,plain,
% 1.62/1.87 (elem!1 = inj_0(s(elem!1))),
% 1.62/1.87 inference(symmetry,[status(thm)],[20])).
% 1.62/1.87 tff(1171,plain,
% 1.62/1.87 (elem!1 = s(s(elem!1))),
% 1.62/1.87 inference(transitivity,[status(thm)],[1170, 1169, 104])).
% 1.62/1.87 tff(1172,plain,
% 1.62/1.87 (b(elem!1, z) <=> b(s(s(elem!1)), z)),
% 1.62/1.87 inference(monotonicity,[status(thm)],[1171])).
% 1.62/1.87 tff(1173,assumption,(~(elem!1 = z)), introduced(assumption)).
% 1.62/1.87 tff(1174,plain,
% 1.62/1.87 (r(z, elem!1) <=> r(z, s(s(elem!1)))),
% 1.62/1.87 inference(monotonicity,[status(thm)],[1171])).
% 1.62/1.87 tff(1175,plain,
% 1.62/1.87 (r(z, s(s(elem!1))) <=> r(z, elem!1)),
% 1.62/1.87 inference(symmetry,[status(thm)],[1174])).
% 1.62/1.87 tff(1176,plain,
% 1.62/1.87 (r(z, elem!1)),
% 1.62/1.87 inference(modus_ponens,[status(thm)],[365, 1175])).
% 1.62/1.87 tff(1177,assumption,(s(s(s(elem!1))) = s(elem!1)), introduced(assumption)).
% 1.62/1.87 tff(1178,plain,
% 1.62/1.87 (r(s(s(s(elem!1))), z) <=> r(s(elem!1), z)),
% 1.62/1.87 inference(monotonicity,[status(thm)],[1177])).
% 1.62/1.87 tff(1179,plain,
% 1.62/1.87 (r(s(elem!1), z) <=> r(s(s(s(elem!1))), z)),
% 1.62/1.87 inference(symmetry,[status(thm)],[1178])).
% 1.62/1.87 tff(1180,plain,
% 1.62/1.87 ((~r(s(elem!1), z)) <=> (~r(s(s(s(elem!1))), z))),
% 1.62/1.87 inference(monotonicity,[status(thm)],[1179])).
% 1.62/1.87 tff(1181,assumption,(~r(s(elem!1), z)), introduced(assumption)).
% 1.62/1.87 tff(1182,plain,
% 1.62/1.87 (~r(s(s(s(elem!1))), z)),
% 1.62/1.87 inference(modus_ponens,[status(thm)],[1181, 1180])).
% 1.62/1.87 tff(1183,plain,
% 1.62/1.87 ($false),
% 1.62/1.87 inference(unit_resolution,[status(thm)],[154, 1182])).
% 1.62/1.87 tff(1184,plain,((~(s(s(s(elem!1))) = s(elem!1))) | (~r(s(s(s(elem!1))), z)) | r(s(elem!1), z)), inference(lemma,lemma(discharge,[]))).
% 1.62/1.87 tff(1185,plain,
% 1.62/1.87 (r(s(elem!1), z)),
% 1.62/1.87 inference(unit_resolution,[status(thm)],[1184, 1167, 154])).
% 1.62/1.87 tff(1186,plain,
% 1.62/1.87 ((s(elem!1) = s(s(elem!1))) <=> (s(s(elem!1)) = s(elem!1))),
% 1.62/1.87 inference(commutativity,[status(thm)],[])).
% 1.62/1.87 tff(1187,plain,
% 1.62/1.87 ((s(elem!1) = elem!1) <=> (s(elem!1) = s(s(elem!1)))),
% 1.62/1.87 inference(monotonicity,[status(thm)],[1171])).
% 1.62/1.87 tff(1188,plain,
% 1.62/1.87 ((s(elem!1) = elem!1) <=> (s(s(elem!1)) = s(elem!1))),
% 1.62/1.87 inference(transitivity,[status(thm)],[1187, 1186])).
% 1.62/1.87 tff(1189,plain,
% 1.62/1.87 ((s(s(elem!1)) = s(elem!1)) <=> (s(elem!1) = elem!1)),
% 1.62/1.87 inference(symmetry,[status(thm)],[1188])).
% 1.62/1.87 tff(1190,plain,
% 1.62/1.87 ((~(s(s(elem!1)) = s(elem!1))) <=> (~(s(elem!1) = elem!1))),
% 1.62/1.87 inference(monotonicity,[status(thm)],[1189])).
% 1.62/1.87 tff(1191,plain,
% 1.62/1.87 ((s(s(s(s(elem!1)))) = s(s(s(elem!1)))) <=> (s(s(s(elem!1))) = s(s(s(s(elem!1)))))),
% 1.62/1.87 inference(commutativity,[status(thm)],[])).
% 1.62/1.87 tff(1192,plain,
% 1.62/1.87 ((s(s(elem!1)) = s(elem!1)) <=> (s(s(s(s(elem!1)))) = s(s(s(elem!1))))),
% 1.62/1.87 inference(monotonicity,[status(thm)],[1153, 1168])).
% 1.62/1.87 tff(1193,plain,
% 1.62/1.87 ((s(s(elem!1)) = s(elem!1)) <=> (s(s(s(elem!1))) = s(s(s(s(elem!1)))))),
% 1.62/1.87 inference(transitivity,[status(thm)],[1192, 1191])).
% 1.62/1.87 tff(1194,plain,
% 1.62/1.87 ((s(s(s(elem!1))) = s(s(s(s(elem!1))))) <=> (s(s(elem!1)) = s(elem!1))),
% 1.62/1.87 inference(symmetry,[status(thm)],[1193])).
% 1.62/1.87 tff(1195,plain,
% 1.62/1.87 ((~(s(s(s(elem!1))) = s(s(s(s(elem!1)))))) <=> (~(s(s(elem!1)) = s(elem!1)))),
% 1.62/1.87 inference(monotonicity,[status(thm)],[1194])).
% 1.62/1.87 tff(1196,plain,
% 1.62/1.87 (~(s(s(elem!1)) = s(elem!1))),
% 1.62/1.87 inference(modus_ponens,[status(thm)],[361, 1195])).
% 1.62/1.87 tff(1197,plain,
% 1.62/1.87 (~(s(elem!1) = elem!1)),
% 1.62/1.87 inference(modus_ponens,[status(thm)],[1196, 1190])).
% 1.62/1.87 tff(1198,plain,
% 1.62/1.87 (elem!1 = s(s(s(s(elem!1))))),
% 1.62/1.87 inference(transitivity,[status(thm)],[1170, 1169, 104, 1153])).
% 1.62/1.87 tff(1199,plain,
% 1.62/1.87 (b(elem!1, s(z)) <=> b(s(s(s(s(elem!1)))), s(z))),
% 1.62/1.87 inference(monotonicity,[status(thm)],[1198])).
% 1.62/1.87 tff(1200,plain,
% 1.62/1.87 (b(s(s(s(s(elem!1)))), s(z)) <=> b(elem!1, s(z))),
% 1.62/1.87 inference(symmetry,[status(thm)],[1199])).
% 1.62/1.87 tff(1201,plain,
% 1.62/1.87 (b(s(s(elem!1)), s(z)) <=> b(s(s(s(s(elem!1)))), s(z))),
% 1.62/1.87 inference(monotonicity,[status(thm)],[1153])).
% 1.62/1.87 tff(1202,plain,
% 1.62/1.87 (b(s(s(s(s(elem!1)))), s(z))),
% 1.62/1.87 inference(modus_ponens,[status(thm)],[310, 1201])).
% 1.62/1.87 tff(1203,plain,
% 1.62/1.87 (b(elem!1, s(z))),
% 1.62/1.87 inference(modus_ponens,[status(thm)],[1202, 1200])).
% 1.62/1.87 tff(1204,plain,
% 1.62/1.87 (b(s(z), elem!1) <=> b(s(z), s(s(s(s(elem!1)))))),
% 1.62/1.87 inference(monotonicity,[status(thm)],[1198])).
% 1.62/1.87 tff(1205,plain,
% 1.62/1.87 (b(s(z), s(s(s(s(elem!1))))) <=> b(s(z), elem!1)),
% 1.62/1.87 inference(symmetry,[status(thm)],[1204])).
% 1.62/1.87 tff(1206,plain,
% 1.62/1.87 (b(s(z), s(s(elem!1))) <=> b(s(z), s(s(s(s(elem!1)))))),
% 1.62/1.87 inference(monotonicity,[status(thm)],[1153])).
% 1.62/1.87 tff(1207,plain,
% 1.62/1.87 (b(s(z), s(s(s(s(elem!1)))))),
% 1.62/1.87 inference(modus_ponens,[status(thm)],[376, 1206])).
% 1.62/1.87 tff(1208,plain,
% 1.62/1.87 (b(s(z), elem!1)),
% 1.62/1.87 inference(modus_ponens,[status(thm)],[1207, 1205])).
% 1.62/1.87 tff(1209,plain,
% 1.62/1.87 (b(s(z), s(s(s(elem!1)))) <=> b(s(z), s(elem!1))),
% 1.62/1.87 inference(monotonicity,[status(thm)],[1167])).
% 1.62/1.87 tff(1210,plain,
% 1.62/1.87 (b(s(z), s(elem!1))),
% 1.62/1.87 inference(modus_ponens,[status(thm)],[241, 1209])).
% 1.62/1.87 tff(1211,assumption,(b(s(z), s(elem!1))), introduced(assumption)).
% 1.62/1.87 tff(1212,assumption,(b(elem!1, s(z))), introduced(assumption)).
% 1.62/1.87 tff(1213,assumption,(b(s(elem!1), elem!1)), introduced(assumption)).
% 1.62/1.87 tff(1214,plain,
% 1.62/1.87 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(z))) | (~b(s(elem!1), elem!1)) | (~b(s(z), s(s(elem!1)))) | (~b(s(z), s(elem!1))) | (~b(s(z), elem!1)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(z))) | (~b(s(elem!1), elem!1)) | (~b(s(z), s(s(elem!1)))) | (~b(s(z), s(elem!1))) | (~b(s(z), elem!1)))),
% 1.62/1.87 inference(rewrite,[status(thm)],[])).
% 1.62/1.87 tff(1215,plain,
% 1.62/1.87 (((~b(s(z), s(s(elem!1)))) | (~b(s(z), s(s(elem!1)))) | (~b(elem!1, s(z))) | (~b(s(elem!1), elem!1)) | (~b(s(z), elem!1)) | (~b(s(z), s(elem!1)))) <=> ((~b(elem!1, s(z))) | (~b(s(elem!1), elem!1)) | (~b(s(z), s(s(elem!1)))) | (~b(s(z), s(elem!1))) | (~b(s(z), elem!1)))),
% 1.62/1.87 inference(rewrite,[status(thm)],[])).
% 1.62/1.87 tff(1216,plain,
% 1.62/1.87 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(elem!1)))) | (~b(s(z), s(s(elem!1)))) | (~b(elem!1, s(z))) | (~b(s(elem!1), elem!1)) | (~b(s(z), elem!1)) | (~b(s(z), s(elem!1))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(z))) | (~b(s(elem!1), elem!1)) | (~b(s(z), s(s(elem!1)))) | (~b(s(z), s(elem!1))) | (~b(s(z), elem!1))))),
% 1.62/1.87 inference(monotonicity,[status(thm)],[1215])).
% 1.62/1.87 tff(1217,plain,
% 1.62/1.87 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(elem!1)))) | (~b(s(z), s(s(elem!1)))) | (~b(elem!1, s(z))) | (~b(s(elem!1), elem!1)) | (~b(s(z), elem!1)) | (~b(s(z), s(elem!1))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(z))) | (~b(s(elem!1), elem!1)) | (~b(s(z), s(s(elem!1)))) | (~b(s(z), s(elem!1))) | (~b(s(z), elem!1)))),
% 1.62/1.87 inference(transitivity,[status(thm)],[1216, 1214])).
% 1.62/1.87 tff(1218,plain,
% 1.62/1.87 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(elem!1)))) | (~b(s(z), s(s(elem!1)))) | (~b(elem!1, s(z))) | (~b(s(elem!1), elem!1)) | (~b(s(z), elem!1)) | (~b(s(z), s(elem!1))))),
% 1.62/1.87 inference(quant_inst,[status(thm)],[])).
% 1.62/1.87 tff(1219,plain,
% 1.62/1.87 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(z))) | (~b(s(elem!1), elem!1)) | (~b(s(z), s(s(elem!1)))) | (~b(s(z), s(elem!1))) | (~b(s(z), elem!1))),
% 1.62/1.87 inference(modus_ponens,[status(thm)],[1218, 1217])).
% 1.62/1.87 tff(1220,plain,
% 1.62/1.87 ($false),
% 1.62/1.87 inference(unit_resolution,[status(thm)],[1219, 166, 376, 1213, 1212, 642, 1211])).
% 1.62/1.87 tff(1221,plain,((~b(elem!1, s(z))) | (~b(s(z), s(s(elem!1)))) | (~b(s(elem!1), elem!1)) | (~b(s(z), elem!1)) | (~b(s(z), s(elem!1)))), inference(lemma,lemma(discharge,[]))).
% 1.62/1.87 tff(1222,plain,
% 1.62/1.87 (~b(s(elem!1), elem!1)),
% 1.62/1.87 inference(unit_resolution,[status(thm)],[1221, 1210, 376, 1208, 1203])).
% 1.62/1.87 tff(1223,plain,
% 1.62/1.87 (((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((s(elem!1) = elem!1) | b(s(elem!1), elem!1) | r(s(elem!1), elem!1))) <=> ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (s(elem!1) = elem!1) | b(s(elem!1), elem!1) | r(s(elem!1), elem!1))),
% 1.62/1.87 inference(rewrite,[status(thm)],[])).
% 1.62/1.87 tff(1224,plain,
% 1.62/1.87 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((s(elem!1) = elem!1) | b(s(elem!1), elem!1) | r(s(elem!1), elem!1))),
% 1.62/1.87 inference(quant_inst,[status(thm)],[])).
% 1.62/1.87 tff(1225,plain,
% 1.62/1.87 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (s(elem!1) = elem!1) | b(s(elem!1), elem!1) | r(s(elem!1), elem!1)),
% 1.62/1.87 inference(modus_ponens,[status(thm)],[1224, 1223])).
% 1.62/1.87 tff(1226,plain,
% 1.62/1.87 ((s(elem!1) = elem!1) | b(s(elem!1), elem!1) | r(s(elem!1), elem!1)),
% 1.62/1.87 inference(unit_resolution,[status(thm)],[1225, 79])).
% 1.62/1.87 tff(1227,plain,
% 1.62/1.87 (r(s(elem!1), elem!1)),
% 1.62/1.87 inference(unit_resolution,[status(thm)],[1226, 1222, 1197])).
% 1.62/1.87 tff(1228,plain,
% 1.62/1.87 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, z)) | (~r(s(elem!1), elem!1)) | (~r(z, elem!1)) | (~r(s(elem!1), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(elem!1, z)) | (~r(s(elem!1), elem!1)) | (~r(z, elem!1)) | (~r(s(elem!1), z)))),
% 1.62/1.87 inference(rewrite,[status(thm)],[])).
% 1.62/1.87 tff(1229,plain,
% 1.62/1.87 (((~r(z, elem!1)) | (~r(elem!1, z)) | (~r(s(elem!1), z)) | (~r(s(elem!1), elem!1))) <=> ((~r(elem!1, z)) | (~r(s(elem!1), elem!1)) | (~r(z, elem!1)) | (~r(s(elem!1), z)))),
% 1.62/1.87 inference(rewrite,[status(thm)],[])).
% 1.62/1.87 tff(1230,plain,
% 1.62/1.87 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, elem!1)) | (~r(elem!1, z)) | (~r(s(elem!1), z)) | (~r(s(elem!1), elem!1)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, z)) | (~r(s(elem!1), elem!1)) | (~r(z, elem!1)) | (~r(s(elem!1), z))))),
% 1.62/1.87 inference(monotonicity,[status(thm)],[1229])).
% 1.62/1.87 tff(1231,plain,
% 1.62/1.87 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, elem!1)) | (~r(elem!1, z)) | (~r(s(elem!1), z)) | (~r(s(elem!1), elem!1)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(elem!1, z)) | (~r(s(elem!1), elem!1)) | (~r(z, elem!1)) | (~r(s(elem!1), z)))),
% 1.62/1.87 inference(transitivity,[status(thm)],[1230, 1228])).
% 1.62/1.87 tff(1232,plain,
% 1.62/1.87 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, elem!1)) | (~r(elem!1, z)) | (~r(s(elem!1), z)) | (~r(s(elem!1), elem!1)))),
% 1.62/1.87 inference(quant_inst,[status(thm)],[])).
% 1.62/1.87 tff(1233,plain,
% 1.62/1.87 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(elem!1, z)) | (~r(s(elem!1), elem!1)) | (~r(z, elem!1)) | (~r(s(elem!1), z))),
% 1.62/1.87 inference(modus_ponens,[status(thm)],[1232, 1231])).
% 1.62/1.87 tff(1234,plain,
% 1.62/1.87 ((~r(elem!1, z)) | (~r(s(elem!1), elem!1)) | (~r(z, elem!1)) | (~r(s(elem!1), z))),
% 1.62/1.87 inference(unit_resolution,[status(thm)],[1233, 197])).
% 1.62/1.87 tff(1235,plain,
% 1.62/1.87 (~r(elem!1, z)),
% 1.62/1.87 inference(unit_resolution,[status(thm)],[1234, 1227, 1185, 1176])).
% 1.62/1.87 tff(1236,plain,
% 1.62/1.87 (((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((elem!1 = z) | b(elem!1, z) | r(elem!1, z))) <=> ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (elem!1 = z) | b(elem!1, z) | r(elem!1, z))),
% 1.62/1.87 inference(rewrite,[status(thm)],[])).
% 1.62/1.87 tff(1237,plain,
% 1.62/1.87 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((elem!1 = z) | b(elem!1, z) | r(elem!1, z))),
% 1.62/1.87 inference(quant_inst,[status(thm)],[])).
% 1.62/1.87 tff(1238,plain,
% 1.62/1.87 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (elem!1 = z) | b(elem!1, z) | r(elem!1, z)),
% 1.62/1.87 inference(modus_ponens,[status(thm)],[1237, 1236])).
% 1.62/1.87 tff(1239,plain,
% 1.62/1.87 ((elem!1 = z) | b(elem!1, z) | r(elem!1, z)),
% 1.62/1.87 inference(unit_resolution,[status(thm)],[1238, 79])).
% 1.62/1.87 tff(1240,plain,
% 1.62/1.87 (b(elem!1, z)),
% 1.62/1.87 inference(unit_resolution,[status(thm)],[1239, 1235, 1173])).
% 1.62/1.87 tff(1241,plain,
% 1.62/1.87 (b(s(s(elem!1)), z)),
% 1.62/1.87 inference(modus_ponens,[status(thm)],[1240, 1172])).
% 1.62/1.87 tff(1242,plain,
% 1.62/1.87 (b(s(s(s(s(elem!1)))), z)),
% 1.62/1.87 inference(modus_ponens,[status(thm)],[1241, 1156])).
% 1.62/1.88 tff(1243,plain,
% 1.62/1.88 (b(z, s(s(s(elem!1)))) <=> b(z, s(elem!1))),
% 1.62/1.88 inference(monotonicity,[status(thm)],[1167])).
% 1.62/1.88 tff(1244,plain,
% 1.62/1.88 (b(z, s(elem!1))),
% 1.62/1.88 inference(modus_ponens,[status(thm)],[240, 1243])).
% 1.62/1.88 tff(1245,plain,
% 1.62/1.88 (r(s(s(s(elem!1))), s(s(z))) <=> r(s(elem!1), s(s(z)))),
% 1.62/1.88 inference(monotonicity,[status(thm)],[1177])).
% 1.62/1.88 tff(1246,plain,
% 1.62/1.88 (r(s(elem!1), s(s(z))) <=> r(s(s(s(elem!1))), s(s(z)))),
% 1.62/1.88 inference(symmetry,[status(thm)],[1245])).
% 1.62/1.88 tff(1247,assumption,(r(s(elem!1), s(s(z)))), introduced(assumption)).
% 1.62/1.88 tff(1248,plain,
% 1.62/1.88 (r(s(s(s(elem!1))), s(s(z)))),
% 1.62/1.88 inference(modus_ponens,[status(thm)],[1247, 1246])).
% 1.62/1.88 tff(1249,plain,
% 1.62/1.88 ($false),
% 1.62/1.88 inference(unit_resolution,[status(thm)],[213, 1248])).
% 1.62/1.88 tff(1250,plain,((~r(s(elem!1), s(s(z)))) | r(s(s(s(elem!1))), s(s(z))) | (~(s(s(s(elem!1))) = s(elem!1)))), inference(lemma,lemma(discharge,[]))).
% 1.62/1.88 tff(1251,plain,
% 1.62/1.88 (~r(s(elem!1), s(s(z)))),
% 1.62/1.88 inference(unit_resolution,[status(thm)],[1250, 1167, 213])).
% 1.62/1.88 tff(1252,plain,
% 1.62/1.88 ((s(s(z)) = s(elem!1)) <=> (s(elem!1) = s(s(z)))),
% 1.62/1.88 inference(commutativity,[status(thm)],[])).
% 1.62/1.88 tff(1253,plain,
% 1.62/1.88 ((s(s(z)) = s(s(s(elem!1)))) <=> (s(s(z)) = s(elem!1))),
% 1.62/1.88 inference(monotonicity,[status(thm)],[1167])).
% 1.62/1.88 tff(1254,plain,
% 1.62/1.88 ((s(s(z)) = s(s(s(elem!1)))) <=> (s(elem!1) = s(s(z)))),
% 1.62/1.88 inference(transitivity,[status(thm)],[1253, 1252])).
% 1.62/1.88 tff(1255,plain,
% 1.62/1.88 ((~(s(s(z)) = s(s(s(elem!1))))) <=> (~(s(elem!1) = s(s(z))))),
% 1.62/1.88 inference(monotonicity,[status(thm)],[1254])).
% 1.62/1.88 tff(1256,plain,
% 1.62/1.88 (~(s(elem!1) = s(s(z)))),
% 1.62/1.88 inference(modus_ponens,[status(thm)],[209, 1255])).
% 1.62/1.88 tff(1257,plain,
% 1.62/1.88 (((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((s(elem!1) = s(s(z))) | b(s(elem!1), s(s(z))) | r(s(elem!1), s(s(z))))) <=> ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (s(elem!1) = s(s(z))) | b(s(elem!1), s(s(z))) | r(s(elem!1), s(s(z))))),
% 1.62/1.88 inference(rewrite,[status(thm)],[])).
% 1.62/1.88 tff(1258,plain,
% 1.62/1.88 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((s(elem!1) = s(s(z))) | b(s(elem!1), s(s(z))) | r(s(elem!1), s(s(z))))),
% 1.62/1.88 inference(quant_inst,[status(thm)],[])).
% 1.62/1.88 tff(1259,plain,
% 1.62/1.88 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (s(elem!1) = s(s(z))) | b(s(elem!1), s(s(z))) | r(s(elem!1), s(s(z)))),
% 1.62/1.88 inference(modus_ponens,[status(thm)],[1258, 1257])).
% 1.62/1.88 tff(1260,plain,
% 1.62/1.88 ((s(elem!1) = s(s(z))) | b(s(elem!1), s(s(z))) | r(s(elem!1), s(s(z)))),
% 1.62/1.88 inference(unit_resolution,[status(thm)],[1259, 79])).
% 1.62/1.88 tff(1261,plain,
% 1.62/1.88 (b(s(elem!1), s(s(z)))),
% 1.62/1.88 inference(unit_resolution,[status(thm)],[1260, 1256, 1251])).
% 1.62/1.88 tff(1262,plain,
% 1.62/1.88 (b(s(s(elem!1)), s(s(z))) <=> b(s(s(s(s(elem!1)))), s(s(z)))),
% 1.62/1.88 inference(monotonicity,[status(thm)],[1153])).
% 1.62/1.88 tff(1263,plain,
% 1.62/1.88 (b(s(s(s(s(elem!1)))), s(s(z)))),
% 1.62/1.88 inference(modus_ponens,[status(thm)],[405, 1262])).
% 1.62/1.88 tff(1264,plain,
% 1.62/1.88 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), z)) | (~b(z, s(elem!1))) | (~b(s(s(s(s(elem!1)))), s(z))) | (~b(s(elem!1), s(s(z)))) | (~b(s(s(s(s(elem!1)))), s(s(z)))) | (~b(s(s(s(s(elem!1)))), z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), z)) | (~b(z, s(elem!1))) | (~b(s(s(s(s(elem!1)))), s(z))) | (~b(s(elem!1), s(s(z)))) | (~b(s(s(s(s(elem!1)))), s(s(z)))) | (~b(s(s(s(s(elem!1)))), z)))),
% 1.62/1.88 inference(rewrite,[status(thm)],[])).
% 1.62/1.88 tff(1265,plain,
% 1.62/1.88 (((~b(s(elem!1), s(s(z)))) | (~b(s(s(s(s(elem!1)))), s(s(z)))) | (~b(z, s(elem!1))) | (~b(s(z), z)) | (~b(s(s(s(s(elem!1)))), z)) | (~b(s(s(s(s(elem!1)))), s(z)))) <=> ((~b(s(z), z)) | (~b(z, s(elem!1))) | (~b(s(s(s(s(elem!1)))), s(z))) | (~b(s(elem!1), s(s(z)))) | (~b(s(s(s(s(elem!1)))), s(s(z)))) | (~b(s(s(s(s(elem!1)))), z)))),
% 1.62/1.88 inference(rewrite,[status(thm)],[])).
% 1.62/1.88 tff(1266,plain,
% 1.62/1.88 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), s(s(z)))) | (~b(s(s(s(s(elem!1)))), s(s(z)))) | (~b(z, s(elem!1))) | (~b(s(z), z)) | (~b(s(s(s(s(elem!1)))), z)) | (~b(s(s(s(s(elem!1)))), s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), z)) | (~b(z, s(elem!1))) | (~b(s(s(s(s(elem!1)))), s(z))) | (~b(s(elem!1), s(s(z)))) | (~b(s(s(s(s(elem!1)))), s(s(z)))) | (~b(s(s(s(s(elem!1)))), z))))),
% 1.62/1.88 inference(monotonicity,[status(thm)],[1265])).
% 1.62/1.88 tff(1267,plain,
% 1.62/1.88 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), s(s(z)))) | (~b(s(s(s(s(elem!1)))), s(s(z)))) | (~b(z, s(elem!1))) | (~b(s(z), z)) | (~b(s(s(s(s(elem!1)))), z)) | (~b(s(s(s(s(elem!1)))), s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), z)) | (~b(z, s(elem!1))) | (~b(s(s(s(s(elem!1)))), s(z))) | (~b(s(elem!1), s(s(z)))) | (~b(s(s(s(s(elem!1)))), s(s(z)))) | (~b(s(s(s(s(elem!1)))), z)))),
% 1.62/1.88 inference(transitivity,[status(thm)],[1266, 1264])).
% 1.62/1.88 tff(1268,plain,
% 1.62/1.88 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), s(s(z)))) | (~b(s(s(s(s(elem!1)))), s(s(z)))) | (~b(z, s(elem!1))) | (~b(s(z), z)) | (~b(s(s(s(s(elem!1)))), z)) | (~b(s(s(s(s(elem!1)))), s(z))))),
% 1.62/1.88 inference(quant_inst,[status(thm)],[])).
% 1.62/1.88 tff(1269,plain,
% 1.62/1.88 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), z)) | (~b(z, s(elem!1))) | (~b(s(s(s(s(elem!1)))), s(z))) | (~b(s(elem!1), s(s(z)))) | (~b(s(s(s(s(elem!1)))), s(s(z)))) | (~b(s(s(s(s(elem!1)))), z))),
% 1.62/1.88 inference(modus_ponens,[status(thm)],[1268, 1267])).
% 1.62/1.88 tff(1270,plain,
% 1.62/1.88 (~b(s(s(s(s(elem!1)))), z)),
% 1.62/1.88 inference(unit_resolution,[status(thm)],[1269, 166, 1263, 53, 1261, 1202, 1244])).
% 1.62/1.88 tff(1271,plain,
% 1.62/1.88 ($false),
% 1.62/1.88 inference(unit_resolution,[status(thm)],[1270, 1242])).
% 1.62/1.88 tff(1272,plain,((~(s(s(elem!1)) = s(s(s(s(elem!1)))))) | (~b(s(z), z)) | (elem!1 = z) | (~b(s(z), s(s(elem!1)))) | (~r(z, s(s(elem!1)))) | (s(s(s(elem!1))) = s(s(s(s(elem!1))))) | (~b(z, s(s(s(elem!1))))) | (~b(s(z), s(s(s(elem!1))))) | (~b(s(s(elem!1)), s(z))) | (~b(s(s(elem!1)), s(s(z)))) | (~r(s(s(s(elem!1))), z)) | r(s(s(s(elem!1))), s(s(z)))), inference(lemma,lemma(discharge,[]))).
% 1.62/1.88 tff(1273,plain,
% 1.62/1.88 (~(s(s(elem!1)) = s(s(s(s(elem!1)))))),
% 1.62/1.88 inference(unit_resolution,[status(thm)],[1272, 1152, 53, 375, 365, 358, 1145, 924, 310, 541, 154, 571])).
% 1.62/1.88 tff(1274,plain,
% 1.62/1.88 (b(s(s(elem!1)), s(s(s(s(elem!1)))))),
% 1.62/1.88 inference(unit_resolution,[status(thm)],[827, 1273, 570])).
% 1.62/1.88 tff(1275,plain,
% 1.62/1.88 ((s(s(z)) = s(s(s(s(elem!1))))) <=> (s(s(s(s(elem!1)))) = s(s(z)))),
% 1.62/1.88 inference(commutativity,[status(thm)],[])).
% 1.62/1.88 tff(1276,plain,
% 1.62/1.88 ((s(s(s(s(elem!1)))) = s(s(z))) <=> (s(s(z)) = s(s(s(s(elem!1)))))),
% 1.62/1.88 inference(symmetry,[status(thm)],[1275])).
% 1.62/1.88 tff(1277,plain,
% 1.62/1.88 ((~(s(s(s(s(elem!1)))) = s(s(z)))) <=> (~(s(s(z)) = s(s(s(s(elem!1))))))),
% 1.62/1.88 inference(monotonicity,[status(thm)],[1276])).
% 1.62/1.88 tff(1278,plain,
% 1.62/1.88 (~(s(s(z)) = s(s(s(s(elem!1)))))),
% 1.62/1.88 inference(modus_ponens,[status(thm)],[733, 1277])).
% 1.62/1.88 tff(1279,plain,
% 1.62/1.88 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), z)) | (~r(s(s(z)), s(s(s(elem!1))))) | (~r(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~r(s(s(z)), s(s(s(s(elem!1)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(elem!1))), z)) | (~r(s(s(z)), s(s(s(elem!1))))) | (~r(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~r(s(s(z)), s(s(s(s(elem!1)))))))),
% 1.62/1.88 inference(rewrite,[status(thm)],[])).
% 1.62/1.88 tff(1280,plain,
% 1.62/1.88 (((~r(s(s(s(elem!1))), z)) | (~r(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~r(s(s(z)), s(s(s(elem!1))))) | (~r(s(s(z)), s(s(s(s(elem!1))))))) <=> ((~r(s(s(s(elem!1))), z)) | (~r(s(s(z)), s(s(s(elem!1))))) | (~r(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~r(s(s(z)), s(s(s(s(elem!1)))))))),
% 1.62/1.88 inference(rewrite,[status(thm)],[])).
% 1.62/1.88 tff(1281,plain,
% 1.62/1.88 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), z)) | (~r(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~r(s(s(z)), s(s(s(elem!1))))) | (~r(s(s(z)), s(s(s(s(elem!1)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), z)) | (~r(s(s(z)), s(s(s(elem!1))))) | (~r(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~r(s(s(z)), s(s(s(s(elem!1))))))))),
% 1.62/1.88 inference(monotonicity,[status(thm)],[1280])).
% 1.62/1.88 tff(1282,plain,
% 1.62/1.88 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), z)) | (~r(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~r(s(s(z)), s(s(s(elem!1))))) | (~r(s(s(z)), s(s(s(s(elem!1)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(elem!1))), z)) | (~r(s(s(z)), s(s(s(elem!1))))) | (~r(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~r(s(s(z)), s(s(s(s(elem!1)))))))),
% 1.62/1.88 inference(transitivity,[status(thm)],[1281, 1279])).
% 1.62/1.88 tff(1283,plain,
% 1.62/1.88 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), z)) | (~r(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~r(s(s(z)), s(s(s(elem!1))))) | (~r(s(s(z)), s(s(s(s(elem!1)))))))),
% 1.62/1.88 inference(quant_inst,[status(thm)],[])).
% 1.62/1.88 tff(1284,plain,
% 1.62/1.88 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(elem!1))), z)) | (~r(s(s(z)), s(s(s(elem!1))))) | (~r(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~r(s(s(z)), s(s(s(s(elem!1))))))),
% 1.62/1.88 inference(modus_ponens,[status(thm)],[1283, 1282])).
% 1.62/1.88 tff(1285,plain,
% 1.62/1.88 (~r(s(s(z)), s(s(s(s(elem!1)))))),
% 1.62/1.88 inference(unit_resolution,[status(thm)],[1284, 197, 154, 281, 1048])).
% 1.62/1.88 tff(1286,plain,
% 1.62/1.88 (((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((s(s(z)) = s(s(s(s(elem!1))))) | b(s(s(z)), s(s(s(s(elem!1))))) | r(s(s(z)), s(s(s(s(elem!1))))))) <=> ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (s(s(z)) = s(s(s(s(elem!1))))) | b(s(s(z)), s(s(s(s(elem!1))))) | r(s(s(z)), s(s(s(s(elem!1))))))),
% 1.62/1.88 inference(rewrite,[status(thm)],[])).
% 1.62/1.88 tff(1287,plain,
% 1.62/1.88 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((s(s(z)) = s(s(s(s(elem!1))))) | b(s(s(z)), s(s(s(s(elem!1))))) | r(s(s(z)), s(s(s(s(elem!1))))))),
% 1.62/1.88 inference(quant_inst,[status(thm)],[])).
% 1.62/1.88 tff(1288,plain,
% 1.62/1.88 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (s(s(z)) = s(s(s(s(elem!1))))) | b(s(s(z)), s(s(s(s(elem!1))))) | r(s(s(z)), s(s(s(s(elem!1)))))),
% 1.62/1.88 inference(modus_ponens,[status(thm)],[1287, 1286])).
% 1.62/1.88 tff(1289,plain,
% 1.62/1.88 ((s(s(z)) = s(s(s(s(elem!1))))) | b(s(s(z)), s(s(s(s(elem!1)))))),
% 1.62/1.88 inference(unit_resolution,[status(thm)],[1288, 79, 1285])).
% 1.62/1.88 tff(1290,plain,
% 1.62/1.88 (b(s(s(z)), s(s(s(s(elem!1)))))),
% 1.62/1.88 inference(unit_resolution,[status(thm)],[1289, 1278])).
% 1.62/1.88 tff(1291,plain,
% 1.62/1.88 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), z)) | (~r(s(s(z)), s(s(s(elem!1))))) | (~r(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~r(s(s(s(s(elem!1)))), s(s(z)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(elem!1))), z)) | (~r(s(s(z)), s(s(s(elem!1))))) | (~r(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~r(s(s(s(s(elem!1)))), s(s(z)))))),
% 1.62/1.88 inference(rewrite,[status(thm)],[])).
% 1.62/1.88 tff(1292,plain,
% 1.62/1.88 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), z)) | (~r(s(s(z)), s(s(s(elem!1))))) | (~r(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~r(s(s(s(s(elem!1)))), s(s(z)))))),
% 1.62/1.88 inference(quant_inst,[status(thm)],[])).
% 1.62/1.88 tff(1293,plain,
% 1.62/1.88 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(elem!1))), z)) | (~r(s(s(z)), s(s(s(elem!1))))) | (~r(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~r(s(s(s(s(elem!1)))), s(s(z))))),
% 1.62/1.88 inference(modus_ponens,[status(thm)],[1292, 1291])).
% 1.62/1.88 tff(1294,plain,
% 1.62/1.88 (~r(s(s(s(s(elem!1)))), s(s(z)))),
% 1.62/1.88 inference(unit_resolution,[status(thm)],[1293, 197, 154, 281, 1048])).
% 1.62/1.88 tff(1295,plain,
% 1.62/1.88 (((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((s(s(s(s(elem!1)))) = s(s(z))) | b(s(s(s(s(elem!1)))), s(s(z))) | r(s(s(s(s(elem!1)))), s(s(z))))) <=> ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (s(s(s(s(elem!1)))) = s(s(z))) | b(s(s(s(s(elem!1)))), s(s(z))) | r(s(s(s(s(elem!1)))), s(s(z))))),
% 1.62/1.88 inference(rewrite,[status(thm)],[])).
% 1.62/1.88 tff(1296,plain,
% 1.62/1.88 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((s(s(s(s(elem!1)))) = s(s(z))) | b(s(s(s(s(elem!1)))), s(s(z))) | r(s(s(s(s(elem!1)))), s(s(z))))),
% 1.62/1.88 inference(quant_inst,[status(thm)],[])).
% 1.62/1.88 tff(1297,plain,
% 1.62/1.88 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (s(s(s(s(elem!1)))) = s(s(z))) | b(s(s(s(s(elem!1)))), s(s(z))) | r(s(s(s(s(elem!1)))), s(s(z)))),
% 1.62/1.88 inference(modus_ponens,[status(thm)],[1296, 1295])).
% 1.62/1.88 tff(1298,plain,
% 1.62/1.88 ((s(s(s(s(elem!1)))) = s(s(z))) | b(s(s(s(s(elem!1)))), s(s(z))) | r(s(s(s(s(elem!1)))), s(s(z)))),
% 1.62/1.88 inference(unit_resolution,[status(thm)],[1297, 79])).
% 1.62/1.88 tff(1299,plain,
% 1.62/1.88 (b(s(s(s(s(elem!1)))), s(s(z))) | r(s(s(s(s(elem!1)))), s(s(z)))),
% 1.62/1.88 inference(unit_resolution,[status(thm)],[1298, 733])).
% 1.62/1.88 tff(1300,plain,
% 1.62/1.88 (b(s(s(s(s(elem!1)))), s(s(z)))),
% 1.62/1.88 inference(unit_resolution,[status(thm)],[1299, 1294])).
% 1.62/1.88 tff(1301,plain,
% 1.62/1.88 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), s(s(z)))) | (~b(s(s(elem!1)), s(s(s(s(elem!1)))))) | (~b(s(s(z)), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), s(s(z)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(elem!1)), s(s(z)))) | (~b(s(s(elem!1)), s(s(s(s(elem!1)))))) | (~b(s(s(z)), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), s(s(z)))))),
% 1.62/1.88 inference(rewrite,[status(thm)],[])).
% 1.62/1.88 tff(1302,plain,
% 1.62/1.88 (((~b(s(s(z)), s(s(s(s(elem!1)))))) | (~b(s(s(elem!1)), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), s(s(z)))) | (~b(s(s(z)), s(s(s(s(elem!1)))))) | (~b(s(s(elem!1)), s(s(s(s(elem!1)))))) | (~b(s(s(elem!1)), s(s(z))))) <=> ((~b(s(s(elem!1)), s(s(z)))) | (~b(s(s(elem!1)), s(s(s(s(elem!1)))))) | (~b(s(s(z)), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), s(s(z)))))),
% 1.62/1.88 inference(rewrite,[status(thm)],[])).
% 1.62/1.88 tff(1303,plain,
% 1.62/1.88 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), s(s(s(s(elem!1)))))) | (~b(s(s(elem!1)), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), s(s(z)))) | (~b(s(s(z)), s(s(s(s(elem!1)))))) | (~b(s(s(elem!1)), s(s(s(s(elem!1)))))) | (~b(s(s(elem!1)), s(s(z)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), s(s(z)))) | (~b(s(s(elem!1)), s(s(s(s(elem!1)))))) | (~b(s(s(z)), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), s(s(z))))))),
% 1.62/1.88 inference(monotonicity,[status(thm)],[1302])).
% 1.62/1.88 tff(1304,plain,
% 1.62/1.88 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), s(s(s(s(elem!1)))))) | (~b(s(s(elem!1)), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), s(s(z)))) | (~b(s(s(z)), s(s(s(s(elem!1)))))) | (~b(s(s(elem!1)), s(s(s(s(elem!1)))))) | (~b(s(s(elem!1)), s(s(z)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(elem!1)), s(s(z)))) | (~b(s(s(elem!1)), s(s(s(s(elem!1)))))) | (~b(s(s(z)), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), s(s(z)))))),
% 1.62/1.88 inference(transitivity,[status(thm)],[1303, 1301])).
% 1.62/1.88 tff(1305,plain,
% 1.62/1.88 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), s(s(s(s(elem!1)))))) | (~b(s(s(elem!1)), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), s(s(z)))) | (~b(s(s(z)), s(s(s(s(elem!1)))))) | (~b(s(s(elem!1)), s(s(s(s(elem!1)))))) | (~b(s(s(elem!1)), s(s(z)))))),
% 1.62/1.88 inference(quant_inst,[status(thm)],[])).
% 1.62/1.88 tff(1306,plain,
% 1.62/1.88 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(elem!1)), s(s(z)))) | (~b(s(s(elem!1)), s(s(s(s(elem!1)))))) | (~b(s(s(z)), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), s(s(z))))),
% 1.62/1.88 inference(modus_ponens,[status(thm)],[1305, 1304])).
% 1.62/1.88 tff(1307,plain,
% 1.62/1.88 ($false),
% 1.62/1.88 inference(unit_resolution,[status(thm)],[1306, 166, 1300, 405, 1046, 1290])).
% 1.62/1.88 tff(1308,plain,((~r(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~b(s(s(elem!1)), s(s(z)))) | (~b(s(s(elem!1)), s(s(s(s(elem!1)))))) | (~r(s(s(s(elem!1))), z)) | (~r(s(s(z)), s(s(s(elem!1)))))), inference(lemma,lemma(discharge,[]))).
% 1.62/1.88 tff(1309,plain,
% 1.62/1.88 (~r(s(s(s(s(elem!1)))), s(s(s(elem!1))))),
% 1.62/1.88 inference(unit_resolution,[status(thm)],[1308, 541, 1274, 154, 531])).
% 1.62/1.88 tff(1310,plain,
% 1.62/1.88 (b(s(s(s(s(elem!1)))), s(s(s(elem!1))))),
% 1.62/1.88 inference(unit_resolution,[status(thm)],[1065, 1309, 364])).
% 1.62/1.88 tff(1311,assumption,(b(s(s(s(elem!1))), s(s(s(s(elem!1)))))), introduced(assumption)).
% 1.62/1.88 tff(1312,plain,
% 1.62/1.88 ($false),
% 1.62/1.88 inference(unit_resolution,[status(thm)],[1082, 166, 463, 1046, 1311, 1107])).
% 1.62/1.88 tff(1313,plain,((~b(s(s(s(elem!1))), s(s(s(s(elem!1)))))) | (~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(s(s(elem!1)), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), s(s(s(elem!1)))))), inference(lemma,lemma(discharge,[]))).
% 1.62/1.88 tff(1314,plain,
% 1.62/1.88 (~b(s(s(s(elem!1))), s(s(s(s(elem!1)))))),
% 1.62/1.88 inference(unit_resolution,[status(thm)],[1313, 462, 1274, 1310])).
% 1.62/1.88 tff(1315,plain,
% 1.62/1.88 (r(s(s(s(elem!1))), s(s(s(s(elem!1)))))),
% 1.62/1.88 inference(unit_resolution,[status(thm)],[696, 1314, 358])).
% 1.62/1.88 tff(1316,plain,
% 1.62/1.88 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), s(z))) | (~r(s(s(z)), s(z))) | (~r(s(z), s(s(s(s(elem!1)))))) | (~r(s(s(z)), s(s(s(elem!1))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(elem!1))), s(z))) | (~r(s(s(z)), s(z))) | (~r(s(z), s(s(s(s(elem!1)))))) | (~r(s(s(z)), s(s(s(elem!1))))))),
% 1.62/1.88 inference(rewrite,[status(thm)],[])).
% 1.62/1.88 tff(1317,plain,
% 1.62/1.88 (((~r(s(z), s(s(s(s(elem!1)))))) | (~r(s(s(s(elem!1))), s(z))) | (~r(s(s(z)), s(z))) | (~r(s(s(z)), s(s(s(elem!1)))))) <=> ((~r(s(s(s(elem!1))), s(z))) | (~r(s(s(z)), s(z))) | (~r(s(z), s(s(s(s(elem!1)))))) | (~r(s(s(z)), s(s(s(elem!1))))))),
% 1.62/1.88 inference(rewrite,[status(thm)],[])).
% 1.62/1.88 tff(1318,plain,
% 1.62/1.88 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(s(s(s(elem!1)))))) | (~r(s(s(s(elem!1))), s(z))) | (~r(s(s(z)), s(z))) | (~r(s(s(z)), s(s(s(elem!1))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), s(z))) | (~r(s(s(z)), s(z))) | (~r(s(z), s(s(s(s(elem!1)))))) | (~r(s(s(z)), s(s(s(elem!1)))))))),
% 1.62/1.88 inference(monotonicity,[status(thm)],[1317])).
% 1.62/1.88 tff(1319,plain,
% 1.62/1.88 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(s(s(s(elem!1)))))) | (~r(s(s(s(elem!1))), s(z))) | (~r(s(s(z)), s(z))) | (~r(s(s(z)), s(s(s(elem!1))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(elem!1))), s(z))) | (~r(s(s(z)), s(z))) | (~r(s(z), s(s(s(s(elem!1)))))) | (~r(s(s(z)), s(s(s(elem!1))))))),
% 1.62/1.88 inference(transitivity,[status(thm)],[1318, 1316])).
% 1.62/1.88 tff(1320,plain,
% 1.62/1.88 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(s(s(s(elem!1)))))) | (~r(s(s(s(elem!1))), s(z))) | (~r(s(s(z)), s(z))) | (~r(s(s(z)), s(s(s(elem!1))))))),
% 1.62/1.89 inference(quant_inst,[status(thm)],[])).
% 1.62/1.89 tff(1321,plain,
% 1.62/1.89 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(elem!1))), s(z))) | (~r(s(s(z)), s(z))) | (~r(s(z), s(s(s(s(elem!1)))))) | (~r(s(s(z)), s(s(s(elem!1)))))),
% 1.62/1.89 inference(modus_ponens,[status(thm)],[1320, 1319])).
% 1.62/1.89 tff(1322,plain,
% 1.62/1.89 ($false),
% 1.62/1.89 inference(unit_resolution,[status(thm)],[1321, 197, 350, 392, 699, 281])).
% 1.62/1.89 tff(1323,plain,((~r(s(z), s(s(s(s(elem!1)))))) | (~r(s(s(s(elem!1))), s(z))) | (~r(s(s(z)), s(z))) | (~r(s(s(z)), s(s(s(elem!1)))))), inference(lemma,lemma(discharge,[]))).
% 1.62/1.89 tff(1324,plain,
% 1.62/1.89 (~r(s(z), s(s(s(s(elem!1)))))),
% 1.62/1.89 inference(unit_resolution,[status(thm)],[1323, 551, 350, 531])).
% 1.62/1.89 tff(1325,plain,
% 1.62/1.89 (b(s(z), s(s(s(s(elem!1)))))),
% 1.62/1.89 inference(unit_resolution,[status(thm)],[681, 1324])).
% 1.62/1.89 tff(1326,assumption,(b(s(s(s(s(elem!1)))), z)), introduced(assumption)).
% 1.62/1.89 tff(1327,assumption,(b(s(z), s(s(s(s(elem!1)))))), introduced(assumption)).
% 1.62/1.89 tff(1328,plain,
% 1.62/1.89 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(z, s(s(s(elem!1))))) | (~b(s(s(elem!1)), s(z))) | (~b(s(s(elem!1)), s(s(s(s(elem!1)))))) | (~b(s(z), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(z, s(s(s(elem!1))))) | (~b(s(s(elem!1)), s(z))) | (~b(s(s(elem!1)), s(s(s(s(elem!1)))))) | (~b(s(z), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), z)))),
% 1.62/1.89 inference(rewrite,[status(thm)],[])).
% 1.62/1.89 tff(1329,plain,
% 1.62/1.89 (((~b(z, s(s(s(elem!1))))) | (~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(s(s(s(s(elem!1)))), z)) | (~b(s(z), s(s(s(s(elem!1)))))) | (~b(s(s(elem!1)), s(s(s(s(elem!1)))))) | (~b(s(s(elem!1)), s(z)))) <=> ((~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(z, s(s(s(elem!1))))) | (~b(s(s(elem!1)), s(z))) | (~b(s(s(elem!1)), s(s(s(s(elem!1)))))) | (~b(s(z), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), z)))),
% 1.62/1.89 inference(rewrite,[status(thm)],[])).
% 1.62/1.89 tff(1330,plain,
% 1.62/1.89 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(s(elem!1))))) | (~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(s(s(s(s(elem!1)))), z)) | (~b(s(z), s(s(s(s(elem!1)))))) | (~b(s(s(elem!1)), s(s(s(s(elem!1)))))) | (~b(s(s(elem!1)), s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(z, s(s(s(elem!1))))) | (~b(s(s(elem!1)), s(z))) | (~b(s(s(elem!1)), s(s(s(s(elem!1)))))) | (~b(s(z), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), z))))),
% 1.62/1.89 inference(monotonicity,[status(thm)],[1329])).
% 1.62/1.89 tff(1331,plain,
% 1.62/1.89 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(s(elem!1))))) | (~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(s(s(s(s(elem!1)))), z)) | (~b(s(z), s(s(s(s(elem!1)))))) | (~b(s(s(elem!1)), s(s(s(s(elem!1)))))) | (~b(s(s(elem!1)), s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(z, s(s(s(elem!1))))) | (~b(s(s(elem!1)), s(z))) | (~b(s(s(elem!1)), s(s(s(s(elem!1)))))) | (~b(s(z), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), z)))),
% 1.62/1.89 inference(transitivity,[status(thm)],[1330, 1328])).
% 1.62/1.89 tff(1332,plain,
% 1.62/1.89 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(s(elem!1))))) | (~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(s(s(s(s(elem!1)))), z)) | (~b(s(z), s(s(s(s(elem!1)))))) | (~b(s(s(elem!1)), s(s(s(s(elem!1)))))) | (~b(s(s(elem!1)), s(z))))),
% 1.62/1.89 inference(quant_inst,[status(thm)],[])).
% 1.62/1.89 tff(1333,plain,
% 1.62/1.89 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(z, s(s(s(elem!1))))) | (~b(s(s(elem!1)), s(z))) | (~b(s(s(elem!1)), s(s(s(s(elem!1)))))) | (~b(s(z), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), z))),
% 1.62/1.89 inference(modus_ponens,[status(thm)],[1332, 1331])).
% 1.62/1.89 tff(1334,plain,
% 1.62/1.89 ($false),
% 1.62/1.89 inference(unit_resolution,[status(thm)],[1333, 166, 463, 240, 310, 1046, 1327, 1326])).
% 1.62/1.89 tff(1335,plain,((~b(s(s(s(s(elem!1)))), z)) | (~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(z, s(s(s(elem!1))))) | (~b(s(s(elem!1)), s(z))) | (~b(s(s(elem!1)), s(s(s(s(elem!1)))))) | (~b(s(z), s(s(s(s(elem!1))))))), inference(lemma,lemma(discharge,[]))).
% 1.62/1.89 tff(1336,plain,
% 1.62/1.89 (~b(s(s(s(s(elem!1)))), z)),
% 1.62/1.89 inference(unit_resolution,[status(thm)],[1335, 462, 1145, 310, 1274, 1325])).
% 1.62/1.89 tff(1337,plain,
% 1.62/1.89 (((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((s(s(s(s(elem!1)))) = z) | b(s(s(s(s(elem!1)))), z) | r(s(s(s(s(elem!1)))), z))) <=> ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (s(s(s(s(elem!1)))) = z) | b(s(s(s(s(elem!1)))), z) | r(s(s(s(s(elem!1)))), z))),
% 1.62/1.89 inference(rewrite,[status(thm)],[])).
% 1.62/1.89 tff(1338,plain,
% 1.62/1.89 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((s(s(s(s(elem!1)))) = z) | b(s(s(s(s(elem!1)))), z) | r(s(s(s(s(elem!1)))), z))),
% 1.62/1.89 inference(quant_inst,[status(thm)],[])).
% 1.62/1.89 tff(1339,plain,
% 1.62/1.89 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (s(s(s(s(elem!1)))) = z) | b(s(s(s(s(elem!1)))), z) | r(s(s(s(s(elem!1)))), z)),
% 1.62/1.89 inference(modus_ponens,[status(thm)],[1338, 1337])).
% 1.62/1.89 tff(1340,plain,
% 1.62/1.89 (r(s(s(s(s(elem!1)))), z)),
% 1.62/1.89 inference(unit_resolution,[status(thm)],[1339, 79, 626, 1336])).
% 1.62/1.89 tff(1341,plain,
% 1.62/1.89 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), z)) | (~r(s(s(s(elem!1))), s(s(s(s(elem!1)))))) | (~r(z, s(s(z)))) | (~r(s(s(s(s(elem!1)))), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(elem!1))), z)) | (~r(s(s(s(elem!1))), s(s(s(s(elem!1)))))) | (~r(z, s(s(z)))) | (~r(s(s(s(s(elem!1)))), z)))),
% 1.62/1.89 inference(rewrite,[status(thm)],[])).
% 1.62/1.89 tff(1342,plain,
% 1.62/1.89 (((~r(z, s(s(z)))) | (~r(s(s(s(s(elem!1)))), z)) | (~r(s(s(s(elem!1))), z)) | (~r(s(s(s(elem!1))), s(s(s(s(elem!1))))))) <=> ((~r(s(s(s(elem!1))), z)) | (~r(s(s(s(elem!1))), s(s(s(s(elem!1)))))) | (~r(z, s(s(z)))) | (~r(s(s(s(s(elem!1)))), z)))),
% 1.62/1.89 inference(rewrite,[status(thm)],[])).
% 1.62/1.89 tff(1343,plain,
% 1.62/1.89 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(z)))) | (~r(s(s(s(s(elem!1)))), z)) | (~r(s(s(s(elem!1))), z)) | (~r(s(s(s(elem!1))), s(s(s(s(elem!1)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), z)) | (~r(s(s(s(elem!1))), s(s(s(s(elem!1)))))) | (~r(z, s(s(z)))) | (~r(s(s(s(s(elem!1)))), z))))),
% 1.62/1.89 inference(monotonicity,[status(thm)],[1342])).
% 1.62/1.89 tff(1344,plain,
% 1.62/1.89 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(z)))) | (~r(s(s(s(s(elem!1)))), z)) | (~r(s(s(s(elem!1))), z)) | (~r(s(s(s(elem!1))), s(s(s(s(elem!1)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(elem!1))), z)) | (~r(s(s(s(elem!1))), s(s(s(s(elem!1)))))) | (~r(z, s(s(z)))) | (~r(s(s(s(s(elem!1)))), z)))),
% 1.62/1.89 inference(transitivity,[status(thm)],[1343, 1341])).
% 1.62/1.89 tff(1345,plain,
% 1.62/1.89 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(z)))) | (~r(s(s(s(s(elem!1)))), z)) | (~r(s(s(s(elem!1))), z)) | (~r(s(s(s(elem!1))), s(s(s(s(elem!1)))))))),
% 1.62/1.89 inference(quant_inst,[status(thm)],[])).
% 1.62/1.89 tff(1346,plain,
% 1.62/1.89 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(elem!1))), z)) | (~r(s(s(s(elem!1))), s(s(s(s(elem!1)))))) | (~r(z, s(s(z)))) | (~r(s(s(s(s(elem!1)))), z))),
% 1.62/1.89 inference(modus_ponens,[status(thm)],[1345, 1344])).
% 1.62/1.89 tff(1347,plain,
% 1.62/1.89 ($false),
% 1.62/1.89 inference(unit_resolution,[status(thm)],[1346, 197, 154, 155, 1340, 1315])).
% 1.62/1.89 tff(1348,plain,((s(s(z)) = s(s(elem!1))) | (~r(s(s(s(elem!1))), z)) | (~r(z, s(s(z)))) | (~b(s(s(elem!1)), s(z))) | (~r(s(s(s(elem!1))), s(z))) | (~b(s(z), z)) | (~r(z, s(s(elem!1)))) | (~r(z, s(z))) | (s(s(elem!1)) = s(s(s(elem!1))))), inference(lemma,lemma(discharge,[]))).
% 1.62/1.89 tff(1349,plain,
% 1.62/1.89 (s(s(z)) = s(s(elem!1))),
% 1.62/1.89 inference(unit_resolution,[status(thm)],[1348, 154, 155, 310, 350, 53, 365, 323, 45])).
% 1.62/1.89 tff(1350,plain,
% 1.62/1.89 ((s(s(s(s(elem!1)))) = s(s(z))) <=> (s(s(s(s(elem!1)))) = s(s(elem!1)))),
% 1.62/1.89 inference(monotonicity,[status(thm)],[1349])).
% 1.62/1.89 tff(1351,plain,
% 1.62/1.89 ((s(s(s(s(elem!1)))) = s(s(z))) <=> (s(s(elem!1)) = s(s(s(s(elem!1)))))),
% 1.62/1.89 inference(transitivity,[status(thm)],[1350, 123])).
% 1.62/1.89 tff(1352,plain,
% 1.62/1.89 ((~(s(s(s(s(elem!1)))) = s(s(z)))) <=> (~(s(s(elem!1)) = s(s(s(s(elem!1))))))),
% 1.62/1.89 inference(monotonicity,[status(thm)],[1351])).
% 1.62/1.89 tff(1353,plain,
% 1.62/1.89 (~(s(s(elem!1)) = s(s(s(s(elem!1)))))),
% 1.62/1.89 inference(modus_ponens,[status(thm)],[733, 1352])).
% 1.62/1.89 tff(1354,plain,
% 1.62/1.89 (s(elem!1) = s(z)),
% 1.62/1.89 inference(unit_resolution,[status(thm)],[43, 1349])).
% 1.62/1.89 tff(1355,plain,
% 1.62/1.89 (z = elem!1),
% 1.62/1.89 inference(unit_resolution,[status(thm)],[30, 1354])).
% 1.62/1.89 tff(1356,plain,
% 1.62/1.89 (r(z, s(s(elem!1))) <=> r(elem!1, s(s(elem!1)))),
% 1.62/1.89 inference(monotonicity,[status(thm)],[1355])).
% 1.62/1.89 tff(1357,plain,
% 1.62/1.89 (r(elem!1, s(s(elem!1)))),
% 1.62/1.89 inference(modus_ponens,[status(thm)],[365, 1356])).
% 1.62/1.89 tff(1358,plain,
% 1.62/1.89 (r(s(s(s(elem!1))), elem!1)),
% 1.62/1.89 inference(unit_resolution,[status(thm)],[966, 1355, 154])).
% 1.62/1.89 tff(1359,plain,
% 1.62/1.89 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(z), s(s(s(elem!1))))) | (~b(s(z), s(s(elem!1)))) | (~b(s(s(elem!1)), s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(z), s(s(s(elem!1))))) | (~b(s(z), s(s(elem!1)))) | (~b(s(s(elem!1)), s(z))))),
% 1.62/1.89 inference(rewrite,[status(thm)],[])).
% 1.62/1.89 tff(1360,plain,
% 1.62/1.89 (((~b(s(z), s(s(elem!1)))) | (~b(s(z), s(s(elem!1)))) | (~b(s(s(elem!1)), s(z))) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(z), s(s(elem!1)))) | (~b(s(z), s(s(s(elem!1)))))) <=> ((~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(z), s(s(s(elem!1))))) | (~b(s(z), s(s(elem!1)))) | (~b(s(s(elem!1)), s(z))))),
% 1.62/1.89 inference(rewrite,[status(thm)],[])).
% 1.62/1.89 tff(1361,plain,
% 1.62/1.89 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(elem!1)))) | (~b(s(z), s(s(elem!1)))) | (~b(s(s(elem!1)), s(z))) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(z), s(s(elem!1)))) | (~b(s(z), s(s(s(elem!1))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(z), s(s(s(elem!1))))) | (~b(s(z), s(s(elem!1)))) | (~b(s(s(elem!1)), s(z)))))),
% 1.62/1.89 inference(monotonicity,[status(thm)],[1360])).
% 1.62/1.89 tff(1362,plain,
% 1.62/1.89 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(elem!1)))) | (~b(s(z), s(s(elem!1)))) | (~b(s(s(elem!1)), s(z))) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(z), s(s(elem!1)))) | (~b(s(z), s(s(s(elem!1))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(z), s(s(s(elem!1))))) | (~b(s(z), s(s(elem!1)))) | (~b(s(s(elem!1)), s(z))))),
% 1.62/1.89 inference(transitivity,[status(thm)],[1361, 1359])).
% 1.62/1.89 tff(1363,plain,
% 1.62/1.89 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(elem!1)))) | (~b(s(z), s(s(elem!1)))) | (~b(s(s(elem!1)), s(z))) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(z), s(s(elem!1)))) | (~b(s(z), s(s(s(elem!1))))))),
% 1.62/1.89 inference(quant_inst,[status(thm)],[])).
% 1.62/1.89 tff(1364,plain,
% 1.62/1.89 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(z), s(s(s(elem!1))))) | (~b(s(z), s(s(elem!1)))) | (~b(s(s(elem!1)), s(z)))),
% 1.62/1.89 inference(modus_ponens,[status(thm)],[1363, 1362])).
% 1.62/1.89 tff(1365,plain,
% 1.62/1.89 ($false),
% 1.62/1.89 inference(unit_resolution,[status(thm)],[1364, 166, 376, 839, 241, 310])).
% 1.62/1.89 tff(1366,plain,((~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(z), s(s(elem!1)))) | (~b(s(z), s(s(s(elem!1))))) | (~b(s(s(elem!1)), s(z)))), inference(lemma,lemma(discharge,[]))).
% 1.62/1.89 tff(1367,plain,
% 1.62/1.89 (~b(s(s(s(elem!1))), s(s(elem!1)))),
% 1.62/1.89 inference(unit_resolution,[status(thm)],[1366, 375, 924, 310])).
% 1.62/1.89 tff(1368,plain,
% 1.62/1.89 (r(s(s(s(elem!1))), s(s(elem!1)))),
% 1.62/1.89 inference(unit_resolution,[status(thm)],[889, 1367, 51])).
% 1.62/1.89 tff(1369,plain,
% 1.62/1.89 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(s(elem!1)))) | (~r(s(s(s(elem!1))), s(s(elem!1)))) | (~r(s(s(s(elem!1))), elem!1)) | (~r(s(s(elem!1)), s(s(s(s(elem!1)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(elem!1, s(s(elem!1)))) | (~r(s(s(s(elem!1))), s(s(elem!1)))) | (~r(s(s(s(elem!1))), elem!1)) | (~r(s(s(elem!1)), s(s(s(s(elem!1)))))))),
% 1.62/1.89 inference(rewrite,[status(thm)],[])).
% 1.62/1.89 tff(1370,plain,
% 1.62/1.89 (((~r(s(s(elem!1)), s(s(s(s(elem!1)))))) | (~r(elem!1, s(s(elem!1)))) | (~r(s(s(s(elem!1))), s(s(elem!1)))) | (~r(s(s(s(elem!1))), elem!1))) <=> ((~r(elem!1, s(s(elem!1)))) | (~r(s(s(s(elem!1))), s(s(elem!1)))) | (~r(s(s(s(elem!1))), elem!1)) | (~r(s(s(elem!1)), s(s(s(s(elem!1)))))))),
% 1.62/1.89 inference(rewrite,[status(thm)],[])).
% 1.62/1.89 tff(1371,plain,
% 1.62/1.89 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(elem!1)), s(s(s(s(elem!1)))))) | (~r(elem!1, s(s(elem!1)))) | (~r(s(s(s(elem!1))), s(s(elem!1)))) | (~r(s(s(s(elem!1))), elem!1)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(s(elem!1)))) | (~r(s(s(s(elem!1))), s(s(elem!1)))) | (~r(s(s(s(elem!1))), elem!1)) | (~r(s(s(elem!1)), s(s(s(s(elem!1))))))))),
% 1.62/1.89 inference(monotonicity,[status(thm)],[1370])).
% 1.62/1.89 tff(1372,plain,
% 1.62/1.89 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(elem!1)), s(s(s(s(elem!1)))))) | (~r(elem!1, s(s(elem!1)))) | (~r(s(s(s(elem!1))), s(s(elem!1)))) | (~r(s(s(s(elem!1))), elem!1)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(elem!1, s(s(elem!1)))) | (~r(s(s(s(elem!1))), s(s(elem!1)))) | (~r(s(s(s(elem!1))), elem!1)) | (~r(s(s(elem!1)), s(s(s(s(elem!1)))))))),
% 1.62/1.89 inference(transitivity,[status(thm)],[1371, 1369])).
% 1.62/1.89 tff(1373,plain,
% 1.62/1.89 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(elem!1)), s(s(s(s(elem!1)))))) | (~r(elem!1, s(s(elem!1)))) | (~r(s(s(s(elem!1))), s(s(elem!1)))) | (~r(s(s(s(elem!1))), elem!1)))),
% 1.62/1.89 inference(quant_inst,[status(thm)],[])).
% 1.62/1.89 tff(1374,plain,
% 1.62/1.89 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(elem!1, s(s(elem!1)))) | (~r(s(s(s(elem!1))), s(s(elem!1)))) | (~r(s(s(s(elem!1))), elem!1)) | (~r(s(s(elem!1)), s(s(s(s(elem!1))))))),
% 1.62/1.89 inference(modus_ponens,[status(thm)],[1373, 1372])).
% 1.62/1.89 tff(1375,plain,
% 1.62/1.89 ($false),
% 1.62/1.89 inference(unit_resolution,[status(thm)],[1374, 197, 905, 561, 1013, 1027])).
% 1.62/1.89 tff(1376,plain,((~r(s(s(elem!1)), s(s(s(s(elem!1)))))) | (~r(s(s(s(elem!1))), s(s(elem!1)))) | (~r(s(s(s(elem!1))), elem!1)) | (~r(elem!1, s(s(elem!1))))), inference(lemma,lemma(discharge,[]))).
% 1.62/1.89 tff(1377,plain,
% 1.62/1.89 (~r(s(s(elem!1)), s(s(s(s(elem!1)))))),
% 1.62/1.89 inference(unit_resolution,[status(thm)],[1376, 1368, 1358, 1357])).
% 1.62/1.89 tff(1378,plain,
% 1.62/1.89 (b(s(s(elem!1)), s(s(s(s(elem!1)))))),
% 1.62/1.89 inference(unit_resolution,[status(thm)],[827, 1377, 1353])).
% 1.62/1.89 tff(1379,plain,
% 1.62/1.89 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), z)) | (~r(s(s(s(elem!1))), s(s(elem!1)))) | (~r(z, s(s(elem!1)))) | (~r(s(s(elem!1)), s(s(s(elem!1))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(elem!1))), z)) | (~r(s(s(s(elem!1))), s(s(elem!1)))) | (~r(z, s(s(elem!1)))) | (~r(s(s(elem!1)), s(s(s(elem!1))))))),
% 1.62/1.89 inference(rewrite,[status(thm)],[])).
% 1.62/1.89 tff(1380,plain,
% 1.62/1.89 (((~r(s(s(elem!1)), s(s(s(elem!1))))) | (~r(z, s(s(elem!1)))) | (~r(s(s(s(elem!1))), s(s(elem!1)))) | (~r(s(s(s(elem!1))), z))) <=> ((~r(s(s(s(elem!1))), z)) | (~r(s(s(s(elem!1))), s(s(elem!1)))) | (~r(z, s(s(elem!1)))) | (~r(s(s(elem!1)), s(s(s(elem!1))))))),
% 1.62/1.89 inference(rewrite,[status(thm)],[])).
% 1.62/1.89 tff(1381,plain,
% 1.62/1.89 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(elem!1)), s(s(s(elem!1))))) | (~r(z, s(s(elem!1)))) | (~r(s(s(s(elem!1))), s(s(elem!1)))) | (~r(s(s(s(elem!1))), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), z)) | (~r(s(s(s(elem!1))), s(s(elem!1)))) | (~r(z, s(s(elem!1)))) | (~r(s(s(elem!1)), s(s(s(elem!1)))))))),
% 1.62/1.89 inference(monotonicity,[status(thm)],[1380])).
% 1.62/1.89 tff(1382,plain,
% 1.62/1.89 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(elem!1)), s(s(s(elem!1))))) | (~r(z, s(s(elem!1)))) | (~r(s(s(s(elem!1))), s(s(elem!1)))) | (~r(s(s(s(elem!1))), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(elem!1))), z)) | (~r(s(s(s(elem!1))), s(s(elem!1)))) | (~r(z, s(s(elem!1)))) | (~r(s(s(elem!1)), s(s(s(elem!1))))))),
% 1.62/1.89 inference(transitivity,[status(thm)],[1381, 1379])).
% 1.62/1.89 tff(1383,plain,
% 1.62/1.89 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(elem!1)), s(s(s(elem!1))))) | (~r(z, s(s(elem!1)))) | (~r(s(s(s(elem!1))), s(s(elem!1)))) | (~r(s(s(s(elem!1))), z)))),
% 1.62/1.89 inference(quant_inst,[status(thm)],[])).
% 1.62/1.89 tff(1384,plain,
% 1.62/1.89 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(elem!1))), z)) | (~r(s(s(s(elem!1))), s(s(elem!1)))) | (~r(z, s(s(elem!1)))) | (~r(s(s(elem!1)), s(s(s(elem!1)))))),
% 1.62/1.89 inference(modus_ponens,[status(thm)],[1383, 1382])).
% 1.62/1.89 tff(1385,plain,
% 1.62/1.89 ($false),
% 1.62/1.89 inference(unit_resolution,[status(thm)],[1384, 197, 154, 377, 365, 905])).
% 1.62/1.89 tff(1386,plain,((~r(s(s(s(elem!1))), s(s(elem!1)))) | (~r(s(s(s(elem!1))), z)) | (~r(s(s(elem!1)), s(s(s(elem!1))))) | (~r(z, s(s(elem!1))))), inference(lemma,lemma(discharge,[]))).
% 1.62/1.89 tff(1387,plain,
% 1.62/1.89 (~r(s(s(elem!1)), s(s(s(elem!1))))),
% 1.62/1.89 inference(unit_resolution,[status(thm)],[1386, 1368, 365, 154])).
% 1.62/1.89 tff(1388,plain,
% 1.62/1.89 (b(s(s(elem!1)), s(s(s(elem!1))))),
% 1.62/1.89 inference(unit_resolution,[status(thm)],[461, 1387, 45])).
% 1.62/1.89 tff(1389,plain,
% 1.62/1.89 ((s(s(s(s(elem!1)))) = z) <=> (s(s(s(s(elem!1)))) = elem!1)),
% 1.62/1.89 inference(monotonicity,[status(thm)],[1355])).
% 1.62/1.89 tff(1390,plain,
% 1.62/1.89 ((~(s(s(s(s(elem!1)))) = z)) <=> (~(s(s(s(s(elem!1)))) = elem!1))),
% 1.62/1.89 inference(monotonicity,[status(thm)],[1389])).
% 1.62/1.89 tff(1391,plain,
% 1.62/1.89 (~(s(s(s(s(elem!1)))) = elem!1)),
% 1.62/1.89 inference(modus_ponens,[status(thm)],[626, 1390])).
% 1.62/1.89 tff(1392,plain,
% 1.62/1.89 (r(elem!1, s(z))),
% 1.62/1.89 inference(unit_resolution,[status(thm)],[741, 1355, 323])).
% 1.62/1.89 tff(1393,plain,
% 1.62/1.89 (elem!1 = z),
% 1.62/1.89 inference(symmetry,[status(thm)],[1355])).
% 1.72/1.90 tff(1394,plain,
% 1.72/1.90 ((s(s(elem!1)) = elem!1) <=> (s(s(elem!1)) = z)),
% 1.72/1.90 inference(monotonicity,[status(thm)],[1393])).
% 1.72/1.90 tff(1395,plain,
% 1.72/1.90 ((s(s(elem!1)) = z) <=> (s(s(elem!1)) = elem!1)),
% 1.72/1.90 inference(symmetry,[status(thm)],[1394])).
% 1.72/1.90 tff(1396,plain,
% 1.72/1.90 ((~(s(s(elem!1)) = z)) <=> (~(s(s(elem!1)) = elem!1))),
% 1.72/1.90 inference(monotonicity,[status(thm)],[1395])).
% 1.72/1.90 tff(1397,plain,
% 1.72/1.90 (~(s(s(elem!1)) = elem!1)),
% 1.72/1.90 inference(modus_ponens,[status(thm)],[108, 1396])).
% 1.72/1.90 tff(1398,plain,
% 1.72/1.90 (~r(s(s(elem!1)), elem!1)),
% 1.72/1.90 inference(unit_resolution,[status(thm)],[1018, 1368, 1392, 1358])).
% 1.72/1.90 tff(1399,plain,
% 1.72/1.90 (b(s(s(elem!1)), elem!1)),
% 1.72/1.90 inference(unit_resolution,[status(thm)],[784, 1398, 1397])).
% 1.72/1.90 tff(1400,plain,
% 1.72/1.90 (b(s(z), z) <=> b(s(z), elem!1)),
% 1.72/1.90 inference(monotonicity,[status(thm)],[1355])).
% 1.72/1.90 tff(1401,plain,
% 1.72/1.90 (b(s(z), elem!1)),
% 1.72/1.90 inference(modus_ponens,[status(thm)],[53, 1400])).
% 1.72/1.90 tff(1402,assumption,(b(s(s(s(s(elem!1)))), s(z))), introduced(assumption)).
% 1.72/1.90 tff(1403,plain,
% 1.72/1.90 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(s(z), s(s(elem!1)))) | (~b(s(s(elem!1)), s(z))) | (~b(s(s(elem!1)), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(s(z), s(s(elem!1)))) | (~b(s(s(elem!1)), s(z))) | (~b(s(s(elem!1)), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), s(z))))),
% 1.72/1.90 inference(rewrite,[status(thm)],[])).
% 1.72/1.90 tff(1404,plain,
% 1.72/1.90 (((~b(s(s(elem!1)), 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(s(s(elem!1)))), s(z))) | (~b(s(s(elem!1)), s(z))) | (~b(s(s(elem!1)), s(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(z))) | (~b(s(s(elem!1)), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), s(z))))),
% 1.72/1.90 inference(rewrite,[status(thm)],[])).
% 1.72/1.90 tff(1405,plain,
% 1.72/1.90 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(s(z), s(s(elem!1)))) | (~b(s(s(s(s(elem!1)))), s(z))) | (~b(s(s(elem!1)), s(z))) | (~b(s(s(elem!1)), s(s(s(s(elem!1)))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(s(z), s(s(elem!1)))) | (~b(s(s(elem!1)), s(z))) | (~b(s(s(elem!1)), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), s(z)))))),
% 1.72/1.90 inference(monotonicity,[status(thm)],[1404])).
% 1.72/1.90 tff(1406,plain,
% 1.72/1.90 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(s(z), s(s(elem!1)))) | (~b(s(s(s(s(elem!1)))), s(z))) | (~b(s(s(elem!1)), s(z))) | (~b(s(s(elem!1)), s(s(s(s(elem!1)))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(s(z), s(s(elem!1)))) | (~b(s(s(elem!1)), s(z))) | (~b(s(s(elem!1)), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), s(z))))),
% 1.72/1.90 inference(transitivity,[status(thm)],[1405, 1403])).
% 1.72/1.90 tff(1407,plain,
% 1.72/1.90 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(s(z), s(s(elem!1)))) | (~b(s(s(s(s(elem!1)))), s(z))) | (~b(s(s(elem!1)), s(z))) | (~b(s(s(elem!1)), s(s(s(s(elem!1)))))))),
% 1.72/1.90 inference(quant_inst,[status(thm)],[])).
% 1.72/1.90 tff(1408,plain,
% 1.72/1.90 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(s(z), s(s(elem!1)))) | (~b(s(s(elem!1)), s(z))) | (~b(s(s(elem!1)), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), s(z)))),
% 1.72/1.90 inference(modus_ponens,[status(thm)],[1407, 1406])).
% 1.72/1.90 tff(1409,plain,
% 1.72/1.90 ($false),
% 1.72/1.90 inference(unit_resolution,[status(thm)],[1408, 166, 376, 463, 310, 1046, 1402])).
% 1.72/1.90 tff(1410,plain,((~b(s(s(s(s(elem!1)))), s(z))) | (~b(s(z), s(s(elem!1)))) | (~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(s(s(elem!1)), s(z))) | (~b(s(s(elem!1)), s(s(s(s(elem!1))))))), inference(lemma,lemma(discharge,[]))).
% 1.72/1.90 tff(1411,plain,
% 1.72/1.90 (~b(s(s(s(s(elem!1)))), s(z))),
% 1.72/1.90 inference(unit_resolution,[status(thm)],[1410, 1378, 375, 310, 1388])).
% 1.72/1.90 tff(1412,plain,
% 1.72/1.90 (r(s(s(s(s(elem!1)))), s(z))),
% 1.72/1.90 inference(unit_resolution,[status(thm)],[661, 1411])).
% 1.72/1.90 tff(1413,plain,
% 1.72/1.90 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(s(s(s(elem!1)))))) | (~r(elem!1, s(z))) | (~r(s(z), s(s(s(s(elem!1)))))) | (~r(s(s(s(s(elem!1)))), s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(elem!1, s(s(s(s(elem!1)))))) | (~r(elem!1, s(z))) | (~r(s(z), s(s(s(s(elem!1)))))) | (~r(s(s(s(s(elem!1)))), s(z))))),
% 1.72/1.90 inference(rewrite,[status(thm)],[])).
% 1.72/1.90 tff(1414,plain,
% 1.72/1.90 (((~r(s(s(s(s(elem!1)))), s(z))) | (~r(s(z), s(s(s(s(elem!1)))))) | (~r(elem!1, s(s(s(s(elem!1)))))) | (~r(elem!1, s(z)))) <=> ((~r(elem!1, s(s(s(s(elem!1)))))) | (~r(elem!1, s(z))) | (~r(s(z), s(s(s(s(elem!1)))))) | (~r(s(s(s(s(elem!1)))), s(z))))),
% 1.72/1.90 inference(rewrite,[status(thm)],[])).
% 1.72/1.90 tff(1415,plain,
% 1.72/1.90 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(elem!1)))), s(z))) | (~r(s(z), s(s(s(s(elem!1)))))) | (~r(elem!1, s(s(s(s(elem!1)))))) | (~r(elem!1, s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(s(s(s(elem!1)))))) | (~r(elem!1, s(z))) | (~r(s(z), s(s(s(s(elem!1)))))) | (~r(s(s(s(s(elem!1)))), s(z)))))),
% 1.72/1.90 inference(monotonicity,[status(thm)],[1414])).
% 1.72/1.90 tff(1416,plain,
% 1.72/1.90 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(elem!1)))), s(z))) | (~r(s(z), s(s(s(s(elem!1)))))) | (~r(elem!1, s(s(s(s(elem!1)))))) | (~r(elem!1, s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(elem!1, s(s(s(s(elem!1)))))) | (~r(elem!1, s(z))) | (~r(s(z), s(s(s(s(elem!1)))))) | (~r(s(s(s(s(elem!1)))), s(z))))),
% 1.72/1.90 inference(transitivity,[status(thm)],[1415, 1413])).
% 1.72/1.90 tff(1417,plain,
% 1.72/1.90 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(elem!1)))), s(z))) | (~r(s(z), s(s(s(s(elem!1)))))) | (~r(elem!1, s(s(s(s(elem!1)))))) | (~r(elem!1, s(z))))),
% 1.72/1.90 inference(quant_inst,[status(thm)],[])).
% 1.72/1.90 tff(1418,plain,
% 1.72/1.90 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(elem!1, s(s(s(s(elem!1)))))) | (~r(elem!1, s(z))) | (~r(s(z), s(s(s(s(elem!1)))))) | (~r(s(s(s(s(elem!1)))), s(z)))),
% 1.72/1.90 inference(modus_ponens,[status(thm)],[1417, 1416])).
% 1.72/1.90 tff(1419,plain,
% 1.72/1.90 ($false),
% 1.72/1.90 inference(unit_resolution,[status(thm)],[1418, 197, 744, 700, 699, 1047])).
% 1.72/1.90 tff(1420,plain,((~r(s(z), s(s(s(s(elem!1)))))) | (~r(elem!1, s(z))) | (~r(s(s(s(s(elem!1)))), s(z))) | (~r(elem!1, s(s(s(s(elem!1))))))), inference(lemma,lemma(discharge,[]))).
% 1.72/1.90 tff(1421,plain,
% 1.72/1.90 (~r(elem!1, s(s(s(s(elem!1)))))),
% 1.72/1.90 inference(unit_resolution,[status(thm)],[1420, 699, 744, 700])).
% 1.72/1.90 tff(1422,plain,
% 1.72/1.90 (~r(elem!1, s(s(s(s(z)))))),
% 1.72/1.90 inference(unit_resolution,[status(thm)],[1093, 1421, 34])).
% 1.72/1.90 tff(1423,plain,
% 1.72/1.90 (b(elem!1, s(s(s(s(z)))))),
% 1.72/1.90 inference(unit_resolution,[status(thm)],[1098, 1422, 1045])).
% 1.72/1.90 tff(1424,plain,
% 1.72/1.90 (b(elem!1, s(s(s(s(elem!1)))))),
% 1.72/1.90 inference(unit_resolution,[status(thm)],[1105, 1423, 34])).
% 1.72/1.90 tff(1425,plain,
% 1.72/1.90 (~b(s(s(s(s(elem!1)))), s(s(s(elem!1))))),
% 1.72/1.90 inference(unit_resolution,[status(thm)],[1116, 1424, 642, 310, 786, 463])).
% 1.72/1.90 tff(1426,plain,
% 1.72/1.90 (r(s(s(s(s(elem!1)))), s(s(s(elem!1))))),
% 1.72/1.90 inference(unit_resolution,[status(thm)],[1065, 1425, 1058])).
% 1.72/1.90 tff(1427,plain,
% 1.72/1.90 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), s(z))) | (~r(s(z), s(s(s(s(elem!1)))))) | (~r(s(s(s(s(elem!1)))), s(z))) | (~r(s(s(s(s(elem!1)))), s(s(s(elem!1))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(elem!1))), s(z))) | (~r(s(z), s(s(s(s(elem!1)))))) | (~r(s(s(s(s(elem!1)))), s(z))) | (~r(s(s(s(s(elem!1)))), s(s(s(elem!1))))))),
% 1.72/1.90 inference(rewrite,[status(thm)],[])).
% 1.72/1.90 tff(1428,plain,
% 1.72/1.90 (((~r(s(z), s(s(s(s(elem!1)))))) | (~r(s(s(s(elem!1))), s(z))) | (~r(s(s(s(s(elem!1)))), s(z))) | (~r(s(s(s(s(elem!1)))), s(s(s(elem!1)))))) <=> ((~r(s(s(s(elem!1))), s(z))) | (~r(s(z), s(s(s(s(elem!1)))))) | (~r(s(s(s(s(elem!1)))), s(z))) | (~r(s(s(s(s(elem!1)))), s(s(s(elem!1))))))),
% 1.72/1.90 inference(rewrite,[status(thm)],[])).
% 1.72/1.90 tff(1429,plain,
% 1.72/1.90 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(s(s(s(elem!1)))))) | (~r(s(s(s(elem!1))), s(z))) | (~r(s(s(s(s(elem!1)))), s(z))) | (~r(s(s(s(s(elem!1)))), s(s(s(elem!1))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), s(z))) | (~r(s(z), s(s(s(s(elem!1)))))) | (~r(s(s(s(s(elem!1)))), s(z))) | (~r(s(s(s(s(elem!1)))), s(s(s(elem!1)))))))),
% 1.72/1.90 inference(monotonicity,[status(thm)],[1428])).
% 1.72/1.90 tff(1430,plain,
% 1.72/1.90 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(s(s(s(elem!1)))))) | (~r(s(s(s(elem!1))), s(z))) | (~r(s(s(s(s(elem!1)))), s(z))) | (~r(s(s(s(s(elem!1)))), s(s(s(elem!1))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(elem!1))), s(z))) | (~r(s(z), s(s(s(s(elem!1)))))) | (~r(s(s(s(s(elem!1)))), s(z))) | (~r(s(s(s(s(elem!1)))), s(s(s(elem!1))))))),
% 1.72/1.90 inference(transitivity,[status(thm)],[1429, 1427])).
% 1.72/1.90 tff(1431,plain,
% 1.72/1.90 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(s(s(s(elem!1)))))) | (~r(s(s(s(elem!1))), s(z))) | (~r(s(s(s(s(elem!1)))), s(z))) | (~r(s(s(s(s(elem!1)))), s(s(s(elem!1))))))),
% 1.72/1.90 inference(quant_inst,[status(thm)],[])).
% 1.72/1.90 tff(1432,plain,
% 1.72/1.90 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(elem!1))), s(z))) | (~r(s(z), s(s(s(s(elem!1)))))) | (~r(s(s(s(s(elem!1)))), s(z))) | (~r(s(s(s(s(elem!1)))), s(s(s(elem!1)))))),
% 1.72/1.90 inference(modus_ponens,[status(thm)],[1431, 1430])).
% 1.72/1.90 tff(1433,plain,
% 1.72/1.90 ($false),
% 1.72/1.90 inference(unit_resolution,[status(thm)],[1432, 197, 350, 700, 699, 1426])).
% 1.72/1.90 tff(1434,plain,((~r(s(z), s(s(s(s(elem!1)))))) | (~r(s(s(s(elem!1))), s(z))) | (~r(s(s(s(s(elem!1)))), s(z))) | (s(s(s(s(elem!1)))) = s(s(s(elem!1)))) | (~b(s(z), elem!1)) | (~b(s(s(elem!1)), s(z))) | (~b(s(s(elem!1)), elem!1)) | (~b(s(s(elem!1)), s(s(s(elem!1))))) | (~(s(s(z)) = s(s(elem!1)))) | (~r(elem!1, s(z)))), inference(lemma,lemma(discharge,[]))).
% 1.72/1.90 tff(1435,plain,
% 1.72/1.90 (~r(s(z), s(s(s(s(elem!1)))))),
% 1.72/1.90 inference(unit_resolution,[status(thm)],[1434, 1412, 350, 364, 1401, 310, 1399, 1388, 1349, 1392])).
% 1.72/1.90 tff(1436,plain,
% 1.72/1.90 (b(s(z), s(s(s(s(elem!1)))))),
% 1.72/1.90 inference(unit_resolution,[status(thm)],[681, 1435])).
% 1.72/1.90 tff(1437,plain,
% 1.72/1.90 (~b(s(s(s(s(elem!1)))), z)),
% 1.72/1.90 inference(unit_resolution,[status(thm)],[1335, 1436, 1145, 310, 1378, 1388])).
% 1.72/1.90 tff(1438,plain,
% 1.72/1.90 (b(s(s(s(s(elem!1)))), z) <=> b(s(s(s(s(elem!1)))), elem!1)),
% 1.72/1.90 inference(monotonicity,[status(thm)],[12])).
% 1.72/1.90 tff(1439,plain,
% 1.72/1.90 (b(s(s(s(s(elem!1)))), elem!1) <=> b(s(s(s(s(elem!1)))), z)),
% 1.72/1.90 inference(symmetry,[status(thm)],[1438])).
% 1.72/1.90 tff(1440,plain,
% 1.72/1.90 (b(s(s(s(s(elem!1)))), z)),
% 1.72/1.90 inference(modus_ponens,[status(thm)],[640, 1439])).
% 1.72/1.90 tff(1441,assumption,(~b(s(s(s(s(elem!1)))), z)), introduced(assumption)).
% 1.72/1.90 tff(1442,plain,
% 1.72/1.90 ($false),
% 1.72/1.90 inference(unit_resolution,[status(thm)],[1441, 1440])).
% 1.72/1.90 tff(1443,plain,((~b(s(s(s(s(elem!1)))), elem!1)) | b(s(s(s(s(elem!1)))), z) | (~(z = elem!1))), inference(lemma,lemma(discharge,[]))).
% 1.72/1.90 tff(1444,plain,
% 1.72/1.90 (~b(s(s(s(s(elem!1)))), elem!1)),
% 1.72/1.90 inference(unit_resolution,[status(thm)],[1443, 1437, 1355])).
% 1.72/1.90 tff(1445,plain,
% 1.72/1.90 (r(s(s(s(s(elem!1)))), elem!1)),
% 1.72/1.90 inference(unit_resolution,[status(thm)],[719, 1444, 1391])).
% 1.72/1.90 tff(1446,plain,
% 1.72/1.90 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(z))) | (~r(s(s(s(elem!1))), elem!1)) | (~r(s(s(s(s(elem!1)))), elem!1)) | (~r(s(s(s(s(elem!1)))), s(s(s(elem!1))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(elem!1, s(z))) | (~r(s(s(s(elem!1))), elem!1)) | (~r(s(s(s(s(elem!1)))), elem!1)) | (~r(s(s(s(s(elem!1)))), s(s(s(elem!1))))))),
% 1.72/1.90 inference(rewrite,[status(thm)],[])).
% 1.72/1.90 tff(1447,plain,
% 1.72/1.90 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(z))) | (~r(s(s(s(elem!1))), elem!1)) | (~r(s(s(s(s(elem!1)))), elem!1)) | (~r(s(s(s(s(elem!1)))), s(s(s(elem!1))))))),
% 1.72/1.90 inference(quant_inst,[status(thm)],[])).
% 1.72/1.90 tff(1448,plain,
% 1.72/1.90 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(elem!1, s(z))) | (~r(s(s(s(elem!1))), elem!1)) | (~r(s(s(s(s(elem!1)))), elem!1)) | (~r(s(s(s(s(elem!1)))), s(s(s(elem!1)))))),
% 1.72/1.90 inference(modus_ponens,[status(thm)],[1447, 1446])).
% 1.72/1.90 tff(1449,plain,
% 1.72/1.90 (~r(s(s(s(s(elem!1)))), s(s(s(elem!1))))),
% 1.72/1.90 inference(unit_resolution,[status(thm)],[1448, 197, 1392, 1445, 1358])).
% 1.72/1.90 tff(1450,plain,
% 1.72/1.90 (b(s(s(s(s(elem!1)))), s(s(s(elem!1))))),
% 1.72/1.90 inference(unit_resolution,[status(thm)],[1065, 1449, 364])).
% 1.72/1.90 tff(1451,plain,
% 1.72/1.90 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), elem!1)) | (~r(elem!1, s(z))) | (~r(s(s(s(elem!1))), s(s(s(s(elem!1)))))) | (~r(s(s(s(s(elem!1)))), elem!1)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(elem!1))), elem!1)) | (~r(elem!1, s(z))) | (~r(s(s(s(elem!1))), s(s(s(s(elem!1)))))) | (~r(s(s(s(s(elem!1)))), elem!1)))),
% 1.72/1.90 inference(rewrite,[status(thm)],[])).
% 1.72/1.90 tff(1452,plain,
% 1.72/1.90 (((~r(elem!1, s(z))) | (~r(s(s(s(s(elem!1)))), elem!1)) | (~r(s(s(s(elem!1))), elem!1)) | (~r(s(s(s(elem!1))), s(s(s(s(elem!1))))))) <=> ((~r(s(s(s(elem!1))), elem!1)) | (~r(elem!1, s(z))) | (~r(s(s(s(elem!1))), s(s(s(s(elem!1)))))) | (~r(s(s(s(s(elem!1)))), elem!1)))),
% 1.72/1.90 inference(rewrite,[status(thm)],[])).
% 1.72/1.90 tff(1453,plain,
% 1.72/1.90 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(z))) | (~r(s(s(s(s(elem!1)))), elem!1)) | (~r(s(s(s(elem!1))), elem!1)) | (~r(s(s(s(elem!1))), s(s(s(s(elem!1)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), elem!1)) | (~r(elem!1, s(z))) | (~r(s(s(s(elem!1))), s(s(s(s(elem!1)))))) | (~r(s(s(s(s(elem!1)))), elem!1))))),
% 1.72/1.90 inference(monotonicity,[status(thm)],[1452])).
% 1.72/1.90 tff(1454,plain,
% 1.72/1.90 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(z))) | (~r(s(s(s(s(elem!1)))), elem!1)) | (~r(s(s(s(elem!1))), elem!1)) | (~r(s(s(s(elem!1))), s(s(s(s(elem!1)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(elem!1))), elem!1)) | (~r(elem!1, s(z))) | (~r(s(s(s(elem!1))), s(s(s(s(elem!1)))))) | (~r(s(s(s(s(elem!1)))), elem!1)))),
% 1.72/1.90 inference(transitivity,[status(thm)],[1453, 1451])).
% 1.72/1.90 tff(1455,plain,
% 1.72/1.90 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(z))) | (~r(s(s(s(s(elem!1)))), elem!1)) | (~r(s(s(s(elem!1))), elem!1)) | (~r(s(s(s(elem!1))), s(s(s(s(elem!1)))))))),
% 1.72/1.90 inference(quant_inst,[status(thm)],[])).
% 1.72/1.90 tff(1456,plain,
% 1.72/1.90 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(elem!1))), elem!1)) | (~r(elem!1, s(z))) | (~r(s(s(s(elem!1))), s(s(s(s(elem!1)))))) | (~r(s(s(s(s(elem!1)))), elem!1))),
% 1.72/1.90 inference(modus_ponens,[status(thm)],[1455, 1454])).
% 1.72/1.90 tff(1457,plain,
% 1.72/1.90 (~r(s(s(s(elem!1))), s(s(s(s(elem!1)))))),
% 1.72/1.90 inference(unit_resolution,[status(thm)],[1456, 197, 1392, 1445, 1358])).
% 1.72/1.90 tff(1458,plain,
% 1.72/1.90 (b(s(s(s(elem!1))), s(s(s(s(elem!1)))))),
% 1.72/1.90 inference(unit_resolution,[status(thm)],[696, 1457, 358])).
% 1.72/1.90 tff(1459,plain,
% 1.72/1.90 ($false),
% 1.72/1.90 inference(unit_resolution,[status(thm)],[1313, 1458, 1450, 1388, 1378])).
% 1.72/1.90 tff(1460,plain,((~r(s(s(s(elem!1))), z)) | (~b(s(s(elem!1)), s(z))) | (~r(s(s(s(elem!1))), s(z))) | (s(s(elem!1)) = s(s(s(elem!1)))) | (~r(z, s(s(elem!1)))) | (~b(s(z), z)) | (~r(z, s(z))) | (~r(z, s(s(z))))), inference(lemma,lemma(discharge,[]))).
% 1.72/1.90 tff(1461,plain,
% 1.72/1.90 (~r(s(s(s(elem!1))), z)),
% 1.72/1.90 inference(unit_resolution,[status(thm)],[1460, 365, 350, 45, 310, 53, 323, 155])).
% 1.72/1.90 tff(1462,plain,
% 1.72/1.90 (b(s(s(s(elem!1))), z)),
% 1.72/1.90 inference(unit_resolution,[status(thm)],[94, 1461])).
% 1.72/1.90 tff(1463,plain,
% 1.72/1.90 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(s(elem!1))))) | (~b(s(z), z)) | (~b(s(z), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(s(s(elem!1))))) | (~b(s(z), z)) | (~b(s(z), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), z)))),
% 1.72/1.90 inference(rewrite,[status(thm)],[])).
% 1.72/1.90 tff(1464,plain,
% 1.72/1.90 (((~b(z, s(s(s(elem!1))))) | (~b(s(z), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), z)) | (~b(z, s(s(s(elem!1))))) | (~b(s(z), s(s(s(elem!1))))) | (~b(s(z), z))) <=> ((~b(z, s(s(s(elem!1))))) | (~b(s(z), z)) | (~b(s(z), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), z)))),
% 1.72/1.90 inference(rewrite,[status(thm)],[])).
% 1.72/1.90 tff(1465,plain,
% 1.72/1.90 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(s(elem!1))))) | (~b(s(z), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), z)) | (~b(z, s(s(s(elem!1))))) | (~b(s(z), s(s(s(elem!1))))) | (~b(s(z), z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(s(elem!1))))) | (~b(s(z), z)) | (~b(s(z), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), z))))),
% 1.72/1.90 inference(monotonicity,[status(thm)],[1464])).
% 1.72/1.90 tff(1466,plain,
% 1.72/1.90 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(s(elem!1))))) | (~b(s(z), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), z)) | (~b(z, s(s(s(elem!1))))) | (~b(s(z), s(s(s(elem!1))))) | (~b(s(z), z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(s(s(elem!1))))) | (~b(s(z), z)) | (~b(s(z), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), z)))),
% 1.72/1.91 inference(transitivity,[status(thm)],[1465, 1463])).
% 1.72/1.91 tff(1467,plain,
% 1.72/1.91 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(s(elem!1))))) | (~b(s(z), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), z)) | (~b(z, s(s(s(elem!1))))) | (~b(s(z), s(s(s(elem!1))))) | (~b(s(z), z)))),
% 1.72/1.91 inference(quant_inst,[status(thm)],[])).
% 1.72/1.91 tff(1468,plain,
% 1.72/1.91 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(s(s(elem!1))))) | (~b(s(z), z)) | (~b(s(z), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), z))),
% 1.72/1.91 inference(modus_ponens,[status(thm)],[1467, 1466])).
% 1.72/1.91 tff(1469,plain,
% 1.72/1.91 ($false),
% 1.72/1.91 inference(unit_resolution,[status(thm)],[1468, 166, 241, 240, 53, 121])).
% 1.72/1.91 tff(1470,plain,((~b(z, s(s(s(elem!1))))) | (~b(s(z), s(s(s(elem!1))))) | (~b(s(z), z)) | (~b(s(s(s(elem!1))), z))), inference(lemma,lemma(discharge,[]))).
% 1.72/1.91 tff(1471,plain,
% 1.72/1.91 (~b(z, s(s(s(elem!1))))),
% 1.72/1.91 inference(unit_resolution,[status(thm)],[1470, 924, 53, 1462])).
% 1.72/1.91 tff(1472,plain,
% 1.72/1.91 (r(z, s(s(s(elem!1))))),
% 1.72/1.91 inference(unit_resolution,[status(thm)],[261, 1471])).
% 1.72/1.91 tff(1473,plain,
% 1.72/1.91 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), s(z))) | (~r(z, s(z))) | (~r(s(z), s(s(s(s(elem!1)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), s(z))) | (~r(z, s(z))) | (~r(s(z), s(s(s(s(elem!1)))))))),
% 1.72/1.91 inference(rewrite,[status(thm)],[])).
% 1.72/1.91 tff(1474,plain,
% 1.72/1.91 (((~r(s(z), s(s(s(s(elem!1)))))) | (~r(s(s(s(elem!1))), s(z))) | (~r(z, s(z))) | (~r(z, s(s(s(elem!1)))))) <=> ((~r(z, s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), s(z))) | (~r(z, s(z))) | (~r(s(z), s(s(s(s(elem!1)))))))),
% 1.72/1.91 inference(rewrite,[status(thm)],[])).
% 1.72/1.91 tff(1475,plain,
% 1.72/1.91 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(s(s(s(elem!1)))))) | (~r(s(s(s(elem!1))), s(z))) | (~r(z, s(z))) | (~r(z, s(s(s(elem!1))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), s(z))) | (~r(z, s(z))) | (~r(s(z), s(s(s(s(elem!1))))))))),
% 1.72/1.91 inference(monotonicity,[status(thm)],[1474])).
% 1.72/1.91 tff(1476,plain,
% 1.72/1.91 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(s(s(s(elem!1)))))) | (~r(s(s(s(elem!1))), s(z))) | (~r(z, s(z))) | (~r(z, s(s(s(elem!1))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), s(z))) | (~r(z, s(z))) | (~r(s(z), s(s(s(s(elem!1)))))))),
% 1.72/1.91 inference(transitivity,[status(thm)],[1475, 1473])).
% 1.72/1.91 tff(1477,plain,
% 1.72/1.91 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(s(s(s(elem!1)))))) | (~r(s(s(s(elem!1))), s(z))) | (~r(z, s(z))) | (~r(z, s(s(s(elem!1))))))),
% 1.72/1.91 inference(quant_inst,[status(thm)],[])).
% 1.72/1.91 tff(1478,plain,
% 1.72/1.91 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), s(z))) | (~r(z, s(z))) | (~r(s(z), s(s(s(s(elem!1))))))),
% 1.72/1.91 inference(modus_ponens,[status(thm)],[1477, 1476])).
% 1.72/1.91 tff(1479,plain,
% 1.72/1.91 ($false),
% 1.72/1.91 inference(unit_resolution,[status(thm)],[1478, 197, 350, 323, 699, 282])).
% 1.72/1.91 tff(1480,plain,((~r(s(z), s(s(s(s(elem!1)))))) | (~r(s(s(s(elem!1))), s(z))) | (~r(z, s(z))) | (~r(z, s(s(s(elem!1)))))), inference(lemma,lemma(discharge,[]))).
% 1.72/1.91 tff(1481,plain,
% 1.72/1.91 (~r(s(z), s(s(s(s(elem!1)))))),
% 1.72/1.91 inference(unit_resolution,[status(thm)],[1480, 1472, 323, 350])).
% 1.72/1.91 tff(1482,plain,
% 1.72/1.91 (b(s(z), s(s(s(s(elem!1)))))),
% 1.72/1.91 inference(unit_resolution,[status(thm)],[681, 1481])).
% 1.72/1.91 tff(1483,plain,
% 1.72/1.91 ((z = s(s(s(s(elem!1))))) <=> (s(s(s(s(elem!1)))) = z)),
% 1.72/1.91 inference(commutativity,[status(thm)],[])).
% 1.72/1.91 tff(1484,plain,
% 1.72/1.91 ((s(s(s(s(elem!1)))) = z) <=> (z = s(s(s(s(elem!1)))))),
% 1.72/1.91 inference(symmetry,[status(thm)],[1483])).
% 1.72/1.91 tff(1485,plain,
% 1.72/1.91 ((~(s(s(s(s(elem!1)))) = z)) <=> (~(z = s(s(s(s(elem!1))))))),
% 1.72/1.91 inference(monotonicity,[status(thm)],[1484])).
% 1.72/1.91 tff(1486,plain,
% 1.72/1.91 (~(z = s(s(s(s(elem!1)))))),
% 1.72/1.91 inference(modus_ponens,[status(thm)],[626, 1485])).
% 1.72/1.91 tff(1487,plain,
% 1.72/1.91 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), s(z))) | (~r(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~r(z, s(s(s(s(elem!1)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), s(z))) | (~r(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~r(z, s(s(s(s(elem!1)))))))),
% 1.72/1.91 inference(rewrite,[status(thm)],[])).
% 1.72/1.91 tff(1488,plain,
% 1.72/1.91 (((~r(s(s(s(elem!1))), s(z))) | (~r(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~r(z, s(s(s(elem!1))))) | (~r(z, s(s(s(s(elem!1))))))) <=> ((~r(z, s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), s(z))) | (~r(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~r(z, s(s(s(s(elem!1)))))))),
% 1.72/1.91 inference(rewrite,[status(thm)],[])).
% 1.72/1.91 tff(1489,plain,
% 1.72/1.91 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), s(z))) | (~r(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~r(z, s(s(s(elem!1))))) | (~r(z, s(s(s(s(elem!1)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), s(z))) | (~r(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~r(z, s(s(s(s(elem!1))))))))),
% 1.72/1.91 inference(monotonicity,[status(thm)],[1488])).
% 1.72/1.91 tff(1490,plain,
% 1.72/1.91 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), s(z))) | (~r(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~r(z, s(s(s(elem!1))))) | (~r(z, s(s(s(s(elem!1)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), s(z))) | (~r(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~r(z, s(s(s(s(elem!1)))))))),
% 1.72/1.91 inference(transitivity,[status(thm)],[1489, 1487])).
% 1.72/1.91 tff(1491,plain,
% 1.72/1.91 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), s(z))) | (~r(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~r(z, s(s(s(elem!1))))) | (~r(z, s(s(s(s(elem!1)))))))),
% 1.72/1.91 inference(quant_inst,[status(thm)],[])).
% 1.72/1.91 tff(1492,plain,
% 1.72/1.91 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), s(z))) | (~r(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~r(z, s(s(s(s(elem!1))))))),
% 1.72/1.91 inference(modus_ponens,[status(thm)],[1491, 1490])).
% 1.72/1.91 tff(1493,plain,
% 1.72/1.91 (~r(z, s(s(s(s(elem!1)))))),
% 1.72/1.91 inference(unit_resolution,[status(thm)],[1492, 197, 350, 282, 1048])).
% 1.72/1.91 tff(1494,plain,
% 1.72/1.91 (((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((z = s(s(s(s(elem!1))))) | b(z, s(s(s(s(elem!1))))) | r(z, s(s(s(s(elem!1))))))) <=> ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (z = s(s(s(s(elem!1))))) | b(z, s(s(s(s(elem!1))))) | r(z, s(s(s(s(elem!1))))))),
% 1.72/1.91 inference(rewrite,[status(thm)],[])).
% 1.72/1.91 tff(1495,plain,
% 1.72/1.91 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((z = s(s(s(s(elem!1))))) | b(z, s(s(s(s(elem!1))))) | r(z, s(s(s(s(elem!1))))))),
% 1.72/1.91 inference(quant_inst,[status(thm)],[])).
% 1.72/1.91 tff(1496,plain,
% 1.72/1.91 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (z = s(s(s(s(elem!1))))) | b(z, s(s(s(s(elem!1))))) | r(z, s(s(s(s(elem!1)))))),
% 1.72/1.91 inference(modus_ponens,[status(thm)],[1495, 1494])).
% 1.72/1.91 tff(1497,plain,
% 1.72/1.91 ((z = s(s(s(s(elem!1))))) | b(z, s(s(s(s(elem!1)))))),
% 1.72/1.91 inference(unit_resolution,[status(thm)],[1496, 79, 1493])).
% 1.72/1.91 tff(1498,plain,
% 1.72/1.91 (b(z, s(s(s(s(elem!1)))))),
% 1.72/1.91 inference(unit_resolution,[status(thm)],[1497, 1486])).
% 1.72/1.91 tff(1499,plain,
% 1.72/1.91 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), s(z))) | (~r(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~r(s(s(s(s(elem!1)))), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), s(z))) | (~r(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~r(s(s(s(s(elem!1)))), z)))),
% 1.72/1.91 inference(rewrite,[status(thm)],[])).
% 1.72/1.91 tff(1500,plain,
% 1.72/1.91 (((~r(s(s(s(elem!1))), s(z))) | (~r(z, s(s(s(elem!1))))) | (~r(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~r(s(s(s(s(elem!1)))), z))) <=> ((~r(z, s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), s(z))) | (~r(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~r(s(s(s(s(elem!1)))), z)))),
% 1.72/1.91 inference(rewrite,[status(thm)],[])).
% 1.72/1.91 tff(1501,plain,
% 1.72/1.91 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), s(z))) | (~r(z, s(s(s(elem!1))))) | (~r(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~r(s(s(s(s(elem!1)))), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), s(z))) | (~r(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~r(s(s(s(s(elem!1)))), z))))),
% 1.72/1.91 inference(monotonicity,[status(thm)],[1500])).
% 1.72/1.91 tff(1502,plain,
% 1.72/1.91 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), s(z))) | (~r(z, s(s(s(elem!1))))) | (~r(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~r(s(s(s(s(elem!1)))), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), s(z))) | (~r(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~r(s(s(s(s(elem!1)))), z)))),
% 1.72/1.91 inference(transitivity,[status(thm)],[1501, 1499])).
% 1.72/1.91 tff(1503,plain,
% 1.72/1.91 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), s(z))) | (~r(z, s(s(s(elem!1))))) | (~r(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~r(s(s(s(s(elem!1)))), z)))),
% 1.72/1.91 inference(quant_inst,[status(thm)],[])).
% 1.72/1.91 tff(1504,plain,
% 1.72/1.91 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), s(z))) | (~r(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~r(s(s(s(s(elem!1)))), z))),
% 1.72/1.91 inference(modus_ponens,[status(thm)],[1503, 1502])).
% 1.72/1.91 tff(1505,plain,
% 1.72/1.91 (~r(s(s(s(s(elem!1)))), z)),
% 1.72/1.91 inference(unit_resolution,[status(thm)],[1504, 197, 350, 282, 1048])).
% 1.72/1.91 tff(1506,plain,
% 1.72/1.91 (b(s(s(s(s(elem!1)))), z)),
% 1.72/1.91 inference(unit_resolution,[status(thm)],[1339, 79, 626, 1505])).
% 1.72/1.91 tff(1507,plain,
% 1.72/1.91 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), z)) | (~b(s(z), s(s(s(s(elem!1)))))) | (~b(z, s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), z)) | (~b(s(z), s(s(s(s(elem!1)))))) | (~b(z, s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), z)))),
% 1.72/1.91 inference(rewrite,[status(thm)],[])).
% 1.72/1.91 tff(1508,plain,
% 1.72/1.91 (((~b(z, s(s(s(s(elem!1)))))) | (~b(s(z), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), z)) | (~b(z, s(s(s(s(elem!1)))))) | (~b(s(z), s(s(s(s(elem!1)))))) | (~b(s(z), z))) <=> ((~b(s(z), z)) | (~b(s(z), s(s(s(s(elem!1)))))) | (~b(z, s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), z)))),
% 1.72/1.91 inference(rewrite,[status(thm)],[])).
% 1.72/1.91 tff(1509,plain,
% 1.72/1.91 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(s(s(elem!1)))))) | (~b(s(z), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), z)) | (~b(z, s(s(s(s(elem!1)))))) | (~b(s(z), s(s(s(s(elem!1)))))) | (~b(s(z), z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), z)) | (~b(s(z), s(s(s(s(elem!1)))))) | (~b(z, s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), z))))),
% 1.72/1.91 inference(monotonicity,[status(thm)],[1508])).
% 1.72/1.91 tff(1510,plain,
% 1.72/1.91 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(s(s(elem!1)))))) | (~b(s(z), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), z)) | (~b(z, s(s(s(s(elem!1)))))) | (~b(s(z), s(s(s(s(elem!1)))))) | (~b(s(z), z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), z)) | (~b(s(z), s(s(s(s(elem!1)))))) | (~b(z, s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), z)))),
% 1.72/1.91 inference(transitivity,[status(thm)],[1509, 1507])).
% 1.72/1.91 tff(1511,plain,
% 1.72/1.91 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(s(s(elem!1)))))) | (~b(s(z), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), z)) | (~b(z, s(s(s(s(elem!1)))))) | (~b(s(z), s(s(s(s(elem!1)))))) | (~b(s(z), z)))),
% 1.72/1.91 inference(quant_inst,[status(thm)],[])).
% 1.72/1.91 tff(1512,plain,
% 1.72/1.91 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), z)) | (~b(s(z), s(s(s(s(elem!1)))))) | (~b(z, s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), z))),
% 1.72/1.91 inference(modus_ponens,[status(thm)],[1511, 1510])).
% 1.72/1.91 tff(1513,plain,
% 1.72/1.91 ($false),
% 1.72/1.91 inference(unit_resolution,[status(thm)],[1512, 166, 53, 1327, 1506, 1498])).
% 1.72/1.91 tff(1514,plain,((~r(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~b(s(z), z)) | (~b(s(z), s(s(s(s(elem!1)))))) | (~r(s(s(s(elem!1))), s(z))) | (~r(z, s(s(s(elem!1)))))), inference(lemma,lemma(discharge,[]))).
% 1.72/1.91 tff(1515,plain,
% 1.72/1.91 (~r(s(s(s(s(elem!1)))), s(s(s(elem!1))))),
% 1.72/1.91 inference(unit_resolution,[status(thm)],[1514, 1482, 53, 350, 1472])).
% 1.72/1.91 tff(1516,plain,
% 1.72/1.91 (b(s(s(s(s(elem!1)))), s(s(s(elem!1))))),
% 1.72/1.91 inference(unit_resolution,[status(thm)],[1065, 1515, 364])).
% 1.72/1.91 tff(1517,plain,
% 1.72/1.91 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(s(elem!1))))) | (~r(s(z), s(s(elem!1)))) | (~r(s(s(s(elem!1))), s(z))) | (~r(z, s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, s(s(s(elem!1))))) | (~r(s(z), s(s(elem!1)))) | (~r(s(s(s(elem!1))), s(z))) | (~r(z, s(z))))),
% 1.72/1.91 inference(rewrite,[status(thm)],[])).
% 1.72/1.91 tff(1518,plain,
% 1.72/1.91 (((~r(s(z), s(s(elem!1)))) | (~r(s(s(s(elem!1))), s(z))) | (~r(z, s(z))) | (~r(z, s(s(s(elem!1)))))) <=> ((~r(z, s(s(s(elem!1))))) | (~r(s(z), s(s(elem!1)))) | (~r(s(s(s(elem!1))), s(z))) | (~r(z, s(z))))),
% 1.72/1.91 inference(rewrite,[status(thm)],[])).
% 1.72/1.91 tff(1519,plain,
% 1.72/1.91 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(s(elem!1)))) | (~r(s(s(s(elem!1))), s(z))) | (~r(z, s(z))) | (~r(z, s(s(s(elem!1))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(s(elem!1))))) | (~r(s(z), s(s(elem!1)))) | (~r(s(s(s(elem!1))), s(z))) | (~r(z, s(z)))))),
% 1.72/1.91 inference(monotonicity,[status(thm)],[1518])).
% 1.72/1.91 tff(1520,plain,
% 1.72/1.91 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(s(elem!1)))) | (~r(s(s(s(elem!1))), s(z))) | (~r(z, s(z))) | (~r(z, s(s(s(elem!1))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, s(s(s(elem!1))))) | (~r(s(z), s(s(elem!1)))) | (~r(s(s(s(elem!1))), s(z))) | (~r(z, s(z))))),
% 1.72/1.91 inference(transitivity,[status(thm)],[1519, 1517])).
% 1.72/1.91 tff(1521,plain,
% 1.72/1.91 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(s(elem!1)))) | (~r(s(s(s(elem!1))), s(z))) | (~r(z, s(z))) | (~r(z, s(s(s(elem!1))))))),
% 1.72/1.91 inference(quant_inst,[status(thm)],[])).
% 1.72/1.91 tff(1522,plain,
% 1.72/1.91 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, s(s(s(elem!1))))) | (~r(s(z), s(s(elem!1)))) | (~r(s(s(s(elem!1))), s(z))) | (~r(z, s(z)))),
% 1.72/1.91 inference(modus_ponens,[status(thm)],[1521, 1520])).
% 1.72/1.91 tff(1523,plain,
% 1.72/1.91 ($false),
% 1.72/1.91 inference(unit_resolution,[status(thm)],[1522, 197, 311, 350, 323, 282])).
% 1.72/1.91 tff(1524,plain,((~r(s(z), s(s(elem!1)))) | (~r(s(s(s(elem!1))), s(z))) | (~r(z, s(z))) | (~r(z, s(s(s(elem!1)))))), inference(lemma,lemma(discharge,[]))).
% 1.72/1.92 tff(1525,plain,
% 1.72/1.92 (~r(s(z), s(s(elem!1)))),
% 1.72/1.92 inference(unit_resolution,[status(thm)],[1524, 1472, 323, 350])).
% 1.72/1.92 tff(1526,plain,
% 1.72/1.92 (b(s(z), s(s(elem!1)))),
% 1.72/1.92 inference(unit_resolution,[status(thm)],[84, 1525])).
% 1.72/1.92 tff(1527,plain,
% 1.72/1.92 (~b(s(s(s(elem!1))), s(s(elem!1)))),
% 1.72/1.92 inference(unit_resolution,[status(thm)],[1366, 1526, 924, 310])).
% 1.72/1.92 tff(1528,plain,
% 1.72/1.92 (r(s(s(s(elem!1))), s(s(elem!1)))),
% 1.72/1.92 inference(unit_resolution,[status(thm)],[889, 1527, 51])).
% 1.72/1.92 tff(1529,plain,
% 1.72/1.92 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), s(s(elem!1)))) | (~r(z, s(s(elem!1)))) | (~r(s(s(elem!1)), s(s(s(s(elem!1)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), s(s(elem!1)))) | (~r(z, s(s(elem!1)))) | (~r(s(s(elem!1)), s(s(s(s(elem!1)))))))),
% 1.72/1.92 inference(rewrite,[status(thm)],[])).
% 1.72/1.92 tff(1530,plain,
% 1.72/1.92 (((~r(s(s(elem!1)), s(s(s(s(elem!1)))))) | (~r(s(s(s(elem!1))), s(s(elem!1)))) | (~r(z, s(s(elem!1)))) | (~r(z, s(s(s(elem!1)))))) <=> ((~r(z, s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), s(s(elem!1)))) | (~r(z, s(s(elem!1)))) | (~r(s(s(elem!1)), s(s(s(s(elem!1)))))))),
% 1.72/1.92 inference(rewrite,[status(thm)],[])).
% 1.72/1.92 tff(1531,plain,
% 1.72/1.92 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(elem!1)), s(s(s(s(elem!1)))))) | (~r(s(s(s(elem!1))), s(s(elem!1)))) | (~r(z, s(s(elem!1)))) | (~r(z, s(s(s(elem!1))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), s(s(elem!1)))) | (~r(z, s(s(elem!1)))) | (~r(s(s(elem!1)), s(s(s(s(elem!1))))))))),
% 1.72/1.92 inference(monotonicity,[status(thm)],[1530])).
% 1.72/1.92 tff(1532,plain,
% 1.72/1.92 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(elem!1)), s(s(s(s(elem!1)))))) | (~r(s(s(s(elem!1))), s(s(elem!1)))) | (~r(z, s(s(elem!1)))) | (~r(z, s(s(s(elem!1))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), s(s(elem!1)))) | (~r(z, s(s(elem!1)))) | (~r(s(s(elem!1)), s(s(s(s(elem!1)))))))),
% 1.72/1.92 inference(transitivity,[status(thm)],[1531, 1529])).
% 1.72/1.92 tff(1533,plain,
% 1.72/1.92 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(elem!1)), s(s(s(s(elem!1)))))) | (~r(s(s(s(elem!1))), s(s(elem!1)))) | (~r(z, s(s(elem!1)))) | (~r(z, s(s(s(elem!1))))))),
% 1.72/1.92 inference(quant_inst,[status(thm)],[])).
% 1.72/1.92 tff(1534,plain,
% 1.72/1.92 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), s(s(elem!1)))) | (~r(z, s(s(elem!1)))) | (~r(s(s(elem!1)), s(s(s(s(elem!1))))))),
% 1.72/1.92 inference(modus_ponens,[status(thm)],[1533, 1532])).
% 1.72/1.92 tff(1535,plain,
% 1.72/1.92 ($false),
% 1.72/1.92 inference(unit_resolution,[status(thm)],[1534, 197, 365, 905, 561, 282])).
% 1.72/1.92 tff(1536,plain,((~r(s(s(elem!1)), s(s(s(s(elem!1)))))) | (~r(z, s(s(elem!1)))) | (~r(s(s(s(elem!1))), s(s(elem!1)))) | (~r(z, s(s(s(elem!1)))))), inference(lemma,lemma(discharge,[]))).
% 1.72/1.92 tff(1537,plain,
% 1.72/1.92 (~r(s(s(elem!1)), s(s(s(s(elem!1)))))),
% 1.72/1.92 inference(unit_resolution,[status(thm)],[1536, 365, 1528, 1472])).
% 1.72/1.92 tff(1538,plain,
% 1.72/1.92 (~r(s(s(elem!1)), s(s(s(elem!1))))),
% 1.72/1.92 inference(unit_resolution,[status(thm)],[933, 1472, 365, 350])).
% 1.72/1.92 tff(1539,plain,
% 1.72/1.92 (b(s(s(elem!1)), s(s(s(elem!1))))),
% 1.72/1.92 inference(unit_resolution,[status(thm)],[461, 1538, 45])).
% 1.72/1.92 tff(1540,plain,
% 1.72/1.92 (inj_0(s(s(s(elem!1)))) = inj_0(s(elem!1))),
% 1.72/1.92 inference(symmetry,[status(thm)],[1169])).
% 1.72/1.92 tff(1541,plain,
% 1.72/1.92 (s(s(s(s(elem!1)))) = elem!1),
% 1.72/1.92 inference(transitivity,[status(thm)],[1154, 105, 1540, 20])).
% 1.72/1.92 tff(1542,plain,
% 1.72/1.92 (b(s(s(s(s(elem!1)))), s(s(s(z)))) <=> b(elem!1, s(s(s(z))))),
% 1.72/1.92 inference(monotonicity,[status(thm)],[1541])).
% 1.72/1.92 tff(1543,plain,
% 1.72/1.92 (b(elem!1, s(s(s(z)))) <=> b(s(s(s(s(elem!1)))), s(s(s(z))))),
% 1.72/1.92 inference(symmetry,[status(thm)],[1542])).
% 1.72/1.92 tff(1544,plain,
% 1.72/1.92 (inj_0(s(s(s(elem!1)))) = inj_0(s(elem!1))),
% 1.72/1.92 inference(monotonicity,[status(thm)],[1177])).
% 1.72/1.92 tff(1545,plain,
% 1.72/1.92 (inj_0(s(elem!1)) = inj_0(s(s(s(elem!1))))),
% 1.72/1.92 inference(symmetry,[status(thm)],[1544])).
% 1.72/1.92 tff(1546,assumption,(s(s(s(z))) = elem!1), introduced(assumption)).
% 1.72/1.92 tff(1547,plain,
% 1.72/1.92 (s(s(s(z))) = s(s(elem!1))),
% 1.72/1.92 inference(transitivity,[status(thm)],[1546, 1170, 1545, 104])).
% 1.72/1.92 tff(1548,plain,
% 1.72/1.92 (inj_0(s(s(s(z)))) = inj_0(s(s(elem!1)))),
% 1.72/1.92 inference(monotonicity,[status(thm)],[1547])).
% 1.72/1.92 tff(1549,plain,
% 1.72/1.92 (inj_0(s(s(elem!1))) = inj_0(s(s(s(z))))),
% 1.72/1.92 inference(symmetry,[status(thm)],[1548])).
% 1.72/1.92 tff(1550,plain,
% 1.72/1.92 (s(elem!1) = s(s(z))),
% 1.72/1.92 inference(transitivity,[status(thm)],[39, 1549, 134])).
% 1.72/1.92 tff(1551,plain,
% 1.72/1.92 ((s(s(z)) = s(s(s(elem!1)))) <=> (s(s(z)) = s(elem!1))),
% 1.72/1.92 inference(monotonicity,[status(thm)],[1177])).
% 1.72/1.92 tff(1552,plain,
% 1.72/1.92 ((s(s(z)) = s(s(s(elem!1)))) <=> (s(elem!1) = s(s(z)))),
% 1.72/1.92 inference(transitivity,[status(thm)],[1551, 1252])).
% 1.72/1.92 tff(1553,plain,
% 1.72/1.92 ((~(s(s(z)) = s(s(s(elem!1))))) <=> (~(s(elem!1) = s(s(z))))),
% 1.72/1.92 inference(monotonicity,[status(thm)],[1552])).
% 1.72/1.92 tff(1554,plain,
% 1.72/1.92 (~(s(elem!1) = s(s(z)))),
% 1.72/1.92 inference(modus_ponens,[status(thm)],[209, 1553])).
% 1.72/1.92 tff(1555,plain,
% 1.72/1.92 ($false),
% 1.72/1.92 inference(unit_resolution,[status(thm)],[1554, 1550])).
% 1.72/1.92 tff(1556,plain,((~(s(s(s(z))) = elem!1)) | (~(s(s(s(elem!1))) = s(elem!1)))), inference(lemma,lemma(discharge,[]))).
% 1.72/1.92 tff(1557,plain,
% 1.72/1.92 (~(s(s(s(z))) = elem!1)),
% 1.72/1.92 inference(unit_resolution,[status(thm)],[1556, 1167])).
% 1.72/1.92 tff(1558,plain,
% 1.72/1.92 ((s(s(s(z))) = elem!1) <=> (elem!1 = s(s(s(z))))),
% 1.72/1.92 inference(commutativity,[status(thm)],[])).
% 1.72/1.92 tff(1559,plain,
% 1.72/1.92 ((elem!1 = s(s(s(z)))) <=> (s(s(s(z))) = elem!1)),
% 1.72/1.92 inference(symmetry,[status(thm)],[1558])).
% 1.72/1.92 tff(1560,assumption,(elem!1 = s(s(s(z)))), introduced(assumption)).
% 1.72/1.92 tff(1561,plain,
% 1.72/1.92 (s(s(s(z))) = elem!1),
% 1.72/1.92 inference(modus_ponens,[status(thm)],[1560, 1559])).
% 1.72/1.92 tff(1562,assumption,(~(s(s(s(z))) = elem!1)), introduced(assumption)).
% 1.72/1.92 tff(1563,plain,
% 1.72/1.92 ($false),
% 1.72/1.92 inference(unit_resolution,[status(thm)],[1562, 1561])).
% 1.72/1.92 tff(1564,plain,((~(elem!1 = s(s(s(z))))) | (s(s(s(z))) = elem!1)), inference(lemma,lemma(discharge,[]))).
% 1.72/1.92 tff(1565,plain,
% 1.72/1.92 (~(elem!1 = s(s(s(z))))),
% 1.72/1.92 inference(unit_resolution,[status(thm)],[1564, 1557])).
% 1.72/1.92 tff(1566,plain,
% 1.72/1.92 ((s(s(s(s(elem!1)))) = s(s(z))) <=> (s(s(elem!1)) = s(s(z)))),
% 1.72/1.92 inference(monotonicity,[status(thm)],[1154])).
% 1.72/1.92 tff(1567,plain,
% 1.72/1.92 ((s(s(s(s(elem!1)))) = s(s(z))) <=> (s(s(z)) = s(s(elem!1)))),
% 1.72/1.92 inference(transitivity,[status(thm)],[1566, 127])).
% 1.72/1.92 tff(1568,plain,
% 1.72/1.92 ((~(s(s(s(s(elem!1)))) = s(s(z)))) <=> (~(s(s(z)) = s(s(elem!1))))),
% 1.72/1.92 inference(monotonicity,[status(thm)],[1567])).
% 1.72/1.92 tff(1569,plain,
% 1.72/1.92 (~(s(s(z)) = s(s(elem!1)))),
% 1.72/1.92 inference(modus_ponens,[status(thm)],[733, 1568])).
% 1.72/1.92 tff(1570,plain,
% 1.72/1.92 (~r(s(z), s(s(elem!1)))),
% 1.72/1.92 inference(unit_resolution,[status(thm)],[1524, 282, 323, 350])).
% 1.72/1.92 tff(1571,plain,
% 1.72/1.92 (b(s(z), s(s(elem!1)))),
% 1.72/1.92 inference(unit_resolution,[status(thm)],[84, 1570])).
% 1.72/1.92 tff(1572,plain,
% 1.72/1.92 ((~(s(s(s(s(elem!1)))) = s(s(z)))) <=> (~(s(s(elem!1)) = s(s(z))))),
% 1.72/1.92 inference(monotonicity,[status(thm)],[1566])).
% 1.72/1.92 tff(1573,plain,
% 1.72/1.92 (~(s(s(elem!1)) = s(s(z)))),
% 1.72/1.92 inference(modus_ponens,[status(thm)],[733, 1572])).
% 1.72/1.92 tff(1574,plain,
% 1.72/1.92 (~b(s(s(z)), s(s(elem!1)))),
% 1.72/1.92 inference(unit_resolution,[status(thm)],[507, 273, 155, 365, 11, 463, 350, 53, 310, 376])).
% 1.72/1.92 tff(1575,plain,
% 1.72/1.92 (r(s(s(z)), s(s(elem!1)))),
% 1.72/1.92 inference(unit_resolution,[status(thm)],[390, 1574, 52])).
% 1.72/1.92 tff(1576,plain,
% 1.72/1.92 (~r(s(s(elem!1)), s(s(z)))),
% 1.72/1.92 inference(unit_resolution,[status(thm)],[517, 1575, 155, 365])).
% 1.72/1.92 tff(1577,plain,
% 1.72/1.92 (b(s(s(elem!1)), s(s(z)))),
% 1.72/1.92 inference(unit_resolution,[status(thm)],[441, 1576, 11])).
% 1.72/1.92 tff(1578,plain,
% 1.72/1.92 (r(s(s(s(elem!1))), s(s(z)))),
% 1.72/1.92 inference(unit_resolution,[status(thm)],[501, 1577, 463, 273])).
% 1.72/1.92 tff(1579,plain,
% 1.72/1.92 (~b(s(s(z)), s(z))),
% 1.72/1.92 inference(unit_resolution,[status(thm)],[549, 1577, 463, 376, 310])).
% 1.72/1.92 tff(1580,plain,
% 1.72/1.92 (r(s(s(z)), s(z))),
% 1.72/1.92 inference(unit_resolution,[status(thm)],[308, 1579])).
% 1.72/1.92 tff(1581,plain,
% 1.72/1.92 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(s(elem!1))))) | (~r(s(s(z)), s(z))) | (~r(s(s(s(elem!1))), s(s(z)))) | (~r(z, s(s(z)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, s(s(s(elem!1))))) | (~r(s(s(z)), s(z))) | (~r(s(s(s(elem!1))), s(s(z)))) | (~r(z, s(s(z)))))),
% 1.72/1.92 inference(rewrite,[status(thm)],[])).
% 1.72/1.92 tff(1582,plain,
% 1.72/1.92 (((~r(s(s(z)), s(z))) | (~r(s(s(s(elem!1))), s(s(z)))) | (~r(z, s(s(z)))) | (~r(z, s(s(s(elem!1)))))) <=> ((~r(z, s(s(s(elem!1))))) | (~r(s(s(z)), s(z))) | (~r(s(s(s(elem!1))), s(s(z)))) | (~r(z, s(s(z)))))),
% 1.72/1.92 inference(rewrite,[status(thm)],[])).
% 1.72/1.92 tff(1583,plain,
% 1.72/1.92 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(z)), s(z))) | (~r(s(s(s(elem!1))), s(s(z)))) | (~r(z, s(s(z)))) | (~r(z, s(s(s(elem!1))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(s(elem!1))))) | (~r(s(s(z)), s(z))) | (~r(s(s(s(elem!1))), s(s(z)))) | (~r(z, s(s(z))))))),
% 1.72/1.92 inference(monotonicity,[status(thm)],[1582])).
% 1.72/1.92 tff(1584,plain,
% 1.72/1.92 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(z)), s(z))) | (~r(s(s(s(elem!1))), s(s(z)))) | (~r(z, s(s(z)))) | (~r(z, s(s(s(elem!1))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, s(s(s(elem!1))))) | (~r(s(s(z)), s(z))) | (~r(s(s(s(elem!1))), s(s(z)))) | (~r(z, s(s(z)))))),
% 1.72/1.92 inference(transitivity,[status(thm)],[1583, 1581])).
% 1.72/1.92 tff(1585,plain,
% 1.72/1.92 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(z)), s(z))) | (~r(s(s(s(elem!1))), s(s(z)))) | (~r(z, s(s(z)))) | (~r(z, s(s(s(elem!1))))))),
% 1.72/1.92 inference(quant_inst,[status(thm)],[])).
% 1.72/1.92 tff(1586,plain,
% 1.72/1.92 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, s(s(s(elem!1))))) | (~r(s(s(z)), s(z))) | (~r(s(s(s(elem!1))), s(s(z)))) | (~r(z, s(s(z))))),
% 1.72/1.92 inference(modus_ponens,[status(thm)],[1585, 1584])).
% 1.72/1.92 tff(1587,plain,
% 1.72/1.92 ($false),
% 1.72/1.92 inference(unit_resolution,[status(thm)],[1586, 197, 155, 392, 282, 464])).
% 1.72/1.92 tff(1588,plain,((~r(z, s(s(z)))) | (~r(s(s(z)), s(z))) | (~r(z, s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), s(s(z))))), inference(lemma,lemma(discharge,[]))).
% 1.72/1.92 tff(1589,plain,
% 1.72/1.92 ($false),
% 1.72/1.92 inference(unit_resolution,[status(thm)],[1588, 1580, 1578, 155, 282])).
% 1.72/1.92 tff(1590,plain,(r(s(s(z)), s(s(s(elem!1)))) | (~r(z, s(s(z)))) | (~r(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(z))) | (s(s(elem!1)) = s(s(z))) | (~r(z, s(s(elem!1)))) | (s(s(z)) = s(s(elem!1))) | (~r(s(s(s(elem!1))), s(z))) | (~b(s(z), z))), inference(lemma,lemma(discharge,[]))).
% 1.72/1.92 tff(1591,plain,
% 1.72/1.92 (r(s(s(z)), s(s(s(elem!1))))),
% 1.72/1.92 inference(unit_resolution,[status(thm)],[1590, 1573, 282, 463, 1571, 310, 155, 365, 1569, 350, 53])).
% 1.72/1.92 tff(1592,plain,
% 1.72/1.92 (~r(s(s(elem!1)), s(s(z)))),
% 1.72/1.92 inference(unit_resolution,[status(thm)],[539, 1591, 155, 365])).
% 1.72/1.92 tff(1593,plain,
% 1.72/1.92 (b(s(s(elem!1)), s(s(z)))),
% 1.72/1.92 inference(unit_resolution,[status(thm)],[441, 1592, 1573])).
% 1.72/1.92 tff(1594,plain,
% 1.72/1.92 (~b(s(s(z)), s(s(elem!1)))),
% 1.72/1.92 inference(unit_resolution,[status(thm)],[558, 1593, 1571, 982])).
% 1.72/1.92 tff(1595,plain,
% 1.72/1.92 (r(s(s(z)), s(s(elem!1)))),
% 1.72/1.92 inference(unit_resolution,[status(thm)],[390, 1594, 1569])).
% 1.72/1.92 tff(1596,plain,
% 1.72/1.92 (r(z, s(s(s(s(elem!1))))) <=> r(z, s(s(elem!1)))),
% 1.72/1.92 inference(monotonicity,[status(thm)],[1154])).
% 1.72/1.92 tff(1597,plain,
% 1.72/1.92 (r(z, s(s(elem!1))) <=> r(z, s(s(s(s(elem!1)))))),
% 1.72/1.92 inference(symmetry,[status(thm)],[1596])).
% 1.72/1.92 tff(1598,plain,
% 1.72/1.92 (r(z, s(s(s(s(elem!1)))))),
% 1.72/1.92 inference(modus_ponens,[status(thm)],[365, 1597])).
% 1.72/1.92 tff(1599,plain,
% 1.72/1.92 (r(s(s(z)), s(s(s(s(elem!1))))) <=> r(s(s(z)), s(s(elem!1)))),
% 1.72/1.92 inference(monotonicity,[status(thm)],[1154])).
% 1.72/1.92 tff(1600,plain,
% 1.72/1.92 (r(s(s(z)), s(s(elem!1))) <=> r(s(s(z)), s(s(s(s(elem!1)))))),
% 1.72/1.92 inference(symmetry,[status(thm)],[1599])).
% 1.72/1.92 tff(1601,plain,
% 1.72/1.92 (r(s(s(z)), s(s(s(s(elem!1)))))),
% 1.72/1.92 inference(modus_ponens,[status(thm)],[333, 1600])).
% 1.72/1.92 tff(1602,plain,
% 1.72/1.92 (r(s(s(s(s(elem!1)))), s(s(s(z)))) <=> r(elem!1, s(s(s(z))))),
% 1.72/1.92 inference(monotonicity,[status(thm)],[1541])).
% 1.72/1.92 tff(1603,plain,
% 1.72/1.92 (r(elem!1, s(s(s(z)))) <=> r(s(s(s(s(elem!1)))), s(s(s(z))))),
% 1.72/1.92 inference(symmetry,[status(thm)],[1602])).
% 1.72/1.92 tff(1604,assumption,(r(elem!1, s(s(s(z))))), introduced(assumption)).
% 1.72/1.92 tff(1605,plain,
% 1.72/1.92 (r(s(s(s(s(elem!1)))), s(s(s(z))))),
% 1.72/1.92 inference(modus_ponens,[status(thm)],[1604, 1603])).
% 1.72/1.92 tff(1606,plain,
% 1.72/1.92 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(z)))) | (~r(z, s(s(s(s(elem!1)))))) | (~r(s(s(z)), s(s(s(s(elem!1)))))) | (~r(s(s(s(s(elem!1)))), s(s(s(z))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, s(s(z)))) | (~r(z, s(s(s(s(elem!1)))))) | (~r(s(s(z)), s(s(s(s(elem!1)))))) | (~r(s(s(s(s(elem!1)))), s(s(s(z))))))),
% 1.72/1.92 inference(rewrite,[status(thm)],[])).
% 1.72/1.92 tff(1607,plain,
% 1.72/1.92 (((~r(s(s(s(s(elem!1)))), s(s(s(z))))) | (~r(s(s(z)), s(s(s(s(elem!1)))))) | (~r(z, s(s(s(s(elem!1)))))) | (~r(z, s(s(z))))) <=> ((~r(z, s(s(z)))) | (~r(z, s(s(s(s(elem!1)))))) | (~r(s(s(z)), s(s(s(s(elem!1)))))) | (~r(s(s(s(s(elem!1)))), s(s(s(z))))))),
% 1.72/1.92 inference(rewrite,[status(thm)],[])).
% 1.72/1.92 tff(1608,plain,
% 1.72/1.92 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(elem!1)))), s(s(s(z))))) | (~r(s(s(z)), s(s(s(s(elem!1)))))) | (~r(z, s(s(s(s(elem!1)))))) | (~r(z, s(s(z)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(z)))) | (~r(z, s(s(s(s(elem!1)))))) | (~r(s(s(z)), s(s(s(s(elem!1)))))) | (~r(s(s(s(s(elem!1)))), s(s(s(z)))))))),
% 1.72/1.92 inference(monotonicity,[status(thm)],[1607])).
% 1.72/1.92 tff(1609,plain,
% 1.72/1.92 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(elem!1)))), s(s(s(z))))) | (~r(s(s(z)), s(s(s(s(elem!1)))))) | (~r(z, s(s(s(s(elem!1)))))) | (~r(z, s(s(z)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, s(s(z)))) | (~r(z, s(s(s(s(elem!1)))))) | (~r(s(s(z)), s(s(s(s(elem!1)))))) | (~r(s(s(s(s(elem!1)))), s(s(s(z))))))),
% 1.72/1.92 inference(transitivity,[status(thm)],[1608, 1606])).
% 1.72/1.92 tff(1610,plain,
% 1.72/1.92 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(elem!1)))), s(s(s(z))))) | (~r(s(s(z)), s(s(s(s(elem!1)))))) | (~r(z, s(s(s(s(elem!1)))))) | (~r(z, s(s(z)))))),
% 1.72/1.92 inference(quant_inst,[status(thm)],[])).
% 1.72/1.92 tff(1611,plain,
% 1.72/1.92 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, s(s(z)))) | (~r(z, s(s(s(s(elem!1)))))) | (~r(s(s(z)), s(s(s(s(elem!1)))))) | (~r(s(s(s(s(elem!1)))), s(s(s(z)))))),
% 1.72/1.92 inference(modus_ponens,[status(thm)],[1610, 1609])).
% 1.72/1.92 tff(1612,plain,
% 1.72/1.92 ((~r(z, s(s(s(s(elem!1)))))) | (~r(s(s(z)), s(s(s(s(elem!1)))))) | (~r(s(s(s(s(elem!1)))), s(s(s(z)))))),
% 1.72/1.92 inference(unit_resolution,[status(thm)],[1611, 197, 155])).
% 1.72/1.92 tff(1613,plain,
% 1.72/1.92 ($false),
% 1.72/1.92 inference(unit_resolution,[status(thm)],[1612, 1605, 1601, 1598])).
% 1.72/1.92 tff(1614,plain,((~r(elem!1, s(s(s(z))))) | (~r(z, s(s(z)))) | (~r(z, s(s(elem!1)))) | (~(s(s(elem!1)) = s(s(s(s(elem!1)))))) | (~r(s(s(z)), s(s(elem!1))))), inference(lemma,lemma(discharge,[]))).
% 1.72/1.92 tff(1615,plain,
% 1.72/1.92 (~r(elem!1, s(s(s(z))))),
% 1.72/1.92 inference(unit_resolution,[status(thm)],[1614, 1153, 365, 155, 1595])).
% 1.72/1.92 tff(1616,plain,
% 1.72/1.92 (((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((elem!1 = s(s(s(z)))) | b(elem!1, s(s(s(z)))) | r(elem!1, s(s(s(z)))))) <=> ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (elem!1 = s(s(s(z)))) | b(elem!1, s(s(s(z)))) | r(elem!1, s(s(s(z)))))),
% 1.72/1.92 inference(rewrite,[status(thm)],[])).
% 1.72/1.92 tff(1617,plain,
% 1.72/1.92 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((elem!1 = s(s(s(z)))) | b(elem!1, s(s(s(z)))) | r(elem!1, s(s(s(z)))))),
% 1.72/1.92 inference(quant_inst,[status(thm)],[])).
% 1.72/1.92 tff(1618,plain,
% 1.72/1.92 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (elem!1 = s(s(s(z)))) | b(elem!1, s(s(s(z)))) | r(elem!1, s(s(s(z))))),
% 1.72/1.92 inference(modus_ponens,[status(thm)],[1617, 1616])).
% 1.72/1.92 tff(1619,plain,
% 1.72/1.92 ((elem!1 = s(s(s(z)))) | b(elem!1, s(s(s(z)))) | r(elem!1, s(s(s(z))))),
% 1.72/1.92 inference(unit_resolution,[status(thm)],[1618, 79])).
% 1.72/1.92 tff(1620,plain,
% 1.72/1.92 (b(elem!1, s(s(s(z))))),
% 1.72/1.92 inference(unit_resolution,[status(thm)],[1619, 1615, 1565])).
% 1.72/1.92 tff(1621,plain,
% 1.72/1.92 (b(s(s(s(s(elem!1)))), s(s(s(z))))),
% 1.72/1.92 inference(modus_ponens,[status(thm)],[1620, 1543])).
% 1.72/1.92 tff(1622,plain,
% 1.72/1.92 (~b(s(s(z)), s(z))),
% 1.72/1.92 inference(unit_resolution,[status(thm)],[549, 1593, 463, 1571, 310])).
% 1.72/1.92 tff(1623,plain,
% 1.72/1.92 (r(s(s(z)), s(z))),
% 1.72/1.92 inference(unit_resolution,[status(thm)],[308, 1622])).
% 1.72/1.92 tff(1624,plain,
% 1.72/1.92 (b(s(s(elem!1)), s(elem!1)) <=> b(s(s(s(s(elem!1)))), s(s(s(elem!1))))),
% 1.72/1.92 inference(monotonicity,[status(thm)],[1153, 1168])).
% 1.72/1.92 tff(1625,plain,
% 1.72/1.92 (b(s(s(s(s(elem!1)))), s(s(s(elem!1)))) <=> b(s(s(elem!1)), s(elem!1))),
% 1.72/1.92 inference(symmetry,[status(thm)],[1624])).
% 1.72/1.92 tff(1626,plain,
% 1.72/1.92 (b(s(s(elem!1)), s(s(s(elem!1)))) <=> b(s(s(s(s(elem!1)))), s(s(s(elem!1))))),
% 1.72/1.92 inference(monotonicity,[status(thm)],[1153])).
% 1.72/1.92 tff(1627,plain,
% 1.72/1.92 (b(s(s(s(s(elem!1)))), s(s(s(elem!1))))),
% 1.72/1.92 inference(modus_ponens,[status(thm)],[463, 1626])).
% 1.72/1.92 tff(1628,plain,
% 1.72/1.92 (b(s(s(elem!1)), s(elem!1))),
% 1.72/1.92 inference(modus_ponens,[status(thm)],[1627, 1625])).
% 1.72/1.92 tff(1629,plain,
% 1.72/1.92 (b(s(s(s(s(elem!1)))), s(elem!1)) <=> b(s(s(elem!1)), s(elem!1))),
% 1.72/1.92 inference(monotonicity,[status(thm)],[1154])).
% 1.72/1.92 tff(1630,plain,
% 1.72/1.92 (b(s(s(elem!1)), s(elem!1)) <=> b(s(s(s(s(elem!1)))), s(elem!1))),
% 1.72/1.92 inference(symmetry,[status(thm)],[1629])).
% 1.72/1.92 tff(1631,assumption,(b(s(s(elem!1)), s(elem!1))), introduced(assumption)).
% 1.72/1.92 tff(1632,plain,
% 1.72/1.92 (b(s(s(s(s(elem!1)))), s(elem!1))),
% 1.72/1.92 inference(modus_ponens,[status(thm)],[1631, 1630])).
% 1.72/1.92 tff(1633,assumption,(~b(s(s(s(s(elem!1)))), s(elem!1))), introduced(assumption)).
% 1.72/1.92 tff(1634,plain,
% 1.72/1.92 ($false),
% 1.72/1.92 inference(unit_resolution,[status(thm)],[1633, 1632])).
% 1.72/1.92 tff(1635,plain,(b(s(s(s(s(elem!1)))), s(elem!1)) | (~b(s(s(elem!1)), s(elem!1))) | (~(s(s(elem!1)) = s(s(s(s(elem!1))))))), inference(lemma,lemma(discharge,[]))).
% 1.72/1.92 tff(1636,plain,
% 1.72/1.92 (b(s(s(s(s(elem!1)))), s(elem!1))),
% 1.72/1.92 inference(unit_resolution,[status(thm)],[1635, 1628, 1153])).
% 1.72/1.92 tff(1637,plain,
% 1.72/1.92 (b(s(z), s(s(s(s(elem!1)))))),
% 1.72/1.92 inference(modus_ponens,[status(thm)],[1571, 1206])).
% 1.72/1.92 tff(1638,plain,
% 1.72/1.92 (~r(s(s(s(elem!1))), s(s(z)))),
% 1.72/1.92 inference(unit_resolution,[status(thm)],[1588, 1623, 155, 282])).
% 1.72/1.92 tff(1639,plain,
% 1.72/1.92 (~r(s(elem!1), s(s(z)))),
% 1.72/1.92 inference(unit_resolution,[status(thm)],[1250, 1638, 1167])).
% 1.72/1.92 tff(1640,plain,
% 1.72/1.92 (b(s(elem!1), s(s(z)))),
% 1.72/1.92 inference(unit_resolution,[status(thm)],[1260, 1639, 1256])).
% 1.72/1.92 tff(1641,assumption,(b(s(s(s(s(elem!1)))), s(elem!1))), introduced(assumption)).
% 1.72/1.92 tff(1642,assumption,(b(s(elem!1), s(s(z)))), introduced(assumption)).
% 1.72/1.92 tff(1643,plain,
% 1.72/1.92 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), z)) | (~b(s(z), s(elem!1))) | (~b(s(s(s(s(elem!1)))), s(elem!1))) | (~b(s(s(z)), z)) | (~b(s(z), s(s(s(s(elem!1)))))) | (~b(s(elem!1), s(s(z)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), z)) | (~b(s(z), s(elem!1))) | (~b(s(s(s(s(elem!1)))), s(elem!1))) | (~b(s(s(z)), z)) | (~b(s(z), s(s(s(s(elem!1)))))) | (~b(s(elem!1), s(s(z)))))),
% 1.72/1.92 inference(rewrite,[status(thm)],[])).
% 1.72/1.92 tff(1644,plain,
% 1.72/1.92 (((~b(s(s(z)), z)) | (~b(s(z), z)) | (~b(s(elem!1), s(s(z)))) | (~b(s(s(s(s(elem!1)))), s(elem!1))) | (~b(s(z), s(elem!1))) | (~b(s(z), s(s(s(s(elem!1))))))) <=> ((~b(s(z), z)) | (~b(s(z), s(elem!1))) | (~b(s(s(s(s(elem!1)))), s(elem!1))) | (~b(s(s(z)), z)) | (~b(s(z), s(s(s(s(elem!1)))))) | (~b(s(elem!1), s(s(z)))))),
% 1.72/1.92 inference(rewrite,[status(thm)],[])).
% 1.72/1.92 tff(1645,plain,
% 1.72/1.92 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), z)) | (~b(s(z), z)) | (~b(s(elem!1), s(s(z)))) | (~b(s(s(s(s(elem!1)))), s(elem!1))) | (~b(s(z), s(elem!1))) | (~b(s(z), s(s(s(s(elem!1)))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), z)) | (~b(s(z), s(elem!1))) | (~b(s(s(s(s(elem!1)))), s(elem!1))) | (~b(s(s(z)), z)) | (~b(s(z), s(s(s(s(elem!1)))))) | (~b(s(elem!1), s(s(z))))))),
% 1.72/1.92 inference(monotonicity,[status(thm)],[1644])).
% 1.72/1.92 tff(1646,plain,
% 1.72/1.92 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), z)) | (~b(s(z), z)) | (~b(s(elem!1), s(s(z)))) | (~b(s(s(s(s(elem!1)))), s(elem!1))) | (~b(s(z), s(elem!1))) | (~b(s(z), s(s(s(s(elem!1)))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), z)) | (~b(s(z), s(elem!1))) | (~b(s(s(s(s(elem!1)))), s(elem!1))) | (~b(s(s(z)), z)) | (~b(s(z), s(s(s(s(elem!1)))))) | (~b(s(elem!1), s(s(z)))))),
% 1.72/1.92 inference(transitivity,[status(thm)],[1645, 1643])).
% 1.72/1.92 tff(1647,plain,
% 1.72/1.92 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), z)) | (~b(s(z), z)) | (~b(s(elem!1), s(s(z)))) | (~b(s(s(s(s(elem!1)))), s(elem!1))) | (~b(s(z), s(elem!1))) | (~b(s(z), s(s(s(s(elem!1)))))))),
% 1.72/1.92 inference(quant_inst,[status(thm)],[])).
% 1.72/1.92 tff(1648,plain,
% 1.72/1.92 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), z)) | (~b(s(z), s(elem!1))) | (~b(s(s(s(s(elem!1)))), s(elem!1))) | (~b(s(s(z)), z)) | (~b(s(z), s(s(s(s(elem!1)))))) | (~b(s(elem!1), s(s(z))))),
% 1.72/1.92 inference(modus_ponens,[status(thm)],[1647, 1646])).
% 1.72/1.92 tff(1649,plain,
% 1.72/1.92 ($false),
% 1.72/1.92 inference(unit_resolution,[status(thm)],[1648, 166, 53, 1642, 1211, 1327, 122, 1641])).
% 1.72/1.92 tff(1650,plain,((~b(s(s(z)), z)) | (~b(s(z), z)) | (~b(s(elem!1), s(s(z)))) | (~b(s(z), s(elem!1))) | (~b(s(z), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), s(elem!1)))), inference(lemma,lemma(discharge,[]))).
% 1.72/1.92 tff(1651,plain,
% 1.72/1.92 (~b(s(s(z)), z)),
% 1.72/1.92 inference(unit_resolution,[status(thm)],[1650, 1640, 53, 1210, 1637, 1636])).
% 1.72/1.92 tff(1652,plain,
% 1.72/1.92 (r(s(s(z)), z)),
% 1.72/1.92 inference(unit_resolution,[status(thm)],[186, 1651])).
% 1.72/1.92 tff(1653,assumption,(r(s(z), s(s(s(z))))), introduced(assumption)).
% 1.72/1.92 tff(1654,plain,
% 1.72/1.92 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(z))) | (~r(s(s(z)), s(z))) | (~r(s(s(z)), z)) | (~r(s(z), s(s(s(z))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, s(z))) | (~r(s(s(z)), s(z))) | (~r(s(s(z)), z)) | (~r(s(z), s(s(s(z))))))),
% 1.72/1.92 inference(rewrite,[status(thm)],[])).
% 1.72/1.92 tff(1655,plain,
% 1.72/1.92 (((~r(s(z), s(s(s(z))))) | (~r(z, s(z))) | (~r(s(s(z)), s(z))) | (~r(s(s(z)), z))) <=> ((~r(z, s(z))) | (~r(s(s(z)), s(z))) | (~r(s(s(z)), z)) | (~r(s(z), s(s(s(z))))))),
% 1.72/1.92 inference(rewrite,[status(thm)],[])).
% 1.72/1.92 tff(1656,plain,
% 1.72/1.92 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(s(s(z))))) | (~r(z, s(z))) | (~r(s(s(z)), s(z))) | (~r(s(s(z)), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(z))) | (~r(s(s(z)), s(z))) | (~r(s(s(z)), z)) | (~r(s(z), s(s(s(z)))))))),
% 1.72/1.92 inference(monotonicity,[status(thm)],[1655])).
% 1.72/1.93 tff(1657,plain,
% 1.72/1.93 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(s(s(z))))) | (~r(z, s(z))) | (~r(s(s(z)), s(z))) | (~r(s(s(z)), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, s(z))) | (~r(s(s(z)), s(z))) | (~r(s(s(z)), z)) | (~r(s(z), s(s(s(z))))))),
% 1.72/1.93 inference(transitivity,[status(thm)],[1656, 1654])).
% 1.72/1.93 tff(1658,plain,
% 1.72/1.93 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(s(s(z))))) | (~r(z, s(z))) | (~r(s(s(z)), s(z))) | (~r(s(s(z)), z)))),
% 1.72/1.93 inference(quant_inst,[status(thm)],[])).
% 1.72/1.93 tff(1659,plain,
% 1.72/1.93 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, s(z))) | (~r(s(s(z)), s(z))) | (~r(s(s(z)), z)) | (~r(s(z), s(s(s(z)))))),
% 1.72/1.93 inference(modus_ponens,[status(thm)],[1658, 1657])).
% 1.72/1.93 tff(1660,plain,
% 1.72/1.93 ($false),
% 1.72/1.93 inference(unit_resolution,[status(thm)],[1659, 197, 323, 392, 866, 1653])).
% 1.72/1.93 tff(1661,plain,((~r(s(z), s(s(s(z))))) | (~r(z, s(z))) | (~r(s(s(z)), s(z))) | (~r(s(s(z)), z))), inference(lemma,lemma(discharge,[]))).
% 1.72/1.93 tff(1662,plain,
% 1.72/1.93 (~r(s(z), s(s(s(z))))),
% 1.72/1.93 inference(unit_resolution,[status(thm)],[1661, 1652, 1623, 323])).
% 1.72/1.93 tff(1663,assumption,(s(z) = s(s(s(z)))), introduced(assumption)).
% 1.72/1.93 tff(1664,plain,
% 1.72/1.93 (inj_0(s(z)) = inj_0(s(s(s(z))))),
% 1.72/1.93 inference(monotonicity,[status(thm)],[1663])).
% 1.72/1.93 tff(1665,plain,
% 1.72/1.93 (inj_0(s(s(s(z)))) = inj_0(s(z))),
% 1.72/1.93 inference(symmetry,[status(thm)],[1664])).
% 1.72/1.93 tff(1666,plain,
% 1.72/1.93 (s(s(z)) = inj_0(s(s(s(z))))),
% 1.72/1.93 inference(symmetry,[status(thm)],[134])).
% 1.72/1.93 tff(1667,plain,
% 1.72/1.93 (s(s(z)) = z),
% 1.72/1.93 inference(transitivity,[status(thm)],[1666, 1665, 25])).
% 1.72/1.93 tff(1668,plain,
% 1.72/1.93 ($false),
% 1.72/1.93 inference(unit_resolution,[status(thm)],[145, 1667])).
% 1.72/1.93 tff(1669,plain,(~(s(z) = s(s(s(z))))), inference(lemma,lemma(discharge,[]))).
% 1.72/1.93 tff(1670,plain,
% 1.72/1.93 (((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((s(z) = s(s(s(z)))) | b(s(z), s(s(s(z)))) | r(s(z), s(s(s(z)))))) <=> ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (s(z) = s(s(s(z)))) | b(s(z), s(s(s(z)))) | r(s(z), s(s(s(z)))))),
% 1.72/1.93 inference(rewrite,[status(thm)],[])).
% 1.72/1.93 tff(1671,plain,
% 1.72/1.93 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((s(z) = s(s(s(z)))) | b(s(z), s(s(s(z)))) | r(s(z), s(s(s(z)))))),
% 1.72/1.93 inference(quant_inst,[status(thm)],[])).
% 1.72/1.93 tff(1672,plain,
% 1.72/1.93 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (s(z) = s(s(s(z)))) | b(s(z), s(s(s(z)))) | r(s(z), s(s(s(z))))),
% 1.72/1.93 inference(modus_ponens,[status(thm)],[1671, 1670])).
% 1.72/1.93 tff(1673,plain,
% 1.72/1.93 ((s(z) = s(s(s(z)))) | b(s(z), s(s(s(z)))) | r(s(z), s(s(s(z))))),
% 1.72/1.93 inference(unit_resolution,[status(thm)],[1672, 79])).
% 1.72/1.93 tff(1674,plain,
% 1.72/1.93 (b(s(z), s(s(s(z)))) | r(s(z), s(s(s(z))))),
% 1.72/1.93 inference(unit_resolution,[status(thm)],[1673, 1669])).
% 1.72/1.93 tff(1675,plain,
% 1.72/1.93 (b(s(z), s(s(s(z))))),
% 1.72/1.93 inference(unit_resolution,[status(thm)],[1674, 1662])).
% 1.72/1.93 tff(1676,assumption,(r(s(s(s(z))), s(s(z)))), introduced(assumption)).
% 1.72/1.93 tff(1677,assumption,(r(z, s(s(s(z))))), introduced(assumption)).
% 1.72/1.93 tff(1678,plain,
% 1.72/1.93 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(s(z))))) | (~r(s(s(z)), s(z))) | (~r(z, s(s(z)))) | (~r(s(s(s(z))), s(s(z)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, s(s(s(z))))) | (~r(s(s(z)), s(z))) | (~r(z, s(s(z)))) | (~r(s(s(s(z))), s(s(z)))))),
% 1.72/1.93 inference(rewrite,[status(thm)],[])).
% 1.72/1.93 tff(1679,plain,
% 1.72/1.93 (((~r(s(s(z)), s(z))) | (~r(s(s(s(z))), s(s(z)))) | (~r(z, s(s(z)))) | (~r(z, s(s(s(z)))))) <=> ((~r(z, s(s(s(z))))) | (~r(s(s(z)), s(z))) | (~r(z, s(s(z)))) | (~r(s(s(s(z))), s(s(z)))))),
% 1.72/1.93 inference(rewrite,[status(thm)],[])).
% 1.72/1.93 tff(1680,plain,
% 1.72/1.93 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(z)), s(z))) | (~r(s(s(s(z))), s(s(z)))) | (~r(z, s(s(z)))) | (~r(z, s(s(s(z))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(s(z))))) | (~r(s(s(z)), s(z))) | (~r(z, s(s(z)))) | (~r(s(s(s(z))), s(s(z))))))),
% 1.72/1.93 inference(monotonicity,[status(thm)],[1679])).
% 1.72/1.93 tff(1681,plain,
% 1.72/1.93 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(z)), s(z))) | (~r(s(s(s(z))), s(s(z)))) | (~r(z, s(s(z)))) | (~r(z, s(s(s(z))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, s(s(s(z))))) | (~r(s(s(z)), s(z))) | (~r(z, s(s(z)))) | (~r(s(s(s(z))), s(s(z)))))),
% 1.72/1.93 inference(transitivity,[status(thm)],[1680, 1678])).
% 1.72/1.93 tff(1682,plain,
% 1.72/1.93 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(z)), s(z))) | (~r(s(s(s(z))), s(s(z)))) | (~r(z, s(s(z)))) | (~r(z, s(s(s(z))))))),
% 1.72/1.93 inference(quant_inst,[status(thm)],[])).
% 1.72/1.93 tff(1683,plain,
% 1.72/1.93 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, s(s(s(z))))) | (~r(s(s(z)), s(z))) | (~r(z, s(s(z)))) | (~r(s(s(s(z))), s(s(z))))),
% 1.72/1.93 inference(modus_ponens,[status(thm)],[1682, 1681])).
% 1.72/1.93 tff(1684,plain,
% 1.72/1.93 ($false),
% 1.72/1.93 inference(unit_resolution,[status(thm)],[1683, 197, 155, 392, 1677, 1676])).
% 1.72/1.93 tff(1685,plain,((~r(s(s(s(z))), s(s(z)))) | (~r(z, s(s(z)))) | (~r(s(s(z)), s(z))) | (~r(z, s(s(s(z)))))), inference(lemma,lemma(discharge,[]))).
% 1.72/1.93 tff(1686,plain,
% 1.72/1.93 (~r(z, s(s(s(z))))),
% 1.72/1.93 inference(unit_resolution,[status(thm)],[1685, 1676, 155, 392])).
% 1.72/1.93 tff(1687,plain,
% 1.72/1.93 ((z = s(s(s(z)))) <=> (s(s(s(z))) = z)),
% 1.72/1.93 inference(commutativity,[status(thm)],[])).
% 1.72/1.93 tff(1688,plain,
% 1.72/1.93 ((s(s(s(z))) = z) <=> (z = s(s(s(z))))),
% 1.72/1.93 inference(symmetry,[status(thm)],[1687])).
% 1.72/1.93 tff(1689,plain,
% 1.72/1.93 ((~(s(s(s(z))) = z)) <=> (~(z = s(s(s(z)))))),
% 1.72/1.93 inference(monotonicity,[status(thm)],[1688])).
% 1.72/1.93 tff(1690,plain,
% 1.72/1.93 ((~![X: $i] : (~(s(X) = z))) | (~(s(s(s(z))) = z))),
% 1.72/1.93 inference(quant_inst,[status(thm)],[])).
% 1.72/1.93 tff(1691,plain,
% 1.72/1.93 (~(s(s(s(z))) = z)),
% 1.72/1.93 inference(unit_resolution,[status(thm)],[1690, 65])).
% 1.72/1.93 tff(1692,plain,
% 1.72/1.93 (~(z = s(s(s(z))))),
% 1.72/1.93 inference(modus_ponens,[status(thm)],[1691, 1689])).
% 1.72/1.93 tff(1693,plain,
% 1.72/1.93 (((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((z = s(s(s(z)))) | b(z, s(s(s(z)))) | r(z, s(s(s(z)))))) <=> ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (z = s(s(s(z)))) | b(z, s(s(s(z)))) | r(z, s(s(s(z)))))),
% 1.72/1.93 inference(rewrite,[status(thm)],[])).
% 1.72/1.93 tff(1694,plain,
% 1.72/1.93 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((z = s(s(s(z)))) | b(z, s(s(s(z)))) | r(z, s(s(s(z)))))),
% 1.72/1.93 inference(quant_inst,[status(thm)],[])).
% 1.72/1.93 tff(1695,plain,
% 1.72/1.93 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (z = s(s(s(z)))) | b(z, s(s(s(z)))) | r(z, s(s(s(z))))),
% 1.72/1.93 inference(modus_ponens,[status(thm)],[1694, 1693])).
% 1.72/1.93 tff(1696,plain,
% 1.72/1.93 ((z = s(s(s(z)))) | b(z, s(s(s(z)))) | r(z, s(s(s(z))))),
% 1.72/1.93 inference(unit_resolution,[status(thm)],[1695, 79])).
% 1.72/1.93 tff(1697,plain,
% 1.72/1.93 (b(z, s(s(s(z)))) | r(z, s(s(s(z))))),
% 1.72/1.93 inference(unit_resolution,[status(thm)],[1696, 1692])).
% 1.72/1.93 tff(1698,plain,
% 1.72/1.93 (b(z, s(s(s(z))))),
% 1.72/1.93 inference(unit_resolution,[status(thm)],[1697, 1686])).
% 1.72/1.93 tff(1699,assumption,(b(s(s(s(z))), z)), introduced(assumption)).
% 1.72/1.93 tff(1700,assumption,(b(z, s(s(s(z))))), introduced(assumption)).
% 1.72/1.93 tff(1701,plain,
% 1.72/1.93 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), z)) | (~b(s(s(s(z))), z)) | (~b(s(z), s(s(s(z))))) | (~b(z, s(s(s(z))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), z)) | (~b(s(s(s(z))), z)) | (~b(s(z), s(s(s(z))))) | (~b(z, s(s(s(z))))))),
% 1.72/1.93 inference(rewrite,[status(thm)],[])).
% 1.72/1.93 tff(1702,plain,
% 1.72/1.93 (((~b(s(s(s(z))), z)) | (~b(s(z), z)) | (~b(z, s(s(s(z))))) | (~b(s(s(s(z))), z)) | (~b(s(z), z)) | (~b(s(z), s(s(s(z)))))) <=> ((~b(s(z), z)) | (~b(s(s(s(z))), z)) | (~b(s(z), s(s(s(z))))) | (~b(z, s(s(s(z))))))),
% 1.72/1.93 inference(rewrite,[status(thm)],[])).
% 1.72/1.93 tff(1703,plain,
% 1.72/1.93 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), z)) | (~b(s(z), z)) | (~b(z, s(s(s(z))))) | (~b(s(s(s(z))), z)) | (~b(s(z), z)) | (~b(s(z), s(s(s(z))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), z)) | (~b(s(s(s(z))), z)) | (~b(s(z), s(s(s(z))))) | (~b(z, s(s(s(z)))))))),
% 1.72/1.93 inference(monotonicity,[status(thm)],[1702])).
% 1.72/1.93 tff(1704,plain,
% 1.72/1.93 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), z)) | (~b(s(z), z)) | (~b(z, s(s(s(z))))) | (~b(s(s(s(z))), z)) | (~b(s(z), z)) | (~b(s(z), s(s(s(z))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), z)) | (~b(s(s(s(z))), z)) | (~b(s(z), s(s(s(z))))) | (~b(z, s(s(s(z))))))),
% 1.72/1.93 inference(transitivity,[status(thm)],[1703, 1701])).
% 1.72/1.93 tff(1705,plain,
% 1.72/1.93 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), z)) | (~b(s(z), z)) | (~b(z, s(s(s(z))))) | (~b(s(s(s(z))), z)) | (~b(s(z), z)) | (~b(s(z), s(s(s(z))))))),
% 1.72/1.93 inference(quant_inst,[status(thm)],[])).
% 1.72/1.93 tff(1706,plain,
% 1.72/1.93 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), z)) | (~b(s(s(s(z))), z)) | (~b(s(z), s(s(s(z))))) | (~b(z, s(s(s(z)))))),
% 1.72/1.93 inference(modus_ponens,[status(thm)],[1705, 1704])).
% 1.72/1.93 tff(1707,plain,
% 1.72/1.93 ($false),
% 1.72/1.93 inference(unit_resolution,[status(thm)],[1706, 166, 53, 988, 1700, 1699])).
% 1.72/1.93 tff(1708,plain,((~b(s(s(s(z))), z)) | (~b(s(z), z)) | (~b(s(z), s(s(s(z))))) | (~b(z, s(s(s(z)))))), inference(lemma,lemma(discharge,[]))).
% 1.72/1.93 tff(1709,plain,
% 1.72/1.93 (~b(s(s(s(z))), z)),
% 1.72/1.93 inference(unit_resolution,[status(thm)],[1708, 1698, 53, 988])).
% 1.72/1.93 tff(1710,plain,
% 1.72/1.93 (((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((s(s(s(z))) = z) | b(s(s(s(z))), z) | r(s(s(s(z))), z))) <=> ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (s(s(s(z))) = z) | b(s(s(s(z))), z) | r(s(s(s(z))), z))),
% 1.72/1.93 inference(rewrite,[status(thm)],[])).
% 1.72/1.93 tff(1711,plain,
% 1.72/1.93 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((s(s(s(z))) = z) | b(s(s(s(z))), z) | r(s(s(s(z))), z))),
% 1.72/1.93 inference(quant_inst,[status(thm)],[])).
% 1.72/1.93 tff(1712,plain,
% 1.72/1.93 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (s(s(s(z))) = z) | b(s(s(s(z))), z) | r(s(s(s(z))), z)),
% 1.72/1.93 inference(modus_ponens,[status(thm)],[1711, 1710])).
% 1.72/1.93 tff(1713,plain,
% 1.72/1.93 (b(s(s(s(z))), z) | r(s(s(s(z))), z)),
% 1.72/1.93 inference(unit_resolution,[status(thm)],[1712, 79, 1691])).
% 1.72/1.93 tff(1714,plain,
% 1.72/1.93 (r(s(s(s(z))), z)),
% 1.72/1.93 inference(unit_resolution,[status(thm)],[1713, 1709])).
% 1.72/1.93 tff(1715,plain,
% 1.72/1.93 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(z)))) | (~r(s(s(z)), z)) | (~r(s(s(s(z))), z)) | (~r(s(s(s(z))), s(s(z)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, s(s(z)))) | (~r(s(s(z)), z)) | (~r(s(s(s(z))), z)) | (~r(s(s(s(z))), s(s(z)))))),
% 1.72/1.93 inference(rewrite,[status(thm)],[])).
% 1.72/1.93 tff(1716,plain,
% 1.72/1.93 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(z)))) | (~r(s(s(z)), z)) | (~r(s(s(s(z))), z)) | (~r(s(s(s(z))), s(s(z)))))),
% 1.72/1.93 inference(quant_inst,[status(thm)],[])).
% 1.72/1.93 tff(1717,plain,
% 1.72/1.93 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, s(s(z)))) | (~r(s(s(z)), z)) | (~r(s(s(s(z))), z)) | (~r(s(s(s(z))), s(s(z))))),
% 1.72/1.93 inference(modus_ponens,[status(thm)],[1716, 1715])).
% 1.72/1.93 tff(1718,plain,
% 1.72/1.93 ($false),
% 1.72/1.93 inference(unit_resolution,[status(thm)],[1717, 197, 155, 866, 1676, 1714])).
% 1.72/1.93 tff(1719,plain,((~r(s(s(s(z))), s(s(z)))) | (~r(z, s(s(z)))) | (~r(s(s(z)), z)) | (~b(s(z), z)) | (~b(s(z), s(s(s(z))))) | (~r(s(s(z)), s(z)))), inference(lemma,lemma(discharge,[]))).
% 1.72/1.93 tff(1720,plain,
% 1.72/1.93 (~r(s(s(s(z))), s(s(z)))),
% 1.72/1.93 inference(unit_resolution,[status(thm)],[1719, 1652, 155, 53, 1675, 1623])).
% 1.72/1.93 tff(1721,plain,
% 1.72/1.93 (b(s(s(s(z))), s(s(z)))),
% 1.72/1.93 inference(unit_resolution,[status(thm)],[1010, 1720])).
% 1.72/1.93 tff(1722,plain,
% 1.72/1.93 (~b(s(s(z)), s(s(s(z))))),
% 1.72/1.93 inference(unit_resolution,[status(thm)],[996, 1721, 982, 1675])).
% 1.72/1.93 tff(1723,plain,
% 1.72/1.93 ((s(s(s(z))) = s(s(z))) <=> (s(s(z)) = s(s(s(z))))),
% 1.72/1.93 inference(commutativity,[status(thm)],[])).
% 1.72/1.93 tff(1724,plain,
% 1.72/1.93 ((~(s(s(s(z))) = s(s(z)))) <=> (~(s(s(z)) = s(s(s(z)))))),
% 1.72/1.93 inference(monotonicity,[status(thm)],[1723])).
% 1.72/1.93 tff(1725,plain,
% 1.72/1.93 (~(s(s(z)) = s(s(s(z))))),
% 1.72/1.93 inference(modus_ponens,[status(thm)],[1003, 1724])).
% 1.72/1.93 tff(1726,plain,
% 1.72/1.93 (((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((s(s(z)) = s(s(s(z)))) | b(s(s(z)), s(s(s(z)))) | r(s(s(z)), s(s(s(z)))))) <=> ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (s(s(z)) = s(s(s(z)))) | b(s(s(z)), s(s(s(z)))) | r(s(s(z)), s(s(s(z)))))),
% 1.72/1.93 inference(rewrite,[status(thm)],[])).
% 1.72/1.93 tff(1727,plain,
% 1.72/1.93 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((s(s(z)) = s(s(s(z)))) | b(s(s(z)), s(s(s(z)))) | r(s(s(z)), s(s(s(z)))))),
% 1.72/1.93 inference(quant_inst,[status(thm)],[])).
% 1.72/1.93 tff(1728,plain,
% 1.72/1.93 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (s(s(z)) = s(s(s(z)))) | b(s(s(z)), s(s(s(z)))) | r(s(s(z)), s(s(s(z))))),
% 1.72/1.93 inference(modus_ponens,[status(thm)],[1727, 1726])).
% 1.72/1.93 tff(1729,plain,
% 1.72/1.93 ((s(s(z)) = s(s(s(z)))) | b(s(s(z)), s(s(s(z)))) | r(s(s(z)), s(s(s(z))))),
% 1.72/1.93 inference(unit_resolution,[status(thm)],[1728, 79])).
% 1.72/1.93 tff(1730,plain,
% 1.72/1.93 (b(s(s(z)), s(s(s(z)))) | r(s(s(z)), s(s(s(z))))),
% 1.72/1.93 inference(unit_resolution,[status(thm)],[1729, 1725])).
% 1.72/1.93 tff(1731,plain,
% 1.72/1.93 (r(s(s(z)), s(s(s(z))))),
% 1.72/1.93 inference(unit_resolution,[status(thm)],[1730, 1722])).
% 1.72/1.93 tff(1732,assumption,(r(s(s(z)), s(s(s(z))))), introduced(assumption)).
% 1.72/1.93 tff(1733,assumption,(r(s(s(s(z))), z)), introduced(assumption)).
% 1.72/1.93 tff(1734,plain,
% 1.72/1.93 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(z)), z)) | (~r(s(s(z)), s(s(s(z))))) | (~r(z, s(s(z)))) | (~r(s(s(s(z))), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(z)), z)) | (~r(s(s(z)), s(s(s(z))))) | (~r(z, s(s(z)))) | (~r(s(s(s(z))), z)))),
% 1.72/1.93 inference(rewrite,[status(thm)],[])).
% 1.72/1.93 tff(1735,plain,
% 1.72/1.93 (((~r(z, s(s(z)))) | (~r(s(s(s(z))), z)) | (~r(s(s(z)), z)) | (~r(s(s(z)), s(s(s(z)))))) <=> ((~r(s(s(z)), z)) | (~r(s(s(z)), s(s(s(z))))) | (~r(z, s(s(z)))) | (~r(s(s(s(z))), z)))),
% 1.72/1.93 inference(rewrite,[status(thm)],[])).
% 1.72/1.93 tff(1736,plain,
% 1.72/1.93 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(z)))) | (~r(s(s(s(z))), z)) | (~r(s(s(z)), z)) | (~r(s(s(z)), s(s(s(z))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(z)), z)) | (~r(s(s(z)), s(s(s(z))))) | (~r(z, s(s(z)))) | (~r(s(s(s(z))), z))))),
% 1.72/1.93 inference(monotonicity,[status(thm)],[1735])).
% 1.72/1.93 tff(1737,plain,
% 1.72/1.93 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(z)))) | (~r(s(s(s(z))), z)) | (~r(s(s(z)), z)) | (~r(s(s(z)), s(s(s(z))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(z)), z)) | (~r(s(s(z)), s(s(s(z))))) | (~r(z, s(s(z)))) | (~r(s(s(s(z))), z)))),
% 1.72/1.93 inference(transitivity,[status(thm)],[1736, 1734])).
% 1.72/1.93 tff(1738,plain,
% 1.72/1.93 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(z)))) | (~r(s(s(s(z))), z)) | (~r(s(s(z)), z)) | (~r(s(s(z)), s(s(s(z))))))),
% 1.72/1.93 inference(quant_inst,[status(thm)],[])).
% 1.72/1.94 tff(1739,plain,
% 1.72/1.94 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(z)), z)) | (~r(s(s(z)), s(s(s(z))))) | (~r(z, s(s(z)))) | (~r(s(s(s(z))), z))),
% 1.72/1.94 inference(modus_ponens,[status(thm)],[1738, 1737])).
% 1.72/1.94 tff(1740,plain,
% 1.72/1.94 ($false),
% 1.72/1.94 inference(unit_resolution,[status(thm)],[1739, 197, 155, 866, 1733, 1732])).
% 1.72/1.94 tff(1741,plain,((~r(s(s(s(z))), z)) | (~r(z, s(s(z)))) | (~r(s(s(z)), z)) | (~r(s(s(z)), s(s(s(z)))))), inference(lemma,lemma(discharge,[]))).
% 1.72/1.94 tff(1742,plain,
% 1.72/1.94 (~r(s(s(s(z))), z)),
% 1.72/1.94 inference(unit_resolution,[status(thm)],[1741, 1731, 1652, 155])).
% 1.72/1.94 tff(1743,plain,
% 1.72/1.94 (b(s(s(s(z))), z)),
% 1.72/1.94 inference(unit_resolution,[status(thm)],[1713, 1742])).
% 1.72/1.94 tff(1744,plain,
% 1.72/1.94 (~b(z, s(s(s(z))))),
% 1.72/1.94 inference(unit_resolution,[status(thm)],[1708, 1743, 53, 1675])).
% 1.72/1.94 tff(1745,plain,
% 1.72/1.94 (r(z, s(s(s(z))))),
% 1.72/1.94 inference(unit_resolution,[status(thm)],[1697, 1744])).
% 1.72/1.94 tff(1746,assumption,(r(s(s(s(z))), s(z))), introduced(assumption)).
% 1.72/1.94 tff(1747,plain,
% 1.72/1.94 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(s(z))))) | (~r(s(s(z)), z)) | (~r(s(s(z)), s(s(s(z))))) | (~r(s(s(s(z))), s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, s(s(s(z))))) | (~r(s(s(z)), z)) | (~r(s(s(z)), s(s(s(z))))) | (~r(s(s(s(z))), s(z))))),
% 1.72/1.94 inference(rewrite,[status(thm)],[])).
% 1.72/1.94 tff(1748,plain,
% 1.72/1.94 (((~r(s(s(s(z))), s(z))) | (~r(z, s(s(s(z))))) | (~r(s(s(z)), s(s(s(z))))) | (~r(s(s(z)), z))) <=> ((~r(z, s(s(s(z))))) | (~r(s(s(z)), z)) | (~r(s(s(z)), s(s(s(z))))) | (~r(s(s(s(z))), s(z))))),
% 1.72/1.94 inference(rewrite,[status(thm)],[])).
% 1.72/1.94 tff(1749,plain,
% 1.72/1.94 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(z))), s(z))) | (~r(z, s(s(s(z))))) | (~r(s(s(z)), s(s(s(z))))) | (~r(s(s(z)), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(s(z))))) | (~r(s(s(z)), z)) | (~r(s(s(z)), s(s(s(z))))) | (~r(s(s(s(z))), s(z)))))),
% 1.72/1.94 inference(monotonicity,[status(thm)],[1748])).
% 1.72/1.94 tff(1750,plain,
% 1.72/1.94 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(z))), s(z))) | (~r(z, s(s(s(z))))) | (~r(s(s(z)), s(s(s(z))))) | (~r(s(s(z)), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, s(s(s(z))))) | (~r(s(s(z)), z)) | (~r(s(s(z)), s(s(s(z))))) | (~r(s(s(s(z))), s(z))))),
% 1.72/1.94 inference(transitivity,[status(thm)],[1749, 1747])).
% 1.72/1.94 tff(1751,plain,
% 1.72/1.94 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(z))), s(z))) | (~r(z, s(s(s(z))))) | (~r(s(s(z)), s(s(s(z))))) | (~r(s(s(z)), z)))),
% 1.72/1.94 inference(quant_inst,[status(thm)],[])).
% 1.72/1.94 tff(1752,plain,
% 1.72/1.94 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, s(s(s(z))))) | (~r(s(s(z)), z)) | (~r(s(s(z)), s(s(s(z))))) | (~r(s(s(s(z))), s(z)))),
% 1.72/1.94 inference(modus_ponens,[status(thm)],[1751, 1750])).
% 1.72/1.94 tff(1753,plain,
% 1.72/1.94 ($false),
% 1.72/1.94 inference(unit_resolution,[status(thm)],[1752, 197, 866, 1677, 1746, 1732])).
% 1.72/1.94 tff(1754,plain,((~r(s(s(s(z))), s(z))) | (~r(s(s(z)), z)) | (~r(z, s(s(s(z))))) | (~r(s(s(z)), s(s(s(z)))))), inference(lemma,lemma(discharge,[]))).
% 1.72/1.94 tff(1755,plain,
% 1.72/1.94 (~r(s(s(s(z))), s(z))),
% 1.72/1.94 inference(unit_resolution,[status(thm)],[1754, 1652, 1745, 1731])).
% 1.72/1.94 tff(1756,plain,
% 1.72/1.94 ((s(z) = s(s(s(z)))) <=> (s(s(s(z))) = s(z))),
% 1.72/1.94 inference(commutativity,[status(thm)],[])).
% 1.72/1.94 tff(1757,plain,
% 1.72/1.94 ((~(s(z) = s(s(s(z))))) <=> (~(s(s(s(z))) = s(z)))),
% 1.72/1.94 inference(monotonicity,[status(thm)],[1756])).
% 1.72/1.94 tff(1758,plain,
% 1.72/1.94 (~(s(s(s(z))) = s(z))),
% 1.72/1.94 inference(modus_ponens,[status(thm)],[1669, 1757])).
% 1.72/1.94 tff(1759,plain,
% 1.72/1.94 (((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((s(s(s(z))) = s(z)) | b(s(s(s(z))), s(z)) | r(s(s(s(z))), s(z)))) <=> ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (s(s(s(z))) = s(z)) | b(s(s(s(z))), s(z)) | r(s(s(s(z))), s(z)))),
% 1.72/1.94 inference(rewrite,[status(thm)],[])).
% 1.72/1.94 tff(1760,plain,
% 1.72/1.94 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((s(s(s(z))) = s(z)) | b(s(s(s(z))), s(z)) | r(s(s(s(z))), s(z)))),
% 1.72/1.94 inference(quant_inst,[status(thm)],[])).
% 1.72/1.94 tff(1761,plain,
% 1.72/1.94 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (s(s(s(z))) = s(z)) | b(s(s(s(z))), s(z)) | r(s(s(s(z))), s(z))),
% 1.72/1.94 inference(modus_ponens,[status(thm)],[1760, 1759])).
% 1.72/1.94 tff(1762,plain,
% 1.72/1.94 ((s(s(s(z))) = s(z)) | b(s(s(s(z))), s(z)) | r(s(s(s(z))), s(z))),
% 1.72/1.94 inference(unit_resolution,[status(thm)],[1761, 79])).
% 1.72/1.94 tff(1763,plain,
% 1.72/1.94 (b(s(s(s(z))), s(z)) | r(s(s(s(z))), s(z))),
% 1.72/1.94 inference(unit_resolution,[status(thm)],[1762, 1758])).
% 1.72/1.94 tff(1764,plain,
% 1.72/1.94 (b(s(s(s(z))), s(z))),
% 1.72/1.94 inference(unit_resolution,[status(thm)],[1763, 1755])).
% 1.72/1.94 tff(1765,plain,
% 1.72/1.94 (b(s(s(s(s(elem!1)))), s(s(z)))),
% 1.72/1.94 inference(modus_ponens,[status(thm)],[1593, 1262])).
% 1.72/1.94 tff(1766,plain,
% 1.72/1.94 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(elem!1))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(s(elem!1)))), s(z))) | (~b(s(elem!1), s(s(z)))) | (~b(s(s(s(s(elem!1)))), s(s(z)))) | (~b(s(s(s(s(elem!1)))), s(s(s(z))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), s(elem!1))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(s(elem!1)))), s(z))) | (~b(s(elem!1), s(s(z)))) | (~b(s(s(s(s(elem!1)))), s(s(z)))) | (~b(s(s(s(s(elem!1)))), s(s(s(z))))))),
% 1.72/1.94 inference(rewrite,[status(thm)],[])).
% 1.72/1.94 tff(1767,plain,
% 1.72/1.94 (((~b(s(elem!1), s(s(z)))) | (~b(s(s(s(s(elem!1)))), s(s(z)))) | (~b(s(z), s(elem!1))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(s(elem!1)))), s(z))) | (~b(s(s(s(s(elem!1)))), s(s(s(z)))))) <=> ((~b(s(z), s(elem!1))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(s(elem!1)))), s(z))) | (~b(s(elem!1), s(s(z)))) | (~b(s(s(s(s(elem!1)))), s(s(z)))) | (~b(s(s(s(s(elem!1)))), s(s(s(z))))))),
% 1.72/1.94 inference(rewrite,[status(thm)],[])).
% 1.72/1.94 tff(1768,plain,
% 1.72/1.94 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), s(s(z)))) | (~b(s(s(s(s(elem!1)))), s(s(z)))) | (~b(s(z), s(elem!1))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(s(elem!1)))), s(z))) | (~b(s(s(s(s(elem!1)))), s(s(s(z))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(elem!1))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(s(elem!1)))), s(z))) | (~b(s(elem!1), s(s(z)))) | (~b(s(s(s(s(elem!1)))), s(s(z)))) | (~b(s(s(s(s(elem!1)))), s(s(s(z)))))))),
% 1.72/1.94 inference(monotonicity,[status(thm)],[1767])).
% 1.72/1.94 tff(1769,plain,
% 1.72/1.94 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), s(s(z)))) | (~b(s(s(s(s(elem!1)))), s(s(z)))) | (~b(s(z), s(elem!1))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(s(elem!1)))), s(z))) | (~b(s(s(s(s(elem!1)))), s(s(s(z))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), s(elem!1))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(s(elem!1)))), s(z))) | (~b(s(elem!1), s(s(z)))) | (~b(s(s(s(s(elem!1)))), s(s(z)))) | (~b(s(s(s(s(elem!1)))), s(s(s(z))))))),
% 1.72/1.94 inference(transitivity,[status(thm)],[1768, 1766])).
% 1.72/1.94 tff(1770,plain,
% 1.72/1.94 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), s(s(z)))) | (~b(s(s(s(s(elem!1)))), s(s(z)))) | (~b(s(z), s(elem!1))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(s(elem!1)))), s(z))) | (~b(s(s(s(s(elem!1)))), s(s(s(z))))))),
% 1.72/1.94 inference(quant_inst,[status(thm)],[])).
% 1.72/1.94 tff(1771,plain,
% 1.72/1.94 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), s(elem!1))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(s(elem!1)))), s(z))) | (~b(s(elem!1), s(s(z)))) | (~b(s(s(s(s(elem!1)))), s(s(z)))) | (~b(s(s(s(s(elem!1)))), s(s(s(z)))))),
% 1.72/1.94 inference(modus_ponens,[status(thm)],[1770, 1769])).
% 1.72/1.94 tff(1772,plain,
% 1.72/1.94 ($false),
% 1.72/1.94 inference(unit_resolution,[status(thm)],[1771, 166, 1765, 1640, 1210, 1202, 1764, 1621])).
% 1.72/1.94 tff(1773,plain,((~(s(s(elem!1)) = s(s(s(s(elem!1)))))) | (~b(s(z), z)) | (~r(z, s(s(z)))) | (~r(z, s(z))) | (~r(z, s(s(elem!1)))) | (~r(z, s(s(s(elem!1))))) | (~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(s(s(elem!1)), s(z))) | (~r(s(s(s(elem!1))), s(z))) | (~b(s(z), s(s(s(elem!1)))))), inference(lemma,lemma(discharge,[]))).
% 1.72/1.94 tff(1774,plain,
% 1.72/1.94 (~(s(s(elem!1)) = s(s(s(s(elem!1)))))),
% 1.72/1.94 inference(unit_resolution,[status(thm)],[1773, 365, 155, 323, 53, 1472, 1539, 310, 350, 924])).
% 1.72/1.94 tff(1775,plain,
% 1.72/1.94 (b(s(s(elem!1)), s(s(s(s(elem!1)))))),
% 1.72/1.94 inference(unit_resolution,[status(thm)],[827, 1774, 1537])).
% 1.72/1.94 tff(1776,plain,
% 1.72/1.94 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), z)) | (~b(s(z), s(s(elem!1)))) | (~b(s(s(s(elem!1))), z)) | (~b(s(s(elem!1)), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~b(s(z), s(s(s(s(elem!1)))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), z)) | (~b(s(z), s(s(elem!1)))) | (~b(s(s(s(elem!1))), z)) | (~b(s(s(elem!1)), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~b(s(z), s(s(s(s(elem!1)))))))),
% 1.72/1.94 inference(rewrite,[status(thm)],[])).
% 1.72/1.94 tff(1777,plain,
% 1.72/1.94 (((~b(s(s(s(elem!1))), z)) | (~b(s(z), z)) | (~b(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~b(s(s(elem!1)), s(s(s(s(elem!1)))))) | (~b(s(z), s(s(s(s(elem!1)))))) | (~b(s(z), s(s(elem!1))))) <=> ((~b(s(z), z)) | (~b(s(z), s(s(elem!1)))) | (~b(s(s(s(elem!1))), z)) | (~b(s(s(elem!1)), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~b(s(z), s(s(s(s(elem!1)))))))),
% 1.72/1.94 inference(rewrite,[status(thm)],[])).
% 1.72/1.94 tff(1778,plain,
% 1.72/1.94 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), z)) | (~b(s(z), z)) | (~b(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~b(s(s(elem!1)), s(s(s(s(elem!1)))))) | (~b(s(z), s(s(s(s(elem!1)))))) | (~b(s(z), s(s(elem!1)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), z)) | (~b(s(z), s(s(elem!1)))) | (~b(s(s(s(elem!1))), z)) | (~b(s(s(elem!1)), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~b(s(z), s(s(s(s(elem!1))))))))),
% 1.72/1.94 inference(monotonicity,[status(thm)],[1777])).
% 1.72/1.94 tff(1779,plain,
% 1.72/1.94 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), z)) | (~b(s(z), z)) | (~b(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~b(s(s(elem!1)), s(s(s(s(elem!1)))))) | (~b(s(z), s(s(s(s(elem!1)))))) | (~b(s(z), s(s(elem!1)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), z)) | (~b(s(z), s(s(elem!1)))) | (~b(s(s(s(elem!1))), z)) | (~b(s(s(elem!1)), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~b(s(z), s(s(s(s(elem!1)))))))),
% 1.72/1.94 inference(transitivity,[status(thm)],[1778, 1776])).
% 1.72/1.94 tff(1780,plain,
% 1.72/1.94 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), z)) | (~b(s(z), z)) | (~b(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~b(s(s(elem!1)), s(s(s(s(elem!1)))))) | (~b(s(z), s(s(s(s(elem!1)))))) | (~b(s(z), s(s(elem!1)))))),
% 1.72/1.94 inference(quant_inst,[status(thm)],[])).
% 1.72/1.94 tff(1781,plain,
% 1.72/1.94 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), z)) | (~b(s(z), s(s(elem!1)))) | (~b(s(s(s(elem!1))), z)) | (~b(s(s(elem!1)), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~b(s(z), s(s(s(s(elem!1))))))),
% 1.72/1.94 inference(modus_ponens,[status(thm)],[1780, 1779])).
% 1.72/1.94 tff(1782,plain,
% 1.72/1.94 ($false),
% 1.72/1.94 inference(unit_resolution,[status(thm)],[1781, 166, 1526, 53, 1462, 1775, 1482, 1516])).
% 1.72/1.94 tff(1783,plain,((~r(z, s(s(elem!1)))) | (~b(s(z), z)) | (~r(s(s(s(elem!1))), s(z))) | (~r(z, s(z))) | (~r(z, s(s(z)))) | (~b(s(s(elem!1)), s(z))) | (s(s(elem!1)) = s(s(s(elem!1))))), inference(lemma,lemma(discharge,[]))).
% 1.72/1.94 tff(1784,plain,
% 1.72/1.94 (~r(z, s(s(elem!1)))),
% 1.72/1.94 inference(unit_resolution,[status(thm)],[1783, 350, 53, 323, 155, 310, 45])).
% 1.72/1.94 tff(1785,assumption,(z = s(s(elem!1))), introduced(assumption)).
% 1.72/1.94 tff(1786,plain,
% 1.72/1.94 (s(s(elem!1)) = z),
% 1.72/1.94 inference(symmetry,[status(thm)],[1785])).
% 1.72/1.94 tff(1787,plain,
% 1.72/1.94 ($false),
% 1.72/1.94 inference(unit_resolution,[status(thm)],[108, 1786])).
% 1.72/1.94 tff(1788,plain,(~(z = s(s(elem!1)))), inference(lemma,lemma(discharge,[]))).
% 1.72/1.94 tff(1789,assumption,(~r(z, s(s(elem!1)))), introduced(assumption)).
% 1.72/1.94 tff(1790,assumption,(~b(z, s(s(elem!1)))), introduced(assumption)).
% 1.72/1.94 tff(1791,plain,
% 1.72/1.94 (((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((z = s(s(elem!1))) | b(z, s(s(elem!1))) | r(z, s(s(elem!1))))) <=> ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (z = s(s(elem!1))) | b(z, s(s(elem!1))) | r(z, s(s(elem!1))))),
% 1.72/1.94 inference(rewrite,[status(thm)],[])).
% 1.72/1.94 tff(1792,plain,
% 1.72/1.94 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((z = s(s(elem!1))) | b(z, s(s(elem!1))) | r(z, s(s(elem!1))))),
% 1.72/1.94 inference(quant_inst,[status(thm)],[])).
% 1.72/1.94 tff(1793,plain,
% 1.72/1.94 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (z = s(s(elem!1))) | b(z, s(s(elem!1))) | r(z, s(s(elem!1)))),
% 1.72/1.94 inference(modus_ponens,[status(thm)],[1792, 1791])).
% 1.72/1.94 tff(1794,plain,
% 1.72/1.94 ($false),
% 1.72/1.94 inference(unit_resolution,[status(thm)],[1793, 79, 1790, 1789, 1788])).
% 1.72/1.94 tff(1795,plain,(r(z, s(s(elem!1))) | b(z, s(s(elem!1)))), inference(lemma,lemma(discharge,[]))).
% 1.72/1.94 tff(1796,plain,
% 1.72/1.94 (b(z, s(s(elem!1)))),
% 1.72/1.94 inference(unit_resolution,[status(thm)],[1795, 1784])).
% 1.72/1.94 tff(1797,plain,
% 1.72/1.94 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(elem!1)))) | (~b(s(z), z)) | (~b(s(s(elem!1)), z)) | (~b(s(s(elem!1)), s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(s(elem!1)))) | (~b(s(z), z)) | (~b(s(s(elem!1)), z)) | (~b(s(s(elem!1)), s(z))))),
% 1.72/1.94 inference(rewrite,[status(thm)],[])).
% 1.72/1.94 tff(1798,plain,
% 1.72/1.94 (((~b(s(s(elem!1)), s(z))) | (~b(s(s(elem!1)), s(z))) | (~b(z, s(s(elem!1)))) | (~b(s(z), z)) | (~b(s(s(elem!1)), z)) | (~b(s(s(elem!1)), s(z)))) <=> ((~b(z, s(s(elem!1)))) | (~b(s(z), z)) | (~b(s(s(elem!1)), z)) | (~b(s(s(elem!1)), s(z))))),
% 1.72/1.94 inference(rewrite,[status(thm)],[])).
% 1.72/1.94 tff(1799,plain,
% 1.72/1.94 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), s(z))) | (~b(s(s(elem!1)), s(z))) | (~b(z, s(s(elem!1)))) | (~b(s(z), z)) | (~b(s(s(elem!1)), z)) | (~b(s(s(elem!1)), s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(elem!1)))) | (~b(s(z), z)) | (~b(s(s(elem!1)), z)) | (~b(s(s(elem!1)), s(z)))))),
% 1.72/1.94 inference(monotonicity,[status(thm)],[1798])).
% 1.72/1.94 tff(1800,plain,
% 1.72/1.94 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), s(z))) | (~b(s(s(elem!1)), s(z))) | (~b(z, s(s(elem!1)))) | (~b(s(z), z)) | (~b(s(s(elem!1)), z)) | (~b(s(s(elem!1)), s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(s(elem!1)))) | (~b(s(z), z)) | (~b(s(s(elem!1)), z)) | (~b(s(s(elem!1)), s(z))))),
% 1.72/1.94 inference(transitivity,[status(thm)],[1799, 1797])).
% 1.72/1.94 tff(1801,plain,
% 1.72/1.94 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), s(z))) | (~b(s(s(elem!1)), s(z))) | (~b(z, s(s(elem!1)))) | (~b(s(z), z)) | (~b(s(s(elem!1)), z)) | (~b(s(s(elem!1)), s(z))))),
% 1.72/1.94 inference(quant_inst,[status(thm)],[])).
% 1.72/1.94 tff(1802,plain,
% 1.72/1.94 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(s(elem!1)))) | (~b(s(z), z)) | (~b(s(s(elem!1)), z)) | (~b(s(s(elem!1)), s(z)))),
% 1.72/1.94 inference(modus_ponens,[status(thm)],[1801, 1800])).
% 1.72/1.94 tff(1803,plain,
% 1.72/1.94 (~b(s(s(elem!1)), z)),
% 1.72/1.94 inference(unit_resolution,[status(thm)],[1802, 166, 1796, 53, 310])).
% 1.72/1.94 tff(1804,plain,
% 1.72/1.94 (r(s(s(elem!1)), z)),
% 1.72/1.94 inference(unit_resolution,[status(thm)],[608, 1803])).
% 1.72/1.94 tff(1805,plain,
% 1.72/1.94 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(elem!1)))) | (~b(s(z), z)) | (~b(s(z), s(s(elem!1)))) | (~b(s(s(elem!1)), s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(s(elem!1)))) | (~b(s(z), z)) | (~b(s(z), s(s(elem!1)))) | (~b(s(s(elem!1)), s(z))))),
% 1.72/1.94 inference(rewrite,[status(thm)],[])).
% 1.72/1.94 tff(1806,plain,
% 1.72/1.94 (((~b(s(z), z)) | (~b(s(z), z)) | (~b(s(s(elem!1)), s(z))) | (~b(z, s(s(elem!1)))) | (~b(s(z), s(s(elem!1)))) | (~b(s(z), z))) <=> ((~b(z, s(s(elem!1)))) | (~b(s(z), z)) | (~b(s(z), s(s(elem!1)))) | (~b(s(s(elem!1)), s(z))))),
% 1.72/1.94 inference(rewrite,[status(thm)],[])).
% 1.72/1.94 tff(1807,plain,
% 1.72/1.94 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), z)) | (~b(s(z), z)) | (~b(s(s(elem!1)), s(z))) | (~b(z, s(s(elem!1)))) | (~b(s(z), s(s(elem!1)))) | (~b(s(z), z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(elem!1)))) | (~b(s(z), z)) | (~b(s(z), s(s(elem!1)))) | (~b(s(s(elem!1)), s(z)))))),
% 1.72/1.94 inference(monotonicity,[status(thm)],[1806])).
% 1.72/1.94 tff(1808,plain,
% 1.72/1.94 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), z)) | (~b(s(z), z)) | (~b(s(s(elem!1)), s(z))) | (~b(z, s(s(elem!1)))) | (~b(s(z), s(s(elem!1)))) | (~b(s(z), z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(s(elem!1)))) | (~b(s(z), z)) | (~b(s(z), s(s(elem!1)))) | (~b(s(s(elem!1)), s(z))))),
% 1.72/1.94 inference(transitivity,[status(thm)],[1807, 1805])).
% 1.72/1.94 tff(1809,plain,
% 1.72/1.94 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), z)) | (~b(s(z), z)) | (~b(s(s(elem!1)), s(z))) | (~b(z, s(s(elem!1)))) | (~b(s(z), s(s(elem!1)))) | (~b(s(z), z)))),
% 1.72/1.94 inference(quant_inst,[status(thm)],[])).
% 1.72/1.94 tff(1810,plain,
% 1.72/1.94 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(s(elem!1)))) | (~b(s(z), z)) | (~b(s(z), s(s(elem!1)))) | (~b(s(s(elem!1)), s(z)))),
% 1.72/1.94 inference(modus_ponens,[status(thm)],[1809, 1808])).
% 1.72/1.94 tff(1811,plain,
% 1.72/1.94 (~b(s(z), s(s(elem!1)))),
% 1.72/1.94 inference(unit_resolution,[status(thm)],[1810, 166, 1796, 53, 310])).
% 1.72/1.94 tff(1812,plain,
% 1.72/1.94 (r(s(z), s(s(elem!1)))),
% 1.72/1.94 inference(unit_resolution,[status(thm)],[84, 1811])).
% 1.72/1.94 tff(1813,plain,
% 1.72/1.94 (~r(z, s(s(s(elem!1))))),
% 1.72/1.94 inference(unit_resolution,[status(thm)],[1524, 1812, 323, 350])).
% 1.72/1.95 tff(1814,plain,
% 1.72/1.95 (b(z, s(s(s(elem!1))))),
% 1.72/1.95 inference(unit_resolution,[status(thm)],[261, 1813])).
% 1.72/1.95 tff(1815,plain,
% 1.72/1.95 (~r(s(s(s(elem!1))), z)),
% 1.72/1.95 inference(unit_resolution,[status(thm)],[373, 1812, 323, 350])).
% 1.72/1.95 tff(1816,plain,
% 1.72/1.95 (b(s(s(s(elem!1))), z)),
% 1.72/1.95 inference(unit_resolution,[status(thm)],[94, 1815])).
% 1.72/1.95 tff(1817,plain,
% 1.72/1.95 (~b(s(z), s(s(s(elem!1))))),
% 1.72/1.95 inference(unit_resolution,[status(thm)],[1470, 1814, 53, 1816])).
% 1.72/1.95 tff(1818,plain,
% 1.72/1.95 (r(s(z), s(s(s(elem!1))))),
% 1.72/1.95 inference(unit_resolution,[status(thm)],[116, 1817])).
% 1.72/1.95 tff(1819,plain,
% 1.72/1.95 (~r(s(s(elem!1)), s(s(s(elem!1))))),
% 1.72/1.95 inference(unit_resolution,[status(thm)],[764, 1818, 350, 1812])).
% 1.72/1.95 tff(1820,assumption,(b(z, s(s(elem!1)))), introduced(assumption)).
% 1.72/1.95 tff(1821,assumption,(~r(s(s(elem!1)), s(s(s(elem!1))))), introduced(assumption)).
% 1.72/1.95 tff(1822,plain,
% 1.72/1.95 (b(s(s(elem!1)), s(s(s(elem!1))))),
% 1.72/1.95 inference(unit_resolution,[status(thm)],[461, 45, 1821])).
% 1.72/1.95 tff(1823,assumption,(~r(s(s(s(elem!1))), s(s(elem!1)))), introduced(assumption)).
% 1.72/1.95 tff(1824,plain,
% 1.72/1.95 (b(s(s(s(elem!1))), s(s(elem!1)))),
% 1.72/1.95 inference(unit_resolution,[status(thm)],[889, 51, 1823])).
% 1.72/1.95 tff(1825,plain,
% 1.72/1.95 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(z, s(s(s(elem!1))))) | (~b(z, s(s(elem!1)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(z, s(s(s(elem!1))))) | (~b(z, s(s(elem!1)))))),
% 1.72/1.95 inference(rewrite,[status(thm)],[])).
% 1.72/1.95 tff(1826,plain,
% 1.72/1.95 (((~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(z, s(s(elem!1)))) | (~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(z, s(s(elem!1)))) | (~b(z, s(s(s(elem!1)))))) <=> ((~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(z, s(s(s(elem!1))))) | (~b(z, s(s(elem!1)))))),
% 1.72/1.95 inference(rewrite,[status(thm)],[])).
% 1.72/1.95 tff(1827,plain,
% 1.72/1.95 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(z, s(s(elem!1)))) | (~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(z, s(s(elem!1)))) | (~b(z, s(s(s(elem!1))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(z, s(s(s(elem!1))))) | (~b(z, s(s(elem!1))))))),
% 1.72/1.95 inference(monotonicity,[status(thm)],[1826])).
% 1.72/1.95 tff(1828,plain,
% 1.72/1.95 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(z, s(s(elem!1)))) | (~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(z, s(s(elem!1)))) | (~b(z, s(s(s(elem!1))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(z, s(s(s(elem!1))))) | (~b(z, s(s(elem!1)))))),
% 1.72/1.95 inference(transitivity,[status(thm)],[1827, 1825])).
% 1.72/1.95 tff(1829,plain,
% 1.72/1.95 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(z, s(s(elem!1)))) | (~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(z, s(s(elem!1)))) | (~b(z, s(s(s(elem!1))))))),
% 1.72/1.95 inference(quant_inst,[status(thm)],[])).
% 1.72/1.95 tff(1830,plain,
% 1.72/1.95 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(z, s(s(s(elem!1))))) | (~b(z, s(s(elem!1))))),
% 1.72/1.95 inference(modus_ponens,[status(thm)],[1829, 1828])).
% 1.72/1.95 tff(1831,plain,
% 1.72/1.95 ($false),
% 1.72/1.95 inference(unit_resolution,[status(thm)],[1830, 166, 463, 839, 240, 1820])).
% 1.72/1.95 tff(1832,plain,((~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(z, s(s(s(elem!1))))) | (~b(z, s(s(elem!1))))), inference(lemma,lemma(discharge,[]))).
% 1.72/1.95 tff(1833,plain,
% 1.72/1.95 ($false),
% 1.72/1.95 inference(unit_resolution,[status(thm)],[1832, 1824, 1822, 1820, 240])).
% 1.72/1.95 tff(1834,plain,((s(s(elem!1)) = s(s(s(elem!1)))) | (~b(z, s(s(elem!1)))) | (~b(z, s(s(s(elem!1))))) | r(s(s(s(elem!1))), s(s(elem!1))) | r(s(s(elem!1)), s(s(s(elem!1))))), inference(lemma,lemma(discharge,[]))).
% 1.72/1.95 tff(1835,plain,
% 1.72/1.95 (r(s(s(s(elem!1))), s(s(elem!1)))),
% 1.72/1.95 inference(unit_resolution,[status(thm)],[1834, 1819, 1796, 45, 1814])).
% 1.72/1.95 tff(1836,plain,
% 1.72/1.95 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), s(s(elem!1)))) | (~r(s(z), s(s(elem!1)))) | (~r(s(s(s(elem!1))), s(z))) | (~r(s(s(elem!1)), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(elem!1))), s(s(elem!1)))) | (~r(s(z), s(s(elem!1)))) | (~r(s(s(s(elem!1))), s(z))) | (~r(s(s(elem!1)), z)))),
% 1.72/1.95 inference(rewrite,[status(thm)],[])).
% 1.72/1.95 tff(1837,plain,
% 1.72/1.95 (((~r(s(s(elem!1)), z)) | (~r(s(z), s(s(elem!1)))) | (~r(s(s(s(elem!1))), s(s(elem!1)))) | (~r(s(s(s(elem!1))), s(z)))) <=> ((~r(s(s(s(elem!1))), s(s(elem!1)))) | (~r(s(z), s(s(elem!1)))) | (~r(s(s(s(elem!1))), s(z))) | (~r(s(s(elem!1)), z)))),
% 1.72/1.95 inference(rewrite,[status(thm)],[])).
% 1.72/1.95 tff(1838,plain,
% 1.72/1.95 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(elem!1)), z)) | (~r(s(z), s(s(elem!1)))) | (~r(s(s(s(elem!1))), s(s(elem!1)))) | (~r(s(s(s(elem!1))), s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), s(s(elem!1)))) | (~r(s(z), s(s(elem!1)))) | (~r(s(s(s(elem!1))), s(z))) | (~r(s(s(elem!1)), z))))),
% 1.72/1.95 inference(monotonicity,[status(thm)],[1837])).
% 1.72/1.95 tff(1839,plain,
% 1.72/1.95 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(elem!1)), z)) | (~r(s(z), s(s(elem!1)))) | (~r(s(s(s(elem!1))), s(s(elem!1)))) | (~r(s(s(s(elem!1))), s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(elem!1))), s(s(elem!1)))) | (~r(s(z), s(s(elem!1)))) | (~r(s(s(s(elem!1))), s(z))) | (~r(s(s(elem!1)), z)))),
% 1.72/1.95 inference(transitivity,[status(thm)],[1838, 1836])).
% 1.72/1.95 tff(1840,plain,
% 1.72/1.95 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(elem!1)), z)) | (~r(s(z), s(s(elem!1)))) | (~r(s(s(s(elem!1))), s(s(elem!1)))) | (~r(s(s(s(elem!1))), s(z))))),
% 1.72/1.95 inference(quant_inst,[status(thm)],[])).
% 1.72/1.95 tff(1841,plain,
% 1.72/1.95 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(elem!1))), s(s(elem!1)))) | (~r(s(z), s(s(elem!1)))) | (~r(s(s(s(elem!1))), s(z))) | (~r(s(s(elem!1)), z))),
% 1.72/1.95 inference(modus_ponens,[status(thm)],[1840, 1839])).
% 1.72/1.95 tff(1842,plain,
% 1.72/1.95 ($false),
% 1.72/1.95 inference(unit_resolution,[status(thm)],[1841, 197, 1812, 350, 1835, 1804])).
% 1.72/1.95 tff(1843,plain,((~r(s(s(s(elem!1))), s(z))) | (s(s(elem!1)) = s(s(s(elem!1)))) | (~b(s(z), z)) | (~r(z, s(z))) | (~b(s(s(elem!1)), s(z))) | (~r(z, s(s(z))))), inference(lemma,lemma(discharge,[]))).
% 1.72/1.95 tff(1844,plain,
% 1.72/1.95 (~r(s(s(s(elem!1))), s(z))),
% 1.72/1.95 inference(unit_resolution,[status(thm)],[1843, 53, 45, 323, 310, 155])).
% 1.72/1.95 tff(1845,plain,
% 1.72/1.95 (((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((s(s(s(elem!1))) = s(z)) | b(s(s(s(elem!1))), s(z)) | r(s(s(s(elem!1))), s(z)))) <=> ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (s(s(s(elem!1))) = s(z)) | b(s(s(s(elem!1))), s(z)) | r(s(s(s(elem!1))), s(z)))),
% 1.72/1.95 inference(rewrite,[status(thm)],[])).
% 1.72/1.95 tff(1846,plain,
% 1.72/1.95 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((s(s(s(elem!1))) = s(z)) | b(s(s(s(elem!1))), s(z)) | r(s(s(s(elem!1))), s(z)))),
% 1.72/1.95 inference(quant_inst,[status(thm)],[])).
% 1.72/1.95 tff(1847,plain,
% 1.72/1.95 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (s(s(s(elem!1))) = s(z)) | b(s(s(s(elem!1))), s(z)) | r(s(s(s(elem!1))), s(z))),
% 1.72/1.95 inference(modus_ponens,[status(thm)],[1846, 1845])).
% 1.72/1.95 tff(1848,plain,
% 1.72/1.95 ((s(s(s(elem!1))) = s(z)) | b(s(s(s(elem!1))), s(z)) | r(s(s(s(elem!1))), s(z))),
% 1.72/1.95 inference(unit_resolution,[status(thm)],[1847, 79])).
% 1.72/1.95 tff(1849,plain,
% 1.72/1.95 (b(s(s(s(elem!1))), s(z)) | r(s(s(s(elem!1))), s(z))),
% 1.72/1.95 inference(unit_resolution,[status(thm)],[1848, 110])).
% 1.72/1.95 tff(1850,plain,
% 1.72/1.95 (b(s(s(s(elem!1))), s(z))),
% 1.72/1.95 inference(unit_resolution,[status(thm)],[1849, 1844])).
% 1.72/1.95 tff(1851,plain,
% 1.72/1.95 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(z), s(s(elem!1)))) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(s(elem!1)), s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(z), s(s(elem!1)))) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(s(elem!1)), s(z))))),
% 1.72/1.95 inference(rewrite,[status(thm)],[])).
% 1.72/1.95 tff(1852,plain,
% 1.72/1.95 (((~b(s(s(elem!1)), s(z))) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(z), s(s(elem!1)))) | (~b(s(s(elem!1)), s(z))) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(s(s(elem!1))), s(s(elem!1))))) <=> ((~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(z), s(s(elem!1)))) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(s(elem!1)), s(z))))),
% 1.72/1.95 inference(rewrite,[status(thm)],[])).
% 1.72/1.95 tff(1853,plain,
% 1.72/1.95 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), s(z))) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(z), s(s(elem!1)))) | (~b(s(s(elem!1)), s(z))) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(s(s(elem!1))), s(s(elem!1)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(z), s(s(elem!1)))) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(s(elem!1)), s(z)))))),
% 1.72/1.95 inference(monotonicity,[status(thm)],[1852])).
% 1.72/1.95 tff(1854,plain,
% 1.72/1.95 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), s(z))) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(z), s(s(elem!1)))) | (~b(s(s(elem!1)), s(z))) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(s(s(elem!1))), s(s(elem!1)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(z), s(s(elem!1)))) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(s(elem!1)), s(z))))),
% 1.72/1.95 inference(transitivity,[status(thm)],[1853, 1851])).
% 1.72/1.95 tff(1855,plain,
% 1.72/1.95 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), s(z))) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(z), s(s(elem!1)))) | (~b(s(s(elem!1)), s(z))) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(s(s(elem!1))), s(s(elem!1)))))),
% 1.72/1.95 inference(quant_inst,[status(thm)],[])).
% 1.72/1.95 tff(1856,plain,
% 1.72/1.95 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(z), s(s(elem!1)))) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(s(elem!1)), s(z)))),
% 1.72/1.95 inference(modus_ponens,[status(thm)],[1855, 1854])).
% 1.72/1.95 tff(1857,plain,
% 1.72/1.95 ($false),
% 1.72/1.95 inference(unit_resolution,[status(thm)],[1856, 166, 376, 839, 96, 310])).
% 1.72/1.95 tff(1858,plain,((~b(s(s(elem!1)), s(z))) | (~b(s(z), s(s(elem!1)))) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(s(s(elem!1))), s(z)))), inference(lemma,lemma(discharge,[]))).
% 1.72/1.95 tff(1859,plain,
% 1.72/1.95 (~b(s(s(s(elem!1))), s(s(elem!1)))),
% 1.72/1.95 inference(unit_resolution,[status(thm)],[1858, 376, 310, 1850])).
% 1.72/1.95 tff(1860,plain,
% 1.72/1.95 (r(s(s(s(elem!1))), s(s(elem!1)))),
% 1.72/1.95 inference(unit_resolution,[status(thm)],[889, 1859, 51])).
% 1.72/1.95 tff(1861,plain,
% 1.72/1.95 (~b(s(s(elem!1)), z)),
% 1.72/1.95 inference(unit_resolution,[status(thm)],[1802, 166, 1820, 53, 310])).
% 1.72/1.95 tff(1862,plain,
% 1.72/1.95 (r(s(s(elem!1)), z)),
% 1.72/1.95 inference(unit_resolution,[status(thm)],[608, 1861])).
% 1.72/1.95 tff(1863,assumption,(~(s(s(s(elem!1))) = s(s(elem!1)))), introduced(assumption)).
% 1.72/1.95 tff(1864,plain,
% 1.72/1.95 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(z, s(s(elem!1)))) | (~b(s(z), z)) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(s(elem!1)), s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(z, s(s(elem!1)))) | (~b(s(z), z)) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(s(elem!1)), s(z))))),
% 1.72/1.95 inference(rewrite,[status(thm)],[])).
% 1.72/1.95 tff(1865,plain,
% 1.72/1.95 (((~b(z, s(s(elem!1)))) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(z), z)) | (~b(s(s(elem!1)), s(z))) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(s(s(elem!1))), s(s(elem!1))))) <=> ((~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(z, s(s(elem!1)))) | (~b(s(z), z)) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(s(elem!1)), s(z))))),
% 1.72/1.95 inference(rewrite,[status(thm)],[])).
% 1.72/1.95 tff(1866,plain,
% 1.72/1.95 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(elem!1)))) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(z), z)) | (~b(s(s(elem!1)), s(z))) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(s(s(elem!1))), s(s(elem!1)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(z, s(s(elem!1)))) | (~b(s(z), z)) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(s(elem!1)), s(z)))))),
% 1.72/1.95 inference(monotonicity,[status(thm)],[1865])).
% 1.72/1.95 tff(1867,plain,
% 1.72/1.95 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(elem!1)))) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(z), z)) | (~b(s(s(elem!1)), s(z))) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(s(s(elem!1))), s(s(elem!1)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(z, s(s(elem!1)))) | (~b(s(z), z)) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(s(elem!1)), s(z))))),
% 1.72/1.95 inference(transitivity,[status(thm)],[1866, 1864])).
% 1.72/1.95 tff(1868,plain,
% 1.72/1.95 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(elem!1)))) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(z), z)) | (~b(s(s(elem!1)), s(z))) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(s(s(elem!1))), s(s(elem!1)))))),
% 1.72/1.95 inference(quant_inst,[status(thm)],[])).
% 1.72/1.95 tff(1869,plain,
% 1.72/1.95 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(z, s(s(elem!1)))) | (~b(s(z), z)) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(s(elem!1)), s(z)))),
% 1.72/1.95 inference(modus_ponens,[status(thm)],[1868, 1867])).
% 1.72/1.95 tff(1870,plain,
% 1.72/1.95 ($false),
% 1.72/1.95 inference(unit_resolution,[status(thm)],[1869, 166, 839, 1820, 53, 96, 310])).
% 1.72/1.95 tff(1871,plain,((~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(z, s(s(elem!1)))) | (~b(s(z), z)) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(s(elem!1)), s(z)))), inference(lemma,lemma(discharge,[]))).
% 1.72/1.95 tff(1872,plain,
% 1.72/1.95 (~b(s(s(s(elem!1))), s(s(elem!1)))),
% 1.72/1.95 inference(unit_resolution,[status(thm)],[1871, 1820, 53, 96, 310])).
% 1.72/1.95 tff(1873,plain,
% 1.72/1.95 (r(s(s(s(elem!1))), s(s(elem!1)))),
% 1.72/1.95 inference(unit_resolution,[status(thm)],[889, 1872, 1863])).
% 1.72/1.95 tff(1874,plain,
% 1.72/1.95 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(elem!1)))) | (~b(s(z), z)) | (~b(s(s(s(elem!1))), z)) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(s(elem!1)), s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(s(elem!1)))) | (~b(s(z), z)) | (~b(s(s(s(elem!1))), z)) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(s(elem!1)), s(z))))),
% 1.72/1.95 inference(rewrite,[status(thm)],[])).
% 1.72/1.95 tff(1875,plain,
% 1.72/1.95 (((~b(s(s(elem!1)), s(z))) | (~b(s(s(s(elem!1))), s(z))) | (~b(z, s(s(elem!1)))) | (~b(s(z), z)) | (~b(s(s(s(elem!1))), z)) | (~b(s(s(s(elem!1))), s(z)))) <=> ((~b(z, s(s(elem!1)))) | (~b(s(z), z)) | (~b(s(s(s(elem!1))), z)) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(s(elem!1)), s(z))))),
% 1.72/1.95 inference(rewrite,[status(thm)],[])).
% 1.72/1.95 tff(1876,plain,
% 1.72/1.95 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), s(z))) | (~b(s(s(s(elem!1))), s(z))) | (~b(z, s(s(elem!1)))) | (~b(s(z), z)) | (~b(s(s(s(elem!1))), z)) | (~b(s(s(s(elem!1))), s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(elem!1)))) | (~b(s(z), z)) | (~b(s(s(s(elem!1))), z)) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(s(elem!1)), s(z)))))),
% 1.72/1.95 inference(monotonicity,[status(thm)],[1875])).
% 1.72/1.95 tff(1877,plain,
% 1.72/1.95 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), s(z))) | (~b(s(s(s(elem!1))), s(z))) | (~b(z, s(s(elem!1)))) | (~b(s(z), z)) | (~b(s(s(s(elem!1))), z)) | (~b(s(s(s(elem!1))), s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(s(elem!1)))) | (~b(s(z), z)) | (~b(s(s(s(elem!1))), z)) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(s(elem!1)), s(z))))),
% 1.72/1.95 inference(transitivity,[status(thm)],[1876, 1874])).
% 1.72/1.95 tff(1878,plain,
% 1.72/1.95 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), s(z))) | (~b(s(s(s(elem!1))), s(z))) | (~b(z, s(s(elem!1)))) | (~b(s(z), z)) | (~b(s(s(s(elem!1))), z)) | (~b(s(s(s(elem!1))), s(z))))),
% 1.72/1.95 inference(quant_inst,[status(thm)],[])).
% 1.72/1.95 tff(1879,plain,
% 1.72/1.95 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(s(elem!1)))) | (~b(s(z), z)) | (~b(s(s(s(elem!1))), z)) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(s(elem!1)), s(z)))),
% 1.72/1.95 inference(modus_ponens,[status(thm)],[1878, 1877])).
% 1.72/1.95 tff(1880,plain,
% 1.72/1.95 (~b(s(s(s(elem!1))), z)),
% 1.72/1.95 inference(unit_resolution,[status(thm)],[1879, 166, 1820, 53, 96, 310])).
% 1.72/1.95 tff(1881,plain,
% 1.72/1.95 (r(s(s(s(elem!1))), z)),
% 1.72/1.95 inference(unit_resolution,[status(thm)],[94, 1880])).
% 1.72/1.95 tff(1882,plain,
% 1.72/1.95 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(z)))) | (~r(s(s(elem!1)), z)) | (~r(s(s(s(elem!1))), z)) | (~r(s(s(s(elem!1))), s(s(elem!1)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, s(s(z)))) | (~r(s(s(elem!1)), z)) | (~r(s(s(s(elem!1))), z)) | (~r(s(s(s(elem!1))), s(s(elem!1)))))),
% 1.72/1.95 inference(rewrite,[status(thm)],[])).
% 1.72/1.95 tff(1883,plain,
% 1.72/1.95 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(z)))) | (~r(s(s(elem!1)), z)) | (~r(s(s(s(elem!1))), z)) | (~r(s(s(s(elem!1))), s(s(elem!1)))))),
% 1.72/1.95 inference(quant_inst,[status(thm)],[])).
% 1.72/1.95 tff(1884,plain,
% 1.72/1.95 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, s(s(z)))) | (~r(s(s(elem!1)), z)) | (~r(s(s(s(elem!1))), z)) | (~r(s(s(s(elem!1))), s(s(elem!1))))),
% 1.72/1.96 inference(modus_ponens,[status(thm)],[1883, 1882])).
% 1.72/1.96 tff(1885,plain,
% 1.72/1.96 ($false),
% 1.72/1.96 inference(unit_resolution,[status(thm)],[1884, 197, 1881, 155, 1873, 1862])).
% 1.72/1.96 tff(1886,plain,((~b(z, s(s(elem!1)))) | (~r(z, s(s(z)))) | (~b(s(z), z)) | (~b(s(s(elem!1)), s(z))) | (~b(s(s(s(elem!1))), s(z))) | (s(s(s(elem!1))) = s(s(elem!1)))), inference(lemma,lemma(discharge,[]))).
% 1.72/1.96 tff(1887,plain,
% 1.72/1.96 (~b(z, s(s(elem!1)))),
% 1.72/1.96 inference(unit_resolution,[status(thm)],[1886, 53, 155, 310, 1850, 51])).
% 1.72/1.96 tff(1888,plain,
% 1.72/1.96 (r(z, s(s(elem!1)))),
% 1.72/1.96 inference(unit_resolution,[status(thm)],[1795, 1887])).
% 1.72/1.96 tff(1889,plain,
% 1.72/1.96 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(s(z), s(s(s(elem!1))))) | (~b(s(z), s(s(elem!1)))) | (~b(s(s(s(elem!1))), s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(s(z), s(s(s(elem!1))))) | (~b(s(z), s(s(elem!1)))) | (~b(s(s(s(elem!1))), s(z))))),
% 1.72/1.96 inference(rewrite,[status(thm)],[])).
% 1.72/1.96 tff(1890,plain,
% 1.72/1.96 (((~b(s(z), s(s(elem!1)))) | (~b(s(z), s(s(elem!1)))) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(s(z), 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(s(elem!1))))) | (~b(s(z), s(s(elem!1)))) | (~b(s(s(s(elem!1))), s(z))))),
% 1.72/1.96 inference(rewrite,[status(thm)],[])).
% 1.72/1.96 tff(1891,plain,
% 1.72/1.96 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(elem!1)))) | (~b(s(z), s(s(elem!1)))) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(s(z), s(s(s(elem!1))))) | (~b(s(z), s(s(elem!1)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(s(z), s(s(s(elem!1))))) | (~b(s(z), s(s(elem!1)))) | (~b(s(s(s(elem!1))), s(z)))))),
% 1.72/1.96 inference(monotonicity,[status(thm)],[1890])).
% 1.72/1.96 tff(1892,plain,
% 1.72/1.96 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(elem!1)))) | (~b(s(z), s(s(elem!1)))) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(s(z), s(s(s(elem!1))))) | (~b(s(z), s(s(elem!1)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(s(z), s(s(s(elem!1))))) | (~b(s(z), s(s(elem!1)))) | (~b(s(s(s(elem!1))), s(z))))),
% 1.72/1.96 inference(transitivity,[status(thm)],[1891, 1889])).
% 1.72/1.96 tff(1893,plain,
% 1.72/1.96 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(elem!1)))) | (~b(s(z), s(s(elem!1)))) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(s(z), s(s(s(elem!1))))) | (~b(s(z), s(s(elem!1)))))),
% 1.72/1.96 inference(quant_inst,[status(thm)],[])).
% 1.72/1.96 tff(1894,plain,
% 1.72/1.96 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(s(z), s(s(s(elem!1))))) | (~b(s(z), s(s(elem!1)))) | (~b(s(s(s(elem!1))), s(z)))),
% 1.72/1.96 inference(modus_ponens,[status(thm)],[1893, 1892])).
% 1.72/1.96 tff(1895,plain,
% 1.72/1.96 (~b(s(z), s(s(s(elem!1))))),
% 1.72/1.96 inference(unit_resolution,[status(thm)],[1894, 166, 376, 463, 96])).
% 1.72/1.96 tff(1896,plain,
% 1.72/1.96 (r(s(z), s(s(s(elem!1))))),
% 1.72/1.96 inference(unit_resolution,[status(thm)],[116, 1895])).
% 1.72/1.96 tff(1897,plain,
% 1.72/1.96 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(s(z), s(s(elem!1)))) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(s(elem!1)), s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(s(z), s(s(elem!1)))) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(s(elem!1)), s(z))))),
% 1.72/1.96 inference(rewrite,[status(thm)],[])).
% 1.72/1.96 tff(1898,plain,
% 1.72/1.96 (((~b(s(s(elem!1)), 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(s(elem!1))), s(z))) | (~b(s(s(elem!1)), s(z))) | (~b(s(s(elem!1)), 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(s(elem!1))), s(z))) | (~b(s(s(elem!1)), s(z))))),
% 1.72/1.96 inference(rewrite,[status(thm)],[])).
% 1.72/1.96 tff(1899,plain,
% 1.72/1.96 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(s(z), s(s(elem!1)))) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(s(elem!1)), s(z))) | (~b(s(s(elem!1)), s(s(s(elem!1))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(s(z), s(s(elem!1)))) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(s(elem!1)), s(z)))))),
% 1.72/1.96 inference(monotonicity,[status(thm)],[1898])).
% 1.72/1.96 tff(1900,plain,
% 1.72/1.96 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(s(z), s(s(elem!1)))) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(s(elem!1)), s(z))) | (~b(s(s(elem!1)), s(s(s(elem!1))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(s(z), s(s(elem!1)))) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(s(elem!1)), s(z))))),
% 1.72/1.96 inference(transitivity,[status(thm)],[1899, 1897])).
% 1.72/1.96 tff(1901,plain,
% 1.72/1.96 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(s(z), s(s(elem!1)))) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(s(elem!1)), s(z))) | (~b(s(s(elem!1)), s(s(s(elem!1))))))),
% 1.72/1.96 inference(quant_inst,[status(thm)],[])).
% 1.72/1.96 tff(1902,plain,
% 1.72/1.96 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(s(z), s(s(elem!1)))) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(s(elem!1)), s(z)))),
% 1.72/1.96 inference(modus_ponens,[status(thm)],[1901, 1900])).
% 1.72/1.96 tff(1903,plain,
% 1.72/1.96 (~b(s(s(elem!1)), s(z))),
% 1.72/1.96 inference(unit_resolution,[status(thm)],[1902, 166, 376, 463, 96])).
% 1.72/1.96 tff(1904,plain,
% 1.72/1.96 ((s(s(elem!1)) = s(z)) <=> (s(z) = s(s(elem!1)))),
% 1.72/1.96 inference(commutativity,[status(thm)],[])).
% 1.72/1.96 tff(1905,plain,
% 1.72/1.96 ((s(z) = s(s(elem!1))) <=> (s(s(elem!1)) = s(z))),
% 1.72/1.96 inference(symmetry,[status(thm)],[1904])).
% 1.72/1.96 tff(1906,plain,
% 1.72/1.96 ((~(s(z) = s(s(elem!1)))) <=> (~(s(s(elem!1)) = s(z)))),
% 1.72/1.96 inference(monotonicity,[status(thm)],[1905])).
% 1.72/1.96 tff(1907,plain,
% 1.72/1.96 (~(s(s(elem!1)) = s(z))),
% 1.72/1.96 inference(modus_ponens,[status(thm)],[69, 1906])).
% 1.72/1.96 tff(1908,plain,
% 1.72/1.96 (((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((s(s(elem!1)) = s(z)) | b(s(s(elem!1)), s(z)) | r(s(s(elem!1)), s(z)))) <=> ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (s(s(elem!1)) = s(z)) | b(s(s(elem!1)), s(z)) | r(s(s(elem!1)), s(z)))),
% 1.72/1.96 inference(rewrite,[status(thm)],[])).
% 1.72/1.96 tff(1909,plain,
% 1.72/1.96 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((s(s(elem!1)) = s(z)) | b(s(s(elem!1)), s(z)) | r(s(s(elem!1)), s(z)))),
% 1.72/1.96 inference(quant_inst,[status(thm)],[])).
% 1.72/1.96 tff(1910,plain,
% 1.72/1.96 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (s(s(elem!1)) = s(z)) | b(s(s(elem!1)), s(z)) | r(s(s(elem!1)), s(z))),
% 1.72/1.96 inference(modus_ponens,[status(thm)],[1909, 1908])).
% 1.72/1.96 tff(1911,plain,
% 1.72/1.96 ((s(s(elem!1)) = s(z)) | b(s(s(elem!1)), s(z)) | r(s(s(elem!1)), s(z))),
% 1.72/1.96 inference(unit_resolution,[status(thm)],[1910, 79])).
% 1.72/1.96 tff(1912,plain,
% 1.72/1.96 (b(s(s(elem!1)), s(z)) | r(s(s(elem!1)), s(z))),
% 1.72/1.96 inference(unit_resolution,[status(thm)],[1911, 1907])).
% 1.72/1.96 tff(1913,plain,
% 1.72/1.96 (r(s(s(elem!1)), s(z))),
% 1.72/1.96 inference(unit_resolution,[status(thm)],[1912, 1903])).
% 1.72/1.96 tff(1914,plain,
% 1.72/1.96 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), s(s(elem!1)))) | (~r(z, s(s(elem!1)))) | (~r(s(s(elem!1)), s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), s(s(elem!1)))) | (~r(z, s(s(elem!1)))) | (~r(s(s(elem!1)), s(z))))),
% 1.72/1.96 inference(rewrite,[status(thm)],[])).
% 1.72/1.96 tff(1915,plain,
% 1.72/1.96 (((~r(s(s(elem!1)), s(z))) | (~r(s(s(s(elem!1))), s(s(elem!1)))) | (~r(z, s(s(elem!1)))) | (~r(z, s(s(s(elem!1)))))) <=> ((~r(z, s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), s(s(elem!1)))) | (~r(z, s(s(elem!1)))) | (~r(s(s(elem!1)), s(z))))),
% 1.72/1.96 inference(rewrite,[status(thm)],[])).
% 1.72/1.96 tff(1916,plain,
% 1.72/1.96 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(elem!1)), s(z))) | (~r(s(s(s(elem!1))), s(s(elem!1)))) | (~r(z, s(s(elem!1)))) | (~r(z, s(s(s(elem!1))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), s(s(elem!1)))) | (~r(z, s(s(elem!1)))) | (~r(s(s(elem!1)), s(z)))))),
% 1.72/1.96 inference(monotonicity,[status(thm)],[1915])).
% 1.72/1.96 tff(1917,plain,
% 1.72/1.96 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(elem!1)), s(z))) | (~r(s(s(s(elem!1))), s(s(elem!1)))) | (~r(z, s(s(elem!1)))) | (~r(z, s(s(s(elem!1))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), s(s(elem!1)))) | (~r(z, s(s(elem!1)))) | (~r(s(s(elem!1)), s(z))))),
% 1.72/1.96 inference(transitivity,[status(thm)],[1916, 1914])).
% 1.72/1.96 tff(1918,plain,
% 1.72/1.96 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(elem!1)), s(z))) | (~r(s(s(s(elem!1))), s(s(elem!1)))) | (~r(z, s(s(elem!1)))) | (~r(z, s(s(s(elem!1))))))),
% 1.72/1.96 inference(quant_inst,[status(thm)],[])).
% 1.72/1.96 tff(1919,plain,
% 1.72/1.96 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), s(s(elem!1)))) | (~r(z, s(s(elem!1)))) | (~r(s(s(elem!1)), s(z)))),
% 1.72/1.96 inference(modus_ponens,[status(thm)],[1918, 1917])).
% 1.72/1.96 tff(1920,plain,
% 1.72/1.96 (~r(z, s(s(s(elem!1))))),
% 1.72/1.96 inference(unit_resolution,[status(thm)],[1919, 197, 1913, 365, 905])).
% 1.72/1.96 tff(1921,plain,
% 1.72/1.96 (b(z, s(s(s(elem!1))))),
% 1.72/1.96 inference(unit_resolution,[status(thm)],[261, 1920])).
% 1.72/1.96 tff(1922,plain,
% 1.72/1.96 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(z, s(s(s(elem!1))))) | (~b(s(z), s(s(elem!1)))) | (~b(s(s(s(elem!1))), s(z))) | (~b(z, s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(z, s(s(s(elem!1))))) | (~b(s(z), s(s(elem!1)))) | (~b(s(s(s(elem!1))), s(z))) | (~b(z, s(z))))),
% 1.72/1.96 inference(rewrite,[status(thm)],[])).
% 1.72/1.96 tff(1923,plain,
% 1.72/1.96 (((~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(z, s(s(s(elem!1))))) | (~b(s(z), s(s(elem!1)))) | (~b(s(s(s(elem!1))), s(z))) | (~b(z, s(z))) | (~b(z, s(s(s(elem!1)))))) <=> ((~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(z, s(s(s(elem!1))))) | (~b(s(z), s(s(elem!1)))) | (~b(s(s(s(elem!1))), s(z))) | (~b(z, s(z))))),
% 1.72/1.96 inference(rewrite,[status(thm)],[])).
% 1.72/1.96 tff(1924,plain,
% 1.72/1.96 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(z, s(s(s(elem!1))))) | (~b(s(z), s(s(elem!1)))) | (~b(s(s(s(elem!1))), s(z))) | (~b(z, s(z))) | (~b(z, s(s(s(elem!1))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(z, s(s(s(elem!1))))) | (~b(s(z), s(s(elem!1)))) | (~b(s(s(s(elem!1))), s(z))) | (~b(z, s(z)))))),
% 1.72/1.96 inference(monotonicity,[status(thm)],[1923])).
% 1.72/1.96 tff(1925,plain,
% 1.72/1.96 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(z, s(s(s(elem!1))))) | (~b(s(z), s(s(elem!1)))) | (~b(s(s(s(elem!1))), s(z))) | (~b(z, s(z))) | (~b(z, s(s(s(elem!1))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(z, s(s(s(elem!1))))) | (~b(s(z), s(s(elem!1)))) | (~b(s(s(s(elem!1))), s(z))) | (~b(z, s(z))))),
% 1.72/1.96 inference(transitivity,[status(thm)],[1924, 1922])).
% 1.72/1.96 tff(1926,plain,
% 1.72/1.96 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(z, s(s(s(elem!1))))) | (~b(s(z), s(s(elem!1)))) | (~b(s(s(s(elem!1))), s(z))) | (~b(z, s(z))) | (~b(z, s(s(s(elem!1))))))),
% 1.72/1.96 inference(quant_inst,[status(thm)],[])).
% 1.72/1.96 tff(1927,plain,
% 1.72/1.96 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(z, s(s(s(elem!1))))) | (~b(s(z), s(s(elem!1)))) | (~b(s(s(s(elem!1))), s(z))) | (~b(z, s(z)))),
% 1.72/1.96 inference(modus_ponens,[status(thm)],[1926, 1925])).
% 1.72/1.96 tff(1928,plain,
% 1.72/1.96 (~b(z, s(z))),
% 1.72/1.96 inference(unit_resolution,[status(thm)],[1927, 166, 376, 463, 1921, 96])).
% 1.72/1.96 tff(1929,plain,
% 1.72/1.96 (r(z, s(z))),
% 1.72/1.96 inference(unit_resolution,[status(thm)],[321, 1928])).
% 1.72/1.96 tff(1930,plain,
% 1.72/1.96 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(elem!1)))) | (~r(z, s(z))) | (~r(s(z), s(s(s(elem!1))))) | (~r(s(s(elem!1)), s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, s(s(elem!1)))) | (~r(z, s(z))) | (~r(s(z), s(s(s(elem!1))))) | (~r(s(s(elem!1)), s(z))))),
% 1.72/1.96 inference(rewrite,[status(thm)],[])).
% 1.72/1.96 tff(1931,plain,
% 1.72/1.96 (((~r(s(z), s(s(s(elem!1))))) | (~r(s(s(elem!1)), s(z))) | (~r(z, s(z))) | (~r(z, s(s(elem!1))))) <=> ((~r(z, s(s(elem!1)))) | (~r(z, s(z))) | (~r(s(z), s(s(s(elem!1))))) | (~r(s(s(elem!1)), s(z))))),
% 1.72/1.96 inference(rewrite,[status(thm)],[])).
% 1.72/1.96 tff(1932,plain,
% 1.72/1.96 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(s(s(elem!1))))) | (~r(s(s(elem!1)), s(z))) | (~r(z, s(z))) | (~r(z, s(s(elem!1)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(elem!1)))) | (~r(z, s(z))) | (~r(s(z), s(s(s(elem!1))))) | (~r(s(s(elem!1)), s(z)))))),
% 1.72/1.96 inference(monotonicity,[status(thm)],[1931])).
% 1.72/1.96 tff(1933,plain,
% 1.72/1.96 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(s(s(elem!1))))) | (~r(s(s(elem!1)), s(z))) | (~r(z, s(z))) | (~r(z, s(s(elem!1)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, s(s(elem!1)))) | (~r(z, s(z))) | (~r(s(z), s(s(s(elem!1))))) | (~r(s(s(elem!1)), s(z))))),
% 1.72/1.96 inference(transitivity,[status(thm)],[1932, 1930])).
% 1.72/1.96 tff(1934,plain,
% 1.72/1.96 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(s(s(elem!1))))) | (~r(s(s(elem!1)), s(z))) | (~r(z, s(z))) | (~r(z, s(s(elem!1)))))),
% 1.72/1.96 inference(quant_inst,[status(thm)],[])).
% 1.72/1.96 tff(1935,plain,
% 1.72/1.96 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, s(s(elem!1)))) | (~r(z, s(z))) | (~r(s(z), s(s(s(elem!1))))) | (~r(s(s(elem!1)), s(z)))),
% 1.72/1.96 inference(modus_ponens,[status(thm)],[1934, 1933])).
% 1.72/1.96 tff(1936,plain,
% 1.72/1.96 ($false),
% 1.72/1.96 inference(unit_resolution,[status(thm)],[1935, 197, 1929, 1913, 365, 1896])).
% 1.72/1.96 tff(1937,plain,((~r(z, s(s(elem!1)))) | (~b(s(z), s(s(elem!1)))) | (~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(z))) | (~r(s(s(s(elem!1))), s(s(elem!1))))), inference(lemma,lemma(discharge,[]))).
% 1.72/1.96 tff(1938,plain,
% 1.72/1.96 (~b(s(s(elem!1)), s(s(s(elem!1))))),
% 1.72/1.96 inference(unit_resolution,[status(thm)],[1937, 1860, 1850, 1888, 376])).
% 1.72/1.96 tff(1939,plain,
% 1.72/1.96 (r(s(s(elem!1)), s(s(s(elem!1))))),
% 1.72/1.96 inference(unit_resolution,[status(thm)],[461, 1938, 45])).
% 1.72/1.96 tff(1940,plain,
% 1.72/1.96 (~r(s(s(s(elem!1))), z)),
% 1.72/1.96 inference(unit_resolution,[status(thm)],[1386, 1939, 1888, 1860])).
% 1.72/1.96 tff(1941,plain,
% 1.72/1.96 (b(s(s(s(elem!1))), z)),
% 1.72/1.96 inference(unit_resolution,[status(thm)],[94, 1940])).
% 1.72/1.96 tff(1942,plain,
% 1.72/1.96 (s(s(z)) = s(s(elem!1))),
% 1.72/1.96 inference(unit_resolution,[status(thm)],[456, 1939, 376, 310, 155, 323, 1888])).
% 1.72/1.96 tff(1943,plain,
% 1.72/1.96 (s(elem!1) = s(z)),
% 1.72/1.96 inference(unit_resolution,[status(thm)],[43, 1942])).
% 1.72/1.96 tff(1944,plain,
% 1.72/1.96 (z = elem!1),
% 1.72/1.96 inference(unit_resolution,[status(thm)],[30, 1943])).
% 1.72/1.96 tff(1945,plain,
% 1.72/1.96 (b(s(s(s(elem!1))), elem!1)),
% 1.72/1.96 inference(unit_resolution,[status(thm)],[634, 1944, 1941])).
% 1.72/1.96 tff(1946,plain,
% 1.72/1.96 (b(s(z), z) <=> b(s(z), elem!1)),
% 1.72/1.96 inference(monotonicity,[status(thm)],[1944])).
% 1.72/1.96 tff(1947,plain,
% 1.72/1.96 (b(s(z), elem!1)),
% 1.72/1.96 inference(modus_ponens,[status(thm)],[53, 1946])).
% 1.72/1.96 tff(1948,plain,
% 1.72/1.96 (b(z, s(s(s(elem!1)))) <=> b(elem!1, s(s(s(elem!1))))),
% 1.72/1.96 inference(monotonicity,[status(thm)],[1944])).
% 1.72/1.96 tff(1949,plain,
% 1.72/1.96 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), s(s(elem!1)))) | (~r(z, s(s(elem!1)))) | (~r(s(s(elem!1)), s(s(s(elem!1))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), s(s(elem!1)))) | (~r(z, s(s(elem!1)))) | (~r(s(s(elem!1)), s(s(s(elem!1))))))),
% 1.72/1.96 inference(rewrite,[status(thm)],[])).
% 1.72/1.96 tff(1950,plain,
% 1.72/1.96 (((~r(s(s(elem!1)), s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), s(s(elem!1)))) | (~r(z, s(s(elem!1)))) | (~r(z, s(s(s(elem!1)))))) <=> ((~r(z, s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), s(s(elem!1)))) | (~r(z, s(s(elem!1)))) | (~r(s(s(elem!1)), s(s(s(elem!1))))))),
% 1.72/1.96 inference(rewrite,[status(thm)],[])).
% 1.72/1.96 tff(1951,plain,
% 1.72/1.96 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(elem!1)), s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), s(s(elem!1)))) | (~r(z, s(s(elem!1)))) | (~r(z, s(s(s(elem!1))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), s(s(elem!1)))) | (~r(z, s(s(elem!1)))) | (~r(s(s(elem!1)), s(s(s(elem!1)))))))),
% 1.72/1.96 inference(monotonicity,[status(thm)],[1950])).
% 1.72/1.96 tff(1952,plain,
% 1.72/1.96 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(elem!1)), s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), s(s(elem!1)))) | (~r(z, s(s(elem!1)))) | (~r(z, s(s(s(elem!1))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), s(s(elem!1)))) | (~r(z, s(s(elem!1)))) | (~r(s(s(elem!1)), s(s(s(elem!1))))))),
% 1.72/1.96 inference(transitivity,[status(thm)],[1951, 1949])).
% 1.72/1.96 tff(1953,plain,
% 1.72/1.96 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(elem!1)), s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), s(s(elem!1)))) | (~r(z, s(s(elem!1)))) | (~r(z, s(s(s(elem!1))))))),
% 1.72/1.97 inference(quant_inst,[status(thm)],[])).
% 1.72/1.97 tff(1954,plain,
% 1.72/1.97 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), s(s(elem!1)))) | (~r(z, s(s(elem!1)))) | (~r(s(s(elem!1)), s(s(s(elem!1)))))),
% 1.72/1.97 inference(modus_ponens,[status(thm)],[1953, 1952])).
% 1.72/1.97 tff(1955,plain,
% 1.72/1.97 ($false),
% 1.72/1.97 inference(unit_resolution,[status(thm)],[1954, 197, 377, 365, 905, 282])).
% 1.72/1.97 tff(1956,plain,((~r(s(s(s(elem!1))), s(s(elem!1)))) | (~r(s(s(elem!1)), s(s(s(elem!1))))) | (~r(z, s(s(elem!1)))) | (~r(z, s(s(s(elem!1)))))), inference(lemma,lemma(discharge,[]))).
% 1.72/1.97 tff(1957,plain,
% 1.72/1.97 (~r(z, s(s(s(elem!1))))),
% 1.72/1.97 inference(unit_resolution,[status(thm)],[1956, 1939, 1888, 1860])).
% 1.72/1.97 tff(1958,plain,
% 1.72/1.97 (b(z, s(s(s(elem!1))))),
% 1.72/1.97 inference(unit_resolution,[status(thm)],[261, 1957])).
% 1.72/1.97 tff(1959,plain,
% 1.72/1.97 (b(elem!1, s(s(s(elem!1))))),
% 1.72/1.97 inference(modus_ponens,[status(thm)],[1958, 1948])).
% 1.72/1.97 tff(1960,plain,
% 1.72/1.97 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(z), elem!1)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(z), elem!1)))),
% 1.72/1.97 inference(rewrite,[status(thm)],[])).
% 1.72/1.97 tff(1961,plain,
% 1.72/1.97 (((~b(s(s(s(elem!1))), s(z))) | (~b(s(s(s(elem!1))), s(z))) | (~b(elem!1, s(s(s(elem!1))))) | (~b(s(z), elem!1)) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(s(s(elem!1))), s(z)))) <=> ((~b(elem!1, s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(z), elem!1)))),
% 1.72/1.97 inference(rewrite,[status(thm)],[])).
% 1.72/1.97 tff(1962,plain,
% 1.72/1.97 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), s(z))) | (~b(s(s(s(elem!1))), s(z))) | (~b(elem!1, s(s(s(elem!1))))) | (~b(s(z), elem!1)) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(s(s(elem!1))), s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(z), elem!1))))),
% 1.72/1.97 inference(monotonicity,[status(thm)],[1961])).
% 1.72/1.97 tff(1963,plain,
% 1.72/1.97 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), s(z))) | (~b(s(s(s(elem!1))), s(z))) | (~b(elem!1, s(s(s(elem!1))))) | (~b(s(z), elem!1)) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(s(s(elem!1))), s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(z), elem!1)))),
% 1.72/1.97 inference(transitivity,[status(thm)],[1962, 1960])).
% 1.72/1.97 tff(1964,plain,
% 1.72/1.97 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), s(z))) | (~b(s(s(s(elem!1))), s(z))) | (~b(elem!1, s(s(s(elem!1))))) | (~b(s(z), elem!1)) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(s(s(elem!1))), s(z))))),
% 1.72/1.97 inference(quant_inst,[status(thm)],[])).
% 1.72/1.97 tff(1965,plain,
% 1.72/1.97 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(z), elem!1))),
% 1.72/1.97 inference(modus_ponens,[status(thm)],[1964, 1963])).
% 1.72/1.97 tff(1966,plain,
% 1.72/1.97 ($false),
% 1.72/1.97 inference(unit_resolution,[status(thm)],[1965, 166, 1959, 1850, 1947, 1945])).
% 1.72/1.97 tff(1967,plain,((~b(s(z), s(s(elem!1)))) | (~b(s(z), z)) | (~b(s(s(elem!1)), s(z))) | (~r(z, s(s(z)))) | (~r(z, s(z))) | (s(s(elem!1)) = s(s(s(elem!1))))), inference(lemma,lemma(discharge,[]))).
% 1.72/1.97 tff(1968,plain,
% 1.72/1.97 (~b(s(z), s(s(elem!1)))),
% 1.72/1.97 inference(unit_resolution,[status(thm)],[1967, 53, 310, 155, 323, 45])).
% 1.72/1.97 tff(1969,plain,
% 1.72/1.97 (r(s(z), s(s(elem!1)))),
% 1.72/1.97 inference(unit_resolution,[status(thm)],[84, 1968])).
% 1.72/1.97 tff(1970,assumption,(r(s(s(elem!1)), z)), introduced(assumption)).
% 1.72/1.97 tff(1971,plain,
% 1.72/1.97 ($false),
% 1.72/1.97 inference(unit_resolution,[status(thm)],[898, 197, 311, 323, 365, 1970])).
% 1.72/1.97 tff(1972,plain,((~r(s(s(elem!1)), z)) | (~r(s(z), s(s(elem!1)))) | (~r(z, s(z))) | (~r(z, s(s(elem!1))))), inference(lemma,lemma(discharge,[]))).
% 1.72/1.97 tff(1973,plain,
% 1.72/1.97 (~r(s(s(elem!1)), z)),
% 1.72/1.97 inference(unit_resolution,[status(thm)],[1972, 1969, 323, 1888])).
% 1.72/1.97 tff(1974,plain,
% 1.72/1.97 (b(s(s(elem!1)), z)),
% 1.72/1.97 inference(unit_resolution,[status(thm)],[608, 1973])).
% 1.72/1.97 tff(1975,plain,
% 1.72/1.97 (~r(s(s(elem!1)), s(s(s(elem!1))))),
% 1.72/1.97 inference(unit_resolution,[status(thm)],[413, 1969, 323, 1888])).
% 1.72/1.97 tff(1976,plain,
% 1.72/1.97 (b(s(s(elem!1)), s(s(s(elem!1))))),
% 1.72/1.97 inference(unit_resolution,[status(thm)],[461, 1975, 45])).
% 1.72/1.97 tff(1977,plain,
% 1.72/1.97 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(z, s(s(s(elem!1))))) | (~b(s(z), z)) | (~b(s(s(elem!1)), z)) | (~b(s(s(s(elem!1))), s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(z, s(s(s(elem!1))))) | (~b(s(z), z)) | (~b(s(s(elem!1)), z)) | (~b(s(s(s(elem!1))), s(z))))),
% 1.72/1.97 inference(rewrite,[status(thm)],[])).
% 1.72/1.97 tff(1978,plain,
% 1.72/1.97 (((~b(s(z), z)) | (~b(s(s(elem!1)), z)) | (~b(s(s(s(elem!1))), s(z))) | (~b(z, s(s(s(elem!1))))) | (~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(s(s(elem!1)), z))) <=> ((~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(z, s(s(s(elem!1))))) | (~b(s(z), z)) | (~b(s(s(elem!1)), z)) | (~b(s(s(s(elem!1))), s(z))))),
% 1.72/1.97 inference(rewrite,[status(thm)],[])).
% 1.72/1.97 tff(1979,plain,
% 1.72/1.97 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), z)) | (~b(s(s(elem!1)), z)) | (~b(s(s(s(elem!1))), s(z))) | (~b(z, s(s(s(elem!1))))) | (~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(s(s(elem!1)), z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(z, s(s(s(elem!1))))) | (~b(s(z), z)) | (~b(s(s(elem!1)), z)) | (~b(s(s(s(elem!1))), s(z)))))),
% 1.72/1.97 inference(monotonicity,[status(thm)],[1978])).
% 1.72/1.97 tff(1980,plain,
% 1.72/1.97 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), z)) | (~b(s(s(elem!1)), z)) | (~b(s(s(s(elem!1))), s(z))) | (~b(z, s(s(s(elem!1))))) | (~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(s(s(elem!1)), z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(z, s(s(s(elem!1))))) | (~b(s(z), z)) | (~b(s(s(elem!1)), z)) | (~b(s(s(s(elem!1))), s(z))))),
% 1.72/1.97 inference(transitivity,[status(thm)],[1979, 1977])).
% 1.72/1.97 tff(1981,plain,
% 1.72/1.97 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), z)) | (~b(s(s(elem!1)), z)) | (~b(s(s(s(elem!1))), s(z))) | (~b(z, s(s(s(elem!1))))) | (~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(s(s(elem!1)), z)))),
% 1.72/1.97 inference(quant_inst,[status(thm)],[])).
% 1.72/1.97 tff(1982,plain,
% 1.72/1.97 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(z, s(s(s(elem!1))))) | (~b(s(z), z)) | (~b(s(s(elem!1)), z)) | (~b(s(s(s(elem!1))), s(z)))),
% 1.72/1.97 inference(modus_ponens,[status(thm)],[1981, 1980])).
% 1.72/1.97 tff(1983,plain,
% 1.72/1.97 ($false),
% 1.72/1.97 inference(unit_resolution,[status(thm)],[1982, 166, 463, 240, 53, 96, 592])).
% 1.72/1.97 tff(1984,plain,((~b(z, s(s(s(elem!1))))) | (~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(s(z), z)) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(s(elem!1)), z))), inference(lemma,lemma(discharge,[]))).
% 1.72/1.97 tff(1985,plain,
% 1.72/1.97 (~b(z, s(s(s(elem!1))))),
% 1.72/1.97 inference(unit_resolution,[status(thm)],[1984, 1976, 53, 1850, 1974])).
% 1.72/1.97 tff(1986,plain,
% 1.72/1.97 (r(z, s(s(s(elem!1))))),
% 1.72/1.97 inference(unit_resolution,[status(thm)],[261, 1985])).
% 1.72/1.97 tff(1987,plain,
% 1.72/1.97 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(s(z), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(s(elem!1)), s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(s(z), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(s(elem!1)), s(z))))),
% 1.72/1.97 inference(rewrite,[status(thm)],[])).
% 1.72/1.97 tff(1988,plain,
% 1.72/1.97 (((~b(s(z), s(s(s(elem!1))))) | (~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(z), s(s(s(elem!1))))) | (~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(s(s(elem!1)), s(z)))) <=> ((~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(s(z), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(s(elem!1)), s(z))))),
% 1.72/1.97 inference(rewrite,[status(thm)],[])).
% 1.72/1.97 tff(1989,plain,
% 1.72/1.97 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(s(elem!1))))) | (~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(z), s(s(s(elem!1))))) | (~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(s(s(elem!1)), s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(s(z), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(s(elem!1)), s(z)))))),
% 1.72/1.97 inference(monotonicity,[status(thm)],[1988])).
% 1.72/1.97 tff(1990,plain,
% 1.72/1.97 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(s(elem!1))))) | (~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(z), s(s(s(elem!1))))) | (~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(s(s(elem!1)), s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(s(z), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(s(elem!1)), s(z))))),
% 1.72/1.97 inference(transitivity,[status(thm)],[1989, 1987])).
% 1.72/1.97 tff(1991,plain,
% 1.72/1.97 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(s(elem!1))))) | (~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(z), s(s(s(elem!1))))) | (~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(s(s(elem!1)), s(z))))),
% 1.72/1.97 inference(quant_inst,[status(thm)],[])).
% 1.72/1.97 tff(1992,plain,
% 1.72/1.97 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(s(z), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(s(elem!1)), s(z)))),
% 1.72/1.97 inference(modus_ponens,[status(thm)],[1991, 1990])).
% 1.72/1.97 tff(1993,plain,
% 1.72/1.97 ($false),
% 1.72/1.97 inference(unit_resolution,[status(thm)],[1992, 166, 463, 241, 96, 310])).
% 1.72/1.97 tff(1994,plain,((~b(s(z), s(s(s(elem!1))))) | (~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(s(elem!1)), s(z)))), inference(lemma,lemma(discharge,[]))).
% 1.72/1.97 tff(1995,plain,
% 1.72/1.97 (~b(s(z), s(s(s(elem!1))))),
% 1.72/1.97 inference(unit_resolution,[status(thm)],[1994, 1976, 310, 1850])).
% 1.72/1.97 tff(1996,plain,
% 1.72/1.97 (r(s(z), s(s(s(elem!1))))),
% 1.72/1.97 inference(unit_resolution,[status(thm)],[116, 1995])).
% 1.72/1.97 tff(1997,plain,
% 1.72/1.97 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), s(s(elem!1)))) | (~r(z, s(z))) | (~r(s(z), s(s(s(elem!1))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), s(s(elem!1)))) | (~r(z, s(z))) | (~r(s(z), s(s(s(elem!1))))))),
% 1.72/1.97 inference(rewrite,[status(thm)],[])).
% 1.72/1.97 tff(1998,plain,
% 1.72/1.97 (((~r(s(s(s(elem!1))), s(s(elem!1)))) | (~r(s(z), s(s(s(elem!1))))) | (~r(z, s(s(s(elem!1))))) | (~r(z, s(z)))) <=> ((~r(z, s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), s(s(elem!1)))) | (~r(z, s(z))) | (~r(s(z), s(s(s(elem!1))))))),
% 1.72/1.97 inference(rewrite,[status(thm)],[])).
% 1.72/1.97 tff(1999,plain,
% 1.72/1.97 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), s(s(elem!1)))) | (~r(s(z), s(s(s(elem!1))))) | (~r(z, s(s(s(elem!1))))) | (~r(z, s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), s(s(elem!1)))) | (~r(z, s(z))) | (~r(s(z), s(s(s(elem!1)))))))),
% 1.72/1.97 inference(monotonicity,[status(thm)],[1998])).
% 1.72/1.97 tff(2000,plain,
% 1.72/1.97 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), s(s(elem!1)))) | (~r(s(z), s(s(s(elem!1))))) | (~r(z, s(s(s(elem!1))))) | (~r(z, s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), s(s(elem!1)))) | (~r(z, s(z))) | (~r(s(z), s(s(s(elem!1))))))),
% 1.72/1.97 inference(transitivity,[status(thm)],[1999, 1997])).
% 1.72/1.97 tff(2001,plain,
% 1.72/1.97 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), s(s(elem!1)))) | (~r(s(z), s(s(s(elem!1))))) | (~r(z, s(s(s(elem!1))))) | (~r(z, s(z))))),
% 1.72/1.97 inference(quant_inst,[status(thm)],[])).
% 1.72/1.97 tff(2002,plain,
% 1.72/1.97 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), s(s(elem!1)))) | (~r(z, s(z))) | (~r(s(z), s(s(s(elem!1)))))),
% 1.72/1.97 inference(modus_ponens,[status(thm)],[2001, 2000])).
% 1.72/1.97 tff(2003,plain,
% 1.72/1.97 ($false),
% 1.72/1.97 inference(unit_resolution,[status(thm)],[2002, 197, 323, 905, 119, 282])).
% 1.72/1.97 tff(2004,plain,((~r(s(s(s(elem!1))), s(s(elem!1)))) | (~r(z, s(z))) | (~r(s(z), s(s(s(elem!1))))) | (~r(z, s(s(s(elem!1)))))), inference(lemma,lemma(discharge,[]))).
% 1.72/1.97 tff(2005,plain,
% 1.72/1.97 (~r(s(s(s(elem!1))), s(s(elem!1)))),
% 1.72/1.97 inference(unit_resolution,[status(thm)],[2004, 1996, 323, 1986])).
% 1.72/1.97 tff(2006,plain,
% 1.72/1.97 (b(s(s(s(elem!1))), s(s(elem!1)))),
% 1.72/1.97 inference(unit_resolution,[status(thm)],[889, 2005, 51])).
% 1.72/1.97 tff(2007,plain,
% 1.72/1.97 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(s(elem!1)), s(z))) | (~b(s(s(s(s(elem!1)))), s(z))) | (~b(s(z), s(s(s(s(elem!1)))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(s(elem!1)), s(z))) | (~b(s(s(s(s(elem!1)))), s(z))) | (~b(s(z), s(s(s(s(elem!1)))))))),
% 1.72/1.97 inference(rewrite,[status(thm)],[])).
% 1.72/1.97 tff(2008,plain,
% 1.72/1.97 (((~b(s(s(s(s(elem!1)))), s(z))) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(z), s(s(s(s(elem!1)))))) | (~b(s(s(elem!1)), s(z))) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(s(s(elem!1))), s(s(elem!1))))) <=> ((~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(s(elem!1)), s(z))) | (~b(s(s(s(s(elem!1)))), s(z))) | (~b(s(z), s(s(s(s(elem!1)))))))),
% 1.72/1.97 inference(rewrite,[status(thm)],[])).
% 1.72/1.97 tff(2009,plain,
% 1.72/1.97 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(elem!1)))), s(z))) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(z), s(s(s(s(elem!1)))))) | (~b(s(s(elem!1)), s(z))) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(s(s(elem!1))), s(s(elem!1)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(s(elem!1)), s(z))) | (~b(s(s(s(s(elem!1)))), s(z))) | (~b(s(z), s(s(s(s(elem!1))))))))),
% 1.72/1.97 inference(monotonicity,[status(thm)],[2008])).
% 1.72/1.97 tff(2010,plain,
% 1.72/1.97 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(elem!1)))), s(z))) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(z), s(s(s(s(elem!1)))))) | (~b(s(s(elem!1)), s(z))) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(s(s(elem!1))), s(s(elem!1)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(s(elem!1)), s(z))) | (~b(s(s(s(s(elem!1)))), s(z))) | (~b(s(z), s(s(s(s(elem!1)))))))),
% 1.72/1.97 inference(transitivity,[status(thm)],[2009, 2007])).
% 1.72/1.97 tff(2011,plain,
% 1.72/1.97 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(elem!1)))), s(z))) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(z), s(s(s(s(elem!1)))))) | (~b(s(s(elem!1)), s(z))) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(s(s(elem!1))), s(s(elem!1)))))),
% 1.72/1.97 inference(quant_inst,[status(thm)],[])).
% 1.72/1.97 tff(2012,plain,
% 1.72/1.97 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(s(elem!1)), s(z))) | (~b(s(s(s(s(elem!1)))), s(z))) | (~b(s(z), s(s(s(s(elem!1))))))),
% 1.72/1.97 inference(modus_ponens,[status(thm)],[2011, 2010])).
% 1.72/1.97 tff(2013,plain,
% 1.72/1.97 ($false),
% 1.72/1.97 inference(unit_resolution,[status(thm)],[2012, 166, 839, 96, 310, 1402, 1327])).
% 1.72/1.97 tff(2014,plain,((~b(s(s(s(s(elem!1)))), s(z))) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(s(elem!1)), s(z))) | (~b(s(z), s(s(s(s(elem!1))))))), inference(lemma,lemma(discharge,[]))).
% 1.72/1.97 tff(2015,plain,
% 1.72/1.97 (~b(s(s(s(s(elem!1)))), s(z))),
% 1.72/1.97 inference(unit_resolution,[status(thm)],[2014, 1327, 96, 310, 839])).
% 1.72/1.97 tff(2016,plain,
% 1.72/1.97 (r(s(s(s(s(elem!1)))), s(z))),
% 1.72/1.97 inference(unit_resolution,[status(thm)],[661, 2015])).
% 1.72/1.97 tff(2017,plain,
% 1.72/1.97 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(s(elem!1)))) | (~r(z, s(z))) | (~r(s(s(s(s(elem!1)))), s(z))) | (~r(z, s(s(s(s(elem!1)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(z), s(s(elem!1)))) | (~r(z, s(z))) | (~r(s(s(s(s(elem!1)))), s(z))) | (~r(z, s(s(s(s(elem!1)))))))),
% 1.72/1.97 inference(rewrite,[status(thm)],[])).
% 1.72/1.97 tff(2018,plain,
% 1.72/1.97 (((~r(s(z), s(s(elem!1)))) | (~r(s(s(s(s(elem!1)))), s(z))) | (~r(z, s(z))) | (~r(z, s(s(s(s(elem!1))))))) <=> ((~r(s(z), s(s(elem!1)))) | (~r(z, s(z))) | (~r(s(s(s(s(elem!1)))), s(z))) | (~r(z, s(s(s(s(elem!1)))))))),
% 1.72/1.97 inference(rewrite,[status(thm)],[])).
% 1.72/1.97 tff(2019,plain,
% 1.72/1.97 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(s(elem!1)))) | (~r(s(s(s(s(elem!1)))), s(z))) | (~r(z, s(z))) | (~r(z, s(s(s(s(elem!1)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(s(elem!1)))) | (~r(z, s(z))) | (~r(s(s(s(s(elem!1)))), s(z))) | (~r(z, s(s(s(s(elem!1))))))))),
% 1.72/1.98 inference(monotonicity,[status(thm)],[2018])).
% 1.72/1.98 tff(2020,plain,
% 1.72/1.98 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(s(elem!1)))) | (~r(s(s(s(s(elem!1)))), s(z))) | (~r(z, s(z))) | (~r(z, s(s(s(s(elem!1)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(z), s(s(elem!1)))) | (~r(z, s(z))) | (~r(s(s(s(s(elem!1)))), s(z))) | (~r(z, s(s(s(s(elem!1)))))))),
% 1.72/1.98 inference(transitivity,[status(thm)],[2019, 2017])).
% 1.72/1.98 tff(2021,plain,
% 1.72/1.98 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(s(elem!1)))) | (~r(s(s(s(s(elem!1)))), s(z))) | (~r(z, s(z))) | (~r(z, s(s(s(s(elem!1)))))))),
% 1.72/1.98 inference(quant_inst,[status(thm)],[])).
% 1.72/1.98 tff(2022,plain,
% 1.72/1.98 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(z), s(s(elem!1)))) | (~r(z, s(z))) | (~r(s(s(s(s(elem!1)))), s(z))) | (~r(z, s(s(s(s(elem!1))))))),
% 1.72/1.98 inference(modus_ponens,[status(thm)],[2021, 2020])).
% 1.72/1.98 tff(2023,plain,
% 1.72/1.98 (~r(z, s(s(s(s(elem!1)))))),
% 1.72/1.98 inference(unit_resolution,[status(thm)],[2022, 197, 311, 323, 2016])).
% 1.72/1.98 tff(2024,plain,
% 1.72/1.98 ((z = s(s(s(s(elem!1))))) | b(z, s(s(s(s(elem!1)))))),
% 1.72/1.98 inference(unit_resolution,[status(thm)],[1496, 79, 2023])).
% 1.72/1.98 tff(2025,plain,
% 1.72/1.98 (b(z, s(s(s(s(elem!1)))))),
% 1.72/1.98 inference(unit_resolution,[status(thm)],[2024, 1486])).
% 1.72/1.98 tff(2026,plain,
% 1.72/1.98 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(s(elem!1)))) | (~r(z, s(z))) | (~r(s(s(s(s(elem!1)))), s(z))) | (~r(s(s(s(s(elem!1)))), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(z), s(s(elem!1)))) | (~r(z, s(z))) | (~r(s(s(s(s(elem!1)))), s(z))) | (~r(s(s(s(s(elem!1)))), z)))),
% 1.72/1.98 inference(rewrite,[status(thm)],[])).
% 1.72/1.98 tff(2027,plain,
% 1.72/1.98 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(s(elem!1)))) | (~r(z, s(z))) | (~r(s(s(s(s(elem!1)))), s(z))) | (~r(s(s(s(s(elem!1)))), z)))),
% 1.72/1.98 inference(quant_inst,[status(thm)],[])).
% 1.72/1.98 tff(2028,plain,
% 1.72/1.98 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(z), s(s(elem!1)))) | (~r(z, s(z))) | (~r(s(s(s(s(elem!1)))), s(z))) | (~r(s(s(s(s(elem!1)))), z))),
% 1.72/1.98 inference(modus_ponens,[status(thm)],[2027, 2026])).
% 1.72/1.98 tff(2029,plain,
% 1.72/1.98 (~r(s(s(s(s(elem!1)))), z)),
% 1.72/1.98 inference(unit_resolution,[status(thm)],[2028, 197, 311, 323, 2016])).
% 1.72/1.98 tff(2030,plain,
% 1.72/1.98 (b(s(s(s(s(elem!1)))), z)),
% 1.72/1.98 inference(unit_resolution,[status(thm)],[1339, 79, 626, 2029])).
% 1.72/1.98 tff(2031,plain,
% 1.72/1.98 ($false),
% 1.72/1.98 inference(unit_resolution,[status(thm)],[1512, 166, 53, 1327, 2030, 2025])).
% 1.72/1.98 tff(2032,plain,((~b(s(z), s(s(s(s(elem!1)))))) | (~b(s(z), z)) | (~r(s(z), s(s(elem!1)))) | (~r(z, s(z))) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(s(elem!1)), s(z))) | (~b(s(s(s(elem!1))), s(s(elem!1))))), inference(lemma,lemma(discharge,[]))).
% 1.72/1.98 tff(2033,plain,
% 1.72/1.98 (~b(s(z), s(s(s(s(elem!1)))))),
% 1.72/1.98 inference(unit_resolution,[status(thm)],[2032, 2006, 1969, 323, 1850, 310, 53])).
% 1.72/1.98 tff(2034,plain,
% 1.72/1.98 (r(s(z), s(s(s(s(elem!1)))))),
% 1.72/1.98 inference(unit_resolution,[status(thm)],[681, 2033])).
% 1.72/1.98 tff(2035,plain,
% 1.72/1.98 (~r(z, s(s(s(s(elem!1)))))),
% 1.72/1.98 inference(unit_resolution,[status(thm)],[2022, 197, 311, 323, 700])).
% 1.72/1.98 tff(2036,plain,
% 1.72/1.98 ((z = s(s(s(s(elem!1))))) | b(z, s(s(s(s(elem!1)))))),
% 1.72/1.98 inference(unit_resolution,[status(thm)],[1496, 79, 2035])).
% 1.72/1.98 tff(2037,plain,
% 1.72/1.98 (b(z, s(s(s(s(elem!1)))))),
% 1.72/1.98 inference(unit_resolution,[status(thm)],[2036, 1486])).
% 1.72/1.98 tff(2038,plain,
% 1.72/1.98 (~r(s(s(s(s(elem!1)))), z)),
% 1.72/1.98 inference(unit_resolution,[status(thm)],[2028, 197, 311, 323, 700])).
% 1.72/1.98 tff(2039,plain,
% 1.72/1.98 (b(s(s(s(s(elem!1)))), z)),
% 1.72/1.98 inference(unit_resolution,[status(thm)],[1339, 79, 626, 2038])).
% 1.72/1.98 tff(2040,plain,
% 1.72/1.98 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), z)) | (~b(s(s(elem!1)), z)) | (~b(s(s(elem!1)), s(z))) | (~b(z, s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), z)) | (~b(s(s(elem!1)), z)) | (~b(s(s(elem!1)), s(z))) | (~b(z, s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), z)))),
% 1.72/1.98 inference(rewrite,[status(thm)],[])).
% 1.72/1.98 tff(2041,plain,
% 1.72/1.98 (((~b(s(s(s(s(elem!1)))), z)) | (~b(s(s(elem!1)), z)) | (~b(z, s(s(s(s(elem!1)))))) | (~b(s(z), z)) | (~b(s(s(elem!1)), z)) | (~b(s(s(elem!1)), s(z)))) <=> ((~b(s(z), z)) | (~b(s(s(elem!1)), z)) | (~b(s(s(elem!1)), s(z))) | (~b(z, s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), z)))),
% 1.72/1.98 inference(rewrite,[status(thm)],[])).
% 1.72/1.98 tff(2042,plain,
% 1.72/1.98 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(elem!1)))), z)) | (~b(s(s(elem!1)), z)) | (~b(z, s(s(s(s(elem!1)))))) | (~b(s(z), z)) | (~b(s(s(elem!1)), z)) | (~b(s(s(elem!1)), s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), z)) | (~b(s(s(elem!1)), z)) | (~b(s(s(elem!1)), s(z))) | (~b(z, s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), z))))),
% 1.72/1.98 inference(monotonicity,[status(thm)],[2041])).
% 1.72/1.98 tff(2043,plain,
% 1.72/1.98 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(elem!1)))), z)) | (~b(s(s(elem!1)), z)) | (~b(z, s(s(s(s(elem!1)))))) | (~b(s(z), z)) | (~b(s(s(elem!1)), z)) | (~b(s(s(elem!1)), s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), z)) | (~b(s(s(elem!1)), z)) | (~b(s(s(elem!1)), s(z))) | (~b(z, s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), z)))),
% 1.72/1.98 inference(transitivity,[status(thm)],[2042, 2040])).
% 1.72/1.98 tff(2044,plain,
% 1.72/1.98 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(elem!1)))), z)) | (~b(s(s(elem!1)), z)) | (~b(z, s(s(s(s(elem!1)))))) | (~b(s(z), z)) | (~b(s(s(elem!1)), z)) | (~b(s(s(elem!1)), s(z))))),
% 1.72/1.98 inference(quant_inst,[status(thm)],[])).
% 1.72/1.98 tff(2045,plain,
% 1.72/1.98 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), z)) | (~b(s(s(elem!1)), z)) | (~b(s(s(elem!1)), s(z))) | (~b(z, s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), z))),
% 1.72/1.98 inference(modus_ponens,[status(thm)],[2044, 2043])).
% 1.72/1.98 tff(2046,plain,
% 1.72/1.98 ($false),
% 1.72/1.98 inference(unit_resolution,[status(thm)],[2045, 166, 53, 310, 592, 2039, 2037])).
% 1.72/1.98 tff(2047,plain,((~r(s(s(s(s(elem!1)))), s(z))) | (~b(s(z), z)) | (~b(s(s(elem!1)), s(z))) | (~b(s(s(elem!1)), z)) | (~r(s(z), s(s(elem!1)))) | (~r(z, s(z)))), inference(lemma,lemma(discharge,[]))).
% 1.72/1.98 tff(2048,plain,
% 1.72/1.98 (~r(s(s(s(s(elem!1)))), s(z))),
% 1.72/1.98 inference(unit_resolution,[status(thm)],[2047, 53, 310, 1974, 1969, 323])).
% 1.72/1.98 tff(2049,plain,
% 1.72/1.98 (b(s(s(s(s(elem!1)))), s(z))),
% 1.72/1.98 inference(unit_resolution,[status(thm)],[661, 2048])).
% 1.72/1.98 tff(2050,plain,
% 1.72/1.98 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(s(elem!1))))) | (~r(z, s(z))) | (~r(s(z), s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), s(s(z)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, s(s(s(elem!1))))) | (~r(z, s(z))) | (~r(s(z), s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), s(s(z)))))),
% 1.72/1.98 inference(rewrite,[status(thm)],[])).
% 1.72/1.98 tff(2051,plain,
% 1.72/1.98 (((~r(s(s(s(elem!1))), s(s(z)))) | (~r(s(z), s(s(s(elem!1))))) | (~r(z, s(s(s(elem!1))))) | (~r(z, s(z)))) <=> ((~r(z, s(s(s(elem!1))))) | (~r(z, s(z))) | (~r(s(z), s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), s(s(z)))))),
% 1.72/1.98 inference(rewrite,[status(thm)],[])).
% 1.72/1.98 tff(2052,plain,
% 1.72/1.98 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), s(s(z)))) | (~r(s(z), s(s(s(elem!1))))) | (~r(z, s(s(s(elem!1))))) | (~r(z, s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(s(elem!1))))) | (~r(z, s(z))) | (~r(s(z), s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), s(s(z))))))),
% 1.72/1.98 inference(monotonicity,[status(thm)],[2051])).
% 1.72/1.98 tff(2053,plain,
% 1.72/1.98 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), s(s(z)))) | (~r(s(z), s(s(s(elem!1))))) | (~r(z, s(s(s(elem!1))))) | (~r(z, s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, s(s(s(elem!1))))) | (~r(z, s(z))) | (~r(s(z), s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), s(s(z)))))),
% 1.72/1.98 inference(transitivity,[status(thm)],[2052, 2050])).
% 1.72/1.98 tff(2054,plain,
% 1.72/1.98 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), s(s(z)))) | (~r(s(z), s(s(s(elem!1))))) | (~r(z, s(s(s(elem!1))))) | (~r(z, s(z))))),
% 1.72/1.98 inference(quant_inst,[status(thm)],[])).
% 1.72/1.98 tff(2055,plain,
% 1.72/1.98 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, s(s(s(elem!1))))) | (~r(z, s(z))) | (~r(s(z), s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), s(s(z))))),
% 1.72/1.98 inference(modus_ponens,[status(thm)],[2054, 2053])).
% 1.72/1.98 tff(2056,plain,
% 1.72/1.98 ($false),
% 1.72/1.98 inference(unit_resolution,[status(thm)],[2055, 197, 323, 119, 282, 464])).
% 1.72/1.98 tff(2057,plain,((~r(s(z), s(s(s(elem!1))))) | (~r(z, s(z))) | (~r(z, s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), s(s(z))))), inference(lemma,lemma(discharge,[]))).
% 1.72/1.98 tff(2058,plain,
% 1.72/1.98 (~r(s(s(s(elem!1))), s(s(z)))),
% 1.72/1.98 inference(unit_resolution,[status(thm)],[2057, 1986, 323, 1996])).
% 1.72/1.98 tff(2059,plain,
% 1.72/1.98 (b(s(s(s(elem!1))), s(s(z)))),
% 1.72/1.98 inference(unit_resolution,[status(thm)],[218, 2058])).
% 1.72/1.98 tff(2060,assumption,(b(s(s(s(elem!1))), s(s(z)))), introduced(assumption)).
% 1.72/1.98 tff(2061,plain,
% 1.72/1.98 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(s(s(elem!1))), s(s(z)))) | (~b(s(s(z)), s(s(elem!1)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(s(s(elem!1))), s(s(z)))) | (~b(s(s(z)), s(s(elem!1)))))),
% 1.72/1.98 inference(rewrite,[status(thm)],[])).
% 1.72/1.98 tff(2062,plain,
% 1.72/1.98 (((~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(s(s(z)), s(s(elem!1)))) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(s(s(elem!1))), s(s(z))))) <=> ((~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(s(s(elem!1))), s(s(z)))) | (~b(s(s(z)), s(s(elem!1)))))),
% 1.72/1.98 inference(rewrite,[status(thm)],[])).
% 1.72/1.98 tff(2063,plain,
% 1.72/1.98 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(s(s(z)), s(s(elem!1)))) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(s(s(elem!1))), s(s(z)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(s(s(elem!1))), s(s(z)))) | (~b(s(s(z)), s(s(elem!1))))))),
% 1.72/1.98 inference(monotonicity,[status(thm)],[2062])).
% 1.72/1.98 tff(2064,plain,
% 1.72/1.98 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(s(s(z)), s(s(elem!1)))) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(s(s(elem!1))), s(s(z)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(s(s(elem!1))), s(s(z)))) | (~b(s(s(z)), s(s(elem!1)))))),
% 1.72/1.98 inference(transitivity,[status(thm)],[2063, 2061])).
% 1.72/1.98 tff(2065,plain,
% 1.72/1.98 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(s(s(z)), s(s(elem!1)))) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(s(s(elem!1))), s(s(z)))))),
% 1.72/1.98 inference(quant_inst,[status(thm)],[])).
% 1.72/1.98 tff(2066,plain,
% 1.72/1.98 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(s(s(elem!1))), s(s(z)))) | (~b(s(s(z)), s(s(elem!1))))),
% 1.72/1.98 inference(modus_ponens,[status(thm)],[2065, 2064])).
% 1.72/1.98 tff(2067,plain,
% 1.72/1.98 ($false),
% 1.72/1.98 inference(unit_resolution,[status(thm)],[2066, 166, 463, 839, 446, 2060])).
% 1.72/1.98 tff(2068,plain,((~b(s(s(z)), s(s(elem!1)))) | (~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(s(s(elem!1))), s(s(z))))), inference(lemma,lemma(discharge,[]))).
% 1.72/1.98 tff(2069,plain,
% 1.72/1.98 (~b(s(s(z)), s(s(elem!1)))),
% 1.72/1.98 inference(unit_resolution,[status(thm)],[2068, 1976, 2006, 2059])).
% 1.72/1.98 tff(2070,plain,
% 1.72/1.98 (~b(z, s(s(s(elem!1))))),
% 1.72/1.98 inference(unit_resolution,[status(thm)],[1984, 463, 53, 96, 592])).
% 1.72/1.98 tff(2071,plain,
% 1.72/1.98 (r(z, s(s(s(elem!1))))),
% 1.72/1.98 inference(unit_resolution,[status(thm)],[261, 2070])).
% 1.72/1.98 tff(2072,assumption,(~b(s(s(z)), s(s(elem!1)))), introduced(assumption)).
% 1.72/1.98 tff(2073,plain,
% 1.72/1.98 (r(s(s(z)), s(s(elem!1)))),
% 1.72/1.98 inference(unit_resolution,[status(thm)],[390, 52, 2072])).
% 1.72/1.98 tff(2074,plain,
% 1.72/1.98 (~r(s(s(elem!1)), s(s(s(s(elem!1)))))),
% 1.72/1.98 inference(unit_resolution,[status(thm)],[569, 2073, 155, 365])).
% 1.72/1.98 tff(2075,plain,
% 1.72/1.98 (~r(s(s(s(elem!1))), s(s(z)))),
% 1.72/1.98 inference(unit_resolution,[status(thm)],[2057, 2071, 323, 119])).
% 1.72/1.98 tff(2076,assumption,(~b(s(s(elem!1)), s(s(z)))), introduced(assumption)).
% 1.72/1.98 tff(2077,plain,
% 1.72/1.98 (r(s(s(elem!1)), s(s(z)))),
% 1.72/1.98 inference(unit_resolution,[status(thm)],[441, 132, 2076])).
% 1.72/1.98 tff(2078,plain,
% 1.72/1.98 ($false),
% 1.72/1.98 inference(unit_resolution,[status(thm)],[517, 2077, 2073, 155, 365])).
% 1.72/1.98 tff(2079,plain,((s(s(z)) = s(s(elem!1))) | (~r(z, s(s(z)))) | (~r(z, s(s(elem!1)))) | b(s(s(elem!1)), s(s(z))) | b(s(s(z)), s(s(elem!1)))), inference(lemma,lemma(discharge,[]))).
% 1.72/1.98 tff(2080,plain,
% 1.72/1.98 (b(s(s(elem!1)), s(s(z)))),
% 1.72/1.98 inference(unit_resolution,[status(thm)],[2079, 52, 365, 155, 2072])).
% 1.72/1.98 tff(2081,plain,
% 1.72/1.98 (b(s(s(s(s(elem!1)))), s(s(s(elem!1)))) <=> b(s(s(s(s(elem!1)))), s(elem!1))),
% 1.72/1.98 inference(monotonicity,[status(thm)],[1167])).
% 1.72/1.98 tff(2082,plain,
% 1.72/1.98 (b(s(s(s(s(elem!1)))), s(elem!1))),
% 1.72/1.98 inference(modus_ponens,[status(thm)],[1627, 2081])).
% 1.72/1.98 tff(2083,plain,
% 1.72/1.98 (b(s(s(elem!1)), z) <=> b(s(s(s(s(elem!1)))), z)),
% 1.72/1.98 inference(monotonicity,[status(thm)],[1153])).
% 1.72/1.98 tff(2084,plain,
% 1.72/1.98 (b(s(s(s(s(elem!1)))), z)),
% 1.72/1.98 inference(modus_ponens,[status(thm)],[592, 2083])).
% 1.72/1.98 tff(2085,plain,
% 1.72/1.98 (r(s(z), s(s(s(elem!1)))) <=> r(s(z), s(elem!1))),
% 1.72/1.98 inference(monotonicity,[status(thm)],[1167])).
% 1.72/1.98 tff(2086,plain,
% 1.72/1.98 (r(s(z), s(elem!1))),
% 1.72/1.98 inference(modus_ponens,[status(thm)],[119, 2085])).
% 1.72/1.98 tff(2087,assumption,(r(s(z), s(elem!1))), introduced(assumption)).
% 1.72/1.98 tff(2088,plain,
% 1.72/1.98 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(z))) | (~r(s(s(z)), s(z))) | (~r(s(z), s(elem!1))) | (~r(z, s(s(z)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, s(z))) | (~r(s(s(z)), s(z))) | (~r(s(z), s(elem!1))) | (~r(z, s(s(z)))))),
% 1.72/1.98 inference(rewrite,[status(thm)],[])).
% 1.72/1.98 tff(2089,plain,
% 1.72/1.98 (((~r(s(z), s(elem!1))) | (~r(s(s(z)), s(z))) | (~r(z, s(z))) | (~r(z, s(s(z))))) <=> ((~r(z, s(z))) | (~r(s(s(z)), s(z))) | (~r(s(z), s(elem!1))) | (~r(z, s(s(z)))))),
% 1.72/1.98 inference(rewrite,[status(thm)],[])).
% 1.72/1.98 tff(2090,plain,
% 1.72/1.98 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(elem!1))) | (~r(s(s(z)), s(z))) | (~r(z, s(z))) | (~r(z, s(s(z)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(z))) | (~r(s(s(z)), s(z))) | (~r(s(z), s(elem!1))) | (~r(z, s(s(z))))))),
% 1.72/1.98 inference(monotonicity,[status(thm)],[2089])).
% 1.72/1.98 tff(2091,plain,
% 1.72/1.98 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(elem!1))) | (~r(s(s(z)), s(z))) | (~r(z, s(z))) | (~r(z, s(s(z)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, s(z))) | (~r(s(s(z)), s(z))) | (~r(s(z), s(elem!1))) | (~r(z, s(s(z)))))),
% 1.72/1.99 inference(transitivity,[status(thm)],[2090, 2088])).
% 1.72/1.99 tff(2092,plain,
% 1.72/1.99 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(elem!1))) | (~r(s(s(z)), s(z))) | (~r(z, s(z))) | (~r(z, s(s(z)))))),
% 1.72/1.99 inference(quant_inst,[status(thm)],[])).
% 1.72/1.99 tff(2093,plain,
% 1.72/1.99 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, s(z))) | (~r(s(s(z)), s(z))) | (~r(s(z), s(elem!1))) | (~r(z, s(s(z))))),
% 1.72/1.99 inference(modus_ponens,[status(thm)],[2092, 2091])).
% 1.72/1.99 tff(2094,plain,
% 1.72/1.99 ($false),
% 1.72/1.99 inference(unit_resolution,[status(thm)],[2093, 197, 155, 323, 392, 2087])).
% 1.72/1.99 tff(2095,plain,((~r(s(s(z)), s(z))) | (~r(z, s(s(z)))) | (~r(z, s(z))) | (~r(s(z), s(elem!1)))), inference(lemma,lemma(discharge,[]))).
% 1.72/1.99 tff(2096,plain,
% 1.72/1.99 (~r(s(s(z)), s(z))),
% 1.72/1.99 inference(unit_resolution,[status(thm)],[2095, 2086, 323, 155])).
% 1.72/1.99 tff(2097,plain,
% 1.72/1.99 (b(s(s(z)), s(z))),
% 1.72/1.99 inference(unit_resolution,[status(thm)],[308, 2096])).
% 1.72/1.99 tff(2098,plain,
% 1.72/1.99 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), z)) | (~b(s(s(s(s(elem!1)))), s(elem!1))) | (~b(s(s(z)), s(z))) | (~b(s(elem!1), s(s(z)))) | (~b(s(s(s(s(elem!1)))), s(s(z)))) | (~b(s(s(s(s(elem!1)))), z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), z)) | (~b(s(s(s(s(elem!1)))), s(elem!1))) | (~b(s(s(z)), s(z))) | (~b(s(elem!1), s(s(z)))) | (~b(s(s(s(s(elem!1)))), s(s(z)))) | (~b(s(s(s(s(elem!1)))), z)))),
% 1.72/1.99 inference(rewrite,[status(thm)],[])).
% 1.72/1.99 tff(2099,plain,
% 1.72/1.99 (((~b(s(z), z)) | (~b(s(s(s(s(elem!1)))), z)) | (~b(s(s(z)), s(z))) | (~b(s(elem!1), s(s(z)))) | (~b(s(s(s(s(elem!1)))), s(s(z)))) | (~b(s(s(s(s(elem!1)))), s(elem!1)))) <=> ((~b(s(z), z)) | (~b(s(s(s(s(elem!1)))), s(elem!1))) | (~b(s(s(z)), s(z))) | (~b(s(elem!1), s(s(z)))) | (~b(s(s(s(s(elem!1)))), s(s(z)))) | (~b(s(s(s(s(elem!1)))), z)))),
% 1.72/1.99 inference(rewrite,[status(thm)],[])).
% 1.72/1.99 tff(2100,plain,
% 1.72/1.99 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), z)) | (~b(s(s(s(s(elem!1)))), z)) | (~b(s(s(z)), s(z))) | (~b(s(elem!1), s(s(z)))) | (~b(s(s(s(s(elem!1)))), s(s(z)))) | (~b(s(s(s(s(elem!1)))), s(elem!1))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), z)) | (~b(s(s(s(s(elem!1)))), s(elem!1))) | (~b(s(s(z)), s(z))) | (~b(s(elem!1), s(s(z)))) | (~b(s(s(s(s(elem!1)))), s(s(z)))) | (~b(s(s(s(s(elem!1)))), z))))),
% 1.72/1.99 inference(monotonicity,[status(thm)],[2099])).
% 1.72/1.99 tff(2101,plain,
% 1.72/1.99 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), z)) | (~b(s(s(s(s(elem!1)))), z)) | (~b(s(s(z)), s(z))) | (~b(s(elem!1), s(s(z)))) | (~b(s(s(s(s(elem!1)))), s(s(z)))) | (~b(s(s(s(s(elem!1)))), s(elem!1))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), z)) | (~b(s(s(s(s(elem!1)))), s(elem!1))) | (~b(s(s(z)), s(z))) | (~b(s(elem!1), s(s(z)))) | (~b(s(s(s(s(elem!1)))), s(s(z)))) | (~b(s(s(s(s(elem!1)))), z)))),
% 1.72/1.99 inference(transitivity,[status(thm)],[2100, 2098])).
% 1.72/1.99 tff(2102,plain,
% 1.72/1.99 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), z)) | (~b(s(s(s(s(elem!1)))), z)) | (~b(s(s(z)), s(z))) | (~b(s(elem!1), s(s(z)))) | (~b(s(s(s(s(elem!1)))), s(s(z)))) | (~b(s(s(s(s(elem!1)))), s(elem!1))))),
% 1.72/1.99 inference(quant_inst,[status(thm)],[])).
% 1.72/1.99 tff(2103,plain,
% 1.72/1.99 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), z)) | (~b(s(s(s(s(elem!1)))), s(elem!1))) | (~b(s(s(z)), s(z))) | (~b(s(elem!1), s(s(z)))) | (~b(s(s(s(s(elem!1)))), s(s(z)))) | (~b(s(s(s(s(elem!1)))), z))),
% 1.72/1.99 inference(modus_ponens,[status(thm)],[2102, 2101])).
% 1.72/1.99 tff(2104,plain,
% 1.72/1.99 ($false),
% 1.72/1.99 inference(unit_resolution,[status(thm)],[2103, 166, 1263, 53, 1261, 2097, 2084, 2082])).
% 1.72/1.99 tff(2105,plain,((~(s(s(elem!1)) = s(s(s(s(elem!1)))))) | (~b(s(z), z)) | (~r(z, s(z))) | (~r(z, s(s(z)))) | (~r(s(z), s(s(s(elem!1))))) | (~b(s(s(elem!1)), z)) | (~b(s(s(elem!1)), s(s(z)))) | (~b(s(s(elem!1)), s(s(s(elem!1))))) | r(s(s(s(elem!1))), s(s(z)))), inference(lemma,lemma(discharge,[]))).
% 1.72/1.99 tff(2106,plain,
% 1.72/1.99 (~(s(s(elem!1)) = s(s(s(s(elem!1)))))),
% 1.72/1.99 inference(unit_resolution,[status(thm)],[2105, 2080, 323, 155, 119, 592, 53, 463, 2075])).
% 1.72/1.99 tff(2107,plain,
% 1.72/1.99 (b(s(s(elem!1)), s(s(s(s(elem!1)))))),
% 1.72/1.99 inference(unit_resolution,[status(thm)],[827, 2106, 2074])).
% 1.72/1.99 tff(2108,plain,
% 1.72/1.99 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(z), z)) | (~b(s(s(s(elem!1))), z)) | (~b(s(s(elem!1)), s(s(s(s(elem!1)))))) | (~b(s(s(s(elem!1))), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(z), z)) | (~b(s(s(s(elem!1))), z)) | (~b(s(s(elem!1)), s(s(s(s(elem!1)))))) | (~b(s(s(s(elem!1))), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), s(z))))),
% 1.72/1.99 inference(rewrite,[status(thm)],[])).
% 1.72/1.99 tff(2109,plain,
% 1.72/1.99 (((~b(s(z), z)) | (~b(s(s(s(elem!1))), z)) | (~b(s(s(s(s(elem!1)))), s(z))) | (~b(s(s(elem!1)), s(s(s(s(elem!1)))))) | (~b(s(s(s(elem!1))), s(s(s(s(elem!1)))))) | (~b(s(s(s(elem!1))), s(s(elem!1))))) <=> ((~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(z), z)) | (~b(s(s(s(elem!1))), z)) | (~b(s(s(elem!1)), s(s(s(s(elem!1)))))) | (~b(s(s(s(elem!1))), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), s(z))))),
% 1.72/1.99 inference(rewrite,[status(thm)],[])).
% 1.72/1.99 tff(2110,plain,
% 1.72/1.99 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), z)) | (~b(s(s(s(elem!1))), z)) | (~b(s(s(s(s(elem!1)))), s(z))) | (~b(s(s(elem!1)), s(s(s(s(elem!1)))))) | (~b(s(s(s(elem!1))), s(s(s(s(elem!1)))))) | (~b(s(s(s(elem!1))), s(s(elem!1)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(z), z)) | (~b(s(s(s(elem!1))), z)) | (~b(s(s(elem!1)), s(s(s(s(elem!1)))))) | (~b(s(s(s(elem!1))), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), s(z)))))),
% 1.72/1.99 inference(monotonicity,[status(thm)],[2109])).
% 1.72/1.99 tff(2111,plain,
% 1.72/1.99 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), z)) | (~b(s(s(s(elem!1))), z)) | (~b(s(s(s(s(elem!1)))), s(z))) | (~b(s(s(elem!1)), s(s(s(s(elem!1)))))) | (~b(s(s(s(elem!1))), s(s(s(s(elem!1)))))) | (~b(s(s(s(elem!1))), s(s(elem!1)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(z), z)) | (~b(s(s(s(elem!1))), z)) | (~b(s(s(elem!1)), s(s(s(s(elem!1)))))) | (~b(s(s(s(elem!1))), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), s(z))))),
% 1.72/1.99 inference(transitivity,[status(thm)],[2110, 2108])).
% 1.72/1.99 tff(2112,plain,
% 1.72/1.99 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), z)) | (~b(s(s(s(elem!1))), z)) | (~b(s(s(s(s(elem!1)))), s(z))) | (~b(s(s(elem!1)), s(s(s(s(elem!1)))))) | (~b(s(s(s(elem!1))), s(s(s(s(elem!1)))))) | (~b(s(s(s(elem!1))), s(s(elem!1)))))),
% 1.72/1.99 inference(quant_inst,[status(thm)],[])).
% 1.72/1.99 tff(2113,plain,
% 1.72/1.99 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(z), z)) | (~b(s(s(s(elem!1))), z)) | (~b(s(s(elem!1)), s(s(s(s(elem!1)))))) | (~b(s(s(s(elem!1))), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), s(z)))),
% 1.72/1.99 inference(modus_ponens,[status(thm)],[2112, 2111])).
% 1.72/1.99 tff(2114,plain,
% 1.72/1.99 (~b(s(s(s(elem!1))), s(s(s(s(elem!1)))))),
% 1.72/1.99 inference(unit_resolution,[status(thm)],[2113, 166, 839, 53, 121, 2107, 1402])).
% 1.72/1.99 tff(2115,plain,
% 1.72/1.99 (r(s(s(s(elem!1))), s(s(s(s(elem!1)))))),
% 1.72/1.99 inference(unit_resolution,[status(thm)],[696, 2114, 361])).
% 1.72/1.99 tff(2116,plain,
% 1.72/1.99 ((~(s(s(elem!1)) = s(s(s(s(elem!1)))))) <=> (~(s(s(s(s(elem!1)))) = s(s(elem!1))))),
% 1.72/1.99 inference(monotonicity,[status(thm)],[124])).
% 1.72/1.99 tff(2117,plain,
% 1.72/1.99 (~(s(s(s(s(elem!1)))) = s(s(elem!1)))),
% 1.72/1.99 inference(modus_ponens,[status(thm)],[2106, 2116])).
% 1.72/1.99 tff(2118,plain,
% 1.72/1.99 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(s(s(elem!1))))) | (~r(s(z), s(s(s(s(elem!1)))))) | (~r(s(s(s(elem!1))), s(s(s(s(elem!1)))))) | (~r(s(s(s(s(elem!1)))), s(s(s(elem!1))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(z), s(s(s(elem!1))))) | (~r(s(z), s(s(s(s(elem!1)))))) | (~r(s(s(s(elem!1))), s(s(s(s(elem!1)))))) | (~r(s(s(s(s(elem!1)))), s(s(s(elem!1))))))),
% 1.72/1.99 inference(rewrite,[status(thm)],[])).
% 1.72/1.99 tff(2119,plain,
% 1.72/1.99 (((~r(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), s(s(s(s(elem!1)))))) | (~r(s(z), s(s(s(s(elem!1)))))) | (~r(s(z), s(s(s(elem!1)))))) <=> ((~r(s(z), s(s(s(elem!1))))) | (~r(s(z), s(s(s(s(elem!1)))))) | (~r(s(s(s(elem!1))), s(s(s(s(elem!1)))))) | (~r(s(s(s(s(elem!1)))), s(s(s(elem!1))))))),
% 1.72/1.99 inference(rewrite,[status(thm)],[])).
% 1.72/1.99 tff(2120,plain,
% 1.72/1.99 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), s(s(s(s(elem!1)))))) | (~r(s(z), s(s(s(s(elem!1)))))) | (~r(s(z), s(s(s(elem!1))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(s(s(elem!1))))) | (~r(s(z), s(s(s(s(elem!1)))))) | (~r(s(s(s(elem!1))), s(s(s(s(elem!1)))))) | (~r(s(s(s(s(elem!1)))), s(s(s(elem!1)))))))),
% 1.72/1.99 inference(monotonicity,[status(thm)],[2119])).
% 1.72/1.99 tff(2121,plain,
% 1.72/1.99 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), s(s(s(s(elem!1)))))) | (~r(s(z), s(s(s(s(elem!1)))))) | (~r(s(z), s(s(s(elem!1))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(z), s(s(s(elem!1))))) | (~r(s(z), s(s(s(s(elem!1)))))) | (~r(s(s(s(elem!1))), s(s(s(s(elem!1)))))) | (~r(s(s(s(s(elem!1)))), s(s(s(elem!1))))))),
% 1.72/1.99 inference(transitivity,[status(thm)],[2120, 2118])).
% 1.72/1.99 tff(2122,plain,
% 1.72/1.99 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), s(s(s(s(elem!1)))))) | (~r(s(z), s(s(s(s(elem!1)))))) | (~r(s(z), s(s(s(elem!1))))))),
% 1.72/1.99 inference(quant_inst,[status(thm)],[])).
% 1.72/1.99 tff(2123,plain,
% 1.72/1.99 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(z), s(s(s(elem!1))))) | (~r(s(z), s(s(s(s(elem!1)))))) | (~r(s(s(s(elem!1))), s(s(s(s(elem!1)))))) | (~r(s(s(s(s(elem!1)))), s(s(s(elem!1)))))),
% 1.72/1.99 inference(modus_ponens,[status(thm)],[2122, 2121])).
% 1.72/1.99 tff(2124,plain,
% 1.72/1.99 ($false),
% 1.72/1.99 inference(unit_resolution,[status(thm)],[2123, 197, 699, 119, 1048, 698])).
% 1.72/1.99 tff(2125,plain,((~r(s(s(s(elem!1))), s(s(s(s(elem!1)))))) | (~r(s(z), s(s(s(s(elem!1)))))) | (~r(s(z), s(s(s(elem!1))))) | (~r(s(s(s(s(elem!1)))), s(s(s(elem!1)))))), inference(lemma,lemma(discharge,[]))).
% 1.72/1.99 tff(2126,plain,
% 1.72/1.99 (~r(s(s(s(s(elem!1)))), s(s(s(elem!1))))),
% 1.72/1.99 inference(unit_resolution,[status(thm)],[2125, 2115, 119, 699])).
% 1.72/1.99 tff(2127,plain,
% 1.72/1.99 (b(s(s(s(s(elem!1)))), s(s(s(elem!1))))),
% 1.72/1.99 inference(unit_resolution,[status(thm)],[1065, 2126, 1038])).
% 1.72/1.99 tff(2128,plain,
% 1.72/1.99 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(s(s(s(elem!1)))), s(s(elem!1)))) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~b(s(s(s(s(elem!1)))), s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(s(s(s(elem!1)))), s(s(elem!1)))) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~b(s(s(s(s(elem!1)))), s(z))))),
% 1.72/1.99 inference(rewrite,[status(thm)],[])).
% 1.72/1.99 tff(2129,plain,
% 1.72/1.99 (((~b(s(s(s(elem!1))), s(z))) | (~b(s(s(s(s(elem!1)))), s(z))) | (~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(s(s(s(elem!1)))), s(s(elem!1)))) | (~b(s(s(s(s(elem!1)))), s(s(s(elem!1)))))) <=> ((~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(s(s(s(elem!1)))), s(s(elem!1)))) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~b(s(s(s(s(elem!1)))), s(z))))),
% 1.72/1.99 inference(rewrite,[status(thm)],[])).
% 1.72/1.99 tff(2130,plain,
% 1.72/1.99 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), s(z))) | (~b(s(s(s(s(elem!1)))), s(z))) | (~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(s(s(s(elem!1)))), s(s(elem!1)))) | (~b(s(s(s(s(elem!1)))), s(s(s(elem!1))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(s(s(s(elem!1)))), s(s(elem!1)))) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~b(s(s(s(s(elem!1)))), s(z)))))),
% 1.72/1.99 inference(monotonicity,[status(thm)],[2129])).
% 1.72/1.99 tff(2131,plain,
% 1.72/1.99 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), s(z))) | (~b(s(s(s(s(elem!1)))), s(z))) | (~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(s(s(s(elem!1)))), s(s(elem!1)))) | (~b(s(s(s(s(elem!1)))), s(s(s(elem!1))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(s(s(s(elem!1)))), s(s(elem!1)))) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~b(s(s(s(s(elem!1)))), s(z))))),
% 1.72/1.99 inference(transitivity,[status(thm)],[2130, 2128])).
% 1.72/1.99 tff(2132,plain,
% 1.72/1.99 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), s(z))) | (~b(s(s(s(s(elem!1)))), s(z))) | (~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(s(s(s(elem!1)))), s(s(elem!1)))) | (~b(s(s(s(s(elem!1)))), s(s(s(elem!1))))))),
% 1.72/1.99 inference(quant_inst,[status(thm)],[])).
% 1.72/1.99 tff(2133,plain,
% 1.72/1.99 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(s(s(s(elem!1)))), s(s(elem!1)))) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~b(s(s(s(s(elem!1)))), s(z)))),
% 1.72/1.99 inference(modus_ponens,[status(thm)],[2132, 2131])).
% 1.72/1.99 tff(2134,plain,
% 1.72/1.99 ((~b(s(s(s(s(elem!1)))), s(s(elem!1)))) | (~b(s(s(s(s(elem!1)))), s(s(s(elem!1)))))),
% 1.72/1.99 inference(unit_resolution,[status(thm)],[2133, 166, 463, 839, 96, 1402])).
% 1.72/1.99 tff(2135,plain,
% 1.72/1.99 (~b(s(s(s(s(elem!1)))), s(s(elem!1)))),
% 1.72/1.99 inference(unit_resolution,[status(thm)],[2134, 2127])).
% 1.72/1.99 tff(2136,plain,
% 1.72/1.99 (r(s(s(s(s(elem!1)))), s(s(elem!1)))),
% 1.72/1.99 inference(unit_resolution,[status(thm)],[813, 2135, 2117])).
% 1.72/1.99 tff(2137,plain,
% 1.72/1.99 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(s(s(elem!1))))) | (~r(s(z), s(s(s(s(elem!1)))))) | (~r(s(s(s(elem!1))), s(s(s(s(elem!1)))))) | (~r(s(s(s(s(elem!1)))), s(s(elem!1)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(z), s(s(s(elem!1))))) | (~r(s(z), s(s(s(s(elem!1)))))) | (~r(s(s(s(elem!1))), s(s(s(s(elem!1)))))) | (~r(s(s(s(s(elem!1)))), s(s(elem!1)))))),
% 1.72/1.99 inference(rewrite,[status(thm)],[])).
% 1.72/1.99 tff(2138,plain,
% 1.72/1.99 (((~r(s(s(s(s(elem!1)))), s(s(elem!1)))) | (~r(s(s(s(elem!1))), s(s(s(s(elem!1)))))) | (~r(s(z), s(s(s(s(elem!1)))))) | (~r(s(z), s(s(s(elem!1)))))) <=> ((~r(s(z), s(s(s(elem!1))))) | (~r(s(z), s(s(s(s(elem!1)))))) | (~r(s(s(s(elem!1))), s(s(s(s(elem!1)))))) | (~r(s(s(s(s(elem!1)))), s(s(elem!1)))))),
% 1.72/1.99 inference(rewrite,[status(thm)],[])).
% 1.72/1.99 tff(2139,plain,
% 1.72/1.99 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(elem!1)))), s(s(elem!1)))) | (~r(s(s(s(elem!1))), s(s(s(s(elem!1)))))) | (~r(s(z), s(s(s(s(elem!1)))))) | (~r(s(z), s(s(s(elem!1))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(s(s(elem!1))))) | (~r(s(z), s(s(s(s(elem!1)))))) | (~r(s(s(s(elem!1))), s(s(s(s(elem!1)))))) | (~r(s(s(s(s(elem!1)))), s(s(elem!1))))))),
% 1.72/1.99 inference(monotonicity,[status(thm)],[2138])).
% 1.72/1.99 tff(2140,plain,
% 1.72/1.99 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(elem!1)))), s(s(elem!1)))) | (~r(s(s(s(elem!1))), s(s(s(s(elem!1)))))) | (~r(s(z), s(s(s(s(elem!1)))))) | (~r(s(z), s(s(s(elem!1))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(z), s(s(s(elem!1))))) | (~r(s(z), s(s(s(s(elem!1)))))) | (~r(s(s(s(elem!1))), s(s(s(s(elem!1)))))) | (~r(s(s(s(s(elem!1)))), s(s(elem!1)))))),
% 1.72/1.99 inference(transitivity,[status(thm)],[2139, 2137])).
% 1.72/1.99 tff(2141,plain,
% 1.72/1.99 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(elem!1)))), s(s(elem!1)))) | (~r(s(s(s(elem!1))), s(s(s(s(elem!1)))))) | (~r(s(z), s(s(s(s(elem!1)))))) | (~r(s(z), s(s(s(elem!1))))))),
% 1.72/1.99 inference(quant_inst,[status(thm)],[])).
% 1.72/1.99 tff(2142,plain,
% 1.72/1.99 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(z), s(s(s(elem!1))))) | (~r(s(z), s(s(s(s(elem!1)))))) | (~r(s(s(s(elem!1))), s(s(s(s(elem!1)))))) | (~r(s(s(s(s(elem!1)))), s(s(elem!1))))),
% 1.72/2.00 inference(modus_ponens,[status(thm)],[2141, 2140])).
% 1.72/2.00 tff(2143,plain,
% 1.72/2.00 ($false),
% 1.72/2.00 inference(unit_resolution,[status(thm)],[2142, 197, 699, 119, 2136, 2115])).
% 1.72/2.00 tff(2144,plain,((s(s(z)) = s(s(elem!1))) | (~r(s(z), s(s(s(s(elem!1)))))) | (~r(s(z), s(s(s(elem!1))))) | (~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(s(s(s(elem!1)))), s(z))) | (s(s(s(elem!1))) = s(s(s(s(elem!1))))) | (~b(s(z), z)) | (~b(s(s(s(elem!1))), z)) | (~r(z, s(z))) | (~r(z, s(s(z)))) | (~b(s(s(elem!1)), z)) | (~r(z, s(s(elem!1)))) | b(s(s(z)), s(s(elem!1)))), inference(lemma,lemma(discharge,[]))).
% 1.72/2.00 tff(2145,plain,
% 1.72/2.00 (~b(s(s(s(elem!1))), z)),
% 1.72/2.00 inference(unit_resolution,[status(thm)],[2144, 2072, 119, 463, 839, 96, 1402, 361, 53, 52, 323, 155, 592, 365, 699])).
% 1.72/2.00 tff(2146,plain,
% 1.72/2.00 (r(s(s(s(elem!1))), z)),
% 1.72/2.00 inference(unit_resolution,[status(thm)],[94, 2145])).
% 1.72/2.00 tff(2147,plain,
% 1.72/2.00 (b(s(s(elem!1)), s(s(z)))),
% 1.72/2.00 inference(unit_resolution,[status(thm)],[2079, 2072, 365, 155, 52])).
% 1.72/2.00 tff(2148,plain,
% 1.72/2.00 (r(s(s(z)), s(s(s(elem!1))))),
% 1.72/2.00 inference(unit_resolution,[status(thm)],[501, 2147, 463, 2075])).
% 1.72/2.00 tff(2149,plain,
% 1.72/2.00 ($false),
% 1.72/2.00 inference(unit_resolution,[status(thm)],[290, 2148, 2146, 155, 2071])).
% 1.72/2.00 tff(2150,plain,(b(s(s(z)), s(s(elem!1))) | (~r(z, s(s(z)))) | (~b(s(s(elem!1)), s(s(s(elem!1))))) | (~r(z, s(s(elem!1)))) | (s(s(z)) = s(s(elem!1))) | (~r(s(z), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(s(s(s(elem!1)))), s(z))) | (s(s(s(elem!1))) = s(s(s(s(elem!1))))) | (~b(s(z), z)) | (~r(z, s(z))) | (~b(s(s(elem!1)), z)) | (~r(s(z), s(s(s(s(elem!1))))))), inference(lemma,lemma(discharge,[]))).
% 1.72/2.00 tff(2151,plain,
% 1.72/2.00 (s(s(z)) = s(s(elem!1))),
% 1.72/2.00 inference(unit_resolution,[status(thm)],[2150, 2069, 1976, 1888, 155, 1996, 2006, 1850, 2049, 358, 53, 323, 1974, 2034])).
% 1.72/2.00 tff(2152,plain,
% 1.72/2.00 (b(s(s(s(z))), s(s(s(s(z))))) <=> b(s(s(s(elem!1))), s(s(s(s(elem!1)))))),
% 1.72/2.00 inference(monotonicity,[status(thm)],[1086, 1087])).
% 1.72/2.00 tff(2153,plain,
% 1.72/2.00 (s(s(elem!1)) = s(s(z))),
% 1.72/2.00 inference(unit_resolution,[status(thm)],[17, 620])).
% 1.72/2.00 tff(2154,plain,
% 1.72/2.00 (b(s(s(s(s(elem!1)))), s(s(z))) <=> b(s(s(s(s(elem!1)))), s(s(elem!1)))),
% 1.72/2.00 inference(monotonicity,[status(thm)],[34])).
% 1.72/2.00 tff(2155,plain,
% 1.72/2.00 (b(s(s(s(s(elem!1)))), s(s(elem!1))) <=> b(s(s(s(s(elem!1)))), s(s(z)))),
% 1.72/2.00 inference(symmetry,[status(thm)],[2154])).
% 1.72/2.00 tff(2156,plain,
% 1.72/2.00 ((~b(s(s(s(s(elem!1)))), s(s(elem!1)))) <=> (~b(s(s(s(s(elem!1)))), s(s(z))))),
% 1.72/2.00 inference(monotonicity,[status(thm)],[2155])).
% 1.72/2.00 tff(2157,plain,
% 1.72/2.00 (b(s(s(s(elem!1))), elem!1)),
% 1.72/2.00 inference(unit_resolution,[status(thm)],[634, 620, 121])).
% 1.72/2.00 tff(2158,plain,
% 1.72/2.00 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(z), elem!1)) | (~b(s(s(elem!1)), s(s(s(s(elem!1)))))) | (~b(s(s(s(elem!1))), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(z), elem!1)) | (~b(s(s(elem!1)), s(s(s(s(elem!1)))))) | (~b(s(s(s(elem!1))), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), s(z))))),
% 1.72/2.00 inference(rewrite,[status(thm)],[])).
% 1.72/2.00 tff(2159,plain,
% 1.72/2.00 (((~b(s(z), elem!1)) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(s(s(s(elem!1)))), s(z))) | (~b(s(s(elem!1)), s(s(s(s(elem!1)))))) | (~b(s(s(s(elem!1))), s(s(s(s(elem!1)))))) | (~b(s(s(s(elem!1))), s(s(elem!1))))) <=> ((~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(z), elem!1)) | (~b(s(s(elem!1)), s(s(s(s(elem!1)))))) | (~b(s(s(s(elem!1))), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), s(z))))),
% 1.72/2.00 inference(rewrite,[status(thm)],[])).
% 1.72/2.00 tff(2160,plain,
% 1.72/2.00 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), elem!1)) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(s(s(s(elem!1)))), s(z))) | (~b(s(s(elem!1)), s(s(s(s(elem!1)))))) | (~b(s(s(s(elem!1))), s(s(s(s(elem!1)))))) | (~b(s(s(s(elem!1))), s(s(elem!1)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(z), elem!1)) | (~b(s(s(elem!1)), s(s(s(s(elem!1)))))) | (~b(s(s(s(elem!1))), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), s(z)))))),
% 1.72/2.00 inference(monotonicity,[status(thm)],[2159])).
% 1.72/2.00 tff(2161,plain,
% 1.72/2.00 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), elem!1)) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(s(s(s(elem!1)))), s(z))) | (~b(s(s(elem!1)), s(s(s(s(elem!1)))))) | (~b(s(s(s(elem!1))), s(s(s(s(elem!1)))))) | (~b(s(s(s(elem!1))), s(s(elem!1)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(z), elem!1)) | (~b(s(s(elem!1)), s(s(s(s(elem!1)))))) | (~b(s(s(s(elem!1))), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), s(z))))),
% 1.72/2.00 inference(transitivity,[status(thm)],[2160, 2158])).
% 1.72/2.00 tff(2162,plain,
% 1.72/2.00 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), elem!1)) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(s(s(s(elem!1)))), s(z))) | (~b(s(s(elem!1)), s(s(s(s(elem!1)))))) | (~b(s(s(s(elem!1))), s(s(s(s(elem!1)))))) | (~b(s(s(s(elem!1))), s(s(elem!1)))))),
% 1.72/2.00 inference(quant_inst,[status(thm)],[])).
% 1.72/2.00 tff(2163,plain,
% 1.72/2.00 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(z), elem!1)) | (~b(s(s(elem!1)), s(s(s(s(elem!1)))))) | (~b(s(s(s(elem!1))), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), s(z)))),
% 1.72/2.00 inference(modus_ponens,[status(thm)],[2162, 2161])).
% 1.72/2.00 tff(2164,plain,
% 1.72/2.00 ($false),
% 1.72/2.00 inference(unit_resolution,[status(thm)],[2163, 166, 839, 642, 1046, 1402, 641, 1311])).
% 1.72/2.00 tff(2165,plain,((~b(s(s(elem!1)), s(s(s(s(elem!1)))))) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(z), elem!1)) | (~b(s(s(s(s(elem!1)))), s(z))) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(s(s(elem!1))), s(s(s(s(elem!1))))))), inference(lemma,lemma(discharge,[]))).
% 1.72/2.00 tff(2166,plain,
% 1.72/2.00 (~b(s(s(elem!1)), s(s(s(s(elem!1)))))),
% 1.72/2.00 inference(unit_resolution,[status(thm)],[2165, 1311, 642, 1402, 641, 839])).
% 1.72/2.00 tff(2167,plain,
% 1.72/2.00 (r(s(s(elem!1)), s(s(s(s(elem!1)))))),
% 1.72/2.00 inference(unit_resolution,[status(thm)],[827, 2166, 816])).
% 1.72/2.00 tff(2168,assumption,(r(s(s(s(s(elem!1)))), s(s(z)))), introduced(assumption)).
% 1.72/2.00 tff(2169,plain,
% 1.72/2.00 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(s(elem!1)))) | (~r(s(z), s(s(s(s(elem!1)))))) | (~r(s(s(elem!1)), s(s(s(s(elem!1)))))) | (~r(s(s(s(s(elem!1)))), s(s(z)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(z), s(s(elem!1)))) | (~r(s(z), s(s(s(s(elem!1)))))) | (~r(s(s(elem!1)), s(s(s(s(elem!1)))))) | (~r(s(s(s(s(elem!1)))), s(s(z)))))),
% 1.72/2.00 inference(rewrite,[status(thm)],[])).
% 1.72/2.00 tff(2170,plain,
% 1.72/2.00 (((~r(s(s(s(s(elem!1)))), s(s(z)))) | (~r(s(s(elem!1)), s(s(s(s(elem!1)))))) | (~r(s(z), s(s(s(s(elem!1)))))) | (~r(s(z), s(s(elem!1))))) <=> ((~r(s(z), s(s(elem!1)))) | (~r(s(z), s(s(s(s(elem!1)))))) | (~r(s(s(elem!1)), s(s(s(s(elem!1)))))) | (~r(s(s(s(s(elem!1)))), s(s(z)))))),
% 1.72/2.00 inference(rewrite,[status(thm)],[])).
% 1.72/2.00 tff(2171,plain,
% 1.72/2.00 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(elem!1)))), s(s(z)))) | (~r(s(s(elem!1)), s(s(s(s(elem!1)))))) | (~r(s(z), s(s(s(s(elem!1)))))) | (~r(s(z), s(s(elem!1)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(s(elem!1)))) | (~r(s(z), s(s(s(s(elem!1)))))) | (~r(s(s(elem!1)), s(s(s(s(elem!1)))))) | (~r(s(s(s(s(elem!1)))), s(s(z))))))),
% 1.72/2.00 inference(monotonicity,[status(thm)],[2170])).
% 1.72/2.00 tff(2172,plain,
% 1.72/2.00 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(elem!1)))), s(s(z)))) | (~r(s(s(elem!1)), s(s(s(s(elem!1)))))) | (~r(s(z), s(s(s(s(elem!1)))))) | (~r(s(z), s(s(elem!1)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(z), s(s(elem!1)))) | (~r(s(z), s(s(s(s(elem!1)))))) | (~r(s(s(elem!1)), s(s(s(s(elem!1)))))) | (~r(s(s(s(s(elem!1)))), s(s(z)))))),
% 1.72/2.00 inference(transitivity,[status(thm)],[2171, 2169])).
% 1.72/2.00 tff(2173,plain,
% 1.72/2.00 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(elem!1)))), s(s(z)))) | (~r(s(s(elem!1)), s(s(s(s(elem!1)))))) | (~r(s(z), s(s(s(s(elem!1)))))) | (~r(s(z), s(s(elem!1)))))),
% 1.72/2.00 inference(quant_inst,[status(thm)],[])).
% 1.72/2.00 tff(2174,plain,
% 1.72/2.00 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(z), s(s(elem!1)))) | (~r(s(z), s(s(s(s(elem!1)))))) | (~r(s(s(elem!1)), s(s(s(s(elem!1)))))) | (~r(s(s(s(s(elem!1)))), s(s(z))))),
% 1.72/2.00 inference(modus_ponens,[status(thm)],[2173, 2172])).
% 1.72/2.00 tff(2175,plain,
% 1.72/2.00 ($false),
% 1.72/2.00 inference(unit_resolution,[status(thm)],[2174, 197, 311, 2168, 561, 699])).
% 1.72/2.00 tff(2176,plain,((~r(s(s(s(s(elem!1)))), s(s(z)))) | (~r(s(z), s(s(elem!1)))) | (~r(s(s(elem!1)), s(s(s(s(elem!1)))))) | (~r(s(z), s(s(s(s(elem!1))))))), inference(lemma,lemma(discharge,[]))).
% 1.72/2.00 tff(2177,plain,
% 1.72/2.00 (~r(s(s(s(s(elem!1)))), s(s(z)))),
% 1.72/2.00 inference(unit_resolution,[status(thm)],[2176, 2167, 311, 699])).
% 1.72/2.00 tff(2178,plain,
% 1.72/2.00 (b(s(s(s(s(elem!1)))), s(s(z)))),
% 1.72/2.00 inference(unit_resolution,[status(thm)],[1299, 2177])).
% 1.72/2.00 tff(2179,plain,
% 1.72/2.00 (b(s(s(s(s(elem!1)))), s(s(elem!1)))),
% 1.72/2.00 inference(modus_ponens,[status(thm)],[2178, 2154])).
% 1.72/2.00 tff(2180,plain,
% 1.72/2.00 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(s(s(s(elem!1)))), s(s(elem!1)))) | (~b(s(s(s(elem!1))), s(s(s(s(elem!1)))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(s(s(s(elem!1)))), s(s(elem!1)))) | (~b(s(s(s(elem!1))), s(s(s(s(elem!1)))))))),
% 1.72/2.00 inference(rewrite,[status(thm)],[])).
% 1.72/2.00 tff(2181,plain,
% 1.72/2.00 (((~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(s(s(s(s(elem!1)))), s(s(elem!1)))) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(s(s(elem!1))), s(s(s(s(elem!1))))))) <=> ((~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(s(s(s(elem!1)))), s(s(elem!1)))) | (~b(s(s(s(elem!1))), s(s(s(s(elem!1)))))))),
% 1.72/2.00 inference(rewrite,[status(thm)],[])).
% 1.72/2.00 tff(2182,plain,
% 1.72/2.00 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(s(s(s(s(elem!1)))), s(s(elem!1)))) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(s(s(elem!1))), s(s(s(s(elem!1)))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(s(s(s(elem!1)))), s(s(elem!1)))) | (~b(s(s(s(elem!1))), s(s(s(s(elem!1))))))))),
% 1.72/2.00 inference(monotonicity,[status(thm)],[2181])).
% 1.72/2.00 tff(2183,plain,
% 1.72/2.00 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(s(s(s(s(elem!1)))), s(s(elem!1)))) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(s(s(elem!1))), s(s(s(s(elem!1)))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(s(s(s(elem!1)))), s(s(elem!1)))) | (~b(s(s(s(elem!1))), s(s(s(s(elem!1)))))))),
% 1.72/2.00 inference(transitivity,[status(thm)],[2182, 2180])).
% 1.72/2.00 tff(2184,plain,
% 1.72/2.00 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(s(s(s(s(elem!1)))), s(s(elem!1)))) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(s(s(elem!1))), s(s(s(s(elem!1)))))))),
% 1.72/2.00 inference(quant_inst,[status(thm)],[])).
% 1.72/2.00 tff(2185,plain,
% 1.72/2.00 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(s(s(s(elem!1)))), s(s(elem!1)))) | (~b(s(s(s(elem!1))), s(s(s(s(elem!1))))))),
% 1.72/2.00 inference(modus_ponens,[status(thm)],[2184, 2183])).
% 1.72/2.00 tff(2186,plain,
% 1.72/2.00 ($false),
% 1.72/2.00 inference(unit_resolution,[status(thm)],[2185, 166, 463, 839, 2179, 1311])).
% 1.72/2.00 tff(2187,plain,((~b(s(s(s(elem!1))), s(s(s(s(elem!1)))))) | (~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~(s(s(z)) = s(s(elem!1)))) | (~r(s(z), s(s(elem!1)))) | (~r(s(z), s(s(s(s(elem!1)))))) | (~b(s(z), elem!1)) | (~b(s(s(s(s(elem!1)))), s(z))) | (~b(s(s(s(elem!1))), elem!1))), inference(lemma,lemma(discharge,[]))).
% 1.72/2.00 tff(2188,plain,
% 1.72/2.00 (~b(s(s(s(elem!1))), s(s(s(s(elem!1)))))),
% 1.72/2.00 inference(unit_resolution,[status(thm)],[2187, 34, 839, 463, 311, 699, 637, 1402, 2157])).
% 1.72/2.00 tff(2189,plain,
% 1.72/2.00 (r(s(s(s(elem!1))), s(s(s(s(elem!1)))))),
% 1.72/2.00 inference(unit_resolution,[status(thm)],[696, 2188, 361])).
% 1.72/2.00 tff(2190,plain,
% 1.72/2.00 (~r(s(s(s(s(elem!1)))), s(s(s(elem!1))))),
% 1.72/2.00 inference(unit_resolution,[status(thm)],[2125, 2189, 119, 699])).
% 1.72/2.00 tff(2191,plain,
% 1.72/2.00 (b(s(s(s(s(elem!1)))), s(s(s(elem!1))))),
% 1.72/2.00 inference(unit_resolution,[status(thm)],[1065, 2190, 1038])).
% 1.72/2.00 tff(2192,plain,
% 1.72/2.00 (~b(s(s(s(s(elem!1)))), s(s(elem!1)))),
% 1.72/2.00 inference(unit_resolution,[status(thm)],[2134, 2191])).
% 1.72/2.00 tff(2193,plain,
% 1.72/2.00 (~b(s(s(s(s(elem!1)))), s(s(z)))),
% 1.72/2.00 inference(modus_ponens,[status(thm)],[2192, 2156])).
% 1.72/2.00 tff(2194,plain,
% 1.72/2.00 (r(s(s(s(s(elem!1)))), s(s(z)))),
% 1.72/2.00 inference(unit_resolution,[status(thm)],[1299, 2193])).
% 1.72/2.00 tff(2195,plain,
% 1.72/2.00 (s(s(s(elem!1))) = s(s(s(z)))),
% 1.72/2.00 inference(monotonicity,[status(thm)],[128])).
% 1.72/2.00 tff(2196,plain,
% 1.72/2.00 (s(s(s(s(elem!1)))) = s(s(s(s(z))))),
% 1.72/2.00 inference(monotonicity,[status(thm)],[2195])).
% 1.72/2.00 tff(2197,plain,
% 1.72/2.00 (s(s(s(s(z)))) = s(s(s(s(elem!1))))),
% 1.72/2.00 inference(symmetry,[status(thm)],[2196])).
% 1.72/2.00 tff(2198,plain,
% 1.72/2.00 (r(s(z), s(s(s(s(z))))) <=> r(s(z), s(s(s(s(elem!1)))))),
% 1.72/2.00 inference(monotonicity,[status(thm)],[2197])).
% 1.72/2.00 tff(2199,plain,
% 1.72/2.00 (r(s(z), s(s(s(s(elem!1))))) <=> r(s(z), s(s(s(s(z)))))),
% 1.72/2.00 inference(symmetry,[status(thm)],[2198])).
% 1.72/2.00 tff(2200,plain,
% 1.72/2.00 (r(s(z), s(s(s(s(z)))))),
% 1.72/2.00 inference(modus_ponens,[status(thm)],[699, 2199])).
% 1.72/2.00 tff(2201,plain,
% 1.72/2.00 (s(s(s(z))) = s(s(s(elem!1)))),
% 1.72/2.00 inference(symmetry,[status(thm)],[2195])).
% 1.72/2.00 tff(2202,plain,
% 1.72/2.00 (r(s(z), s(s(s(z)))) <=> r(s(z), s(s(s(elem!1))))),
% 1.72/2.00 inference(monotonicity,[status(thm)],[2201])).
% 1.72/2.00 tff(2203,plain,
% 1.72/2.00 (r(s(z), s(s(s(elem!1)))) <=> r(s(z), s(s(s(z))))),
% 1.72/2.00 inference(symmetry,[status(thm)],[2202])).
% 1.72/2.00 tff(2204,plain,
% 1.72/2.00 (r(s(z), s(s(s(z))))),
% 1.72/2.00 inference(modus_ponens,[status(thm)],[119, 2203])).
% 1.72/2.00 tff(2205,plain,
% 1.72/2.00 (r(s(s(s(s(z)))), s(s(z))) <=> r(s(s(s(s(elem!1)))), s(s(z)))),
% 1.72/2.00 inference(monotonicity,[status(thm)],[2197])).
% 1.72/2.00 tff(2206,plain,
% 1.72/2.00 (r(s(s(s(s(elem!1)))), s(s(z))) <=> r(s(s(s(s(z)))), s(s(z)))),
% 1.72/2.00 inference(symmetry,[status(thm)],[2205])).
% 1.72/2.00 tff(2207,plain,
% 1.72/2.00 (r(s(s(s(s(z)))), s(s(z)))),
% 1.72/2.00 inference(modus_ponens,[status(thm)],[2168, 2206])).
% 1.72/2.00 tff(2208,assumption,(r(s(s(s(z))), s(s(s(s(z)))))), introduced(assumption)).
% 1.72/2.00 tff(2209,plain,
% 1.72/2.00 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(s(s(z))))) | (~r(s(s(s(s(z)))), s(s(z)))) | (~r(s(s(s(z))), s(s(s(s(z)))))) | (~r(s(z), s(s(s(s(z)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(z), s(s(s(z))))) | (~r(s(s(s(s(z)))), s(s(z)))) | (~r(s(s(s(z))), s(s(s(s(z)))))) | (~r(s(z), s(s(s(s(z)))))))),
% 1.72/2.00 inference(rewrite,[status(thm)],[])).
% 1.72/2.00 tff(2210,plain,
% 1.72/2.00 (((~r(s(s(s(s(z)))), s(s(z)))) | (~r(s(s(s(z))), s(s(s(s(z)))))) | (~r(s(z), s(s(s(s(z)))))) | (~r(s(z), s(s(s(z)))))) <=> ((~r(s(z), s(s(s(z))))) | (~r(s(s(s(s(z)))), s(s(z)))) | (~r(s(s(s(z))), s(s(s(s(z)))))) | (~r(s(z), s(s(s(s(z)))))))),
% 1.72/2.00 inference(rewrite,[status(thm)],[])).
% 1.72/2.00 tff(2211,plain,
% 1.72/2.00 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(z)))), s(s(z)))) | (~r(s(s(s(z))), s(s(s(s(z)))))) | (~r(s(z), s(s(s(s(z)))))) | (~r(s(z), s(s(s(z))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(s(s(z))))) | (~r(s(s(s(s(z)))), s(s(z)))) | (~r(s(s(s(z))), s(s(s(s(z)))))) | (~r(s(z), s(s(s(s(z))))))))),
% 1.72/2.00 inference(monotonicity,[status(thm)],[2210])).
% 1.72/2.00 tff(2212,plain,
% 1.72/2.00 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(z)))), s(s(z)))) | (~r(s(s(s(z))), s(s(s(s(z)))))) | (~r(s(z), s(s(s(s(z)))))) | (~r(s(z), s(s(s(z))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(z), s(s(s(z))))) | (~r(s(s(s(s(z)))), s(s(z)))) | (~r(s(s(s(z))), s(s(s(s(z)))))) | (~r(s(z), s(s(s(s(z)))))))),
% 1.72/2.00 inference(transitivity,[status(thm)],[2211, 2209])).
% 1.72/2.00 tff(2213,plain,
% 1.72/2.00 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(z)))), s(s(z)))) | (~r(s(s(s(z))), s(s(s(s(z)))))) | (~r(s(z), s(s(s(s(z)))))) | (~r(s(z), s(s(s(z))))))),
% 1.72/2.00 inference(quant_inst,[status(thm)],[])).
% 1.72/2.00 tff(2214,plain,
% 1.72/2.00 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(z), s(s(s(z))))) | (~r(s(s(s(s(z)))), s(s(z)))) | (~r(s(s(s(z))), s(s(s(s(z)))))) | (~r(s(z), s(s(s(s(z))))))),
% 1.72/2.00 inference(modus_ponens,[status(thm)],[2213, 2212])).
% 1.72/2.00 tff(2215,plain,
% 1.72/2.00 ((~r(s(z), s(s(s(z))))) | (~r(s(s(s(s(z)))), s(s(z)))) | (~r(s(z), s(s(s(s(z))))))),
% 1.72/2.00 inference(unit_resolution,[status(thm)],[2214, 197, 2208])).
% 1.72/2.00 tff(2216,plain,
% 1.72/2.00 ($false),
% 1.72/2.00 inference(unit_resolution,[status(thm)],[2215, 2207, 2204, 2200])).
% 1.72/2.00 tff(2217,plain,((~r(s(s(s(s(elem!1)))), s(s(z)))) | (~r(s(s(s(z))), s(s(s(s(z)))))) | (~r(s(z), s(s(s(s(elem!1)))))) | (~(s(s(elem!1)) = s(s(z)))) | (~r(s(z), s(s(s(elem!1)))))), inference(lemma,lemma(discharge,[]))).
% 1.72/2.00 tff(2218,plain,
% 1.72/2.00 (~r(s(s(s(z))), s(s(s(s(z)))))),
% 1.72/2.00 inference(unit_resolution,[status(thm)],[2217, 2194, 699, 2153, 119])).
% 1.72/2.00 tff(2219,assumption,(s(s(s(z))) = s(s(s(s(z))))), introduced(assumption)).
% 1.72/2.00 tff(2220,plain,
% 1.72/2.00 (inj_0(s(s(s(z)))) = inj_0(s(s(s(s(z)))))),
% 1.72/2.00 inference(monotonicity,[status(thm)],[2219])).
% 1.72/2.00 tff(2221,plain,
% 1.72/2.00 (inj_0(s(s(s(s(z))))) = inj_0(s(s(s(z))))),
% 1.72/2.00 inference(symmetry,[status(thm)],[2220])).
% 1.72/2.00 tff(2222,plain,
% 1.72/2.00 ((~![Xk!0: $i] : (inj_0(s(Xk!0)) = Xk!0)) | (inj_0(s(s(s(s(z))))) = s(s(s(z))))),
% 1.72/2.00 inference(quant_inst,[status(thm)],[])).
% 1.72/2.00 tff(2223,plain,
% 1.72/2.00 (inj_0(s(s(s(s(z))))) = s(s(s(z)))),
% 1.72/2.01 inference(unit_resolution,[status(thm)],[2222, 8])).
% 1.72/2.01 tff(2224,plain,
% 1.72/2.01 (s(s(z)) = s(s(s(s(z))))),
% 1.72/2.01 inference(transitivity,[status(thm)],[1666, 2220, 2223, 2219])).
% 1.72/2.01 tff(2225,plain,
% 1.72/2.01 (inj_0(s(s(z))) = inj_0(s(s(s(s(z)))))),
% 1.72/2.01 inference(monotonicity,[status(thm)],[2224])).
% 1.72/2.01 tff(2226,plain,
% 1.72/2.01 (s(z) = s(s(z))),
% 1.72/2.01 inference(transitivity,[status(thm)],[206, 2225, 2221, 134])).
% 1.72/2.01 tff(2227,plain,
% 1.72/2.01 ($false),
% 1.72/2.01 inference(unit_resolution,[status(thm)],[302, 2226])).
% 1.72/2.01 tff(2228,plain,(~(s(s(s(z))) = s(s(s(s(z)))))), inference(lemma,lemma(discharge,[]))).
% 1.72/2.01 tff(2229,plain,
% 1.72/2.01 (((~![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))))))),
% 1.72/2.01 inference(rewrite,[status(thm)],[])).
% 1.72/2.01 tff(2230,plain,
% 1.72/2.01 ((~![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))))))),
% 1.72/2.01 inference(quant_inst,[status(thm)],[])).
% 1.72/2.01 tff(2231,plain,
% 1.72/2.01 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (s(s(s(z))) = s(s(s(s(z))))) | b(s(s(s(z))), s(s(s(s(z))))) | r(s(s(s(z))), s(s(s(s(z)))))),
% 1.72/2.01 inference(modus_ponens,[status(thm)],[2230, 2229])).
% 1.72/2.01 tff(2232,plain,
% 1.72/2.01 ((s(s(s(z))) = s(s(s(s(z))))) | b(s(s(s(z))), s(s(s(s(z))))) | r(s(s(s(z))), s(s(s(s(z)))))),
% 1.72/2.01 inference(unit_resolution,[status(thm)],[2231, 79])).
% 1.72/2.01 tff(2233,plain,
% 1.72/2.01 (b(s(s(s(z))), s(s(s(s(z))))) | r(s(s(s(z))), s(s(s(s(z)))))),
% 1.72/2.01 inference(unit_resolution,[status(thm)],[2232, 2228])).
% 1.72/2.01 tff(2234,plain,
% 1.72/2.01 (b(s(s(s(z))), s(s(s(s(z)))))),
% 1.72/2.01 inference(unit_resolution,[status(thm)],[2233, 2218])).
% 1.72/2.01 tff(2235,plain,
% 1.72/2.01 (b(s(s(s(elem!1))), s(s(s(s(elem!1)))))),
% 1.72/2.01 inference(modus_ponens,[status(thm)],[2234, 2152])).
% 1.72/2.01 tff(2236,plain,
% 1.72/2.01 ($false),
% 1.72/2.01 inference(unit_resolution,[status(thm)],[2188, 2235])).
% 1.72/2.01 tff(2237,plain,((~(s(s(z)) = s(s(elem!1)))) | (~r(s(z), s(s(s(s(elem!1)))))) | (~r(s(z), s(s(s(elem!1))))) | (~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(s(s(s(elem!1)))), s(z))) | (s(s(s(elem!1))) = s(s(s(s(elem!1))))) | (~r(s(z), s(s(elem!1)))) | (~b(s(z), z)) | (~b(s(s(s(elem!1))), z))), inference(lemma,lemma(discharge,[]))).
% 1.72/2.01 tff(2238,plain,
% 1.72/2.01 (~b(s(s(s(elem!1))), z)),
% 1.72/2.01 inference(unit_resolution,[status(thm)],[2237, 2151, 1996, 1976, 2006, 1850, 2049, 358, 1969, 53, 2034])).
% 1.72/2.01 tff(2239,plain,
% 1.72/2.01 (r(s(s(s(elem!1))), z)),
% 1.72/2.01 inference(unit_resolution,[status(thm)],[94, 2238])).
% 1.72/2.01 tff(2240,plain,
% 1.72/2.01 (s(elem!1) = s(z)),
% 1.72/2.01 inference(unit_resolution,[status(thm)],[43, 2151])).
% 1.72/2.01 tff(2241,plain,
% 1.72/2.01 (z = elem!1),
% 1.72/2.01 inference(unit_resolution,[status(thm)],[30, 2240])).
% 1.72/2.01 tff(2242,plain,
% 1.72/2.01 (r(s(s(s(elem!1))), elem!1)),
% 1.72/2.01 inference(unit_resolution,[status(thm)],[966, 2241, 2239])).
% 1.72/2.01 tff(2243,plain,
% 1.72/2.01 (r(z, s(s(s(elem!1)))) <=> r(elem!1, s(s(s(elem!1))))),
% 1.72/2.01 inference(monotonicity,[status(thm)],[2241])).
% 1.72/2.01 tff(2244,plain,
% 1.72/2.01 (r(elem!1, s(s(s(elem!1))))),
% 1.72/2.01 inference(modus_ponens,[status(thm)],[1986, 2243])).
% 1.72/2.01 tff(2245,plain,
% 1.72/2.01 (r(elem!1, s(z))),
% 1.72/2.01 inference(unit_resolution,[status(thm)],[741, 2241, 323])).
% 1.72/2.01 tff(2246,plain,
% 1.72/2.01 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(s(s(elem!1))))) | (~r(s(z), s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), elem!1)) | (~r(elem!1, s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(elem!1, s(s(s(elem!1))))) | (~r(s(z), s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), elem!1)) | (~r(elem!1, s(z))))),
% 1.72/2.01 inference(rewrite,[status(thm)],[])).
% 1.72/2.01 tff(2247,plain,
% 1.72/2.01 (((~r(s(s(s(elem!1))), elem!1)) | (~r(s(z), s(s(s(elem!1))))) | (~r(elem!1, s(s(s(elem!1))))) | (~r(elem!1, s(z)))) <=> ((~r(elem!1, s(s(s(elem!1))))) | (~r(s(z), s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), elem!1)) | (~r(elem!1, s(z))))),
% 1.72/2.01 inference(rewrite,[status(thm)],[])).
% 1.72/2.01 tff(2248,plain,
% 1.72/2.01 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), elem!1)) | (~r(s(z), s(s(s(elem!1))))) | (~r(elem!1, s(s(s(elem!1))))) | (~r(elem!1, s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(s(s(elem!1))))) | (~r(s(z), s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), elem!1)) | (~r(elem!1, s(z)))))),
% 1.72/2.01 inference(monotonicity,[status(thm)],[2247])).
% 1.72/2.01 tff(2249,plain,
% 1.72/2.01 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), elem!1)) | (~r(s(z), s(s(s(elem!1))))) | (~r(elem!1, s(s(s(elem!1))))) | (~r(elem!1, s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(elem!1, s(s(s(elem!1))))) | (~r(s(z), s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), elem!1)) | (~r(elem!1, s(z))))),
% 1.72/2.01 inference(transitivity,[status(thm)],[2248, 2246])).
% 1.72/2.01 tff(2250,plain,
% 1.72/2.01 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), elem!1)) | (~r(s(z), s(s(s(elem!1))))) | (~r(elem!1, s(s(s(elem!1))))) | (~r(elem!1, s(z))))),
% 1.72/2.01 inference(quant_inst,[status(thm)],[])).
% 1.72/2.01 tff(2251,plain,
% 1.72/2.01 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(elem!1, s(s(s(elem!1))))) | (~r(s(z), s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), elem!1)) | (~r(elem!1, s(z)))),
% 1.72/2.01 inference(modus_ponens,[status(thm)],[2250, 2249])).
% 1.72/2.01 tff(2252,plain,
% 1.72/2.01 ($false),
% 1.72/2.01 inference(unit_resolution,[status(thm)],[2251, 197, 2245, 2244, 1996, 2242])).
% 1.72/2.01 tff(2253,plain,((~b(s(z), z)) | (~r(z, s(z))) | (~r(z, s(s(z)))) | (~b(s(s(elem!1)), s(z))) | (s(s(elem!1)) = s(s(s(elem!1))))), inference(lemma,lemma(discharge,[]))).
% 1.72/2.01 tff(2254,plain,
% 1.72/2.01 ($false),
% 1.72/2.01 inference(unit_resolution,[status(thm)],[2253, 349, 339, 155, 310, 323])).
% 1.72/2.01 tff(2255,plain,((~r(s(s(z)), s(s(elem!1)))) | (~r(z, s(s(z)))) | (~b(s(s(elem!1)), s(z))) | (~r(z, s(z))) | (~r(s(z), s(s(z))))), inference(lemma,lemma(discharge,[]))).
% 1.72/2.01 tff(2256,plain,
% 1.72/2.01 (~r(s(s(z)), s(s(elem!1)))),
% 1.72/2.01 inference(unit_resolution,[status(thm)],[2255, 322, 310, 152, 120])).
% 1.72/2.01 tff(2257,plain,
% 1.72/2.01 (b(z, s(s(z))) <=> b(z, s(s(elem!1)))),
% 1.72/2.01 inference(monotonicity,[status(thm)],[34])).
% 1.72/2.01 tff(2258,plain,
% 1.72/2.01 (b(z, s(s(elem!1))) <=> b(z, s(s(z)))),
% 1.72/2.01 inference(symmetry,[status(thm)],[2257])).
% 1.72/2.01 tff(2259,plain,
% 1.72/2.01 (b(z, s(s(z)))),
% 1.72/2.01 inference(modus_ponens,[status(thm)],[1820, 2258])).
% 1.72/2.01 tff(2260,plain,
% 1.72/2.01 ($false),
% 1.72/2.01 inference(unit_resolution,[status(thm)],[125, 2259])).
% 1.72/2.01 tff(2261,plain,((~(s(s(z)) = s(s(elem!1)))) | b(z, s(s(z))) | (~b(z, s(s(elem!1))))), inference(lemma,lemma(discharge,[]))).
% 1.72/2.01 tff(2262,plain,
% 1.72/2.01 (~b(z, s(s(elem!1)))),
% 1.72/2.01 inference(unit_resolution,[status(thm)],[2261, 34, 125])).
% 1.72/2.01 tff(2263,plain,
% 1.72/2.01 (r(z, s(s(elem!1)))),
% 1.72/2.01 inference(unit_resolution,[status(thm)],[1795, 2262])).
% 1.72/2.01 tff(2264,plain,
% 1.72/2.01 (~r(s(s(elem!1)), s(s(s(elem!1))))),
% 1.72/2.01 inference(unit_resolution,[status(thm)],[413, 2263, 311, 322])).
% 1.72/2.01 tff(2265,plain,
% 1.72/2.01 (~b(s(z), z)),
% 1.72/2.01 inference(unit_resolution,[status(thm)],[2253, 45, 155, 310, 322])).
% 1.72/2.01 tff(2266,plain,
% 1.72/2.01 (r(s(z), z)),
% 1.72/2.01 inference(unit_resolution,[status(thm)],[230, 2265])).
% 1.72/2.01 tff(2267,plain,
% 1.72/2.01 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(s(elem!1)))) | (~r(s(s(elem!1)), z)) | (~r(s(z), z)) | (~r(z, s(s(z)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(z), s(s(elem!1)))) | (~r(s(s(elem!1)), z)) | (~r(s(z), z)) | (~r(z, s(s(z)))))),
% 1.72/2.01 inference(rewrite,[status(thm)],[])).
% 1.72/2.01 tff(2268,plain,
% 1.72/2.01 (((~r(z, s(s(z)))) | (~r(s(s(elem!1)), z)) | (~r(s(z), z)) | (~r(s(z), s(s(elem!1))))) <=> ((~r(s(z), s(s(elem!1)))) | (~r(s(s(elem!1)), z)) | (~r(s(z), z)) | (~r(z, s(s(z)))))),
% 1.72/2.01 inference(rewrite,[status(thm)],[])).
% 1.72/2.01 tff(2269,plain,
% 1.72/2.01 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(z)))) | (~r(s(s(elem!1)), z)) | (~r(s(z), z)) | (~r(s(z), s(s(elem!1)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(s(elem!1)))) | (~r(s(s(elem!1)), z)) | (~r(s(z), z)) | (~r(z, s(s(z))))))),
% 1.72/2.01 inference(monotonicity,[status(thm)],[2268])).
% 1.72/2.01 tff(2270,plain,
% 1.72/2.01 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(z)))) | (~r(s(s(elem!1)), z)) | (~r(s(z), z)) | (~r(s(z), s(s(elem!1)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(z), s(s(elem!1)))) | (~r(s(s(elem!1)), z)) | (~r(s(z), z)) | (~r(z, s(s(z)))))),
% 1.72/2.01 inference(transitivity,[status(thm)],[2269, 2267])).
% 1.72/2.01 tff(2271,plain,
% 1.72/2.01 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(z)))) | (~r(s(s(elem!1)), z)) | (~r(s(z), z)) | (~r(s(z), s(s(elem!1)))))),
% 1.72/2.01 inference(quant_inst,[status(thm)],[])).
% 1.72/2.01 tff(2272,plain,
% 1.72/2.01 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(z), s(s(elem!1)))) | (~r(s(s(elem!1)), z)) | (~r(s(z), z)) | (~r(z, s(s(z))))),
% 1.72/2.01 inference(modus_ponens,[status(thm)],[2271, 2270])).
% 1.72/2.01 tff(2273,plain,
% 1.72/2.01 ($false),
% 1.72/2.01 inference(unit_resolution,[status(thm)],[2272, 197, 311, 155, 97, 1970])).
% 1.72/2.01 tff(2274,plain,((~r(s(s(elem!1)), z)) | (~r(s(z), s(s(elem!1)))) | (~r(z, s(s(z)))) | (~r(s(z), z))), inference(lemma,lemma(discharge,[]))).
% 1.72/2.01 tff(2275,plain,
% 1.72/2.01 (~r(s(s(elem!1)), z)),
% 1.72/2.01 inference(unit_resolution,[status(thm)],[2274, 2266, 155, 311])).
% 1.72/2.01 tff(2276,plain,
% 1.72/2.01 (b(s(s(elem!1)), z)),
% 1.72/2.01 inference(unit_resolution,[status(thm)],[608, 2275])).
% 1.72/2.01 tff(2277,plain,
% 1.72/2.01 (~r(s(s(z)), s(s(elem!1)))),
% 1.72/2.01 inference(unit_resolution,[status(thm)],[347, 2266, 155, 120])).
% 1.72/2.01 tff(2278,plain,
% 1.72/2.01 (~r(s(s(s(elem!1))), z)),
% 1.72/2.01 inference(unit_resolution,[status(thm)],[373, 350, 311, 323])).
% 1.72/2.01 tff(2279,plain,
% 1.72/2.01 (b(s(s(s(elem!1))), z)),
% 1.72/2.01 inference(unit_resolution,[status(thm)],[94, 2278])).
% 1.72/2.01 tff(2280,plain,
% 1.72/2.01 (~r(z, s(s(s(elem!1))))),
% 1.72/2.01 inference(unit_resolution,[status(thm)],[1524, 350, 311, 323])).
% 1.72/2.01 tff(2281,plain,
% 1.72/2.01 (b(z, s(s(s(elem!1))))),
% 1.72/2.01 inference(unit_resolution,[status(thm)],[261, 2280])).
% 1.72/2.01 tff(2282,plain,
% 1.72/2.01 ($false),
% 1.72/2.01 inference(unit_resolution,[status(thm)],[600, 2281, 2279, 463, 592])).
% 1.72/2.01 tff(2283,plain,((~r(s(s(s(elem!1))), s(z))) | (~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(s(s(elem!1)), z)) | (~r(s(z), s(s(elem!1)))) | (~r(z, s(z)))), inference(lemma,lemma(discharge,[]))).
% 1.72/2.01 tff(2284,plain,
% 1.72/2.01 (~r(s(s(s(elem!1))), s(z))),
% 1.72/2.01 inference(unit_resolution,[status(thm)],[2283, 1822, 2276, 311, 322])).
% 1.72/2.01 tff(2285,plain,
% 1.72/2.01 (b(s(s(s(elem!1))), s(z))),
% 1.72/2.01 inference(unit_resolution,[status(thm)],[1849, 2284])).
% 1.72/2.01 tff(2286,plain,
% 1.72/2.01 ((elem!1 = s(s(s(s(elem!1))))) <=> (s(s(s(s(elem!1)))) = elem!1)),
% 1.72/2.01 inference(commutativity,[status(thm)],[])).
% 1.72/2.01 tff(2287,plain,
% 1.72/2.01 ((s(s(s(s(elem!1)))) = elem!1) <=> (elem!1 = s(s(s(s(elem!1)))))),
% 1.72/2.01 inference(symmetry,[status(thm)],[2286])).
% 1.72/2.01 tff(2288,assumption,(~r(s(s(z)), s(s(elem!1)))), introduced(assumption)).
% 1.72/2.01 tff(2289,plain,
% 1.72/2.01 (~b(s(z), s(s(s(elem!1))))),
% 1.72/2.01 inference(unit_resolution,[status(thm)],[1994, 1822, 310, 96])).
% 1.72/2.01 tff(2290,plain,
% 1.72/2.01 (r(s(z), s(s(s(elem!1))))),
% 1.72/2.01 inference(unit_resolution,[status(thm)],[116, 2289])).
% 1.72/2.01 tff(2291,plain,
% 1.72/2.01 (~b(s(s(s(elem!1))), s(s(z)))),
% 1.72/2.01 inference(unit_resolution,[status(thm)],[2068, 1822, 446, 1824])).
% 1.72/2.01 tff(2292,plain,
% 1.72/2.01 (r(s(s(s(elem!1))), s(s(z)))),
% 1.72/2.01 inference(unit_resolution,[status(thm)],[218, 2291])).
% 1.72/2.01 tff(2293,plain,
% 1.72/2.01 (~r(z, s(s(s(elem!1))))),
% 1.72/2.01 inference(unit_resolution,[status(thm)],[2057, 2292, 323, 2290])).
% 1.72/2.01 tff(2294,plain,
% 1.72/2.01 (b(z, s(s(s(elem!1))))),
% 1.72/2.01 inference(unit_resolution,[status(thm)],[261, 2293])).
% 1.72/2.01 tff(2295,plain,
% 1.72/2.01 (~b(s(s(s(elem!1))), z)),
% 1.72/2.01 inference(unit_resolution,[status(thm)],[600, 2294, 592, 1822])).
% 1.72/2.01 tff(2296,plain,
% 1.84/2.01 (r(s(s(s(elem!1))), z)),
% 1.84/2.01 inference(unit_resolution,[status(thm)],[94, 2295])).
% 1.84/2.01 tff(2297,plain,
% 1.84/2.01 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), z)) | (~r(s(z), s(s(s(elem!1))))) | (~r(s(z), s(s(z)))) | (~r(s(s(z)), s(s(s(elem!1))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(elem!1))), z)) | (~r(s(z), s(s(s(elem!1))))) | (~r(s(z), s(s(z)))) | (~r(s(s(z)), s(s(s(elem!1))))))),
% 1.84/2.01 inference(rewrite,[status(thm)],[])).
% 1.84/2.01 tff(2298,plain,
% 1.84/2.01 (((~r(s(s(s(elem!1))), z)) | (~r(s(s(z)), s(s(s(elem!1))))) | (~r(s(z), s(s(s(elem!1))))) | (~r(s(z), s(s(z))))) <=> ((~r(s(s(s(elem!1))), z)) | (~r(s(z), s(s(s(elem!1))))) | (~r(s(z), s(s(z)))) | (~r(s(s(z)), s(s(s(elem!1))))))),
% 1.84/2.01 inference(rewrite,[status(thm)],[])).
% 1.84/2.01 tff(2299,plain,
% 1.84/2.01 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), z)) | (~r(s(s(z)), s(s(s(elem!1))))) | (~r(s(z), s(s(s(elem!1))))) | (~r(s(z), s(s(z)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), z)) | (~r(s(z), s(s(s(elem!1))))) | (~r(s(z), s(s(z)))) | (~r(s(s(z)), s(s(s(elem!1)))))))),
% 1.84/2.01 inference(monotonicity,[status(thm)],[2298])).
% 1.84/2.01 tff(2300,plain,
% 1.84/2.01 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), z)) | (~r(s(s(z)), s(s(s(elem!1))))) | (~r(s(z), s(s(s(elem!1))))) | (~r(s(z), s(s(z)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(elem!1))), z)) | (~r(s(z), s(s(s(elem!1))))) | (~r(s(z), s(s(z)))) | (~r(s(s(z)), s(s(s(elem!1))))))),
% 1.84/2.01 inference(transitivity,[status(thm)],[2299, 2297])).
% 1.84/2.01 tff(2301,plain,
% 1.84/2.01 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), z)) | (~r(s(s(z)), s(s(s(elem!1))))) | (~r(s(z), s(s(s(elem!1))))) | (~r(s(z), s(s(z)))))),
% 1.84/2.01 inference(quant_inst,[status(thm)],[])).
% 1.84/2.01 tff(2302,plain,
% 1.84/2.01 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(elem!1))), z)) | (~r(s(z), s(s(s(elem!1))))) | (~r(s(z), s(s(z)))) | (~r(s(s(z)), s(s(s(elem!1)))))),
% 1.84/2.01 inference(modus_ponens,[status(thm)],[2301, 2300])).
% 1.84/2.01 tff(2303,plain,
% 1.84/2.01 ($false),
% 1.84/2.01 inference(unit_resolution,[status(thm)],[2302, 197, 154, 120, 119, 281])).
% 1.84/2.01 tff(2304,plain,((~r(s(s(z)), s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), z)) | (~r(s(z), s(s(z)))) | (~r(s(z), s(s(s(elem!1)))))), inference(lemma,lemma(discharge,[]))).
% 1.84/2.01 tff(2305,plain,
% 1.84/2.01 (~r(s(s(z)), s(s(s(elem!1))))),
% 1.84/2.01 inference(unit_resolution,[status(thm)],[2304, 2296, 120, 2290])).
% 1.84/2.01 tff(2306,plain,
% 1.84/2.01 (b(s(s(z)), s(s(s(elem!1))))),
% 1.84/2.01 inference(unit_resolution,[status(thm)],[279, 2305])).
% 1.84/2.01 tff(2307,plain,
% 1.84/2.01 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~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(s(elem!1))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~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(s(elem!1))))))),
% 1.84/2.01 inference(rewrite,[status(thm)],[])).
% 1.84/2.01 tff(2308,plain,
% 1.84/2.01 (((~b(s(s(elem!1)), s(z))) | (~b(s(s(z)), s(z))) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(s(s(z)), s(s(s(elem!1))))) | (~b(s(s(z)), s(s(elem!1))))) <=> ((~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(s(elem!1)), s(z))) | (~b(s(s(z)), s(s(elem!1)))) | (~b(s(s(z)), s(z))) | (~b(s(s(z)), s(s(s(elem!1))))))),
% 1.84/2.01 inference(rewrite,[status(thm)],[])).
% 1.84/2.01 tff(2309,plain,
% 1.84/2.01 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), s(z))) | (~b(s(s(z)), s(z))) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(s(s(z)), s(s(s(elem!1))))) | (~b(s(s(z)), s(s(elem!1)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~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(s(elem!1)))))))),
% 1.84/2.01 inference(monotonicity,[status(thm)],[2308])).
% 1.84/2.01 tff(2310,plain,
% 1.84/2.01 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), s(z))) | (~b(s(s(z)), s(z))) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(s(s(z)), s(s(s(elem!1))))) | (~b(s(s(z)), s(s(elem!1)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~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(s(elem!1))))))),
% 1.84/2.01 inference(transitivity,[status(thm)],[2309, 2307])).
% 1.84/2.01 tff(2311,plain,
% 1.84/2.01 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), s(z))) | (~b(s(s(z)), s(z))) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(s(s(z)), s(s(s(elem!1))))) | (~b(s(s(z)), s(s(elem!1)))))),
% 1.84/2.01 inference(quant_inst,[status(thm)],[])).
% 1.84/2.01 tff(2312,plain,
% 1.84/2.01 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(s(elem!1)), s(z))) | (~b(s(s(z)), s(s(elem!1)))) | (~b(s(s(z)), s(z))) | (~b(s(s(z)), s(s(s(elem!1)))))),
% 1.84/2.01 inference(modus_ponens,[status(thm)],[2311, 2310])).
% 1.84/2.01 tff(2313,plain,
% 1.84/2.01 ($false),
% 1.84/2.01 inference(unit_resolution,[status(thm)],[2312, 166, 1822, 1824, 310, 446, 156, 2306])).
% 1.84/2.01 tff(2314,plain,((s(s(elem!1)) = s(s(s(elem!1)))) | (~b(s(s(elem!1)), s(z))) | (~b(s(s(z)), s(s(elem!1)))) | (~b(s(s(z)), s(z))) | (~r(s(z), s(s(z)))) | (~b(s(s(elem!1)), z)) | (~r(z, s(z))) | (~b(s(s(s(elem!1))), s(z))) | r(s(s(s(elem!1))), s(s(elem!1))) | r(s(s(elem!1)), s(s(s(elem!1))))), inference(lemma,lemma(discharge,[]))).
% 1.84/2.01 tff(2315,plain,
% 1.84/2.01 (~b(s(s(z)), s(s(elem!1)))),
% 1.84/2.01 inference(unit_resolution,[status(thm)],[2314, 96, 45, 156, 120, 310, 323, 592, 1823, 1821])).
% 1.84/2.01 tff(2316,plain,
% 1.84/2.01 (s(s(z)) = s(s(elem!1))),
% 1.84/2.01 inference(unit_resolution,[status(thm)],[390, 2315, 2288])).
% 1.84/2.01 tff(2317,plain,
% 1.84/2.01 (s(elem!1) = s(z)),
% 1.84/2.01 inference(unit_resolution,[status(thm)],[43, 2316])).
% 1.84/2.01 tff(2318,plain,
% 1.84/2.01 (z = elem!1),
% 1.84/2.01 inference(unit_resolution,[status(thm)],[30, 2317])).
% 1.84/2.01 tff(2319,plain,
% 1.84/2.01 ((s(s(s(s(elem!1)))) = z) <=> (s(s(s(s(elem!1)))) = elem!1)),
% 1.84/2.01 inference(monotonicity,[status(thm)],[2318])).
% 1.84/2.01 tff(2320,plain,
% 1.84/2.01 ((s(s(s(s(elem!1)))) = z) <=> (elem!1 = s(s(s(s(elem!1)))))),
% 1.84/2.01 inference(transitivity,[status(thm)],[2319, 2287])).
% 1.84/2.01 tff(2321,plain,
% 1.84/2.01 ((~(s(s(s(s(elem!1)))) = z)) <=> (~(elem!1 = s(s(s(s(elem!1))))))),
% 1.84/2.01 inference(monotonicity,[status(thm)],[2320])).
% 1.84/2.01 tff(2322,plain,
% 1.84/2.01 (~(elem!1 = s(s(s(s(elem!1)))))),
% 1.84/2.01 inference(modus_ponens,[status(thm)],[626, 2321])).
% 1.84/2.01 tff(2323,plain,
% 1.84/2.01 (b(s(s(elem!1)), z) <=> b(s(s(elem!1)), elem!1)),
% 1.84/2.01 inference(monotonicity,[status(thm)],[2318])).
% 1.84/2.01 tff(2324,plain,
% 1.84/2.01 (b(s(s(elem!1)), elem!1)),
% 1.84/2.01 inference(modus_ponens,[status(thm)],[592, 2323])).
% 1.84/2.01 tff(2325,plain,
% 1.84/2.01 ((s(s(s(s(elem!1)))) = s(s(z))) <=> (s(s(s(s(elem!1)))) = s(s(elem!1)))),
% 1.84/2.01 inference(monotonicity,[status(thm)],[2316])).
% 1.84/2.02 tff(2326,plain,
% 1.84/2.02 ((s(s(s(s(elem!1)))) = s(s(z))) <=> (s(s(elem!1)) = s(s(s(s(elem!1)))))),
% 1.84/2.02 inference(transitivity,[status(thm)],[2325, 123])).
% 1.84/2.02 tff(2327,plain,
% 1.84/2.02 ((~(s(s(s(s(elem!1)))) = s(s(z)))) <=> (~(s(s(elem!1)) = s(s(s(s(elem!1))))))),
% 1.84/2.02 inference(monotonicity,[status(thm)],[2326])).
% 1.84/2.02 tff(2328,plain,
% 1.84/2.02 (~(s(s(elem!1)) = s(s(s(s(elem!1)))))),
% 1.84/2.02 inference(modus_ponens,[status(thm)],[733, 2327])).
% 1.84/2.02 tff(2329,plain,
% 1.84/2.02 (b(s(s(s(elem!1))), s(s(elem!1)))),
% 1.84/2.02 inference(unit_resolution,[status(thm)],[889, 1823, 51])).
% 1.84/2.02 tff(2330,plain,
% 1.84/2.02 (~b(s(z), s(s(s(elem!1))))),
% 1.84/2.02 inference(unit_resolution,[status(thm)],[1994, 96, 310, 1822])).
% 1.84/2.02 tff(2331,plain,
% 1.84/2.02 (r(s(z), s(s(s(elem!1))))),
% 1.84/2.02 inference(unit_resolution,[status(thm)],[116, 2330])).
% 1.84/2.02 tff(2332,plain,
% 1.84/2.02 (~b(z, s(s(s(elem!1))))),
% 1.84/2.02 inference(unit_resolution,[status(thm)],[1832, 839, 463, 1820])).
% 1.84/2.02 tff(2333,plain,
% 1.84/2.02 (r(z, s(s(s(elem!1))))),
% 1.84/2.02 inference(unit_resolution,[status(thm)],[261, 2332])).
% 1.84/2.02 tff(2334,plain,
% 1.84/2.02 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(z, s(s(elem!1)))) | (~b(s(s(s(elem!1))), z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(z, s(s(elem!1)))) | (~b(s(s(s(elem!1))), z)))),
% 1.84/2.02 inference(rewrite,[status(thm)],[])).
% 1.84/2.02 tff(2335,plain,
% 1.84/2.02 (((~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(z, s(s(elem!1)))) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(s(s(elem!1))), z))) <=> ((~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(z, s(s(elem!1)))) | (~b(s(s(s(elem!1))), z)))),
% 1.84/2.02 inference(rewrite,[status(thm)],[])).
% 1.84/2.02 tff(2336,plain,
% 1.84/2.02 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(z, s(s(elem!1)))) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(s(s(elem!1))), z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(z, s(s(elem!1)))) | (~b(s(s(s(elem!1))), z))))),
% 1.84/2.02 inference(monotonicity,[status(thm)],[2335])).
% 1.84/2.02 tff(2337,plain,
% 1.84/2.02 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(z, s(s(elem!1)))) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(s(s(elem!1))), z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(z, s(s(elem!1)))) | (~b(s(s(s(elem!1))), z)))),
% 1.84/2.02 inference(transitivity,[status(thm)],[2336, 2334])).
% 1.84/2.02 tff(2338,plain,
% 1.84/2.02 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(z, s(s(elem!1)))) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(s(s(elem!1))), z)))),
% 1.84/2.02 inference(quant_inst,[status(thm)],[])).
% 1.84/2.02 tff(2339,plain,
% 1.84/2.02 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(z, s(s(elem!1)))) | (~b(s(s(s(elem!1))), z))),
% 1.84/2.02 inference(modus_ponens,[status(thm)],[2338, 2337])).
% 1.84/2.02 tff(2340,plain,
% 1.84/2.02 (~b(s(s(s(elem!1))), z)),
% 1.84/2.02 inference(unit_resolution,[status(thm)],[2339, 166, 463, 839, 1820])).
% 1.84/2.02 tff(2341,plain,
% 1.84/2.02 (r(s(s(s(elem!1))), z)),
% 1.84/2.02 inference(unit_resolution,[status(thm)],[94, 2340])).
% 1.84/2.02 tff(2342,plain,
% 1.84/2.02 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), z)) | (~r(z, s(s(s(elem!1))))) | (~r(s(z), z)) | (~r(s(z), s(s(s(elem!1))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(elem!1))), z)) | (~r(z, s(s(s(elem!1))))) | (~r(s(z), z)) | (~r(s(z), s(s(s(elem!1))))))),
% 1.84/2.02 inference(rewrite,[status(thm)],[])).
% 1.84/2.02 tff(2343,plain,
% 1.84/2.02 (((~r(z, s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), z)) | (~r(s(z), z)) | (~r(s(z), s(s(s(elem!1)))))) <=> ((~r(s(s(s(elem!1))), z)) | (~r(z, s(s(s(elem!1))))) | (~r(s(z), z)) | (~r(s(z), s(s(s(elem!1))))))),
% 1.84/2.02 inference(rewrite,[status(thm)],[])).
% 1.84/2.02 tff(2344,plain,
% 1.84/2.02 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), z)) | (~r(s(z), z)) | (~r(s(z), s(s(s(elem!1))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), z)) | (~r(z, s(s(s(elem!1))))) | (~r(s(z), z)) | (~r(s(z), s(s(s(elem!1)))))))),
% 1.84/2.02 inference(monotonicity,[status(thm)],[2343])).
% 1.84/2.02 tff(2345,plain,
% 1.84/2.02 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), z)) | (~r(s(z), z)) | (~r(s(z), s(s(s(elem!1))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(elem!1))), z)) | (~r(z, s(s(s(elem!1))))) | (~r(s(z), z)) | (~r(s(z), s(s(s(elem!1))))))),
% 1.84/2.02 inference(transitivity,[status(thm)],[2344, 2342])).
% 1.84/2.02 tff(2346,plain,
% 1.84/2.02 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), z)) | (~r(s(z), z)) | (~r(s(z), s(s(s(elem!1))))))),
% 1.84/2.02 inference(quant_inst,[status(thm)],[])).
% 1.84/2.02 tff(2347,plain,
% 1.84/2.02 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(elem!1))), z)) | (~r(z, s(s(s(elem!1))))) | (~r(s(z), z)) | (~r(s(z), s(s(s(elem!1)))))),
% 1.84/2.02 inference(modus_ponens,[status(thm)],[2346, 2345])).
% 1.84/2.02 tff(2348,plain,
% 1.84/2.02 ($false),
% 1.84/2.02 inference(unit_resolution,[status(thm)],[2347, 197, 2341, 97, 119, 2333])).
% 1.84/2.02 tff(2349,plain,((~b(s(s(s(elem!1))), s(s(elem!1)))) | (~r(s(z), z)) | (~r(s(z), s(s(s(elem!1))))) | (~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(z, s(s(elem!1))))), inference(lemma,lemma(discharge,[]))).
% 1.84/2.02 tff(2350,plain,
% 1.84/2.02 (~b(z, s(s(elem!1)))),
% 1.84/2.02 inference(unit_resolution,[status(thm)],[2349, 2331, 1822, 97, 2329])).
% 1.84/2.02 tff(2351,plain,
% 1.84/2.02 (r(z, s(s(elem!1)))),
% 1.84/2.02 inference(unit_resolution,[status(thm)],[1795, 2350])).
% 1.84/2.02 tff(2352,plain,
% 1.84/2.02 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(elem!1)))) | (~r(s(z), z)) | (~r(s(z), s(s(z)))) | (~r(s(s(z)), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, s(s(elem!1)))) | (~r(s(z), z)) | (~r(s(z), s(s(z)))) | (~r(s(s(z)), z)))),
% 1.84/2.02 inference(rewrite,[status(thm)],[])).
% 1.84/2.02 tff(2353,plain,
% 1.84/2.02 (((~r(z, s(s(elem!1)))) | (~r(s(s(z)), z)) | (~r(s(z), z)) | (~r(s(z), s(s(z))))) <=> ((~r(z, s(s(elem!1)))) | (~r(s(z), z)) | (~r(s(z), s(s(z)))) | (~r(s(s(z)), z)))),
% 1.84/2.02 inference(rewrite,[status(thm)],[])).
% 1.84/2.02 tff(2354,plain,
% 1.84/2.02 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(elem!1)))) | (~r(s(s(z)), z)) | (~r(s(z), z)) | (~r(s(z), s(s(z)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(elem!1)))) | (~r(s(z), z)) | (~r(s(z), s(s(z)))) | (~r(s(s(z)), z))))),
% 1.84/2.02 inference(monotonicity,[status(thm)],[2353])).
% 1.84/2.02 tff(2355,plain,
% 1.84/2.02 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(elem!1)))) | (~r(s(s(z)), z)) | (~r(s(z), z)) | (~r(s(z), s(s(z)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, s(s(elem!1)))) | (~r(s(z), z)) | (~r(s(z), s(s(z)))) | (~r(s(s(z)), z)))),
% 1.84/2.02 inference(transitivity,[status(thm)],[2354, 2352])).
% 1.84/2.02 tff(2356,plain,
% 1.84/2.02 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(elem!1)))) | (~r(s(s(z)), z)) | (~r(s(z), z)) | (~r(s(z), s(s(z)))))),
% 1.84/2.02 inference(quant_inst,[status(thm)],[])).
% 1.84/2.02 tff(2357,plain,
% 1.84/2.02 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, s(s(elem!1)))) | (~r(s(z), z)) | (~r(s(z), s(s(z)))) | (~r(s(s(z)), z))),
% 1.84/2.02 inference(modus_ponens,[status(thm)],[2356, 2355])).
% 1.84/2.02 tff(2358,plain,
% 1.84/2.02 ($false),
% 1.84/2.02 inference(unit_resolution,[status(thm)],[2357, 197, 120, 97, 365, 866])).
% 1.84/2.02 tff(2359,plain,((~r(z, s(s(elem!1)))) | (~r(s(z), s(s(z)))) | (~r(s(z), z)) | (~r(s(s(z)), z))), inference(lemma,lemma(discharge,[]))).
% 1.84/2.02 tff(2360,plain,
% 1.84/2.02 (~r(s(s(z)), z)),
% 1.84/2.02 inference(unit_resolution,[status(thm)],[2359, 2351, 97, 120])).
% 1.84/2.02 tff(2361,plain,
% 1.84/2.02 (b(s(s(z)), z)),
% 1.84/2.02 inference(unit_resolution,[status(thm)],[186, 2360])).
% 1.84/2.02 tff(2362,plain,
% 1.84/2.02 (b(s(s(z)), s(s(s(elem!1)))) <=> b(s(s(elem!1)), s(s(s(elem!1))))),
% 1.84/2.02 inference(monotonicity,[status(thm)],[2316])).
% 1.84/2.02 tff(2363,plain,
% 1.84/2.02 (b(s(s(elem!1)), s(s(s(elem!1)))) <=> b(s(s(z)), s(s(s(elem!1))))),
% 1.84/2.02 inference(symmetry,[status(thm)],[2362])).
% 1.84/2.02 tff(2364,plain,
% 1.84/2.02 (b(s(s(z)), s(s(s(elem!1))))),
% 1.84/2.02 inference(modus_ponens,[status(thm)],[1822, 2363])).
% 1.84/2.02 tff(2365,plain,
% 1.84/2.02 ((~(s(s(s(s(elem!1)))) = z)) <=> (~(s(s(s(s(elem!1)))) = elem!1))),
% 1.84/2.02 inference(monotonicity,[status(thm)],[2319])).
% 1.84/2.02 tff(2366,plain,
% 1.84/2.02 (~(s(s(s(s(elem!1)))) = elem!1)),
% 1.84/2.02 inference(modus_ponens,[status(thm)],[626, 2365])).
% 1.84/2.02 tff(2367,plain,
% 1.84/2.02 (r(elem!1, s(z))),
% 1.84/2.02 inference(unit_resolution,[status(thm)],[741, 2318, 323])).
% 1.84/2.02 tff(2368,plain,
% 1.84/2.02 (r(s(z), z) <=> r(s(z), elem!1)),
% 1.84/2.02 inference(monotonicity,[status(thm)],[2318])).
% 1.84/2.02 tff(2369,plain,
% 1.84/2.02 (r(s(z), elem!1)),
% 1.84/2.02 inference(modus_ponens,[status(thm)],[97, 2368])).
% 1.84/2.02 tff(2370,plain,
% 1.84/2.02 (s(s(s(s(elem!1)))) = s(s(s(s(z))))),
% 1.84/2.02 inference(symmetry,[status(thm)],[1087])).
% 1.84/2.02 tff(2371,plain,
% 1.84/2.02 (b(s(s(s(elem!1))), s(s(s(s(elem!1))))) <=> b(s(s(s(elem!1))), s(s(s(s(z)))))),
% 1.84/2.02 inference(monotonicity,[status(thm)],[2370])).
% 1.84/2.02 tff(2372,plain,
% 1.84/2.02 (b(s(s(s(elem!1))), s(s(s(s(z))))) <=> b(s(s(s(elem!1))), s(s(s(s(elem!1)))))),
% 1.84/2.02 inference(symmetry,[status(thm)],[2371])).
% 1.84/2.02 tff(2373,plain,
% 1.84/2.02 (b(s(s(s(z))), s(s(s(s(z))))) <=> b(s(s(s(elem!1))), s(s(s(s(z)))))),
% 1.84/2.02 inference(monotonicity,[status(thm)],[1086])).
% 1.84/2.02 tff(2374,plain,
% 1.84/2.02 (b(s(s(s(z))), s(s(s(s(z))))) <=> b(s(s(s(elem!1))), s(s(s(s(elem!1)))))),
% 1.84/2.02 inference(transitivity,[status(thm)],[2373, 2372])).
% 1.84/2.02 tff(2375,plain,
% 1.84/2.02 ((s(s(s(s(elem!1)))) = z) <=> (elem!1 = s(s(s(s(elem!1)))))),
% 1.84/2.02 inference(transitivity,[status(thm)],[623, 2287])).
% 1.84/2.02 tff(2376,plain,
% 1.84/2.02 ((~(s(s(s(s(elem!1)))) = z)) <=> (~(elem!1 = s(s(s(s(elem!1))))))),
% 1.84/2.02 inference(monotonicity,[status(thm)],[2375])).
% 1.84/2.02 tff(2377,plain,
% 1.84/2.02 (~(elem!1 = s(s(s(s(elem!1)))))),
% 1.84/2.02 inference(modus_ponens,[status(thm)],[626, 2376])).
% 1.84/2.02 tff(2378,plain,
% 1.84/2.02 (b(s(s(z)), s(s(s(elem!1)))) <=> b(s(s(elem!1)), s(s(s(elem!1))))),
% 1.84/2.02 inference(monotonicity,[status(thm)],[34])).
% 1.84/2.02 tff(2379,plain,
% 1.84/2.02 (b(s(s(elem!1)), s(s(s(elem!1)))) <=> b(s(s(z)), s(s(s(elem!1))))),
% 1.84/2.02 inference(symmetry,[status(thm)],[2378])).
% 1.84/2.02 tff(2380,plain,
% 1.84/2.02 (b(s(s(z)), s(s(s(elem!1))))),
% 1.84/2.02 inference(modus_ponens,[status(thm)],[463, 2379])).
% 1.84/2.02 tff(2381,assumption,(r(s(z), elem!1)), introduced(assumption)).
% 1.84/2.02 tff(2382,plain,
% 1.84/2.02 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), elem!1)) | (~r(elem!1, s(z))) | (~r(s(z), s(s(s(s(elem!1)))))) | (~r(s(s(s(s(elem!1)))), elem!1)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(z), elem!1)) | (~r(elem!1, s(z))) | (~r(s(z), s(s(s(s(elem!1)))))) | (~r(s(s(s(s(elem!1)))), elem!1)))),
% 1.84/2.02 inference(rewrite,[status(thm)],[])).
% 1.84/2.02 tff(2383,plain,
% 1.84/2.02 (((~r(elem!1, s(z))) | (~r(s(s(s(s(elem!1)))), elem!1)) | (~r(s(z), elem!1)) | (~r(s(z), s(s(s(s(elem!1))))))) <=> ((~r(s(z), elem!1)) | (~r(elem!1, s(z))) | (~r(s(z), s(s(s(s(elem!1)))))) | (~r(s(s(s(s(elem!1)))), elem!1)))),
% 1.84/2.02 inference(rewrite,[status(thm)],[])).
% 1.84/2.02 tff(2384,plain,
% 1.84/2.02 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(z))) | (~r(s(s(s(s(elem!1)))), elem!1)) | (~r(s(z), elem!1)) | (~r(s(z), s(s(s(s(elem!1)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), elem!1)) | (~r(elem!1, s(z))) | (~r(s(z), s(s(s(s(elem!1)))))) | (~r(s(s(s(s(elem!1)))), elem!1))))),
% 1.84/2.02 inference(monotonicity,[status(thm)],[2383])).
% 1.84/2.02 tff(2385,plain,
% 1.84/2.02 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(z))) | (~r(s(s(s(s(elem!1)))), elem!1)) | (~r(s(z), elem!1)) | (~r(s(z), s(s(s(s(elem!1)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(z), elem!1)) | (~r(elem!1, s(z))) | (~r(s(z), s(s(s(s(elem!1)))))) | (~r(s(s(s(s(elem!1)))), elem!1)))),
% 1.84/2.02 inference(transitivity,[status(thm)],[2384, 2382])).
% 1.84/2.02 tff(2386,plain,
% 1.84/2.02 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(z))) | (~r(s(s(s(s(elem!1)))), elem!1)) | (~r(s(z), elem!1)) | (~r(s(z), s(s(s(s(elem!1)))))))),
% 1.84/2.02 inference(quant_inst,[status(thm)],[])).
% 1.84/2.02 tff(2387,plain,
% 1.84/2.02 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(z), elem!1)) | (~r(elem!1, s(z))) | (~r(s(z), s(s(s(s(elem!1)))))) | (~r(s(s(s(s(elem!1)))), elem!1))),
% 1.84/2.02 inference(modus_ponens,[status(thm)],[2386, 2385])).
% 1.84/2.02 tff(2388,plain,
% 1.84/2.02 ($false),
% 1.84/2.02 inference(unit_resolution,[status(thm)],[2387, 197, 744, 2381, 699, 743])).
% 1.84/2.02 tff(2389,plain,((~r(s(s(s(s(elem!1)))), elem!1)) | (~r(elem!1, s(z))) | (~r(s(z), elem!1)) | (~r(s(z), s(s(s(s(elem!1))))))), inference(lemma,lemma(discharge,[]))).
% 1.84/2.02 tff(2390,plain,
% 1.84/2.02 (~r(s(s(s(s(elem!1)))), elem!1)),
% 1.84/2.02 inference(unit_resolution,[status(thm)],[2389, 699, 2381, 744])).
% 1.84/2.02 tff(2391,plain,
% 1.84/2.02 (b(s(s(s(s(elem!1)))), elem!1)),
% 1.84/2.02 inference(unit_resolution,[status(thm)],[719, 2390, 627])).
% 1.84/2.02 tff(2392,plain,
% 1.84/2.02 (b(z, s(s(s(s(elem!1))))) <=> b(elem!1, s(s(s(s(elem!1)))))),
% 1.84/2.02 inference(monotonicity,[status(thm)],[12])).
% 1.84/2.02 tff(2393,plain,
% 1.84/2.02 ((~b(z, s(s(s(s(elem!1)))))) <=> (~b(elem!1, s(s(s(s(elem!1))))))),
% 1.84/2.02 inference(monotonicity,[status(thm)],[2392])).
% 1.84/2.02 tff(2394,plain,
% 1.84/2.02 (b(s(s(s(s(elem!1)))), z)),
% 1.84/2.02 inference(unit_resolution,[status(thm)],[1443, 640, 12])).
% 1.84/2.02 tff(2395,assumption,(~(s(s(elem!1)) = s(s(s(s(elem!1)))))), introduced(assumption)).
% 1.84/2.02 tff(2396,plain,
% 1.84/2.02 (~b(s(s(elem!1)), s(s(s(s(elem!1)))))),
% 1.84/2.02 inference(unit_resolution,[status(thm)],[1126, 1108, 640, 786])).
% 1.84/2.02 tff(2397,plain,
% 1.84/2.02 (r(s(s(elem!1)), s(s(s(s(elem!1)))))),
% 1.84/2.02 inference(unit_resolution,[status(thm)],[827, 2396, 2395])).
% 1.84/2.02 tff(2398,assumption,(b(z, s(s(s(s(elem!1)))))), introduced(assumption)).
% 1.84/2.02 tff(2399,plain,
% 1.84/2.02 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), z)) | (~b(s(s(s(s(elem!1)))), s(s(z)))) | (~b(z, s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(z)), z)) | (~b(s(s(s(s(elem!1)))), s(s(z)))) | (~b(z, s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), z)))),
% 1.84/2.02 inference(rewrite,[status(thm)],[])).
% 1.84/2.02 tff(2400,plain,
% 1.84/2.02 (((~b(s(s(s(s(elem!1)))), z)) | (~b(s(s(s(s(elem!1)))), z)) | (~b(z, s(s(s(s(elem!1)))))) | (~b(s(s(z)), z)) | (~b(s(s(s(s(elem!1)))), z)) | (~b(s(s(s(s(elem!1)))), s(s(z))))) <=> ((~b(s(s(z)), z)) | (~b(s(s(s(s(elem!1)))), s(s(z)))) | (~b(z, s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), z)))),
% 1.84/2.02 inference(rewrite,[status(thm)],[])).
% 1.84/2.02 tff(2401,plain,
% 1.84/2.02 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(elem!1)))), z)) | (~b(s(s(s(s(elem!1)))), z)) | (~b(z, s(s(s(s(elem!1)))))) | (~b(s(s(z)), z)) | (~b(s(s(s(s(elem!1)))), z)) | (~b(s(s(s(s(elem!1)))), s(s(z)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), z)) | (~b(s(s(s(s(elem!1)))), s(s(z)))) | (~b(z, s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), z))))),
% 1.84/2.02 inference(monotonicity,[status(thm)],[2400])).
% 1.84/2.02 tff(2402,plain,
% 1.84/2.02 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(elem!1)))), z)) | (~b(s(s(s(s(elem!1)))), z)) | (~b(z, s(s(s(s(elem!1)))))) | (~b(s(s(z)), z)) | (~b(s(s(s(s(elem!1)))), z)) | (~b(s(s(s(s(elem!1)))), s(s(z)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(z)), z)) | (~b(s(s(s(s(elem!1)))), s(s(z)))) | (~b(z, s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), z)))),
% 1.84/2.02 inference(transitivity,[status(thm)],[2401, 2399])).
% 1.84/2.02 tff(2403,plain,
% 1.84/2.02 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(elem!1)))), z)) | (~b(s(s(s(s(elem!1)))), z)) | (~b(z, s(s(s(s(elem!1)))))) | (~b(s(s(z)), z)) | (~b(s(s(s(s(elem!1)))), z)) | (~b(s(s(s(s(elem!1)))), s(s(z)))))),
% 1.84/2.02 inference(quant_inst,[status(thm)],[])).
% 1.84/2.02 tff(2404,plain,
% 1.84/2.02 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(z)), z)) | (~b(s(s(s(s(elem!1)))), s(s(z)))) | (~b(z, s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), z))),
% 1.84/2.02 inference(modus_ponens,[status(thm)],[2403, 2402])).
% 1.84/2.02 tff(2405,plain,
% 1.84/2.02 (~b(s(s(s(s(elem!1)))), s(s(z)))),
% 1.84/2.02 inference(unit_resolution,[status(thm)],[2404, 166, 122, 1326, 2398])).
% 1.84/2.02 tff(2406,plain,
% 1.84/2.02 (r(s(s(s(s(elem!1)))), s(s(z)))),
% 1.84/2.02 inference(unit_resolution,[status(thm)],[1299, 2405])).
% 1.84/2.02 tff(2407,plain,
% 1.84/2.02 (~r(s(z), s(s(s(s(elem!1)))))),
% 1.84/2.02 inference(unit_resolution,[status(thm)],[2176, 2406, 311, 561])).
% 1.84/2.02 tff(2408,plain,
% 1.84/2.02 (b(s(z), s(s(s(s(elem!1)))))),
% 1.84/2.02 inference(unit_resolution,[status(thm)],[681, 2407])).
% 1.84/2.02 tff(2409,plain,
% 1.84/2.02 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), s(z))) | (~b(s(s(z)), z)) | (~b(s(s(z)), s(z))) | (~b(s(s(z)), s(s(s(elem!1))))) | (~b(s(z), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(s(z)), z)) | (~b(s(s(z)), s(z))) | (~b(s(s(z)), s(s(s(elem!1))))) | (~b(s(z), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), z)))),
% 1.84/2.02 inference(rewrite,[status(thm)],[])).
% 1.84/2.02 tff(2410,plain,
% 1.84/2.02 (((~b(s(s(s(s(elem!1)))), z)) | (~b(s(s(z)), z)) | (~b(s(z), s(s(s(s(elem!1)))))) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(s(z)), s(z))) | (~b(s(s(z)), s(s(s(elem!1)))))) <=> ((~b(s(s(s(elem!1))), s(z))) | (~b(s(s(z)), z)) | (~b(s(s(z)), s(z))) | (~b(s(s(z)), s(s(s(elem!1))))) | (~b(s(z), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), z)))),
% 1.84/2.02 inference(rewrite,[status(thm)],[])).
% 1.84/2.02 tff(2411,plain,
% 1.84/2.02 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(elem!1)))), z)) | (~b(s(s(z)), z)) | (~b(s(z), s(s(s(s(elem!1)))))) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(s(z)), s(z))) | (~b(s(s(z)), s(s(s(elem!1))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), s(z))) | (~b(s(s(z)), z)) | (~b(s(s(z)), s(z))) | (~b(s(s(z)), s(s(s(elem!1))))) | (~b(s(z), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), z))))),
% 1.84/2.03 inference(monotonicity,[status(thm)],[2410])).
% 1.84/2.03 tff(2412,plain,
% 1.84/2.03 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(elem!1)))), z)) | (~b(s(s(z)), z)) | (~b(s(z), s(s(s(s(elem!1)))))) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(s(z)), s(z))) | (~b(s(s(z)), s(s(s(elem!1))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(s(z)), z)) | (~b(s(s(z)), s(z))) | (~b(s(s(z)), s(s(s(elem!1))))) | (~b(s(z), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), z)))),
% 1.84/2.03 inference(transitivity,[status(thm)],[2411, 2409])).
% 1.84/2.03 tff(2413,plain,
% 1.84/2.03 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(elem!1)))), z)) | (~b(s(s(z)), z)) | (~b(s(z), s(s(s(s(elem!1)))))) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(s(z)), s(z))) | (~b(s(s(z)), s(s(s(elem!1))))))),
% 1.84/2.03 inference(quant_inst,[status(thm)],[])).
% 1.84/2.03 tff(2414,plain,
% 1.84/2.03 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(s(z)), z)) | (~b(s(s(z)), s(z))) | (~b(s(s(z)), s(s(s(elem!1))))) | (~b(s(z), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), z))),
% 1.84/2.03 inference(modus_ponens,[status(thm)],[2413, 2412])).
% 1.84/2.03 tff(2415,plain,
% 1.84/2.03 ($false),
% 1.84/2.03 inference(unit_resolution,[status(thm)],[2414, 166, 96, 156, 2408, 263, 122, 1326])).
% 1.84/2.03 tff(2416,plain,((~b(s(s(z)), z)) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(s(z)), s(z))) | (~b(s(s(z)), s(s(s(elem!1))))) | (~b(s(s(s(s(elem!1)))), z)) | (~r(s(z), s(s(elem!1)))) | (~r(s(s(elem!1)), s(s(s(s(elem!1)))))) | (~b(z, s(s(s(s(elem!1))))))), inference(lemma,lemma(discharge,[]))).
% 1.84/2.03 tff(2417,plain,
% 1.84/2.03 (~b(z, s(s(s(s(elem!1)))))),
% 1.84/2.03 inference(unit_resolution,[status(thm)],[2416, 2397, 156, 2394, 263, 311, 122, 96])).
% 1.84/2.03 tff(2418,plain,
% 1.84/2.03 (~b(elem!1, s(s(s(s(elem!1)))))),
% 1.84/2.03 inference(modus_ponens,[status(thm)],[2417, 2393])).
% 1.84/2.03 tff(2419,plain,
% 1.84/2.03 ($false),
% 1.84/2.03 inference(unit_resolution,[status(thm)],[1108, 2418])).
% 1.84/2.03 tff(2420,plain,((~b(elem!1, s(s(s(s(elem!1)))))) | (~(z = elem!1)) | (~b(s(s(z)), s(z))) | (~b(s(s(z)), s(s(s(elem!1))))) | (~r(s(z), s(s(elem!1)))) | (~b(s(s(z)), z)) | (~b(s(s(s(elem!1))), s(z))) | (s(s(elem!1)) = s(s(s(s(elem!1))))) | (~b(s(s(s(s(elem!1)))), elem!1)) | (~b(s(s(elem!1)), elem!1))), inference(lemma,lemma(discharge,[]))).
% 1.84/2.03 tff(2421,plain,
% 1.84/2.03 (~b(elem!1, s(s(s(s(elem!1)))))),
% 1.84/2.03 inference(unit_resolution,[status(thm)],[2420, 2391, 156, 2380, 311, 122, 96, 816, 620, 786])).
% 1.84/2.03 tff(2422,assumption,(~(elem!1 = s(s(s(s(elem!1)))))), introduced(assumption)).
% 1.84/2.03 tff(2423,plain,
% 1.84/2.03 (((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((elem!1 = s(s(s(s(elem!1))))) | b(elem!1, s(s(s(s(elem!1))))) | r(elem!1, s(s(s(s(elem!1))))))) <=> ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (elem!1 = s(s(s(s(elem!1))))) | b(elem!1, s(s(s(s(elem!1))))) | r(elem!1, s(s(s(s(elem!1))))))),
% 1.84/2.03 inference(rewrite,[status(thm)],[])).
% 1.84/2.03 tff(2424,plain,
% 1.84/2.03 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((elem!1 = s(s(s(s(elem!1))))) | b(elem!1, s(s(s(s(elem!1))))) | r(elem!1, s(s(s(s(elem!1))))))),
% 1.84/2.03 inference(quant_inst,[status(thm)],[])).
% 1.84/2.03 tff(2425,plain,
% 1.84/2.03 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (elem!1 = s(s(s(s(elem!1))))) | b(elem!1, s(s(s(s(elem!1))))) | r(elem!1, s(s(s(s(elem!1)))))),
% 1.84/2.03 inference(modus_ponens,[status(thm)],[2424, 2423])).
% 1.84/2.03 tff(2426,plain,
% 1.84/2.03 ($false),
% 1.84/2.03 inference(unit_resolution,[status(thm)],[2425, 79, 1103, 1091, 2422])).
% 1.84/2.03 tff(2427,plain,(b(elem!1, s(s(s(s(elem!1))))) | r(elem!1, s(s(s(s(elem!1))))) | (elem!1 = s(s(s(s(elem!1)))))), inference(lemma,lemma(discharge,[]))).
% 1.84/2.03 tff(2428,plain,
% 1.84/2.03 (r(elem!1, s(s(s(s(elem!1)))))),
% 1.84/2.03 inference(unit_resolution,[status(thm)],[2427, 2421, 2377])).
% 1.84/2.03 tff(2429,plain,
% 1.84/2.03 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(s(s(s(elem!1)))))) | (~r(elem!1, s(z))) | (~r(s(z), s(s(s(s(elem!1)))))) | (~r(s(s(s(s(elem!1)))), s(s(s(elem!1))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(elem!1, s(s(s(s(elem!1)))))) | (~r(elem!1, s(z))) | (~r(s(z), s(s(s(s(elem!1)))))) | (~r(s(s(s(s(elem!1)))), s(s(s(elem!1))))))),
% 1.84/2.03 inference(rewrite,[status(thm)],[])).
% 1.84/2.03 tff(2430,plain,
% 1.84/2.03 (((~r(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~r(s(z), s(s(s(s(elem!1)))))) | (~r(elem!1, s(s(s(s(elem!1)))))) | (~r(elem!1, s(z)))) <=> ((~r(elem!1, s(s(s(s(elem!1)))))) | (~r(elem!1, s(z))) | (~r(s(z), s(s(s(s(elem!1)))))) | (~r(s(s(s(s(elem!1)))), s(s(s(elem!1))))))),
% 1.84/2.03 inference(rewrite,[status(thm)],[])).
% 1.84/2.03 tff(2431,plain,
% 1.84/2.03 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~r(s(z), s(s(s(s(elem!1)))))) | (~r(elem!1, s(s(s(s(elem!1)))))) | (~r(elem!1, s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(s(s(s(elem!1)))))) | (~r(elem!1, s(z))) | (~r(s(z), s(s(s(s(elem!1)))))) | (~r(s(s(s(s(elem!1)))), s(s(s(elem!1)))))))),
% 1.84/2.03 inference(monotonicity,[status(thm)],[2430])).
% 1.84/2.03 tff(2432,plain,
% 1.84/2.03 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~r(s(z), s(s(s(s(elem!1)))))) | (~r(elem!1, s(s(s(s(elem!1)))))) | (~r(elem!1, s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(elem!1, s(s(s(s(elem!1)))))) | (~r(elem!1, s(z))) | (~r(s(z), s(s(s(s(elem!1)))))) | (~r(s(s(s(s(elem!1)))), s(s(s(elem!1))))))),
% 1.84/2.03 inference(transitivity,[status(thm)],[2431, 2429])).
% 1.84/2.03 tff(2433,plain,
% 1.84/2.03 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~r(s(z), s(s(s(s(elem!1)))))) | (~r(elem!1, s(s(s(s(elem!1)))))) | (~r(elem!1, s(z))))),
% 1.84/2.03 inference(quant_inst,[status(thm)],[])).
% 1.84/2.03 tff(2434,plain,
% 1.84/2.03 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(elem!1, s(s(s(s(elem!1)))))) | (~r(elem!1, s(z))) | (~r(s(z), s(s(s(s(elem!1)))))) | (~r(s(s(s(s(elem!1)))), s(s(s(elem!1)))))),
% 1.84/2.03 inference(modus_ponens,[status(thm)],[2433, 2432])).
% 1.84/2.03 tff(2435,plain,
% 1.84/2.03 ($false),
% 1.84/2.03 inference(unit_resolution,[status(thm)],[2434, 197, 744, 699, 1048, 1047])).
% 1.84/2.03 tff(2436,plain,((~r(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~r(elem!1, s(z))) | (~r(s(z), s(s(s(s(elem!1)))))) | (~r(elem!1, s(s(s(s(elem!1))))))), inference(lemma,lemma(discharge,[]))).
% 1.84/2.03 tff(2437,plain,
% 1.84/2.03 (~r(s(s(s(s(elem!1)))), s(s(s(elem!1))))),
% 1.84/2.03 inference(unit_resolution,[status(thm)],[2436, 699, 744, 2428])).
% 1.84/2.03 tff(2438,plain,
% 1.84/2.03 (b(s(s(s(s(elem!1)))), s(s(s(elem!1))))),
% 1.84/2.03 inference(unit_resolution,[status(thm)],[1065, 2437, 1058])).
% 1.84/2.03 tff(2439,plain,
% 1.84/2.03 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(s(s(elem!1)), elem!1)) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(s(s(s(elem!1)))), s(s(elem!1)))) | (~b(s(s(s(s(elem!1)))), elem!1)) | (~b(s(s(s(s(elem!1)))), s(s(s(elem!1))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(s(s(elem!1)), elem!1)) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(s(s(s(elem!1)))), s(s(elem!1)))) | (~b(s(s(s(s(elem!1)))), elem!1)) | (~b(s(s(s(s(elem!1)))), s(s(s(elem!1))))))),
% 1.84/2.03 inference(rewrite,[status(thm)],[])).
% 1.84/2.03 tff(2440,plain,
% 1.84/2.03 (((~b(s(s(elem!1)), elem!1)) | (~b(s(s(s(s(elem!1)))), elem!1)) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~b(s(s(s(s(elem!1)))), s(s(elem!1))))) <=> ((~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(s(s(elem!1)), elem!1)) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(s(s(s(elem!1)))), s(s(elem!1)))) | (~b(s(s(s(s(elem!1)))), elem!1)) | (~b(s(s(s(s(elem!1)))), s(s(s(elem!1))))))),
% 1.84/2.03 inference(rewrite,[status(thm)],[])).
% 1.84/2.03 tff(2441,plain,
% 1.84/2.03 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), elem!1)) | (~b(s(s(s(s(elem!1)))), elem!1)) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~b(s(s(s(s(elem!1)))), s(s(elem!1)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(s(s(elem!1)), elem!1)) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(s(s(s(elem!1)))), s(s(elem!1)))) | (~b(s(s(s(s(elem!1)))), elem!1)) | (~b(s(s(s(s(elem!1)))), s(s(s(elem!1)))))))),
% 1.84/2.03 inference(monotonicity,[status(thm)],[2440])).
% 1.84/2.03 tff(2442,plain,
% 1.84/2.03 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), elem!1)) | (~b(s(s(s(s(elem!1)))), elem!1)) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~b(s(s(s(s(elem!1)))), s(s(elem!1)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(s(s(elem!1)), elem!1)) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(s(s(s(elem!1)))), s(s(elem!1)))) | (~b(s(s(s(s(elem!1)))), elem!1)) | (~b(s(s(s(s(elem!1)))), s(s(s(elem!1))))))),
% 1.84/2.03 inference(transitivity,[status(thm)],[2441, 2439])).
% 1.84/2.03 tff(2443,plain,
% 1.84/2.03 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), elem!1)) | (~b(s(s(s(s(elem!1)))), elem!1)) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~b(s(s(s(s(elem!1)))), s(s(elem!1)))))),
% 1.84/2.03 inference(quant_inst,[status(thm)],[])).
% 1.84/2.03 tff(2444,plain,
% 1.84/2.03 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(s(s(elem!1)), elem!1)) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(s(s(s(elem!1)))), s(s(elem!1)))) | (~b(s(s(s(s(elem!1)))), elem!1)) | (~b(s(s(s(s(elem!1)))), s(s(s(elem!1)))))),
% 1.84/2.03 inference(modus_ponens,[status(thm)],[2443, 2442])).
% 1.84/2.03 tff(2445,plain,
% 1.84/2.03 ((~b(s(s(s(s(elem!1)))), s(s(elem!1)))) | (~b(s(s(s(s(elem!1)))), s(s(s(elem!1)))))),
% 1.84/2.03 inference(unit_resolution,[status(thm)],[2444, 166, 463, 786, 839, 2391])).
% 1.84/2.03 tff(2446,plain,
% 1.84/2.03 (~b(s(s(s(s(elem!1)))), s(s(elem!1)))),
% 1.84/2.03 inference(unit_resolution,[status(thm)],[2445, 2438])).
% 1.84/2.03 tff(2447,plain,
% 1.84/2.03 (~b(s(s(s(s(elem!1)))), s(s(z)))),
% 1.84/2.03 inference(modus_ponens,[status(thm)],[2446, 2156])).
% 1.84/2.03 tff(2448,plain,
% 1.84/2.03 (r(s(s(s(s(elem!1)))), s(s(z)))),
% 1.84/2.03 inference(unit_resolution,[status(thm)],[1299, 2447])).
% 1.84/2.03 tff(2449,plain,
% 1.84/2.03 (~r(s(s(s(z))), s(s(s(s(z)))))),
% 1.84/2.03 inference(unit_resolution,[status(thm)],[2217, 2448, 699, 2153, 119])).
% 1.84/2.03 tff(2450,plain,
% 1.84/2.03 (b(s(s(s(z))), s(s(s(s(z)))))),
% 1.84/2.03 inference(unit_resolution,[status(thm)],[2233, 2449])).
% 1.84/2.03 tff(2451,plain,
% 1.84/2.03 (b(s(s(s(elem!1))), s(s(s(s(elem!1)))))),
% 1.84/2.03 inference(modus_ponens,[status(thm)],[2450, 2374])).
% 1.84/2.03 tff(2452,plain,
% 1.84/2.03 (~r(s(s(elem!1)), s(s(s(s(elem!1)))))),
% 1.84/2.03 inference(unit_resolution,[status(thm)],[2176, 2448, 311, 699])).
% 1.84/2.03 tff(2453,plain,
% 1.84/2.03 (b(s(s(elem!1)), s(s(s(s(elem!1)))))),
% 1.84/2.03 inference(unit_resolution,[status(thm)],[827, 2452, 816])).
% 1.84/2.03 tff(2454,plain,
% 1.84/2.03 (~b(s(s(s(elem!1))), s(s(s(s(elem!1)))))),
% 1.84/2.03 inference(unit_resolution,[status(thm)],[1313, 2453, 463, 2438])).
% 1.84/2.03 tff(2455,plain,
% 1.84/2.03 ($false),
% 1.84/2.03 inference(unit_resolution,[status(thm)],[2454, 2451])).
% 1.84/2.03 tff(2456,plain,((~r(s(z), s(s(s(s(elem!1)))))) | (~(s(s(z)) = s(s(elem!1)))) | (~b(s(s(elem!1)), s(s(s(elem!1))))) | (~r(s(z), s(s(s(elem!1))))) | (~r(s(z), s(s(elem!1)))) | (~b(s(s(elem!1)), elem!1)) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (s(s(s(s(elem!1)))) = s(s(s(elem!1)))) | (~r(elem!1, s(z))) | (~b(s(s(z)), s(z))) | (~b(s(s(z)), z)) | (~b(s(s(s(elem!1))), s(z))) | (~r(s(z), elem!1))), inference(lemma,lemma(discharge,[]))).
% 1.84/2.03 tff(2457,plain,
% 1.84/2.03 (~r(s(z), s(s(s(s(elem!1)))))),
% 1.84/2.03 inference(unit_resolution,[status(thm)],[2456, 2316, 1822, 2331, 311, 2324, 2329, 364, 2367, 156, 2361, 96, 2369])).
% 1.84/2.03 tff(2458,plain,
% 1.84/2.03 (b(s(z), s(s(s(s(elem!1)))))),
% 1.84/2.03 inference(unit_resolution,[status(thm)],[681, 2457])).
% 1.84/2.03 tff(2459,plain,
% 1.84/2.03 (~b(s(s(s(s(elem!1)))), s(z))),
% 1.84/2.03 inference(unit_resolution,[status(thm)],[2014, 2458, 96, 310, 2329])).
% 1.84/2.03 tff(2460,plain,
% 1.84/2.03 (r(s(s(s(s(elem!1)))), s(z))),
% 1.84/2.03 inference(unit_resolution,[status(thm)],[661, 2459])).
% 1.84/2.03 tff(2461,plain,
% 1.84/2.03 (~r(s(s(s(s(elem!1)))), elem!1)),
% 1.84/2.03 inference(unit_resolution,[status(thm)],[749, 2460, 2331, 2367])).
% 1.84/2.03 tff(2462,plain,
% 1.84/2.03 (b(s(s(s(s(elem!1)))), elem!1)),
% 1.84/2.03 inference(unit_resolution,[status(thm)],[719, 2461, 2366])).
% 1.84/2.03 tff(2463,plain,
% 1.84/2.03 (~b(elem!1, s(s(s(s(elem!1)))))),
% 1.84/2.03 inference(unit_resolution,[status(thm)],[2420, 2462, 156, 2364, 311, 2361, 96, 2328, 2318, 2324])).
% 1.84/2.03 tff(2464,plain,
% 1.84/2.03 (r(elem!1, s(s(s(s(elem!1)))))),
% 1.84/2.03 inference(unit_resolution,[status(thm)],[2427, 2463, 2322])).
% 1.84/2.03 tff(2465,plain,
% 1.84/2.03 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(s(s(s(elem!1)))))) | (~r(s(z), s(s(elem!1)))) | (~r(elem!1, s(z))) | (~r(s(s(s(s(elem!1)))), s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(elem!1, s(s(s(s(elem!1)))))) | (~r(s(z), s(s(elem!1)))) | (~r(elem!1, s(z))) | (~r(s(s(s(s(elem!1)))), s(z))))),
% 1.84/2.03 inference(rewrite,[status(thm)],[])).
% 1.84/2.03 tff(2466,plain,
% 1.84/2.03 (((~r(s(z), s(s(elem!1)))) | (~r(s(s(s(s(elem!1)))), s(z))) | (~r(elem!1, s(z))) | (~r(elem!1, s(s(s(s(elem!1))))))) <=> ((~r(elem!1, s(s(s(s(elem!1)))))) | (~r(s(z), s(s(elem!1)))) | (~r(elem!1, s(z))) | (~r(s(s(s(s(elem!1)))), s(z))))),
% 1.84/2.03 inference(rewrite,[status(thm)],[])).
% 1.84/2.03 tff(2467,plain,
% 1.84/2.03 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(s(elem!1)))) | (~r(s(s(s(s(elem!1)))), s(z))) | (~r(elem!1, s(z))) | (~r(elem!1, s(s(s(s(elem!1)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(s(s(s(elem!1)))))) | (~r(s(z), s(s(elem!1)))) | (~r(elem!1, s(z))) | (~r(s(s(s(s(elem!1)))), s(z)))))),
% 1.84/2.03 inference(monotonicity,[status(thm)],[2466])).
% 1.84/2.03 tff(2468,plain,
% 1.84/2.03 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(s(elem!1)))) | (~r(s(s(s(s(elem!1)))), s(z))) | (~r(elem!1, s(z))) | (~r(elem!1, s(s(s(s(elem!1)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(elem!1, s(s(s(s(elem!1)))))) | (~r(s(z), s(s(elem!1)))) | (~r(elem!1, s(z))) | (~r(s(s(s(s(elem!1)))), s(z))))),
% 1.84/2.03 inference(transitivity,[status(thm)],[2467, 2465])).
% 1.84/2.03 tff(2469,plain,
% 1.84/2.03 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(s(elem!1)))) | (~r(s(s(s(s(elem!1)))), s(z))) | (~r(elem!1, s(z))) | (~r(elem!1, s(s(s(s(elem!1)))))))),
% 1.84/2.03 inference(quant_inst,[status(thm)],[])).
% 1.84/2.03 tff(2470,plain,
% 1.84/2.03 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(elem!1, s(s(s(s(elem!1)))))) | (~r(s(z), s(s(elem!1)))) | (~r(elem!1, s(z))) | (~r(s(s(s(s(elem!1)))), s(z)))),
% 1.84/2.03 inference(modus_ponens,[status(thm)],[2469, 2468])).
% 1.84/2.03 tff(2471,plain,
% 1.84/2.03 ($false),
% 1.84/2.03 inference(unit_resolution,[status(thm)],[2470, 197, 311, 2367, 2460, 2464])).
% 1.84/2.03 tff(2472,plain,((~b(s(s(s(elem!1))), s(z))) | (~r(s(z), s(s(elem!1)))) | (~b(s(s(z)), s(z))) | (~b(s(s(elem!1)), s(z))) | (~b(s(s(elem!1)), z)) | (~r(s(z), z)) | (~r(z, s(z))) | (~r(s(z), s(s(z)))) | r(s(s(z)), s(s(elem!1))) | (s(s(elem!1)) = s(s(s(elem!1)))) | r(s(s(s(elem!1))), s(s(elem!1))) | r(s(s(elem!1)), s(s(s(elem!1))))), inference(lemma,lemma(discharge,[]))).
% 1.84/2.03 tff(2473,plain,
% 1.84/2.03 (r(s(s(s(elem!1))), s(s(elem!1)))),
% 1.84/2.03 inference(unit_resolution,[status(thm)],[2472, 2285, 156, 310, 2276, 2266, 322, 120, 2277, 45, 311, 1821])).
% 1.84/2.03 tff(2474,plain,
% 1.84/2.03 (~b(s(z), s(s(s(elem!1))))),
% 1.84/2.03 inference(unit_resolution,[status(thm)],[1994, 2285, 310, 1822])).
% 1.84/2.03 tff(2475,plain,
% 1.84/2.03 (r(s(z), s(s(s(elem!1))))),
% 1.84/2.03 inference(unit_resolution,[status(thm)],[116, 2474])).
% 1.84/2.03 tff(2476,plain,
% 1.84/2.03 (~r(z, s(s(s(elem!1))))),
% 1.84/2.03 inference(unit_resolution,[status(thm)],[2004, 2475, 322, 2473])).
% 1.84/2.03 tff(2477,plain,
% 1.84/2.03 (b(z, s(s(s(elem!1))))),
% 1.84/2.03 inference(unit_resolution,[status(thm)],[261, 2476])).
% 1.84/2.03 tff(2478,plain,
% 1.84/2.03 (~b(s(s(s(elem!1))), z)),
% 1.84/2.03 inference(unit_resolution,[status(thm)],[600, 2477, 1822, 2276])).
% 1.84/2.03 tff(2479,plain,
% 1.84/2.03 (r(s(s(s(elem!1))), z)),
% 1.84/2.03 inference(unit_resolution,[status(thm)],[94, 2478])).
% 1.84/2.03 tff(2480,assumption,(~(s(z) = s(s(s(elem!1))))), introduced(assumption)).
% 1.84/2.03 tff(2481,assumption,(r(z, elem!1)), introduced(assumption)).
% 1.84/2.03 tff(2482,plain,
% 1.84/2.03 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, elem!1)) | (~r(s(s(s(elem!1))), z)) | (~r(s(z), z)) | (~r(s(z), s(s(s(elem!1))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, elem!1)) | (~r(s(s(s(elem!1))), z)) | (~r(s(z), z)) | (~r(s(z), s(s(s(elem!1))))))),
% 1.84/2.03 inference(rewrite,[status(thm)],[])).
% 1.84/2.03 tff(2483,plain,
% 1.84/2.03 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, elem!1)) | (~r(s(s(s(elem!1))), z)) | (~r(s(z), z)) | (~r(s(z), s(s(s(elem!1))))))),
% 1.84/2.03 inference(quant_inst,[status(thm)],[])).
% 1.84/2.03 tff(2484,plain,
% 1.84/2.03 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, elem!1)) | (~r(s(s(s(elem!1))), z)) | (~r(s(z), z)) | (~r(s(z), s(s(s(elem!1)))))),
% 1.84/2.03 inference(modus_ponens,[status(thm)],[2483, 2482])).
% 1.84/2.03 tff(2485,plain,
% 1.84/2.03 (~r(s(z), s(s(s(elem!1))))),
% 1.84/2.03 inference(unit_resolution,[status(thm)],[2484, 197, 2481, 154, 97])).
% 1.84/2.03 tff(2486,plain,
% 1.84/2.03 ((s(z) = s(s(s(elem!1)))) | r(s(z), s(s(s(elem!1))))),
% 1.84/2.03 inference(unit_resolution,[status(thm)],[115, 79, 98])).
% 1.84/2.03 tff(2487,plain,
% 1.84/2.03 ($false),
% 1.84/2.03 inference(unit_resolution,[status(thm)],[2486, 2485, 2480])).
% 1.84/2.03 tff(2488,plain,((s(z) = s(s(s(elem!1)))) | b(s(z), s(s(s(elem!1)))) | (~r(z, elem!1)) | (~r(s(s(s(elem!1))), z)) | (~r(s(z), z))), inference(lemma,lemma(discharge,[]))).
% 1.84/2.03 tff(2489,plain,
% 1.84/2.03 (b(s(z), s(s(s(elem!1)))) | (~r(z, elem!1)) | (~r(s(s(s(elem!1))), z)) | (~r(s(z), z))),
% 1.84/2.03 inference(unit_resolution,[status(thm)],[2488, 112])).
% 1.84/2.03 tff(2490,plain,
% 1.84/2.03 (~r(z, elem!1)),
% 1.84/2.03 inference(unit_resolution,[status(thm)],[2489, 2479, 2266, 2474])).
% 1.84/2.03 tff(2491,plain,
% 1.84/2.03 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), z)) | (~r(s(z), s(s(z)))) | (~r(s(s(z)), z)) | (~r(z, s(s(z)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(z), z)) | (~r(s(z), s(s(z)))) | (~r(s(s(z)), z)) | (~r(z, s(s(z)))))),
% 1.84/2.03 inference(rewrite,[status(thm)],[])).
% 1.84/2.03 tff(2492,plain,
% 1.84/2.03 (((~r(z, s(s(z)))) | (~r(s(s(z)), z)) | (~r(s(z), z)) | (~r(s(z), s(s(z))))) <=> ((~r(s(z), z)) | (~r(s(z), s(s(z)))) | (~r(s(s(z)), z)) | (~r(z, s(s(z)))))),
% 1.84/2.04 inference(rewrite,[status(thm)],[])).
% 1.84/2.04 tff(2493,plain,
% 1.84/2.04 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(z)))) | (~r(s(s(z)), z)) | (~r(s(z), z)) | (~r(s(z), s(s(z)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), z)) | (~r(s(z), s(s(z)))) | (~r(s(s(z)), z)) | (~r(z, s(s(z))))))),
% 1.84/2.04 inference(monotonicity,[status(thm)],[2492])).
% 1.84/2.04 tff(2494,plain,
% 1.84/2.04 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(z)))) | (~r(s(s(z)), z)) | (~r(s(z), z)) | (~r(s(z), s(s(z)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(z), z)) | (~r(s(z), s(s(z)))) | (~r(s(s(z)), z)) | (~r(z, s(s(z)))))),
% 1.84/2.04 inference(transitivity,[status(thm)],[2493, 2491])).
% 1.84/2.04 tff(2495,plain,
% 1.84/2.04 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(z)))) | (~r(s(s(z)), z)) | (~r(s(z), z)) | (~r(s(z), s(s(z)))))),
% 1.84/2.04 inference(quant_inst,[status(thm)],[])).
% 1.84/2.04 tff(2496,plain,
% 1.84/2.04 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(z), z)) | (~r(s(z), s(s(z)))) | (~r(s(s(z)), z)) | (~r(z, s(s(z))))),
% 1.84/2.04 inference(modus_ponens,[status(thm)],[2495, 2494])).
% 1.84/2.04 tff(2497,plain,
% 1.84/2.04 ($false),
% 1.84/2.04 inference(unit_resolution,[status(thm)],[2496, 197, 120, 155, 97, 866])).
% 1.84/2.04 tff(2498,plain,((~r(s(s(z)), z)) | (~r(s(z), s(s(z)))) | (~r(z, s(s(z)))) | (~r(s(z), z))), inference(lemma,lemma(discharge,[]))).
% 1.84/2.04 tff(2499,plain,
% 1.84/2.04 (~r(s(s(z)), z)),
% 1.84/2.04 inference(unit_resolution,[status(thm)],[2498, 2266, 155, 120])).
% 1.84/2.04 tff(2500,plain,
% 1.84/2.04 (b(s(s(z)), z)),
% 1.84/2.04 inference(unit_resolution,[status(thm)],[186, 2499])).
% 1.84/2.04 tff(2501,plain,
% 1.84/2.04 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), s(s(elem!1)))) | (~r(s(z), s(s(elem!1)))) | (~r(s(s(elem!1)), elem!1)) | (~r(s(z), s(s(s(elem!1))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(elem!1))), s(s(elem!1)))) | (~r(s(z), s(s(elem!1)))) | (~r(s(s(elem!1)), elem!1)) | (~r(s(z), s(s(s(elem!1))))))),
% 1.84/2.04 inference(rewrite,[status(thm)],[])).
% 1.84/2.04 tff(2502,plain,
% 1.84/2.04 (((~r(s(s(elem!1)), elem!1)) | (~r(s(s(s(elem!1))), s(s(elem!1)))) | (~r(s(z), s(s(elem!1)))) | (~r(s(z), s(s(s(elem!1)))))) <=> ((~r(s(s(s(elem!1))), s(s(elem!1)))) | (~r(s(z), s(s(elem!1)))) | (~r(s(s(elem!1)), elem!1)) | (~r(s(z), s(s(s(elem!1))))))),
% 1.84/2.04 inference(rewrite,[status(thm)],[])).
% 1.84/2.04 tff(2503,plain,
% 1.84/2.04 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(elem!1)), elem!1)) | (~r(s(s(s(elem!1))), s(s(elem!1)))) | (~r(s(z), s(s(elem!1)))) | (~r(s(z), s(s(s(elem!1))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), s(s(elem!1)))) | (~r(s(z), s(s(elem!1)))) | (~r(s(s(elem!1)), elem!1)) | (~r(s(z), s(s(s(elem!1)))))))),
% 1.84/2.04 inference(monotonicity,[status(thm)],[2502])).
% 1.84/2.04 tff(2504,plain,
% 1.84/2.04 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(elem!1)), elem!1)) | (~r(s(s(s(elem!1))), s(s(elem!1)))) | (~r(s(z), s(s(elem!1)))) | (~r(s(z), s(s(s(elem!1))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(elem!1))), s(s(elem!1)))) | (~r(s(z), s(s(elem!1)))) | (~r(s(s(elem!1)), elem!1)) | (~r(s(z), s(s(s(elem!1))))))),
% 1.84/2.04 inference(transitivity,[status(thm)],[2503, 2501])).
% 1.84/2.04 tff(2505,plain,
% 1.84/2.04 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(elem!1)), elem!1)) | (~r(s(s(s(elem!1))), s(s(elem!1)))) | (~r(s(z), s(s(elem!1)))) | (~r(s(z), s(s(s(elem!1))))))),
% 1.84/2.04 inference(quant_inst,[status(thm)],[])).
% 1.84/2.04 tff(2506,plain,
% 1.84/2.04 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(elem!1))), s(s(elem!1)))) | (~r(s(z), s(s(elem!1)))) | (~r(s(s(elem!1)), elem!1)) | (~r(s(z), s(s(s(elem!1)))))),
% 1.84/2.04 inference(modus_ponens,[status(thm)],[2505, 2504])).
% 1.84/2.04 tff(2507,plain,
% 1.84/2.04 ($false),
% 1.84/2.04 inference(unit_resolution,[status(thm)],[2506, 197, 311, 768, 905, 119])).
% 1.84/2.04 tff(2508,plain,((~r(s(s(elem!1)), elem!1)) | (~r(s(z), s(s(elem!1)))) | (~r(s(s(s(elem!1))), s(s(elem!1)))) | (~r(s(z), s(s(s(elem!1)))))), inference(lemma,lemma(discharge,[]))).
% 1.84/2.04 tff(2509,plain,
% 1.84/2.04 (~r(s(s(elem!1)), elem!1)),
% 1.84/2.04 inference(unit_resolution,[status(thm)],[2508, 2473, 311, 2475])).
% 1.84/2.04 tff(2510,assumption,(~r(z, elem!1)), introduced(assumption)).
% 1.84/2.04 tff(2511,plain,
% 1.84/2.04 (((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((z = elem!1) | b(z, elem!1) | r(z, elem!1))) <=> ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (z = elem!1) | b(z, elem!1) | r(z, elem!1))),
% 1.84/2.04 inference(rewrite,[status(thm)],[])).
% 1.84/2.04 tff(2512,plain,
% 1.84/2.04 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((z = elem!1) | b(z, elem!1) | r(z, elem!1))),
% 1.84/2.04 inference(quant_inst,[status(thm)],[])).
% 1.84/2.04 tff(2513,plain,
% 1.84/2.04 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (z = elem!1) | b(z, elem!1) | r(z, elem!1)),
% 1.84/2.04 inference(modus_ponens,[status(thm)],[2512, 2511])).
% 1.84/2.04 tff(2514,plain,
% 1.84/2.04 ((z = elem!1) | b(z, elem!1) | r(z, elem!1)),
% 1.84/2.04 inference(unit_resolution,[status(thm)],[2513, 79])).
% 1.84/2.04 tff(2515,plain,
% 1.84/2.04 (b(z, elem!1)),
% 1.84/2.04 inference(unit_resolution,[status(thm)],[2514, 1146, 2510])).
% 1.84/2.04 tff(2516,plain,
% 1.84/2.04 (b(s(s(z)), s(s(elem!1)))),
% 1.84/2.04 inference(unit_resolution,[status(thm)],[390, 52, 2288])).
% 1.84/2.04 tff(2517,assumption,(b(z, elem!1)), introduced(assumption)).
% 1.84/2.04 tff(2518,plain,
% 1.84/2.04 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(z))) | (~b(s(s(elem!1)), z)) | (~b(z, elem!1)) | (~b(s(s(z)), s(s(elem!1)))) | (~b(s(s(z)), z)) | (~b(s(s(z)), s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(z))) | (~b(s(s(elem!1)), z)) | (~b(z, elem!1)) | (~b(s(s(z)), s(s(elem!1)))) | (~b(s(s(z)), z)) | (~b(s(s(z)), s(z))))),
% 1.84/2.04 inference(rewrite,[status(thm)],[])).
% 1.84/2.04 tff(2519,plain,
% 1.84/2.04 (((~b(elem!1, s(z))) | (~b(s(s(z)), s(z))) | (~b(z, elem!1)) | (~b(s(s(elem!1)), z)) | (~b(s(s(z)), z)) | (~b(s(s(z)), s(s(elem!1))))) <=> ((~b(elem!1, s(z))) | (~b(s(s(elem!1)), z)) | (~b(z, elem!1)) | (~b(s(s(z)), s(s(elem!1)))) | (~b(s(s(z)), z)) | (~b(s(s(z)), s(z))))),
% 1.84/2.04 inference(rewrite,[status(thm)],[])).
% 1.84/2.04 tff(2520,plain,
% 1.84/2.04 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(z))) | (~b(s(s(z)), s(z))) | (~b(z, elem!1)) | (~b(s(s(elem!1)), z)) | (~b(s(s(z)), z)) | (~b(s(s(z)), s(s(elem!1)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(z))) | (~b(s(s(elem!1)), z)) | (~b(z, elem!1)) | (~b(s(s(z)), s(s(elem!1)))) | (~b(s(s(z)), z)) | (~b(s(s(z)), s(z)))))),
% 1.84/2.04 inference(monotonicity,[status(thm)],[2519])).
% 1.84/2.04 tff(2521,plain,
% 1.84/2.04 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(z))) | (~b(s(s(z)), s(z))) | (~b(z, elem!1)) | (~b(s(s(elem!1)), z)) | (~b(s(s(z)), z)) | (~b(s(s(z)), s(s(elem!1)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(z))) | (~b(s(s(elem!1)), z)) | (~b(z, elem!1)) | (~b(s(s(z)), s(s(elem!1)))) | (~b(s(s(z)), z)) | (~b(s(s(z)), s(z))))),
% 1.84/2.04 inference(transitivity,[status(thm)],[2520, 2518])).
% 1.84/2.04 tff(2522,plain,
% 1.84/2.04 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(z))) | (~b(s(s(z)), s(z))) | (~b(z, elem!1)) | (~b(s(s(elem!1)), z)) | (~b(s(s(z)), z)) | (~b(s(s(z)), s(s(elem!1)))))),
% 1.84/2.04 inference(quant_inst,[status(thm)],[])).
% 1.84/2.04 tff(2523,plain,
% 1.84/2.04 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(z))) | (~b(s(s(elem!1)), z)) | (~b(z, elem!1)) | (~b(s(s(z)), s(s(elem!1)))) | (~b(s(s(z)), z)) | (~b(s(s(z)), s(z)))),
% 1.84/2.04 inference(modus_ponens,[status(thm)],[2522, 2521])).
% 1.84/2.04 tff(2524,plain,
% 1.84/2.04 ($false),
% 1.84/2.04 inference(unit_resolution,[status(thm)],[2523, 166, 2517, 1212, 592, 446, 156, 122])).
% 1.84/2.04 tff(2525,plain,((~b(elem!1, s(z))) | (~b(z, elem!1)) | (~b(s(s(elem!1)), z)) | (~b(s(s(z)), s(s(elem!1)))) | (~b(s(s(z)), s(z))) | (~b(s(s(z)), z))), inference(lemma,lemma(discharge,[]))).
% 1.84/2.04 tff(2526,plain,
% 1.84/2.04 (~b(elem!1, s(z))),
% 1.84/2.04 inference(unit_resolution,[status(thm)],[2525, 2515, 592, 2516, 156, 122])).
% 1.84/2.04 tff(2527,assumption,(~b(elem!1, s(z))), introduced(assumption)).
% 1.84/2.04 tff(2528,assumption,(elem!1 = s(z)), introduced(assumption)).
% 1.84/2.04 tff(2529,plain,
% 1.84/2.04 (b(z, elem!1) <=> b(z, s(z))),
% 1.84/2.04 inference(monotonicity,[status(thm)],[2528])).
% 1.84/2.04 tff(2530,plain,
% 1.84/2.04 (b(z, s(z)) <=> b(z, elem!1)),
% 1.84/2.04 inference(symmetry,[status(thm)],[2529])).
% 1.84/2.04 tff(2531,plain,
% 1.84/2.04 ((~b(z, s(z))) <=> (~b(z, elem!1))),
% 1.84/2.04 inference(monotonicity,[status(thm)],[2530])).
% 1.84/2.04 tff(2532,plain,
% 1.84/2.04 (~b(z, elem!1)),
% 1.84/2.04 inference(modus_ponens,[status(thm)],[312, 2531])).
% 1.84/2.04 tff(2533,plain,
% 1.84/2.04 ($false),
% 1.84/2.04 inference(unit_resolution,[status(thm)],[2517, 2532])).
% 1.84/2.04 tff(2534,plain,((~(elem!1 = s(z))) | (~b(z, elem!1)) | b(z, s(z))), inference(lemma,lemma(discharge,[]))).
% 1.84/2.04 tff(2535,plain,
% 1.84/2.04 (~(elem!1 = s(z))),
% 1.84/2.04 inference(unit_resolution,[status(thm)],[2534, 2517, 312])).
% 1.84/2.04 tff(2536,plain,
% 1.84/2.04 (((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((elem!1 = s(z)) | b(elem!1, s(z)) | r(elem!1, s(z)))) <=> ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (elem!1 = s(z)) | b(elem!1, s(z)) | r(elem!1, s(z)))),
% 1.84/2.04 inference(rewrite,[status(thm)],[])).
% 1.84/2.04 tff(2537,plain,
% 1.84/2.04 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((elem!1 = s(z)) | b(elem!1, s(z)) | r(elem!1, s(z)))),
% 1.84/2.04 inference(quant_inst,[status(thm)],[])).
% 1.84/2.04 tff(2538,plain,
% 1.84/2.04 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (elem!1 = s(z)) | b(elem!1, s(z)) | r(elem!1, s(z))),
% 1.84/2.04 inference(modus_ponens,[status(thm)],[2537, 2536])).
% 1.84/2.04 tff(2539,plain,
% 1.84/2.04 ((elem!1 = s(z)) | b(elem!1, s(z)) | r(elem!1, s(z))),
% 1.84/2.04 inference(unit_resolution,[status(thm)],[2538, 79])).
% 1.84/2.04 tff(2540,plain,
% 1.84/2.04 (r(elem!1, s(z))),
% 1.84/2.04 inference(unit_resolution,[status(thm)],[2539, 2535, 2527])).
% 1.84/2.04 tff(2541,plain,
% 1.84/2.04 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, z)) | (~r(s(z), s(s(elem!1)))) | (~r(z, s(z))) | (~r(elem!1, s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(elem!1, z)) | (~r(s(z), s(s(elem!1)))) | (~r(z, s(z))) | (~r(elem!1, s(z))))),
% 1.84/2.04 inference(rewrite,[status(thm)],[])).
% 1.84/2.04 tff(2542,plain,
% 1.84/2.04 (((~r(s(z), s(s(elem!1)))) | (~r(z, s(z))) | (~r(elem!1, s(z))) | (~r(elem!1, z))) <=> ((~r(elem!1, z)) | (~r(s(z), s(s(elem!1)))) | (~r(z, s(z))) | (~r(elem!1, s(z))))),
% 1.84/2.04 inference(rewrite,[status(thm)],[])).
% 1.84/2.04 tff(2543,plain,
% 1.84/2.04 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(s(elem!1)))) | (~r(z, s(z))) | (~r(elem!1, s(z))) | (~r(elem!1, z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, z)) | (~r(s(z), s(s(elem!1)))) | (~r(z, s(z))) | (~r(elem!1, s(z)))))),
% 1.84/2.04 inference(monotonicity,[status(thm)],[2542])).
% 1.84/2.04 tff(2544,plain,
% 1.84/2.04 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(s(elem!1)))) | (~r(z, s(z))) | (~r(elem!1, s(z))) | (~r(elem!1, z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(elem!1, z)) | (~r(s(z), s(s(elem!1)))) | (~r(z, s(z))) | (~r(elem!1, s(z))))),
% 1.84/2.04 inference(transitivity,[status(thm)],[2543, 2541])).
% 1.84/2.04 tff(2545,plain,
% 1.84/2.04 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(s(elem!1)))) | (~r(z, s(z))) | (~r(elem!1, s(z))) | (~r(elem!1, z)))),
% 1.84/2.04 inference(quant_inst,[status(thm)],[])).
% 1.84/2.04 tff(2546,plain,
% 1.84/2.04 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(elem!1, z)) | (~r(s(z), s(s(elem!1)))) | (~r(z, s(z))) | (~r(elem!1, s(z)))),
% 1.84/2.04 inference(modus_ponens,[status(thm)],[2545, 2544])).
% 1.84/2.04 tff(2547,plain,
% 1.84/2.04 (~r(elem!1, z)),
% 1.84/2.04 inference(unit_resolution,[status(thm)],[2546, 197, 311, 2540, 322])).
% 1.84/2.04 tff(2548,plain,
% 1.84/2.04 (b(elem!1, z)),
% 1.84/2.04 inference(unit_resolution,[status(thm)],[1239, 2547, 1173])).
% 1.84/2.04 tff(2549,plain,
% 1.84/2.04 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), elem!1)) | (~b(s(s(elem!1)), z)) | (~b(elem!1, z)) | (~b(z, elem!1)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(elem!1)), elem!1)) | (~b(s(s(elem!1)), z)) | (~b(elem!1, z)) | (~b(z, elem!1)))),
% 1.84/2.04 inference(rewrite,[status(thm)],[])).
% 1.84/2.04 tff(2550,plain,
% 1.84/2.04 (((~b(elem!1, z)) | (~b(s(s(elem!1)), z)) | (~b(z, elem!1)) | (~b(elem!1, z)) | (~b(s(s(elem!1)), z)) | (~b(s(s(elem!1)), elem!1))) <=> ((~b(s(s(elem!1)), elem!1)) | (~b(s(s(elem!1)), z)) | (~b(elem!1, z)) | (~b(z, elem!1)))),
% 1.84/2.04 inference(rewrite,[status(thm)],[])).
% 1.84/2.04 tff(2551,plain,
% 1.84/2.04 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, z)) | (~b(s(s(elem!1)), z)) | (~b(z, elem!1)) | (~b(elem!1, z)) | (~b(s(s(elem!1)), z)) | (~b(s(s(elem!1)), elem!1)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), elem!1)) | (~b(s(s(elem!1)), z)) | (~b(elem!1, z)) | (~b(z, elem!1))))),
% 1.84/2.04 inference(monotonicity,[status(thm)],[2550])).
% 1.84/2.04 tff(2552,plain,
% 1.84/2.04 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, z)) | (~b(s(s(elem!1)), z)) | (~b(z, elem!1)) | (~b(elem!1, z)) | (~b(s(s(elem!1)), z)) | (~b(s(s(elem!1)), elem!1)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(elem!1)), elem!1)) | (~b(s(s(elem!1)), z)) | (~b(elem!1, z)) | (~b(z, elem!1)))),
% 1.84/2.04 inference(transitivity,[status(thm)],[2551, 2549])).
% 1.84/2.04 tff(2553,plain,
% 1.84/2.04 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, z)) | (~b(s(s(elem!1)), z)) | (~b(z, elem!1)) | (~b(elem!1, z)) | (~b(s(s(elem!1)), z)) | (~b(s(s(elem!1)), elem!1)))),
% 1.84/2.04 inference(quant_inst,[status(thm)],[])).
% 1.84/2.04 tff(2554,plain,
% 1.84/2.04 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(elem!1)), elem!1)) | (~b(s(s(elem!1)), z)) | (~b(elem!1, z)) | (~b(z, elem!1))),
% 1.84/2.04 inference(modus_ponens,[status(thm)],[2553, 2552])).
% 1.84/2.04 tff(2555,plain,
% 1.84/2.04 ($false),
% 1.84/2.04 inference(unit_resolution,[status(thm)],[2554, 166, 2517, 2548, 786, 592])).
% 1.84/2.04 tff(2556,plain,((~b(z, elem!1)) | (~b(s(s(elem!1)), elem!1)) | (~b(s(s(elem!1)), z)) | (elem!1 = z) | (~r(s(z), s(s(elem!1)))) | b(elem!1, s(z)) | b(z, s(z))), inference(lemma,lemma(discharge,[]))).
% 1.84/2.04 tff(2557,plain,
% 1.84/2.04 (~b(s(s(elem!1)), elem!1)),
% 1.84/2.04 inference(unit_resolution,[status(thm)],[2556, 2526, 312, 1152, 311, 2515, 592])).
% 1.84/2.04 tff(2558,plain,
% 1.84/2.04 (s(s(elem!1)) = elem!1),
% 1.84/2.04 inference(unit_resolution,[status(thm)],[784, 2557, 778])).
% 1.84/2.04 tff(2559,assumption,(s(s(elem!1)) = elem!1), introduced(assumption)).
% 1.84/2.04 tff(2560,plain,
% 1.84/2.04 (s(s(s(elem!1))) = s(elem!1)),
% 1.84/2.04 inference(monotonicity,[status(thm)],[2559])).
% 1.84/2.04 tff(2561,plain,
% 1.84/2.04 ($false),
% 1.84/2.04 inference(unit_resolution,[status(thm)],[1164, 2560])).
% 1.84/2.04 tff(2562,plain,((~(s(s(elem!1)) = elem!1)) | (s(s(s(elem!1))) = s(elem!1))), inference(lemma,lemma(discharge,[]))).
% 1.84/2.04 tff(2563,plain,
% 1.84/2.04 (s(s(s(elem!1))) = s(elem!1)),
% 1.84/2.04 inference(unit_resolution,[status(thm)],[2562, 2558])).
% 1.84/2.04 tff(2564,plain,
% 1.84/2.04 (inj_0(s(s(s(elem!1)))) = inj_0(s(elem!1))),
% 1.84/2.04 inference(monotonicity,[status(thm)],[2563])).
% 1.84/2.04 tff(2565,plain,
% 1.84/2.04 (s(s(elem!1)) = elem!1),
% 1.84/2.04 inference(transitivity,[status(thm)],[105, 2564, 20])).
% 1.84/2.04 tff(2566,plain,
% 1.84/2.04 (b(s(s(elem!1)), s(z)) <=> b(elem!1, s(z))),
% 1.84/2.04 inference(monotonicity,[status(thm)],[2565])).
% 1.84/2.04 tff(2567,plain,
% 1.84/2.04 (b(elem!1, s(z)) <=> b(s(s(elem!1)), s(z))),
% 1.84/2.04 inference(symmetry,[status(thm)],[2566])).
% 1.84/2.04 tff(2568,plain,
% 1.84/2.04 ((~b(elem!1, s(z))) <=> (~b(s(s(elem!1)), s(z)))),
% 1.84/2.04 inference(monotonicity,[status(thm)],[2567])).
% 1.84/2.04 tff(2569,plain,
% 1.84/2.04 (~b(s(s(elem!1)), s(z))),
% 1.84/2.04 inference(modus_ponens,[status(thm)],[2526, 2568])).
% 1.84/2.04 tff(2570,plain,
% 1.84/2.04 ($false),
% 1.84/2.04 inference(unit_resolution,[status(thm)],[310, 2569])).
% 1.84/2.04 tff(2571,plain,((s(s(z)) = s(s(elem!1))) | (~b(s(s(elem!1)), s(z))) | r(s(s(elem!1)), elem!1) | b(z, s(z)) | (~r(s(z), s(s(elem!1)))) | (~b(s(s(elem!1)), z)) | (~b(s(s(z)), s(z))) | (~b(s(s(z)), z)) | r(z, elem!1) | r(s(s(z)), s(s(elem!1)))), inference(lemma,lemma(discharge,[]))).
% 1.84/2.04 tff(2572,plain,
% 1.84/2.04 (s(s(z)) = s(s(elem!1))),
% 1.84/2.04 inference(unit_resolution,[status(thm)],[2571, 2509, 310, 312, 311, 2276, 156, 2500, 2490, 2277])).
% 1.84/2.04 tff(2573,plain,
% 1.84/2.04 (s(elem!1) = s(z)),
% 1.84/2.04 inference(unit_resolution,[status(thm)],[43, 2572])).
% 1.84/2.04 tff(2574,plain,
% 1.84/2.04 (z = elem!1),
% 1.84/2.04 inference(unit_resolution,[status(thm)],[30, 2573])).
% 1.84/2.04 tff(2575,plain,
% 1.84/2.04 (r(s(s(s(elem!1))), elem!1)),
% 1.84/2.04 inference(unit_resolution,[status(thm)],[966, 2574, 2479])).
% 1.84/2.04 tff(2576,plain,
% 1.84/2.04 (r(s(z), z) <=> r(s(z), elem!1)),
% 1.84/2.04 inference(monotonicity,[status(thm)],[2574])).
% 1.84/2.04 tff(2577,plain,
% 1.84/2.04 (r(s(z), elem!1)),
% 1.84/2.04 inference(modus_ponens,[status(thm)],[2266, 2576])).
% 1.84/2.04 tff(2578,plain,
% 1.84/2.04 (r(elem!1, s(z))),
% 1.84/2.04 inference(unit_resolution,[status(thm)],[741, 2574, 322])).
% 1.84/2.04 tff(2579,plain,
% 1.84/2.04 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), elem!1)) | (~r(s(z), s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), elem!1)) | (~r(elem!1, s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(z), elem!1)) | (~r(s(z), s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), elem!1)) | (~r(elem!1, s(z))))),
% 1.84/2.04 inference(rewrite,[status(thm)],[])).
% 1.84/2.04 tff(2580,plain,
% 1.84/2.04 (((~r(elem!1, s(z))) | (~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)) | (~r(elem!1, s(z))))),
% 1.84/2.04 inference(rewrite,[status(thm)],[])).
% 1.84/2.04 tff(2581,plain,
% 1.84/2.04 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(z))) | (~r(s(s(s(elem!1))), elem!1)) | (~r(s(z), elem!1)) | (~r(s(z), s(s(s(elem!1))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), elem!1)) | (~r(s(z), s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), elem!1)) | (~r(elem!1, s(z)))))),
% 1.84/2.04 inference(monotonicity,[status(thm)],[2580])).
% 1.84/2.04 tff(2582,plain,
% 1.84/2.04 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(z))) | (~r(s(s(s(elem!1))), elem!1)) | (~r(s(z), elem!1)) | (~r(s(z), s(s(s(elem!1))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(z), elem!1)) | (~r(s(z), s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), elem!1)) | (~r(elem!1, s(z))))),
% 1.84/2.04 inference(transitivity,[status(thm)],[2581, 2579])).
% 1.84/2.05 tff(2583,plain,
% 1.84/2.05 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(z))) | (~r(s(s(s(elem!1))), elem!1)) | (~r(s(z), elem!1)) | (~r(s(z), s(s(s(elem!1))))))),
% 1.84/2.05 inference(quant_inst,[status(thm)],[])).
% 1.84/2.05 tff(2584,plain,
% 1.84/2.05 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(z), elem!1)) | (~r(s(z), s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), elem!1)) | (~r(elem!1, s(z)))),
% 1.84/2.05 inference(modus_ponens,[status(thm)],[2583, 2582])).
% 1.84/2.05 tff(2585,plain,
% 1.84/2.05 ($false),
% 1.84/2.05 inference(unit_resolution,[status(thm)],[2584, 197, 2578, 2577, 2475, 2575])).
% 1.84/2.05 tff(2586,plain,((s(s(elem!1)) = s(s(s(elem!1)))) | (~b(s(s(elem!1)), s(z))) | b(z, s(z)) | (~r(s(z), s(s(elem!1)))) | (~b(s(s(z)), s(z))) | (~r(z, s(s(z)))) | (~r(s(z), s(s(z)))) | r(s(s(elem!1)), s(s(s(elem!1))))), inference(lemma,lemma(discharge,[]))).
% 1.84/2.05 tff(2587,plain,
% 1.84/2.05 (s(s(elem!1)) = s(s(s(elem!1)))),
% 1.84/2.05 inference(unit_resolution,[status(thm)],[2586, 2264, 312, 311, 156, 152, 120, 310])).
% 1.84/2.05 tff(2588,plain,
% 1.84/2.05 (s(s(s(elem!1))) = s(s(elem!1))),
% 1.84/2.05 inference(symmetry,[status(thm)],[2587])).
% 1.84/2.05 tff(2589,plain,
% 1.84/2.05 (inj_0(s(s(elem!1))) = inj_0(s(s(s(elem!1))))),
% 1.84/2.05 inference(monotonicity,[status(thm)],[334])).
% 1.84/2.05 tff(2590,plain,
% 1.84/2.05 (inj_0(s(s(s(elem!1)))) = inj_0(s(s(elem!1)))),
% 1.84/2.05 inference(symmetry,[status(thm)],[2589])).
% 1.84/2.05 tff(2591,plain,
% 1.84/2.05 (s(s(s(elem!1))) = s(s(elem!1))),
% 1.84/2.05 inference(symmetry,[status(thm)],[334])).
% 1.84/2.05 tff(2592,plain,
% 1.84/2.05 (s(s(s(elem!1))) = s(elem!1)),
% 1.84/2.05 inference(transitivity,[status(thm)],[2591, 105, 2590, 38])).
% 1.84/2.05 tff(2593,plain,
% 1.84/2.05 ($false),
% 1.84/2.05 inference(unit_resolution,[status(thm)],[1164, 2592])).
% 1.84/2.05 tff(2594,plain,((~(s(s(elem!1)) = s(s(s(elem!1))))) | (s(s(s(elem!1))) = s(elem!1))), inference(lemma,lemma(discharge,[]))).
% 1.84/2.05 tff(2595,plain,
% 1.84/2.05 (s(s(s(elem!1))) = s(elem!1)),
% 1.84/2.05 inference(unit_resolution,[status(thm)],[2594, 2587])).
% 1.84/2.05 tff(2596,plain,
% 1.84/2.05 (s(elem!1) = s(s(s(elem!1)))),
% 1.84/2.05 inference(symmetry,[status(thm)],[2595])).
% 1.84/2.05 tff(2597,plain,
% 1.84/2.05 (s(z) = s(elem!1)),
% 1.84/2.05 inference(symmetry,[status(thm)],[619])).
% 1.84/2.05 tff(2598,plain,
% 1.84/2.05 (s(z) = s(s(elem!1))),
% 1.84/2.05 inference(transitivity,[status(thm)],[2597, 2596, 2588])).
% 1.84/2.05 tff(2599,plain,
% 1.84/2.05 ($false),
% 1.84/2.05 inference(unit_resolution,[status(thm)],[69, 2598])).
% 1.84/2.05 tff(2600,plain,((~(s(s(z)) = s(s(elem!1)))) | b(z, s(z)) | (~r(s(z), s(s(elem!1)))) | (~b(s(s(z)), s(z))) | (~r(s(z), s(s(z)))) | (~b(s(s(elem!1)), s(z))) | b(z, s(s(z)))), inference(lemma,lemma(discharge,[]))).
% 1.84/2.05 tff(2601,plain,
% 1.84/2.05 (~(s(s(z)) = s(s(elem!1)))),
% 1.84/2.05 inference(unit_resolution,[status(thm)],[2600, 312, 311, 156, 120, 310, 125])).
% 1.84/2.05 tff(2602,plain,
% 1.84/2.05 (b(s(s(z)), s(s(elem!1)))),
% 1.84/2.05 inference(unit_resolution,[status(thm)],[390, 2601, 2256])).
% 1.84/2.05 tff(2603,plain,
% 1.84/2.05 (~b(s(z), z)),
% 1.84/2.05 inference(unit_resolution,[status(thm)],[2253, 45, 152, 310, 322])).
% 1.84/2.05 tff(2604,plain,
% 1.84/2.05 (r(s(z), z)),
% 1.84/2.05 inference(unit_resolution,[status(thm)],[230, 2603])).
% 1.84/2.05 tff(2605,plain,
% 1.84/2.05 (r(s(s(elem!1)), s(s(s(elem!1))))),
% 1.84/2.05 inference(unit_resolution,[status(thm)],[2586, 45, 312, 311, 156, 152, 120, 310])).
% 1.84/2.05 tff(2606,plain,
% 1.84/2.05 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), s(z))) | (~r(z, s(z))) | (~r(s(z), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), s(z))) | (~r(z, s(z))) | (~r(s(z), z)))),
% 1.84/2.05 inference(rewrite,[status(thm)],[])).
% 1.84/2.05 tff(2607,plain,
% 1.84/2.05 (((~r(s(z), z)) | (~r(s(s(s(elem!1))), s(z))) | (~r(z, s(z))) | (~r(z, s(s(s(elem!1)))))) <=> ((~r(z, s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), s(z))) | (~r(z, s(z))) | (~r(s(z), z)))),
% 1.84/2.05 inference(rewrite,[status(thm)],[])).
% 1.84/2.05 tff(2608,plain,
% 1.84/2.05 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), z)) | (~r(s(s(s(elem!1))), s(z))) | (~r(z, s(z))) | (~r(z, s(s(s(elem!1))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), s(z))) | (~r(z, s(z))) | (~r(s(z), z))))),
% 1.84/2.05 inference(monotonicity,[status(thm)],[2607])).
% 1.84/2.05 tff(2609,plain,
% 1.84/2.05 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), z)) | (~r(s(s(s(elem!1))), s(z))) | (~r(z, s(z))) | (~r(z, s(s(s(elem!1))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), s(z))) | (~r(z, s(z))) | (~r(s(z), z)))),
% 1.84/2.05 inference(transitivity,[status(thm)],[2608, 2606])).
% 1.84/2.05 tff(2610,plain,
% 1.84/2.05 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), z)) | (~r(s(s(s(elem!1))), s(z))) | (~r(z, s(z))) | (~r(z, s(s(s(elem!1))))))),
% 1.84/2.05 inference(quant_inst,[status(thm)],[])).
% 1.84/2.05 tff(2611,plain,
% 1.84/2.05 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), s(z))) | (~r(z, s(z))) | (~r(s(z), z))),
% 1.84/2.05 inference(modus_ponens,[status(thm)],[2610, 2609])).
% 1.84/2.05 tff(2612,plain,
% 1.84/2.05 ($false),
% 1.84/2.05 inference(unit_resolution,[status(thm)],[2611, 197, 350, 323, 97, 282])).
% 1.84/2.05 tff(2613,plain,((~r(s(s(s(elem!1))), s(z))) | (~r(z, s(z))) | (~r(s(z), z)) | (~r(z, s(s(s(elem!1)))))), inference(lemma,lemma(discharge,[]))).
% 1.84/2.05 tff(2614,plain,
% 1.84/2.05 (~r(z, s(s(s(elem!1))))),
% 1.84/2.05 inference(unit_resolution,[status(thm)],[2613, 350, 97, 323])).
% 1.84/2.05 tff(2615,plain,
% 1.84/2.05 (b(z, s(s(s(elem!1))))),
% 1.84/2.05 inference(unit_resolution,[status(thm)],[261, 2614])).
% 1.84/2.05 tff(2616,plain,
% 1.84/2.05 (~r(z, s(s(elem!1)))),
% 1.84/2.05 inference(unit_resolution,[status(thm)],[413, 311, 323, 377])).
% 1.84/2.05 tff(2617,plain,
% 1.84/2.05 (b(z, s(s(elem!1)))),
% 1.84/2.05 inference(unit_resolution,[status(thm)],[1795, 2616])).
% 1.84/2.05 tff(2618,plain,
% 1.84/2.05 (~r(s(z), s(s(s(elem!1))))),
% 1.84/2.05 inference(unit_resolution,[status(thm)],[764, 311, 377, 350])).
% 1.84/2.05 tff(2619,plain,
% 1.84/2.05 (b(s(z), s(s(s(elem!1))))),
% 1.84/2.05 inference(unit_resolution,[status(thm)],[116, 2618])).
% 1.84/2.05 tff(2620,plain,
% 1.84/2.05 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), s(s(elem!1)))) | (~r(s(z), s(s(elem!1)))) | (~r(s(s(s(elem!1))), s(z))) | (~r(s(s(elem!1)), s(s(s(elem!1))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(elem!1))), s(s(elem!1)))) | (~r(s(z), s(s(elem!1)))) | (~r(s(s(s(elem!1))), s(z))) | (~r(s(s(elem!1)), s(s(s(elem!1))))))),
% 1.84/2.05 inference(rewrite,[status(thm)],[])).
% 1.84/2.05 tff(2621,plain,
% 1.84/2.05 (((~r(s(s(elem!1)), s(s(s(elem!1))))) | (~r(s(z), s(s(elem!1)))) | (~r(s(s(s(elem!1))), s(s(elem!1)))) | (~r(s(s(s(elem!1))), s(z)))) <=> ((~r(s(s(s(elem!1))), s(s(elem!1)))) | (~r(s(z), s(s(elem!1)))) | (~r(s(s(s(elem!1))), s(z))) | (~r(s(s(elem!1)), s(s(s(elem!1))))))),
% 1.84/2.05 inference(rewrite,[status(thm)],[])).
% 1.84/2.05 tff(2622,plain,
% 1.84/2.05 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(elem!1)), s(s(s(elem!1))))) | (~r(s(z), s(s(elem!1)))) | (~r(s(s(s(elem!1))), s(s(elem!1)))) | (~r(s(s(s(elem!1))), s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), s(s(elem!1)))) | (~r(s(z), s(s(elem!1)))) | (~r(s(s(s(elem!1))), s(z))) | (~r(s(s(elem!1)), s(s(s(elem!1)))))))),
% 1.84/2.05 inference(monotonicity,[status(thm)],[2621])).
% 1.84/2.05 tff(2623,plain,
% 1.84/2.05 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(elem!1)), s(s(s(elem!1))))) | (~r(s(z), s(s(elem!1)))) | (~r(s(s(s(elem!1))), s(s(elem!1)))) | (~r(s(s(s(elem!1))), s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(elem!1))), s(s(elem!1)))) | (~r(s(z), s(s(elem!1)))) | (~r(s(s(s(elem!1))), s(z))) | (~r(s(s(elem!1)), s(s(s(elem!1))))))),
% 1.84/2.05 inference(transitivity,[status(thm)],[2622, 2620])).
% 1.84/2.05 tff(2624,plain,
% 1.84/2.05 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(elem!1)), s(s(s(elem!1))))) | (~r(s(z), s(s(elem!1)))) | (~r(s(s(s(elem!1))), s(s(elem!1)))) | (~r(s(s(s(elem!1))), s(z))))),
% 1.84/2.05 inference(quant_inst,[status(thm)],[])).
% 1.84/2.05 tff(2625,plain,
% 1.84/2.05 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(elem!1))), s(s(elem!1)))) | (~r(s(z), s(s(elem!1)))) | (~r(s(s(s(elem!1))), s(z))) | (~r(s(s(elem!1)), s(s(s(elem!1)))))),
% 1.84/2.05 inference(modus_ponens,[status(thm)],[2624, 2623])).
% 1.84/2.05 tff(2626,plain,
% 1.84/2.05 ($false),
% 1.84/2.05 inference(unit_resolution,[status(thm)],[2625, 197, 311, 350, 377, 905])).
% 1.84/2.05 tff(2627,plain,((~r(s(z), s(s(elem!1)))) | (~r(s(s(s(elem!1))), s(z))) | (~r(s(s(elem!1)), s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), s(s(elem!1))))), inference(lemma,lemma(discharge,[]))).
% 1.84/2.05 tff(2628,plain,
% 1.84/2.05 (~r(s(s(s(elem!1))), s(s(elem!1)))),
% 1.84/2.05 inference(unit_resolution,[status(thm)],[2627, 311, 377, 350])).
% 1.84/2.05 tff(2629,plain,
% 1.84/2.05 (b(s(s(s(elem!1))), s(s(elem!1)))),
% 1.84/2.05 inference(unit_resolution,[status(thm)],[889, 2628, 1863])).
% 1.84/2.05 tff(2630,plain,
% 1.84/2.05 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(z, s(s(s(elem!1))))) | (~b(z, s(s(elem!1)))) | (~b(s(z), s(s(s(elem!1))))) | (~b(s(s(elem!1)), s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(z, s(s(s(elem!1))))) | (~b(z, s(s(elem!1)))) | (~b(s(z), s(s(s(elem!1))))) | (~b(s(s(elem!1)), s(z))))),
% 1.84/2.05 inference(rewrite,[status(thm)],[])).
% 1.84/2.05 tff(2631,plain,
% 1.84/2.05 (((~b(s(z), s(s(s(elem!1))))) | (~b(z, s(s(s(elem!1))))) | (~b(s(s(elem!1)), s(z))) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(z, s(s(elem!1)))) | (~b(z, s(s(s(elem!1)))))) <=> ((~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(z, s(s(s(elem!1))))) | (~b(z, s(s(elem!1)))) | (~b(s(z), s(s(s(elem!1))))) | (~b(s(s(elem!1)), s(z))))),
% 1.84/2.05 inference(rewrite,[status(thm)],[])).
% 1.84/2.05 tff(2632,plain,
% 1.84/2.05 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(s(elem!1))))) | (~b(z, s(s(s(elem!1))))) | (~b(s(s(elem!1)), s(z))) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(z, s(s(elem!1)))) | (~b(z, s(s(s(elem!1))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(z, s(s(s(elem!1))))) | (~b(z, s(s(elem!1)))) | (~b(s(z), s(s(s(elem!1))))) | (~b(s(s(elem!1)), s(z)))))),
% 1.84/2.05 inference(monotonicity,[status(thm)],[2631])).
% 1.84/2.05 tff(2633,plain,
% 1.84/2.05 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(s(elem!1))))) | (~b(z, s(s(s(elem!1))))) | (~b(s(s(elem!1)), s(z))) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(z, s(s(elem!1)))) | (~b(z, s(s(s(elem!1))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(z, s(s(s(elem!1))))) | (~b(z, s(s(elem!1)))) | (~b(s(z), s(s(s(elem!1))))) | (~b(s(s(elem!1)), s(z))))),
% 1.84/2.05 inference(transitivity,[status(thm)],[2632, 2630])).
% 1.84/2.05 tff(2634,plain,
% 1.84/2.05 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(s(elem!1))))) | (~b(z, s(s(s(elem!1))))) | (~b(s(s(elem!1)), s(z))) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(z, s(s(elem!1)))) | (~b(z, s(s(s(elem!1))))))),
% 1.84/2.05 inference(quant_inst,[status(thm)],[])).
% 1.84/2.05 tff(2635,plain,
% 1.84/2.05 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(z, s(s(s(elem!1))))) | (~b(z, s(s(elem!1)))) | (~b(s(z), s(s(s(elem!1))))) | (~b(s(s(elem!1)), s(z)))),
% 1.84/2.05 inference(modus_ponens,[status(thm)],[2634, 2633])).
% 1.84/2.05 tff(2636,plain,
% 1.84/2.05 ($false),
% 1.84/2.05 inference(unit_resolution,[status(thm)],[2635, 166, 2629, 2619, 240, 2617, 310])).
% 1.84/2.05 tff(2637,plain,((~r(s(z), s(s(elem!1)))) | (~b(z, s(s(s(elem!1))))) | (~b(s(s(elem!1)), s(z))) | (s(s(s(elem!1))) = s(s(elem!1))) | (~r(s(s(elem!1)), s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), s(z))) | (~r(z, s(z)))), inference(lemma,lemma(discharge,[]))).
% 1.84/2.05 tff(2638,plain,
% 1.84/2.05 (~r(s(z), s(s(elem!1)))),
% 1.84/2.05 inference(unit_resolution,[status(thm)],[2637, 2615, 310, 1863, 377, 350, 323])).
% 1.84/2.05 tff(2639,plain,
% 1.84/2.05 (b(s(z), s(s(elem!1)))),
% 1.84/2.05 inference(unit_resolution,[status(thm)],[84, 2638])).
% 1.84/2.05 tff(2640,plain,
% 1.84/2.05 ((s(elem!1) = s(s(z))) <=> (s(s(z)) = s(elem!1))),
% 1.84/2.05 inference(symmetry,[status(thm)],[1252])).
% 1.84/2.05 tff(2641,plain,
% 1.84/2.05 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(z))) | (~r(s(z), z)) | (~r(s(s(s(s(elem!1)))), s(z))) | (~r(s(s(s(s(elem!1)))), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, s(z))) | (~r(s(z), z)) | (~r(s(s(s(s(elem!1)))), s(z))) | (~r(s(s(s(s(elem!1)))), z)))),
% 1.84/2.05 inference(rewrite,[status(thm)],[])).
% 1.84/2.05 tff(2642,plain,
% 1.84/2.05 (((~r(s(z), z)) | (~r(z, s(z))) | (~r(s(s(s(s(elem!1)))), s(z))) | (~r(s(s(s(s(elem!1)))), z))) <=> ((~r(z, s(z))) | (~r(s(z), z)) | (~r(s(s(s(s(elem!1)))), s(z))) | (~r(s(s(s(s(elem!1)))), z)))),
% 1.84/2.05 inference(rewrite,[status(thm)],[])).
% 1.84/2.05 tff(2643,plain,
% 1.84/2.05 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), z)) | (~r(z, s(z))) | (~r(s(s(s(s(elem!1)))), s(z))) | (~r(s(s(s(s(elem!1)))), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(z))) | (~r(s(z), z)) | (~r(s(s(s(s(elem!1)))), s(z))) | (~r(s(s(s(s(elem!1)))), z))))),
% 1.84/2.05 inference(monotonicity,[status(thm)],[2642])).
% 1.84/2.05 tff(2644,plain,
% 1.84/2.05 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), z)) | (~r(z, s(z))) | (~r(s(s(s(s(elem!1)))), s(z))) | (~r(s(s(s(s(elem!1)))), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, s(z))) | (~r(s(z), z)) | (~r(s(s(s(s(elem!1)))), s(z))) | (~r(s(s(s(s(elem!1)))), z)))),
% 1.84/2.05 inference(transitivity,[status(thm)],[2643, 2641])).
% 1.84/2.05 tff(2645,plain,
% 1.84/2.05 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), z)) | (~r(z, s(z))) | (~r(s(s(s(s(elem!1)))), s(z))) | (~r(s(s(s(s(elem!1)))), z)))),
% 1.84/2.05 inference(quant_inst,[status(thm)],[])).
% 1.84/2.05 tff(2646,plain,
% 1.84/2.05 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, s(z))) | (~r(s(z), z)) | (~r(s(s(s(s(elem!1)))), s(z))) | (~r(s(s(s(s(elem!1)))), z))),
% 1.84/2.05 inference(modus_ponens,[status(thm)],[2645, 2644])).
% 1.84/2.05 tff(2647,plain,
% 1.84/2.05 (~r(s(s(s(s(elem!1)))), z)),
% 1.84/2.05 inference(unit_resolution,[status(thm)],[2646, 197, 323, 97, 700])).
% 1.84/2.05 tff(2648,plain,
% 1.84/2.05 (b(s(s(s(s(elem!1)))), z)),
% 1.84/2.05 inference(unit_resolution,[status(thm)],[1339, 79, 626, 2647])).
% 1.84/2.05 tff(2649,plain,
% 1.84/2.05 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), z)) | (~r(s(s(s(elem!1))), s(z))) | (~r(s(s(s(s(elem!1)))), s(z))) | (~r(s(s(s(s(elem!1)))), s(s(s(elem!1))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(z), z)) | (~r(s(s(s(elem!1))), s(z))) | (~r(s(s(s(s(elem!1)))), s(z))) | (~r(s(s(s(s(elem!1)))), s(s(s(elem!1))))))),
% 1.84/2.05 inference(rewrite,[status(thm)],[])).
% 1.84/2.05 tff(2650,plain,
% 1.84/2.05 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), z)) | (~r(s(s(s(elem!1))), s(z))) | (~r(s(s(s(s(elem!1)))), s(z))) | (~r(s(s(s(s(elem!1)))), s(s(s(elem!1))))))),
% 1.84/2.05 inference(quant_inst,[status(thm)],[])).
% 1.84/2.05 tff(2651,plain,
% 1.84/2.05 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(z), z)) | (~r(s(s(s(elem!1))), s(z))) | (~r(s(s(s(s(elem!1)))), s(z))) | (~r(s(s(s(s(elem!1)))), s(s(s(elem!1)))))),
% 1.84/2.05 inference(modus_ponens,[status(thm)],[2650, 2649])).
% 1.84/2.05 tff(2652,plain,
% 1.84/2.05 (~r(s(s(s(s(elem!1)))), s(s(s(elem!1))))),
% 1.84/2.05 inference(unit_resolution,[status(thm)],[2651, 197, 350, 97, 700])).
% 1.84/2.05 tff(2653,plain,
% 1.84/2.05 (b(s(s(s(s(elem!1)))), s(s(s(elem!1))))),
% 1.84/2.05 inference(unit_resolution,[status(thm)],[1065, 2652, 1058])).
% 1.84/2.05 tff(2654,plain,
% 1.84/2.05 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), z)) | (~r(s(s(s(elem!1))), s(z))) | (~r(z, s(z))) | (~r(s(z), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(elem!1))), z)) | (~r(s(s(s(elem!1))), s(z))) | (~r(z, s(z))) | (~r(s(z), z)))),
% 1.84/2.05 inference(rewrite,[status(thm)],[])).
% 1.84/2.05 tff(2655,plain,
% 1.84/2.05 (((~r(s(z), z)) | (~r(z, s(z))) | (~r(s(s(s(elem!1))), s(z))) | (~r(s(s(s(elem!1))), z))) <=> ((~r(s(s(s(elem!1))), z)) | (~r(s(s(s(elem!1))), s(z))) | (~r(z, s(z))) | (~r(s(z), z)))),
% 1.84/2.05 inference(rewrite,[status(thm)],[])).
% 1.84/2.05 tff(2656,plain,
% 1.84/2.05 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), z)) | (~r(z, s(z))) | (~r(s(s(s(elem!1))), s(z))) | (~r(s(s(s(elem!1))), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), z)) | (~r(s(s(s(elem!1))), s(z))) | (~r(z, s(z))) | (~r(s(z), z))))),
% 1.84/2.05 inference(monotonicity,[status(thm)],[2655])).
% 1.84/2.05 tff(2657,plain,
% 1.84/2.05 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), z)) | (~r(z, s(z))) | (~r(s(s(s(elem!1))), s(z))) | (~r(s(s(s(elem!1))), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(elem!1))), z)) | (~r(s(s(s(elem!1))), s(z))) | (~r(z, s(z))) | (~r(s(z), z)))),
% 1.84/2.05 inference(transitivity,[status(thm)],[2656, 2654])).
% 1.84/2.05 tff(2658,plain,
% 1.84/2.05 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), z)) | (~r(z, s(z))) | (~r(s(s(s(elem!1))), s(z))) | (~r(s(s(s(elem!1))), z)))),
% 1.84/2.05 inference(quant_inst,[status(thm)],[])).
% 1.84/2.05 tff(2659,plain,
% 1.84/2.05 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(elem!1))), z)) | (~r(s(s(s(elem!1))), s(z))) | (~r(z, s(z))) | (~r(s(z), z))),
% 1.84/2.05 inference(modus_ponens,[status(thm)],[2658, 2657])).
% 1.84/2.05 tff(2660,plain,
% 1.84/2.05 (~r(s(s(s(elem!1))), z)),
% 1.84/2.05 inference(unit_resolution,[status(thm)],[2659, 197, 350, 323, 97])).
% 1.84/2.05 tff(2661,plain,
% 1.84/2.05 (b(s(s(s(elem!1))), z)),
% 1.84/2.05 inference(unit_resolution,[status(thm)],[94, 2660])).
% 1.84/2.05 tff(2662,plain,
% 1.84/2.05 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), z)) | (~b(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~b(s(s(s(s(elem!1)))), z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), z)) | (~b(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~b(s(s(s(s(elem!1)))), z)))),
% 1.84/2.05 inference(rewrite,[status(thm)],[])).
% 1.84/2.05 tff(2663,plain,
% 1.84/2.05 (((~b(z, s(s(s(elem!1))))) | (~b(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), z)) | (~b(z, s(s(s(elem!1))))) | (~b(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~b(s(s(s(s(elem!1)))), z))) <=> ((~b(z, s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), z)) | (~b(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~b(s(s(s(s(elem!1)))), z)))),
% 1.84/2.05 inference(rewrite,[status(thm)],[])).
% 1.84/2.05 tff(2664,plain,
% 1.84/2.05 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(s(elem!1))))) | (~b(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), z)) | (~b(z, s(s(s(elem!1))))) | (~b(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~b(s(s(s(s(elem!1)))), z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), z)) | (~b(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~b(s(s(s(s(elem!1)))), z))))),
% 1.84/2.06 inference(monotonicity,[status(thm)],[2663])).
% 1.84/2.06 tff(2665,plain,
% 1.84/2.06 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(s(elem!1))))) | (~b(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), z)) | (~b(z, s(s(s(elem!1))))) | (~b(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~b(s(s(s(s(elem!1)))), z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), z)) | (~b(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~b(s(s(s(s(elem!1)))), z)))),
% 1.84/2.06 inference(transitivity,[status(thm)],[2664, 2662])).
% 1.84/2.06 tff(2666,plain,
% 1.84/2.06 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(s(elem!1))))) | (~b(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), z)) | (~b(z, s(s(s(elem!1))))) | (~b(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~b(s(s(s(s(elem!1)))), z)))),
% 1.84/2.06 inference(quant_inst,[status(thm)],[])).
% 1.84/2.06 tff(2667,plain,
% 1.84/2.06 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), z)) | (~b(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~b(s(s(s(s(elem!1)))), z))),
% 1.84/2.06 inference(modus_ponens,[status(thm)],[2666, 2665])).
% 1.84/2.06 tff(2668,plain,
% 1.84/2.06 ($false),
% 1.84/2.06 inference(unit_resolution,[status(thm)],[2667, 166, 2615, 2661, 2653, 2648])).
% 1.84/2.06 tff(2669,plain,((~r(s(s(s(s(elem!1)))), s(z))) | (s(s(s(s(elem!1)))) = s(s(s(elem!1)))) | (~r(z, s(z))) | (~r(s(z), z)) | (~r(s(s(s(elem!1))), s(z)))), inference(lemma,lemma(discharge,[]))).
% 1.84/2.06 tff(2670,plain,
% 1.84/2.06 (~r(s(s(s(s(elem!1)))), s(z))),
% 1.84/2.06 inference(unit_resolution,[status(thm)],[2669, 350, 323, 97, 1038])).
% 1.84/2.06 tff(2671,plain,
% 1.84/2.06 (b(s(s(s(s(elem!1)))), s(z))),
% 1.84/2.06 inference(unit_resolution,[status(thm)],[661, 2670])).
% 1.84/2.06 tff(2672,plain,
% 1.84/2.06 (~b(s(s(s(s(elem!1)))), s(s(elem!1)))),
% 1.84/2.06 inference(unit_resolution,[status(thm)],[804, 166, 376, 310, 2671])).
% 1.84/2.06 tff(2673,plain,
% 1.84/2.06 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(z))) | (~r(s(z), z)) | (~r(s(s(z)), s(z))) | (~r(z, s(s(z)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, s(z))) | (~r(s(z), z)) | (~r(s(s(z)), s(z))) | (~r(z, s(s(z)))))),
% 1.84/2.06 inference(rewrite,[status(thm)],[])).
% 1.84/2.06 tff(2674,plain,
% 1.84/2.06 (((~r(s(z), z)) | (~r(s(s(z)), s(z))) | (~r(z, s(z))) | (~r(z, s(s(z))))) <=> ((~r(z, s(z))) | (~r(s(z), z)) | (~r(s(s(z)), s(z))) | (~r(z, s(s(z)))))),
% 1.84/2.06 inference(rewrite,[status(thm)],[])).
% 1.84/2.06 tff(2675,plain,
% 1.84/2.06 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), z)) | (~r(s(s(z)), s(z))) | (~r(z, s(z))) | (~r(z, s(s(z)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(z))) | (~r(s(z), z)) | (~r(s(s(z)), s(z))) | (~r(z, s(s(z))))))),
% 1.84/2.06 inference(monotonicity,[status(thm)],[2674])).
% 1.84/2.06 tff(2676,plain,
% 1.84/2.06 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), z)) | (~r(s(s(z)), s(z))) | (~r(z, s(z))) | (~r(z, s(s(z)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, s(z))) | (~r(s(z), z)) | (~r(s(s(z)), s(z))) | (~r(z, s(s(z)))))),
% 1.84/2.06 inference(transitivity,[status(thm)],[2675, 2673])).
% 1.84/2.06 tff(2677,plain,
% 1.84/2.06 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), z)) | (~r(s(s(z)), s(z))) | (~r(z, s(z))) | (~r(z, s(s(z)))))),
% 1.84/2.06 inference(quant_inst,[status(thm)],[])).
% 1.84/2.06 tff(2678,plain,
% 1.84/2.06 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, s(z))) | (~r(s(z), z)) | (~r(s(s(z)), s(z))) | (~r(z, s(s(z))))),
% 1.84/2.06 inference(modus_ponens,[status(thm)],[2677, 2676])).
% 1.84/2.06 tff(2679,plain,
% 1.84/2.06 ($false),
% 1.84/2.06 inference(unit_resolution,[status(thm)],[2678, 197, 155, 323, 97, 392])).
% 1.84/2.06 tff(2680,plain,((~r(s(z), z)) | (~r(z, s(s(z)))) | (~r(z, s(z))) | (~r(s(s(z)), s(z)))), inference(lemma,lemma(discharge,[]))).
% 1.84/2.06 tff(2681,plain,
% 1.84/2.06 (~r(s(s(z)), s(z))),
% 1.84/2.06 inference(unit_resolution,[status(thm)],[2680, 97, 155, 323])).
% 1.84/2.06 tff(2682,plain,
% 1.84/2.06 (b(s(s(z)), s(z))),
% 1.84/2.06 inference(unit_resolution,[status(thm)],[308, 2681])).
% 1.84/2.06 tff(2683,plain,
% 1.84/2.06 (~b(s(s(z)), s(s(elem!1)))),
% 1.84/2.06 inference(unit_resolution,[status(thm)],[454, 376, 310, 2682])).
% 1.84/2.06 tff(2684,plain,
% 1.84/2.06 (r(s(s(z)), s(s(elem!1)))),
% 1.84/2.06 inference(unit_resolution,[status(thm)],[390, 2683, 52])).
% 1.84/2.06 tff(2685,plain,
% 1.84/2.06 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(elem!1)))) | (~b(s(s(elem!1)), s(s(z)))) | (~b(s(s(elem!1)), s(z))) | (~b(s(s(z)), s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), s(s(elem!1)))) | (~b(s(s(elem!1)), s(s(z)))) | (~b(s(s(elem!1)), s(z))) | (~b(s(s(z)), s(z))))),
% 1.84/2.06 inference(rewrite,[status(thm)],[])).
% 1.84/2.06 tff(2686,plain,
% 1.84/2.06 (((~b(s(s(elem!1)), s(z))) | (~b(s(s(elem!1)), s(z))) | (~b(s(z), s(s(elem!1)))) | (~b(s(s(z)), s(z))) | (~b(s(s(elem!1)), s(z))) | (~b(s(s(elem!1)), s(s(z))))) <=> ((~b(s(z), s(s(elem!1)))) | (~b(s(s(elem!1)), s(s(z)))) | (~b(s(s(elem!1)), s(z))) | (~b(s(s(z)), s(z))))),
% 1.84/2.06 inference(rewrite,[status(thm)],[])).
% 1.84/2.06 tff(2687,plain,
% 1.84/2.06 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), s(z))) | (~b(s(s(elem!1)), s(z))) | (~b(s(z), s(s(elem!1)))) | (~b(s(s(z)), s(z))) | (~b(s(s(elem!1)), s(z))) | (~b(s(s(elem!1)), s(s(z)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(elem!1)))) | (~b(s(s(elem!1)), s(s(z)))) | (~b(s(s(elem!1)), s(z))) | (~b(s(s(z)), s(z)))))),
% 1.84/2.06 inference(monotonicity,[status(thm)],[2686])).
% 1.84/2.06 tff(2688,plain,
% 1.84/2.06 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), s(z))) | (~b(s(s(elem!1)), s(z))) | (~b(s(z), s(s(elem!1)))) | (~b(s(s(z)), s(z))) | (~b(s(s(elem!1)), s(z))) | (~b(s(s(elem!1)), s(s(z)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), s(s(elem!1)))) | (~b(s(s(elem!1)), s(s(z)))) | (~b(s(s(elem!1)), s(z))) | (~b(s(s(z)), s(z))))),
% 1.84/2.06 inference(transitivity,[status(thm)],[2687, 2685])).
% 1.84/2.06 tff(2689,plain,
% 1.84/2.06 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), s(z))) | (~b(s(s(elem!1)), s(z))) | (~b(s(z), s(s(elem!1)))) | (~b(s(s(z)), s(z))) | (~b(s(s(elem!1)), s(z))) | (~b(s(s(elem!1)), s(s(z)))))),
% 1.84/2.06 inference(quant_inst,[status(thm)],[])).
% 1.84/2.06 tff(2690,plain,
% 1.84/2.06 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), s(s(elem!1)))) | (~b(s(s(elem!1)), s(s(z)))) | (~b(s(s(elem!1)), s(z))) | (~b(s(s(z)), s(z)))),
% 1.84/2.06 inference(modus_ponens,[status(thm)],[2689, 2688])).
% 1.84/2.06 tff(2691,plain,
% 1.84/2.06 (~b(s(s(elem!1)), s(s(z)))),
% 1.84/2.06 inference(unit_resolution,[status(thm)],[2690, 166, 376, 310, 2682])).
% 1.84/2.06 tff(2692,plain,
% 1.84/2.06 (r(s(s(elem!1)), s(s(z)))),
% 1.84/2.06 inference(unit_resolution,[status(thm)],[441, 2691, 132])).
% 1.84/2.06 tff(2693,plain,
% 1.84/2.06 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(elem!1)))) | (~b(s(s(elem!1)), s(z))) | (~b(s(s(z)), s(z))) | (~b(s(s(s(s(elem!1)))), s(z))) | (~b(s(s(s(s(elem!1)))), s(s(z)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), s(s(elem!1)))) | (~b(s(s(elem!1)), s(z))) | (~b(s(s(z)), s(z))) | (~b(s(s(s(s(elem!1)))), s(z))) | (~b(s(s(s(s(elem!1)))), s(s(z)))))),
% 1.84/2.06 inference(rewrite,[status(thm)],[])).
% 1.84/2.06 tff(2694,plain,
% 1.84/2.06 (((~b(s(s(elem!1)), s(z))) | (~b(s(s(s(s(elem!1)))), s(z))) | (~b(s(z), s(s(elem!1)))) | (~b(s(s(z)), s(z))) | (~b(s(s(s(s(elem!1)))), s(z))) | (~b(s(s(s(s(elem!1)))), s(s(z))))) <=> ((~b(s(z), s(s(elem!1)))) | (~b(s(s(elem!1)), s(z))) | (~b(s(s(z)), s(z))) | (~b(s(s(s(s(elem!1)))), s(z))) | (~b(s(s(s(s(elem!1)))), s(s(z)))))),
% 1.84/2.06 inference(rewrite,[status(thm)],[])).
% 1.84/2.06 tff(2695,plain,
% 1.84/2.06 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), s(z))) | (~b(s(s(s(s(elem!1)))), s(z))) | (~b(s(z), s(s(elem!1)))) | (~b(s(s(z)), s(z))) | (~b(s(s(s(s(elem!1)))), s(z))) | (~b(s(s(s(s(elem!1)))), s(s(z)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(elem!1)))) | (~b(s(s(elem!1)), s(z))) | (~b(s(s(z)), s(z))) | (~b(s(s(s(s(elem!1)))), s(z))) | (~b(s(s(s(s(elem!1)))), s(s(z))))))),
% 1.84/2.06 inference(monotonicity,[status(thm)],[2694])).
% 1.84/2.06 tff(2696,plain,
% 1.84/2.06 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), s(z))) | (~b(s(s(s(s(elem!1)))), s(z))) | (~b(s(z), s(s(elem!1)))) | (~b(s(s(z)), s(z))) | (~b(s(s(s(s(elem!1)))), s(z))) | (~b(s(s(s(s(elem!1)))), s(s(z)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), s(s(elem!1)))) | (~b(s(s(elem!1)), s(z))) | (~b(s(s(z)), s(z))) | (~b(s(s(s(s(elem!1)))), s(z))) | (~b(s(s(s(s(elem!1)))), s(s(z)))))),
% 1.84/2.06 inference(transitivity,[status(thm)],[2695, 2693])).
% 1.84/2.06 tff(2697,plain,
% 1.84/2.06 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), s(z))) | (~b(s(s(s(s(elem!1)))), s(z))) | (~b(s(z), s(s(elem!1)))) | (~b(s(s(z)), s(z))) | (~b(s(s(s(s(elem!1)))), s(z))) | (~b(s(s(s(s(elem!1)))), s(s(z)))))),
% 1.84/2.06 inference(quant_inst,[status(thm)],[])).
% 1.84/2.06 tff(2698,plain,
% 1.84/2.06 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), s(s(elem!1)))) | (~b(s(s(elem!1)), s(z))) | (~b(s(s(z)), s(z))) | (~b(s(s(s(s(elem!1)))), s(z))) | (~b(s(s(s(s(elem!1)))), s(s(z))))),
% 1.84/2.06 inference(modus_ponens,[status(thm)],[2697, 2696])).
% 1.84/2.06 tff(2699,plain,
% 1.84/2.06 (~b(s(s(s(s(elem!1)))), s(s(z)))),
% 1.84/2.06 inference(unit_resolution,[status(thm)],[2698, 166, 376, 310, 2682, 2671])).
% 1.84/2.06 tff(2700,plain,
% 1.84/2.06 (r(s(s(s(s(elem!1)))), s(s(z)))),
% 1.84/2.06 inference(unit_resolution,[status(thm)],[1299, 2699])).
% 1.84/2.06 tff(2701,plain,
% 1.84/2.06 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(z)), s(s(elem!1)))) | (~r(s(s(elem!1)), s(s(z)))) | (~r(s(s(s(s(elem!1)))), s(s(elem!1)))) | (~r(s(s(s(s(elem!1)))), s(s(z)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(z)), s(s(elem!1)))) | (~r(s(s(elem!1)), s(s(z)))) | (~r(s(s(s(s(elem!1)))), s(s(elem!1)))) | (~r(s(s(s(s(elem!1)))), s(s(z)))))),
% 1.84/2.06 inference(rewrite,[status(thm)],[])).
% 1.84/2.06 tff(2702,plain,
% 1.84/2.06 (((~r(s(s(z)), s(s(elem!1)))) | (~r(s(s(elem!1)), s(s(z)))) | (~r(s(s(s(s(elem!1)))), s(s(z)))) | (~r(s(s(s(s(elem!1)))), s(s(elem!1))))) <=> ((~r(s(s(z)), s(s(elem!1)))) | (~r(s(s(elem!1)), s(s(z)))) | (~r(s(s(s(s(elem!1)))), s(s(elem!1)))) | (~r(s(s(s(s(elem!1)))), s(s(z)))))),
% 1.84/2.06 inference(rewrite,[status(thm)],[])).
% 1.84/2.06 tff(2703,plain,
% 1.84/2.06 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(z)), s(s(elem!1)))) | (~r(s(s(elem!1)), s(s(z)))) | (~r(s(s(s(s(elem!1)))), s(s(z)))) | (~r(s(s(s(s(elem!1)))), s(s(elem!1)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(z)), s(s(elem!1)))) | (~r(s(s(elem!1)), s(s(z)))) | (~r(s(s(s(s(elem!1)))), s(s(elem!1)))) | (~r(s(s(s(s(elem!1)))), s(s(z))))))),
% 1.84/2.06 inference(monotonicity,[status(thm)],[2702])).
% 1.84/2.06 tff(2704,plain,
% 1.84/2.06 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(z)), s(s(elem!1)))) | (~r(s(s(elem!1)), s(s(z)))) | (~r(s(s(s(s(elem!1)))), s(s(z)))) | (~r(s(s(s(s(elem!1)))), s(s(elem!1)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(z)), s(s(elem!1)))) | (~r(s(s(elem!1)), s(s(z)))) | (~r(s(s(s(s(elem!1)))), s(s(elem!1)))) | (~r(s(s(s(s(elem!1)))), s(s(z)))))),
% 1.84/2.06 inference(transitivity,[status(thm)],[2703, 2701])).
% 1.84/2.06 tff(2705,plain,
% 1.84/2.06 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(z)), s(s(elem!1)))) | (~r(s(s(elem!1)), s(s(z)))) | (~r(s(s(s(s(elem!1)))), s(s(z)))) | (~r(s(s(s(s(elem!1)))), s(s(elem!1)))))),
% 1.84/2.06 inference(quant_inst,[status(thm)],[])).
% 1.84/2.06 tff(2706,plain,
% 1.84/2.06 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(z)), s(s(elem!1)))) | (~r(s(s(elem!1)), s(s(z)))) | (~r(s(s(s(s(elem!1)))), s(s(elem!1)))) | (~r(s(s(s(s(elem!1)))), s(s(z))))),
% 1.84/2.06 inference(modus_ponens,[status(thm)],[2705, 2704])).
% 1.84/2.06 tff(2707,plain,
% 1.84/2.06 (~r(s(s(s(s(elem!1)))), s(s(elem!1)))),
% 1.84/2.06 inference(unit_resolution,[status(thm)],[2706, 197, 2700, 2692, 2684])).
% 1.84/2.06 tff(2708,plain,
% 1.84/2.06 (s(s(s(s(elem!1)))) = s(s(elem!1))),
% 1.84/2.06 inference(unit_resolution,[status(thm)],[813, 2707, 2672])).
% 1.84/2.06 tff(2709,plain,
% 1.84/2.06 (s(s(s(elem!1))) = s(elem!1)),
% 1.84/2.06 inference(unit_resolution,[status(thm)],[1166, 2708])).
% 1.84/2.06 tff(2710,plain,
% 1.84/2.06 ((s(s(z)) = s(s(s(elem!1)))) <=> (s(s(z)) = s(elem!1))),
% 1.84/2.06 inference(monotonicity,[status(thm)],[2709])).
% 1.84/2.06 tff(2711,plain,
% 1.84/2.06 ((s(s(z)) = s(s(s(elem!1)))) <=> (s(elem!1) = s(s(z)))),
% 1.84/2.06 inference(transitivity,[status(thm)],[2710, 1252])).
% 1.84/2.06 tff(2712,plain,
% 1.84/2.06 ((s(s(z)) = s(s(s(elem!1)))) <=> (s(s(z)) = s(elem!1))),
% 1.84/2.06 inference(transitivity,[status(thm)],[2711, 2640])).
% 1.84/2.06 tff(2713,plain,
% 1.84/2.06 ((~(s(s(z)) = s(s(s(elem!1))))) <=> (~(s(s(z)) = s(elem!1)))),
% 1.84/2.06 inference(monotonicity,[status(thm)],[2712])).
% 1.84/2.06 tff(2714,plain,
% 1.84/2.06 (~(s(s(z)) = s(elem!1))),
% 1.84/2.06 inference(modus_ponens,[status(thm)],[209, 2713])).
% 1.84/2.06 tff(2715,plain,
% 1.84/2.06 (~b(s(s(elem!1)), s(s(s(s(elem!1)))))),
% 1.84/2.06 inference(unit_resolution,[status(thm)],[822, 166, 376, 310, 2671])).
% 1.84/2.06 tff(2716,plain,
% 1.84/2.06 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(z)), s(s(elem!1)))) | (~r(s(s(elem!1)), s(s(z)))) | (~r(s(s(elem!1)), s(s(s(s(elem!1)))))) | (~r(s(s(s(s(elem!1)))), s(s(z)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(z)), s(s(elem!1)))) | (~r(s(s(elem!1)), s(s(z)))) | (~r(s(s(elem!1)), s(s(s(s(elem!1)))))) | (~r(s(s(s(s(elem!1)))), s(s(z)))))),
% 1.84/2.06 inference(rewrite,[status(thm)],[])).
% 1.84/2.06 tff(2717,plain,
% 1.84/2.06 (((~r(s(s(z)), s(s(elem!1)))) | (~r(s(s(s(s(elem!1)))), s(s(z)))) | (~r(s(s(elem!1)), s(s(z)))) | (~r(s(s(elem!1)), s(s(s(s(elem!1))))))) <=> ((~r(s(s(z)), s(s(elem!1)))) | (~r(s(s(elem!1)), s(s(z)))) | (~r(s(s(elem!1)), s(s(s(s(elem!1)))))) | (~r(s(s(s(s(elem!1)))), s(s(z)))))),
% 1.84/2.06 inference(rewrite,[status(thm)],[])).
% 1.84/2.06 tff(2718,plain,
% 1.84/2.06 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(z)), s(s(elem!1)))) | (~r(s(s(s(s(elem!1)))), s(s(z)))) | (~r(s(s(elem!1)), s(s(z)))) | (~r(s(s(elem!1)), s(s(s(s(elem!1)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(z)), s(s(elem!1)))) | (~r(s(s(elem!1)), s(s(z)))) | (~r(s(s(elem!1)), s(s(s(s(elem!1)))))) | (~r(s(s(s(s(elem!1)))), s(s(z))))))),
% 1.84/2.06 inference(monotonicity,[status(thm)],[2717])).
% 1.84/2.06 tff(2719,plain,
% 1.84/2.06 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(z)), s(s(elem!1)))) | (~r(s(s(s(s(elem!1)))), s(s(z)))) | (~r(s(s(elem!1)), s(s(z)))) | (~r(s(s(elem!1)), s(s(s(s(elem!1)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(z)), s(s(elem!1)))) | (~r(s(s(elem!1)), s(s(z)))) | (~r(s(s(elem!1)), s(s(s(s(elem!1)))))) | (~r(s(s(s(s(elem!1)))), s(s(z)))))),
% 1.84/2.06 inference(transitivity,[status(thm)],[2718, 2716])).
% 1.84/2.06 tff(2720,plain,
% 1.84/2.06 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(z)), s(s(elem!1)))) | (~r(s(s(s(s(elem!1)))), s(s(z)))) | (~r(s(s(elem!1)), s(s(z)))) | (~r(s(s(elem!1)), s(s(s(s(elem!1)))))))),
% 1.84/2.06 inference(quant_inst,[status(thm)],[])).
% 1.84/2.06 tff(2721,plain,
% 1.84/2.06 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(z)), s(s(elem!1)))) | (~r(s(s(elem!1)), s(s(z)))) | (~r(s(s(elem!1)), s(s(s(s(elem!1)))))) | (~r(s(s(s(s(elem!1)))), s(s(z))))),
% 1.84/2.06 inference(modus_ponens,[status(thm)],[2720, 2719])).
% 1.84/2.06 tff(2722,plain,
% 1.84/2.06 (~r(s(s(elem!1)), s(s(s(s(elem!1)))))),
% 1.84/2.06 inference(unit_resolution,[status(thm)],[2721, 197, 2700, 2692, 2684])).
% 1.84/2.06 tff(2723,plain,
% 1.84/2.06 (s(s(elem!1)) = s(s(s(s(elem!1))))),
% 1.84/2.06 inference(unit_resolution,[status(thm)],[827, 2722, 2715])).
% 1.84/2.06 tff(2724,plain,
% 1.84/2.06 (s(s(s(s(elem!1)))) = s(s(elem!1))),
% 1.84/2.06 inference(symmetry,[status(thm)],[2723])).
% 1.84/2.06 tff(2725,plain,
% 1.84/2.06 (r(s(elem!1), s(s(s(s(elem!1))))) <=> r(s(elem!1), s(s(elem!1)))),
% 1.84/2.06 inference(monotonicity,[status(thm)],[2724])).
% 1.84/2.06 tff(2726,plain,
% 1.84/2.06 (r(s(elem!1), s(s(elem!1))) <=> r(s(elem!1), s(s(s(s(elem!1)))))),
% 1.84/2.06 inference(symmetry,[status(thm)],[2725])).
% 1.84/2.06 tff(2727,plain,
% 1.84/2.06 ((s(s(elem!1)) = s(elem!1)) <=> (s(elem!1) = s(s(elem!1)))),
% 1.84/2.06 inference(symmetry,[status(thm)],[1186])).
% 1.84/2.06 tff(2728,plain,
% 1.84/2.06 (s(elem!1) = s(s(s(elem!1)))),
% 1.84/2.06 inference(symmetry,[status(thm)],[2709])).
% 1.84/2.06 tff(2729,plain,
% 1.84/2.06 ((s(s(elem!1)) = s(elem!1)) <=> (s(s(s(s(elem!1)))) = s(s(s(elem!1))))),
% 1.84/2.06 inference(monotonicity,[status(thm)],[2723, 2728])).
% 1.84/2.06 tff(2730,plain,
% 1.84/2.06 ((s(s(elem!1)) = s(elem!1)) <=> (s(s(s(elem!1))) = s(s(s(s(elem!1)))))),
% 1.84/2.06 inference(transitivity,[status(thm)],[2729, 1191])).
% 1.84/2.06 tff(2731,plain,
% 1.84/2.06 ((s(s(s(elem!1))) = s(s(s(s(elem!1))))) <=> (s(s(elem!1)) = s(elem!1))),
% 1.84/2.06 inference(symmetry,[status(thm)],[2730])).
% 1.84/2.06 tff(2732,plain,
% 1.84/2.06 ((s(s(s(elem!1))) = s(s(s(s(elem!1))))) <=> (s(elem!1) = s(s(elem!1)))),
% 1.84/2.06 inference(transitivity,[status(thm)],[2731, 2727])).
% 1.84/2.06 tff(2733,plain,
% 1.84/2.06 ((~(s(s(s(elem!1))) = s(s(s(s(elem!1)))))) <=> (~(s(elem!1) = s(s(elem!1))))),
% 1.84/2.06 inference(monotonicity,[status(thm)],[2732])).
% 1.84/2.06 tff(2734,plain,
% 1.84/2.06 (~(s(elem!1) = s(s(elem!1)))),
% 1.84/2.06 inference(modus_ponens,[status(thm)],[361, 2733])).
% 1.84/2.06 tff(2735,plain,
% 1.84/2.06 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(elem!1)), z)) | (~r(s(s(z)), s(s(elem!1)))) | (~r(s(s(elem!1)), s(s(z)))) | (~r(z, s(s(z)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(elem!1)), z)) | (~r(s(s(z)), s(s(elem!1)))) | (~r(s(s(elem!1)), s(s(z)))) | (~r(z, s(s(z)))))),
% 1.84/2.06 inference(rewrite,[status(thm)],[])).
% 1.84/2.06 tff(2736,plain,
% 1.84/2.07 (((~r(s(s(z)), s(s(elem!1)))) | (~r(z, s(s(z)))) | (~r(s(s(elem!1)), s(s(z)))) | (~r(s(s(elem!1)), z))) <=> ((~r(s(s(elem!1)), z)) | (~r(s(s(z)), s(s(elem!1)))) | (~r(s(s(elem!1)), s(s(z)))) | (~r(z, s(s(z)))))),
% 1.84/2.07 inference(rewrite,[status(thm)],[])).
% 1.84/2.07 tff(2737,plain,
% 1.84/2.07 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(z)), s(s(elem!1)))) | (~r(z, s(s(z)))) | (~r(s(s(elem!1)), s(s(z)))) | (~r(s(s(elem!1)), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(elem!1)), z)) | (~r(s(s(z)), s(s(elem!1)))) | (~r(s(s(elem!1)), s(s(z)))) | (~r(z, s(s(z))))))),
% 1.84/2.07 inference(monotonicity,[status(thm)],[2736])).
% 1.84/2.07 tff(2738,plain,
% 1.84/2.07 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(z)), s(s(elem!1)))) | (~r(z, s(s(z)))) | (~r(s(s(elem!1)), s(s(z)))) | (~r(s(s(elem!1)), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(elem!1)), z)) | (~r(s(s(z)), s(s(elem!1)))) | (~r(s(s(elem!1)), s(s(z)))) | (~r(z, s(s(z)))))),
% 1.84/2.07 inference(transitivity,[status(thm)],[2737, 2735])).
% 1.84/2.07 tff(2739,plain,
% 1.84/2.07 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(z)), s(s(elem!1)))) | (~r(z, s(s(z)))) | (~r(s(s(elem!1)), s(s(z)))) | (~r(s(s(elem!1)), z)))),
% 1.84/2.07 inference(quant_inst,[status(thm)],[])).
% 1.84/2.07 tff(2740,plain,
% 1.84/2.07 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(elem!1)), z)) | (~r(s(s(z)), s(s(elem!1)))) | (~r(s(s(elem!1)), s(s(z)))) | (~r(z, s(s(z))))),
% 1.84/2.07 inference(modus_ponens,[status(thm)],[2739, 2738])).
% 1.84/2.07 tff(2741,plain,
% 1.84/2.07 (~r(s(s(elem!1)), z)),
% 1.84/2.07 inference(unit_resolution,[status(thm)],[2740, 197, 2692, 155, 2684])).
% 1.84/2.07 tff(2742,plain,
% 1.84/2.07 (b(s(s(elem!1)), z)),
% 1.84/2.07 inference(unit_resolution,[status(thm)],[608, 2741])).
% 1.84/2.07 tff(2743,plain,
% 1.84/2.07 (~r(z, s(s(elem!1)))),
% 1.84/2.07 inference(unit_resolution,[status(thm)],[456, 376, 377, 310, 155, 323, 52])).
% 1.84/2.07 tff(2744,plain,
% 1.84/2.07 (b(z, s(s(elem!1)))),
% 1.84/2.07 inference(unit_resolution,[status(thm)],[1795, 2743])).
% 1.84/2.07 tff(2745,plain,
% 1.84/2.07 (b(s(s(s(elem!1))), z) <=> b(s(elem!1), z)),
% 1.84/2.07 inference(monotonicity,[status(thm)],[2709])).
% 1.84/2.07 tff(2746,plain,
% 1.84/2.07 (b(s(elem!1), z)),
% 1.84/2.07 inference(modus_ponens,[status(thm)],[2661, 2745])).
% 1.84/2.07 tff(2747,assumption,(b(s(elem!1), z)), introduced(assumption)).
% 1.84/2.07 tff(2748,assumption,(b(s(elem!1), s(s(elem!1)))), introduced(assumption)).
% 1.84/2.07 tff(2749,plain,
% 1.84/2.07 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), z)) | (~b(z, s(s(elem!1)))) | (~b(s(elem!1), s(s(elem!1)))) | (~b(s(s(elem!1)), z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(elem!1), z)) | (~b(z, s(s(elem!1)))) | (~b(s(elem!1), s(s(elem!1)))) | (~b(s(s(elem!1)), z)))),
% 1.84/2.07 inference(rewrite,[status(thm)],[])).
% 1.84/2.07 tff(2750,plain,
% 1.84/2.07 (((~b(z, s(s(elem!1)))) | (~b(s(elem!1), s(s(elem!1)))) | (~b(s(s(elem!1)), z)) | (~b(z, s(s(elem!1)))) | (~b(s(elem!1), s(s(elem!1)))) | (~b(s(elem!1), z))) <=> ((~b(s(elem!1), z)) | (~b(z, s(s(elem!1)))) | (~b(s(elem!1), s(s(elem!1)))) | (~b(s(s(elem!1)), z)))),
% 1.84/2.07 inference(rewrite,[status(thm)],[])).
% 1.84/2.07 tff(2751,plain,
% 1.84/2.07 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(elem!1)))) | (~b(s(elem!1), s(s(elem!1)))) | (~b(s(s(elem!1)), z)) | (~b(z, s(s(elem!1)))) | (~b(s(elem!1), s(s(elem!1)))) | (~b(s(elem!1), z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), z)) | (~b(z, s(s(elem!1)))) | (~b(s(elem!1), s(s(elem!1)))) | (~b(s(s(elem!1)), z))))),
% 1.84/2.07 inference(monotonicity,[status(thm)],[2750])).
% 1.84/2.07 tff(2752,plain,
% 1.84/2.07 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(elem!1)))) | (~b(s(elem!1), s(s(elem!1)))) | (~b(s(s(elem!1)), z)) | (~b(z, s(s(elem!1)))) | (~b(s(elem!1), s(s(elem!1)))) | (~b(s(elem!1), z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(elem!1), z)) | (~b(z, s(s(elem!1)))) | (~b(s(elem!1), s(s(elem!1)))) | (~b(s(s(elem!1)), z)))),
% 1.84/2.07 inference(transitivity,[status(thm)],[2751, 2749])).
% 1.84/2.07 tff(2753,plain,
% 1.84/2.07 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(elem!1)))) | (~b(s(elem!1), s(s(elem!1)))) | (~b(s(s(elem!1)), z)) | (~b(z, s(s(elem!1)))) | (~b(s(elem!1), s(s(elem!1)))) | (~b(s(elem!1), z)))),
% 1.84/2.07 inference(quant_inst,[status(thm)],[])).
% 1.84/2.07 tff(2754,plain,
% 1.84/2.07 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(elem!1), z)) | (~b(z, s(s(elem!1)))) | (~b(s(elem!1), s(s(elem!1)))) | (~b(s(s(elem!1)), z))),
% 1.84/2.07 inference(modus_ponens,[status(thm)],[2753, 2752])).
% 1.84/2.07 tff(2755,plain,
% 1.84/2.07 ($false),
% 1.84/2.07 inference(unit_resolution,[status(thm)],[2754, 166, 2748, 2747, 1820, 592])).
% 1.84/2.07 tff(2756,plain,((~b(s(s(elem!1)), z)) | (~b(s(elem!1), s(s(elem!1)))) | (~b(s(elem!1), z)) | (~b(z, s(s(elem!1))))), inference(lemma,lemma(discharge,[]))).
% 1.84/2.07 tff(2757,plain,
% 1.84/2.07 (~b(s(elem!1), s(s(elem!1)))),
% 1.84/2.07 inference(unit_resolution,[status(thm)],[2756, 2746, 2744, 2742])).
% 1.84/2.07 tff(2758,plain,
% 1.84/2.07 (((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((s(elem!1) = s(s(elem!1))) | b(s(elem!1), s(s(elem!1))) | r(s(elem!1), s(s(elem!1))))) <=> ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (s(elem!1) = s(s(elem!1))) | b(s(elem!1), s(s(elem!1))) | r(s(elem!1), s(s(elem!1))))),
% 1.84/2.07 inference(rewrite,[status(thm)],[])).
% 1.84/2.07 tff(2759,plain,
% 1.84/2.07 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((s(elem!1) = s(s(elem!1))) | b(s(elem!1), s(s(elem!1))) | r(s(elem!1), s(s(elem!1))))),
% 1.84/2.07 inference(quant_inst,[status(thm)],[])).
% 1.84/2.07 tff(2760,plain,
% 1.84/2.07 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (s(elem!1) = s(s(elem!1))) | b(s(elem!1), s(s(elem!1))) | r(s(elem!1), s(s(elem!1)))),
% 1.84/2.07 inference(modus_ponens,[status(thm)],[2759, 2758])).
% 1.84/2.07 tff(2761,plain,
% 1.84/2.07 ((s(elem!1) = s(s(elem!1))) | b(s(elem!1), s(s(elem!1))) | r(s(elem!1), s(s(elem!1)))),
% 1.84/2.07 inference(unit_resolution,[status(thm)],[2760, 79])).
% 1.84/2.07 tff(2762,plain,
% 1.84/2.07 (r(s(elem!1), s(s(elem!1)))),
% 1.84/2.07 inference(unit_resolution,[status(thm)],[2761, 2757, 2734])).
% 1.84/2.07 tff(2763,plain,
% 1.84/2.07 (r(s(elem!1), s(s(s(s(elem!1)))))),
% 1.84/2.07 inference(modus_ponens,[status(thm)],[2762, 2726])).
% 1.84/2.07 tff(2764,plain,
% 1.84/2.07 (r(s(s(z)), s(s(elem!1))) <=> r(s(s(z)), s(s(s(s(elem!1)))))),
% 1.84/2.07 inference(monotonicity,[status(thm)],[2723])).
% 1.84/2.07 tff(2765,plain,
% 1.84/2.07 (r(s(s(z)), s(s(s(s(elem!1)))))),
% 1.84/2.07 inference(modus_ponens,[status(thm)],[2684, 2764])).
% 1.84/2.07 tff(2766,plain,
% 1.84/2.07 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(z)), s(elem!1))) | (~r(s(s(s(s(elem!1)))), s(s(z)))) | (~r(s(s(z)), s(s(s(s(elem!1)))))) | (~r(s(elem!1), s(s(s(s(elem!1)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(z)), s(elem!1))) | (~r(s(s(s(s(elem!1)))), s(s(z)))) | (~r(s(s(z)), s(s(s(s(elem!1)))))) | (~r(s(elem!1), s(s(s(s(elem!1)))))))),
% 1.84/2.07 inference(rewrite,[status(thm)],[])).
% 1.84/2.07 tff(2767,plain,
% 1.84/2.07 (((~r(s(s(s(s(elem!1)))), s(s(z)))) | (~r(s(elem!1), s(s(s(s(elem!1)))))) | (~r(s(s(z)), s(s(s(s(elem!1)))))) | (~r(s(s(z)), s(elem!1)))) <=> ((~r(s(s(z)), s(elem!1))) | (~r(s(s(s(s(elem!1)))), s(s(z)))) | (~r(s(s(z)), s(s(s(s(elem!1)))))) | (~r(s(elem!1), s(s(s(s(elem!1)))))))),
% 1.84/2.07 inference(rewrite,[status(thm)],[])).
% 1.84/2.07 tff(2768,plain,
% 1.84/2.07 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(elem!1)))), s(s(z)))) | (~r(s(elem!1), s(s(s(s(elem!1)))))) | (~r(s(s(z)), s(s(s(s(elem!1)))))) | (~r(s(s(z)), s(elem!1))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(z)), s(elem!1))) | (~r(s(s(s(s(elem!1)))), s(s(z)))) | (~r(s(s(z)), s(s(s(s(elem!1)))))) | (~r(s(elem!1), s(s(s(s(elem!1))))))))),
% 1.84/2.07 inference(monotonicity,[status(thm)],[2767])).
% 1.84/2.07 tff(2769,plain,
% 1.84/2.07 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(elem!1)))), s(s(z)))) | (~r(s(elem!1), s(s(s(s(elem!1)))))) | (~r(s(s(z)), s(s(s(s(elem!1)))))) | (~r(s(s(z)), s(elem!1))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(z)), s(elem!1))) | (~r(s(s(s(s(elem!1)))), s(s(z)))) | (~r(s(s(z)), s(s(s(s(elem!1)))))) | (~r(s(elem!1), s(s(s(s(elem!1)))))))),
% 1.84/2.07 inference(transitivity,[status(thm)],[2768, 2766])).
% 1.84/2.07 tff(2770,plain,
% 1.84/2.07 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(elem!1)))), s(s(z)))) | (~r(s(elem!1), s(s(s(s(elem!1)))))) | (~r(s(s(z)), s(s(s(s(elem!1)))))) | (~r(s(s(z)), s(elem!1))))),
% 1.84/2.07 inference(quant_inst,[status(thm)],[])).
% 1.84/2.07 tff(2771,plain,
% 1.84/2.07 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(z)), s(elem!1))) | (~r(s(s(s(s(elem!1)))), s(s(z)))) | (~r(s(s(z)), s(s(s(s(elem!1)))))) | (~r(s(elem!1), s(s(s(s(elem!1))))))),
% 1.84/2.07 inference(modus_ponens,[status(thm)],[2770, 2769])).
% 1.84/2.07 tff(2772,plain,
% 1.84/2.07 ((~r(s(s(z)), s(elem!1))) | (~r(s(elem!1), s(s(s(s(elem!1))))))),
% 1.84/2.07 inference(unit_resolution,[status(thm)],[2771, 197, 2700, 2765])).
% 1.84/2.07 tff(2773,plain,
% 1.84/2.07 (~r(s(s(z)), s(elem!1))),
% 1.84/2.07 inference(unit_resolution,[status(thm)],[2772, 2763])).
% 1.84/2.07 tff(2774,plain,
% 1.84/2.07 (((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((s(s(z)) = s(elem!1)) | b(s(s(z)), s(elem!1)) | r(s(s(z)), s(elem!1)))) <=> ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (s(s(z)) = s(elem!1)) | b(s(s(z)), s(elem!1)) | r(s(s(z)), s(elem!1)))),
% 1.84/2.07 inference(rewrite,[status(thm)],[])).
% 1.84/2.07 tff(2775,plain,
% 1.84/2.07 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((s(s(z)) = s(elem!1)) | b(s(s(z)), s(elem!1)) | r(s(s(z)), s(elem!1)))),
% 1.84/2.07 inference(quant_inst,[status(thm)],[])).
% 1.84/2.07 tff(2776,plain,
% 1.84/2.07 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (s(s(z)) = s(elem!1)) | b(s(s(z)), s(elem!1)) | r(s(s(z)), s(elem!1))),
% 1.84/2.07 inference(modus_ponens,[status(thm)],[2775, 2774])).
% 1.84/2.07 tff(2777,plain,
% 1.84/2.07 ((s(s(z)) = s(elem!1)) | b(s(s(z)), s(elem!1)) | r(s(s(z)), s(elem!1))),
% 1.84/2.07 inference(unit_resolution,[status(thm)],[2776, 79])).
% 1.84/2.07 tff(2778,plain,
% 1.84/2.07 (b(s(s(z)), s(elem!1))),
% 1.84/2.07 inference(unit_resolution,[status(thm)],[2777, 2773, 2714])).
% 1.84/2.07 tff(2779,plain,
% 1.84/2.07 (b(z, s(s(s(s(elem!1))))) <=> b(z, s(s(elem!1)))),
% 1.84/2.07 inference(monotonicity,[status(thm)],[2724])).
% 1.84/2.07 tff(2780,plain,
% 1.84/2.07 (b(z, s(s(elem!1))) <=> b(z, s(s(s(s(elem!1)))))),
% 1.84/2.07 inference(symmetry,[status(thm)],[2779])).
% 1.84/2.07 tff(2781,plain,
% 1.84/2.07 (b(z, s(s(s(s(elem!1)))))),
% 1.84/2.07 inference(modus_ponens,[status(thm)],[2744, 2780])).
% 1.84/2.07 tff(2782,plain,
% 1.84/2.07 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), z)) | (~b(s(s(z)), z)) | (~b(s(s(z)), s(z))) | (~b(s(s(s(s(elem!1)))), s(z))) | (~b(s(s(z)), s(elem!1))) | (~b(z, s(s(s(s(elem!1)))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(elem!1), z)) | (~b(s(s(z)), z)) | (~b(s(s(z)), s(z))) | (~b(s(s(s(s(elem!1)))), s(z))) | (~b(s(s(z)), s(elem!1))) | (~b(z, s(s(s(s(elem!1)))))))),
% 1.84/2.07 inference(rewrite,[status(thm)],[])).
% 1.84/2.07 tff(2783,plain,
% 1.84/2.07 (((~b(s(s(s(s(elem!1)))), s(z))) | (~b(s(s(z)), s(z))) | (~b(z, s(s(s(s(elem!1)))))) | (~b(s(elem!1), z)) | (~b(s(s(z)), z)) | (~b(s(s(z)), s(elem!1)))) <=> ((~b(s(elem!1), z)) | (~b(s(s(z)), z)) | (~b(s(s(z)), s(z))) | (~b(s(s(s(s(elem!1)))), s(z))) | (~b(s(s(z)), s(elem!1))) | (~b(z, s(s(s(s(elem!1)))))))),
% 1.84/2.07 inference(rewrite,[status(thm)],[])).
% 1.84/2.07 tff(2784,plain,
% 1.84/2.07 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(elem!1)))), s(z))) | (~b(s(s(z)), s(z))) | (~b(z, s(s(s(s(elem!1)))))) | (~b(s(elem!1), z)) | (~b(s(s(z)), z)) | (~b(s(s(z)), s(elem!1))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), z)) | (~b(s(s(z)), z)) | (~b(s(s(z)), s(z))) | (~b(s(s(s(s(elem!1)))), s(z))) | (~b(s(s(z)), s(elem!1))) | (~b(z, s(s(s(s(elem!1))))))))),
% 1.84/2.07 inference(monotonicity,[status(thm)],[2783])).
% 1.84/2.07 tff(2785,plain,
% 1.84/2.07 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(elem!1)))), s(z))) | (~b(s(s(z)), s(z))) | (~b(z, s(s(s(s(elem!1)))))) | (~b(s(elem!1), z)) | (~b(s(s(z)), z)) | (~b(s(s(z)), s(elem!1))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(elem!1), z)) | (~b(s(s(z)), z)) | (~b(s(s(z)), s(z))) | (~b(s(s(s(s(elem!1)))), s(z))) | (~b(s(s(z)), s(elem!1))) | (~b(z, s(s(s(s(elem!1)))))))),
% 1.84/2.07 inference(transitivity,[status(thm)],[2784, 2782])).
% 1.84/2.07 tff(2786,plain,
% 1.84/2.07 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(elem!1)))), s(z))) | (~b(s(s(z)), s(z))) | (~b(z, s(s(s(s(elem!1)))))) | (~b(s(elem!1), z)) | (~b(s(s(z)), z)) | (~b(s(s(z)), s(elem!1))))),
% 1.84/2.07 inference(quant_inst,[status(thm)],[])).
% 1.84/2.07 tff(2787,plain,
% 1.84/2.07 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(elem!1), z)) | (~b(s(s(z)), z)) | (~b(s(s(z)), s(z))) | (~b(s(s(s(s(elem!1)))), s(z))) | (~b(s(s(z)), s(elem!1))) | (~b(z, s(s(s(s(elem!1))))))),
% 1.84/2.07 inference(modus_ponens,[status(thm)],[2786, 2785])).
% 1.84/2.07 tff(2788,plain,
% 1.84/2.07 ((~b(s(s(z)), z)) | (~b(s(s(z)), s(elem!1)))),
% 1.84/2.07 inference(unit_resolution,[status(thm)],[2787, 166, 2746, 2682, 2671, 2781])).
% 1.84/2.07 tff(2789,plain,
% 1.84/2.07 (~b(s(s(z)), z)),
% 1.84/2.07 inference(unit_resolution,[status(thm)],[2788, 2778])).
% 1.84/2.07 tff(2790,plain,
% 1.84/2.07 (r(s(s(z)), z)),
% 1.84/2.07 inference(unit_resolution,[status(thm)],[186, 2789])).
% 1.84/2.07 tff(2791,plain,
% 1.84/2.07 (b(s(s(elem!1)), z) <=> b(s(s(s(s(elem!1)))), z)),
% 1.84/2.07 inference(monotonicity,[status(thm)],[2723])).
% 1.84/2.07 tff(2792,plain,
% 1.84/2.07 (b(s(s(s(s(elem!1)))), z)),
% 1.84/2.07 inference(modus_ponens,[status(thm)],[2742, 2791])).
% 1.84/2.07 tff(2793,plain,
% 1.84/2.07 (b(z, s(s(s(elem!1)))) <=> b(z, s(elem!1))),
% 1.84/2.07 inference(monotonicity,[status(thm)],[2709])).
% 1.84/2.07 tff(2794,plain,
% 1.84/2.07 (b(z, s(elem!1))),
% 1.84/2.07 inference(modus_ponens,[status(thm)],[2615, 2793])).
% 1.84/2.07 tff(2795,plain,
% 1.84/2.07 (r(s(s(s(s(elem!1)))), s(s(s(elem!1)))) <=> r(s(s(s(s(elem!1)))), s(elem!1))),
% 1.84/2.07 inference(monotonicity,[status(thm)],[2709])).
% 1.84/2.07 tff(2796,plain,
% 1.84/2.07 (r(s(s(elem!1)), s(s(s(elem!1)))) <=> r(s(s(s(s(elem!1)))), s(s(s(elem!1))))),
% 1.84/2.07 inference(monotonicity,[status(thm)],[2723])).
% 1.84/2.07 tff(2797,plain,
% 1.84/2.07 (r(s(s(s(s(elem!1)))), s(s(s(elem!1))))),
% 1.84/2.07 inference(modus_ponens,[status(thm)],[377, 2796])).
% 1.84/2.07 tff(2798,plain,
% 1.84/2.07 (r(s(s(s(s(elem!1)))), s(elem!1))),
% 1.84/2.07 inference(modus_ponens,[status(thm)],[2797, 2795])).
% 1.84/2.07 tff(2799,plain,
% 1.84/2.07 (r(s(s(s(elem!1))), s(z)) <=> r(s(elem!1), s(z))),
% 1.84/2.07 inference(monotonicity,[status(thm)],[2709])).
% 1.84/2.07 tff(2800,plain,
% 1.84/2.07 (r(s(elem!1), s(z))),
% 1.84/2.07 inference(modus_ponens,[status(thm)],[350, 2799])).
% 1.84/2.07 tff(2801,plain,
% 1.84/2.07 (s(elem!1) = s(s(s(elem!1)))),
% 1.84/2.07 inference(symmetry,[status(thm)],[1177])).
% 1.84/2.07 tff(2802,plain,
% 1.84/2.07 (inj_0(s(elem!1)) = inj_0(s(s(s(elem!1))))),
% 1.84/2.07 inference(monotonicity,[status(thm)],[2801])).
% 1.84/2.07 tff(2803,plain,
% 1.84/2.07 (inj_0(s(s(s(elem!1)))) = inj_0(s(elem!1))),
% 1.84/2.07 inference(symmetry,[status(thm)],[2802])).
% 1.84/2.07 tff(2804,plain,
% 1.84/2.07 (s(s(s(s(elem!1)))) = elem!1),
% 1.84/2.07 inference(transitivity,[status(thm)],[1154, 105, 2803, 20])).
% 1.84/2.07 tff(2805,plain,
% 1.84/2.07 (r(s(s(s(z))), s(s(s(s(elem!1))))) <=> r(s(s(s(z))), elem!1)),
% 1.84/2.07 inference(monotonicity,[status(thm)],[2804])).
% 1.84/2.07 tff(2806,plain,
% 1.84/2.07 (r(s(s(s(z))), elem!1) <=> r(s(s(s(z))), s(s(s(s(elem!1)))))),
% 1.84/2.07 inference(symmetry,[status(thm)],[2805])).
% 1.84/2.07 tff(2807,plain,
% 1.84/2.07 (~(s(s(s(z))) = elem!1)),
% 1.84/2.07 inference(unit_resolution,[status(thm)],[1556, 1177])).
% 1.84/2.07 tff(2808,plain,
% 1.84/2.07 (elem!1 = s(s(elem!1))),
% 1.84/2.07 inference(transitivity,[status(thm)],[1170, 2802, 104])).
% 1.84/2.07 tff(2809,plain,
% 1.84/2.07 (b(s(s(s(z))), elem!1) <=> b(s(s(s(z))), s(s(elem!1)))),
% 1.84/2.07 inference(monotonicity,[status(thm)],[2808])).
% 1.84/2.07 tff(2810,plain,
% 1.84/2.07 (b(s(s(s(z))), s(s(elem!1))) <=> b(s(s(s(z))), elem!1)),
% 1.84/2.07 inference(symmetry,[status(thm)],[2809])).
% 1.84/2.07 tff(2811,plain,
% 1.84/2.07 (b(s(s(s(z))), s(s(s(s(elem!1))))) <=> b(s(s(s(z))), s(s(elem!1)))),
% 1.84/2.07 inference(monotonicity,[status(thm)],[1154])).
% 1.84/2.07 tff(2812,plain,
% 1.84/2.07 (b(s(s(s(z))), s(s(s(s(elem!1))))) <=> b(s(s(s(z))), elem!1)),
% 1.84/2.07 inference(transitivity,[status(thm)],[2811, 2810])).
% 1.84/2.07 tff(2813,plain,
% 1.84/2.07 ((~b(s(s(s(z))), s(s(s(s(elem!1)))))) <=> (~b(s(s(s(z))), elem!1))),
% 1.84/2.07 inference(monotonicity,[status(thm)],[2812])).
% 1.84/2.07 tff(2814,assumption,(b(z, s(elem!1))), introduced(assumption)).
% 1.84/2.07 tff(2815,plain,
% 1.84/2.07 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), z)) | (~b(z, s(elem!1))) | (~b(s(s(s(z))), z)) | (~b(s(s(s(s(elem!1)))), z)) | (~b(s(s(s(z))), s(s(s(s(elem!1)))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(elem!1), z)) | (~b(z, s(elem!1))) | (~b(s(s(s(z))), z)) | (~b(s(s(s(s(elem!1)))), z)) | (~b(s(s(s(z))), s(s(s(s(elem!1)))))))),
% 1.84/2.07 inference(rewrite,[status(thm)],[])).
% 1.84/2.07 tff(2816,plain,
% 1.84/2.07 (((~b(s(elem!1), z)) | (~b(s(s(s(z))), z)) | (~b(z, s(elem!1))) | (~b(s(s(s(s(elem!1)))), z)) | (~b(s(s(s(z))), z)) | (~b(s(s(s(z))), s(s(s(s(elem!1))))))) <=> ((~b(s(elem!1), z)) | (~b(z, s(elem!1))) | (~b(s(s(s(z))), z)) | (~b(s(s(s(s(elem!1)))), z)) | (~b(s(s(s(z))), s(s(s(s(elem!1)))))))),
% 1.84/2.07 inference(rewrite,[status(thm)],[])).
% 1.84/2.07 tff(2817,plain,
% 1.84/2.07 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), z)) | (~b(s(s(s(z))), z)) | (~b(z, s(elem!1))) | (~b(s(s(s(s(elem!1)))), z)) | (~b(s(s(s(z))), z)) | (~b(s(s(s(z))), s(s(s(s(elem!1)))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), z)) | (~b(z, s(elem!1))) | (~b(s(s(s(z))), z)) | (~b(s(s(s(s(elem!1)))), z)) | (~b(s(s(s(z))), s(s(s(s(elem!1))))))))),
% 1.84/2.07 inference(monotonicity,[status(thm)],[2816])).
% 1.84/2.07 tff(2818,plain,
% 1.84/2.07 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), z)) | (~b(s(s(s(z))), z)) | (~b(z, s(elem!1))) | (~b(s(s(s(s(elem!1)))), z)) | (~b(s(s(s(z))), z)) | (~b(s(s(s(z))), s(s(s(s(elem!1)))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(elem!1), z)) | (~b(z, s(elem!1))) | (~b(s(s(s(z))), z)) | (~b(s(s(s(s(elem!1)))), z)) | (~b(s(s(s(z))), s(s(s(s(elem!1)))))))),
% 1.84/2.07 inference(transitivity,[status(thm)],[2817, 2815])).
% 1.84/2.07 tff(2819,plain,
% 1.84/2.07 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), z)) | (~b(s(s(s(z))), z)) | (~b(z, s(elem!1))) | (~b(s(s(s(s(elem!1)))), z)) | (~b(s(s(s(z))), z)) | (~b(s(s(s(z))), s(s(s(s(elem!1)))))))),
% 1.84/2.07 inference(quant_inst,[status(thm)],[])).
% 1.84/2.07 tff(2820,plain,
% 1.84/2.07 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(elem!1), z)) | (~b(z, s(elem!1))) | (~b(s(s(s(z))), z)) | (~b(s(s(s(s(elem!1)))), z)) | (~b(s(s(s(z))), s(s(s(s(elem!1))))))),
% 1.84/2.08 inference(modus_ponens,[status(thm)],[2819, 2818])).
% 1.84/2.08 tff(2821,plain,
% 1.84/2.08 (~b(s(s(s(z))), s(s(s(s(elem!1)))))),
% 1.84/2.08 inference(unit_resolution,[status(thm)],[2820, 166, 2747, 2814, 1699, 1326])).
% 1.84/2.08 tff(2822,plain,
% 1.84/2.08 (~b(s(s(s(z))), elem!1)),
% 1.84/2.08 inference(modus_ponens,[status(thm)],[2821, 2813])).
% 1.84/2.08 tff(2823,plain,
% 1.84/2.08 (((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((s(s(s(z))) = elem!1) | b(s(s(s(z))), elem!1) | r(s(s(s(z))), elem!1))) <=> ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (s(s(s(z))) = elem!1) | b(s(s(s(z))), elem!1) | r(s(s(s(z))), elem!1))),
% 1.84/2.08 inference(rewrite,[status(thm)],[])).
% 1.84/2.08 tff(2824,plain,
% 1.84/2.08 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((s(s(s(z))) = elem!1) | b(s(s(s(z))), elem!1) | r(s(s(s(z))), elem!1))),
% 1.84/2.08 inference(quant_inst,[status(thm)],[])).
% 1.84/2.08 tff(2825,plain,
% 1.84/2.08 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (s(s(s(z))) = elem!1) | b(s(s(s(z))), elem!1) | r(s(s(s(z))), elem!1)),
% 1.84/2.08 inference(modus_ponens,[status(thm)],[2824, 2823])).
% 1.84/2.08 tff(2826,plain,
% 1.84/2.08 ((s(s(s(z))) = elem!1) | b(s(s(s(z))), elem!1) | r(s(s(s(z))), elem!1)),
% 1.84/2.08 inference(unit_resolution,[status(thm)],[2825, 79])).
% 1.84/2.08 tff(2827,plain,
% 1.84/2.08 (r(s(s(s(z))), elem!1)),
% 1.84/2.08 inference(unit_resolution,[status(thm)],[2826, 2822, 2807])).
% 1.84/2.08 tff(2828,plain,
% 1.84/2.08 (r(s(s(s(z))), s(s(s(s(elem!1)))))),
% 1.84/2.08 inference(modus_ponens,[status(thm)],[2827, 2806])).
% 1.84/2.08 tff(2829,plain,
% 1.84/2.08 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), z)) | (~b(z, s(elem!1))) | (~b(s(s(s(z))), z)) | (~b(s(s(s(z))), s(elem!1))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(elem!1), z)) | (~b(z, s(elem!1))) | (~b(s(s(s(z))), z)) | (~b(s(s(s(z))), s(elem!1))))),
% 1.84/2.08 inference(rewrite,[status(thm)],[])).
% 1.84/2.08 tff(2830,plain,
% 1.84/2.08 (((~b(s(elem!1), z)) | (~b(s(s(s(z))), z)) | (~b(z, s(elem!1))) | (~b(s(elem!1), z)) | (~b(s(s(s(z))), z)) | (~b(s(s(s(z))), s(elem!1)))) <=> ((~b(s(elem!1), z)) | (~b(z, s(elem!1))) | (~b(s(s(s(z))), z)) | (~b(s(s(s(z))), s(elem!1))))),
% 1.84/2.08 inference(rewrite,[status(thm)],[])).
% 1.84/2.08 tff(2831,plain,
% 1.84/2.08 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), z)) | (~b(s(s(s(z))), z)) | (~b(z, s(elem!1))) | (~b(s(elem!1), z)) | (~b(s(s(s(z))), z)) | (~b(s(s(s(z))), s(elem!1))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), z)) | (~b(z, s(elem!1))) | (~b(s(s(s(z))), z)) | (~b(s(s(s(z))), s(elem!1)))))),
% 1.84/2.08 inference(monotonicity,[status(thm)],[2830])).
% 1.84/2.08 tff(2832,plain,
% 1.84/2.08 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), z)) | (~b(s(s(s(z))), z)) | (~b(z, s(elem!1))) | (~b(s(elem!1), z)) | (~b(s(s(s(z))), z)) | (~b(s(s(s(z))), s(elem!1))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(elem!1), z)) | (~b(z, s(elem!1))) | (~b(s(s(s(z))), z)) | (~b(s(s(s(z))), s(elem!1))))),
% 1.84/2.08 inference(transitivity,[status(thm)],[2831, 2829])).
% 1.84/2.08 tff(2833,plain,
% 1.84/2.08 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), z)) | (~b(s(s(s(z))), z)) | (~b(z, s(elem!1))) | (~b(s(elem!1), z)) | (~b(s(s(s(z))), z)) | (~b(s(s(s(z))), s(elem!1))))),
% 1.84/2.08 inference(quant_inst,[status(thm)],[])).
% 1.84/2.08 tff(2834,plain,
% 1.84/2.08 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(elem!1), z)) | (~b(z, s(elem!1))) | (~b(s(s(s(z))), z)) | (~b(s(s(s(z))), s(elem!1)))),
% 1.84/2.08 inference(modus_ponens,[status(thm)],[2833, 2832])).
% 1.84/2.08 tff(2835,plain,
% 1.84/2.08 (~b(s(s(s(z))), s(elem!1))),
% 1.84/2.08 inference(unit_resolution,[status(thm)],[2834, 166, 2747, 2814, 1699])).
% 1.84/2.08 tff(2836,assumption,(s(s(s(z))) = s(elem!1)), introduced(assumption)).
% 1.84/2.08 tff(2837,plain,
% 1.84/2.08 (inj_0(s(s(s(z)))) = inj_0(s(elem!1))),
% 1.84/2.08 inference(monotonicity,[status(thm)],[2836])).
% 1.84/2.08 tff(2838,plain,
% 1.84/2.08 (inj_0(s(elem!1)) = inj_0(s(s(s(z))))),
% 1.84/2.08 inference(symmetry,[status(thm)],[2837])).
% 1.84/2.08 tff(2839,plain,
% 1.84/2.08 (s(s(s(s(elem!1)))) = s(s(z))),
% 1.84/2.08 inference(transitivity,[status(thm)],[1154, 105, 2803, 2838, 134])).
% 1.84/2.08 tff(2840,plain,
% 1.84/2.08 ($false),
% 1.84/2.08 inference(unit_resolution,[status(thm)],[733, 2839])).
% 1.84/2.08 tff(2841,plain,((~(s(s(s(z))) = s(elem!1))) | (~(s(s(elem!1)) = s(s(s(s(elem!1)))))) | (~(s(s(s(elem!1))) = s(elem!1)))), inference(lemma,lemma(discharge,[]))).
% 1.84/2.08 tff(2842,plain,
% 1.84/2.08 (~(s(s(s(z))) = s(elem!1))),
% 1.84/2.08 inference(unit_resolution,[status(thm)],[2841, 1153, 1177])).
% 1.84/2.08 tff(2843,plain,
% 1.84/2.08 (((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((s(s(s(z))) = s(elem!1)) | b(s(s(s(z))), s(elem!1)) | r(s(s(s(z))), s(elem!1)))) <=> ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (s(s(s(z))) = s(elem!1)) | b(s(s(s(z))), s(elem!1)) | r(s(s(s(z))), s(elem!1)))),
% 1.84/2.08 inference(rewrite,[status(thm)],[])).
% 1.84/2.08 tff(2844,plain,
% 1.84/2.08 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((s(s(s(z))) = s(elem!1)) | b(s(s(s(z))), s(elem!1)) | r(s(s(s(z))), s(elem!1)))),
% 1.84/2.08 inference(quant_inst,[status(thm)],[])).
% 1.84/2.08 tff(2845,plain,
% 1.84/2.08 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (s(s(s(z))) = s(elem!1)) | b(s(s(s(z))), s(elem!1)) | r(s(s(s(z))), s(elem!1))),
% 1.84/2.08 inference(modus_ponens,[status(thm)],[2844, 2843])).
% 1.84/2.08 tff(2846,plain,
% 1.84/2.08 (r(s(s(s(z))), s(elem!1))),
% 1.84/2.08 inference(unit_resolution,[status(thm)],[2845, 79, 2842, 2835])).
% 1.84/2.08 tff(2847,assumption,(r(s(s(s(s(elem!1)))), s(elem!1))), introduced(assumption)).
% 1.84/2.08 tff(2848,assumption,(r(s(elem!1), s(z))), introduced(assumption)).
% 1.84/2.08 tff(2849,plain,
% 1.84/2.08 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(elem!1), s(z))) | (~r(s(s(s(z))), s(s(s(s(elem!1)))))) | (~r(s(s(s(s(elem!1)))), s(elem!1))) | (~r(s(s(s(z))), s(elem!1))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(elem!1), s(z))) | (~r(s(s(s(z))), s(s(s(s(elem!1)))))) | (~r(s(s(s(s(elem!1)))), s(elem!1))) | (~r(s(s(s(z))), s(elem!1))))),
% 1.84/2.08 inference(rewrite,[status(thm)],[])).
% 1.84/2.08 tff(2850,plain,
% 1.84/2.08 (((~r(s(elem!1), s(z))) | (~r(s(s(s(s(elem!1)))), s(elem!1))) | (~r(s(s(s(z))), s(elem!1))) | (~r(s(s(s(z))), s(s(s(s(elem!1))))))) <=> ((~r(s(elem!1), s(z))) | (~r(s(s(s(z))), s(s(s(s(elem!1)))))) | (~r(s(s(s(s(elem!1)))), s(elem!1))) | (~r(s(s(s(z))), s(elem!1))))),
% 1.84/2.08 inference(rewrite,[status(thm)],[])).
% 1.84/2.08 tff(2851,plain,
% 1.84/2.08 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(elem!1), s(z))) | (~r(s(s(s(s(elem!1)))), s(elem!1))) | (~r(s(s(s(z))), s(elem!1))) | (~r(s(s(s(z))), s(s(s(s(elem!1)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(elem!1), s(z))) | (~r(s(s(s(z))), s(s(s(s(elem!1)))))) | (~r(s(s(s(s(elem!1)))), s(elem!1))) | (~r(s(s(s(z))), s(elem!1)))))),
% 1.84/2.08 inference(monotonicity,[status(thm)],[2850])).
% 1.84/2.08 tff(2852,plain,
% 1.84/2.08 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(elem!1), s(z))) | (~r(s(s(s(s(elem!1)))), s(elem!1))) | (~r(s(s(s(z))), s(elem!1))) | (~r(s(s(s(z))), s(s(s(s(elem!1)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(elem!1), s(z))) | (~r(s(s(s(z))), s(s(s(s(elem!1)))))) | (~r(s(s(s(s(elem!1)))), s(elem!1))) | (~r(s(s(s(z))), s(elem!1))))),
% 1.84/2.08 inference(transitivity,[status(thm)],[2851, 2849])).
% 1.84/2.08 tff(2853,plain,
% 1.84/2.08 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(elem!1), s(z))) | (~r(s(s(s(s(elem!1)))), s(elem!1))) | (~r(s(s(s(z))), s(elem!1))) | (~r(s(s(s(z))), s(s(s(s(elem!1)))))))),
% 1.84/2.08 inference(quant_inst,[status(thm)],[])).
% 1.84/2.08 tff(2854,plain,
% 1.84/2.08 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(elem!1), s(z))) | (~r(s(s(s(z))), s(s(s(s(elem!1)))))) | (~r(s(s(s(s(elem!1)))), s(elem!1))) | (~r(s(s(s(z))), s(elem!1)))),
% 1.84/2.08 inference(modus_ponens,[status(thm)],[2853, 2852])).
% 1.84/2.08 tff(2855,plain,
% 1.84/2.08 ($false),
% 1.84/2.08 inference(unit_resolution,[status(thm)],[2854, 197, 2848, 2847, 2846, 2828])).
% 1.84/2.08 tff(2856,plain,((~b(s(s(s(z))), z)) | (~r(s(elem!1), s(z))) | (~r(s(s(s(s(elem!1)))), s(elem!1))) | (~(s(s(elem!1)) = s(s(s(s(elem!1)))))) | (~(s(s(s(elem!1))) = s(elem!1))) | (~b(s(elem!1), z)) | (~b(z, s(elem!1))) | (~b(s(s(s(s(elem!1)))), z))), inference(lemma,lemma(discharge,[]))).
% 1.84/2.08 tff(2857,plain,
% 1.84/2.08 (~b(s(s(s(z))), z)),
% 1.84/2.08 inference(unit_resolution,[status(thm)],[2856, 2800, 2798, 2723, 2709, 2746, 2794, 2792])).
% 1.84/2.08 tff(2858,plain,
% 1.84/2.08 (r(s(s(s(z))), z)),
% 1.84/2.08 inference(unit_resolution,[status(thm)],[1713, 2857])).
% 1.84/2.08 tff(2859,plain,
% 1.84/2.08 (~r(s(s(z)), s(s(s(z))))),
% 1.84/2.08 inference(unit_resolution,[status(thm)],[1741, 2858, 2790, 155])).
% 1.84/2.08 tff(2860,plain,
% 1.84/2.08 (b(s(s(z)), s(s(s(z))))),
% 1.84/2.08 inference(unit_resolution,[status(thm)],[1730, 2859])).
% 1.84/2.08 tff(2861,plain,
% 1.84/2.08 (~r(s(z), s(s(z)))),
% 1.84/2.08 inference(unit_resolution,[status(thm)],[347, 2684, 97, 155])).
% 1.84/2.08 tff(2862,plain,
% 1.84/2.08 (b(s(z), s(s(z)))),
% 1.84/2.08 inference(unit_resolution,[status(thm)],[427, 2861])).
% 1.84/2.08 tff(2863,plain,
% 1.84/2.08 (~r(s(s(s(z))), s(s(z)))),
% 1.84/2.08 inference(unit_resolution,[status(thm)],[1717, 197, 155, 2790, 2858])).
% 1.84/2.08 tff(2864,plain,
% 1.84/2.08 (b(s(s(s(z))), s(s(z)))),
% 1.84/2.08 inference(unit_resolution,[status(thm)],[1010, 2863])).
% 1.84/2.08 tff(2865,plain,
% 1.84/2.08 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), z)) | (~r(z, s(s(z)))) | (~r(s(s(s(z))), z)) | (~r(s(z), s(s(s(z))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(z), z)) | (~r(z, s(s(z)))) | (~r(s(s(s(z))), z)) | (~r(s(z), s(s(s(z))))))),
% 1.84/2.08 inference(rewrite,[status(thm)],[])).
% 1.84/2.08 tff(2866,plain,
% 1.84/2.08 (((~r(z, s(s(z)))) | (~r(s(s(s(z))), z)) | (~r(s(z), z)) | (~r(s(z), s(s(s(z)))))) <=> ((~r(s(z), z)) | (~r(z, s(s(z)))) | (~r(s(s(s(z))), z)) | (~r(s(z), s(s(s(z))))))),
% 1.84/2.08 inference(rewrite,[status(thm)],[])).
% 1.84/2.08 tff(2867,plain,
% 1.84/2.08 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(z)))) | (~r(s(s(s(z))), z)) | (~r(s(z), z)) | (~r(s(z), s(s(s(z))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), z)) | (~r(z, s(s(z)))) | (~r(s(s(s(z))), z)) | (~r(s(z), s(s(s(z)))))))),
% 1.84/2.08 inference(monotonicity,[status(thm)],[2866])).
% 1.84/2.08 tff(2868,plain,
% 1.84/2.08 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(z)))) | (~r(s(s(s(z))), z)) | (~r(s(z), z)) | (~r(s(z), s(s(s(z))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(z), z)) | (~r(z, s(s(z)))) | (~r(s(s(s(z))), z)) | (~r(s(z), s(s(s(z))))))),
% 1.84/2.08 inference(transitivity,[status(thm)],[2867, 2865])).
% 1.84/2.08 tff(2869,plain,
% 1.84/2.08 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(z)))) | (~r(s(s(s(z))), z)) | (~r(s(z), z)) | (~r(s(z), s(s(s(z))))))),
% 1.84/2.08 inference(quant_inst,[status(thm)],[])).
% 1.84/2.08 tff(2870,plain,
% 1.84/2.08 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(z), z)) | (~r(z, s(s(z)))) | (~r(s(s(s(z))), z)) | (~r(s(z), s(s(s(z)))))),
% 1.84/2.08 inference(modus_ponens,[status(thm)],[2869, 2868])).
% 1.84/2.08 tff(2871,plain,
% 1.84/2.08 (~r(s(z), s(s(s(z))))),
% 1.84/2.08 inference(unit_resolution,[status(thm)],[2870, 197, 155, 97, 2858])).
% 1.84/2.08 tff(2872,plain,
% 1.84/2.08 (b(s(z), s(s(s(z))))),
% 1.84/2.08 inference(unit_resolution,[status(thm)],[1674, 2871])).
% 1.84/2.08 tff(2873,plain,
% 1.84/2.08 ($false),
% 1.84/2.08 inference(unit_resolution,[status(thm)],[996, 2872, 2864, 2862, 2860])).
% 1.84/2.08 tff(2874,plain,((~b(s(z), s(s(elem!1)))) | (~r(z, s(s(z)))) | (~r(s(z), z)) | (s(s(s(elem!1))) = s(s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), s(z))) | (~r(s(s(elem!1)), s(s(s(elem!1))))) | (~b(s(s(elem!1)), s(z))) | (s(s(z)) = s(s(elem!1))) | (~r(z, s(z)))), inference(lemma,lemma(discharge,[]))).
% 1.84/2.08 tff(2875,plain,
% 1.84/2.08 (s(s(z)) = s(s(elem!1))),
% 1.84/2.08 inference(unit_resolution,[status(thm)],[2874, 2639, 97, 361, 350, 377, 310, 152, 323])).
% 1.84/2.08 tff(2876,plain,
% 1.84/2.08 (s(elem!1) = s(z)),
% 1.84/2.08 inference(unit_resolution,[status(thm)],[43, 2875])).
% 1.84/2.08 tff(2877,plain,
% 1.84/2.08 (z = elem!1),
% 1.84/2.08 inference(unit_resolution,[status(thm)],[30, 2876])).
% 1.84/2.08 tff(2878,plain,
% 1.84/2.08 (b(z, s(s(s(elem!1)))) <=> b(elem!1, s(s(s(elem!1))))),
% 1.84/2.08 inference(monotonicity,[status(thm)],[2877])).
% 1.84/2.08 tff(2879,plain,
% 1.84/2.08 (b(elem!1, s(s(s(elem!1))))),
% 1.84/2.08 inference(modus_ponens,[status(thm)],[2615, 2878])).
% 1.84/2.08 tff(2880,plain,
% 1.84/2.08 (b(s(s(s(elem!1))), elem!1)),
% 1.84/2.08 inference(unit_resolution,[status(thm)],[634, 2877, 2661])).
% 1.84/2.08 tff(2881,plain,
% 1.84/2.08 ((s(s(s(s(z)))) = z) <=> (s(s(s(s(z)))) = elem!1)),
% 1.84/2.08 inference(monotonicity,[status(thm)],[2877])).
% 1.84/2.08 tff(2882,plain,
% 1.84/2.08 ((s(s(s(s(z)))) = z) <=> (elem!1 = s(s(s(s(z)))))),
% 1.84/2.08 inference(transitivity,[status(thm)],[2881, 1039])).
% 1.84/2.08 tff(2883,plain,
% 1.84/2.08 ((~(s(s(s(s(z)))) = z)) <=> (~(elem!1 = s(s(s(s(z))))))),
% 1.84/2.08 inference(monotonicity,[status(thm)],[2882])).
% 1.84/2.08 tff(2884,plain,
% 1.84/2.08 (~(elem!1 = s(s(s(s(z)))))),
% 1.84/2.08 inference(modus_ponens,[status(thm)],[1044, 2883])).
% 1.84/2.08 tff(2885,plain,
% 1.84/2.08 (r(z, s(s(elem!1))) <=> r(elem!1, s(s(elem!1)))),
% 1.84/2.08 inference(monotonicity,[status(thm)],[2877])).
% 1.84/2.08 tff(2886,plain,
% 1.84/2.08 (~b(z, s(s(elem!1)))),
% 1.84/2.08 inference(unit_resolution,[status(thm)],[2261, 2875, 125])).
% 1.84/2.08 tff(2887,plain,
% 1.84/2.08 (r(z, s(s(elem!1)))),
% 1.84/2.08 inference(unit_resolution,[status(thm)],[1795, 2886])).
% 1.84/2.08 tff(2888,plain,
% 1.84/2.08 (r(elem!1, s(s(elem!1)))),
% 1.84/2.08 inference(modus_ponens,[status(thm)],[2887, 2885])).
% 1.84/2.08 tff(2889,plain,
% 1.84/2.08 (~b(s(s(s(s(elem!1)))), s(s(elem!1)))),
% 1.84/2.08 inference(unit_resolution,[status(thm)],[804, 166, 2639, 310, 2671])).
% 1.84/2.08 tff(2890,plain,
% 1.84/2.08 ((s(s(s(s(elem!1)))) = s(s(z))) <=> (s(s(s(s(elem!1)))) = s(s(elem!1)))),
% 1.84/2.08 inference(monotonicity,[status(thm)],[2875])).
% 1.84/2.08 tff(2891,plain,
% 1.84/2.08 ((s(s(s(s(elem!1)))) = s(s(z))) <=> (s(s(elem!1)) = s(s(s(s(elem!1)))))),
% 1.84/2.08 inference(transitivity,[status(thm)],[2890, 123])).
% 1.84/2.08 tff(2892,plain,
% 1.84/2.08 ((s(s(s(s(elem!1)))) = s(s(z))) <=> (s(s(s(s(elem!1)))) = s(s(elem!1)))),
% 1.84/2.08 inference(transitivity,[status(thm)],[2891, 124])).
% 1.84/2.08 tff(2893,plain,
% 1.84/2.08 ((~(s(s(s(s(elem!1)))) = s(s(z)))) <=> (~(s(s(s(s(elem!1)))) = s(s(elem!1))))),
% 1.84/2.08 inference(monotonicity,[status(thm)],[2892])).
% 1.84/2.08 tff(2894,plain,
% 1.84/2.08 (~(s(s(s(s(elem!1)))) = s(s(elem!1)))),
% 1.84/2.08 inference(modus_ponens,[status(thm)],[733, 2893])).
% 1.84/2.08 tff(2895,plain,
% 1.84/2.08 (r(s(s(s(s(elem!1)))), s(s(elem!1)))),
% 1.84/2.08 inference(unit_resolution,[status(thm)],[813, 2894, 2889])).
% 1.84/2.08 tff(2896,plain,
% 1.84/2.08 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(s(s(s(elem!1)))))) | (~r(elem!1, s(s(elem!1)))) | (~r(s(s(elem!1)), s(s(s(elem!1))))) | (~r(s(s(s(s(elem!1)))), s(s(elem!1)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(elem!1, s(s(s(s(elem!1)))))) | (~r(elem!1, s(s(elem!1)))) | (~r(s(s(elem!1)), s(s(s(elem!1))))) | (~r(s(s(s(s(elem!1)))), s(s(elem!1)))))),
% 1.84/2.08 inference(rewrite,[status(thm)],[])).
% 1.84/2.08 tff(2897,plain,
% 1.84/2.08 (((~r(s(s(elem!1)), s(s(s(elem!1))))) | (~r(s(s(s(s(elem!1)))), s(s(elem!1)))) | (~r(elem!1, s(s(elem!1)))) | (~r(elem!1, s(s(s(s(elem!1))))))) <=> ((~r(elem!1, s(s(s(s(elem!1)))))) | (~r(elem!1, s(s(elem!1)))) | (~r(s(s(elem!1)), s(s(s(elem!1))))) | (~r(s(s(s(s(elem!1)))), s(s(elem!1)))))),
% 1.84/2.08 inference(rewrite,[status(thm)],[])).
% 1.84/2.08 tff(2898,plain,
% 1.84/2.08 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(elem!1)), s(s(s(elem!1))))) | (~r(s(s(s(s(elem!1)))), s(s(elem!1)))) | (~r(elem!1, s(s(elem!1)))) | (~r(elem!1, s(s(s(s(elem!1)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(s(s(s(elem!1)))))) | (~r(elem!1, s(s(elem!1)))) | (~r(s(s(elem!1)), s(s(s(elem!1))))) | (~r(s(s(s(s(elem!1)))), s(s(elem!1))))))),
% 1.84/2.08 inference(monotonicity,[status(thm)],[2897])).
% 1.84/2.08 tff(2899,plain,
% 1.84/2.08 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(elem!1)), s(s(s(elem!1))))) | (~r(s(s(s(s(elem!1)))), s(s(elem!1)))) | (~r(elem!1, s(s(elem!1)))) | (~r(elem!1, s(s(s(s(elem!1)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(elem!1, s(s(s(s(elem!1)))))) | (~r(elem!1, s(s(elem!1)))) | (~r(s(s(elem!1)), s(s(s(elem!1))))) | (~r(s(s(s(s(elem!1)))), s(s(elem!1)))))),
% 1.84/2.08 inference(transitivity,[status(thm)],[2898, 2896])).
% 1.84/2.08 tff(2900,plain,
% 1.84/2.08 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(elem!1)), s(s(s(elem!1))))) | (~r(s(s(s(s(elem!1)))), s(s(elem!1)))) | (~r(elem!1, s(s(elem!1)))) | (~r(elem!1, s(s(s(s(elem!1)))))))),
% 1.84/2.08 inference(quant_inst,[status(thm)],[])).
% 1.84/2.08 tff(2901,plain,
% 1.84/2.08 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(elem!1, s(s(s(s(elem!1)))))) | (~r(elem!1, s(s(elem!1)))) | (~r(s(s(elem!1)), s(s(s(elem!1))))) | (~r(s(s(s(s(elem!1)))), s(s(elem!1))))),
% 1.84/2.08 inference(modus_ponens,[status(thm)],[2900, 2899])).
% 1.84/2.08 tff(2902,plain,
% 1.84/2.08 (~r(elem!1, s(s(s(s(elem!1)))))),
% 1.84/2.08 inference(unit_resolution,[status(thm)],[2901, 197, 377, 2895, 2888])).
% 1.84/2.08 tff(2903,plain,
% 1.84/2.08 (~r(elem!1, s(s(s(s(z)))))),
% 1.84/2.08 inference(unit_resolution,[status(thm)],[1093, 2902, 2875])).
% 1.84/2.08 tff(2904,plain,
% 1.84/2.08 (b(elem!1, s(s(s(s(z)))))),
% 1.84/2.08 inference(unit_resolution,[status(thm)],[1098, 2903, 2884])).
% 1.84/2.08 tff(2905,plain,
% 1.84/2.08 (b(elem!1, s(s(s(s(elem!1)))))),
% 1.84/2.08 inference(unit_resolution,[status(thm)],[1105, 2904, 2875])).
% 1.84/2.08 tff(2906,plain,
% 1.84/2.08 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~b(elem!1, s(s(s(s(elem!1)))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~b(elem!1, s(s(s(s(elem!1)))))))),
% 1.84/2.08 inference(rewrite,[status(thm)],[])).
% 1.84/2.08 tff(2907,plain,
% 1.84/2.08 (((~b(elem!1, s(s(s(elem!1))))) | (~b(elem!1, s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~b(elem!1, s(s(s(elem!1))))) | (~b(elem!1, s(s(s(s(elem!1))))))) <=> ((~b(elem!1, s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~b(elem!1, s(s(s(s(elem!1)))))))),
% 1.84/2.08 inference(rewrite,[status(thm)],[])).
% 1.84/2.08 tff(2908,plain,
% 1.84/2.08 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(s(s(elem!1))))) | (~b(elem!1, s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~b(elem!1, s(s(s(elem!1))))) | (~b(elem!1, s(s(s(s(elem!1)))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~b(elem!1, s(s(s(s(elem!1))))))))),
% 1.84/2.08 inference(monotonicity,[status(thm)],[2907])).
% 1.84/2.08 tff(2909,plain,
% 1.84/2.08 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(s(s(elem!1))))) | (~b(elem!1, s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~b(elem!1, s(s(s(elem!1))))) | (~b(elem!1, s(s(s(s(elem!1)))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~b(elem!1, s(s(s(s(elem!1)))))))),
% 1.84/2.09 inference(transitivity,[status(thm)],[2908, 2906])).
% 1.84/2.09 tff(2910,plain,
% 1.84/2.09 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(s(s(elem!1))))) | (~b(elem!1, s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~b(elem!1, s(s(s(elem!1))))) | (~b(elem!1, s(s(s(s(elem!1)))))))),
% 1.84/2.09 inference(quant_inst,[status(thm)],[])).
% 1.84/2.09 tff(2911,plain,
% 1.84/2.09 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~b(elem!1, s(s(s(s(elem!1))))))),
% 1.84/2.09 inference(modus_ponens,[status(thm)],[2910, 2909])).
% 1.84/2.09 tff(2912,plain,
% 1.84/2.09 ((~b(elem!1, s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~b(elem!1, s(s(s(s(elem!1))))))),
% 1.84/2.09 inference(unit_resolution,[status(thm)],[2911, 166])).
% 1.84/2.09 tff(2913,plain,
% 1.84/2.09 (~b(s(s(s(s(elem!1)))), s(s(s(elem!1))))),
% 1.84/2.09 inference(unit_resolution,[status(thm)],[2912, 2905, 2880, 2879])).
% 1.84/2.09 tff(2914,plain,
% 1.84/2.09 (r(s(s(s(s(elem!1)))), s(s(s(elem!1))))),
% 1.84/2.09 inference(unit_resolution,[status(thm)],[1065, 2913, 1038])).
% 1.84/2.09 tff(2915,plain,
% 1.84/2.09 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), s(z))) | (~r(s(s(elem!1)), s(s(s(elem!1))))) | (~r(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~r(s(s(s(s(elem!1)))), s(s(elem!1)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(elem!1))), s(z))) | (~r(s(s(elem!1)), s(s(s(elem!1))))) | (~r(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~r(s(s(s(s(elem!1)))), s(s(elem!1)))))),
% 1.84/2.09 inference(rewrite,[status(thm)],[])).
% 1.84/2.09 tff(2916,plain,
% 1.84/2.09 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), s(z))) | (~r(s(s(elem!1)), s(s(s(elem!1))))) | (~r(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~r(s(s(s(s(elem!1)))), s(s(elem!1)))))),
% 1.84/2.09 inference(quant_inst,[status(thm)],[])).
% 1.84/2.09 tff(2917,plain,
% 1.84/2.09 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(elem!1))), s(z))) | (~r(s(s(elem!1)), s(s(s(elem!1))))) | (~r(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~r(s(s(s(s(elem!1)))), s(s(elem!1))))),
% 1.84/2.09 inference(modus_ponens,[status(thm)],[2916, 2915])).
% 1.84/2.09 tff(2918,plain,
% 1.84/2.09 ($false),
% 1.84/2.09 inference(unit_resolution,[status(thm)],[2917, 197, 350, 377, 2895, 2914])).
% 1.84/2.09 tff(2919,plain,((~r(s(s(s(elem!1))), s(z))) | (~r(s(s(elem!1)), s(s(s(elem!1))))) | (~b(s(s(elem!1)), s(z))) | b(z, s(s(z))) | (~r(s(z), z)) | (s(s(s(elem!1))) = s(s(s(s(elem!1))))) | (~r(z, s(z))) | (s(s(s(elem!1))) = s(s(elem!1)))), inference(lemma,lemma(discharge,[]))).
% 1.84/2.09 tff(2920,plain,
% 1.84/2.09 (~r(s(s(s(elem!1))), s(z))),
% 1.84/2.09 inference(unit_resolution,[status(thm)],[2919, 2605, 310, 125, 2604, 358, 322, 51])).
% 1.84/2.09 tff(2921,plain,
% 1.84/2.09 (b(s(s(s(elem!1))), s(z))),
% 1.84/2.09 inference(unit_resolution,[status(thm)],[1849, 2920])).
% 1.84/2.09 tff(2922,plain,
% 1.84/2.09 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(s(elem!1)), s(z))) | (~b(s(s(z)), s(s(elem!1)))) | (~b(s(s(z)), s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(s(elem!1)), s(z))) | (~b(s(s(z)), s(s(elem!1)))) | (~b(s(s(z)), s(z))))),
% 1.84/2.09 inference(rewrite,[status(thm)],[])).
% 1.84/2.09 tff(2923,plain,
% 1.84/2.09 (((~b(s(s(s(elem!1))), s(z))) | (~b(s(s(z)), s(z))) | (~b(s(z), s(s(s(elem!1))))) | (~b(s(s(elem!1)), s(z))) | (~b(s(s(z)), s(z))) | (~b(s(s(z)), s(s(elem!1))))) <=> ((~b(s(z), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(s(elem!1)), s(z))) | (~b(s(s(z)), s(s(elem!1)))) | (~b(s(s(z)), s(z))))),
% 1.84/2.09 inference(rewrite,[status(thm)],[])).
% 1.84/2.09 tff(2924,plain,
% 1.84/2.09 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), s(z))) | (~b(s(s(z)), s(z))) | (~b(s(z), s(s(s(elem!1))))) | (~b(s(s(elem!1)), s(z))) | (~b(s(s(z)), s(z))) | (~b(s(s(z)), s(s(elem!1)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(s(elem!1)), s(z))) | (~b(s(s(z)), s(s(elem!1)))) | (~b(s(s(z)), s(z)))))),
% 1.84/2.09 inference(monotonicity,[status(thm)],[2923])).
% 1.84/2.09 tff(2925,plain,
% 1.84/2.09 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), s(z))) | (~b(s(s(z)), s(z))) | (~b(s(z), s(s(s(elem!1))))) | (~b(s(s(elem!1)), s(z))) | (~b(s(s(z)), s(z))) | (~b(s(s(z)), s(s(elem!1)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(s(elem!1)), s(z))) | (~b(s(s(z)), s(s(elem!1)))) | (~b(s(s(z)), s(z))))),
% 1.84/2.09 inference(transitivity,[status(thm)],[2924, 2922])).
% 1.84/2.09 tff(2926,plain,
% 1.84/2.09 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), s(z))) | (~b(s(s(z)), s(z))) | (~b(s(z), s(s(s(elem!1))))) | (~b(s(s(elem!1)), s(z))) | (~b(s(s(z)), s(z))) | (~b(s(s(z)), s(s(elem!1)))))),
% 1.84/2.09 inference(quant_inst,[status(thm)],[])).
% 1.84/2.09 tff(2927,plain,
% 1.84/2.09 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(s(elem!1)), s(z))) | (~b(s(s(z)), s(s(elem!1)))) | (~b(s(s(z)), s(z)))),
% 1.84/2.09 inference(modus_ponens,[status(thm)],[2926, 2925])).
% 1.84/2.09 tff(2928,plain,
% 1.84/2.09 ($false),
% 1.84/2.09 inference(unit_resolution,[status(thm)],[2927, 166, 241, 96, 310, 446, 156])).
% 1.84/2.09 tff(2929,plain,((~b(s(z), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(s(elem!1)), s(z))) | (~b(s(s(z)), s(s(elem!1)))) | (~b(s(s(z)), s(z)))), inference(lemma,lemma(discharge,[]))).
% 1.84/2.09 tff(2930,plain,
% 1.84/2.09 (~b(s(z), s(s(s(elem!1))))),
% 1.84/2.09 inference(unit_resolution,[status(thm)],[2929, 2921, 310, 446, 156])).
% 1.84/2.09 tff(2931,plain,
% 1.84/2.09 (r(s(z), s(s(s(elem!1))))),
% 1.84/2.09 inference(unit_resolution,[status(thm)],[116, 2930])).
% 1.84/2.09 tff(2932,plain,
% 1.84/2.09 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(s(elem!1)))) | (~r(s(z), s(s(s(elem!1))))) | (~r(s(s(elem!1)), s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), s(s(z)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(z), s(s(elem!1)))) | (~r(s(z), s(s(s(elem!1))))) | (~r(s(s(elem!1)), s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), s(s(z)))))),
% 1.84/2.09 inference(rewrite,[status(thm)],[])).
% 1.84/2.09 tff(2933,plain,
% 1.84/2.09 (((~r(s(s(s(elem!1))), s(s(z)))) | (~r(s(s(elem!1)), s(s(s(elem!1))))) | (~r(s(z), s(s(s(elem!1))))) | (~r(s(z), s(s(elem!1))))) <=> ((~r(s(z), s(s(elem!1)))) | (~r(s(z), s(s(s(elem!1))))) | (~r(s(s(elem!1)), s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), s(s(z)))))),
% 1.84/2.09 inference(rewrite,[status(thm)],[])).
% 1.84/2.09 tff(2934,plain,
% 1.84/2.09 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), s(s(z)))) | (~r(s(s(elem!1)), s(s(s(elem!1))))) | (~r(s(z), s(s(s(elem!1))))) | (~r(s(z), s(s(elem!1)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(s(elem!1)))) | (~r(s(z), s(s(s(elem!1))))) | (~r(s(s(elem!1)), s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), s(s(z))))))),
% 1.84/2.09 inference(monotonicity,[status(thm)],[2933])).
% 1.84/2.09 tff(2935,plain,
% 1.84/2.09 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), s(s(z)))) | (~r(s(s(elem!1)), s(s(s(elem!1))))) | (~r(s(z), s(s(s(elem!1))))) | (~r(s(z), s(s(elem!1)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(z), s(s(elem!1)))) | (~r(s(z), s(s(s(elem!1))))) | (~r(s(s(elem!1)), s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), s(s(z)))))),
% 1.84/2.09 inference(transitivity,[status(thm)],[2934, 2932])).
% 1.84/2.09 tff(2936,plain,
% 1.84/2.09 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), s(s(z)))) | (~r(s(s(elem!1)), s(s(s(elem!1))))) | (~r(s(z), s(s(s(elem!1))))) | (~r(s(z), s(s(elem!1)))))),
% 1.84/2.09 inference(quant_inst,[status(thm)],[])).
% 1.84/2.09 tff(2937,plain,
% 1.84/2.09 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(z), s(s(elem!1)))) | (~r(s(z), s(s(s(elem!1))))) | (~r(s(s(elem!1)), s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), s(s(z))))),
% 1.84/2.09 inference(modus_ponens,[status(thm)],[2936, 2935])).
% 1.84/2.09 tff(2938,plain,
% 1.84/2.09 ($false),
% 1.84/2.09 inference(unit_resolution,[status(thm)],[2937, 197, 311, 377, 119, 464])).
% 1.84/2.09 tff(2939,plain,((~r(s(s(s(elem!1))), s(s(z)))) | (~r(s(z), s(s(elem!1)))) | (~r(s(s(elem!1)), s(s(s(elem!1))))) | (~r(s(z), s(s(s(elem!1)))))), inference(lemma,lemma(discharge,[]))).
% 1.84/2.09 tff(2940,plain,
% 1.84/2.09 (~r(s(s(s(elem!1))), s(s(z)))),
% 1.84/2.09 inference(unit_resolution,[status(thm)],[2939, 2931, 2605, 311])).
% 1.84/2.09 tff(2941,plain,
% 1.84/2.09 (b(s(s(s(elem!1))), s(s(z)))),
% 1.84/2.09 inference(unit_resolution,[status(thm)],[218, 2940])).
% 1.84/2.09 tff(2942,plain,
% 1.84/2.09 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), s(s(elem!1)))) | (~r(s(z), s(s(elem!1)))) | (~r(s(z), s(s(s(elem!1))))) | (~r(s(s(elem!1)), s(s(s(elem!1))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(elem!1))), s(s(elem!1)))) | (~r(s(z), s(s(elem!1)))) | (~r(s(z), s(s(s(elem!1))))) | (~r(s(s(elem!1)), s(s(s(elem!1))))))),
% 1.84/2.09 inference(rewrite,[status(thm)],[])).
% 1.84/2.09 tff(2943,plain,
% 1.84/2.09 (((~r(s(s(elem!1)), s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), s(s(elem!1)))) | (~r(s(z), s(s(elem!1)))) | (~r(s(z), s(s(s(elem!1)))))) <=> ((~r(s(s(s(elem!1))), s(s(elem!1)))) | (~r(s(z), s(s(elem!1)))) | (~r(s(z), s(s(s(elem!1))))) | (~r(s(s(elem!1)), s(s(s(elem!1))))))),
% 1.84/2.09 inference(rewrite,[status(thm)],[])).
% 1.84/2.09 tff(2944,plain,
% 1.84/2.09 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(elem!1)), s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), s(s(elem!1)))) | (~r(s(z), s(s(elem!1)))) | (~r(s(z), s(s(s(elem!1))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), s(s(elem!1)))) | (~r(s(z), s(s(elem!1)))) | (~r(s(z), s(s(s(elem!1))))) | (~r(s(s(elem!1)), s(s(s(elem!1)))))))),
% 1.84/2.09 inference(monotonicity,[status(thm)],[2943])).
% 1.84/2.09 tff(2945,plain,
% 1.84/2.09 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(elem!1)), s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), s(s(elem!1)))) | (~r(s(z), s(s(elem!1)))) | (~r(s(z), s(s(s(elem!1))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(elem!1))), s(s(elem!1)))) | (~r(s(z), s(s(elem!1)))) | (~r(s(z), s(s(s(elem!1))))) | (~r(s(s(elem!1)), s(s(s(elem!1))))))),
% 1.84/2.09 inference(transitivity,[status(thm)],[2944, 2942])).
% 1.84/2.09 tff(2946,plain,
% 1.84/2.09 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(elem!1)), s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), s(s(elem!1)))) | (~r(s(z), s(s(elem!1)))) | (~r(s(z), s(s(s(elem!1))))))),
% 1.84/2.09 inference(quant_inst,[status(thm)],[])).
% 1.84/2.09 tff(2947,plain,
% 1.84/2.09 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(elem!1))), s(s(elem!1)))) | (~r(s(z), s(s(elem!1)))) | (~r(s(z), s(s(s(elem!1))))) | (~r(s(s(elem!1)), s(s(s(elem!1)))))),
% 1.84/2.09 inference(modus_ponens,[status(thm)],[2946, 2945])).
% 1.84/2.09 tff(2948,plain,
% 1.84/2.09 ($false),
% 1.84/2.09 inference(unit_resolution,[status(thm)],[2947, 197, 311, 377, 905, 119])).
% 1.84/2.09 tff(2949,plain,((~r(s(s(s(elem!1))), s(s(elem!1)))) | (~r(s(z), s(s(elem!1)))) | (~r(s(s(elem!1)), s(s(s(elem!1))))) | (~r(s(z), s(s(s(elem!1)))))), inference(lemma,lemma(discharge,[]))).
% 1.84/2.09 tff(2950,plain,
% 1.84/2.09 (~r(s(s(s(elem!1))), s(s(elem!1)))),
% 1.84/2.09 inference(unit_resolution,[status(thm)],[2949, 2931, 2605, 311])).
% 1.84/2.09 tff(2951,plain,
% 1.84/2.09 (b(s(s(s(elem!1))), s(s(elem!1)))),
% 1.84/2.09 inference(unit_resolution,[status(thm)],[889, 2950, 51])).
% 1.84/2.09 tff(2952,plain,
% 1.84/2.09 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(z))) | (~r(s(z), s(s(z)))) | (~r(s(s(z)), z)) | (~r(z, s(s(z)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, s(z))) | (~r(s(z), s(s(z)))) | (~r(s(s(z)), z)) | (~r(z, s(s(z)))))),
% 1.84/2.09 inference(rewrite,[status(thm)],[])).
% 1.84/2.09 tff(2953,plain,
% 1.84/2.09 (((~r(s(s(z)), z)) | (~r(s(z), s(s(z)))) | (~r(z, s(s(z)))) | (~r(z, s(z)))) <=> ((~r(z, s(z))) | (~r(s(z), s(s(z)))) | (~r(s(s(z)), z)) | (~r(z, s(s(z)))))),
% 1.84/2.09 inference(rewrite,[status(thm)],[])).
% 1.84/2.09 tff(2954,plain,
% 1.84/2.09 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(z)), z)) | (~r(s(z), s(s(z)))) | (~r(z, s(s(z)))) | (~r(z, s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(z))) | (~r(s(z), s(s(z)))) | (~r(s(s(z)), z)) | (~r(z, s(s(z))))))),
% 1.84/2.09 inference(monotonicity,[status(thm)],[2953])).
% 1.84/2.09 tff(2955,plain,
% 1.84/2.09 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(z)), z)) | (~r(s(z), s(s(z)))) | (~r(z, s(s(z)))) | (~r(z, s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, s(z))) | (~r(s(z), s(s(z)))) | (~r(s(s(z)), z)) | (~r(z, s(s(z)))))),
% 1.84/2.09 inference(transitivity,[status(thm)],[2954, 2952])).
% 1.84/2.09 tff(2956,plain,
% 1.84/2.09 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(z)), z)) | (~r(s(z), s(s(z)))) | (~r(z, s(s(z)))) | (~r(z, s(z))))),
% 1.84/2.09 inference(quant_inst,[status(thm)],[])).
% 1.84/2.09 tff(2957,plain,
% 1.84/2.09 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, s(z))) | (~r(s(z), s(s(z)))) | (~r(s(s(z)), z)) | (~r(z, s(s(z))))),
% 1.84/2.09 inference(modus_ponens,[status(thm)],[2956, 2955])).
% 1.84/2.09 tff(2958,plain,
% 1.84/2.09 ($false),
% 1.84/2.09 inference(unit_resolution,[status(thm)],[2957, 197, 120, 155, 323, 866])).
% 1.84/2.09 tff(2959,plain,((~r(s(s(z)), z)) | (~r(s(z), s(s(z)))) | (~r(z, s(s(z)))) | (~r(z, s(z)))), inference(lemma,lemma(discharge,[]))).
% 1.84/2.09 tff(2960,plain,
% 1.84/2.09 (~r(s(s(z)), z)),
% 1.84/2.09 inference(unit_resolution,[status(thm)],[2959, 323, 155, 120])).
% 1.84/2.09 tff(2961,plain,
% 1.84/2.09 (b(s(s(z)), z)),
% 1.84/2.09 inference(unit_resolution,[status(thm)],[186, 2960])).
% 1.84/2.09 tff(2962,plain,
% 1.84/2.09 (b(s(s(z)), z) <=> b(s(s(elem!1)), z)),
% 1.84/2.09 inference(monotonicity,[status(thm)],[34])).
% 1.84/2.09 tff(2963,plain,
% 1.84/2.09 (b(s(s(elem!1)), z)),
% 1.84/2.09 inference(modus_ponens,[status(thm)],[122, 2962])).
% 1.84/2.09 tff(2964,plain,
% 1.84/2.09 ($false),
% 1.84/2.09 inference(unit_resolution,[status(thm)],[603, 2963])).
% 1.84/2.09 tff(2965,plain,((~b(s(s(z)), z)) | b(s(s(elem!1)), z) | (~(s(s(z)) = s(s(elem!1))))), inference(lemma,lemma(discharge,[]))).
% 1.84/2.09 tff(2966,plain,
% 1.84/2.09 (~(s(s(z)) = s(s(elem!1)))),
% 1.84/2.09 inference(unit_resolution,[status(thm)],[2965, 603, 2961])).
% 1.84/2.09 tff(2967,plain,
% 1.84/2.09 (r(s(s(elem!1)), z)),
% 1.84/2.09 inference(unit_resolution,[status(thm)],[608, 603])).
% 1.84/2.09 tff(2968,plain,
% 1.84/2.09 (~r(s(z), z)),
% 1.84/2.09 inference(unit_resolution,[status(thm)],[2274, 2967, 155, 311])).
% 1.84/2.09 tff(2969,plain,
% 1.84/2.09 (b(s(z), z)),
% 1.84/2.09 inference(unit_resolution,[status(thm)],[230, 2968])).
% 1.84/2.09 tff(2970,plain,
% 1.84/2.09 (s(s(elem!1)) = s(s(s(elem!1)))),
% 1.84/2.09 inference(unit_resolution,[status(thm)],[2253, 2969, 155, 310, 323])).
% 1.84/2.09 tff(2971,plain,
% 1.84/2.09 (r(s(s(elem!1)), z) <=> r(s(s(s(elem!1))), z)),
% 1.84/2.09 inference(monotonicity,[status(thm)],[334])).
% 1.84/2.09 tff(2972,plain,
% 1.84/2.09 (r(s(s(s(elem!1))), z)),
% 1.84/2.09 inference(modus_ponens,[status(thm)],[1970, 2971])).
% 1.84/2.09 tff(2973,plain,
% 1.84/2.09 ($false),
% 1.84/2.09 inference(unit_resolution,[status(thm)],[86, 2972])).
% 1.84/2.09 tff(2974,plain,(r(s(s(s(elem!1))), z) | (~r(s(s(elem!1)), z)) | (~(s(s(elem!1)) = s(s(s(elem!1)))))), inference(lemma,lemma(discharge,[]))).
% 1.84/2.09 tff(2975,plain,
% 1.84/2.09 (r(s(s(s(elem!1))), z)),
% 1.84/2.09 inference(unit_resolution,[status(thm)],[2974, 2970, 2967])).
% 1.84/2.09 tff(2976,plain,
% 1.84/2.09 (r(s(z), s(s(elem!1))) <=> r(s(z), s(s(s(elem!1))))),
% 1.84/2.09 inference(monotonicity,[status(thm)],[2970])).
% 1.84/2.09 tff(2977,plain,
% 1.84/2.09 (r(s(z), s(s(s(elem!1))))),
% 1.84/2.09 inference(modus_ponens,[status(thm)],[311, 2976])).
% 1.84/2.09 tff(2978,plain,
% 1.84/2.09 (~r(s(s(z)), s(s(s(elem!1))))),
% 1.84/2.09 inference(unit_resolution,[status(thm)],[2304, 2977, 120, 2975])).
% 1.84/2.09 tff(2979,plain,
% 1.84/2.09 (~r(s(s(z)), s(s(elem!1)))),
% 1.84/2.09 inference(unit_resolution,[status(thm)],[338, 2978, 2970])).
% 1.84/2.09 tff(2980,plain,
% 1.84/2.09 (~(s(s(elem!1)) = s(s(z)))),
% 1.84/2.09 inference(unit_resolution,[status(thm)],[131, 2966])).
% 1.84/2.09 tff(2981,plain,
% 1.84/2.09 (~(z = elem!1)),
% 1.84/2.09 inference(unit_resolution,[status(thm)],[17, 2980])).
% 1.84/2.09 tff(2982,plain,
% 1.84/2.09 (~(s(elem!1) = s(z))),
% 1.84/2.09 inference(unit_resolution,[status(thm)],[30, 2981])).
% 1.84/2.09 tff(2983,plain,
% 1.84/2.09 ((s(s(elem!1)) = s(s(s(s(elem!1))))) <=> (s(s(s(elem!1))) = s(s(s(s(elem!1)))))),
% 1.84/2.09 inference(monotonicity,[status(thm)],[2970])).
% 1.84/2.09 tff(2984,plain,
% 1.84/2.09 ((s(s(s(elem!1))) = s(s(s(s(elem!1))))) <=> (s(s(elem!1)) = s(s(s(s(elem!1)))))),
% 1.84/2.09 inference(symmetry,[status(thm)],[2983])).
% 1.84/2.09 tff(2985,plain,
% 1.84/2.09 (s(s(s(elem!1))) = s(s(elem!1))),
% 1.84/2.09 inference(symmetry,[status(thm)],[2970])).
% 1.84/2.09 tff(2986,plain,
% 1.84/2.09 (s(s(s(s(elem!1)))) = s(s(s(elem!1)))),
% 1.84/2.09 inference(monotonicity,[status(thm)],[2985])).
% 1.84/2.09 tff(2987,plain,
% 1.84/2.09 (s(s(s(elem!1))) = s(s(s(s(elem!1))))),
% 1.84/2.09 inference(symmetry,[status(thm)],[2986])).
% 1.84/2.09 tff(2988,plain,
% 1.84/2.09 (s(s(elem!1)) = s(s(s(s(elem!1))))),
% 1.84/2.09 inference(modus_ponens,[status(thm)],[2987, 2984])).
% 1.84/2.09 tff(2989,plain,
% 1.84/2.09 (~r(z, s(s(elem!1)))),
% 1.84/2.09 inference(unit_resolution,[status(thm)],[1972, 2967, 311, 323])).
% 1.84/2.09 tff(2990,plain,
% 1.84/2.09 (b(z, s(s(elem!1)))),
% 1.84/2.09 inference(unit_resolution,[status(thm)],[1795, 2989])).
% 1.84/2.09 tff(2991,plain,
% 1.84/2.09 (b(s(s(z)), s(s(s(elem!1))))),
% 1.84/2.09 inference(unit_resolution,[status(thm)],[279, 2978])).
% 1.84/2.09 tff(2992,plain,
% 1.84/2.09 (b(z, s(s(s(s(elem!1))))) <=> b(z, s(s(elem!1)))),
% 1.84/2.09 inference(monotonicity,[status(thm)],[1154])).
% 1.84/2.09 tff(2993,plain,
% 1.84/2.09 (b(z, s(s(elem!1))) <=> b(z, s(s(s(s(elem!1)))))),
% 1.84/2.09 inference(symmetry,[status(thm)],[2992])).
% 1.84/2.09 tff(2994,plain,
% 1.84/2.09 (b(z, s(s(s(s(elem!1)))))),
% 1.84/2.09 inference(modus_ponens,[status(thm)],[1820, 2993])).
% 1.84/2.09 tff(2995,plain,
% 1.84/2.09 (b(s(s(z)), s(s(elem!1))) <=> b(s(s(z)), s(s(s(s(elem!1)))))),
% 1.84/2.09 inference(monotonicity,[status(thm)],[1153])).
% 1.84/2.09 tff(2996,plain,
% 1.84/2.09 (b(s(s(z)), s(s(s(s(elem!1)))))),
% 1.84/2.09 inference(modus_ponens,[status(thm)],[446, 2995])).
% 1.84/2.09 tff(2997,plain,
% 1.84/2.09 (b(s(s(z)), s(s(s(elem!1)))) <=> b(s(s(z)), s(elem!1))),
% 1.84/2.09 inference(monotonicity,[status(thm)],[1167])).
% 1.84/2.09 tff(2998,plain,
% 1.84/2.09 (b(s(s(z)), s(elem!1))),
% 1.84/2.09 inference(modus_ponens,[status(thm)],[263, 2997])).
% 1.84/2.09 tff(2999,assumption,(r(s(elem!1), z)), introduced(assumption)).
% 1.84/2.09 tff(3000,plain,
% 1.84/2.09 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(elem!1), z)) | (~r(s(z), s(s(elem!1)))) | (~r(z, s(z))) | (~r(s(elem!1), s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(elem!1), z)) | (~r(s(z), s(s(elem!1)))) | (~r(z, s(z))) | (~r(s(elem!1), s(z))))),
% 1.84/2.09 inference(rewrite,[status(thm)],[])).
% 1.84/2.09 tff(3001,plain,
% 1.84/2.09 (((~r(s(z), s(s(elem!1)))) | (~r(z, s(z))) | (~r(s(elem!1), s(z))) | (~r(s(elem!1), z))) <=> ((~r(s(elem!1), z)) | (~r(s(z), s(s(elem!1)))) | (~r(z, s(z))) | (~r(s(elem!1), s(z))))),
% 1.84/2.09 inference(rewrite,[status(thm)],[])).
% 1.84/2.09 tff(3002,plain,
% 1.84/2.09 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(s(elem!1)))) | (~r(z, s(z))) | (~r(s(elem!1), s(z))) | (~r(s(elem!1), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(elem!1), z)) | (~r(s(z), s(s(elem!1)))) | (~r(z, s(z))) | (~r(s(elem!1), s(z)))))),
% 1.84/2.09 inference(monotonicity,[status(thm)],[3001])).
% 1.84/2.09 tff(3003,plain,
% 1.84/2.09 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(s(elem!1)))) | (~r(z, s(z))) | (~r(s(elem!1), s(z))) | (~r(s(elem!1), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(elem!1), z)) | (~r(s(z), s(s(elem!1)))) | (~r(z, s(z))) | (~r(s(elem!1), s(z))))),
% 1.84/2.09 inference(transitivity,[status(thm)],[3002, 3000])).
% 1.84/2.09 tff(3004,plain,
% 1.84/2.09 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(s(elem!1)))) | (~r(z, s(z))) | (~r(s(elem!1), s(z))) | (~r(s(elem!1), z)))),
% 1.84/2.09 inference(quant_inst,[status(thm)],[])).
% 1.84/2.09 tff(3005,plain,
% 1.84/2.09 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(elem!1), z)) | (~r(s(z), s(s(elem!1)))) | (~r(z, s(z))) | (~r(s(elem!1), s(z)))),
% 1.84/2.09 inference(modus_ponens,[status(thm)],[3004, 3003])).
% 1.84/2.09 tff(3006,plain,
% 1.84/2.09 ($false),
% 1.84/2.09 inference(unit_resolution,[status(thm)],[3005, 197, 311, 2999, 323, 2848])).
% 1.84/2.09 tff(3007,plain,((~r(s(z), s(s(elem!1)))) | (~r(s(elem!1), z)) | (~r(z, s(z))) | (~r(s(elem!1), s(z)))), inference(lemma,lemma(discharge,[]))).
% 1.84/2.09 tff(3008,plain,
% 1.84/2.09 (~r(s(elem!1), s(z))),
% 1.84/2.09 inference(unit_resolution,[status(thm)],[3007, 1185, 323, 311])).
% 1.84/2.09 tff(3009,plain,
% 1.84/2.09 (((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((s(elem!1) = s(z)) | b(s(elem!1), s(z)) | r(s(elem!1), s(z)))) <=> ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (s(elem!1) = s(z)) | b(s(elem!1), s(z)) | r(s(elem!1), s(z)))),
% 1.84/2.09 inference(rewrite,[status(thm)],[])).
% 1.84/2.09 tff(3010,plain,
% 1.84/2.09 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((s(elem!1) = s(z)) | b(s(elem!1), s(z)) | r(s(elem!1), s(z)))),
% 1.84/2.09 inference(quant_inst,[status(thm)],[])).
% 1.84/2.09 tff(3011,plain,
% 1.84/2.09 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (s(elem!1) = s(z)) | b(s(elem!1), s(z)) | r(s(elem!1), s(z))),
% 1.84/2.09 inference(modus_ponens,[status(thm)],[3010, 3009])).
% 1.84/2.09 tff(3012,plain,
% 1.84/2.09 ((s(elem!1) = s(z)) | b(s(elem!1), s(z)) | r(s(elem!1), s(z))),
% 1.84/2.09 inference(unit_resolution,[status(thm)],[3011, 79])).
% 1.84/2.09 tff(3013,plain,
% 1.84/2.09 (b(s(elem!1), s(z))),
% 1.84/2.09 inference(unit_resolution,[status(thm)],[3012, 3008, 41])).
% 1.84/2.09 tff(3014,plain,
% 1.84/2.09 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), z)) | (~b(s(elem!1), s(z))) | (~b(s(s(z)), s(z))) | (~b(s(s(z)), s(elem!1))) | (~b(s(s(z)), s(s(s(s(elem!1)))))) | (~b(z, s(s(s(s(elem!1)))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), z)) | (~b(s(elem!1), s(z))) | (~b(s(s(z)), s(z))) | (~b(s(s(z)), s(elem!1))) | (~b(s(s(z)), s(s(s(s(elem!1)))))) | (~b(z, s(s(s(s(elem!1)))))))),
% 1.84/2.09 inference(rewrite,[status(thm)],[])).
% 1.84/2.09 tff(3015,plain,
% 1.84/2.09 (((~b(z, s(s(s(s(elem!1)))))) | (~b(s(s(z)), s(s(s(s(elem!1)))))) | (~b(s(z), z)) | (~b(s(elem!1), s(z))) | (~b(s(s(z)), s(z))) | (~b(s(s(z)), s(elem!1)))) <=> ((~b(s(z), z)) | (~b(s(elem!1), s(z))) | (~b(s(s(z)), s(z))) | (~b(s(s(z)), s(elem!1))) | (~b(s(s(z)), s(s(s(s(elem!1)))))) | (~b(z, s(s(s(s(elem!1)))))))),
% 1.84/2.09 inference(rewrite,[status(thm)],[])).
% 1.84/2.09 tff(3016,plain,
% 1.84/2.09 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(s(s(elem!1)))))) | (~b(s(s(z)), s(s(s(s(elem!1)))))) | (~b(s(z), z)) | (~b(s(elem!1), s(z))) | (~b(s(s(z)), s(z))) | (~b(s(s(z)), s(elem!1))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), z)) | (~b(s(elem!1), s(z))) | (~b(s(s(z)), s(z))) | (~b(s(s(z)), s(elem!1))) | (~b(s(s(z)), s(s(s(s(elem!1)))))) | (~b(z, s(s(s(s(elem!1))))))))),
% 1.84/2.10 inference(monotonicity,[status(thm)],[3015])).
% 1.84/2.10 tff(3017,plain,
% 1.84/2.10 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(s(s(elem!1)))))) | (~b(s(s(z)), s(s(s(s(elem!1)))))) | (~b(s(z), z)) | (~b(s(elem!1), s(z))) | (~b(s(s(z)), s(z))) | (~b(s(s(z)), s(elem!1))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), z)) | (~b(s(elem!1), s(z))) | (~b(s(s(z)), s(z))) | (~b(s(s(z)), s(elem!1))) | (~b(s(s(z)), s(s(s(s(elem!1)))))) | (~b(z, s(s(s(s(elem!1)))))))),
% 1.84/2.10 inference(transitivity,[status(thm)],[3016, 3014])).
% 1.84/2.10 tff(3018,plain,
% 1.84/2.10 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(s(s(elem!1)))))) | (~b(s(s(z)), s(s(s(s(elem!1)))))) | (~b(s(z), z)) | (~b(s(elem!1), s(z))) | (~b(s(s(z)), s(z))) | (~b(s(s(z)), s(elem!1))))),
% 1.84/2.10 inference(quant_inst,[status(thm)],[])).
% 1.84/2.10 tff(3019,plain,
% 1.84/2.10 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), z)) | (~b(s(elem!1), s(z))) | (~b(s(s(z)), s(z))) | (~b(s(s(z)), s(elem!1))) | (~b(s(s(z)), s(s(s(s(elem!1)))))) | (~b(z, s(s(s(s(elem!1))))))),
% 1.84/2.10 inference(modus_ponens,[status(thm)],[3018, 3017])).
% 1.84/2.10 tff(3020,plain,
% 1.84/2.10 (~b(z, s(s(s(s(elem!1)))))),
% 1.84/2.10 inference(unit_resolution,[status(thm)],[3019, 166, 3013, 53, 2998, 156, 2996])).
% 1.84/2.10 tff(3021,plain,
% 1.84/2.10 ($false),
% 1.84/2.10 inference(unit_resolution,[status(thm)],[3020, 2994])).
% 1.84/2.10 tff(3022,plain,((~(s(s(elem!1)) = s(s(s(s(elem!1)))))) | (~b(z, s(s(elem!1)))) | (~b(s(z), z)) | (~b(s(s(z)), s(z))) | (~b(s(s(z)), s(s(s(elem!1))))) | (~b(s(s(z)), s(s(elem!1)))) | (s(elem!1) = s(z)) | (~r(z, s(z))) | (~r(s(z), s(s(elem!1)))) | (~r(s(s(s(elem!1))), z))), inference(lemma,lemma(discharge,[]))).
% 1.84/2.10 tff(3023,plain,
% 1.84/2.10 (~b(s(s(z)), s(s(elem!1)))),
% 1.84/2.10 inference(unit_resolution,[status(thm)],[3022, 2991, 156, 2990, 2969, 2988, 2982, 323, 311, 2975])).
% 1.84/2.10 tff(3024,plain,
% 1.84/2.10 ($false),
% 1.84/2.10 inference(unit_resolution,[status(thm)],[390, 3023, 2979, 2966])).
% 1.84/2.10 tff(3025,plain,(b(s(s(elem!1)), z) | (~b(s(s(z)), s(z))) | (~r(z, s(z))) | (~r(s(z), s(s(elem!1)))) | (~r(s(z), s(s(z)))) | (~r(z, s(s(z)))) | (~b(s(s(elem!1)), s(z)))), inference(lemma,lemma(discharge,[]))).
% 1.84/2.10 tff(3026,plain,
% 1.84/2.10 (b(s(s(elem!1)), z)),
% 1.84/2.10 inference(unit_resolution,[status(thm)],[3025, 322, 156, 311, 120, 152, 310])).
% 1.84/2.10 tff(3027,plain,
% 1.84/2.10 (~r(z, s(s(elem!1)))),
% 1.84/2.10 inference(unit_resolution,[status(thm)],[413, 2605, 311, 322])).
% 1.84/2.10 tff(3028,plain,
% 1.84/2.10 (b(z, s(s(elem!1)))),
% 1.84/2.10 inference(unit_resolution,[status(thm)],[1795, 3027])).
% 1.84/2.10 tff(3029,plain,
% 1.84/2.10 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(s(s(elem!1))), z)) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(s(elem!1)), s(z))) | (~b(s(z), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(s(s(elem!1))), z)) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(s(elem!1)), s(z))) | (~b(s(z), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), z)))),
% 1.84/2.10 inference(rewrite,[status(thm)],[])).
% 1.84/2.10 tff(3030,plain,
% 1.84/2.10 (((~b(s(s(s(s(elem!1)))), z)) | (~b(s(s(s(elem!1))), z)) | (~b(s(z), s(s(s(s(elem!1)))))) | (~b(s(s(elem!1)), s(z))) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(s(s(elem!1))), s(s(elem!1))))) <=> ((~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(s(s(elem!1))), z)) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(s(elem!1)), s(z))) | (~b(s(z), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), z)))),
% 1.84/2.10 inference(rewrite,[status(thm)],[])).
% 1.84/2.10 tff(3031,plain,
% 1.84/2.10 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(elem!1)))), z)) | (~b(s(s(s(elem!1))), z)) | (~b(s(z), s(s(s(s(elem!1)))))) | (~b(s(s(elem!1)), s(z))) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(s(s(elem!1))), s(s(elem!1)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(s(s(elem!1))), z)) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(s(elem!1)), s(z))) | (~b(s(z), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), z))))),
% 1.84/2.10 inference(monotonicity,[status(thm)],[3030])).
% 1.84/2.10 tff(3032,plain,
% 1.84/2.10 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(elem!1)))), z)) | (~b(s(s(s(elem!1))), z)) | (~b(s(z), s(s(s(s(elem!1)))))) | (~b(s(s(elem!1)), s(z))) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(s(s(elem!1))), s(s(elem!1)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(s(s(elem!1))), z)) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(s(elem!1)), s(z))) | (~b(s(z), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), z)))),
% 1.84/2.10 inference(transitivity,[status(thm)],[3031, 3029])).
% 1.84/2.10 tff(3033,plain,
% 1.84/2.10 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(elem!1)))), z)) | (~b(s(s(s(elem!1))), z)) | (~b(s(z), s(s(s(s(elem!1)))))) | (~b(s(s(elem!1)), s(z))) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(s(s(elem!1))), s(s(elem!1)))))),
% 1.84/2.10 inference(quant_inst,[status(thm)],[])).
% 1.84/2.10 tff(3034,plain,
% 1.84/2.10 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(s(s(elem!1))), z)) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(s(elem!1)), s(z))) | (~b(s(z), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), z))),
% 1.84/2.10 inference(modus_ponens,[status(thm)],[3033, 3032])).
% 1.84/2.10 tff(3035,plain,
% 1.84/2.10 ($false),
% 1.84/2.10 inference(unit_resolution,[status(thm)],[3034, 166, 839, 96, 310, 121, 1327, 2030])).
% 1.84/2.10 tff(3036,plain,((~b(s(z), s(s(s(s(elem!1)))))) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(s(elem!1)), s(z))) | (~b(s(s(s(elem!1))), z)) | (~r(s(z), s(s(elem!1)))) | (~r(z, s(z)))), inference(lemma,lemma(discharge,[]))).
% 1.84/2.10 tff(3037,plain,
% 1.84/2.10 (~b(s(z), s(s(s(s(elem!1)))))),
% 1.84/2.10 inference(unit_resolution,[status(thm)],[3036, 121, 96, 310, 839, 311, 323])).
% 1.84/2.10 tff(3038,plain,
% 1.84/2.10 (r(s(z), s(s(s(s(elem!1)))))),
% 1.84/2.10 inference(unit_resolution,[status(thm)],[681, 3037])).
% 1.84/2.10 tff(3039,assumption,(b(s(s(s(s(elem!1)))), s(s(z)))), introduced(assumption)).
% 1.84/2.10 tff(3040,plain,
% 1.84/2.10 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), s(s(z)))) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(s(elem!1)), s(z))) | (~b(s(s(z)), s(s(elem!1)))) | (~b(s(s(s(elem!1))), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), s(s(z)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(elem!1))), s(s(z)))) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(s(elem!1)), s(z))) | (~b(s(s(z)), s(s(elem!1)))) | (~b(s(s(s(elem!1))), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), s(s(z)))))),
% 1.84/2.10 inference(rewrite,[status(thm)],[])).
% 1.84/2.10 tff(3041,plain,
% 1.84/2.10 (((~b(s(s(elem!1)), s(z))) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(s(z)), s(s(elem!1)))) | (~b(s(s(s(s(elem!1)))), s(s(z)))) | (~b(s(s(s(elem!1))), s(s(z)))) | (~b(s(s(s(elem!1))), s(s(s(s(elem!1))))))) <=> ((~b(s(s(s(elem!1))), s(s(z)))) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(s(elem!1)), s(z))) | (~b(s(s(z)), s(s(elem!1)))) | (~b(s(s(s(elem!1))), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), s(s(z)))))),
% 1.84/2.10 inference(rewrite,[status(thm)],[])).
% 1.84/2.10 tff(3042,plain,
% 1.84/2.10 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), s(z))) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(s(z)), s(s(elem!1)))) | (~b(s(s(s(s(elem!1)))), s(s(z)))) | (~b(s(s(s(elem!1))), s(s(z)))) | (~b(s(s(s(elem!1))), s(s(s(s(elem!1)))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), s(s(z)))) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(s(elem!1)), s(z))) | (~b(s(s(z)), s(s(elem!1)))) | (~b(s(s(s(elem!1))), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), s(s(z))))))),
% 1.84/2.10 inference(monotonicity,[status(thm)],[3041])).
% 1.84/2.10 tff(3043,plain,
% 1.84/2.10 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), s(z))) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(s(z)), s(s(elem!1)))) | (~b(s(s(s(s(elem!1)))), s(s(z)))) | (~b(s(s(s(elem!1))), s(s(z)))) | (~b(s(s(s(elem!1))), s(s(s(s(elem!1)))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(elem!1))), s(s(z)))) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(s(elem!1)), s(z))) | (~b(s(s(z)), s(s(elem!1)))) | (~b(s(s(s(elem!1))), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), s(s(z)))))),
% 1.84/2.10 inference(transitivity,[status(thm)],[3042, 3040])).
% 1.84/2.10 tff(3044,plain,
% 1.84/2.10 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), s(z))) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(s(z)), s(s(elem!1)))) | (~b(s(s(s(s(elem!1)))), s(s(z)))) | (~b(s(s(s(elem!1))), s(s(z)))) | (~b(s(s(s(elem!1))), s(s(s(s(elem!1)))))))),
% 1.84/2.10 inference(quant_inst,[status(thm)],[])).
% 1.84/2.10 tff(3045,plain,
% 1.84/2.10 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(elem!1))), s(s(z)))) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(s(elem!1)), s(z))) | (~b(s(s(z)), s(s(elem!1)))) | (~b(s(s(s(elem!1))), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), s(s(z))))),
% 1.84/2.10 inference(modus_ponens,[status(thm)],[3044, 3043])).
% 1.84/2.10 tff(3046,plain,
% 1.84/2.10 (~b(s(s(s(elem!1))), s(s(s(s(elem!1)))))),
% 1.84/2.10 inference(unit_resolution,[status(thm)],[3045, 166, 3039, 96, 310, 446, 2060])).
% 1.84/2.10 tff(3047,plain,
% 1.84/2.10 (r(s(s(s(elem!1))), s(s(s(s(elem!1)))))),
% 1.84/2.10 inference(unit_resolution,[status(thm)],[696, 3046, 361])).
% 1.84/2.10 tff(3048,plain,
% 1.84/2.10 (~r(s(s(s(s(elem!1)))), s(s(s(elem!1))))),
% 1.84/2.10 inference(unit_resolution,[status(thm)],[2125, 3047, 119, 699])).
% 1.84/2.10 tff(3049,plain,
% 1.84/2.10 (b(s(s(s(s(elem!1)))), s(s(s(elem!1))))),
% 1.84/2.10 inference(unit_resolution,[status(thm)],[1065, 3048, 1038])).
% 1.84/2.10 tff(3050,plain,
% 1.84/2.10 (~r(s(s(s(s(elem!1)))), s(z))),
% 1.84/2.10 inference(unit_resolution,[status(thm)],[708, 3047, 119, 699])).
% 1.84/2.10 tff(3051,plain,
% 1.84/2.10 (b(s(s(s(s(elem!1)))), s(z))),
% 1.84/2.10 inference(unit_resolution,[status(thm)],[661, 3050])).
% 1.84/2.10 tff(3052,plain,
% 1.84/2.10 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), s(s(z)))) | (~b(s(s(elem!1)), s(z))) | (~b(s(s(z)), s(s(elem!1)))) | (~b(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~b(s(s(s(s(elem!1)))), s(z))) | (~b(s(s(s(s(elem!1)))), s(s(z)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(elem!1))), s(s(z)))) | (~b(s(s(elem!1)), s(z))) | (~b(s(s(z)), s(s(elem!1)))) | (~b(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~b(s(s(s(s(elem!1)))), s(z))) | (~b(s(s(s(s(elem!1)))), s(s(z)))))),
% 1.84/2.10 inference(rewrite,[status(thm)],[])).
% 1.84/2.10 tff(3053,plain,
% 1.84/2.10 (((~b(s(s(elem!1)), s(z))) | (~b(s(s(s(s(elem!1)))), s(z))) | (~b(s(s(z)), s(s(elem!1)))) | (~b(s(s(s(elem!1))), s(s(z)))) | (~b(s(s(s(s(elem!1)))), s(s(z)))) | (~b(s(s(s(s(elem!1)))), s(s(s(elem!1)))))) <=> ((~b(s(s(s(elem!1))), s(s(z)))) | (~b(s(s(elem!1)), s(z))) | (~b(s(s(z)), s(s(elem!1)))) | (~b(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~b(s(s(s(s(elem!1)))), s(z))) | (~b(s(s(s(s(elem!1)))), s(s(z)))))),
% 1.84/2.10 inference(rewrite,[status(thm)],[])).
% 1.84/2.10 tff(3054,plain,
% 1.84/2.10 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), s(z))) | (~b(s(s(s(s(elem!1)))), s(z))) | (~b(s(s(z)), s(s(elem!1)))) | (~b(s(s(s(elem!1))), s(s(z)))) | (~b(s(s(s(s(elem!1)))), s(s(z)))) | (~b(s(s(s(s(elem!1)))), s(s(s(elem!1))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), s(s(z)))) | (~b(s(s(elem!1)), s(z))) | (~b(s(s(z)), s(s(elem!1)))) | (~b(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~b(s(s(s(s(elem!1)))), s(z))) | (~b(s(s(s(s(elem!1)))), s(s(z))))))),
% 1.84/2.10 inference(monotonicity,[status(thm)],[3053])).
% 1.84/2.10 tff(3055,plain,
% 1.84/2.10 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), s(z))) | (~b(s(s(s(s(elem!1)))), s(z))) | (~b(s(s(z)), s(s(elem!1)))) | (~b(s(s(s(elem!1))), s(s(z)))) | (~b(s(s(s(s(elem!1)))), s(s(z)))) | (~b(s(s(s(s(elem!1)))), s(s(s(elem!1))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(elem!1))), s(s(z)))) | (~b(s(s(elem!1)), s(z))) | (~b(s(s(z)), s(s(elem!1)))) | (~b(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~b(s(s(s(s(elem!1)))), s(z))) | (~b(s(s(s(s(elem!1)))), s(s(z)))))),
% 1.84/2.10 inference(transitivity,[status(thm)],[3054, 3052])).
% 1.84/2.10 tff(3056,plain,
% 1.84/2.10 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), s(z))) | (~b(s(s(s(s(elem!1)))), s(z))) | (~b(s(s(z)), s(s(elem!1)))) | (~b(s(s(s(elem!1))), s(s(z)))) | (~b(s(s(s(s(elem!1)))), s(s(z)))) | (~b(s(s(s(s(elem!1)))), s(s(s(elem!1))))))),
% 1.84/2.10 inference(quant_inst,[status(thm)],[])).
% 1.84/2.10 tff(3057,plain,
% 1.84/2.10 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(elem!1))), s(s(z)))) | (~b(s(s(elem!1)), s(z))) | (~b(s(s(z)), s(s(elem!1)))) | (~b(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~b(s(s(s(s(elem!1)))), s(z))) | (~b(s(s(s(s(elem!1)))), s(s(z))))),
% 1.84/2.10 inference(modus_ponens,[status(thm)],[3056, 3055])).
% 1.84/2.10 tff(3058,plain,
% 1.84/2.10 ($false),
% 1.84/2.10 inference(unit_resolution,[status(thm)],[3057, 166, 3039, 310, 446, 3051, 3049, 2060])).
% 1.84/2.10 tff(3059,plain,((~b(s(s(s(s(elem!1)))), s(s(z)))) | (~b(s(s(elem!1)), s(z))) | (~b(s(s(z)), s(s(elem!1)))) | (~b(s(s(s(elem!1))), s(s(z)))) | (~r(s(z), s(s(s(elem!1))))) | (~r(s(z), s(s(s(s(elem!1)))))) | (s(s(s(elem!1))) = s(s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(z)))), inference(lemma,lemma(discharge,[]))).
% 1.84/2.10 tff(3060,plain,
% 1.84/2.10 (~b(s(s(s(s(elem!1)))), s(s(z)))),
% 1.84/2.10 inference(unit_resolution,[status(thm)],[3059, 3038, 310, 361, 119, 446, 2060, 96])).
% 1.84/2.10 tff(3061,plain,
% 1.84/2.10 (r(s(s(s(s(elem!1)))), s(s(z)))),
% 1.84/2.10 inference(unit_resolution,[status(thm)],[1299, 3060])).
% 1.84/2.10 tff(3062,plain,
% 1.84/2.10 (~r(s(s(elem!1)), s(s(s(s(elem!1)))))),
% 1.84/2.10 inference(unit_resolution,[status(thm)],[2176, 3061, 311, 3038])).
% 1.84/2.10 tff(3063,assumption,(~r(s(s(elem!1)), s(s(s(s(elem!1)))))), introduced(assumption)).
% 1.84/2.10 tff(3064,assumption,(~b(s(s(s(s(elem!1)))), s(z))), introduced(assumption)).
% 1.84/2.11 tff(3065,plain,
% 1.84/2.11 (r(s(s(s(s(elem!1)))), s(z))),
% 1.84/2.11 inference(unit_resolution,[status(thm)],[661, 3064])).
% 1.84/2.11 tff(3066,plain,
% 1.84/2.11 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(elem!1)))) | (~b(s(s(elem!1)), s(s(s(s(elem!1)))))) | (~b(z, s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(s(elem!1)))) | (~b(s(s(elem!1)), s(s(s(s(elem!1)))))) | (~b(z, s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), z)))),
% 1.84/2.11 inference(rewrite,[status(thm)],[])).
% 1.84/2.11 tff(3067,plain,
% 1.84/2.11 (((~b(z, s(s(s(s(elem!1)))))) | (~b(z, s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), z)) | (~b(s(s(elem!1)), s(s(s(s(elem!1)))))) | (~b(z, s(s(s(s(elem!1)))))) | (~b(z, s(s(elem!1))))) <=> ((~b(z, s(s(elem!1)))) | (~b(s(s(elem!1)), s(s(s(s(elem!1)))))) | (~b(z, s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), z)))),
% 1.84/2.11 inference(rewrite,[status(thm)],[])).
% 1.84/2.11 tff(3068,plain,
% 1.84/2.11 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(s(s(elem!1)))))) | (~b(z, s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), z)) | (~b(s(s(elem!1)), s(s(s(s(elem!1)))))) | (~b(z, s(s(s(s(elem!1)))))) | (~b(z, s(s(elem!1)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(elem!1)))) | (~b(s(s(elem!1)), s(s(s(s(elem!1)))))) | (~b(z, s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), z))))),
% 1.84/2.11 inference(monotonicity,[status(thm)],[3067])).
% 1.84/2.11 tff(3069,plain,
% 1.84/2.11 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(s(s(elem!1)))))) | (~b(z, s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), z)) | (~b(s(s(elem!1)), s(s(s(s(elem!1)))))) | (~b(z, s(s(s(s(elem!1)))))) | (~b(z, s(s(elem!1)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(s(elem!1)))) | (~b(s(s(elem!1)), s(s(s(s(elem!1)))))) | (~b(z, s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), z)))),
% 1.84/2.11 inference(transitivity,[status(thm)],[3068, 3066])).
% 1.84/2.11 tff(3070,plain,
% 1.84/2.11 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(s(s(elem!1)))))) | (~b(z, s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), z)) | (~b(s(s(elem!1)), s(s(s(s(elem!1)))))) | (~b(z, s(s(s(s(elem!1)))))) | (~b(z, s(s(elem!1)))))),
% 1.84/2.11 inference(quant_inst,[status(thm)],[])).
% 1.84/2.11 tff(3071,plain,
% 1.84/2.11 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(s(elem!1)))) | (~b(s(s(elem!1)), s(s(s(s(elem!1)))))) | (~b(z, s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), z))),
% 1.84/2.11 inference(modus_ponens,[status(thm)],[3070, 3069])).
% 1.84/2.11 tff(3072,plain,
% 1.84/2.11 ($false),
% 1.84/2.11 inference(unit_resolution,[status(thm)],[3071, 166, 1820, 1046, 2039, 2037])).
% 1.84/2.11 tff(3073,plain,((~r(s(s(s(s(elem!1)))), s(z))) | (~b(z, s(s(elem!1)))) | (~b(s(s(elem!1)), s(s(s(s(elem!1)))))) | (~r(s(z), s(s(elem!1)))) | (~r(z, s(z)))), inference(lemma,lemma(discharge,[]))).
% 1.84/2.11 tff(3074,plain,
% 1.84/2.11 (~b(s(s(elem!1)), s(s(s(s(elem!1)))))),
% 1.84/2.11 inference(unit_resolution,[status(thm)],[3073, 3065, 1820, 311, 323])).
% 1.84/2.11 tff(3075,plain,
% 1.84/2.11 (s(s(elem!1)) = s(s(s(s(elem!1))))),
% 1.84/2.11 inference(unit_resolution,[status(thm)],[827, 3074, 3063])).
% 1.84/2.11 tff(3076,plain,
% 1.84/2.11 (b(s(s(elem!1)), s(z)) <=> b(s(s(s(s(elem!1)))), s(z))),
% 1.84/2.11 inference(monotonicity,[status(thm)],[3075])).
% 1.84/2.11 tff(3077,plain,
% 1.84/2.11 (b(s(s(s(s(elem!1)))), s(z)) <=> b(s(s(elem!1)), s(z))),
% 1.84/2.11 inference(symmetry,[status(thm)],[3076])).
% 1.84/2.11 tff(3078,plain,
% 1.84/2.11 ((~b(s(s(s(s(elem!1)))), s(z))) <=> (~b(s(s(elem!1)), s(z)))),
% 1.84/2.11 inference(monotonicity,[status(thm)],[3077])).
% 1.84/2.11 tff(3079,plain,
% 1.84/2.11 (~b(s(s(elem!1)), s(z))),
% 1.84/2.11 inference(modus_ponens,[status(thm)],[3064, 3078])).
% 1.84/2.11 tff(3080,plain,
% 1.84/2.11 ($false),
% 1.84/2.11 inference(unit_resolution,[status(thm)],[310, 3079])).
% 1.84/2.11 tff(3081,plain,(b(s(s(s(s(elem!1)))), s(z)) | (~b(s(s(elem!1)), s(z))) | r(s(s(elem!1)), s(s(s(s(elem!1))))) | (~b(z, s(s(elem!1)))) | (~r(s(z), s(s(elem!1)))) | (~r(z, s(z)))), inference(lemma,lemma(discharge,[]))).
% 1.84/2.11 tff(3082,plain,
% 1.84/2.11 (b(s(s(s(s(elem!1)))), s(z))),
% 1.84/2.11 inference(unit_resolution,[status(thm)],[3081, 3062, 310, 311, 1820, 323])).
% 1.84/2.11 tff(3083,plain,
% 1.84/2.11 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(s(s(elem!1))), s(s(z)))) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(s(z)), s(s(elem!1)))) | (~b(s(s(elem!1)), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(s(s(elem!1))), s(s(z)))) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(s(z)), s(s(elem!1)))) | (~b(s(s(elem!1)), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), s(z))))),
% 1.84/2.11 inference(rewrite,[status(thm)],[])).
% 1.84/2.11 tff(3084,plain,
% 1.84/2.11 (((~b(s(s(s(s(elem!1)))), s(z))) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(s(elem!1)), s(s(s(s(elem!1)))))) | (~b(s(s(z)), s(s(elem!1)))) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(s(s(elem!1))), s(s(z))))) <=> ((~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(s(s(elem!1))), s(s(z)))) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(s(z)), s(s(elem!1)))) | (~b(s(s(elem!1)), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), s(z))))),
% 1.84/2.11 inference(rewrite,[status(thm)],[])).
% 1.84/2.11 tff(3085,plain,
% 1.84/2.11 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(elem!1)))), s(z))) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(s(elem!1)), s(s(s(s(elem!1)))))) | (~b(s(s(z)), s(s(elem!1)))) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(s(s(elem!1))), s(s(z)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(s(s(elem!1))), s(s(z)))) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(s(z)), s(s(elem!1)))) | (~b(s(s(elem!1)), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), s(z)))))),
% 1.84/2.11 inference(monotonicity,[status(thm)],[3084])).
% 1.84/2.11 tff(3086,plain,
% 1.84/2.11 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(elem!1)))), s(z))) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(s(elem!1)), s(s(s(s(elem!1)))))) | (~b(s(s(z)), s(s(elem!1)))) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(s(s(elem!1))), s(s(z)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(s(s(elem!1))), s(s(z)))) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(s(z)), s(s(elem!1)))) | (~b(s(s(elem!1)), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), s(z))))),
% 1.84/2.11 inference(transitivity,[status(thm)],[3085, 3083])).
% 1.84/2.11 tff(3087,plain,
% 1.84/2.11 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(elem!1)))), s(z))) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(s(elem!1)), s(s(s(s(elem!1)))))) | (~b(s(s(z)), s(s(elem!1)))) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(s(s(elem!1))), s(s(z)))))),
% 1.84/2.11 inference(quant_inst,[status(thm)],[])).
% 1.84/2.11 tff(3088,plain,
% 1.84/2.11 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(s(s(elem!1))), s(s(z)))) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(s(z)), s(s(elem!1)))) | (~b(s(s(elem!1)), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), s(z)))),
% 1.84/2.11 inference(modus_ponens,[status(thm)],[3087, 3086])).
% 1.84/2.11 tff(3089,plain,
% 1.84/2.11 ($false),
% 1.84/2.11 inference(unit_resolution,[status(thm)],[3088, 166, 839, 96, 446, 1046, 1402, 2060])).
% 1.84/2.11 tff(3090,plain,((~b(s(s(elem!1)), s(s(s(s(elem!1)))))) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(s(z)), s(s(elem!1)))) | (~b(s(s(s(s(elem!1)))), s(z))) | (~b(s(s(s(elem!1))), s(s(z))))), inference(lemma,lemma(discharge,[]))).
% 1.84/2.11 tff(3091,plain,
% 1.84/2.11 (~b(s(s(elem!1)), s(s(s(s(elem!1)))))),
% 1.84/2.11 inference(unit_resolution,[status(thm)],[3090, 3082, 96, 446, 839, 2060])).
% 1.84/2.11 tff(3092,plain,
% 1.84/2.11 (s(s(elem!1)) = s(s(s(s(elem!1))))),
% 1.84/2.11 inference(unit_resolution,[status(thm)],[827, 3091, 3062])).
% 1.84/2.11 tff(3093,plain,
% 1.84/2.11 (s(s(s(s(elem!1)))) = s(s(elem!1))),
% 1.84/2.11 inference(unit_resolution,[status(thm)],[1159, 3092])).
% 1.84/2.11 tff(3094,plain,
% 1.84/2.11 (s(s(s(elem!1))) = s(elem!1)),
% 1.84/2.11 inference(unit_resolution,[status(thm)],[1166, 3093])).
% 1.84/2.11 tff(3095,plain,
% 1.84/2.11 (b(s(s(s(elem!1))), z) <=> b(s(elem!1), z)),
% 1.84/2.11 inference(monotonicity,[status(thm)],[3094])).
% 1.84/2.11 tff(3096,plain,
% 1.84/2.11 (b(s(elem!1), z)),
% 1.84/2.11 inference(modus_ponens,[status(thm)],[121, 3095])).
% 1.84/2.11 tff(3097,plain,
% 1.84/2.11 (s(elem!1) = s(s(s(elem!1)))),
% 1.84/2.11 inference(symmetry,[status(thm)],[3094])).
% 1.84/2.11 tff(3098,plain,
% 1.84/2.11 (b(s(elem!1), s(s(elem!1))) <=> b(s(s(s(elem!1))), s(s(s(s(elem!1)))))),
% 1.84/2.11 inference(monotonicity,[status(thm)],[3097, 3092])).
% 1.84/2.11 tff(3099,plain,
% 1.84/2.11 (b(s(s(s(elem!1))), s(s(s(s(elem!1))))) <=> b(s(elem!1), s(s(elem!1)))),
% 1.84/2.11 inference(symmetry,[status(thm)],[3098])).
% 1.84/2.11 tff(3100,plain,
% 1.84/2.11 (b(s(s(s(elem!1))), s(s(elem!1))) <=> b(s(s(s(elem!1))), s(s(s(s(elem!1)))))),
% 1.84/2.11 inference(monotonicity,[status(thm)],[3092])).
% 1.84/2.11 tff(3101,plain,
% 1.84/2.11 (b(s(s(s(elem!1))), s(s(s(s(elem!1)))))),
% 1.84/2.11 inference(modus_ponens,[status(thm)],[839, 3100])).
% 1.84/2.11 tff(3102,plain,
% 1.84/2.11 (b(s(elem!1), s(s(elem!1)))),
% 1.84/2.11 inference(modus_ponens,[status(thm)],[3101, 3099])).
% 1.84/2.11 tff(3103,plain,
% 1.84/2.11 ($false),
% 1.84/2.11 inference(unit_resolution,[status(thm)],[2756, 3102, 3096, 1820, 592])).
% 1.84/2.11 tff(3104,plain,((~b(s(s(s(elem!1))), z)) | (~b(z, s(s(elem!1)))) | (~b(s(s(elem!1)), z)) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(s(z)), s(s(elem!1)))) | (~b(s(s(s(elem!1))), s(s(z)))) | (~b(s(s(elem!1)), s(z))) | (~r(s(z), s(s(elem!1)))) | (~r(z, s(z))) | (s(s(s(elem!1))) = s(s(s(s(elem!1))))) | (~r(s(z), s(s(s(elem!1)))))), inference(lemma,lemma(discharge,[]))).
% 1.84/2.11 tff(3105,plain,
% 1.84/2.11 (~b(s(s(s(elem!1))), z)),
% 1.84/2.11 inference(unit_resolution,[status(thm)],[3104, 3028, 3026, 2951, 2921, 446, 2941, 310, 311, 322, 358, 2931])).
% 1.84/2.11 tff(3106,plain,
% 1.84/2.11 (r(s(s(s(elem!1))), z)),
% 1.84/2.11 inference(unit_resolution,[status(thm)],[94, 3105])).
% 1.84/2.11 tff(3107,plain,
% 1.84/2.11 ($false),
% 1.84/2.11 inference(unit_resolution,[status(thm)],[237, 197, 3106, 152, 2604, 2931])).
% 1.84/2.11 tff(3108,plain,((s(s(elem!1)) = s(s(s(elem!1)))) | (~b(s(s(z)), s(s(elem!1)))) | (~b(s(s(elem!1)), s(z))) | (~r(s(z), s(s(elem!1)))) | (~b(s(s(z)), s(z))) | b(z, s(s(z))) | b(z, s(z)) | (~r(s(z), s(s(z))))), inference(lemma,lemma(discharge,[]))).
% 1.84/2.11 tff(3109,plain,
% 1.84/2.11 (s(s(elem!1)) = s(s(s(elem!1)))),
% 1.84/2.11 inference(unit_resolution,[status(thm)],[3108, 2602, 310, 311, 156, 125, 312, 120])).
% 1.84/2.11 tff(3110,plain,
% 1.84/2.11 (s(s(s(elem!1))) = s(elem!1)),
% 1.84/2.11 inference(unit_resolution,[status(thm)],[2594, 3109])).
% 1.84/2.11 tff(3111,plain,
% 1.84/2.11 (s(elem!1) = s(s(s(elem!1)))),
% 1.84/2.11 inference(symmetry,[status(thm)],[3110])).
% 1.84/2.11 tff(3112,plain,
% 1.84/2.11 (inj_0(s(elem!1)) = inj_0(s(s(s(elem!1))))),
% 1.84/2.11 inference(monotonicity,[status(thm)],[3111])).
% 1.84/2.11 tff(3113,plain,
% 1.84/2.11 (elem!1 = s(s(s(elem!1)))),
% 1.84/2.11 inference(transitivity,[status(thm)],[1170, 3112, 104, 3109])).
% 1.84/2.11 tff(3114,plain,
% 1.84/2.11 (b(elem!1, s(s(s(z)))) <=> b(s(s(s(elem!1))), s(s(s(z))))),
% 1.84/2.11 inference(monotonicity,[status(thm)],[3113])).
% 1.84/2.11 tff(3115,plain,
% 1.84/2.11 (s(s(s(elem!1))) = s(elem!1)),
% 1.84/2.11 inference(unit_resolution,[status(thm)],[2594, 334])).
% 1.84/2.11 tff(3116,plain,
% 1.84/2.11 (s(elem!1) = s(s(s(elem!1)))),
% 1.84/2.11 inference(symmetry,[status(thm)],[3115])).
% 1.84/2.11 tff(3117,plain,
% 1.84/2.11 (inj_0(s(elem!1)) = inj_0(s(s(s(elem!1))))),
% 1.84/2.11 inference(monotonicity,[status(thm)],[3116])).
% 1.84/2.11 tff(3118,plain,
% 1.84/2.11 (s(s(s(z))) = s(s(s(elem!1)))),
% 1.84/2.11 inference(transitivity,[status(thm)],[1546, 1170, 3117, 104, 334])).
% 1.84/2.11 tff(3119,plain,
% 1.84/2.11 (inj_0(s(s(s(z)))) = inj_0(s(s(s(elem!1))))),
% 1.84/2.11 inference(monotonicity,[status(thm)],[3118])).
% 1.84/2.11 tff(3120,plain,
% 1.84/2.11 (s(s(z)) = s(s(s(elem!1)))),
% 1.84/2.11 inference(transitivity,[status(thm)],[1666, 3119, 104, 334])).
% 1.84/2.11 tff(3121,plain,
% 1.84/2.11 ($false),
% 1.84/2.11 inference(unit_resolution,[status(thm)],[209, 3120])).
% 1.84/2.11 tff(3122,plain,((~(s(s(s(z))) = elem!1)) | (~(s(s(elem!1)) = s(s(s(elem!1)))))), inference(lemma,lemma(discharge,[]))).
% 1.84/2.11 tff(3123,plain,
% 1.84/2.11 (~(s(s(s(z))) = elem!1)),
% 1.84/2.11 inference(unit_resolution,[status(thm)],[3122, 3109])).
% 1.84/2.11 tff(3124,plain,
% 1.84/2.11 (~(elem!1 = s(s(s(z))))),
% 1.84/2.11 inference(unit_resolution,[status(thm)],[1564, 3123])).
% 1.84/2.11 tff(3125,plain,
% 1.84/2.11 (elem!1 = s(s(elem!1))),
% 1.84/2.11 inference(transitivity,[status(thm)],[1170, 3112, 104])).
% 1.84/2.11 tff(3126,plain,
% 1.84/2.11 (r(elem!1, s(s(s(z)))) <=> r(s(s(elem!1)), s(s(s(z))))),
% 1.84/2.11 inference(monotonicity,[status(thm)],[3125])).
% 1.84/2.11 tff(3127,plain,
% 1.84/2.11 (r(s(s(elem!1)), s(s(s(z)))) <=> r(elem!1, s(s(s(z))))),
% 1.84/2.11 inference(symmetry,[status(thm)],[3126])).
% 1.84/2.11 tff(3128,plain,
% 1.84/2.11 (s(s(s(elem!1))) = s(s(elem!1))),
% 1.84/2.11 inference(symmetry,[status(thm)],[3109])).
% 1.84/2.11 tff(3129,plain,
% 1.84/2.11 (r(s(s(s(elem!1))), s(s(s(z)))) <=> r(s(s(elem!1)), s(s(s(z))))),
% 1.84/2.11 inference(monotonicity,[status(thm)],[3128])).
% 1.84/2.11 tff(3130,plain,
% 1.84/2.11 (r(s(s(s(elem!1))), s(s(s(z)))) <=> r(elem!1, s(s(s(z))))),
% 1.84/2.11 inference(transitivity,[status(thm)],[3129, 3127])).
% 1.84/2.11 tff(3131,plain,
% 1.84/2.11 ((~r(s(s(s(elem!1))), s(s(s(z))))) <=> (~r(elem!1, s(s(s(z)))))),
% 1.84/2.11 inference(monotonicity,[status(thm)],[3130])).
% 1.84/2.11 tff(3132,plain,
% 1.84/2.11 (r(z, elem!1) <=> r(z, s(s(s(elem!1))))),
% 1.84/2.11 inference(monotonicity,[status(thm)],[3113])).
% 1.84/2.11 tff(3133,plain,
% 1.84/2.11 (~r(s(s(z)), z)),
% 1.84/2.11 inference(unit_resolution,[status(thm)],[2959, 322, 152, 120])).
% 1.84/2.11 tff(3134,plain,
% 1.84/2.11 (b(s(s(z)), z)),
% 1.84/2.11 inference(unit_resolution,[status(thm)],[186, 3133])).
% 1.84/2.11 tff(3135,plain,
% 1.84/2.11 (r(s(s(elem!1)), elem!1) <=> r(s(s(s(elem!1))), elem!1)),
% 1.84/2.11 inference(monotonicity,[status(thm)],[3109])).
% 1.84/2.11 tff(3136,plain,
% 1.84/2.11 (r(s(s(s(elem!1))), elem!1) <=> r(s(s(elem!1)), elem!1)),
% 1.84/2.11 inference(symmetry,[status(thm)],[3135])).
% 1.84/2.11 tff(3137,plain,
% 1.84/2.11 (r(s(s(s(elem!1))), elem!1) <=> r(s(s(s(elem!1))), s(s(s(elem!1))))),
% 1.84/2.11 inference(monotonicity,[status(thm)],[3113])).
% 1.84/2.11 tff(3138,plain,
% 1.84/2.11 (r(s(s(s(elem!1))), s(s(s(elem!1)))) <=> r(s(s(s(elem!1))), elem!1)),
% 1.84/2.11 inference(symmetry,[status(thm)],[3137])).
% 1.84/2.11 tff(3139,plain,
% 1.84/2.11 (r(s(s(s(elem!1))), s(s(s(elem!1)))) <=> r(s(s(elem!1)), elem!1)),
% 1.84/2.11 inference(transitivity,[status(thm)],[3138, 3136])).
% 1.84/2.11 tff(3140,plain,
% 1.84/2.11 ((~r(s(s(s(elem!1))), s(s(s(elem!1))))) <=> (~r(s(s(elem!1)), elem!1))),
% 1.84/2.11 inference(monotonicity,[status(thm)],[3139])).
% 1.84/2.11 tff(3141,plain,
% 1.84/2.11 (^[X: $i] : refl((~r(X, X)) <=> (~r(X, X)))),
% 1.84/2.11 inference(bind,[status(th)],[])).
% 1.84/2.11 tff(3142,plain,
% 1.84/2.11 (![X: $i] : (~r(X, X)) <=> ![X: $i] : (~r(X, X))),
% 1.84/2.11 inference(quant_intro,[status(thm)],[3141])).
% 1.84/2.11 tff(3143,plain,
% 1.84/2.11 (![X: $i] : (~r(X, X)) <=> ![X: $i] : (~r(X, X))),
% 1.84/2.11 inference(rewrite,[status(thm)],[])).
% 1.84/2.11 tff(3144,axiom,(![X: $i] : (~r(X, X))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','ri')).
% 1.84/2.11 tff(3145,plain,
% 1.84/2.11 (![X: $i] : (~r(X, X))),
% 1.84/2.11 inference(modus_ponens,[status(thm)],[3144, 3143])).
% 1.84/2.11 tff(3146,plain,(
% 1.84/2.11 ![X: $i] : (~r(X, X))),
% 1.84/2.11 inference(skolemize,[status(sab)],[3145])).
% 1.84/2.11 tff(3147,plain,
% 1.84/2.11 (![X: $i] : (~r(X, X))),
% 1.84/2.11 inference(modus_ponens,[status(thm)],[3146, 3142])).
% 1.84/2.11 tff(3148,plain,
% 1.84/2.11 ((~![X: $i] : (~r(X, X))) | (~r(s(s(s(elem!1))), s(s(s(elem!1)))))),
% 1.84/2.11 inference(quant_inst,[status(thm)],[])).
% 1.84/2.11 tff(3149,plain,
% 1.84/2.11 (~r(s(s(s(elem!1))), s(s(s(elem!1))))),
% 1.84/2.11 inference(unit_resolution,[status(thm)],[3148, 3147])).
% 1.84/2.11 tff(3150,plain,
% 1.84/2.11 (~r(s(s(elem!1)), elem!1)),
% 1.84/2.11 inference(modus_ponens,[status(thm)],[3149, 3140])).
% 1.84/2.11 tff(3151,plain,
% 1.84/2.11 (r(z, elem!1)),
% 1.84/2.11 inference(unit_resolution,[status(thm)],[2571, 3150, 310, 312, 311, 3134, 156, 3026, 2601, 2256])).
% 1.84/2.11 tff(3152,plain,
% 1.84/2.11 (r(z, s(s(s(elem!1))))),
% 1.94/2.11 inference(modus_ponens,[status(thm)],[3151, 3132])).
% 1.94/2.11 tff(3153,plain,
% 1.94/2.11 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(s(z)))) | (~b(s(s(s(elem!1))), z)) | (~b(s(s(z)), z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(s(z)))) | (~b(s(s(s(elem!1))), z)) | (~b(s(s(z)), z)))),
% 1.94/2.11 inference(rewrite,[status(thm)],[])).
% 1.94/2.11 tff(3154,plain,
% 1.94/2.11 (((~b(s(s(s(elem!1))), z)) | (~b(s(s(s(elem!1))), z)) | (~b(z, s(s(s(elem!1))))) | (~b(s(s(z)), z)) | (~b(s(s(s(elem!1))), z)) | (~b(s(s(s(elem!1))), s(s(z))))) <=> ((~b(z, s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(s(z)))) | (~b(s(s(s(elem!1))), z)) | (~b(s(s(z)), z)))),
% 1.94/2.11 inference(rewrite,[status(thm)],[])).
% 1.94/2.11 tff(3155,plain,
% 1.94/2.11 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), z)) | (~b(s(s(s(elem!1))), z)) | (~b(z, s(s(s(elem!1))))) | (~b(s(s(z)), z)) | (~b(s(s(s(elem!1))), z)) | (~b(s(s(s(elem!1))), s(s(z)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(s(z)))) | (~b(s(s(s(elem!1))), z)) | (~b(s(s(z)), z))))),
% 1.94/2.11 inference(monotonicity,[status(thm)],[3154])).
% 1.94/2.11 tff(3156,plain,
% 1.94/2.11 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), z)) | (~b(s(s(s(elem!1))), z)) | (~b(z, s(s(s(elem!1))))) | (~b(s(s(z)), z)) | (~b(s(s(s(elem!1))), z)) | (~b(s(s(s(elem!1))), s(s(z)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(s(z)))) | (~b(s(s(s(elem!1))), z)) | (~b(s(s(z)), z)))),
% 1.94/2.11 inference(transitivity,[status(thm)],[3155, 3153])).
% 1.94/2.11 tff(3157,plain,
% 1.94/2.11 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), z)) | (~b(s(s(s(elem!1))), z)) | (~b(z, s(s(s(elem!1))))) | (~b(s(s(z)), z)) | (~b(s(s(s(elem!1))), z)) | (~b(s(s(s(elem!1))), s(s(z)))))),
% 1.94/2.11 inference(quant_inst,[status(thm)],[])).
% 1.94/2.11 tff(3158,plain,
% 1.94/2.11 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(s(z)))) | (~b(s(s(s(elem!1))), z)) | (~b(s(s(z)), z))),
% 1.94/2.11 inference(modus_ponens,[status(thm)],[3157, 3156])).
% 1.94/2.11 tff(3159,plain,
% 1.94/2.11 (~b(s(s(s(elem!1))), s(s(z)))),
% 1.94/2.11 inference(unit_resolution,[status(thm)],[3158, 166, 2281, 2279, 122])).
% 1.94/2.11 tff(3160,plain,
% 1.94/2.11 (r(s(s(s(elem!1))), s(s(z)))),
% 1.94/2.11 inference(unit_resolution,[status(thm)],[218, 3159])).
% 1.94/2.11 tff(3161,plain,
% 1.94/2.11 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), z)) | (~b(s(s(z)), z)) | (~b(s(s(z)), s(s(s(elem!1))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), z)) | (~b(s(s(z)), z)) | (~b(s(s(z)), s(s(s(elem!1))))))),
% 1.94/2.11 inference(rewrite,[status(thm)],[])).
% 1.94/2.11 tff(3162,plain,
% 1.94/2.11 (((~b(s(s(s(elem!1))), z)) | (~b(s(s(z)), z)) | (~b(z, s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), z)) | (~b(s(s(z)), z)) | (~b(s(s(z)), s(s(s(elem!1)))))) <=> ((~b(z, s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), z)) | (~b(s(s(z)), z)) | (~b(s(s(z)), s(s(s(elem!1))))))),
% 1.94/2.11 inference(rewrite,[status(thm)],[])).
% 1.94/2.11 tff(3163,plain,
% 1.94/2.11 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), z)) | (~b(s(s(z)), z)) | (~b(z, s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), z)) | (~b(s(s(z)), z)) | (~b(s(s(z)), s(s(s(elem!1))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), z)) | (~b(s(s(z)), z)) | (~b(s(s(z)), s(s(s(elem!1)))))))),
% 1.94/2.11 inference(monotonicity,[status(thm)],[3162])).
% 1.94/2.11 tff(3164,plain,
% 1.94/2.11 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), z)) | (~b(s(s(z)), z)) | (~b(z, s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), z)) | (~b(s(s(z)), z)) | (~b(s(s(z)), s(s(s(elem!1))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), z)) | (~b(s(s(z)), z)) | (~b(s(s(z)), s(s(s(elem!1))))))),
% 1.94/2.11 inference(transitivity,[status(thm)],[3163, 3161])).
% 1.94/2.11 tff(3165,plain,
% 1.94/2.11 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), z)) | (~b(s(s(z)), z)) | (~b(z, s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), z)) | (~b(s(s(z)), z)) | (~b(s(s(z)), s(s(s(elem!1))))))),
% 1.94/2.11 inference(quant_inst,[status(thm)],[])).
% 1.94/2.11 tff(3166,plain,
% 1.94/2.11 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), z)) | (~b(s(s(z)), z)) | (~b(s(s(z)), s(s(s(elem!1)))))),
% 1.94/2.11 inference(modus_ponens,[status(thm)],[3165, 3164])).
% 1.94/2.11 tff(3167,plain,
% 1.94/2.11 (~b(s(s(z)), s(s(s(elem!1))))),
% 1.94/2.11 inference(unit_resolution,[status(thm)],[3166, 166, 2281, 2279, 122])).
% 1.94/2.11 tff(3168,plain,
% 1.94/2.11 (r(s(s(z)), s(s(s(elem!1))))),
% 1.94/2.11 inference(unit_resolution,[status(thm)],[279, 3167])).
% 1.94/2.11 tff(3169,plain,
% 1.94/2.11 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), s(z))) | (~r(s(z), s(s(z)))) | (~r(s(s(z)), s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), s(s(z)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(elem!1))), s(z))) | (~r(s(z), s(s(z)))) | (~r(s(s(z)), s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), s(s(z)))))),
% 1.94/2.11 inference(rewrite,[status(thm)],[])).
% 1.94/2.11 tff(3170,plain,
% 1.94/2.11 (((~r(s(s(z)), s(s(s(elem!1))))) | (~r(s(z), s(s(z)))) | (~r(s(s(s(elem!1))), s(s(z)))) | (~r(s(s(s(elem!1))), s(z)))) <=> ((~r(s(s(s(elem!1))), s(z))) | (~r(s(z), s(s(z)))) | (~r(s(s(z)), s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), s(s(z)))))),
% 1.94/2.11 inference(rewrite,[status(thm)],[])).
% 1.94/2.11 tff(3171,plain,
% 1.94/2.11 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(z)), s(s(s(elem!1))))) | (~r(s(z), s(s(z)))) | (~r(s(s(s(elem!1))), s(s(z)))) | (~r(s(s(s(elem!1))), s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), s(z))) | (~r(s(z), s(s(z)))) | (~r(s(s(z)), s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), s(s(z))))))),
% 1.94/2.11 inference(monotonicity,[status(thm)],[3170])).
% 1.94/2.11 tff(3172,plain,
% 1.94/2.11 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(z)), s(s(s(elem!1))))) | (~r(s(z), s(s(z)))) | (~r(s(s(s(elem!1))), s(s(z)))) | (~r(s(s(s(elem!1))), s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(elem!1))), s(z))) | (~r(s(z), s(s(z)))) | (~r(s(s(z)), s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), s(s(z)))))),
% 1.94/2.11 inference(transitivity,[status(thm)],[3171, 3169])).
% 1.94/2.11 tff(3173,plain,
% 1.94/2.11 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(z)), s(s(s(elem!1))))) | (~r(s(z), s(s(z)))) | (~r(s(s(s(elem!1))), s(s(z)))) | (~r(s(s(s(elem!1))), s(z))))),
% 1.94/2.12 inference(quant_inst,[status(thm)],[])).
% 1.94/2.12 tff(3174,plain,
% 1.94/2.12 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(elem!1))), s(z))) | (~r(s(z), s(s(z)))) | (~r(s(s(z)), s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), s(s(z))))),
% 1.94/2.12 inference(modus_ponens,[status(thm)],[3173, 3172])).
% 1.94/2.12 tff(3175,plain,
% 1.94/2.12 ($false),
% 1.94/2.12 inference(unit_resolution,[status(thm)],[3174, 197, 120, 350, 3168, 3160])).
% 1.94/2.12 tff(3176,plain,((~r(s(s(s(elem!1))), s(z))) | (~r(s(z), s(s(z)))) | (~b(s(s(z)), z)) | (~r(s(z), s(s(elem!1)))) | (~r(z, s(z)))), inference(lemma,lemma(discharge,[]))).
% 1.94/2.12 tff(3177,plain,
% 1.94/2.12 (~r(s(s(s(elem!1))), s(z))),
% 1.94/2.12 inference(unit_resolution,[status(thm)],[3176, 3134, 120, 311, 322])).
% 1.94/2.12 tff(3178,plain,
% 1.94/2.12 (b(s(s(s(elem!1))), s(z))),
% 1.94/2.12 inference(unit_resolution,[status(thm)],[1849, 3177])).
% 1.94/2.12 tff(3179,plain,
% 1.94/2.12 (~r(s(s(z)), s(s(s(elem!1))))),
% 1.94/2.12 inference(unit_resolution,[status(thm)],[331, 322, 152, 120])).
% 1.94/2.12 tff(3180,plain,
% 1.94/2.12 (b(s(s(z)), s(s(s(elem!1))))),
% 1.94/2.12 inference(unit_resolution,[status(thm)],[279, 3179])).
% 1.94/2.12 tff(3181,plain,
% 1.94/2.12 (~b(s(z), s(s(s(elem!1))))),
% 1.94/2.12 inference(unit_resolution,[status(thm)],[271, 3180, 156, 3178])).
% 1.94/2.12 tff(3182,plain,
% 1.94/2.12 (r(s(z), s(s(s(elem!1))))),
% 1.94/2.12 inference(unit_resolution,[status(thm)],[116, 3181])).
% 1.94/2.12 tff(3183,assumption,(r(s(s(s(elem!1))), s(s(s(z))))), introduced(assumption)).
% 1.94/2.12 tff(3184,plain,
% 1.94/2.12 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), s(s(s(z))))) | (~r(z, s(s(s(elem!1))))) | (~r(z, s(z))) | (~r(s(z), s(s(s(elem!1))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(elem!1))), s(s(s(z))))) | (~r(z, s(s(s(elem!1))))) | (~r(z, s(z))) | (~r(s(z), s(s(s(elem!1))))))),
% 1.94/2.12 inference(rewrite,[status(thm)],[])).
% 1.94/2.12 tff(3185,plain,
% 1.94/2.12 (((~r(s(s(s(elem!1))), s(s(s(z))))) | (~r(s(z), s(s(s(elem!1))))) | (~r(z, s(s(s(elem!1))))) | (~r(z, s(z)))) <=> ((~r(s(s(s(elem!1))), s(s(s(z))))) | (~r(z, s(s(s(elem!1))))) | (~r(z, s(z))) | (~r(s(z), s(s(s(elem!1))))))),
% 1.94/2.12 inference(rewrite,[status(thm)],[])).
% 1.94/2.12 tff(3186,plain,
% 1.94/2.12 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), s(s(s(z))))) | (~r(s(z), s(s(s(elem!1))))) | (~r(z, s(s(s(elem!1))))) | (~r(z, s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), s(s(s(z))))) | (~r(z, s(s(s(elem!1))))) | (~r(z, s(z))) | (~r(s(z), s(s(s(elem!1)))))))),
% 1.94/2.12 inference(monotonicity,[status(thm)],[3185])).
% 1.94/2.12 tff(3187,plain,
% 1.94/2.12 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), s(s(s(z))))) | (~r(s(z), s(s(s(elem!1))))) | (~r(z, s(s(s(elem!1))))) | (~r(z, s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(elem!1))), s(s(s(z))))) | (~r(z, s(s(s(elem!1))))) | (~r(z, s(z))) | (~r(s(z), s(s(s(elem!1))))))),
% 1.94/2.12 inference(transitivity,[status(thm)],[3186, 3184])).
% 1.94/2.12 tff(3188,plain,
% 1.94/2.12 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), s(s(s(z))))) | (~r(s(z), s(s(s(elem!1))))) | (~r(z, s(s(s(elem!1))))) | (~r(z, s(z))))),
% 1.94/2.12 inference(quant_inst,[status(thm)],[])).
% 1.94/2.12 tff(3189,plain,
% 1.94/2.12 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(elem!1))), s(s(s(z))))) | (~r(z, s(s(s(elem!1))))) | (~r(z, s(z))) | (~r(s(z), s(s(s(elem!1)))))),
% 1.94/2.12 inference(modus_ponens,[status(thm)],[3188, 3187])).
% 1.94/2.12 tff(3190,plain,
% 1.94/2.12 ($false),
% 1.94/2.12 inference(unit_resolution,[status(thm)],[3189, 197, 323, 119, 282, 3183])).
% 1.94/2.12 tff(3191,plain,((~r(s(s(s(elem!1))), s(s(s(z))))) | (~r(z, s(z))) | (~r(s(z), s(s(s(elem!1))))) | (~r(z, s(s(s(elem!1)))))), inference(lemma,lemma(discharge,[]))).
% 1.94/2.12 tff(3192,plain,
% 1.94/2.12 (~r(s(s(s(elem!1))), s(s(s(z))))),
% 1.94/2.12 inference(unit_resolution,[status(thm)],[3191, 322, 3182, 3152])).
% 1.94/2.12 tff(3193,plain,
% 1.94/2.12 (~r(elem!1, s(s(s(z))))),
% 1.94/2.12 inference(modus_ponens,[status(thm)],[3192, 3131])).
% 1.94/2.12 tff(3194,plain,
% 1.94/2.12 (b(elem!1, s(s(s(z))))),
% 1.94/2.12 inference(unit_resolution,[status(thm)],[1619, 3193, 3124])).
% 1.94/2.12 tff(3195,plain,
% 1.94/2.12 (b(s(s(s(elem!1))), s(s(s(z))))),
% 1.94/2.12 inference(modus_ponens,[status(thm)],[3194, 3114])).
% 1.94/2.12 tff(3196,plain,
% 1.94/2.12 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(z))) | (~r(s(z), s(s(z)))) | (~r(s(s(z)), s(s(s(z))))) | (~r(z, s(s(z)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, s(z))) | (~r(s(z), s(s(z)))) | (~r(s(s(z)), s(s(s(z))))) | (~r(z, s(s(z)))))),
% 1.94/2.12 inference(rewrite,[status(thm)],[])).
% 1.94/2.12 tff(3197,plain,
% 1.94/2.12 (((~r(s(s(z)), s(s(s(z))))) | (~r(s(z), s(s(z)))) | (~r(z, s(s(z)))) | (~r(z, s(z)))) <=> ((~r(z, s(z))) | (~r(s(z), s(s(z)))) | (~r(s(s(z)), s(s(s(z))))) | (~r(z, s(s(z)))))),
% 1.94/2.12 inference(rewrite,[status(thm)],[])).
% 1.94/2.12 tff(3198,plain,
% 1.94/2.12 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(z)), s(s(s(z))))) | (~r(s(z), s(s(z)))) | (~r(z, s(s(z)))) | (~r(z, s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(z))) | (~r(s(z), s(s(z)))) | (~r(s(s(z)), s(s(s(z))))) | (~r(z, s(s(z))))))),
% 1.94/2.12 inference(monotonicity,[status(thm)],[3197])).
% 1.94/2.12 tff(3199,plain,
% 1.94/2.12 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(z)), s(s(s(z))))) | (~r(s(z), s(s(z)))) | (~r(z, s(s(z)))) | (~r(z, s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, s(z))) | (~r(s(z), s(s(z)))) | (~r(s(s(z)), s(s(s(z))))) | (~r(z, s(s(z)))))),
% 1.94/2.12 inference(transitivity,[status(thm)],[3198, 3196])).
% 1.94/2.12 tff(3200,plain,
% 1.94/2.12 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(z)), s(s(s(z))))) | (~r(s(z), s(s(z)))) | (~r(z, s(s(z)))) | (~r(z, s(z))))),
% 1.94/2.12 inference(quant_inst,[status(thm)],[])).
% 1.94/2.12 tff(3201,plain,
% 1.94/2.12 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, s(z))) | (~r(s(z), s(s(z)))) | (~r(s(s(z)), s(s(s(z))))) | (~r(z, s(s(z))))),
% 1.94/2.12 inference(modus_ponens,[status(thm)],[3200, 3199])).
% 1.94/2.12 tff(3202,plain,
% 1.94/2.12 ($false),
% 1.94/2.12 inference(unit_resolution,[status(thm)],[3201, 197, 120, 155, 323, 1732])).
% 1.94/2.12 tff(3203,plain,((~r(s(s(z)), s(s(s(z))))) | (~r(s(z), s(s(z)))) | (~r(z, s(s(z)))) | (~r(z, s(z)))), inference(lemma,lemma(discharge,[]))).
% 1.94/2.12 tff(3204,plain,
% 1.94/2.12 (~r(s(s(z)), s(s(s(z))))),
% 1.94/2.12 inference(unit_resolution,[status(thm)],[3203, 322, 152, 120])).
% 1.94/2.12 tff(3205,plain,
% 1.94/2.12 (b(s(s(z)), s(s(s(z))))),
% 1.94/2.12 inference(unit_resolution,[status(thm)],[1730, 3204])).
% 1.94/2.12 tff(3206,plain,
% 1.94/2.12 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(z))) | (~r(s(z), s(s(z)))) | (~r(s(s(s(z))), z)) | (~r(s(s(s(z))), s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, s(z))) | (~r(s(z), s(s(z)))) | (~r(s(s(s(z))), z)) | (~r(s(s(s(z))), s(z))))),
% 1.94/2.12 inference(rewrite,[status(thm)],[])).
% 1.94/2.12 tff(3207,plain,
% 1.94/2.12 (((~r(s(z), s(s(z)))) | (~r(z, s(z))) | (~r(s(s(s(z))), s(z))) | (~r(s(s(s(z))), z))) <=> ((~r(z, s(z))) | (~r(s(z), s(s(z)))) | (~r(s(s(s(z))), z)) | (~r(s(s(s(z))), s(z))))),
% 1.94/2.12 inference(rewrite,[status(thm)],[])).
% 1.94/2.12 tff(3208,plain,
% 1.94/2.12 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(s(z)))) | (~r(z, s(z))) | (~r(s(s(s(z))), s(z))) | (~r(s(s(s(z))), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(z))) | (~r(s(z), s(s(z)))) | (~r(s(s(s(z))), z)) | (~r(s(s(s(z))), s(z)))))),
% 1.94/2.12 inference(monotonicity,[status(thm)],[3207])).
% 1.94/2.12 tff(3209,plain,
% 1.94/2.12 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(s(z)))) | (~r(z, s(z))) | (~r(s(s(s(z))), s(z))) | (~r(s(s(s(z))), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, s(z))) | (~r(s(z), s(s(z)))) | (~r(s(s(s(z))), z)) | (~r(s(s(s(z))), s(z))))),
% 1.94/2.12 inference(transitivity,[status(thm)],[3208, 3206])).
% 1.94/2.12 tff(3210,plain,
% 1.94/2.12 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(s(z)))) | (~r(z, s(z))) | (~r(s(s(s(z))), s(z))) | (~r(s(s(s(z))), z)))),
% 1.94/2.12 inference(quant_inst,[status(thm)],[])).
% 1.94/2.12 tff(3211,plain,
% 1.94/2.12 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, s(z))) | (~r(s(z), s(s(z)))) | (~r(s(s(s(z))), z)) | (~r(s(s(s(z))), s(z)))),
% 1.94/2.12 inference(modus_ponens,[status(thm)],[3210, 3209])).
% 1.94/2.12 tff(3212,plain,
% 1.94/2.12 ($false),
% 1.94/2.12 inference(unit_resolution,[status(thm)],[3211, 197, 120, 323, 1746, 1733])).
% 1.94/2.12 tff(3213,plain,((~r(s(s(s(z))), s(z))) | (~r(s(z), s(s(z)))) | (~r(z, s(z))) | (~r(s(s(s(z))), z))), inference(lemma,lemma(discharge,[]))).
% 1.94/2.12 tff(3214,plain,
% 1.94/2.12 (~r(s(s(s(z))), z)),
% 1.94/2.12 inference(unit_resolution,[status(thm)],[3213, 1746, 323, 120])).
% 1.94/2.12 tff(3215,plain,
% 1.94/2.12 (b(s(s(s(z))), z)),
% 1.94/2.12 inference(unit_resolution,[status(thm)],[1713, 3214])).
% 1.94/2.12 tff(3216,plain,
% 1.94/2.12 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), z)) | (~b(s(s(s(z))), z)) | (~b(z, s(s(s(z))))) | (~b(s(s(z)), s(s(s(z))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(z)), z)) | (~b(s(s(s(z))), z)) | (~b(z, s(s(s(z))))) | (~b(s(s(z)), s(s(s(z))))))),
% 1.94/2.12 inference(rewrite,[status(thm)],[])).
% 1.94/2.12 tff(3217,plain,
% 1.94/2.12 (((~b(s(s(s(z))), z)) | (~b(s(s(z)), z)) | (~b(z, s(s(s(z))))) | (~b(s(s(s(z))), z)) | (~b(s(s(z)), z)) | (~b(s(s(z)), s(s(s(z)))))) <=> ((~b(s(s(z)), z)) | (~b(s(s(s(z))), z)) | (~b(z, s(s(s(z))))) | (~b(s(s(z)), s(s(s(z))))))),
% 1.94/2.12 inference(rewrite,[status(thm)],[])).
% 1.94/2.12 tff(3218,plain,
% 1.94/2.12 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), z)) | (~b(s(s(z)), z)) | (~b(z, s(s(s(z))))) | (~b(s(s(s(z))), z)) | (~b(s(s(z)), z)) | (~b(s(s(z)), s(s(s(z))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), z)) | (~b(s(s(s(z))), z)) | (~b(z, s(s(s(z))))) | (~b(s(s(z)), s(s(s(z)))))))),
% 1.94/2.12 inference(monotonicity,[status(thm)],[3217])).
% 1.94/2.12 tff(3219,plain,
% 1.94/2.12 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), z)) | (~b(s(s(z)), z)) | (~b(z, s(s(s(z))))) | (~b(s(s(s(z))), z)) | (~b(s(s(z)), z)) | (~b(s(s(z)), s(s(s(z))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(z)), z)) | (~b(s(s(s(z))), z)) | (~b(z, s(s(s(z))))) | (~b(s(s(z)), s(s(s(z))))))),
% 1.94/2.12 inference(transitivity,[status(thm)],[3218, 3216])).
% 1.94/2.12 tff(3220,plain,
% 1.94/2.12 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), z)) | (~b(s(s(z)), z)) | (~b(z, s(s(s(z))))) | (~b(s(s(s(z))), z)) | (~b(s(s(z)), z)) | (~b(s(s(z)), s(s(s(z))))))),
% 1.94/2.12 inference(quant_inst,[status(thm)],[])).
% 1.94/2.12 tff(3221,plain,
% 1.94/2.12 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(z)), z)) | (~b(s(s(s(z))), z)) | (~b(z, s(s(s(z))))) | (~b(s(s(z)), s(s(s(z)))))),
% 1.94/2.12 inference(modus_ponens,[status(thm)],[3220, 3219])).
% 1.94/2.12 tff(3222,plain,
% 1.94/2.12 ($false),
% 1.94/2.12 inference(unit_resolution,[status(thm)],[3221, 166, 122, 986, 1699, 1700])).
% 1.94/2.12 tff(3223,plain,((~b(s(s(s(z))), z)) | (~b(s(s(z)), z)) | (~b(s(s(z)), s(s(s(z))))) | (~b(z, s(s(s(z)))))), inference(lemma,lemma(discharge,[]))).
% 1.94/2.12 tff(3224,plain,
% 1.94/2.12 (~b(z, s(s(s(z))))),
% 1.94/2.12 inference(unit_resolution,[status(thm)],[3223, 3215, 986, 122])).
% 1.94/2.12 tff(3225,plain,
% 1.94/2.12 (r(z, s(s(s(z))))),
% 1.94/2.12 inference(unit_resolution,[status(thm)],[1697, 3224])).
% 1.94/2.12 tff(3226,plain,
% 1.94/2.12 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(s(z))))) | (~r(z, s(z))) | (~r(s(z), s(s(z)))) | (~r(s(s(s(z))), s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, s(s(s(z))))) | (~r(z, s(z))) | (~r(s(z), s(s(z)))) | (~r(s(s(s(z))), s(z))))),
% 1.94/2.12 inference(rewrite,[status(thm)],[])).
% 1.94/2.12 tff(3227,plain,
% 1.94/2.12 (((~r(s(z), s(s(z)))) | (~r(s(s(s(z))), s(z))) | (~r(z, s(z))) | (~r(z, s(s(s(z)))))) <=> ((~r(z, s(s(s(z))))) | (~r(z, s(z))) | (~r(s(z), s(s(z)))) | (~r(s(s(s(z))), s(z))))),
% 1.94/2.12 inference(rewrite,[status(thm)],[])).
% 1.94/2.12 tff(3228,plain,
% 1.94/2.12 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(s(z)))) | (~r(s(s(s(z))), s(z))) | (~r(z, s(z))) | (~r(z, s(s(s(z))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(s(z))))) | (~r(z, s(z))) | (~r(s(z), s(s(z)))) | (~r(s(s(s(z))), s(z)))))),
% 1.94/2.12 inference(monotonicity,[status(thm)],[3227])).
% 1.94/2.12 tff(3229,plain,
% 1.94/2.12 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(s(z)))) | (~r(s(s(s(z))), s(z))) | (~r(z, s(z))) | (~r(z, s(s(s(z))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, s(s(s(z))))) | (~r(z, s(z))) | (~r(s(z), s(s(z)))) | (~r(s(s(s(z))), s(z))))),
% 1.94/2.12 inference(transitivity,[status(thm)],[3228, 3226])).
% 1.94/2.12 tff(3230,plain,
% 1.94/2.12 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(s(z)))) | (~r(s(s(s(z))), s(z))) | (~r(z, s(z))) | (~r(z, s(s(s(z))))))),
% 1.94/2.12 inference(quant_inst,[status(thm)],[])).
% 1.94/2.12 tff(3231,plain,
% 1.94/2.12 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, s(s(s(z))))) | (~r(z, s(z))) | (~r(s(z), s(s(z)))) | (~r(s(s(s(z))), s(z)))),
% 1.94/2.12 inference(modus_ponens,[status(thm)],[3230, 3229])).
% 1.94/2.12 tff(3232,plain,
% 1.94/2.12 ($false),
% 1.94/2.12 inference(unit_resolution,[status(thm)],[3231, 197, 120, 323, 3225, 1746])).
% 1.94/2.12 tff(3233,plain,((~r(s(s(s(z))), s(z))) | (~r(s(z), s(s(z)))) | (~r(z, s(z))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(z)), z))), inference(lemma,lemma(discharge,[]))).
% 1.94/2.12 tff(3234,plain,
% 1.94/2.12 (~r(s(s(s(z))), s(z))),
% 1.94/2.12 inference(unit_resolution,[status(thm)],[3233, 322, 120, 3205, 3134])).
% 1.94/2.12 tff(3235,plain,
% 1.94/2.12 (b(s(s(s(z))), s(z))),
% 1.94/2.12 inference(unit_resolution,[status(thm)],[1763, 3234])).
% 1.94/2.12 tff(3236,plain,
% 1.94/2.12 (~r(s(s(s(elem!1))), s(s(z)))),
% 1.94/2.12 inference(unit_resolution,[status(thm)],[2057, 3152, 322, 3182])).
% 1.94/2.12 tff(3237,plain,
% 1.94/2.12 (b(s(s(s(elem!1))), s(s(z)))),
% 1.94/2.12 inference(unit_resolution,[status(thm)],[218, 3236])).
% 1.94/2.12 tff(3238,plain,
% 1.94/2.12 (b(s(s(elem!1)), z) <=> b(s(s(s(elem!1))), z)),
% 1.94/2.12 inference(monotonicity,[status(thm)],[3109])).
% 1.94/2.12 tff(3239,plain,
% 1.94/2.12 (b(s(s(s(elem!1))), z)),
% 1.94/2.12 inference(modus_ponens,[status(thm)],[3026, 3238])).
% 1.94/2.12 tff(3240,assumption,(b(s(s(s(z))), s(z))), introduced(assumption)).
% 1.94/2.12 tff(3241,plain,
% 1.94/2.12 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), s(z))) | (~b(s(s(z)), s(z))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(z)), s(s(s(z))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(z)), s(z))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(z)), s(s(s(z))))))),
% 1.94/2.13 inference(rewrite,[status(thm)],[])).
% 1.94/2.13 tff(3242,plain,
% 1.94/2.13 (((~b(s(s(s(z))), s(z))) | (~b(s(s(z)), s(z))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(z)), s(z))) | (~b(s(s(z)), s(s(s(z)))))) <=> ((~b(s(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))))))),
% 1.94/2.13 inference(rewrite,[status(thm)],[])).
% 1.94/2.13 tff(3243,plain,
% 1.94/2.13 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), s(z))) | (~b(s(s(z)), s(z))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(z)), s(z))) | (~b(s(s(z)), s(s(s(z))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), s(z))) | (~b(s(s(z)), s(z))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(z)), s(s(s(z)))))))),
% 1.94/2.13 inference(monotonicity,[status(thm)],[3242])).
% 1.94/2.13 tff(3244,plain,
% 1.94/2.13 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), s(z))) | (~b(s(s(z)), s(z))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(z)), s(z))) | (~b(s(s(z)), s(s(s(z))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(z)), s(z))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(z)), s(s(s(z))))))),
% 1.94/2.13 inference(transitivity,[status(thm)],[3243, 3241])).
% 1.94/2.13 tff(3245,plain,
% 1.94/2.13 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), s(z))) | (~b(s(s(z)), s(z))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(z)), s(z))) | (~b(s(s(z)), s(s(s(z))))))),
% 1.94/2.13 inference(quant_inst,[status(thm)],[])).
% 1.94/2.13 tff(3246,plain,
% 1.94/2.13 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(z)), s(z))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(z)), s(s(s(z)))))),
% 1.94/2.13 inference(modus_ponens,[status(thm)],[3245, 3244])).
% 1.94/2.13 tff(3247,plain,
% 1.94/2.13 ($false),
% 1.94/2.13 inference(unit_resolution,[status(thm)],[3246, 166, 156, 988, 986, 3240])).
% 1.94/2.13 tff(3248,plain,((~b(s(s(s(z))), s(z))) | (~b(s(s(z)), s(z))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(z)), s(s(s(z)))))), inference(lemma,lemma(discharge,[]))).
% 1.94/2.13 tff(3249,plain,
% 1.94/2.13 (~b(s(z), s(s(s(z))))),
% 1.94/2.13 inference(unit_resolution,[status(thm)],[3248, 3235, 156, 3205])).
% 1.94/2.13 tff(3250,plain,
% 1.94/2.13 (r(s(z), s(s(s(z))))),
% 1.94/2.13 inference(unit_resolution,[status(thm)],[1674, 3249])).
% 1.94/2.13 tff(3251,assumption,(b(s(s(s(elem!1))), s(s(s(z))))), introduced(assumption)).
% 1.94/2.13 tff(3252,assumption,(b(s(s(s(z))), s(s(s(s(z)))))), introduced(assumption)).
% 1.94/2.13 tff(3253,assumption,(b(s(s(s(s(z)))), z)), introduced(assumption)).
% 1.94/2.13 tff(3254,plain,
% 1.94/2.13 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), s(s(z)))) | (~b(s(s(s(elem!1))), z)) | (~b(s(s(s(elem!1))), s(s(s(z))))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(elem!1))), s(s(z)))) | (~b(s(s(s(elem!1))), z)) | (~b(s(s(s(elem!1))), s(s(s(z))))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), z)))),
% 1.94/2.13 inference(rewrite,[status(thm)],[])).
% 1.94/2.13 tff(3255,plain,
% 1.94/2.13 (((~b(s(s(s(s(z)))), z)) | (~b(s(s(s(elem!1))), z)) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(s(elem!1))), s(s(s(z))))) | (~b(s(s(s(elem!1))), s(s(z))))) <=> ((~b(s(s(s(elem!1))), s(s(z)))) | (~b(s(s(s(elem!1))), z)) | (~b(s(s(s(elem!1))), s(s(s(z))))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), z)))),
% 1.94/2.13 inference(rewrite,[status(thm)],[])).
% 1.94/2.13 tff(3256,plain,
% 1.94/2.13 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(z)))), z)) | (~b(s(s(s(elem!1))), z)) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(s(elem!1))), s(s(s(z))))) | (~b(s(s(s(elem!1))), s(s(z)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), s(s(z)))) | (~b(s(s(s(elem!1))), z)) | (~b(s(s(s(elem!1))), s(s(s(z))))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), z))))),
% 1.94/2.13 inference(monotonicity,[status(thm)],[3255])).
% 1.94/2.13 tff(3257,plain,
% 1.94/2.13 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(z)))), z)) | (~b(s(s(s(elem!1))), z)) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(s(elem!1))), s(s(s(z))))) | (~b(s(s(s(elem!1))), s(s(z)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(elem!1))), s(s(z)))) | (~b(s(s(s(elem!1))), z)) | (~b(s(s(s(elem!1))), s(s(s(z))))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), z)))),
% 1.94/2.13 inference(transitivity,[status(thm)],[3256, 3254])).
% 1.94/2.13 tff(3258,plain,
% 1.94/2.13 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(z)))), z)) | (~b(s(s(s(elem!1))), z)) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(s(elem!1))), s(s(s(z))))) | (~b(s(s(s(elem!1))), s(s(z)))))),
% 1.94/2.13 inference(quant_inst,[status(thm)],[])).
% 1.94/2.13 tff(3259,plain,
% 1.94/2.13 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(elem!1))), s(s(z)))) | (~b(s(s(s(elem!1))), z)) | (~b(s(s(s(elem!1))), s(s(s(z))))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), z))),
% 1.94/2.13 inference(modus_ponens,[status(thm)],[3258, 3257])).
% 1.94/2.13 tff(3260,plain,
% 1.94/2.13 ($false),
% 1.94/2.13 inference(unit_resolution,[status(thm)],[3259, 166, 121, 986, 3252, 2060, 3253, 3251])).
% 1.94/2.13 tff(3261,plain,((~b(s(s(s(s(z)))), z)) | (~b(s(s(s(elem!1))), z)) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(elem!1))), s(s(z)))) | (~b(s(s(s(elem!1))), s(s(s(z)))))), inference(lemma,lemma(discharge,[]))).
% 1.94/2.13 tff(3262,plain,
% 1.94/2.13 (~b(s(s(s(s(z)))), z)),
% 1.94/2.13 inference(unit_resolution,[status(thm)],[3261, 3252, 986, 121, 2060, 3251])).
% 1.94/2.13 tff(3263,plain,
% 1.94/2.13 (((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((s(s(s(s(z)))) = z) | b(s(s(s(s(z)))), z) | r(s(s(s(s(z)))), z))) <=> ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (s(s(s(s(z)))) = z) | b(s(s(s(s(z)))), z) | r(s(s(s(s(z)))), z))),
% 1.94/2.13 inference(rewrite,[status(thm)],[])).
% 1.94/2.13 tff(3264,plain,
% 1.94/2.13 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((s(s(s(s(z)))) = z) | b(s(s(s(s(z)))), z) | r(s(s(s(s(z)))), z))),
% 1.94/2.13 inference(quant_inst,[status(thm)],[])).
% 1.94/2.13 tff(3265,plain,
% 1.94/2.13 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (s(s(s(s(z)))) = z) | b(s(s(s(s(z)))), z) | r(s(s(s(s(z)))), z)),
% 1.94/2.13 inference(modus_ponens,[status(thm)],[3264, 3263])).
% 1.94/2.13 tff(3266,plain,
% 1.94/2.13 (b(s(s(s(s(z)))), z) | r(s(s(s(s(z)))), z)),
% 1.94/2.13 inference(unit_resolution,[status(thm)],[3265, 79, 1044])).
% 1.94/2.13 tff(3267,plain,
% 1.94/2.13 (r(s(s(s(s(z)))), z)),
% 1.94/2.13 inference(unit_resolution,[status(thm)],[3266, 3262])).
% 1.94/2.13 tff(3268,plain,
% 1.94/2.13 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), z)) | (~r(z, s(s(z)))) | (~r(s(s(s(s(z)))), z)) | (~r(s(s(s(s(z)))), s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(z), z)) | (~r(z, s(s(z)))) | (~r(s(s(s(s(z)))), z)) | (~r(s(s(s(s(z)))), s(z))))),
% 1.94/2.13 inference(rewrite,[status(thm)],[])).
% 1.94/2.13 tff(3269,plain,
% 1.94/2.13 (((~r(z, s(s(z)))) | (~r(s(z), z)) | (~r(s(s(s(s(z)))), z)) | (~r(s(s(s(s(z)))), s(z)))) <=> ((~r(s(z), z)) | (~r(z, s(s(z)))) | (~r(s(s(s(s(z)))), z)) | (~r(s(s(s(s(z)))), s(z))))),
% 1.94/2.13 inference(rewrite,[status(thm)],[])).
% 1.94/2.13 tff(3270,plain,
% 1.94/2.13 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(z)))) | (~r(s(z), z)) | (~r(s(s(s(s(z)))), z)) | (~r(s(s(s(s(z)))), s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), z)) | (~r(z, s(s(z)))) | (~r(s(s(s(s(z)))), z)) | (~r(s(s(s(s(z)))), s(z)))))),
% 1.94/2.13 inference(monotonicity,[status(thm)],[3269])).
% 1.94/2.13 tff(3271,plain,
% 1.94/2.13 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(z)))) | (~r(s(z), z)) | (~r(s(s(s(s(z)))), z)) | (~r(s(s(s(s(z)))), s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(z), z)) | (~r(z, s(s(z)))) | (~r(s(s(s(s(z)))), z)) | (~r(s(s(s(s(z)))), s(z))))),
% 1.94/2.13 inference(transitivity,[status(thm)],[3270, 3268])).
% 1.94/2.13 tff(3272,plain,
% 1.94/2.13 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(z)))) | (~r(s(z), z)) | (~r(s(s(s(s(z)))), z)) | (~r(s(s(s(s(z)))), s(z))))),
% 1.94/2.13 inference(quant_inst,[status(thm)],[])).
% 1.94/2.13 tff(3273,plain,
% 1.94/2.13 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(z), z)) | (~r(z, s(s(z)))) | (~r(s(s(s(s(z)))), z)) | (~r(s(s(s(s(z)))), s(z)))),
% 1.94/2.13 inference(modus_ponens,[status(thm)],[3272, 3271])).
% 1.94/2.13 tff(3274,plain,
% 1.94/2.13 (~r(s(s(s(s(z)))), s(z))),
% 1.94/2.13 inference(unit_resolution,[status(thm)],[3273, 197, 155, 97, 3267])).
% 1.94/2.13 tff(3275,assumption,(s(s(s(s(z)))) = s(z)), introduced(assumption)).
% 1.94/2.13 tff(3276,plain,
% 1.94/2.13 (inj_0(s(s(s(s(z))))) = inj_0(s(z))),
% 1.94/2.13 inference(monotonicity,[status(thm)],[3275])).
% 1.94/2.13 tff(3277,plain,
% 1.94/2.13 (s(s(s(z))) = inj_0(s(s(s(s(z)))))),
% 1.94/2.13 inference(symmetry,[status(thm)],[2223])).
% 1.94/2.13 tff(3278,plain,
% 1.94/2.13 (s(s(s(z))) = z),
% 1.94/2.13 inference(transitivity,[status(thm)],[3277, 3276, 25])).
% 1.94/2.13 tff(3279,plain,
% 1.94/2.13 ($false),
% 1.94/2.13 inference(unit_resolution,[status(thm)],[1691, 3278])).
% 1.94/2.13 tff(3280,plain,(~(s(s(s(s(z)))) = s(z))), inference(lemma,lemma(discharge,[]))).
% 1.94/2.13 tff(3281,plain,
% 1.94/2.13 (((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((s(s(s(s(z)))) = s(z)) | b(s(s(s(s(z)))), s(z)) | r(s(s(s(s(z)))), s(z)))) <=> ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (s(s(s(s(z)))) = s(z)) | b(s(s(s(s(z)))), s(z)) | r(s(s(s(s(z)))), s(z)))),
% 1.94/2.13 inference(rewrite,[status(thm)],[])).
% 1.94/2.13 tff(3282,plain,
% 1.94/2.13 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((s(s(s(s(z)))) = s(z)) | b(s(s(s(s(z)))), s(z)) | r(s(s(s(s(z)))), s(z)))),
% 1.94/2.13 inference(quant_inst,[status(thm)],[])).
% 1.94/2.13 tff(3283,plain,
% 1.94/2.13 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (s(s(s(s(z)))) = s(z)) | b(s(s(s(s(z)))), s(z)) | r(s(s(s(s(z)))), s(z))),
% 1.94/2.13 inference(modus_ponens,[status(thm)],[3282, 3281])).
% 1.94/2.13 tff(3284,plain,
% 1.94/2.13 ((s(s(s(s(z)))) = s(z)) | b(s(s(s(s(z)))), s(z)) | r(s(s(s(s(z)))), s(z))),
% 1.94/2.13 inference(unit_resolution,[status(thm)],[3283, 79])).
% 1.94/2.13 tff(3285,plain,
% 1.94/2.13 (b(s(s(s(s(z)))), s(z)) | r(s(s(s(s(z)))), s(z))),
% 1.94/2.13 inference(unit_resolution,[status(thm)],[3284, 3280])).
% 1.94/2.13 tff(3286,plain,
% 1.94/2.13 (b(s(s(s(s(z)))), s(z))),
% 1.94/2.13 inference(unit_resolution,[status(thm)],[3285, 3274])).
% 1.94/2.13 tff(3287,plain,
% 1.94/2.13 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), z)) | (~r(z, s(s(z)))) | (~r(s(s(s(s(z)))), z)) | (~r(s(z), s(s(s(s(z)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(z), z)) | (~r(z, s(s(z)))) | (~r(s(s(s(s(z)))), z)) | (~r(s(z), s(s(s(s(z)))))))),
% 1.94/2.13 inference(rewrite,[status(thm)],[])).
% 1.94/2.13 tff(3288,plain,
% 1.94/2.13 (((~r(z, s(s(z)))) | (~r(s(s(s(s(z)))), z)) | (~r(s(z), z)) | (~r(s(z), s(s(s(s(z))))))) <=> ((~r(s(z), z)) | (~r(z, s(s(z)))) | (~r(s(s(s(s(z)))), z)) | (~r(s(z), s(s(s(s(z)))))))),
% 1.94/2.13 inference(rewrite,[status(thm)],[])).
% 1.94/2.13 tff(3289,plain,
% 1.94/2.13 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(z)))) | (~r(s(s(s(s(z)))), z)) | (~r(s(z), z)) | (~r(s(z), s(s(s(s(z)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), z)) | (~r(z, s(s(z)))) | (~r(s(s(s(s(z)))), z)) | (~r(s(z), s(s(s(s(z))))))))),
% 1.94/2.13 inference(monotonicity,[status(thm)],[3288])).
% 1.94/2.13 tff(3290,plain,
% 1.94/2.13 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(z)))) | (~r(s(s(s(s(z)))), z)) | (~r(s(z), z)) | (~r(s(z), s(s(s(s(z)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(z), z)) | (~r(z, s(s(z)))) | (~r(s(s(s(s(z)))), z)) | (~r(s(z), s(s(s(s(z)))))))),
% 1.94/2.13 inference(transitivity,[status(thm)],[3289, 3287])).
% 1.94/2.13 tff(3291,plain,
% 1.94/2.13 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(z)))) | (~r(s(s(s(s(z)))), z)) | (~r(s(z), z)) | (~r(s(z), s(s(s(s(z)))))))),
% 1.94/2.13 inference(quant_inst,[status(thm)],[])).
% 1.94/2.13 tff(3292,plain,
% 1.94/2.13 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(z), z)) | (~r(z, s(s(z)))) | (~r(s(s(s(s(z)))), z)) | (~r(s(z), s(s(s(s(z))))))),
% 1.94/2.13 inference(modus_ponens,[status(thm)],[3291, 3290])).
% 1.94/2.13 tff(3293,plain,
% 1.94/2.13 (~r(s(z), s(s(s(s(z)))))),
% 1.94/2.13 inference(unit_resolution,[status(thm)],[3292, 197, 155, 97, 3267])).
% 1.94/2.13 tff(3294,plain,
% 1.94/2.13 ((s(z) = s(s(s(s(z))))) <=> (s(s(s(s(z)))) = s(z))),
% 1.94/2.13 inference(commutativity,[status(thm)],[])).
% 1.94/2.13 tff(3295,plain,
% 1.94/2.13 ((s(s(s(s(z)))) = s(z)) <=> (s(z) = s(s(s(s(z)))))),
% 1.94/2.13 inference(symmetry,[status(thm)],[3294])).
% 1.94/2.13 tff(3296,plain,
% 1.94/2.13 ((~(s(s(s(s(z)))) = s(z))) <=> (~(s(z) = s(s(s(s(z))))))),
% 1.94/2.13 inference(monotonicity,[status(thm)],[3295])).
% 1.94/2.13 tff(3297,plain,
% 1.94/2.13 (~(s(z) = s(s(s(s(z)))))),
% 1.94/2.13 inference(modus_ponens,[status(thm)],[3280, 3296])).
% 1.94/2.13 tff(3298,plain,
% 1.94/2.13 (((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((s(z) = s(s(s(s(z))))) | b(s(z), s(s(s(s(z))))) | r(s(z), s(s(s(s(z))))))) <=> ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (s(z) = s(s(s(s(z))))) | b(s(z), s(s(s(s(z))))) | r(s(z), s(s(s(s(z))))))),
% 1.94/2.13 inference(rewrite,[status(thm)],[])).
% 1.94/2.13 tff(3299,plain,
% 1.94/2.13 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((s(z) = s(s(s(s(z))))) | b(s(z), s(s(s(s(z))))) | r(s(z), s(s(s(s(z))))))),
% 1.94/2.13 inference(quant_inst,[status(thm)],[])).
% 1.94/2.13 tff(3300,plain,
% 1.94/2.13 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (s(z) = s(s(s(s(z))))) | b(s(z), s(s(s(s(z))))) | r(s(z), s(s(s(s(z)))))),
% 1.94/2.13 inference(modus_ponens,[status(thm)],[3299, 3298])).
% 1.94/2.13 tff(3301,plain,
% 1.94/2.13 ((s(z) = s(s(s(s(z))))) | b(s(z), s(s(s(s(z))))) | r(s(z), s(s(s(s(z)))))),
% 1.94/2.13 inference(unit_resolution,[status(thm)],[3300, 79])).
% 1.94/2.13 tff(3302,plain,
% 1.94/2.13 (b(s(z), s(s(s(s(z))))) | r(s(z), s(s(s(s(z)))))),
% 1.94/2.13 inference(unit_resolution,[status(thm)],[3301, 3297])).
% 1.94/2.13 tff(3303,plain,
% 1.94/2.13 (b(s(z), s(s(s(s(z)))))),
% 1.94/2.13 inference(unit_resolution,[status(thm)],[3302, 3293])).
% 1.94/2.13 tff(3304,plain,
% 1.94/2.13 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), s(z))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(z))), s(s(s(s(z)))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(z))), s(z))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(z))), s(s(s(s(z)))))))),
% 1.94/2.13 inference(rewrite,[status(thm)],[])).
% 1.94/2.13 tff(3305,plain,
% 1.94/2.13 (((~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(z))), s(z))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(z))), s(s(s(s(z))))))) <=> ((~b(s(s(s(z))), s(z))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(z))), s(s(s(s(z)))))))),
% 1.94/2.14 inference(rewrite,[status(thm)],[])).
% 1.94/2.14 tff(3306,plain,
% 1.94/2.14 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(z))), s(z))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(z))), s(s(s(s(z)))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), s(z))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(z))), s(s(s(s(z))))))))),
% 1.94/2.14 inference(monotonicity,[status(thm)],[3305])).
% 1.94/2.14 tff(3307,plain,
% 1.94/2.14 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(z))), s(z))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(z))), s(s(s(s(z)))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(z))), s(z))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(z))), s(s(s(s(z)))))))),
% 1.94/2.14 inference(transitivity,[status(thm)],[3306, 3304])).
% 1.94/2.14 tff(3308,plain,
% 1.94/2.14 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(z))), s(z))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(z))), s(s(s(s(z)))))))),
% 1.94/2.14 inference(quant_inst,[status(thm)],[])).
% 1.94/2.14 tff(3309,plain,
% 1.94/2.14 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(z))), s(z))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(z))), s(s(s(s(z))))))),
% 1.94/2.14 inference(modus_ponens,[status(thm)],[3308, 3307])).
% 1.94/2.14 tff(3310,plain,
% 1.94/2.14 ($false),
% 1.94/2.14 inference(unit_resolution,[status(thm)],[3309, 166, 3252, 3303, 3286, 3240])).
% 1.94/2.14 tff(3311,plain,((~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(z))), s(z))) | (~r(z, s(s(z)))) | (~r(s(z), z)) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(s(elem!1))), z)) | (~b(s(s(s(elem!1))), s(s(z)))) | (~b(s(s(s(elem!1))), s(s(s(z)))))), inference(lemma,lemma(discharge,[]))).
% 1.94/2.14 tff(3312,plain,
% 1.94/2.14 (~b(s(s(s(z))), s(s(s(s(z)))))),
% 1.94/2.14 inference(unit_resolution,[status(thm)],[3311, 97, 155, 3240, 986, 121, 2060, 3251])).
% 1.94/2.14 tff(3313,plain,
% 1.94/2.14 (r(s(s(s(z))), s(s(s(s(z)))))),
% 1.94/2.14 inference(unit_resolution,[status(thm)],[2233, 3312])).
% 1.94/2.14 tff(3314,plain,
% 1.94/2.14 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(s(z))))) | (~r(z, s(z))) | (~r(s(z), s(s(s(z))))) | (~r(s(s(s(z))), s(s(s(s(z)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, s(s(s(z))))) | (~r(z, s(z))) | (~r(s(z), s(s(s(z))))) | (~r(s(s(s(z))), s(s(s(s(z)))))))),
% 1.94/2.14 inference(rewrite,[status(thm)],[])).
% 1.94/2.14 tff(3315,plain,
% 1.94/2.14 (((~r(s(s(s(z))), s(s(s(s(z)))))) | (~r(s(z), s(s(s(z))))) | (~r(z, s(s(s(z))))) | (~r(z, s(z)))) <=> ((~r(z, s(s(s(z))))) | (~r(z, s(z))) | (~r(s(z), s(s(s(z))))) | (~r(s(s(s(z))), s(s(s(s(z)))))))),
% 1.94/2.14 inference(rewrite,[status(thm)],[])).
% 1.94/2.14 tff(3316,plain,
% 1.94/2.14 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(z))), s(s(s(s(z)))))) | (~r(s(z), s(s(s(z))))) | (~r(z, s(s(s(z))))) | (~r(z, s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(s(z))))) | (~r(z, s(z))) | (~r(s(z), s(s(s(z))))) | (~r(s(s(s(z))), s(s(s(s(z))))))))),
% 1.94/2.14 inference(monotonicity,[status(thm)],[3315])).
% 1.94/2.14 tff(3317,plain,
% 1.94/2.14 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(z))), s(s(s(s(z)))))) | (~r(s(z), s(s(s(z))))) | (~r(z, s(s(s(z))))) | (~r(z, s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, s(s(s(z))))) | (~r(z, s(z))) | (~r(s(z), s(s(s(z))))) | (~r(s(s(s(z))), s(s(s(s(z)))))))),
% 1.94/2.14 inference(transitivity,[status(thm)],[3316, 3314])).
% 1.94/2.14 tff(3318,plain,
% 1.94/2.14 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(z))), s(s(s(s(z)))))) | (~r(s(z), s(s(s(z))))) | (~r(z, s(s(s(z))))) | (~r(z, s(z))))),
% 1.94/2.14 inference(quant_inst,[status(thm)],[])).
% 1.94/2.14 tff(3319,plain,
% 1.94/2.14 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, s(s(s(z))))) | (~r(z, s(z))) | (~r(s(z), s(s(s(z))))) | (~r(s(s(s(z))), s(s(s(s(z))))))),
% 1.94/2.14 inference(modus_ponens,[status(thm)],[3318, 3317])).
% 1.94/2.14 tff(3320,plain,
% 1.94/2.14 ($false),
% 1.94/2.14 inference(unit_resolution,[status(thm)],[3319, 197, 323, 1677, 2208, 1653])).
% 1.94/2.14 tff(3321,plain,((~r(z, s(s(s(z))))) | (~r(z, s(z))) | (~r(s(s(s(z))), s(s(s(s(z)))))) | (~r(s(z), s(s(s(z)))))), inference(lemma,lemma(discharge,[]))).
% 1.94/2.14 tff(3322,plain,
% 1.94/2.14 (~r(z, s(s(s(z))))),
% 1.94/2.14 inference(unit_resolution,[status(thm)],[3321, 3313, 323, 1653])).
% 1.94/2.14 tff(3323,plain,
% 1.94/2.14 (b(z, s(s(s(z))))),
% 1.94/2.14 inference(unit_resolution,[status(thm)],[1697, 3322])).
% 1.94/2.14 tff(3324,plain,
% 1.94/2.14 (~b(s(s(s(z))), z)),
% 1.94/2.14 inference(unit_resolution,[status(thm)],[3223, 3323, 986, 122])).
% 1.94/2.14 tff(3325,plain,
% 1.94/2.14 (r(s(s(s(z))), z)),
% 1.94/2.14 inference(unit_resolution,[status(thm)],[1713, 3324])).
% 1.94/2.14 tff(3326,plain,
% 1.94/2.14 ($false),
% 1.94/2.14 inference(unit_resolution,[status(thm)],[2870, 197, 155, 97, 3325, 1653])).
% 1.94/2.14 tff(3327,plain,((~r(s(z), z)) | (~r(z, s(s(z)))) | (~r(s(z), s(s(s(z))))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(z)), z)) | (~r(z, s(z))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(elem!1))), z)) | (~b(s(s(s(elem!1))), s(s(z)))) | (~b(s(s(s(elem!1))), s(s(s(z)))))), inference(lemma,lemma(discharge,[]))).
% 1.94/2.14 tff(3328,plain,
% 1.94/2.14 (~r(s(z), z)),
% 1.94/2.14 inference(unit_resolution,[status(thm)],[3327, 3250, 152, 3205, 3134, 322, 3235, 3239, 3237, 3195])).
% 1.94/2.14 tff(3329,plain,
% 1.94/2.14 (b(s(z), z)),
% 1.94/2.14 inference(unit_resolution,[status(thm)],[230, 3328])).
% 1.94/2.14 tff(3330,plain,
% 1.94/2.14 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), z)) | (~b(s(s(s(elem!1))), s(s(z)))) | (~b(s(s(s(elem!1))), z)) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(elem!1))), s(s(s(z))))) | (~b(s(s(z)), s(s(s(z))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), z)) | (~b(s(s(s(elem!1))), s(s(z)))) | (~b(s(s(s(elem!1))), z)) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(elem!1))), s(s(s(z))))) | (~b(s(s(z)), s(s(s(z))))))),
% 1.94/2.14 inference(rewrite,[status(thm)],[])).
% 1.94/2.14 tff(3331,plain,
% 1.94/2.14 (((~b(s(z), z)) | (~b(s(s(s(elem!1))), z)) | (~b(s(s(s(z))), s(z))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(s(elem!1))), s(s(s(z))))) | (~b(s(s(s(elem!1))), s(s(z))))) <=> ((~b(s(z), z)) | (~b(s(s(s(elem!1))), s(s(z)))) | (~b(s(s(s(elem!1))), z)) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(elem!1))), s(s(s(z))))) | (~b(s(s(z)), s(s(s(z))))))),
% 1.94/2.14 inference(rewrite,[status(thm)],[])).
% 1.94/2.14 tff(3332,plain,
% 1.94/2.14 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), z)) | (~b(s(s(s(elem!1))), z)) | (~b(s(s(s(z))), s(z))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(s(elem!1))), s(s(s(z))))) | (~b(s(s(s(elem!1))), s(s(z)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), z)) | (~b(s(s(s(elem!1))), s(s(z)))) | (~b(s(s(s(elem!1))), z)) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(elem!1))), s(s(s(z))))) | (~b(s(s(z)), s(s(s(z)))))))),
% 1.94/2.14 inference(monotonicity,[status(thm)],[3331])).
% 1.94/2.14 tff(3333,plain,
% 1.94/2.14 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), z)) | (~b(s(s(s(elem!1))), z)) | (~b(s(s(s(z))), s(z))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(s(elem!1))), s(s(s(z))))) | (~b(s(s(s(elem!1))), s(s(z)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), z)) | (~b(s(s(s(elem!1))), s(s(z)))) | (~b(s(s(s(elem!1))), z)) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(elem!1))), s(s(s(z))))) | (~b(s(s(z)), s(s(s(z))))))),
% 1.94/2.14 inference(transitivity,[status(thm)],[3332, 3330])).
% 1.94/2.14 tff(3334,plain,
% 1.94/2.14 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), z)) | (~b(s(s(s(elem!1))), z)) | (~b(s(s(s(z))), s(z))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(s(elem!1))), s(s(s(z))))) | (~b(s(s(s(elem!1))), s(s(z)))))),
% 1.94/2.14 inference(quant_inst,[status(thm)],[])).
% 1.94/2.14 tff(3335,plain,
% 1.94/2.14 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), z)) | (~b(s(s(s(elem!1))), s(s(z)))) | (~b(s(s(s(elem!1))), z)) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(elem!1))), s(s(s(z))))) | (~b(s(s(z)), s(s(s(z)))))),
% 1.94/2.14 inference(modus_ponens,[status(thm)],[3334, 3333])).
% 1.94/2.14 tff(3336,plain,
% 1.94/2.14 ($false),
% 1.94/2.14 inference(unit_resolution,[status(thm)],[3335, 166, 3329, 3239, 3205, 3237, 3235, 3195])).
% 1.94/2.14 tff(3337,plain,(b(z, s(z)) | (~b(s(s(elem!1)), s(z))) | (~r(s(z), s(s(elem!1)))) | (~b(s(s(z)), s(z))) | b(z, s(s(z))) | (~r(s(z), s(s(z))))), inference(lemma,lemma(discharge,[]))).
% 1.94/2.14 tff(3338,plain,
% 1.94/2.14 (b(z, s(z))),
% 1.94/2.14 inference(unit_resolution,[status(thm)],[3337, 156, 311, 310, 125, 120])).
% 1.94/2.14 tff(3339,plain,
% 1.94/2.14 (~b(s(s(s(elem!1))), s(z))),
% 1.94/2.14 inference(unit_resolution,[status(thm)],[292, 154, 155, 156, 118])).
% 1.94/2.14 tff(3340,plain,
% 1.94/2.14 (r(s(s(s(elem!1))), s(z))),
% 1.94/2.14 inference(unit_resolution,[status(thm)],[1849, 3339])).
% 1.94/2.14 tff(3341,plain,
% 1.94/2.14 ((s(s(elem!1)) = s(s(s(elem!1)))) <=> (s(s(s(elem!1))) = s(s(elem!1)))),
% 1.94/2.14 inference(symmetry,[status(thm)],[46])).
% 1.94/2.14 tff(3342,plain,
% 1.94/2.14 ((s(s(z)) = s(s(s(elem!1)))) <=> (s(s(elem!1)) = s(s(s(elem!1))))),
% 1.94/2.14 inference(monotonicity,[status(thm)],[34])).
% 1.94/2.14 tff(3343,plain,
% 1.94/2.14 ((s(s(z)) = s(s(s(elem!1)))) <=> (s(s(s(elem!1))) = s(s(elem!1)))),
% 1.94/2.14 inference(transitivity,[status(thm)],[3342, 3341])).
% 1.94/2.14 tff(3344,plain,
% 1.94/2.14 ((~(s(s(z)) = s(s(s(elem!1))))) <=> (~(s(s(s(elem!1))) = s(s(elem!1))))),
% 1.94/2.14 inference(monotonicity,[status(thm)],[3343])).
% 1.94/2.14 tff(3345,plain,
% 1.94/2.14 (~(s(s(s(elem!1))) = s(s(elem!1)))),
% 1.94/2.14 inference(modus_ponens,[status(thm)],[209, 3344])).
% 1.94/2.14 tff(3346,plain,
% 1.94/2.14 ((s(s(s(z))) = s(s(s(s(z))))) <=> (s(s(s(elem!1))) = s(s(s(s(elem!1)))))),
% 1.94/2.14 inference(monotonicity,[status(thm)],[1086, 1087])).
% 1.94/2.14 tff(3347,plain,
% 1.94/2.14 ((~(s(s(s(z))) = s(s(s(s(z)))))) <=> (~(s(s(s(elem!1))) = s(s(s(s(elem!1))))))),
% 1.94/2.14 inference(monotonicity,[status(thm)],[3346])).
% 1.94/2.14 tff(3348,plain,
% 1.94/2.14 (~(s(s(s(elem!1))) = s(s(s(s(elem!1)))))),
% 1.94/2.14 inference(modus_ponens,[status(thm)],[2228, 3347])).
% 1.94/2.14 tff(3349,plain,
% 1.94/2.14 (~r(s(z), z)),
% 1.94/2.14 inference(unit_resolution,[status(thm)],[2498, 866, 155, 120])).
% 1.94/2.14 tff(3350,plain,
% 1.94/2.14 (b(s(z), z)),
% 1.94/2.14 inference(unit_resolution,[status(thm)],[230, 3349])).
% 1.94/2.14 tff(3351,plain,
% 1.94/2.14 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(elem!1)))) | (~b(s(z), z)) | (~b(z, s(z))) | (~b(s(s(elem!1)), s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(s(elem!1)))) | (~b(s(z), z)) | (~b(z, s(z))) | (~b(s(s(elem!1)), s(z))))),
% 1.94/2.14 inference(rewrite,[status(thm)],[])).
% 1.94/2.14 tff(3352,plain,
% 1.94/2.14 (((~b(z, s(s(elem!1)))) | (~b(z, s(s(elem!1)))) | (~b(s(z), z)) | (~b(s(s(elem!1)), s(z))) | (~b(z, s(z))) | (~b(z, s(s(elem!1))))) <=> ((~b(z, s(s(elem!1)))) | (~b(s(z), z)) | (~b(z, s(z))) | (~b(s(s(elem!1)), s(z))))),
% 1.94/2.14 inference(rewrite,[status(thm)],[])).
% 1.94/2.14 tff(3353,plain,
% 1.94/2.14 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(elem!1)))) | (~b(z, s(s(elem!1)))) | (~b(s(z), z)) | (~b(s(s(elem!1)), s(z))) | (~b(z, s(z))) | (~b(z, s(s(elem!1)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(elem!1)))) | (~b(s(z), z)) | (~b(z, s(z))) | (~b(s(s(elem!1)), s(z)))))),
% 1.94/2.14 inference(monotonicity,[status(thm)],[3352])).
% 1.94/2.14 tff(3354,plain,
% 1.94/2.14 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(elem!1)))) | (~b(z, s(s(elem!1)))) | (~b(s(z), z)) | (~b(s(s(elem!1)), s(z))) | (~b(z, s(z))) | (~b(z, s(s(elem!1)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(s(elem!1)))) | (~b(s(z), z)) | (~b(z, s(z))) | (~b(s(s(elem!1)), s(z))))),
% 1.94/2.14 inference(transitivity,[status(thm)],[3353, 3351])).
% 1.94/2.14 tff(3355,plain,
% 1.94/2.14 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(elem!1)))) | (~b(z, s(s(elem!1)))) | (~b(s(z), z)) | (~b(s(s(elem!1)), s(z))) | (~b(z, s(z))) | (~b(z, s(s(elem!1)))))),
% 1.94/2.14 inference(quant_inst,[status(thm)],[])).
% 1.94/2.14 tff(3356,plain,
% 1.94/2.14 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(s(elem!1)))) | (~b(s(z), z)) | (~b(z, s(z))) | (~b(s(s(elem!1)), s(z)))),
% 1.94/2.14 inference(modus_ponens,[status(thm)],[3355, 3354])).
% 1.94/2.14 tff(3357,plain,
% 1.94/2.14 ($false),
% 1.94/2.14 inference(unit_resolution,[status(thm)],[3356, 166, 1820, 53, 118, 310])).
% 1.94/2.14 tff(3358,plain,((~b(s(s(elem!1)), s(z))) | (~b(z, s(s(elem!1)))) | (~b(s(z), z)) | (~b(z, s(z)))), inference(lemma,lemma(discharge,[]))).
% 1.94/2.14 tff(3359,plain,
% 1.94/2.14 (~b(z, s(s(elem!1)))),
% 1.94/2.14 inference(unit_resolution,[status(thm)],[3358, 3350, 310, 118])).
% 1.94/2.14 tff(3360,plain,
% 1.94/2.14 (r(z, s(s(elem!1)))),
% 1.94/2.14 inference(unit_resolution,[status(thm)],[1795, 3359])).
% 1.94/2.14 tff(3361,plain,
% 1.94/2.14 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), z)) | (~b(s(s(elem!1)), s(s(z)))) | (~b(z, s(z))) | (~b(s(s(elem!1)), s(z))) | (~b(s(s(z)), s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), z)) | (~b(s(s(elem!1)), s(s(z)))) | (~b(z, s(z))) | (~b(s(s(elem!1)), s(z))) | (~b(s(s(z)), s(z))))),
% 1.94/2.14 inference(rewrite,[status(thm)],[])).
% 1.94/2.14 tff(3362,plain,
% 1.94/2.14 (((~b(z, s(z))) | (~b(s(s(elem!1)), s(z))) | (~b(s(z), z)) | (~b(s(s(z)), s(z))) | (~b(s(s(elem!1)), s(z))) | (~b(s(s(elem!1)), s(s(z))))) <=> ((~b(s(z), z)) | (~b(s(s(elem!1)), s(s(z)))) | (~b(z, s(z))) | (~b(s(s(elem!1)), s(z))) | (~b(s(s(z)), s(z))))),
% 1.94/2.14 inference(rewrite,[status(thm)],[])).
% 1.94/2.14 tff(3363,plain,
% 1.94/2.14 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(z))) | (~b(s(s(elem!1)), s(z))) | (~b(s(z), z)) | (~b(s(s(z)), s(z))) | (~b(s(s(elem!1)), s(z))) | (~b(s(s(elem!1)), s(s(z)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), z)) | (~b(s(s(elem!1)), s(s(z)))) | (~b(z, s(z))) | (~b(s(s(elem!1)), s(z))) | (~b(s(s(z)), s(z)))))),
% 1.94/2.14 inference(monotonicity,[status(thm)],[3362])).
% 1.94/2.14 tff(3364,plain,
% 1.94/2.14 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(z))) | (~b(s(s(elem!1)), s(z))) | (~b(s(z), z)) | (~b(s(s(z)), s(z))) | (~b(s(s(elem!1)), s(z))) | (~b(s(s(elem!1)), s(s(z)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), z)) | (~b(s(s(elem!1)), s(s(z)))) | (~b(z, s(z))) | (~b(s(s(elem!1)), s(z))) | (~b(s(s(z)), s(z))))),
% 1.94/2.14 inference(transitivity,[status(thm)],[3363, 3361])).
% 1.94/2.14 tff(3365,plain,
% 1.94/2.14 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(z))) | (~b(s(s(elem!1)), s(z))) | (~b(s(z), z)) | (~b(s(s(z)), s(z))) | (~b(s(s(elem!1)), s(z))) | (~b(s(s(elem!1)), s(s(z)))))),
% 1.94/2.14 inference(quant_inst,[status(thm)],[])).
% 1.94/2.14 tff(3366,plain,
% 1.94/2.14 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), z)) | (~b(s(s(elem!1)), s(s(z)))) | (~b(z, s(z))) | (~b(s(s(elem!1)), s(z))) | (~b(s(s(z)), s(z)))),
% 1.94/2.14 inference(modus_ponens,[status(thm)],[3365, 3364])).
% 1.94/2.14 tff(3367,plain,
% 1.94/2.14 (~b(s(s(elem!1)), s(s(z)))),
% 1.94/2.14 inference(unit_resolution,[status(thm)],[3366, 166, 3350, 118, 310, 156])).
% 1.94/2.14 tff(3368,plain,
% 1.94/2.14 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), z)) | (~b(z, s(z))) | (~b(s(s(elem!1)), s(z))) | (~b(s(s(z)), s(s(elem!1)))) | (~b(s(s(z)), s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), z)) | (~b(z, s(z))) | (~b(s(s(elem!1)), s(z))) | (~b(s(s(z)), s(s(elem!1)))) | (~b(s(s(z)), s(z))))),
% 1.94/2.14 inference(rewrite,[status(thm)],[])).
% 1.94/2.14 tff(3369,plain,
% 1.94/2.14 (((~b(z, s(z))) | (~b(s(s(z)), s(z))) | (~b(s(z), z)) | (~b(s(s(elem!1)), s(z))) | (~b(s(s(z)), s(z))) | (~b(s(s(z)), s(s(elem!1))))) <=> ((~b(s(z), z)) | (~b(z, s(z))) | (~b(s(s(elem!1)), s(z))) | (~b(s(s(z)), s(s(elem!1)))) | (~b(s(s(z)), s(z))))),
% 1.94/2.14 inference(rewrite,[status(thm)],[])).
% 1.94/2.14 tff(3370,plain,
% 1.94/2.14 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(z))) | (~b(s(s(z)), s(z))) | (~b(s(z), z)) | (~b(s(s(elem!1)), s(z))) | (~b(s(s(z)), s(z))) | (~b(s(s(z)), s(s(elem!1)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), z)) | (~b(z, s(z))) | (~b(s(s(elem!1)), s(z))) | (~b(s(s(z)), s(s(elem!1)))) | (~b(s(s(z)), s(z)))))),
% 1.94/2.14 inference(monotonicity,[status(thm)],[3369])).
% 1.94/2.14 tff(3371,plain,
% 1.94/2.14 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(z))) | (~b(s(s(z)), s(z))) | (~b(s(z), z)) | (~b(s(s(elem!1)), s(z))) | (~b(s(s(z)), s(z))) | (~b(s(s(z)), s(s(elem!1)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), z)) | (~b(z, s(z))) | (~b(s(s(elem!1)), s(z))) | (~b(s(s(z)), s(s(elem!1)))) | (~b(s(s(z)), s(z))))),
% 1.94/2.14 inference(transitivity,[status(thm)],[3370, 3368])).
% 1.94/2.14 tff(3372,plain,
% 1.94/2.14 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(z))) | (~b(s(s(z)), s(z))) | (~b(s(z), z)) | (~b(s(s(elem!1)), s(z))) | (~b(s(s(z)), s(z))) | (~b(s(s(z)), s(s(elem!1)))))),
% 1.94/2.14 inference(quant_inst,[status(thm)],[])).
% 1.94/2.14 tff(3373,plain,
% 1.94/2.14 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), z)) | (~b(z, s(z))) | (~b(s(s(elem!1)), s(z))) | (~b(s(s(z)), s(s(elem!1)))) | (~b(s(s(z)), s(z)))),
% 1.94/2.14 inference(modus_ponens,[status(thm)],[3372, 3371])).
% 1.94/2.14 tff(3374,plain,
% 1.94/2.14 (~b(s(s(z)), s(s(elem!1)))),
% 1.94/2.14 inference(unit_resolution,[status(thm)],[3373, 166, 3350, 118, 310, 156])).
% 1.94/2.14 tff(3375,plain,
% 1.94/2.14 (s(s(z)) = s(s(elem!1))),
% 1.94/2.14 inference(unit_resolution,[status(thm)],[2079, 3374, 155, 3367, 3360])).
% 1.94/2.15 tff(3376,plain,
% 1.94/2.15 ((s(s(s(s(elem!1)))) = s(s(z))) <=> (s(s(s(s(elem!1)))) = s(s(elem!1)))),
% 1.94/2.15 inference(monotonicity,[status(thm)],[3375])).
% 1.94/2.15 tff(3377,plain,
% 1.94/2.15 ((s(s(s(s(elem!1)))) = s(s(z))) <=> (s(s(elem!1)) = s(s(s(s(elem!1)))))),
% 1.94/2.15 inference(transitivity,[status(thm)],[3376, 123])).
% 1.94/2.15 tff(3378,plain,
% 1.94/2.15 ((s(s(s(s(elem!1)))) = s(s(z))) <=> (s(s(s(s(elem!1)))) = s(s(elem!1)))),
% 1.94/2.15 inference(transitivity,[status(thm)],[3377, 124])).
% 1.94/2.15 tff(3379,plain,
% 1.94/2.15 ((~(s(s(s(s(elem!1)))) = s(s(z)))) <=> (~(s(s(s(s(elem!1)))) = s(s(elem!1))))),
% 1.94/2.15 inference(monotonicity,[status(thm)],[3378])).
% 1.94/2.15 tff(3380,plain,
% 1.94/2.15 (~(s(s(s(s(elem!1)))) = s(s(elem!1)))),
% 1.94/2.15 inference(modus_ponens,[status(thm)],[733, 3379])).
% 1.94/2.15 tff(3381,plain,
% 1.94/2.15 (s(elem!1) = s(z)),
% 1.94/2.15 inference(unit_resolution,[status(thm)],[43, 3375])).
% 1.94/2.15 tff(3382,plain,
% 1.94/2.15 (z = elem!1),
% 1.94/2.15 inference(unit_resolution,[status(thm)],[30, 3381])).
% 1.94/2.15 tff(3383,plain,
% 1.94/2.15 (r(z, s(s(elem!1))) <=> r(elem!1, s(s(elem!1)))),
% 1.94/2.15 inference(monotonicity,[status(thm)],[3382])).
% 1.94/2.15 tff(3384,plain,
% 1.94/2.15 (r(elem!1, s(s(elem!1)))),
% 1.94/2.15 inference(modus_ponens,[status(thm)],[3360, 3383])).
% 1.94/2.15 tff(3385,plain,
% 1.94/2.15 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), z)) | (~b(s(s(elem!1)), z)) | (~b(z, s(z))) | (~b(s(s(elem!1)), s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), z)) | (~b(s(s(elem!1)), z)) | (~b(z, s(z))) | (~b(s(s(elem!1)), s(z))))),
% 1.94/2.15 inference(rewrite,[status(thm)],[])).
% 1.94/2.15 tff(3386,plain,
% 1.94/2.15 (((~b(z, s(z))) | (~b(s(s(elem!1)), s(z))) | (~b(s(z), z)) | (~b(z, s(z))) | (~b(s(s(elem!1)), s(z))) | (~b(s(s(elem!1)), z))) <=> ((~b(s(z), z)) | (~b(s(s(elem!1)), z)) | (~b(z, s(z))) | (~b(s(s(elem!1)), s(z))))),
% 1.94/2.15 inference(rewrite,[status(thm)],[])).
% 1.94/2.15 tff(3387,plain,
% 1.94/2.15 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(z))) | (~b(s(s(elem!1)), s(z))) | (~b(s(z), z)) | (~b(z, s(z))) | (~b(s(s(elem!1)), s(z))) | (~b(s(s(elem!1)), z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), z)) | (~b(s(s(elem!1)), z)) | (~b(z, s(z))) | (~b(s(s(elem!1)), s(z)))))),
% 1.94/2.15 inference(monotonicity,[status(thm)],[3386])).
% 1.94/2.15 tff(3388,plain,
% 1.94/2.15 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(z))) | (~b(s(s(elem!1)), s(z))) | (~b(s(z), z)) | (~b(z, s(z))) | (~b(s(s(elem!1)), s(z))) | (~b(s(s(elem!1)), z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), z)) | (~b(s(s(elem!1)), z)) | (~b(z, s(z))) | (~b(s(s(elem!1)), s(z))))),
% 1.94/2.15 inference(transitivity,[status(thm)],[3387, 3385])).
% 1.94/2.15 tff(3389,plain,
% 1.94/2.15 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(z))) | (~b(s(s(elem!1)), s(z))) | (~b(s(z), z)) | (~b(z, s(z))) | (~b(s(s(elem!1)), s(z))) | (~b(s(s(elem!1)), z)))),
% 1.94/2.15 inference(quant_inst,[status(thm)],[])).
% 1.94/2.15 tff(3390,plain,
% 1.94/2.15 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), z)) | (~b(s(s(elem!1)), z)) | (~b(z, s(z))) | (~b(s(s(elem!1)), s(z)))),
% 1.94/2.15 inference(modus_ponens,[status(thm)],[3389, 3388])).
% 1.94/2.15 tff(3391,plain,
% 1.94/2.15 (~b(s(s(elem!1)), z)),
% 1.94/2.15 inference(unit_resolution,[status(thm)],[3390, 166, 3350, 118, 310])).
% 1.94/2.15 tff(3392,plain,
% 1.94/2.15 (r(s(s(elem!1)), z)),
% 1.94/2.15 inference(unit_resolution,[status(thm)],[608, 3391])).
% 1.94/2.15 tff(3393,plain,
% 1.94/2.15 (r(s(s(elem!1)), z) <=> r(s(s(elem!1)), elem!1)),
% 1.94/2.15 inference(monotonicity,[status(thm)],[12])).
% 1.94/2.15 tff(3394,plain,
% 1.94/2.15 (r(s(s(elem!1)), elem!1) <=> r(s(s(elem!1)), z)),
% 1.94/2.15 inference(symmetry,[status(thm)],[3393])).
% 1.94/2.15 tff(3395,plain,
% 1.94/2.15 ((~r(s(s(elem!1)), elem!1)) <=> (~r(s(s(elem!1)), z))),
% 1.94/2.15 inference(monotonicity,[status(thm)],[3394])).
% 1.94/2.15 tff(3396,plain,
% 1.94/2.15 (~r(s(s(elem!1)), z)),
% 1.94/2.15 inference(modus_ponens,[status(thm)],[778, 3395])).
% 1.94/2.15 tff(3397,plain,
% 1.94/2.15 ($false),
% 1.94/2.15 inference(unit_resolution,[status(thm)],[1970, 3396])).
% 1.94/2.15 tff(3398,plain,((~(z = elem!1)) | (~r(s(s(elem!1)), z)) | r(s(s(elem!1)), elem!1)), inference(lemma,lemma(discharge,[]))).
% 1.94/2.15 tff(3399,plain,
% 1.94/2.15 (r(s(s(elem!1)), elem!1)),
% 1.94/2.15 inference(unit_resolution,[status(thm)],[3398, 3382, 3392])).
% 1.94/2.15 tff(3400,plain,
% 1.94/2.15 ((s(s(s(s(elem!1)))) = z) <=> (s(s(s(s(elem!1)))) = elem!1)),
% 1.94/2.15 inference(monotonicity,[status(thm)],[3382])).
% 1.94/2.15 tff(3401,plain,
% 1.94/2.15 ((s(s(s(s(elem!1)))) = z) <=> (elem!1 = s(s(s(s(elem!1)))))),
% 1.94/2.15 inference(transitivity,[status(thm)],[3400, 2287])).
% 1.94/2.15 tff(3402,plain,
% 1.94/2.15 ((~(s(s(s(s(elem!1)))) = z)) <=> (~(elem!1 = s(s(s(s(elem!1))))))),
% 1.94/2.15 inference(monotonicity,[status(thm)],[3401])).
% 1.94/2.15 tff(3403,plain,
% 1.94/2.15 (~(elem!1 = s(s(s(s(elem!1)))))),
% 1.94/2.15 inference(modus_ponens,[status(thm)],[626, 3402])).
% 1.94/2.15 tff(3404,plain,
% 1.94/2.15 (b(s(z), z) <=> b(s(z), elem!1)),
% 1.94/2.15 inference(monotonicity,[status(thm)],[3382])).
% 1.94/2.15 tff(3405,plain,
% 1.94/2.15 (b(s(z), elem!1)),
% 1.94/2.15 inference(modus_ponens,[status(thm)],[3350, 3404])).
% 1.94/2.15 tff(3406,plain,
% 1.94/2.15 (b(z, s(z)) <=> b(elem!1, s(z))),
% 1.94/2.15 inference(monotonicity,[status(thm)],[3382])).
% 1.94/2.15 tff(3407,plain,
% 1.94/2.15 (b(elem!1, s(z))),
% 1.94/2.15 inference(modus_ponens,[status(thm)],[118, 3406])).
% 1.94/2.15 tff(3408,assumption,(r(s(s(s(s(elem!1)))), s(s(elem!1)))), introduced(assumption)).
% 1.94/2.15 tff(3409,plain,
% 1.94/2.15 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(s(s(s(elem!1)))))) | (~r(elem!1, s(s(elem!1)))) | (~r(s(s(elem!1)), elem!1)) | (~r(s(s(s(s(elem!1)))), s(s(elem!1)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(elem!1, s(s(s(s(elem!1)))))) | (~r(elem!1, s(s(elem!1)))) | (~r(s(s(elem!1)), elem!1)) | (~r(s(s(s(s(elem!1)))), s(s(elem!1)))))),
% 1.94/2.15 inference(rewrite,[status(thm)],[])).
% 1.94/2.15 tff(3410,plain,
% 1.94/2.15 (((~r(s(s(elem!1)), elem!1)) | (~r(s(s(s(s(elem!1)))), s(s(elem!1)))) | (~r(elem!1, s(s(elem!1)))) | (~r(elem!1, s(s(s(s(elem!1))))))) <=> ((~r(elem!1, s(s(s(s(elem!1)))))) | (~r(elem!1, s(s(elem!1)))) | (~r(s(s(elem!1)), elem!1)) | (~r(s(s(s(s(elem!1)))), s(s(elem!1)))))),
% 1.94/2.15 inference(rewrite,[status(thm)],[])).
% 1.94/2.15 tff(3411,plain,
% 1.94/2.15 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(elem!1)), elem!1)) | (~r(s(s(s(s(elem!1)))), s(s(elem!1)))) | (~r(elem!1, s(s(elem!1)))) | (~r(elem!1, s(s(s(s(elem!1)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(s(s(s(elem!1)))))) | (~r(elem!1, s(s(elem!1)))) | (~r(s(s(elem!1)), elem!1)) | (~r(s(s(s(s(elem!1)))), s(s(elem!1))))))),
% 1.94/2.15 inference(monotonicity,[status(thm)],[3410])).
% 1.94/2.15 tff(3412,plain,
% 1.94/2.15 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(elem!1)), elem!1)) | (~r(s(s(s(s(elem!1)))), s(s(elem!1)))) | (~r(elem!1, s(s(elem!1)))) | (~r(elem!1, s(s(s(s(elem!1)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(elem!1, s(s(s(s(elem!1)))))) | (~r(elem!1, s(s(elem!1)))) | (~r(s(s(elem!1)), elem!1)) | (~r(s(s(s(s(elem!1)))), s(s(elem!1)))))),
% 1.94/2.15 inference(transitivity,[status(thm)],[3411, 3409])).
% 1.94/2.15 tff(3413,plain,
% 1.94/2.15 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(elem!1)), elem!1)) | (~r(s(s(s(s(elem!1)))), s(s(elem!1)))) | (~r(elem!1, s(s(elem!1)))) | (~r(elem!1, s(s(s(s(elem!1)))))))),
% 1.94/2.15 inference(quant_inst,[status(thm)],[])).
% 1.94/2.15 tff(3414,plain,
% 1.94/2.15 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(elem!1, s(s(s(s(elem!1)))))) | (~r(elem!1, s(s(elem!1)))) | (~r(s(s(elem!1)), elem!1)) | (~r(s(s(s(s(elem!1)))), s(s(elem!1))))),
% 1.94/2.15 inference(modus_ponens,[status(thm)],[3413, 3412])).
% 1.94/2.15 tff(3415,plain,
% 1.94/2.15 (~r(elem!1, s(s(s(s(elem!1)))))),
% 1.94/2.15 inference(unit_resolution,[status(thm)],[3414, 197, 768, 3408, 1027])).
% 1.94/2.15 tff(3416,plain,
% 1.94/2.15 (b(elem!1, s(s(s(s(elem!1)))))),
% 1.94/2.15 inference(unit_resolution,[status(thm)],[2427, 3415, 2422])).
% 1.94/2.15 tff(3417,plain,
% 1.94/2.15 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(s(elem!1)))) | (~r(s(s(elem!1)), elem!1)) | (~r(s(s(s(s(elem!1)))), s(z))) | (~r(s(s(s(s(elem!1)))), s(s(elem!1)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(z), s(s(elem!1)))) | (~r(s(s(elem!1)), elem!1)) | (~r(s(s(s(s(elem!1)))), s(z))) | (~r(s(s(s(s(elem!1)))), s(s(elem!1)))))),
% 1.94/2.15 inference(rewrite,[status(thm)],[])).
% 1.94/2.15 tff(3418,plain,
% 1.94/2.15 (((~r(s(s(elem!1)), elem!1)) | (~r(s(z), s(s(elem!1)))) | (~r(s(s(s(s(elem!1)))), s(s(elem!1)))) | (~r(s(s(s(s(elem!1)))), s(z)))) <=> ((~r(s(z), s(s(elem!1)))) | (~r(s(s(elem!1)), elem!1)) | (~r(s(s(s(s(elem!1)))), s(z))) | (~r(s(s(s(s(elem!1)))), s(s(elem!1)))))),
% 1.94/2.15 inference(rewrite,[status(thm)],[])).
% 1.94/2.15 tff(3419,plain,
% 1.94/2.15 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(elem!1)), elem!1)) | (~r(s(z), s(s(elem!1)))) | (~r(s(s(s(s(elem!1)))), s(s(elem!1)))) | (~r(s(s(s(s(elem!1)))), s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(s(elem!1)))) | (~r(s(s(elem!1)), elem!1)) | (~r(s(s(s(s(elem!1)))), s(z))) | (~r(s(s(s(s(elem!1)))), s(s(elem!1))))))),
% 1.94/2.15 inference(monotonicity,[status(thm)],[3418])).
% 1.94/2.15 tff(3420,plain,
% 1.94/2.15 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(elem!1)), elem!1)) | (~r(s(z), s(s(elem!1)))) | (~r(s(s(s(s(elem!1)))), s(s(elem!1)))) | (~r(s(s(s(s(elem!1)))), s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(z), s(s(elem!1)))) | (~r(s(s(elem!1)), elem!1)) | (~r(s(s(s(s(elem!1)))), s(z))) | (~r(s(s(s(s(elem!1)))), s(s(elem!1)))))),
% 1.94/2.15 inference(transitivity,[status(thm)],[3419, 3417])).
% 1.94/2.15 tff(3421,plain,
% 1.94/2.15 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(elem!1)), elem!1)) | (~r(s(z), s(s(elem!1)))) | (~r(s(s(s(s(elem!1)))), s(s(elem!1)))) | (~r(s(s(s(s(elem!1)))), s(z))))),
% 1.94/2.15 inference(quant_inst,[status(thm)],[])).
% 1.94/2.15 tff(3422,plain,
% 1.94/2.15 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(z), s(s(elem!1)))) | (~r(s(s(elem!1)), elem!1)) | (~r(s(s(s(s(elem!1)))), s(z))) | (~r(s(s(s(s(elem!1)))), s(s(elem!1))))),
% 1.94/2.15 inference(modus_ponens,[status(thm)],[3421, 3420])).
% 1.94/2.15 tff(3423,plain,
% 1.94/2.15 (~r(s(s(s(s(elem!1)))), s(z))),
% 1.94/2.15 inference(unit_resolution,[status(thm)],[3422, 197, 311, 768, 3408])).
% 1.94/2.15 tff(3424,plain,
% 1.94/2.15 (b(s(s(s(s(elem!1)))), s(z))),
% 1.94/2.15 inference(unit_resolution,[status(thm)],[661, 3423])).
% 1.94/2.15 tff(3425,plain,
% 1.94/2.15 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(z))) | (~b(s(z), elem!1)) | (~b(elem!1, s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(z))) | (~b(s(z), elem!1)) | (~b(elem!1, s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), s(z))))),
% 1.94/2.15 inference(rewrite,[status(thm)],[])).
% 1.94/2.15 tff(3426,plain,
% 1.94/2.15 (((~b(elem!1, s(z))) | (~b(elem!1, s(z))) | (~b(s(z), elem!1)) | (~b(s(s(s(s(elem!1)))), s(z))) | (~b(elem!1, s(z))) | (~b(elem!1, s(s(s(s(elem!1))))))) <=> ((~b(elem!1, s(z))) | (~b(s(z), elem!1)) | (~b(elem!1, s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), s(z))))),
% 1.94/2.15 inference(rewrite,[status(thm)],[])).
% 1.94/2.15 tff(3427,plain,
% 1.94/2.15 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(z))) | (~b(elem!1, s(z))) | (~b(s(z), elem!1)) | (~b(s(s(s(s(elem!1)))), s(z))) | (~b(elem!1, s(z))) | (~b(elem!1, s(s(s(s(elem!1)))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(z))) | (~b(s(z), elem!1)) | (~b(elem!1, s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), s(z)))))),
% 1.94/2.15 inference(monotonicity,[status(thm)],[3426])).
% 1.94/2.15 tff(3428,plain,
% 1.94/2.15 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(z))) | (~b(elem!1, s(z))) | (~b(s(z), elem!1)) | (~b(s(s(s(s(elem!1)))), s(z))) | (~b(elem!1, s(z))) | (~b(elem!1, s(s(s(s(elem!1)))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(z))) | (~b(s(z), elem!1)) | (~b(elem!1, s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), s(z))))),
% 1.94/2.15 inference(transitivity,[status(thm)],[3427, 3425])).
% 1.94/2.15 tff(3429,plain,
% 1.94/2.15 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(z))) | (~b(elem!1, s(z))) | (~b(s(z), elem!1)) | (~b(s(s(s(s(elem!1)))), s(z))) | (~b(elem!1, s(z))) | (~b(elem!1, s(s(s(s(elem!1)))))))),
% 1.94/2.15 inference(quant_inst,[status(thm)],[])).
% 1.94/2.15 tff(3430,plain,
% 1.94/2.15 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(z))) | (~b(s(z), elem!1)) | (~b(elem!1, s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), s(z)))),
% 1.94/2.15 inference(modus_ponens,[status(thm)],[3429, 3428])).
% 1.94/2.15 tff(3431,plain,
% 1.94/2.15 ($false),
% 1.94/2.15 inference(unit_resolution,[status(thm)],[3430, 166, 1212, 642, 3424, 3416])).
% 1.94/2.15 tff(3432,plain,((~r(s(s(s(s(elem!1)))), s(s(elem!1)))) | (~b(elem!1, s(z))) | (~b(s(z), elem!1)) | (elem!1 = s(s(s(s(elem!1))))) | (~r(s(s(elem!1)), elem!1)) | (~r(elem!1, s(s(elem!1)))) | (~r(s(z), s(s(elem!1))))), inference(lemma,lemma(discharge,[]))).
% 1.94/2.15 tff(3433,plain,
% 1.94/2.15 (~r(s(s(s(s(elem!1)))), s(s(elem!1)))),
% 1.94/2.15 inference(unit_resolution,[status(thm)],[3432, 3407, 3405, 3403, 3399, 3384, 311])).
% 1.94/2.15 tff(3434,plain,
% 1.94/2.15 (b(s(s(s(s(elem!1)))), s(s(elem!1)))),
% 1.94/2.15 inference(unit_resolution,[status(thm)],[813, 3433, 3380])).
% 1.94/2.15 tff(3435,plain,
% 1.94/2.15 (s(s(s(z))) = s(s(s(elem!1)))),
% 1.94/2.15 inference(monotonicity,[status(thm)],[3375])).
% 1.94/2.15 tff(3436,plain,
% 1.94/2.15 (b(s(s(elem!1)), s(s(s(z)))) <=> b(s(s(elem!1)), s(s(s(elem!1))))),
% 1.94/2.15 inference(monotonicity,[status(thm)],[3435])).
% 1.94/2.15 tff(3437,plain,
% 1.94/2.15 (b(s(s(z)), s(s(s(z)))) <=> b(s(s(elem!1)), s(s(s(z))))),
% 1.94/2.15 inference(monotonicity,[status(thm)],[3375])).
% 1.94/2.15 tff(3438,plain,
% 1.94/2.15 (b(s(s(z)), s(s(s(z)))) <=> b(s(s(elem!1)), s(s(s(elem!1))))),
% 1.94/2.15 inference(transitivity,[status(thm)],[3437, 3436])).
% 1.94/2.15 tff(3439,plain,
% 1.94/2.15 (r(s(s(s(z))), z) <=> r(s(s(s(z))), elem!1)),
% 1.94/2.15 inference(monotonicity,[status(thm)],[3382])).
% 1.94/2.15 tff(3440,plain,
% 1.94/2.15 (r(s(s(s(z))), elem!1) <=> r(s(s(s(z))), z)),
% 1.94/2.15 inference(symmetry,[status(thm)],[3439])).
% 1.94/2.15 tff(3441,plain,
% 1.94/2.15 (r(s(s(s(z))), elem!1) <=> r(s(s(s(elem!1))), elem!1)),
% 1.94/2.15 inference(monotonicity,[status(thm)],[3435])).
% 1.94/2.15 tff(3442,plain,
% 1.94/2.15 (r(s(s(s(elem!1))), elem!1) <=> r(s(s(s(z))), elem!1)),
% 1.94/2.15 inference(symmetry,[status(thm)],[3441])).
% 1.94/2.15 tff(3443,plain,
% 1.94/2.15 (r(s(s(s(elem!1))), elem!1) <=> r(s(s(s(z))), z)),
% 1.94/2.15 inference(transitivity,[status(thm)],[3442, 3440])).
% 1.94/2.15 tff(3444,plain,
% 1.94/2.15 (r(s(s(s(elem!1))), elem!1)),
% 1.94/2.15 inference(unit_resolution,[status(thm)],[966, 3382, 154])).
% 1.94/2.15 tff(3445,plain,
% 1.94/2.15 (r(s(s(s(z))), z)),
% 1.94/2.15 inference(modus_ponens,[status(thm)],[3444, 3443])).
% 1.94/2.15 tff(3446,plain,
% 1.94/2.15 (~r(s(s(z)), s(s(s(z))))),
% 1.94/2.15 inference(unit_resolution,[status(thm)],[1741, 3445, 155, 866])).
% 1.94/2.15 tff(3447,plain,
% 1.94/2.15 (b(s(s(z)), s(s(s(z))))),
% 1.94/2.15 inference(unit_resolution,[status(thm)],[1730, 3446])).
% 1.94/2.15 tff(3448,plain,
% 1.94/2.15 (b(s(s(elem!1)), s(s(s(elem!1))))),
% 1.94/2.15 inference(modus_ponens,[status(thm)],[3447, 3438])).
% 1.94/2.15 tff(3449,plain,
% 1.94/2.15 (~r(s(s(s(elem!1))), s(s(z)))),
% 1.94/2.15 inference(unit_resolution,[status(thm)],[874, 866, 350, 120])).
% 1.94/2.15 tff(3450,plain,
% 1.94/2.15 (r(s(s(s(elem!1))), s(s(z))) <=> r(s(s(s(elem!1))), s(s(elem!1)))),
% 1.94/2.15 inference(monotonicity,[status(thm)],[34])).
% 1.94/2.15 tff(3451,plain,
% 1.94/2.15 (r(s(s(s(elem!1))), s(s(elem!1))) <=> r(s(s(s(elem!1))), s(s(z)))),
% 1.94/2.15 inference(symmetry,[status(thm)],[3450])).
% 1.94/2.15 tff(3452,plain,
% 1.94/2.15 (r(s(s(s(elem!1))), s(s(z)))),
% 1.94/2.15 inference(modus_ponens,[status(thm)],[905, 3451])).
% 1.94/2.15 tff(3453,plain,
% 1.94/2.15 ($false),
% 1.94/2.15 inference(unit_resolution,[status(thm)],[213, 3452])).
% 1.94/2.15 tff(3454,plain,((~r(s(s(s(elem!1))), s(s(elem!1)))) | r(s(s(s(elem!1))), s(s(z))) | (~(s(s(z)) = s(s(elem!1))))), inference(lemma,lemma(discharge,[]))).
% 1.94/2.15 tff(3455,plain,
% 1.94/2.15 (~r(s(s(s(elem!1))), s(s(elem!1)))),
% 1.94/2.15 inference(unit_resolution,[status(thm)],[3454, 3375, 3449])).
% 1.94/2.15 tff(3456,plain,
% 1.94/2.15 (b(s(s(s(elem!1))), s(s(elem!1)))),
% 1.94/2.15 inference(unit_resolution,[status(thm)],[889, 3455, 1863])).
% 1.94/2.15 tff(3457,assumption,(b(s(s(s(s(elem!1)))), s(s(elem!1)))), introduced(assumption)).
% 1.94/2.15 tff(3458,plain,
% 1.94/2.15 ($false),
% 1.94/2.15 inference(unit_resolution,[status(thm)],[2185, 166, 463, 839, 3457, 1311])).
% 1.94/2.15 tff(3459,plain,((~b(s(s(s(s(elem!1)))), s(s(elem!1)))) | (~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(s(s(elem!1))), s(s(s(s(elem!1))))))), inference(lemma,lemma(discharge,[]))).
% 1.94/2.15 tff(3460,plain,
% 1.94/2.15 (~b(s(s(s(elem!1))), s(s(s(s(elem!1)))))),
% 1.94/2.15 inference(unit_resolution,[status(thm)],[3459, 3434, 3456, 3448])).
% 1.94/2.15 tff(3461,plain,
% 1.94/2.15 (r(s(s(s(elem!1))), s(s(s(s(elem!1)))))),
% 1.94/2.15 inference(unit_resolution,[status(thm)],[696, 3460, 361])).
% 1.94/2.15 tff(3462,plain,
% 1.94/2.15 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(s(elem!1)))) | (~r(s(s(s(elem!1))), s(z))) | (~r(s(s(s(elem!1))), s(s(s(s(elem!1)))))) | (~r(s(s(s(s(elem!1)))), s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(z), s(s(elem!1)))) | (~r(s(s(s(elem!1))), s(z))) | (~r(s(s(s(elem!1))), s(s(s(s(elem!1)))))) | (~r(s(s(s(s(elem!1)))), s(z))))),
% 1.94/2.15 inference(rewrite,[status(thm)],[])).
% 1.94/2.15 tff(3463,plain,
% 1.94/2.15 (((~r(s(z), s(s(elem!1)))) | (~r(s(s(s(s(elem!1)))), s(z))) | (~r(s(s(s(elem!1))), s(z))) | (~r(s(s(s(elem!1))), s(s(s(s(elem!1))))))) <=> ((~r(s(z), s(s(elem!1)))) | (~r(s(s(s(elem!1))), s(z))) | (~r(s(s(s(elem!1))), s(s(s(s(elem!1)))))) | (~r(s(s(s(s(elem!1)))), s(z))))),
% 1.94/2.15 inference(rewrite,[status(thm)],[])).
% 1.94/2.15 tff(3464,plain,
% 1.94/2.15 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(s(elem!1)))) | (~r(s(s(s(s(elem!1)))), s(z))) | (~r(s(s(s(elem!1))), s(z))) | (~r(s(s(s(elem!1))), s(s(s(s(elem!1)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(s(elem!1)))) | (~r(s(s(s(elem!1))), s(z))) | (~r(s(s(s(elem!1))), s(s(s(s(elem!1)))))) | (~r(s(s(s(s(elem!1)))), s(z)))))),
% 1.94/2.15 inference(monotonicity,[status(thm)],[3463])).
% 1.94/2.15 tff(3465,plain,
% 1.94/2.15 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(s(elem!1)))) | (~r(s(s(s(s(elem!1)))), s(z))) | (~r(s(s(s(elem!1))), s(z))) | (~r(s(s(s(elem!1))), s(s(s(s(elem!1)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(z), s(s(elem!1)))) | (~r(s(s(s(elem!1))), s(z))) | (~r(s(s(s(elem!1))), s(s(s(s(elem!1)))))) | (~r(s(s(s(s(elem!1)))), s(z))))),
% 1.94/2.15 inference(transitivity,[status(thm)],[3464, 3462])).
% 1.94/2.15 tff(3466,plain,
% 1.94/2.15 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(s(elem!1)))) | (~r(s(s(s(s(elem!1)))), s(z))) | (~r(s(s(s(elem!1))), s(z))) | (~r(s(s(s(elem!1))), s(s(s(s(elem!1)))))))),
% 1.94/2.15 inference(quant_inst,[status(thm)],[])).
% 1.94/2.16 tff(3467,plain,
% 1.94/2.16 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(z), s(s(elem!1)))) | (~r(s(s(s(elem!1))), s(z))) | (~r(s(s(s(elem!1))), s(s(s(s(elem!1)))))) | (~r(s(s(s(s(elem!1)))), s(z)))),
% 1.94/2.16 inference(modus_ponens,[status(thm)],[3466, 3465])).
% 1.94/2.16 tff(3468,plain,
% 1.94/2.16 ($false),
% 1.94/2.16 inference(unit_resolution,[status(thm)],[3467, 197, 311, 350, 700, 698])).
% 1.94/2.16 tff(3469,plain,((~r(s(s(s(s(elem!1)))), s(z))) | (~r(s(z), s(s(elem!1)))) | (~r(s(s(s(elem!1))), s(z))) | (~r(s(s(s(elem!1))), s(s(s(s(elem!1))))))), inference(lemma,lemma(discharge,[]))).
% 1.94/2.16 tff(3470,plain,
% 1.94/2.16 (~r(s(s(s(s(elem!1)))), s(z))),
% 1.94/2.16 inference(unit_resolution,[status(thm)],[3469, 3461, 350, 311])).
% 1.94/2.16 tff(3471,plain,
% 1.94/2.16 (b(s(s(s(s(elem!1)))), s(z))),
% 1.94/2.16 inference(unit_resolution,[status(thm)],[661, 3470])).
% 1.94/2.16 tff(3472,plain,
% 1.94/2.16 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(z))) | (~b(s(s(s(s(elem!1)))), s(s(elem!1)))) | (~b(s(s(elem!1)), s(z))) | (~b(s(z), elem!1)) | (~b(s(s(s(s(elem!1)))), s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(z))) | (~b(s(s(s(s(elem!1)))), s(s(elem!1)))) | (~b(s(s(elem!1)), s(z))) | (~b(s(z), elem!1)) | (~b(s(s(s(s(elem!1)))), s(z))))),
% 1.94/2.16 inference(rewrite,[status(thm)],[])).
% 1.94/2.16 tff(3473,plain,
% 1.94/2.16 (((~b(elem!1, s(z))) | (~b(s(s(s(s(elem!1)))), s(z))) | (~b(s(z), elem!1)) | (~b(s(s(elem!1)), s(z))) | (~b(s(s(s(s(elem!1)))), s(z))) | (~b(s(s(s(s(elem!1)))), s(s(elem!1))))) <=> ((~b(elem!1, s(z))) | (~b(s(s(s(s(elem!1)))), s(s(elem!1)))) | (~b(s(s(elem!1)), s(z))) | (~b(s(z), elem!1)) | (~b(s(s(s(s(elem!1)))), s(z))))),
% 1.94/2.16 inference(rewrite,[status(thm)],[])).
% 1.94/2.16 tff(3474,plain,
% 1.94/2.16 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(z))) | (~b(s(s(s(s(elem!1)))), s(z))) | (~b(s(z), elem!1)) | (~b(s(s(elem!1)), s(z))) | (~b(s(s(s(s(elem!1)))), s(z))) | (~b(s(s(s(s(elem!1)))), s(s(elem!1)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(z))) | (~b(s(s(s(s(elem!1)))), s(s(elem!1)))) | (~b(s(s(elem!1)), s(z))) | (~b(s(z), elem!1)) | (~b(s(s(s(s(elem!1)))), s(z)))))),
% 1.94/2.16 inference(monotonicity,[status(thm)],[3473])).
% 1.94/2.16 tff(3475,plain,
% 1.94/2.16 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(z))) | (~b(s(s(s(s(elem!1)))), s(z))) | (~b(s(z), elem!1)) | (~b(s(s(elem!1)), s(z))) | (~b(s(s(s(s(elem!1)))), s(z))) | (~b(s(s(s(s(elem!1)))), s(s(elem!1)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(z))) | (~b(s(s(s(s(elem!1)))), s(s(elem!1)))) | (~b(s(s(elem!1)), s(z))) | (~b(s(z), elem!1)) | (~b(s(s(s(s(elem!1)))), s(z))))),
% 1.94/2.16 inference(transitivity,[status(thm)],[3474, 3472])).
% 1.94/2.16 tff(3476,plain,
% 1.94/2.16 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(z))) | (~b(s(s(s(s(elem!1)))), s(z))) | (~b(s(z), elem!1)) | (~b(s(s(elem!1)), s(z))) | (~b(s(s(s(s(elem!1)))), s(z))) | (~b(s(s(s(s(elem!1)))), s(s(elem!1)))))),
% 1.94/2.16 inference(quant_inst,[status(thm)],[])).
% 1.94/2.16 tff(3477,plain,
% 1.94/2.16 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(z))) | (~b(s(s(s(s(elem!1)))), s(s(elem!1)))) | (~b(s(s(elem!1)), s(z))) | (~b(s(z), elem!1)) | (~b(s(s(s(s(elem!1)))), s(z)))),
% 1.94/2.16 inference(modus_ponens,[status(thm)],[3476, 3475])).
% 1.94/2.16 tff(3478,plain,
% 1.94/2.16 ($false),
% 1.94/2.16 inference(unit_resolution,[status(thm)],[3477, 166, 3407, 310, 3405, 3471, 3434])).
% 1.94/2.16 tff(3479,plain,((~r(s(s(z)), z)) | (~b(s(s(elem!1)), s(z))) | (~r(s(s(s(elem!1))), s(z))) | (~r(s(z), s(s(elem!1)))) | (s(s(s(elem!1))) = s(s(s(s(elem!1))))) | (~r(z, s(s(z)))) | (~b(z, s(z))) | (~r(s(s(s(elem!1))), z)) | (s(s(s(elem!1))) = s(s(elem!1))) | (~b(s(s(z)), s(z))) | (~r(s(z), s(s(z))))), inference(lemma,lemma(discharge,[]))).
% 1.94/2.16 tff(3480,plain,
% 1.94/2.16 (~r(s(s(z)), z)),
% 1.94/2.16 inference(unit_resolution,[status(thm)],[3479, 350, 310, 311, 361, 155, 118, 154, 1863, 156, 120])).
% 1.94/2.16 tff(3481,plain,
% 1.94/2.16 (b(s(s(z)), z)),
% 1.94/2.16 inference(unit_resolution,[status(thm)],[186, 3480])).
% 1.94/2.16 tff(3482,plain,
% 1.94/2.16 (~b(s(z), z)),
% 1.94/2.16 inference(unit_resolution,[status(thm)],[181, 3481, 156, 118])).
% 1.94/2.16 tff(3483,plain,
% 1.94/2.16 (r(s(z), z)),
% 1.94/2.16 inference(unit_resolution,[status(thm)],[230, 3482])).
% 1.94/2.16 tff(3484,plain,
% 1.94/2.16 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), z)) | (~r(s(s(s(elem!1))), s(z))) | (~r(s(z), z)) | (~r(z, s(s(z)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(elem!1))), z)) | (~r(s(s(s(elem!1))), s(z))) | (~r(s(z), z)) | (~r(z, s(s(z)))))),
% 1.94/2.16 inference(rewrite,[status(thm)],[])).
% 1.94/2.16 tff(3485,plain,
% 1.94/2.16 (((~r(z, s(s(z)))) | (~r(s(z), z)) | (~r(s(s(s(elem!1))), z)) | (~r(s(s(s(elem!1))), s(z)))) <=> ((~r(s(s(s(elem!1))), z)) | (~r(s(s(s(elem!1))), s(z))) | (~r(s(z), z)) | (~r(z, s(s(z)))))),
% 1.94/2.16 inference(rewrite,[status(thm)],[])).
% 1.94/2.16 tff(3486,plain,
% 1.94/2.16 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(z)))) | (~r(s(z), z)) | (~r(s(s(s(elem!1))), z)) | (~r(s(s(s(elem!1))), s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), z)) | (~r(s(s(s(elem!1))), s(z))) | (~r(s(z), z)) | (~r(z, s(s(z))))))),
% 1.94/2.16 inference(monotonicity,[status(thm)],[3485])).
% 1.94/2.16 tff(3487,plain,
% 1.94/2.16 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(z)))) | (~r(s(z), z)) | (~r(s(s(s(elem!1))), z)) | (~r(s(s(s(elem!1))), s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(elem!1))), z)) | (~r(s(s(s(elem!1))), s(z))) | (~r(s(z), z)) | (~r(z, s(s(z)))))),
% 1.94/2.16 inference(transitivity,[status(thm)],[3486, 3484])).
% 1.94/2.16 tff(3488,plain,
% 1.94/2.16 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(z)))) | (~r(s(z), z)) | (~r(s(s(s(elem!1))), z)) | (~r(s(s(s(elem!1))), s(z))))),
% 1.94/2.16 inference(quant_inst,[status(thm)],[])).
% 1.94/2.16 tff(3489,plain,
% 1.94/2.16 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(elem!1))), z)) | (~r(s(s(s(elem!1))), s(z))) | (~r(s(z), z)) | (~r(z, s(s(z))))),
% 1.94/2.16 inference(modus_ponens,[status(thm)],[3488, 3487])).
% 1.94/2.16 tff(3490,plain,
% 1.94/2.16 ($false),
% 1.94/2.16 inference(unit_resolution,[status(thm)],[3489, 197, 154, 155, 350, 3483])).
% 1.94/2.16 tff(3491,plain,((~r(s(s(s(elem!1))), s(z))) | (~r(s(s(s(elem!1))), z)) | (~r(z, s(s(z)))) | (~b(s(s(z)), s(z))) | (~b(z, s(z))) | (~b(s(s(elem!1)), s(z))) | (~r(s(z), s(s(elem!1)))) | (s(s(s(elem!1))) = s(s(s(s(elem!1))))) | (s(s(s(elem!1))) = s(s(elem!1))) | (~r(s(z), s(s(z))))), inference(lemma,lemma(discharge,[]))).
% 1.94/2.16 tff(3492,plain,
% 1.94/2.16 ($false),
% 1.94/2.16 inference(unit_resolution,[status(thm)],[3491, 3348, 3345, 155, 156, 118, 310, 311, 154, 3340, 120])).
% 1.94/2.16 tff(3493,plain,((~(s(s(z)) = s(s(elem!1)))) | (~r(z, s(s(z)))) | (~b(s(s(z)), s(z))) | (~b(z, s(z))) | (~b(s(s(elem!1)), s(z))) | (~r(s(z), s(s(elem!1)))) | (~r(s(s(s(elem!1))), z)) | (~r(s(z), s(s(z))))), inference(lemma,lemma(discharge,[]))).
% 1.94/2.16 tff(3494,plain,
% 1.94/2.16 (~(s(s(z)) = s(s(elem!1)))),
% 1.94/2.16 inference(unit_resolution,[status(thm)],[3493, 154, 156, 118, 310, 311, 155, 120])).
% 1.94/2.16 tff(3495,plain,
% 1.94/2.16 (~b(z, s(s(elem!1)))),
% 1.94/2.16 inference(unit_resolution,[status(thm)],[3358, 53, 310, 118])).
% 1.94/2.16 tff(3496,plain,
% 1.94/2.16 (r(z, s(s(elem!1)))),
% 1.94/2.16 inference(unit_resolution,[status(thm)],[1795, 3495])).
% 1.94/2.16 tff(3497,plain,
% 1.94/2.16 (~b(s(s(elem!1)), s(s(z)))),
% 1.94/2.16 inference(unit_resolution,[status(thm)],[3366, 166, 53, 118, 310, 156])).
% 1.94/2.16 tff(3498,plain,
% 1.94/2.16 (~b(s(s(z)), s(s(elem!1)))),
% 1.94/2.16 inference(unit_resolution,[status(thm)],[3373, 166, 53, 118, 310, 156])).
% 1.94/2.16 tff(3499,plain,
% 1.94/2.16 ($false),
% 1.94/2.16 inference(unit_resolution,[status(thm)],[2079, 3498, 3497, 155, 52, 3496])).
% 1.94/2.16 tff(3500,plain,((~b(s(z), z)) | (~r(z, s(s(z)))) | (s(s(z)) = s(s(elem!1))) | (~b(z, s(z))) | (~b(s(s(elem!1)), s(z))) | (~b(s(s(z)), s(z)))), inference(lemma,lemma(discharge,[]))).
% 1.94/2.16 tff(3501,plain,
% 1.94/2.16 (~b(s(z), z)),
% 1.94/2.16 inference(unit_resolution,[status(thm)],[3500, 3494, 155, 118, 310, 156])).
% 1.94/2.16 tff(3502,plain,
% 1.94/2.16 (r(s(z), z)),
% 1.94/2.16 inference(unit_resolution,[status(thm)],[230, 3501])).
% 1.94/2.16 tff(3503,plain,
% 1.94/2.16 ($false),
% 1.94/2.16 inference(unit_resolution,[status(thm)],[3489, 197, 154, 155, 3340, 3502])).
% 1.94/2.16 tff(3504,plain,((~r(s(s(s(elem!1))), z)) | (~r(z, s(s(z)))) | (~b(z, s(z))) | (~b(s(s(elem!1)), s(z))) | (~b(s(s(z)), s(z))) | (~r(s(z), s(s(elem!1)))) | (~r(s(z), s(s(z))))), inference(lemma,lemma(discharge,[]))).
% 1.94/2.16 tff(3505,plain,
% 1.94/2.16 (~r(s(s(s(elem!1))), z)),
% 1.94/2.16 inference(unit_resolution,[status(thm)],[3504, 118, 155, 310, 156, 311, 120])).
% 1.94/2.16 tff(3506,plain,
% 1.94/2.16 (b(s(s(s(elem!1))), z)),
% 1.94/2.16 inference(unit_resolution,[status(thm)],[94, 3505])).
% 1.94/2.16 tff(3507,plain,
% 1.94/2.16 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), z)) | (~r(s(z), s(s(z)))) | (~r(s(s(z)), s(s(s(z))))) | (~r(z, s(s(z)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(z), z)) | (~r(s(z), s(s(z)))) | (~r(s(s(z)), s(s(s(z))))) | (~r(z, s(s(z)))))),
% 1.94/2.16 inference(rewrite,[status(thm)],[])).
% 1.94/2.16 tff(3508,plain,
% 1.94/2.16 (((~r(s(s(z)), s(s(s(z))))) | (~r(z, s(s(z)))) | (~r(s(z), s(s(z)))) | (~r(s(z), z))) <=> ((~r(s(z), z)) | (~r(s(z), s(s(z)))) | (~r(s(s(z)), s(s(s(z))))) | (~r(z, s(s(z)))))),
% 1.94/2.16 inference(rewrite,[status(thm)],[])).
% 1.94/2.16 tff(3509,plain,
% 1.94/2.16 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(z)), s(s(s(z))))) | (~r(z, s(s(z)))) | (~r(s(z), s(s(z)))) | (~r(s(z), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), z)) | (~r(s(z), s(s(z)))) | (~r(s(s(z)), s(s(s(z))))) | (~r(z, s(s(z))))))),
% 1.94/2.16 inference(monotonicity,[status(thm)],[3508])).
% 1.94/2.16 tff(3510,plain,
% 1.94/2.16 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(z)), s(s(s(z))))) | (~r(z, s(s(z)))) | (~r(s(z), s(s(z)))) | (~r(s(z), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(z), z)) | (~r(s(z), s(s(z)))) | (~r(s(s(z)), s(s(s(z))))) | (~r(z, s(s(z)))))),
% 1.94/2.16 inference(transitivity,[status(thm)],[3509, 3507])).
% 1.94/2.16 tff(3511,plain,
% 1.94/2.16 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(z)), s(s(s(z))))) | (~r(z, s(s(z)))) | (~r(s(z), s(s(z)))) | (~r(s(z), z)))),
% 1.94/2.16 inference(quant_inst,[status(thm)],[])).
% 1.94/2.16 tff(3512,plain,
% 1.94/2.16 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(z), z)) | (~r(s(z), s(s(z)))) | (~r(s(s(z)), s(s(s(z))))) | (~r(z, s(s(z))))),
% 1.94/2.16 inference(modus_ponens,[status(thm)],[3511, 3510])).
% 1.94/2.16 tff(3513,plain,
% 1.94/2.16 ($false),
% 1.94/2.16 inference(unit_resolution,[status(thm)],[3512, 197, 120, 155, 97, 1732])).
% 1.94/2.16 tff(3514,plain,((~r(s(s(z)), s(s(s(z))))) | (~r(s(z), s(s(z)))) | (~r(z, s(s(z)))) | (~r(s(z), z))), inference(lemma,lemma(discharge,[]))).
% 1.94/2.16 tff(3515,plain,
% 1.94/2.16 (~r(s(s(z)), s(s(s(z))))),
% 1.94/2.16 inference(unit_resolution,[status(thm)],[3514, 97, 155, 120])).
% 1.94/2.16 tff(3516,plain,
% 1.94/2.16 (b(s(s(z)), s(s(s(z))))),
% 1.94/2.16 inference(unit_resolution,[status(thm)],[1730, 3515])).
% 1.94/2.16 tff(3517,plain,
% 1.94/2.16 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), z)) | (~r(z, s(s(z)))) | (~r(s(s(s(z))), z)) | (~r(s(s(s(z))), s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(z), z)) | (~r(z, s(s(z)))) | (~r(s(s(s(z))), z)) | (~r(s(s(s(z))), s(z))))),
% 1.94/2.16 inference(rewrite,[status(thm)],[])).
% 1.94/2.16 tff(3518,plain,
% 1.94/2.16 (((~r(z, s(s(z)))) | (~r(s(z), z)) | (~r(s(s(s(z))), z)) | (~r(s(s(s(z))), s(z)))) <=> ((~r(s(z), z)) | (~r(z, s(s(z)))) | (~r(s(s(s(z))), z)) | (~r(s(s(s(z))), s(z))))),
% 1.94/2.16 inference(rewrite,[status(thm)],[])).
% 1.94/2.16 tff(3519,plain,
% 1.94/2.16 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(z)))) | (~r(s(z), z)) | (~r(s(s(s(z))), z)) | (~r(s(s(s(z))), s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), z)) | (~r(z, s(s(z)))) | (~r(s(s(s(z))), z)) | (~r(s(s(s(z))), s(z)))))),
% 1.94/2.16 inference(monotonicity,[status(thm)],[3518])).
% 1.94/2.16 tff(3520,plain,
% 1.94/2.16 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(z)))) | (~r(s(z), z)) | (~r(s(s(s(z))), z)) | (~r(s(s(s(z))), s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(z), z)) | (~r(z, s(s(z)))) | (~r(s(s(s(z))), z)) | (~r(s(s(s(z))), s(z))))),
% 1.94/2.16 inference(transitivity,[status(thm)],[3519, 3517])).
% 1.94/2.16 tff(3521,plain,
% 1.94/2.16 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(z)))) | (~r(s(z), z)) | (~r(s(s(s(z))), z)) | (~r(s(s(s(z))), s(z))))),
% 1.94/2.16 inference(quant_inst,[status(thm)],[])).
% 1.94/2.16 tff(3522,plain,
% 1.94/2.16 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(z), z)) | (~r(z, s(s(z)))) | (~r(s(s(s(z))), z)) | (~r(s(s(s(z))), s(z)))),
% 1.94/2.16 inference(modus_ponens,[status(thm)],[3521, 3520])).
% 1.94/2.16 tff(3523,plain,
% 1.94/2.16 (~r(s(s(s(z))), s(z))),
% 1.94/2.16 inference(unit_resolution,[status(thm)],[3522, 197, 155, 97, 1733])).
% 1.94/2.16 tff(3524,plain,
% 1.94/2.16 (b(s(s(s(z))), s(z))),
% 1.94/2.16 inference(unit_resolution,[status(thm)],[1763, 3523])).
% 1.94/2.16 tff(3525,plain,
% 1.94/2.16 (~r(s(z), s(s(s(z))))),
% 1.94/2.16 inference(unit_resolution,[status(thm)],[2870, 197, 155, 97, 1733])).
% 1.94/2.16 tff(3526,plain,
% 1.94/2.16 (b(s(z), s(s(s(z))))),
% 1.94/2.16 inference(unit_resolution,[status(thm)],[1674, 3525])).
% 1.94/2.16 tff(3527,plain,
% 1.94/2.16 ($false),
% 1.94/2.16 inference(unit_resolution,[status(thm)],[3248, 3526, 3524, 156, 986])).
% 1.94/2.16 tff(3528,plain,((~r(s(s(s(z))), z)) | (~b(s(s(z)), s(z))) | (~b(s(s(z)), s(s(s(z))))) | (~r(z, s(s(z)))) | (~r(s(z), z))), inference(lemma,lemma(discharge,[]))).
% 1.94/2.16 tff(3529,plain,
% 1.94/2.16 (~r(s(s(s(z))), z)),
% 1.94/2.16 inference(unit_resolution,[status(thm)],[3528, 3516, 156, 155, 97])).
% 1.94/2.16 tff(3530,plain,
% 1.94/2.16 (b(s(s(s(z))), z)),
% 1.94/2.16 inference(unit_resolution,[status(thm)],[1713, 3529])).
% 1.94/2.16 tff(3531,plain,
% 1.94/2.16 (~r(s(s(elem!1)), z)),
% 1.94/2.16 inference(unit_resolution,[status(thm)],[2274, 97, 155, 311])).
% 1.94/2.16 tff(3532,plain,
% 1.94/2.16 (b(s(s(elem!1)), z)),
% 1.94/2.16 inference(unit_resolution,[status(thm)],[608, 3531])).
% 1.94/2.16 tff(3533,plain,
% 1.94/2.16 (~r(s(s(z)), s(s(elem!1)))),
% 1.94/2.16 inference(unit_resolution,[status(thm)],[347, 97, 155, 120])).
% 1.94/2.16 tff(3534,plain,
% 1.94/2.16 (b(s(s(z)), s(s(elem!1)))),
% 1.94/2.16 inference(unit_resolution,[status(thm)],[390, 52, 3533])).
% 1.94/2.16 tff(3535,plain,
% 1.94/2.16 (~b(s(z), s(s(s(elem!1))))),
% 1.94/2.16 inference(unit_resolution,[status(thm)],[2929, 446, 310, 96, 156])).
% 1.94/2.16 tff(3536,plain,
% 1.94/2.16 (r(s(z), s(s(s(elem!1))))),
% 1.94/2.16 inference(unit_resolution,[status(thm)],[116, 3535])).
% 1.94/2.16 tff(3537,plain,
% 1.94/2.16 (~(s(s(s(elem!1))) = s(s(s(z))))),
% 1.94/2.16 inference(unit_resolution,[status(thm)],[139, 11])).
% 1.94/2.16 tff(3538,plain,
% 1.94/2.16 (~r(s(s(elem!1)), s(s(s(elem!1))))),
% 1.94/2.16 inference(unit_resolution,[status(thm)],[2939, 464, 119, 311])).
% 1.94/2.16 tff(3539,plain,
% 1.94/2.16 (b(s(s(elem!1)), s(s(s(elem!1))))),
% 1.94/2.16 inference(unit_resolution,[status(thm)],[461, 3538, 45])).
% 1.94/2.16 tff(3540,plain,
% 1.94/2.16 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), z)) | (~b(z, s(z))) | (~b(s(s(z)), s(s(elem!1)))) | (~b(s(s(z)), s(z))) | (~b(s(s(z)), s(s(s(elem!1))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), z)) | (~b(z, s(z))) | (~b(s(s(z)), s(s(elem!1)))) | (~b(s(s(z)), s(z))) | (~b(s(s(z)), s(s(s(elem!1))))))),
% 1.94/2.16 inference(rewrite,[status(thm)],[])).
% 1.94/2.16 tff(3541,plain,
% 1.94/2.16 (((~b(z, s(z))) | (~b(s(s(z)), s(z))) | (~b(s(s(s(elem!1))), z)) | (~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(s(s(z)), s(s(s(elem!1))))) | (~b(s(s(z)), s(s(elem!1))))) <=> ((~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), z)) | (~b(z, s(z))) | (~b(s(s(z)), s(s(elem!1)))) | (~b(s(s(z)), s(z))) | (~b(s(s(z)), s(s(s(elem!1))))))),
% 1.94/2.16 inference(rewrite,[status(thm)],[])).
% 1.94/2.16 tff(3542,plain,
% 1.94/2.16 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(z))) | (~b(s(s(z)), s(z))) | (~b(s(s(s(elem!1))), z)) | (~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(s(s(z)), s(s(s(elem!1))))) | (~b(s(s(z)), s(s(elem!1)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), z)) | (~b(z, s(z))) | (~b(s(s(z)), s(s(elem!1)))) | (~b(s(s(z)), s(z))) | (~b(s(s(z)), s(s(s(elem!1)))))))),
% 1.94/2.16 inference(monotonicity,[status(thm)],[3541])).
% 1.94/2.16 tff(3543,plain,
% 1.94/2.16 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(z))) | (~b(s(s(z)), s(z))) | (~b(s(s(s(elem!1))), z)) | (~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(s(s(z)), s(s(s(elem!1))))) | (~b(s(s(z)), s(s(elem!1)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), z)) | (~b(z, s(z))) | (~b(s(s(z)), s(s(elem!1)))) | (~b(s(s(z)), s(z))) | (~b(s(s(z)), s(s(s(elem!1))))))),
% 1.94/2.16 inference(transitivity,[status(thm)],[3542, 3540])).
% 1.94/2.16 tff(3544,plain,
% 1.94/2.16 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(z))) | (~b(s(s(z)), s(z))) | (~b(s(s(s(elem!1))), z)) | (~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(s(s(z)), s(s(s(elem!1))))) | (~b(s(s(z)), s(s(elem!1)))))),
% 1.94/2.16 inference(quant_inst,[status(thm)],[])).
% 1.94/2.16 tff(3545,plain,
% 1.94/2.16 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), z)) | (~b(z, s(z))) | (~b(s(s(z)), s(s(elem!1)))) | (~b(s(s(z)), s(z))) | (~b(s(s(z)), s(s(s(elem!1)))))),
% 1.94/2.16 inference(modus_ponens,[status(thm)],[3544, 3543])).
% 1.94/2.16 tff(3546,plain,
% 1.94/2.16 (~b(s(s(z)), s(s(s(elem!1))))),
% 1.94/2.16 inference(unit_resolution,[status(thm)],[3545, 166, 3539, 118, 121, 446, 156])).
% 1.94/2.16 tff(3547,plain,
% 1.94/2.16 (r(s(s(z)), s(s(s(elem!1))))),
% 1.94/2.16 inference(unit_resolution,[status(thm)],[279, 3546])).
% 1.94/2.16 tff(3548,plain,
% 1.94/2.16 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(s(s(elem!1))))) | (~r(s(z), s(s(z)))) | (~r(s(s(z)), s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), s(s(z)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(z), s(s(s(elem!1))))) | (~r(s(z), s(s(z)))) | (~r(s(s(z)), s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), s(s(z)))))),
% 1.94/2.16 inference(rewrite,[status(thm)],[])).
% 1.94/2.16 tff(3549,plain,
% 1.94/2.16 (((~r(s(s(s(elem!1))), s(s(z)))) | (~r(s(s(z)), s(s(s(elem!1))))) | (~r(s(z), s(s(s(elem!1))))) | (~r(s(z), s(s(z))))) <=> ((~r(s(z), s(s(s(elem!1))))) | (~r(s(z), s(s(z)))) | (~r(s(s(z)), s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), s(s(z)))))),
% 1.94/2.16 inference(rewrite,[status(thm)],[])).
% 1.94/2.16 tff(3550,plain,
% 1.94/2.16 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), s(s(z)))) | (~r(s(s(z)), s(s(s(elem!1))))) | (~r(s(z), s(s(s(elem!1))))) | (~r(s(z), s(s(z)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(s(s(elem!1))))) | (~r(s(z), s(s(z)))) | (~r(s(s(z)), s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), s(s(z))))))),
% 1.94/2.17 inference(monotonicity,[status(thm)],[3549])).
% 1.94/2.17 tff(3551,plain,
% 1.94/2.17 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), s(s(z)))) | (~r(s(s(z)), s(s(s(elem!1))))) | (~r(s(z), s(s(s(elem!1))))) | (~r(s(z), s(s(z)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(z), s(s(s(elem!1))))) | (~r(s(z), s(s(z)))) | (~r(s(s(z)), s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), s(s(z)))))),
% 1.94/2.17 inference(transitivity,[status(thm)],[3550, 3548])).
% 1.94/2.17 tff(3552,plain,
% 1.94/2.17 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), s(s(z)))) | (~r(s(s(z)), s(s(s(elem!1))))) | (~r(s(z), s(s(s(elem!1))))) | (~r(s(z), s(s(z)))))),
% 1.94/2.17 inference(quant_inst,[status(thm)],[])).
% 1.94/2.17 tff(3553,plain,
% 1.94/2.17 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(z), s(s(s(elem!1))))) | (~r(s(z), s(s(z)))) | (~r(s(s(z)), s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), s(s(z))))),
% 1.94/2.17 inference(modus_ponens,[status(thm)],[3552, 3551])).
% 1.94/2.17 tff(3554,plain,
% 1.94/2.17 ($false),
% 1.94/2.17 inference(unit_resolution,[status(thm)],[3553, 197, 120, 119, 3547, 464])).
% 1.94/2.17 tff(3555,plain,((~r(s(s(s(elem!1))), s(s(z)))) | (~r(s(z), s(s(z)))) | (~r(s(z), s(s(s(elem!1))))) | (~b(z, s(z))) | (~b(s(s(s(elem!1))), z)) | (~b(s(s(z)), s(s(elem!1)))) | (~b(s(s(z)), s(z))) | (s(s(elem!1)) = s(s(s(elem!1)))) | (~r(s(z), s(s(elem!1))))), inference(lemma,lemma(discharge,[]))).
% 1.94/2.17 tff(3556,plain,
% 1.94/2.17 (~r(s(s(s(elem!1))), s(s(z)))),
% 1.94/2.17 inference(unit_resolution,[status(thm)],[3555, 45, 3536, 118, 3506, 446, 156, 120, 311])).
% 1.94/2.17 tff(3557,plain,
% 1.94/2.17 (b(s(s(s(elem!1))), s(s(z)))),
% 1.94/2.17 inference(unit_resolution,[status(thm)],[218, 3556])).
% 1.94/2.17 tff(3558,plain,
% 1.94/2.17 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), s(s(z)))) | (~b(s(s(s(elem!1))), s(z))) | (~b(z, s(z))) | (~b(s(s(s(z))), z)) | (~b(s(s(s(elem!1))), s(s(s(z))))) | (~b(s(s(z)), s(s(s(z))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(elem!1))), s(s(z)))) | (~b(s(s(s(elem!1))), s(z))) | (~b(z, s(z))) | (~b(s(s(s(z))), z)) | (~b(s(s(s(elem!1))), s(s(s(z))))) | (~b(s(s(z)), s(s(s(z))))))),
% 1.94/2.17 inference(rewrite,[status(thm)],[])).
% 1.94/2.17 tff(3559,plain,
% 1.94/2.17 (((~b(z, s(z))) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(s(s(z))), z)) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(s(elem!1))), s(s(s(z))))) | (~b(s(s(s(elem!1))), s(s(z))))) <=> ((~b(s(s(s(elem!1))), s(s(z)))) | (~b(s(s(s(elem!1))), s(z))) | (~b(z, s(z))) | (~b(s(s(s(z))), z)) | (~b(s(s(s(elem!1))), s(s(s(z))))) | (~b(s(s(z)), s(s(s(z))))))),
% 1.94/2.17 inference(rewrite,[status(thm)],[])).
% 1.94/2.17 tff(3560,plain,
% 1.94/2.17 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(z))) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(s(s(z))), z)) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(s(elem!1))), s(s(s(z))))) | (~b(s(s(s(elem!1))), s(s(z)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), s(s(z)))) | (~b(s(s(s(elem!1))), s(z))) | (~b(z, s(z))) | (~b(s(s(s(z))), z)) | (~b(s(s(s(elem!1))), s(s(s(z))))) | (~b(s(s(z)), s(s(s(z)))))))),
% 1.94/2.17 inference(monotonicity,[status(thm)],[3559])).
% 1.94/2.17 tff(3561,plain,
% 1.94/2.17 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(z))) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(s(s(z))), z)) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(s(elem!1))), s(s(s(z))))) | (~b(s(s(s(elem!1))), s(s(z)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(elem!1))), s(s(z)))) | (~b(s(s(s(elem!1))), s(z))) | (~b(z, s(z))) | (~b(s(s(s(z))), z)) | (~b(s(s(s(elem!1))), s(s(s(z))))) | (~b(s(s(z)), s(s(s(z))))))),
% 1.94/2.17 inference(transitivity,[status(thm)],[3560, 3558])).
% 1.94/2.17 tff(3562,plain,
% 1.94/2.17 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(z))) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(s(s(z))), z)) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(s(elem!1))), s(s(s(z))))) | (~b(s(s(s(elem!1))), s(s(z)))))),
% 1.94/2.17 inference(quant_inst,[status(thm)],[])).
% 1.94/2.17 tff(3563,plain,
% 1.94/2.17 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(elem!1))), s(s(z)))) | (~b(s(s(s(elem!1))), s(z))) | (~b(z, s(z))) | (~b(s(s(s(z))), z)) | (~b(s(s(s(elem!1))), s(s(s(z))))) | (~b(s(s(z)), s(s(s(z)))))),
% 1.94/2.17 inference(modus_ponens,[status(thm)],[3562, 3561])).
% 1.94/2.17 tff(3564,plain,
% 1.94/2.17 ($false),
% 1.94/2.17 inference(unit_resolution,[status(thm)],[3563, 166, 96, 118, 986, 1699, 2060, 3251])).
% 1.94/2.17 tff(3565,plain,((~b(s(s(s(z))), z)) | (~b(s(s(s(elem!1))), s(z))) | (~b(z, s(z))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(s(elem!1))), s(s(z)))) | (~b(s(s(s(elem!1))), s(s(s(z)))))), inference(lemma,lemma(discharge,[]))).
% 1.94/2.17 tff(3566,plain,
% 1.94/2.17 (~b(s(s(s(elem!1))), s(s(s(z))))),
% 1.94/2.17 inference(unit_resolution,[status(thm)],[3565, 3557, 118, 986, 1699, 96])).
% 1.94/2.17 tff(3567,assumption,(~(s(s(s(elem!1))) = s(s(s(z))))), introduced(assumption)).
% 1.94/2.17 tff(3568,assumption,(~r(s(s(s(elem!1))), s(s(s(z))))), introduced(assumption)).
% 1.94/2.17 tff(3569,assumption,(~b(s(s(s(elem!1))), s(s(s(z))))), introduced(assumption)).
% 1.94/2.17 tff(3570,plain,
% 1.94/2.17 (((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((s(s(s(elem!1))) = s(s(s(z)))) | b(s(s(s(elem!1))), s(s(s(z)))) | r(s(s(s(elem!1))), s(s(s(z)))))) <=> ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (s(s(s(elem!1))) = s(s(s(z)))) | b(s(s(s(elem!1))), s(s(s(z)))) | r(s(s(s(elem!1))), s(s(s(z)))))),
% 1.94/2.17 inference(rewrite,[status(thm)],[])).
% 1.94/2.17 tff(3571,plain,
% 1.94/2.17 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((s(s(s(elem!1))) = s(s(s(z)))) | b(s(s(s(elem!1))), s(s(s(z)))) | r(s(s(s(elem!1))), s(s(s(z)))))),
% 1.94/2.17 inference(quant_inst,[status(thm)],[])).
% 1.94/2.17 tff(3572,plain,
% 1.94/2.17 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (s(s(s(elem!1))) = s(s(s(z)))) | b(s(s(s(elem!1))), s(s(s(z)))) | r(s(s(s(elem!1))), s(s(s(z))))),
% 1.94/2.17 inference(modus_ponens,[status(thm)],[3571, 3570])).
% 1.94/2.17 tff(3573,plain,
% 1.94/2.17 ($false),
% 1.94/2.17 inference(unit_resolution,[status(thm)],[3572, 79, 3569, 3568, 3567])).
% 1.94/2.17 tff(3574,plain,(r(s(s(s(elem!1))), s(s(s(z)))) | b(s(s(s(elem!1))), s(s(s(z)))) | (s(s(s(elem!1))) = s(s(s(z))))), inference(lemma,lemma(discharge,[]))).
% 1.94/2.17 tff(3575,plain,
% 1.94/2.17 (r(s(s(s(elem!1))), s(s(s(z))))),
% 1.94/2.17 inference(unit_resolution,[status(thm)],[3574, 3566, 3537])).
% 1.94/2.17 tff(3576,plain,
% 1.94/2.17 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), s(s(s(z))))) | (~r(s(z), s(s(elem!1)))) | (~r(s(z), s(s(s(elem!1))))) | (~r(s(s(elem!1)), s(s(s(elem!1))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(elem!1))), s(s(s(z))))) | (~r(s(z), s(s(elem!1)))) | (~r(s(z), s(s(s(elem!1))))) | (~r(s(s(elem!1)), s(s(s(elem!1))))))),
% 1.94/2.17 inference(rewrite,[status(thm)],[])).
% 1.94/2.17 tff(3577,plain,
% 1.94/2.17 (((~r(s(s(s(elem!1))), s(s(s(z))))) | (~r(s(s(elem!1)), s(s(s(elem!1))))) | (~r(s(z), s(s(s(elem!1))))) | (~r(s(z), s(s(elem!1))))) <=> ((~r(s(s(s(elem!1))), s(s(s(z))))) | (~r(s(z), s(s(elem!1)))) | (~r(s(z), s(s(s(elem!1))))) | (~r(s(s(elem!1)), s(s(s(elem!1))))))),
% 1.94/2.17 inference(rewrite,[status(thm)],[])).
% 1.94/2.17 tff(3578,plain,
% 1.94/2.17 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), s(s(s(z))))) | (~r(s(s(elem!1)), s(s(s(elem!1))))) | (~r(s(z), s(s(s(elem!1))))) | (~r(s(z), s(s(elem!1)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), s(s(s(z))))) | (~r(s(z), s(s(elem!1)))) | (~r(s(z), s(s(s(elem!1))))) | (~r(s(s(elem!1)), s(s(s(elem!1)))))))),
% 1.94/2.17 inference(monotonicity,[status(thm)],[3577])).
% 1.94/2.17 tff(3579,plain,
% 1.94/2.17 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), s(s(s(z))))) | (~r(s(s(elem!1)), s(s(s(elem!1))))) | (~r(s(z), s(s(s(elem!1))))) | (~r(s(z), s(s(elem!1)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(elem!1))), s(s(s(z))))) | (~r(s(z), s(s(elem!1)))) | (~r(s(z), s(s(s(elem!1))))) | (~r(s(s(elem!1)), s(s(s(elem!1))))))),
% 1.94/2.17 inference(transitivity,[status(thm)],[3578, 3576])).
% 1.94/2.17 tff(3580,plain,
% 1.94/2.17 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), s(s(s(z))))) | (~r(s(s(elem!1)), s(s(s(elem!1))))) | (~r(s(z), s(s(s(elem!1))))) | (~r(s(z), s(s(elem!1)))))),
% 1.94/2.17 inference(quant_inst,[status(thm)],[])).
% 1.94/2.17 tff(3581,plain,
% 1.94/2.17 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(elem!1))), s(s(s(z))))) | (~r(s(z), s(s(elem!1)))) | (~r(s(z), s(s(s(elem!1))))) | (~r(s(s(elem!1)), s(s(s(elem!1)))))),
% 1.94/2.17 inference(modus_ponens,[status(thm)],[3580, 3579])).
% 1.94/2.17 tff(3582,plain,
% 1.94/2.17 ($false),
% 1.94/2.17 inference(unit_resolution,[status(thm)],[3581, 197, 311, 377, 119, 3183])).
% 1.94/2.17 tff(3583,plain,((~r(s(s(s(elem!1))), s(s(s(z))))) | (~r(s(z), s(s(elem!1)))) | (~r(s(s(elem!1)), s(s(s(elem!1))))) | (~r(s(z), s(s(s(elem!1)))))), inference(lemma,lemma(discharge,[]))).
% 1.94/2.17 tff(3584,plain,
% 1.94/2.17 (~r(s(s(elem!1)), s(s(s(elem!1))))),
% 1.94/2.17 inference(unit_resolution,[status(thm)],[3583, 3575, 311, 3536])).
% 1.94/2.17 tff(3585,plain,
% 1.94/2.17 (b(s(s(elem!1)), s(s(s(elem!1))))),
% 1.94/2.17 inference(unit_resolution,[status(thm)],[461, 3584, 45])).
% 1.94/2.17 tff(3586,plain,
% 1.94/2.17 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(z, s(s(elem!1)))) | (~b(s(s(elem!1)), z)) | (~b(s(s(s(elem!1))), z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(z, s(s(elem!1)))) | (~b(s(s(elem!1)), z)) | (~b(s(s(s(elem!1))), z)))),
% 1.94/2.17 inference(rewrite,[status(thm)],[])).
% 1.94/2.17 tff(3587,plain,
% 1.94/2.17 (((~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(z, s(s(elem!1)))) | (~b(s(s(s(elem!1))), z)) | (~b(s(s(elem!1)), z)) | (~b(s(s(elem!1)), s(s(s(elem!1)))))) <=> ((~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(z, s(s(elem!1)))) | (~b(s(s(elem!1)), z)) | (~b(s(s(s(elem!1))), z)))),
% 1.94/2.17 inference(rewrite,[status(thm)],[])).
% 1.94/2.17 tff(3588,plain,
% 1.94/2.17 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(z, s(s(elem!1)))) | (~b(s(s(s(elem!1))), z)) | (~b(s(s(elem!1)), z)) | (~b(s(s(elem!1)), s(s(s(elem!1))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(z, s(s(elem!1)))) | (~b(s(s(elem!1)), z)) | (~b(s(s(s(elem!1))), z))))),
% 1.94/2.17 inference(monotonicity,[status(thm)],[3587])).
% 1.94/2.17 tff(3589,plain,
% 1.94/2.17 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(z, s(s(elem!1)))) | (~b(s(s(s(elem!1))), z)) | (~b(s(s(elem!1)), z)) | (~b(s(s(elem!1)), s(s(s(elem!1))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(z, s(s(elem!1)))) | (~b(s(s(elem!1)), z)) | (~b(s(s(s(elem!1))), z)))),
% 1.94/2.17 inference(transitivity,[status(thm)],[3588, 3586])).
% 1.94/2.17 tff(3590,plain,
% 1.94/2.17 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(z, s(s(elem!1)))) | (~b(s(s(s(elem!1))), z)) | (~b(s(s(elem!1)), z)) | (~b(s(s(elem!1)), s(s(s(elem!1))))))),
% 1.94/2.17 inference(quant_inst,[status(thm)],[])).
% 1.94/2.17 tff(3591,plain,
% 1.94/2.17 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(z, s(s(elem!1)))) | (~b(s(s(elem!1)), z)) | (~b(s(s(s(elem!1))), z))),
% 1.94/2.17 inference(modus_ponens,[status(thm)],[3590, 3589])).
% 1.94/2.17 tff(3592,plain,
% 1.94/2.17 ($false),
% 1.94/2.17 inference(unit_resolution,[status(thm)],[3591, 166, 463, 1820, 121, 592])).
% 1.94/2.17 tff(3593,plain,((~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(z, s(s(elem!1)))) | (~b(s(s(s(elem!1))), z)) | (~b(s(s(elem!1)), z))), inference(lemma,lemma(discharge,[]))).
% 1.94/2.17 tff(3594,plain,
% 1.94/2.17 (~b(z, s(s(elem!1)))),
% 1.94/2.17 inference(unit_resolution,[status(thm)],[3593, 3585, 3506, 592])).
% 1.94/2.17 tff(3595,plain,
% 1.94/2.17 (r(z, s(s(elem!1)))),
% 1.94/2.17 inference(unit_resolution,[status(thm)],[1795, 3594])).
% 1.94/2.17 tff(3596,plain,
% 1.94/2.17 (~b(s(s(z)), s(s(s(elem!1))))),
% 1.94/2.17 inference(unit_resolution,[status(thm)],[3545, 166, 3585, 118, 3506, 446, 156])).
% 1.94/2.17 tff(3597,plain,
% 1.94/2.17 (r(s(s(z)), s(s(s(elem!1))))),
% 1.94/2.17 inference(unit_resolution,[status(thm)],[279, 3596])).
% 1.94/2.17 tff(3598,plain,
% 1.94/2.17 (~r(s(s(elem!1)), s(s(z)))),
% 1.94/2.17 inference(unit_resolution,[status(thm)],[539, 3597, 155, 3595])).
% 1.94/2.17 tff(3599,plain,
% 1.94/2.17 (~b(s(s(s(elem!1))), s(s(elem!1)))),
% 1.94/2.17 inference(unit_resolution,[status(thm)],[2068, 3585, 446, 3557])).
% 1.94/2.17 tff(3600,plain,
% 1.94/2.17 (r(s(s(s(elem!1))), s(s(elem!1)))),
% 1.94/2.17 inference(unit_resolution,[status(thm)],[889, 3599, 51])).
% 1.94/2.17 tff(3601,plain,
% 1.94/2.17 (~r(s(s(z)), s(z))),
% 1.94/2.17 inference(unit_resolution,[status(thm)],[913, 281, 119, 905])).
% 1.94/2.17 tff(3602,plain,
% 1.94/2.17 (b(s(s(z)), s(z))),
% 1.94/2.17 inference(unit_resolution,[status(thm)],[308, 3601])).
% 1.94/2.17 tff(3603,plain,
% 1.94/2.17 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), 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))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(elem!1))), s(s(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))))))),
% 1.94/2.17 inference(rewrite,[status(thm)],[])).
% 1.94/2.17 tff(3604,plain,
% 1.94/2.17 (((~r(s(s(s(elem!1))), s(s(elem!1)))) | (~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(s(elem!1))), 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))))))),
% 1.94/2.17 inference(rewrite,[status(thm)],[])).
% 1.94/2.17 tff(3605,plain,
% 1.94/2.17 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), s(s(elem!1)))) | (~r(s(s(z)), s(s(s(elem!1))))) | (~r(s(z), s(s(s(elem!1))))) | (~r(s(z), s(s(z)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), 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)))))))),
% 1.94/2.17 inference(monotonicity,[status(thm)],[3604])).
% 1.94/2.17 tff(3606,plain,
% 1.94/2.17 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), s(s(elem!1)))) | (~r(s(s(z)), s(s(s(elem!1))))) | (~r(s(z), s(s(s(elem!1))))) | (~r(s(z), s(s(z)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(elem!1))), 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))))))),
% 1.94/2.18 inference(transitivity,[status(thm)],[3605, 3603])).
% 1.94/2.18 tff(3607,plain,
% 1.94/2.18 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), s(s(elem!1)))) | (~r(s(s(z)), s(s(s(elem!1))))) | (~r(s(z), s(s(s(elem!1))))) | (~r(s(z), s(s(z)))))),
% 1.94/2.18 inference(quant_inst,[status(thm)],[])).
% 1.94/2.18 tff(3608,plain,
% 1.94/2.18 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(elem!1))), 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)))))),
% 1.94/2.18 inference(modus_ponens,[status(thm)],[3607, 3606])).
% 1.94/2.18 tff(3609,plain,
% 1.94/2.18 (~r(s(z), s(s(z)))),
% 1.94/2.18 inference(unit_resolution,[status(thm)],[3608, 197, 905, 119, 281])).
% 1.94/2.18 tff(3610,plain,
% 1.94/2.18 (b(s(z), s(s(z)))),
% 1.94/2.18 inference(unit_resolution,[status(thm)],[427, 3609])).
% 1.94/2.18 tff(3611,plain,
% 1.94/2.18 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), s(s(z)))) | (~b(s(s(elem!1)), s(z))) | (~b(s(z), s(s(z)))) | (~b(s(s(z)), s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(elem!1)), s(s(z)))) | (~b(s(s(elem!1)), s(z))) | (~b(s(z), s(s(z)))) | (~b(s(s(z)), s(z))))),
% 1.94/2.18 inference(rewrite,[status(thm)],[])).
% 1.94/2.18 tff(3612,plain,
% 1.94/2.18 (((~b(s(z), s(s(z)))) | (~b(s(s(elem!1)), s(s(z)))) | (~b(s(s(z)), s(z))) | (~b(s(z), s(s(z)))) | (~b(s(s(elem!1)), s(s(z)))) | (~b(s(s(elem!1)), s(z)))) <=> ((~b(s(s(elem!1)), s(s(z)))) | (~b(s(s(elem!1)), s(z))) | (~b(s(z), s(s(z)))) | (~b(s(s(z)), s(z))))),
% 1.94/2.18 inference(rewrite,[status(thm)],[])).
% 1.94/2.18 tff(3613,plain,
% 1.94/2.18 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(z)))) | (~b(s(s(elem!1)), s(s(z)))) | (~b(s(s(z)), s(z))) | (~b(s(z), s(s(z)))) | (~b(s(s(elem!1)), s(s(z)))) | (~b(s(s(elem!1)), s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), s(s(z)))) | (~b(s(s(elem!1)), s(z))) | (~b(s(z), s(s(z)))) | (~b(s(s(z)), s(z)))))),
% 1.94/2.18 inference(monotonicity,[status(thm)],[3612])).
% 1.94/2.18 tff(3614,plain,
% 1.94/2.18 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(z)))) | (~b(s(s(elem!1)), s(s(z)))) | (~b(s(s(z)), s(z))) | (~b(s(z), s(s(z)))) | (~b(s(s(elem!1)), s(s(z)))) | (~b(s(s(elem!1)), s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(elem!1)), s(s(z)))) | (~b(s(s(elem!1)), s(z))) | (~b(s(z), s(s(z)))) | (~b(s(s(z)), s(z))))),
% 1.94/2.18 inference(transitivity,[status(thm)],[3613, 3611])).
% 1.94/2.18 tff(3615,plain,
% 1.94/2.18 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(z)))) | (~b(s(s(elem!1)), s(s(z)))) | (~b(s(s(z)), s(z))) | (~b(s(z), s(s(z)))) | (~b(s(s(elem!1)), s(s(z)))) | (~b(s(s(elem!1)), s(z))))),
% 1.94/2.18 inference(quant_inst,[status(thm)],[])).
% 1.94/2.18 tff(3616,plain,
% 1.94/2.18 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(elem!1)), s(s(z)))) | (~b(s(s(elem!1)), s(z))) | (~b(s(z), s(s(z)))) | (~b(s(s(z)), s(z)))),
% 1.94/2.18 inference(modus_ponens,[status(thm)],[3615, 3614])).
% 1.94/2.18 tff(3617,plain,
% 1.94/2.18 ($false),
% 1.94/2.18 inference(unit_resolution,[status(thm)],[3616, 166, 405, 3610, 310, 3602])).
% 1.94/2.18 tff(3618,plain,((~r(s(s(z)), s(s(s(elem!1))))) | (~b(s(s(elem!1)), s(s(z)))) | (~b(s(s(elem!1)), s(z))) | (~r(s(s(s(elem!1))), s(s(elem!1)))) | (~r(s(z), s(s(s(elem!1)))))), inference(lemma,lemma(discharge,[]))).
% 1.94/2.18 tff(3619,plain,
% 1.94/2.18 (~b(s(s(elem!1)), s(s(z)))),
% 1.94/2.18 inference(unit_resolution,[status(thm)],[3618, 3597, 310, 3600, 3536])).
% 1.94/2.18 tff(3620,plain,
% 1.94/2.18 ($false),
% 1.94/2.18 inference(unit_resolution,[status(thm)],[441, 3619, 3598, 11])).
% 1.94/2.18 tff(3621,plain,((s(s(elem!1)) = s(s(s(elem!1)))) | (s(s(elem!1)) = s(s(z))) | (~b(s(s(elem!1)), s(z))) | (~r(z, s(s(z)))) | (~b(z, s(z))) | (~b(s(s(z)), s(s(elem!1)))) | (~b(s(s(z)), s(z))) | (~b(s(s(elem!1)), z)) | (~r(s(z), s(s(elem!1)))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(s(z))), z)) | (~b(s(s(s(elem!1))), s(z))) | (~r(s(z), s(s(z))))), inference(lemma,lemma(discharge,[]))).
% 1.94/2.18 tff(3622,plain,
% 1.94/2.18 (s(s(elem!1)) = s(s(s(elem!1)))),
% 1.94/2.18 inference(unit_resolution,[status(thm)],[3621, 132, 310, 155, 118, 3534, 156, 3532, 311, 3516, 3530, 96, 120])).
% 1.94/2.18 tff(3623,plain,
% 1.94/2.18 (b(s(s(elem!1)), s(s(s(z)))) <=> b(s(s(s(elem!1))), s(s(s(z))))),
% 1.94/2.18 inference(monotonicity,[status(thm)],[3622])).
% 1.94/2.18 tff(3624,plain,
% 1.94/2.18 ((~b(s(s(elem!1)), s(s(s(z))))) <=> (~b(s(s(s(elem!1))), s(s(s(z)))))),
% 1.94/2.18 inference(monotonicity,[status(thm)],[3623])).
% 1.94/2.18 tff(3625,plain,
% 1.94/2.18 (s(s(s(elem!1))) = s(elem!1)),
% 1.94/2.18 inference(unit_resolution,[status(thm)],[2594, 3622])).
% 1.94/2.18 tff(3626,plain,
% 1.94/2.18 (s(elem!1) = s(s(s(elem!1)))),
% 1.94/2.18 inference(symmetry,[status(thm)],[3625])).
% 1.94/2.18 tff(3627,plain,
% 1.94/2.18 (inj_0(s(elem!1)) = inj_0(s(s(s(elem!1))))),
% 1.94/2.18 inference(monotonicity,[status(thm)],[3626])).
% 1.94/2.18 tff(3628,plain,
% 1.94/2.18 (elem!1 = s(s(s(elem!1)))),
% 1.94/2.18 inference(transitivity,[status(thm)],[1170, 3627, 104, 3622])).
% 1.94/2.18 tff(3629,plain,
% 1.94/2.18 (r(s(z), elem!1) <=> r(s(z), s(s(s(elem!1))))),
% 1.94/2.18 inference(monotonicity,[status(thm)],[3628])).
% 1.94/2.18 tff(3630,plain,
% 1.94/2.18 (r(s(z), s(s(s(elem!1)))) <=> r(s(z), elem!1)),
% 1.94/2.18 inference(symmetry,[status(thm)],[3629])).
% 1.94/2.18 tff(3631,plain,
% 1.94/2.18 (~b(s(z), s(s(s(elem!1))))),
% 1.94/2.18 inference(unit_resolution,[status(thm)],[2929, 3534, 310, 96, 156])).
% 1.94/2.18 tff(3632,plain,
% 1.94/2.18 (r(s(z), s(s(s(elem!1))))),
% 1.94/2.18 inference(unit_resolution,[status(thm)],[116, 3631])).
% 1.94/2.18 tff(3633,plain,
% 1.94/2.18 (r(s(z), elem!1)),
% 1.94/2.18 inference(modus_ponens,[status(thm)],[3632, 3630])).
% 1.94/2.18 tff(3634,plain,
% 1.94/2.18 (~r(s(s(z)), z)),
% 1.94/2.18 inference(unit_resolution,[status(thm)],[2498, 97, 155, 120])).
% 1.94/2.18 tff(3635,plain,
% 1.94/2.18 (b(s(s(z)), z)),
% 1.94/2.18 inference(unit_resolution,[status(thm)],[186, 3634])).
% 1.94/2.18 tff(3636,plain,
% 1.94/2.18 (b(elem!1, s(z)) <=> b(s(s(s(elem!1))), s(z))),
% 1.94/2.18 inference(monotonicity,[status(thm)],[3628])).
% 1.94/2.18 tff(3637,plain,
% 1.94/2.18 (b(s(s(s(elem!1))), s(z)) <=> b(elem!1, s(z))),
% 1.94/2.18 inference(symmetry,[status(thm)],[3636])).
% 1.94/2.18 tff(3638,plain,
% 1.94/2.18 (b(elem!1, s(z))),
% 1.94/2.18 inference(modus_ponens,[status(thm)],[96, 3637])).
% 1.94/2.18 tff(3639,plain,
% 1.94/2.18 (~b(z, elem!1)),
% 1.94/2.18 inference(unit_resolution,[status(thm)],[2525, 3638, 3532, 3534, 156, 3635])).
% 1.94/2.18 tff(3640,plain,
% 1.94/2.18 (r(z, elem!1)),
% 1.94/2.18 inference(unit_resolution,[status(thm)],[2514, 3639, 1146])).
% 1.94/2.18 tff(3641,plain,
% 1.94/2.18 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, elem!1)) | (~r(s(z), elem!1)) | (~r(s(z), z)) | (~r(elem!1, s(s(z)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, elem!1)) | (~r(s(z), elem!1)) | (~r(s(z), z)) | (~r(elem!1, s(s(z)))))),
% 1.94/2.18 inference(rewrite,[status(thm)],[])).
% 1.94/2.18 tff(3642,plain,
% 1.94/2.18 (((~r(elem!1, s(s(z)))) | (~r(z, elem!1)) | (~r(s(z), elem!1)) | (~r(s(z), z))) <=> ((~r(z, elem!1)) | (~r(s(z), elem!1)) | (~r(s(z), z)) | (~r(elem!1, s(s(z)))))),
% 1.94/2.18 inference(rewrite,[status(thm)],[])).
% 1.94/2.18 tff(3643,plain,
% 1.94/2.18 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(s(z)))) | (~r(z, elem!1)) | (~r(s(z), elem!1)) | (~r(s(z), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, elem!1)) | (~r(s(z), elem!1)) | (~r(s(z), z)) | (~r(elem!1, s(s(z))))))),
% 1.94/2.18 inference(monotonicity,[status(thm)],[3642])).
% 1.94/2.18 tff(3644,plain,
% 1.94/2.18 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(s(z)))) | (~r(z, elem!1)) | (~r(s(z), elem!1)) | (~r(s(z), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, elem!1)) | (~r(s(z), elem!1)) | (~r(s(z), z)) | (~r(elem!1, s(s(z)))))),
% 1.94/2.18 inference(transitivity,[status(thm)],[3643, 3641])).
% 1.94/2.18 tff(3645,plain,
% 1.94/2.18 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(s(z)))) | (~r(z, elem!1)) | (~r(s(z), elem!1)) | (~r(s(z), z)))),
% 1.94/2.18 inference(quant_inst,[status(thm)],[])).
% 1.94/2.18 tff(3646,plain,
% 1.94/2.18 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, elem!1)) | (~r(s(z), elem!1)) | (~r(s(z), z)) | (~r(elem!1, s(s(z))))),
% 1.94/2.18 inference(modus_ponens,[status(thm)],[3645, 3644])).
% 1.94/2.18 tff(3647,plain,
% 1.94/2.18 ((~r(z, elem!1)) | (~r(s(z), elem!1)) | (~r(s(z), z)) | (~r(elem!1, s(s(z))))),
% 1.94/2.18 inference(unit_resolution,[status(thm)],[3646, 197])).
% 1.94/2.18 tff(3648,plain,
% 1.94/2.18 (~r(elem!1, s(s(z)))),
% 1.94/2.18 inference(unit_resolution,[status(thm)],[3647, 3640, 97, 3633])).
% 1.94/2.18 tff(3649,plain,
% 1.94/2.18 (s(s(elem!1)) = elem!1),
% 1.94/2.18 inference(transitivity,[status(thm)],[105, 1544, 20])).
% 1.94/2.18 tff(3650,plain,
% 1.94/2.18 (r(s(s(elem!1)), s(s(z))) <=> r(elem!1, s(s(z)))),
% 1.94/2.18 inference(monotonicity,[status(thm)],[3649])).
% 1.94/2.18 tff(3651,plain,
% 1.94/2.18 (r(elem!1, s(s(z))) <=> r(s(s(elem!1)), s(s(z)))),
% 1.94/2.18 inference(symmetry,[status(thm)],[3650])).
% 1.94/2.18 tff(3652,plain,
% 1.94/2.18 ((~r(elem!1, s(s(z)))) <=> (~r(s(s(elem!1)), s(s(z))))),
% 1.94/2.18 inference(monotonicity,[status(thm)],[3651])).
% 1.94/2.18 tff(3653,assumption,(~r(elem!1, s(s(z)))), introduced(assumption)).
% 1.94/2.18 tff(3654,plain,
% 1.94/2.18 (~r(s(s(elem!1)), s(s(z)))),
% 1.94/2.18 inference(modus_ponens,[status(thm)],[3653, 3652])).
% 1.94/2.18 tff(3655,plain,
% 1.94/2.18 ($false),
% 1.94/2.18 inference(unit_resolution,[status(thm)],[393, 3654])).
% 1.94/2.18 tff(3656,plain,((~(s(s(s(elem!1))) = s(elem!1))) | (~r(s(s(elem!1)), s(s(z)))) | r(elem!1, s(s(z)))), inference(lemma,lemma(discharge,[]))).
% 1.94/2.18 tff(3657,plain,
% 1.94/2.18 (~r(s(s(elem!1)), s(s(z)))),
% 1.94/2.18 inference(unit_resolution,[status(thm)],[3656, 3648, 3625])).
% 1.94/2.18 tff(3658,plain,
% 1.94/2.18 (b(s(s(elem!1)), s(s(z)))),
% 1.94/2.18 inference(unit_resolution,[status(thm)],[441, 3657, 132])).
% 1.94/2.18 tff(3659,plain,
% 1.94/2.18 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), s(s(z)))) | (~b(z, s(z))) | (~b(s(s(elem!1)), s(z))) | (~b(s(s(s(z))), z)) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(elem!1)), s(s(s(z))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(elem!1)), s(s(z)))) | (~b(z, s(z))) | (~b(s(s(elem!1)), s(z))) | (~b(s(s(s(z))), z)) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(elem!1)), s(s(s(z))))))),
% 1.94/2.18 inference(rewrite,[status(thm)],[])).
% 1.94/2.18 tff(3660,plain,
% 1.94/2.18 (((~b(z, s(z))) | (~b(s(s(elem!1)), s(z))) | (~b(s(s(s(z))), z)) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(elem!1)), s(s(s(z))))) | (~b(s(s(elem!1)), s(s(z))))) <=> ((~b(s(s(elem!1)), s(s(z)))) | (~b(z, s(z))) | (~b(s(s(elem!1)), s(z))) | (~b(s(s(s(z))), z)) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(elem!1)), s(s(s(z))))))),
% 1.94/2.18 inference(rewrite,[status(thm)],[])).
% 1.94/2.18 tff(3661,plain,
% 1.94/2.18 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(z))) | (~b(s(s(elem!1)), s(z))) | (~b(s(s(s(z))), z)) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(elem!1)), s(s(s(z))))) | (~b(s(s(elem!1)), s(s(z)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), s(s(z)))) | (~b(z, s(z))) | (~b(s(s(elem!1)), s(z))) | (~b(s(s(s(z))), z)) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(elem!1)), s(s(s(z)))))))),
% 1.94/2.18 inference(monotonicity,[status(thm)],[3660])).
% 1.94/2.18 tff(3662,plain,
% 1.94/2.18 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(z))) | (~b(s(s(elem!1)), s(z))) | (~b(s(s(s(z))), z)) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(elem!1)), s(s(s(z))))) | (~b(s(s(elem!1)), s(s(z)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(elem!1)), s(s(z)))) | (~b(z, s(z))) | (~b(s(s(elem!1)), s(z))) | (~b(s(s(s(z))), z)) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(elem!1)), s(s(s(z))))))),
% 1.94/2.18 inference(transitivity,[status(thm)],[3661, 3659])).
% 1.94/2.18 tff(3663,plain,
% 1.94/2.18 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(z))) | (~b(s(s(elem!1)), s(z))) | (~b(s(s(s(z))), z)) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(elem!1)), s(s(s(z))))) | (~b(s(s(elem!1)), s(s(z)))))),
% 1.94/2.18 inference(quant_inst,[status(thm)],[])).
% 1.94/2.18 tff(3664,plain,
% 1.94/2.18 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(elem!1)), s(s(z)))) | (~b(z, s(z))) | (~b(s(s(elem!1)), s(z))) | (~b(s(s(s(z))), z)) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(elem!1)), s(s(s(z)))))),
% 1.94/2.18 inference(modus_ponens,[status(thm)],[3663, 3662])).
% 1.94/2.18 tff(3665,plain,
% 1.94/2.18 ((~b(s(s(elem!1)), s(s(z)))) | (~b(s(s(elem!1)), s(s(s(z)))))),
% 1.94/2.18 inference(unit_resolution,[status(thm)],[3664, 166, 118, 310, 3516, 3530])).
% 1.94/2.18 tff(3666,plain,
% 1.94/2.18 (~b(s(s(elem!1)), s(s(s(z))))),
% 1.94/2.18 inference(unit_resolution,[status(thm)],[3665, 3658])).
% 1.94/2.18 tff(3667,plain,
% 1.94/2.18 (~b(s(s(s(elem!1))), s(s(s(z))))),
% 1.94/2.18 inference(modus_ponens,[status(thm)],[3666, 3624])).
% 1.94/2.18 tff(3668,plain,
% 1.94/2.18 (r(s(s(s(elem!1))), s(s(s(z))))),
% 1.94/2.18 inference(unit_resolution,[status(thm)],[3572, 79, 3667, 140])).
% 1.94/2.18 tff(3669,plain,
% 1.94/2.18 (r(z, elem!1) <=> r(z, s(s(s(elem!1))))),
% 1.94/2.18 inference(monotonicity,[status(thm)],[3628])).
% 1.94/2.18 tff(3670,plain,
% 1.94/2.18 (r(z, s(s(s(elem!1))))),
% 1.94/2.18 inference(modus_ponens,[status(thm)],[3640, 3669])).
% 1.94/2.18 tff(3671,plain,
% 1.94/2.18 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), s(s(s(z))))) | (~r(z, s(s(s(elem!1))))) | (~r(s(z), z)) | (~r(s(z), s(s(s(elem!1))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(elem!1))), s(s(s(z))))) | (~r(z, s(s(s(elem!1))))) | (~r(s(z), z)) | (~r(s(z), s(s(s(elem!1))))))),
% 1.94/2.18 inference(rewrite,[status(thm)],[])).
% 1.94/2.18 tff(3672,plain,
% 1.94/2.18 (((~r(s(s(s(elem!1))), s(s(s(z))))) | (~r(z, s(s(s(elem!1))))) | (~r(s(z), s(s(s(elem!1))))) | (~r(s(z), z))) <=> ((~r(s(s(s(elem!1))), s(s(s(z))))) | (~r(z, s(s(s(elem!1))))) | (~r(s(z), z)) | (~r(s(z), s(s(s(elem!1))))))),
% 1.94/2.18 inference(rewrite,[status(thm)],[])).
% 1.94/2.18 tff(3673,plain,
% 1.94/2.18 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), s(s(s(z))))) | (~r(z, s(s(s(elem!1))))) | (~r(s(z), s(s(s(elem!1))))) | (~r(s(z), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), s(s(s(z))))) | (~r(z, s(s(s(elem!1))))) | (~r(s(z), z)) | (~r(s(z), s(s(s(elem!1)))))))),
% 1.94/2.18 inference(monotonicity,[status(thm)],[3672])).
% 1.94/2.18 tff(3674,plain,
% 1.94/2.18 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), s(s(s(z))))) | (~r(z, s(s(s(elem!1))))) | (~r(s(z), s(s(s(elem!1))))) | (~r(s(z), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(elem!1))), s(s(s(z))))) | (~r(z, s(s(s(elem!1))))) | (~r(s(z), z)) | (~r(s(z), s(s(s(elem!1))))))),
% 1.94/2.18 inference(transitivity,[status(thm)],[3673, 3671])).
% 1.94/2.18 tff(3675,plain,
% 1.94/2.18 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), s(s(s(z))))) | (~r(z, s(s(s(elem!1))))) | (~r(s(z), s(s(s(elem!1))))) | (~r(s(z), z)))),
% 1.94/2.18 inference(quant_inst,[status(thm)],[])).
% 1.94/2.18 tff(3676,plain,
% 1.94/2.18 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(elem!1))), s(s(s(z))))) | (~r(z, s(s(s(elem!1))))) | (~r(s(z), z)) | (~r(s(z), s(s(s(elem!1)))))),
% 1.94/2.18 inference(modus_ponens,[status(thm)],[3675, 3674])).
% 1.94/2.18 tff(3677,plain,
% 1.94/2.18 ($false),
% 1.94/2.18 inference(unit_resolution,[status(thm)],[3676, 197, 97, 3632, 3670, 3668])).
% 1.94/2.18 tff(3678,plain,((s(s(z)) = s(s(elem!1))) | (~r(s(z), z)) | (~b(z, s(z))) | (~b(s(s(elem!1)), s(z))) | (~b(s(s(z)), s(z))) | (~b(s(s(s(elem!1))), s(z))) | (~r(z, s(s(z)))) | (~r(s(z), s(s(elem!1)))) | (~r(s(z), s(s(z))))), inference(lemma,lemma(discharge,[]))).
% 1.94/2.18 tff(3679,plain,
% 1.94/2.18 (s(s(z)) = s(s(elem!1))),
% 1.94/2.18 inference(unit_resolution,[status(thm)],[3678, 97, 118, 310, 156, 96, 155, 311, 120])).
% 1.94/2.18 tff(3680,plain,
% 1.94/2.18 (s(elem!1) = s(z)),
% 1.94/2.18 inference(unit_resolution,[status(thm)],[43, 3679])).
% 1.94/2.18 tff(3681,plain,
% 1.94/2.18 (z = elem!1),
% 1.94/2.18 inference(unit_resolution,[status(thm)],[30, 3680])).
% 1.94/2.18 tff(3682,plain,
% 1.94/2.18 ((s(s(s(s(elem!1)))) = z) <=> (s(s(s(s(elem!1)))) = elem!1)),
% 1.94/2.18 inference(monotonicity,[status(thm)],[3681])).
% 1.94/2.18 tff(3683,plain,
% 1.94/2.18 ((s(s(s(s(elem!1)))) = z) <=> (elem!1 = s(s(s(s(elem!1)))))),
% 1.94/2.18 inference(transitivity,[status(thm)],[3682, 2287])).
% 1.94/2.18 tff(3684,plain,
% 1.94/2.18 ((~(s(s(s(s(elem!1)))) = z)) <=> (~(elem!1 = s(s(s(s(elem!1))))))),
% 1.94/2.18 inference(monotonicity,[status(thm)],[3683])).
% 1.94/2.18 tff(3685,plain,
% 1.94/2.18 (~(elem!1 = s(s(s(s(elem!1)))))),
% 1.94/2.18 inference(modus_ponens,[status(thm)],[626, 3684])).
% 1.94/2.18 tff(3686,plain,
% 1.94/2.18 (b(s(s(s(elem!1))), elem!1)),
% 1.94/2.18 inference(unit_resolution,[status(thm)],[634, 3681, 3506])).
% 1.94/2.18 tff(3687,plain,
% 1.94/2.18 (r(s(elem!1), elem!1) <=> r(s(z), elem!1)),
% 1.94/2.18 inference(monotonicity,[status(thm)],[3680])).
% 1.94/2.18 tff(3688,plain,
% 1.94/2.18 (r(s(z), elem!1) <=> r(s(elem!1), elem!1)),
% 1.94/2.18 inference(symmetry,[status(thm)],[3687])).
% 1.94/2.18 tff(3689,plain,
% 1.94/2.18 (r(s(z), z) <=> r(s(z), elem!1)),
% 1.94/2.18 inference(monotonicity,[status(thm)],[3681])).
% 1.94/2.18 tff(3690,plain,
% 1.94/2.18 (r(s(z), z) <=> r(s(elem!1), elem!1)),
% 1.94/2.18 inference(transitivity,[status(thm)],[3689, 3688])).
% 1.94/2.18 tff(3691,plain,
% 1.94/2.18 (r(s(elem!1), elem!1)),
% 1.94/2.18 inference(modus_ponens,[status(thm)],[97, 3690])).
% 1.94/2.18 tff(3692,plain,
% 1.94/2.18 (r(z, s(s(s(z)))) <=> r(elem!1, s(s(s(z))))),
% 1.94/2.18 inference(monotonicity,[status(thm)],[3681])).
% 1.94/2.18 tff(3693,plain,
% 1.94/2.18 (~b(z, s(s(s(z))))),
% 1.94/2.18 inference(unit_resolution,[status(thm)],[3223, 3530, 3516, 3635])).
% 1.94/2.18 tff(3694,plain,
% 1.94/2.18 (r(z, s(s(s(z))))),
% 1.94/2.18 inference(unit_resolution,[status(thm)],[1697, 3693])).
% 1.94/2.18 tff(3695,plain,
% 1.94/2.18 (r(elem!1, s(s(s(z))))),
% 1.94/2.18 inference(modus_ponens,[status(thm)],[3694, 3692])).
% 1.94/2.18 tff(3696,plain,
% 1.94/2.18 (b(s(s(elem!1)), z) <=> b(s(s(elem!1)), elem!1)),
% 1.94/2.18 inference(monotonicity,[status(thm)],[3681])).
% 1.94/2.18 tff(3697,plain,
% 1.94/2.18 (b(s(s(elem!1)), elem!1)),
% 1.94/2.18 inference(modus_ponens,[status(thm)],[3532, 3696])).
% 1.94/2.18 tff(3698,plain,
% 1.94/2.18 (b(s(s(z)), s(s(s(elem!1)))) <=> b(s(s(elem!1)), s(s(s(elem!1))))),
% 1.94/2.18 inference(monotonicity,[status(thm)],[3679])).
% 1.94/2.18 tff(3699,plain,
% 1.94/2.18 (b(s(s(elem!1)), s(s(s(elem!1)))) <=> b(s(s(z)), s(s(s(elem!1))))),
% 1.94/2.18 inference(symmetry,[status(thm)],[3698])).
% 1.94/2.18 tff(3700,plain,
% 1.94/2.18 (s(s(s(z))) = s(s(s(elem!1)))),
% 1.94/2.18 inference(monotonicity,[status(thm)],[3679])).
% 1.94/2.18 tff(3701,plain,
% 1.94/2.18 (b(s(s(elem!1)), s(s(s(z)))) <=> b(s(s(elem!1)), s(s(s(elem!1))))),
% 1.94/2.18 inference(monotonicity,[status(thm)],[3700])).
% 1.94/2.18 tff(3702,plain,
% 1.94/2.18 (b(s(s(elem!1)), s(s(s(z)))) <=> b(s(s(z)), s(s(s(elem!1))))),
% 1.94/2.18 inference(transitivity,[status(thm)],[3701, 3699])).
% 1.94/2.18 tff(3703,plain,
% 1.94/2.18 (b(s(s(z)), s(s(s(z)))) <=> b(s(s(elem!1)), s(s(s(z))))),
% 1.94/2.18 inference(monotonicity,[status(thm)],[3679])).
% 1.94/2.18 tff(3704,plain,
% 1.94/2.18 (b(s(s(elem!1)), s(s(s(z))))),
% 1.94/2.18 inference(modus_ponens,[status(thm)],[3516, 3703])).
% 1.94/2.18 tff(3705,plain,
% 1.94/2.18 (b(s(s(z)), s(s(s(elem!1))))),
% 1.94/2.18 inference(modus_ponens,[status(thm)],[3704, 3702])).
% 1.94/2.18 tff(3706,plain,
% 1.94/2.18 ((s(s(z)) = s(s(s(elem!1)))) <=> (s(s(elem!1)) = s(s(s(elem!1))))),
% 1.94/2.18 inference(monotonicity,[status(thm)],[3679])).
% 1.94/2.18 tff(3707,plain,
% 1.94/2.18 ((s(s(z)) = s(s(s(elem!1)))) <=> (s(s(s(elem!1))) = s(s(elem!1)))),
% 1.94/2.18 inference(transitivity,[status(thm)],[3706, 3341])).
% 1.94/2.19 tff(3708,plain,
% 1.94/2.19 ((~(s(s(z)) = s(s(s(elem!1))))) <=> (~(s(s(s(elem!1))) = s(s(elem!1))))),
% 1.94/2.19 inference(monotonicity,[status(thm)],[3707])).
% 1.94/2.19 tff(3709,plain,
% 1.94/2.19 (~(s(s(s(elem!1))) = s(s(elem!1)))),
% 1.94/2.19 inference(modus_ponens,[status(thm)],[209, 3708])).
% 1.94/2.19 tff(3710,plain,
% 1.94/2.19 (b(s(s(elem!1)), s(s(s(elem!1))))),
% 1.94/2.19 inference(modus_ponens,[status(thm)],[3704, 3701])).
% 1.94/2.19 tff(3711,plain,
% 1.94/2.19 (~b(s(z), s(s(s(elem!1))))),
% 1.94/2.19 inference(unit_resolution,[status(thm)],[1994, 3710, 310, 96])).
% 1.94/2.19 tff(3712,plain,
% 1.94/2.19 (r(s(z), s(s(s(elem!1))))),
% 1.94/2.19 inference(unit_resolution,[status(thm)],[116, 3711])).
% 1.94/2.19 tff(3713,plain,
% 1.94/2.19 (r(elem!1, s(s(s(z)))) <=> r(elem!1, s(s(s(elem!1))))),
% 1.94/2.19 inference(monotonicity,[status(thm)],[3700])).
% 1.94/2.19 tff(3714,plain,
% 1.94/2.19 (r(elem!1, s(s(s(elem!1))))),
% 1.94/2.19 inference(modus_ponens,[status(thm)],[3695, 3713])).
% 1.94/2.19 tff(3715,plain,
% 1.94/2.19 (r(s(z), elem!1)),
% 1.94/2.19 inference(modus_ponens,[status(thm)],[97, 3689])).
% 1.94/2.19 tff(3716,plain,
% 1.94/2.19 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), s(s(elem!1)))) | (~r(s(z), elem!1)) | (~r(elem!1, s(s(s(elem!1))))) | (~r(s(z), s(s(s(elem!1))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(elem!1))), s(s(elem!1)))) | (~r(s(z), elem!1)) | (~r(elem!1, s(s(s(elem!1))))) | (~r(s(z), s(s(s(elem!1))))))),
% 1.94/2.19 inference(rewrite,[status(thm)],[])).
% 1.94/2.19 tff(3717,plain,
% 1.94/2.19 (((~r(s(s(s(elem!1))), s(s(elem!1)))) | (~r(elem!1, s(s(s(elem!1))))) | (~r(s(z), s(s(s(elem!1))))) | (~r(s(z), elem!1))) <=> ((~r(s(s(s(elem!1))), s(s(elem!1)))) | (~r(s(z), elem!1)) | (~r(elem!1, s(s(s(elem!1))))) | (~r(s(z), s(s(s(elem!1))))))),
% 1.94/2.19 inference(rewrite,[status(thm)],[])).
% 1.94/2.19 tff(3718,plain,
% 1.94/2.19 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), s(s(elem!1)))) | (~r(elem!1, s(s(s(elem!1))))) | (~r(s(z), s(s(s(elem!1))))) | (~r(s(z), elem!1)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), s(s(elem!1)))) | (~r(s(z), elem!1)) | (~r(elem!1, s(s(s(elem!1))))) | (~r(s(z), s(s(s(elem!1)))))))),
% 1.94/2.19 inference(monotonicity,[status(thm)],[3717])).
% 1.94/2.19 tff(3719,plain,
% 1.94/2.19 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), s(s(elem!1)))) | (~r(elem!1, s(s(s(elem!1))))) | (~r(s(z), s(s(s(elem!1))))) | (~r(s(z), elem!1)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(elem!1))), s(s(elem!1)))) | (~r(s(z), elem!1)) | (~r(elem!1, s(s(s(elem!1))))) | (~r(s(z), s(s(s(elem!1))))))),
% 1.94/2.19 inference(transitivity,[status(thm)],[3718, 3716])).
% 1.94/2.19 tff(3720,plain,
% 1.94/2.19 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), s(s(elem!1)))) | (~r(elem!1, s(s(s(elem!1))))) | (~r(s(z), s(s(s(elem!1))))) | (~r(s(z), elem!1)))),
% 1.94/2.19 inference(quant_inst,[status(thm)],[])).
% 1.94/2.19 tff(3721,plain,
% 1.94/2.19 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(elem!1))), s(s(elem!1)))) | (~r(s(z), elem!1)) | (~r(elem!1, s(s(s(elem!1))))) | (~r(s(z), s(s(s(elem!1)))))),
% 1.94/2.19 inference(modus_ponens,[status(thm)],[3720, 3719])).
% 1.94/2.19 tff(3722,plain,
% 1.94/2.19 ($false),
% 1.94/2.19 inference(unit_resolution,[status(thm)],[3721, 197, 2381, 942, 905, 119])).
% 1.94/2.19 tff(3723,plain,((~r(s(s(s(elem!1))), s(s(elem!1)))) | (~r(s(z), elem!1)) | (~r(elem!1, s(s(s(elem!1))))) | (~r(s(z), s(s(s(elem!1)))))), inference(lemma,lemma(discharge,[]))).
% 1.94/2.19 tff(3724,plain,
% 1.94/2.19 (~r(s(s(s(elem!1))), s(s(elem!1)))),
% 1.94/2.19 inference(unit_resolution,[status(thm)],[3723, 3715, 3714, 3712])).
% 1.94/2.19 tff(3725,plain,
% 1.94/2.19 (b(s(s(s(elem!1))), s(s(elem!1)))),
% 1.94/2.19 inference(unit_resolution,[status(thm)],[889, 3724, 3709])).
% 1.94/2.19 tff(3726,plain,
% 1.94/2.19 (b(z, s(z)) <=> b(elem!1, s(z))),
% 1.94/2.19 inference(monotonicity,[status(thm)],[3681])).
% 1.94/2.19 tff(3727,plain,
% 1.94/2.19 (b(elem!1, s(z))),
% 1.94/2.19 inference(modus_ponens,[status(thm)],[118, 3726])).
% 1.94/2.19 tff(3728,assumption,(r(s(elem!1), elem!1)), introduced(assumption)).
% 1.94/2.19 tff(3729,plain,
% 1.94/2.19 (r(s(s(s(s(elem!1)))), s(elem!1)) <=> r(s(s(s(s(elem!1)))), s(z))),
% 1.94/2.19 inference(monotonicity,[status(thm)],[619])).
% 1.94/2.19 tff(3730,plain,
% 1.94/2.19 (r(s(s(s(s(elem!1)))), s(z)) <=> r(s(s(s(s(elem!1)))), s(elem!1))),
% 1.94/2.19 inference(symmetry,[status(thm)],[3729])).
% 1.94/2.19 tff(3731,plain,
% 1.94/2.19 (r(s(s(s(s(elem!1)))), s(elem!1))),
% 1.94/2.19 inference(modus_ponens,[status(thm)],[700, 3730])).
% 1.94/2.19 tff(3732,plain,
% 1.94/2.19 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(elem!1), elem!1)) | (~r(s(s(s(s(elem!1)))), elem!1)) | (~r(elem!1, s(s(s(z))))) | (~r(s(s(s(s(elem!1)))), s(elem!1))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(elem!1), elem!1)) | (~r(s(s(s(s(elem!1)))), elem!1)) | (~r(elem!1, s(s(s(z))))) | (~r(s(s(s(s(elem!1)))), s(elem!1))))),
% 1.94/2.19 inference(rewrite,[status(thm)],[])).
% 1.94/2.19 tff(3733,plain,
% 1.94/2.19 (((~r(elem!1, s(s(s(z))))) | (~r(s(elem!1), elem!1)) | (~r(s(s(s(s(elem!1)))), elem!1)) | (~r(s(s(s(s(elem!1)))), s(elem!1)))) <=> ((~r(s(elem!1), elem!1)) | (~r(s(s(s(s(elem!1)))), elem!1)) | (~r(elem!1, s(s(s(z))))) | (~r(s(s(s(s(elem!1)))), s(elem!1))))),
% 1.94/2.19 inference(rewrite,[status(thm)],[])).
% 1.94/2.19 tff(3734,plain,
% 1.94/2.19 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(s(s(z))))) | (~r(s(elem!1), elem!1)) | (~r(s(s(s(s(elem!1)))), elem!1)) | (~r(s(s(s(s(elem!1)))), s(elem!1))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(elem!1), elem!1)) | (~r(s(s(s(s(elem!1)))), elem!1)) | (~r(elem!1, s(s(s(z))))) | (~r(s(s(s(s(elem!1)))), s(elem!1)))))),
% 1.94/2.19 inference(monotonicity,[status(thm)],[3733])).
% 1.94/2.19 tff(3735,plain,
% 1.94/2.19 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(s(s(z))))) | (~r(s(elem!1), elem!1)) | (~r(s(s(s(s(elem!1)))), elem!1)) | (~r(s(s(s(s(elem!1)))), s(elem!1))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(elem!1), elem!1)) | (~r(s(s(s(s(elem!1)))), elem!1)) | (~r(elem!1, s(s(s(z))))) | (~r(s(s(s(s(elem!1)))), s(elem!1))))),
% 1.94/2.19 inference(transitivity,[status(thm)],[3734, 3732])).
% 1.94/2.19 tff(3736,plain,
% 1.94/2.19 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(s(s(z))))) | (~r(s(elem!1), elem!1)) | (~r(s(s(s(s(elem!1)))), elem!1)) | (~r(s(s(s(s(elem!1)))), s(elem!1))))),
% 1.94/2.19 inference(quant_inst,[status(thm)],[])).
% 1.94/2.19 tff(3737,plain,
% 1.94/2.19 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(elem!1), elem!1)) | (~r(s(s(s(s(elem!1)))), elem!1)) | (~r(elem!1, s(s(s(z))))) | (~r(s(s(s(s(elem!1)))), s(elem!1)))),
% 1.94/2.19 inference(modus_ponens,[status(thm)],[3736, 3735])).
% 1.94/2.19 tff(3738,plain,
% 1.94/2.19 ((~r(s(elem!1), elem!1)) | (~r(s(s(s(s(elem!1)))), elem!1)) | (~r(elem!1, s(s(s(z))))) | (~r(s(s(s(s(elem!1)))), s(elem!1)))),
% 1.94/2.19 inference(unit_resolution,[status(thm)],[3737, 197])).
% 1.94/2.19 tff(3739,plain,
% 1.94/2.19 (~r(s(s(s(s(elem!1)))), elem!1)),
% 1.94/2.19 inference(unit_resolution,[status(thm)],[3738, 3731, 1604, 3728])).
% 1.94/2.19 tff(3740,plain,
% 1.94/2.19 (b(s(s(s(s(elem!1)))), elem!1)),
% 1.94/2.19 inference(unit_resolution,[status(thm)],[719, 3739, 627])).
% 1.94/2.19 tff(3741,plain,
% 1.94/2.19 (r(elem!1, s(s(s(z)))) <=> r(elem!1, s(s(s(elem!1))))),
% 1.94/2.19 inference(monotonicity,[status(thm)],[1086])).
% 1.94/2.19 tff(3742,plain,
% 1.94/2.19 (r(elem!1, s(s(s(elem!1))))),
% 1.94/2.19 inference(modus_ponens,[status(thm)],[1604, 3741])).
% 1.94/2.19 tff(3743,plain,
% 1.94/2.19 (~b(elem!1, s(s(s(s(elem!1)))))),
% 1.94/2.19 inference(unit_resolution,[status(thm)],[2420, 3740, 156, 122, 311, 263, 96, 816, 620, 786])).
% 1.94/2.19 tff(3744,plain,
% 1.94/2.19 (r(elem!1, s(s(s(s(elem!1)))))),
% 1.94/2.19 inference(unit_resolution,[status(thm)],[2427, 3743, 2377])).
% 1.94/2.19 tff(3745,plain,
% 1.94/2.19 (~r(s(s(s(elem!1))), s(s(s(s(elem!1)))))),
% 1.94/2.19 inference(unit_resolution,[status(thm)],[1074, 3744, 3742, 700])).
% 1.94/2.19 tff(3746,plain,
% 1.94/2.19 (b(s(s(s(elem!1))), s(s(s(s(elem!1)))))),
% 1.94/2.19 inference(unit_resolution,[status(thm)],[696, 3745, 3348])).
% 1.94/2.19 tff(3747,plain,
% 1.94/2.19 (~b(s(s(s(s(elem!1)))), s(s(elem!1)))),
% 1.94/2.19 inference(unit_resolution,[status(thm)],[3459, 3746, 463, 839])).
% 1.94/2.19 tff(3748,plain,
% 1.94/2.19 (~b(s(s(s(s(elem!1)))), s(s(z)))),
% 1.94/2.19 inference(modus_ponens,[status(thm)],[3747, 2156])).
% 1.94/2.19 tff(3749,plain,
% 1.94/2.19 (r(s(s(s(s(elem!1)))), s(s(z)))),
% 1.94/2.19 inference(unit_resolution,[status(thm)],[1299, 3748])).
% 1.94/2.19 tff(3750,plain,
% 1.94/2.19 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(z))) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(s(s(s(elem!1)))), elem!1)) | (~b(s(s(s(elem!1))), s(s(s(s(elem!1)))))) | (~b(s(z), s(s(s(s(elem!1)))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(z))) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(s(s(s(elem!1)))), elem!1)) | (~b(s(s(s(elem!1))), s(s(s(s(elem!1)))))) | (~b(s(z), s(s(s(s(elem!1)))))))),
% 1.94/2.19 inference(rewrite,[status(thm)],[])).
% 1.94/2.19 tff(3751,plain,
% 1.94/2.19 (((~b(elem!1, s(z))) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(s(s(s(elem!1)))), elem!1)) | (~b(s(z), s(s(s(s(elem!1)))))) | (~b(s(s(s(elem!1))), s(s(s(s(elem!1)))))) | (~b(s(s(s(elem!1))), s(z)))) <=> ((~b(elem!1, s(z))) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(s(s(s(elem!1)))), elem!1)) | (~b(s(s(s(elem!1))), s(s(s(s(elem!1)))))) | (~b(s(z), s(s(s(s(elem!1)))))))),
% 1.94/2.19 inference(rewrite,[status(thm)],[])).
% 1.94/2.19 tff(3752,plain,
% 1.94/2.19 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(z))) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(s(s(s(elem!1)))), elem!1)) | (~b(s(z), s(s(s(s(elem!1)))))) | (~b(s(s(s(elem!1))), s(s(s(s(elem!1)))))) | (~b(s(s(s(elem!1))), s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(z))) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(s(s(s(elem!1)))), elem!1)) | (~b(s(s(s(elem!1))), s(s(s(s(elem!1)))))) | (~b(s(z), s(s(s(s(elem!1))))))))),
% 1.94/2.19 inference(monotonicity,[status(thm)],[3751])).
% 1.94/2.19 tff(3753,plain,
% 1.94/2.19 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(z))) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(s(s(s(elem!1)))), elem!1)) | (~b(s(z), s(s(s(s(elem!1)))))) | (~b(s(s(s(elem!1))), s(s(s(s(elem!1)))))) | (~b(s(s(s(elem!1))), s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(z))) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(s(s(s(elem!1)))), elem!1)) | (~b(s(s(s(elem!1))), s(s(s(s(elem!1)))))) | (~b(s(z), s(s(s(s(elem!1)))))))),
% 1.94/2.19 inference(transitivity,[status(thm)],[3752, 3750])).
% 1.94/2.19 tff(3754,plain,
% 1.94/2.19 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(z))) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(s(s(s(elem!1)))), elem!1)) | (~b(s(z), s(s(s(s(elem!1)))))) | (~b(s(s(s(elem!1))), s(s(s(s(elem!1)))))) | (~b(s(s(s(elem!1))), s(z))))),
% 1.94/2.19 inference(quant_inst,[status(thm)],[])).
% 1.94/2.19 tff(3755,plain,
% 1.94/2.19 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(z))) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(s(s(s(elem!1)))), elem!1)) | (~b(s(s(s(elem!1))), s(s(s(s(elem!1)))))) | (~b(s(z), s(s(s(s(elem!1))))))),
% 1.94/2.19 inference(modus_ponens,[status(thm)],[3754, 3753])).
% 1.94/2.19 tff(3756,plain,
% 1.94/2.19 ($false),
% 1.94/2.19 inference(unit_resolution,[status(thm)],[3755, 166, 96, 1212, 1327, 1311, 640])).
% 1.94/2.19 tff(3757,plain,((~b(s(z), s(s(s(s(elem!1)))))) | (~b(s(s(s(elem!1))), s(z))) | (~b(elem!1, s(z))) | (~b(s(s(s(elem!1))), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), elem!1))), inference(lemma,lemma(discharge,[]))).
% 1.94/2.19 tff(3758,plain,
% 1.94/2.19 (~b(s(z), s(s(s(s(elem!1)))))),
% 1.94/2.19 inference(unit_resolution,[status(thm)],[3757, 3746, 1212, 96, 3740])).
% 1.94/2.19 tff(3759,plain,
% 1.94/2.19 (r(s(z), s(s(s(s(elem!1)))))),
% 1.94/2.19 inference(unit_resolution,[status(thm)],[681, 3758])).
% 1.94/2.19 tff(3760,plain,
% 1.94/2.19 (~r(s(s(elem!1)), s(s(s(s(elem!1)))))),
% 1.94/2.19 inference(unit_resolution,[status(thm)],[2176, 3759, 311, 3749])).
% 1.94/2.19 tff(3761,plain,
% 1.94/2.19 (b(s(s(elem!1)), s(s(s(s(elem!1)))))),
% 1.94/2.19 inference(unit_resolution,[status(thm)],[827, 3760, 816])).
% 1.94/2.19 tff(3762,plain,
% 1.94/2.19 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(elem!1, s(z))) | (~b(s(s(elem!1)), s(z))) | (~b(s(s(elem!1)), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), elem!1)) | (~b(s(s(s(elem!1))), s(s(s(s(elem!1)))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(elem!1, s(z))) | (~b(s(s(elem!1)), s(z))) | (~b(s(s(elem!1)), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), elem!1)) | (~b(s(s(s(elem!1))), s(s(s(s(elem!1)))))))),
% 1.94/2.19 inference(rewrite,[status(thm)],[])).
% 1.94/2.19 tff(3763,plain,
% 1.94/2.19 (((~b(elem!1, s(z))) | (~b(s(s(elem!1)), s(z))) | (~b(s(s(s(s(elem!1)))), elem!1)) | (~b(s(s(s(elem!1))), s(s(s(s(elem!1)))))) | (~b(s(s(elem!1)), s(s(s(s(elem!1)))))) | (~b(s(s(elem!1)), s(s(s(elem!1)))))) <=> ((~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(elem!1, s(z))) | (~b(s(s(elem!1)), s(z))) | (~b(s(s(elem!1)), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), elem!1)) | (~b(s(s(s(elem!1))), s(s(s(s(elem!1)))))))),
% 1.94/2.19 inference(rewrite,[status(thm)],[])).
% 1.94/2.19 tff(3764,plain,
% 1.94/2.19 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(z))) | (~b(s(s(elem!1)), s(z))) | (~b(s(s(s(s(elem!1)))), elem!1)) | (~b(s(s(s(elem!1))), s(s(s(s(elem!1)))))) | (~b(s(s(elem!1)), s(s(s(s(elem!1)))))) | (~b(s(s(elem!1)), s(s(s(elem!1))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(elem!1, s(z))) | (~b(s(s(elem!1)), s(z))) | (~b(s(s(elem!1)), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), elem!1)) | (~b(s(s(s(elem!1))), s(s(s(s(elem!1))))))))),
% 1.94/2.19 inference(monotonicity,[status(thm)],[3763])).
% 1.94/2.19 tff(3765,plain,
% 1.94/2.19 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(z))) | (~b(s(s(elem!1)), s(z))) | (~b(s(s(s(s(elem!1)))), elem!1)) | (~b(s(s(s(elem!1))), s(s(s(s(elem!1)))))) | (~b(s(s(elem!1)), s(s(s(s(elem!1)))))) | (~b(s(s(elem!1)), s(s(s(elem!1))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(elem!1, s(z))) | (~b(s(s(elem!1)), s(z))) | (~b(s(s(elem!1)), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), elem!1)) | (~b(s(s(s(elem!1))), s(s(s(s(elem!1)))))))),
% 1.94/2.19 inference(transitivity,[status(thm)],[3764, 3762])).
% 1.94/2.19 tff(3766,plain,
% 1.94/2.19 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(z))) | (~b(s(s(elem!1)), s(z))) | (~b(s(s(s(s(elem!1)))), elem!1)) | (~b(s(s(s(elem!1))), s(s(s(s(elem!1)))))) | (~b(s(s(elem!1)), s(s(s(s(elem!1)))))) | (~b(s(s(elem!1)), s(s(s(elem!1))))))),
% 1.94/2.19 inference(quant_inst,[status(thm)],[])).
% 1.94/2.19 tff(3767,plain,
% 1.94/2.19 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(elem!1, s(z))) | (~b(s(s(elem!1)), s(z))) | (~b(s(s(elem!1)), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), elem!1)) | (~b(s(s(s(elem!1))), s(s(s(s(elem!1))))))),
% 1.94/2.19 inference(modus_ponens,[status(thm)],[3766, 3765])).
% 1.94/2.19 tff(3768,plain,
% 1.94/2.19 ($false),
% 1.94/2.19 inference(unit_resolution,[status(thm)],[3767, 166, 463, 1212, 310, 3761, 3746, 3740])).
% 1.94/2.19 tff(3769,plain,((~r(s(s(s(s(elem!1)))), s(z))) | (~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(elem!1, s(z))) | (~b(s(s(elem!1)), s(z))) | (~r(s(z), s(s(elem!1)))) | (~b(s(s(s(elem!1))), s(z))) | (~(s(s(z)) = s(s(elem!1)))) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(s(z)), s(z))) | (~b(s(s(z)), z)) | (~b(s(s(z)), s(s(s(elem!1))))) | (~b(s(s(elem!1)), elem!1)) | (~r(elem!1, s(s(s(z))))) | (~r(s(elem!1), elem!1))), inference(lemma,lemma(discharge,[]))).
% 1.94/2.19 tff(3770,plain,
% 1.94/2.19 (~r(s(s(s(s(elem!1)))), s(z))),
% 1.94/2.19 inference(unit_resolution,[status(thm)],[3769, 3710, 3727, 310, 311, 96, 3679, 3725, 156, 3635, 3705, 3697, 3695, 3691])).
% 1.94/2.19 tff(3771,plain,
% 1.94/2.19 (b(s(s(s(s(elem!1)))), s(z))),
% 1.94/2.19 inference(unit_resolution,[status(thm)],[661, 3770])).
% 1.94/2.19 tff(3772,plain,
% 1.94/2.19 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), elem!1)) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(s(s(elem!1))), elem!1)) | (~b(elem!1, s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(elem!1)), elem!1)) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(s(s(elem!1))), elem!1)) | (~b(elem!1, s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), s(z))))),
% 1.94/2.19 inference(rewrite,[status(thm)],[])).
% 1.94/2.19 tff(3773,plain,
% 1.94/2.19 (((~b(s(s(s(s(elem!1)))), s(z))) | (~b(s(s(s(elem!1))), s(z))) | (~b(elem!1, s(s(s(s(elem!1)))))) | (~b(s(s(elem!1)), elem!1)) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(s(s(elem!1))), s(s(elem!1))))) <=> ((~b(s(s(elem!1)), elem!1)) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(s(s(elem!1))), elem!1)) | (~b(elem!1, s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), s(z))))),
% 1.94/2.19 inference(rewrite,[status(thm)],[])).
% 1.94/2.19 tff(3774,plain,
% 1.94/2.19 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(elem!1)))), s(z))) | (~b(s(s(s(elem!1))), s(z))) | (~b(elem!1, s(s(s(s(elem!1)))))) | (~b(s(s(elem!1)), elem!1)) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(s(s(elem!1))), s(s(elem!1)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), elem!1)) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(s(s(elem!1))), elem!1)) | (~b(elem!1, s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), s(z)))))),
% 1.94/2.19 inference(monotonicity,[status(thm)],[3773])).
% 1.94/2.19 tff(3775,plain,
% 1.94/2.19 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(elem!1)))), s(z))) | (~b(s(s(s(elem!1))), s(z))) | (~b(elem!1, s(s(s(s(elem!1)))))) | (~b(s(s(elem!1)), elem!1)) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(s(s(elem!1))), s(s(elem!1)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(elem!1)), elem!1)) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(s(s(elem!1))), elem!1)) | (~b(elem!1, s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), s(z))))),
% 1.94/2.19 inference(transitivity,[status(thm)],[3774, 3772])).
% 1.94/2.19 tff(3776,plain,
% 1.94/2.19 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(elem!1)))), s(z))) | (~b(s(s(s(elem!1))), s(z))) | (~b(elem!1, s(s(s(s(elem!1)))))) | (~b(s(s(elem!1)), elem!1)) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(s(s(elem!1))), s(s(elem!1)))))),
% 1.94/2.19 inference(quant_inst,[status(thm)],[])).
% 1.94/2.20 tff(3777,plain,
% 1.94/2.20 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(elem!1)), elem!1)) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(s(s(elem!1))), elem!1)) | (~b(elem!1, s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), s(z)))),
% 1.94/2.20 inference(modus_ponens,[status(thm)],[3776, 3775])).
% 1.94/2.20 tff(3778,plain,
% 1.94/2.20 ($false),
% 1.94/2.20 inference(unit_resolution,[status(thm)],[3777, 166, 786, 839, 96, 1402, 641, 1108])).
% 1.94/2.20 tff(3779,plain,((~b(elem!1, s(s(s(s(elem!1)))))) | (~b(s(s(elem!1)), elem!1)) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(s(s(s(elem!1)))), s(z))) | (~b(s(s(s(elem!1))), elem!1))), inference(lemma,lemma(discharge,[]))).
% 1.94/2.20 tff(3780,plain,
% 1.94/2.20 (~b(elem!1, s(s(s(s(elem!1)))))),
% 1.94/2.20 inference(unit_resolution,[status(thm)],[3779, 3697, 3725, 96, 3771, 3686])).
% 1.94/2.20 tff(3781,plain,
% 1.94/2.20 (r(elem!1, s(s(s(s(elem!1)))))),
% 1.94/2.20 inference(unit_resolution,[status(thm)],[2427, 3780, 3685])).
% 1.94/2.20 tff(3782,plain,
% 1.94/2.20 ((s(s(s(s(elem!1)))) = s(s(z))) <=> (s(s(s(s(elem!1)))) = s(s(elem!1)))),
% 1.94/2.20 inference(monotonicity,[status(thm)],[3679])).
% 1.94/2.20 tff(3783,plain,
% 1.94/2.20 ((s(s(s(s(elem!1)))) = s(s(z))) <=> (s(s(elem!1)) = s(s(s(s(elem!1)))))),
% 1.94/2.20 inference(transitivity,[status(thm)],[3782, 123])).
% 1.94/2.20 tff(3784,plain,
% 1.94/2.20 ((s(s(s(s(elem!1)))) = s(s(z))) <=> (s(s(s(s(elem!1)))) = s(s(elem!1)))),
% 1.94/2.20 inference(transitivity,[status(thm)],[3783, 124])).
% 1.94/2.20 tff(3785,plain,
% 1.94/2.20 ((~(s(s(s(s(elem!1)))) = s(s(z)))) <=> (~(s(s(s(s(elem!1)))) = s(s(elem!1))))),
% 1.94/2.20 inference(monotonicity,[status(thm)],[3784])).
% 1.94/2.20 tff(3786,plain,
% 1.94/2.20 (~(s(s(s(s(elem!1)))) = s(s(elem!1)))),
% 1.94/2.20 inference(modus_ponens,[status(thm)],[733, 3785])).
% 1.94/2.20 tff(3787,plain,
% 1.94/2.20 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(z))) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(s(s(s(elem!1)))), s(z))) | (~b(s(z), s(s(s(s(elem!1)))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(z))) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(s(s(s(elem!1)))), s(z))) | (~b(s(z), s(s(s(s(elem!1)))))))),
% 1.94/2.20 inference(rewrite,[status(thm)],[])).
% 1.94/2.20 tff(3788,plain,
% 1.94/2.20 (((~b(s(s(s(s(elem!1)))), s(z))) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(z), s(s(s(s(elem!1)))))) | (~b(elem!1, s(z))) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(s(s(elem!1))), elem!1))) <=> ((~b(elem!1, s(z))) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(s(s(s(elem!1)))), s(z))) | (~b(s(z), s(s(s(s(elem!1)))))))),
% 1.94/2.20 inference(rewrite,[status(thm)],[])).
% 1.94/2.20 tff(3789,plain,
% 1.94/2.20 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(elem!1)))), s(z))) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(z), s(s(s(s(elem!1)))))) | (~b(elem!1, s(z))) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(s(s(elem!1))), elem!1)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(z))) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(s(s(s(elem!1)))), s(z))) | (~b(s(z), s(s(s(s(elem!1))))))))),
% 1.94/2.20 inference(monotonicity,[status(thm)],[3788])).
% 1.94/2.20 tff(3790,plain,
% 1.94/2.20 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(elem!1)))), s(z))) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(z), s(s(s(s(elem!1)))))) | (~b(elem!1, s(z))) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(s(s(elem!1))), elem!1)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(z))) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(s(s(s(elem!1)))), s(z))) | (~b(s(z), s(s(s(s(elem!1)))))))),
% 2.02/2.20 inference(transitivity,[status(thm)],[3789, 3787])).
% 2.02/2.20 tff(3791,plain,
% 2.02/2.20 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(elem!1)))), s(z))) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(z), s(s(s(s(elem!1)))))) | (~b(elem!1, s(z))) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(s(s(elem!1))), elem!1)))),
% 2.02/2.20 inference(quant_inst,[status(thm)],[])).
% 2.02/2.20 tff(3792,plain,
% 2.02/2.20 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(z))) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(s(s(s(elem!1)))), s(z))) | (~b(s(z), s(s(s(s(elem!1))))))),
% 2.02/2.20 inference(modus_ponens,[status(thm)],[3791, 3790])).
% 2.02/2.20 tff(3793,plain,
% 2.02/2.20 ($false),
% 2.02/2.20 inference(unit_resolution,[status(thm)],[3792, 166, 96, 1212, 1402, 1327, 641])).
% 2.02/2.20 tff(3794,plain,((~b(s(z), s(s(s(s(elem!1)))))) | (~b(s(s(s(elem!1))), s(z))) | (~b(elem!1, s(z))) | (~b(s(s(s(s(elem!1)))), s(z))) | (~b(s(s(s(elem!1))), elem!1))), inference(lemma,lemma(discharge,[]))).
% 2.02/2.20 tff(3795,plain,
% 2.02/2.20 (~b(s(z), s(s(s(s(elem!1)))))),
% 2.02/2.20 inference(unit_resolution,[status(thm)],[3794, 3771, 96, 3686, 3727])).
% 2.02/2.20 tff(3796,plain,
% 2.02/2.20 (r(s(z), s(s(s(s(elem!1)))))),
% 2.02/2.20 inference(unit_resolution,[status(thm)],[681, 3795])).
% 2.02/2.20 tff(3797,plain,
% 2.02/2.20 ((s(s(s(elem!1))) = s(s(s(s(elem!1))))) <=> (s(s(s(s(elem!1)))) = s(s(s(elem!1))))),
% 2.02/2.20 inference(symmetry,[status(thm)],[1191])).
% 2.02/2.20 tff(3798,plain,
% 2.02/2.20 ((s(s(s(z))) = s(s(s(s(z))))) <=> (s(s(s(s(elem!1)))) = s(s(s(elem!1))))),
% 2.02/2.20 inference(transitivity,[status(thm)],[3346, 3797])).
% 2.02/2.20 tff(3799,plain,
% 2.02/2.20 ((~(s(s(s(z))) = s(s(s(s(z)))))) <=> (~(s(s(s(s(elem!1)))) = s(s(s(elem!1)))))),
% 2.02/2.20 inference(monotonicity,[status(thm)],[3798])).
% 2.02/2.20 tff(3800,plain,
% 2.02/2.20 (~(s(s(s(s(elem!1)))) = s(s(s(elem!1))))),
% 2.02/2.20 inference(modus_ponens,[status(thm)],[2228, 3799])).
% 2.02/2.20 tff(3801,plain,
% 2.02/2.20 (r(s(s(s(elem!1))), s(s(s(s(elem!1)))))),
% 2.02/2.20 inference(unit_resolution,[status(thm)],[696, 691, 3348])).
% 2.02/2.20 tff(3802,plain,
% 2.02/2.20 (~r(s(s(s(s(elem!1)))), s(s(s(elem!1))))),
% 2.02/2.20 inference(unit_resolution,[status(thm)],[2125, 3801, 119, 699])).
% 2.02/2.20 tff(3803,plain,
% 2.02/2.20 (b(s(s(s(s(elem!1)))), s(s(s(elem!1))))),
% 2.02/2.20 inference(unit_resolution,[status(thm)],[1065, 3802, 3800])).
% 2.02/2.20 tff(3804,plain,
% 2.02/2.20 (~b(s(s(s(s(elem!1)))), s(s(elem!1)))),
% 2.02/2.20 inference(unit_resolution,[status(thm)],[2134, 3803])).
% 2.02/2.20 tff(3805,plain,
% 2.02/2.20 (~b(s(s(s(s(elem!1)))), s(s(z)))),
% 2.02/2.20 inference(modus_ponens,[status(thm)],[3804, 2156])).
% 2.02/2.20 tff(3806,plain,
% 2.02/2.20 (r(s(s(s(s(elem!1)))), s(s(z)))),
% 2.02/2.20 inference(unit_resolution,[status(thm)],[1299, 3805])).
% 2.02/2.20 tff(3807,plain,
% 2.02/2.20 (~r(s(s(s(z))), s(s(s(s(z)))))),
% 2.02/2.20 inference(unit_resolution,[status(thm)],[2217, 3806, 2153, 699, 119])).
% 2.02/2.20 tff(3808,plain,
% 2.02/2.20 (b(s(s(s(z))), s(s(s(s(z)))))),
% 2.02/2.20 inference(unit_resolution,[status(thm)],[2233, 3807])).
% 2.02/2.20 tff(3809,plain,
% 2.02/2.20 (b(s(s(s(elem!1))), s(s(s(s(elem!1)))))),
% 2.02/2.20 inference(modus_ponens,[status(thm)],[3808, 2374])).
% 2.02/2.20 tff(3810,plain,
% 2.02/2.20 ($false),
% 2.02/2.20 inference(unit_resolution,[status(thm)],[691, 3809])).
% 2.02/2.20 tff(3811,plain,(b(s(s(s(elem!1))), s(s(s(s(elem!1))))) | (~(s(s(z)) = s(s(elem!1)))) | (~r(s(z), s(s(s(s(elem!1)))))) | (~r(s(z), s(s(s(elem!1))))) | (~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(s(s(s(elem!1)))), s(z)))), inference(lemma,lemma(discharge,[]))).
% 2.02/2.20 tff(3812,plain,
% 2.02/2.20 (b(s(s(s(elem!1))), s(s(s(s(elem!1)))))),
% 2.02/2.20 inference(unit_resolution,[status(thm)],[3811, 3679, 3796, 3712, 3710, 3725, 96, 3771])).
% 2.02/2.20 tff(3813,plain,
% 2.02/2.20 (~b(s(s(s(s(elem!1)))), s(s(elem!1)))),
% 2.02/2.20 inference(unit_resolution,[status(thm)],[3459, 3812, 3710, 3725])).
% 2.02/2.20 tff(3814,plain,
% 2.02/2.20 (r(s(s(s(s(elem!1)))), s(s(elem!1)))),
% 2.02/2.20 inference(unit_resolution,[status(thm)],[813, 3813, 3786])).
% 2.02/2.20 tff(3815,plain,
% 2.02/2.20 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(s(s(s(elem!1)))))) | (~r(s(z), elem!1)) | (~r(s(z), s(s(s(s(elem!1)))))) | (~r(s(s(s(s(elem!1)))), s(s(elem!1)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(elem!1, s(s(s(s(elem!1)))))) | (~r(s(z), elem!1)) | (~r(s(z), s(s(s(s(elem!1)))))) | (~r(s(s(s(s(elem!1)))), s(s(elem!1)))))),
% 2.02/2.20 inference(rewrite,[status(thm)],[])).
% 2.02/2.20 tff(3816,plain,
% 2.02/2.20 (((~r(s(s(s(s(elem!1)))), s(s(elem!1)))) | (~r(elem!1, s(s(s(s(elem!1)))))) | (~r(s(z), s(s(s(s(elem!1)))))) | (~r(s(z), elem!1))) <=> ((~r(elem!1, s(s(s(s(elem!1)))))) | (~r(s(z), elem!1)) | (~r(s(z), s(s(s(s(elem!1)))))) | (~r(s(s(s(s(elem!1)))), s(s(elem!1)))))),
% 2.02/2.20 inference(rewrite,[status(thm)],[])).
% 2.02/2.20 tff(3817,plain,
% 2.02/2.20 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(elem!1)))), s(s(elem!1)))) | (~r(elem!1, s(s(s(s(elem!1)))))) | (~r(s(z), s(s(s(s(elem!1)))))) | (~r(s(z), elem!1)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(s(s(s(elem!1)))))) | (~r(s(z), elem!1)) | (~r(s(z), s(s(s(s(elem!1)))))) | (~r(s(s(s(s(elem!1)))), s(s(elem!1))))))),
% 2.02/2.20 inference(monotonicity,[status(thm)],[3816])).
% 2.02/2.20 tff(3818,plain,
% 2.02/2.20 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(elem!1)))), s(s(elem!1)))) | (~r(elem!1, s(s(s(s(elem!1)))))) | (~r(s(z), s(s(s(s(elem!1)))))) | (~r(s(z), elem!1)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(elem!1, s(s(s(s(elem!1)))))) | (~r(s(z), elem!1)) | (~r(s(z), s(s(s(s(elem!1)))))) | (~r(s(s(s(s(elem!1)))), s(s(elem!1)))))),
% 2.02/2.20 inference(transitivity,[status(thm)],[3817, 3815])).
% 2.02/2.20 tff(3819,plain,
% 2.02/2.20 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(elem!1)))), s(s(elem!1)))) | (~r(elem!1, s(s(s(s(elem!1)))))) | (~r(s(z), s(s(s(s(elem!1)))))) | (~r(s(z), elem!1)))),
% 2.02/2.20 inference(quant_inst,[status(thm)],[])).
% 2.02/2.20 tff(3820,plain,
% 2.02/2.20 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(elem!1, s(s(s(s(elem!1)))))) | (~r(s(z), elem!1)) | (~r(s(z), s(s(s(s(elem!1)))))) | (~r(s(s(s(s(elem!1)))), s(s(elem!1))))),
% 2.02/2.20 inference(modus_ponens,[status(thm)],[3819, 3818])).
% 2.02/2.20 tff(3821,plain,
% 2.02/2.20 ($false),
% 2.02/2.20 inference(unit_resolution,[status(thm)],[3820, 197, 3715, 3796, 3814, 3781])).
% 2.02/2.20 tff(3822,plain,((~r(s(z), z)) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(s(elem!1)), s(z))) | (~r(s(z), s(s(elem!1)))) | (~b(s(s(z)), s(z))) | (~b(z, s(z))) | (~r(z, s(s(z)))) | (~r(s(z), s(s(z))))), inference(lemma,lemma(discharge,[]))).
% 2.02/2.20 tff(3823,plain,
% 2.02/2.20 (~r(s(z), z)),
% 2.02/2.20 inference(unit_resolution,[status(thm)],[3822, 96, 310, 311, 156, 118, 155, 120])).
% 2.02/2.20 tff(3824,plain,
% 2.02/2.20 (b(s(z), z)),
% 2.02/2.20 inference(unit_resolution,[status(thm)],[230, 3823])).
% 2.02/2.20 tff(3825,plain,
% 2.02/2.20 (s(s(z)) = s(s(elem!1))),
% 2.02/2.20 inference(unit_resolution,[status(thm)],[3500, 3824, 155, 118, 310, 156])).
% 2.02/2.20 tff(3826,plain,
% 2.02/2.20 (s(elem!1) = s(z)),
% 2.02/2.20 inference(unit_resolution,[status(thm)],[43, 3825])).
% 2.02/2.20 tff(3827,plain,
% 2.02/2.20 (z = elem!1),
% 2.02/2.20 inference(unit_resolution,[status(thm)],[30, 3826])).
% 2.02/2.20 tff(3828,plain,
% 2.02/2.20 (b(s(s(s(elem!1))), elem!1)),
% 2.02/2.20 inference(unit_resolution,[status(thm)],[634, 3827, 3506])).
% 2.02/2.20 tff(3829,plain,
% 2.02/2.20 (b(s(z), z) <=> b(s(z), elem!1)),
% 2.02/2.20 inference(monotonicity,[status(thm)],[3827])).
% 2.02/2.20 tff(3830,plain,
% 2.02/2.20 (b(s(z), elem!1)),
% 2.02/2.20 inference(modus_ponens,[status(thm)],[3824, 3829])).
% 2.02/2.20 tff(3831,plain,
% 2.02/2.20 (b(z, s(z)) <=> b(elem!1, s(z))),
% 2.02/2.20 inference(monotonicity,[status(thm)],[3827])).
% 2.02/2.20 tff(3832,plain,
% 2.02/2.20 (b(elem!1, s(z))),
% 2.02/2.20 inference(modus_ponens,[status(thm)],[118, 3831])).
% 2.02/2.20 tff(3833,plain,
% 2.02/2.20 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(z))) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(z), elem!1)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(z))) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(z), elem!1)))),
% 2.02/2.20 inference(rewrite,[status(thm)],[])).
% 2.02/2.20 tff(3834,plain,
% 2.02/2.20 (((~b(s(z), elem!1)) | (~b(s(s(s(elem!1))), elem!1)) | (~b(elem!1, s(z))) | (~b(s(z), elem!1)) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(s(s(elem!1))), s(z)))) <=> ((~b(elem!1, s(z))) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(z), elem!1)))),
% 2.02/2.20 inference(rewrite,[status(thm)],[])).
% 2.02/2.20 tff(3835,plain,
% 2.02/2.20 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), elem!1)) | (~b(s(s(s(elem!1))), elem!1)) | (~b(elem!1, s(z))) | (~b(s(z), elem!1)) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(s(s(elem!1))), s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(z))) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(z), elem!1))))),
% 2.02/2.20 inference(monotonicity,[status(thm)],[3834])).
% 2.02/2.20 tff(3836,plain,
% 2.02/2.20 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), elem!1)) | (~b(s(s(s(elem!1))), elem!1)) | (~b(elem!1, s(z))) | (~b(s(z), elem!1)) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(s(s(elem!1))), s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(z))) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(z), elem!1)))),
% 2.02/2.20 inference(transitivity,[status(thm)],[3835, 3833])).
% 2.02/2.20 tff(3837,plain,
% 2.02/2.20 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), elem!1)) | (~b(s(s(s(elem!1))), elem!1)) | (~b(elem!1, s(z))) | (~b(s(z), elem!1)) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(s(s(elem!1))), s(z))))),
% 2.02/2.20 inference(quant_inst,[status(thm)],[])).
% 2.02/2.20 tff(3838,plain,
% 2.02/2.20 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(z))) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(z), elem!1))),
% 2.02/2.20 inference(modus_ponens,[status(thm)],[3837, 3836])).
% 2.02/2.20 tff(3839,plain,
% 2.02/2.20 ($false),
% 2.02/2.20 inference(unit_resolution,[status(thm)],[3838, 166, 96, 3832, 3830, 3828])).
% 2.02/2.20 tff(3840,plain,((~b(s(s(s(elem!1))), s(z))) | (~b(z, s(z))) | (~r(z, s(s(z)))) | (~b(s(s(elem!1)), s(z))) | (~b(s(s(z)), s(z))) | (~r(s(z), s(s(elem!1)))) | (~r(s(z), s(s(z))))), inference(lemma,lemma(discharge,[]))).
% 2.02/2.20 tff(3841,plain,
% 2.02/2.20 (~b(s(s(s(elem!1))), s(z))),
% 2.02/2.20 inference(unit_resolution,[status(thm)],[3840, 3338, 152, 310, 156, 311, 120])).
% 2.02/2.20 tff(3842,plain,
% 2.02/2.20 (r(s(s(s(elem!1))), s(z))),
% 2.02/2.20 inference(unit_resolution,[status(thm)],[1849, 3841])).
% 2.02/2.20 tff(3843,plain,
% 2.02/2.20 (b(s(s(elem!1)), s(z)) <=> b(s(s(s(elem!1))), s(z))),
% 2.02/2.20 inference(monotonicity,[status(thm)],[334])).
% 2.02/2.20 tff(3844,plain,
% 2.02/2.20 (b(s(s(s(elem!1))), s(z)) <=> b(s(s(elem!1)), s(z))),
% 2.02/2.20 inference(symmetry,[status(thm)],[3843])).
% 2.02/2.20 tff(3845,plain,
% 2.02/2.20 ((~b(s(s(s(elem!1))), s(z))) <=> (~b(s(s(elem!1)), s(z)))),
% 2.02/2.20 inference(monotonicity,[status(thm)],[3844])).
% 2.02/2.20 tff(3846,assumption,(~b(s(s(s(elem!1))), s(z))), introduced(assumption)).
% 2.02/2.20 tff(3847,plain,
% 2.02/2.20 (~b(s(s(elem!1)), s(z))),
% 2.02/2.20 inference(modus_ponens,[status(thm)],[3846, 3845])).
% 2.02/2.20 tff(3848,plain,
% 2.02/2.20 ($false),
% 2.02/2.20 inference(unit_resolution,[status(thm)],[310, 3847])).
% 2.02/2.20 tff(3849,plain,((~(s(s(elem!1)) = s(s(s(elem!1))))) | (~b(s(s(elem!1)), s(z))) | b(s(s(s(elem!1))), s(z))), inference(lemma,lemma(discharge,[]))).
% 2.02/2.20 tff(3850,plain,
% 2.02/2.20 (~(s(s(elem!1)) = s(s(s(elem!1))))),
% 2.02/2.20 inference(unit_resolution,[status(thm)],[3849, 3841, 310])).
% 2.02/2.20 tff(3851,plain,
% 2.02/2.20 (~r(s(s(s(elem!1))), z)),
% 2.02/2.20 inference(unit_resolution,[status(thm)],[3504, 3338, 152, 310, 156, 311, 120])).
% 2.02/2.20 tff(3852,plain,
% 2.02/2.20 (b(s(s(s(elem!1))), z)),
% 2.02/2.20 inference(unit_resolution,[status(thm)],[94, 3851])).
% 2.02/2.20 tff(3853,plain,
% 2.02/2.20 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), z)) | (~b(z, s(z))) | (~b(s(s(z)), z)) | (~b(s(s(z)), s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), z)) | (~b(z, s(z))) | (~b(s(s(z)), z)) | (~b(s(s(z)), s(z))))),
% 2.02/2.20 inference(rewrite,[status(thm)],[])).
% 2.02/2.20 tff(3854,plain,
% 2.02/2.20 (((~b(s(s(s(elem!1))), z)) | (~b(s(s(z)), z)) | (~b(s(z), s(s(s(elem!1))))) | (~b(z, s(z))) | (~b(s(s(z)), s(z))) | (~b(s(s(z)), z))) <=> ((~b(s(z), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), z)) | (~b(z, s(z))) | (~b(s(s(z)), z)) | (~b(s(s(z)), s(z))))),
% 2.02/2.20 inference(rewrite,[status(thm)],[])).
% 2.02/2.20 tff(3855,plain,
% 2.02/2.20 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), z)) | (~b(s(s(z)), z)) | (~b(s(z), s(s(s(elem!1))))) | (~b(z, s(z))) | (~b(s(s(z)), s(z))) | (~b(s(s(z)), z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), z)) | (~b(z, s(z))) | (~b(s(s(z)), z)) | (~b(s(s(z)), s(z)))))),
% 2.02/2.20 inference(monotonicity,[status(thm)],[3854])).
% 2.02/2.20 tff(3856,plain,
% 2.02/2.20 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), z)) | (~b(s(s(z)), z)) | (~b(s(z), s(s(s(elem!1))))) | (~b(z, s(z))) | (~b(s(s(z)), s(z))) | (~b(s(s(z)), z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), z)) | (~b(z, s(z))) | (~b(s(s(z)), z)) | (~b(s(s(z)), s(z))))),
% 2.02/2.20 inference(transitivity,[status(thm)],[3855, 3853])).
% 2.02/2.20 tff(3857,plain,
% 2.02/2.20 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), z)) | (~b(s(s(z)), z)) | (~b(s(z), s(s(s(elem!1))))) | (~b(z, s(z))) | (~b(s(s(z)), s(z))) | (~b(s(s(z)), z)))),
% 2.02/2.20 inference(quant_inst,[status(thm)],[])).
% 2.02/2.20 tff(3858,plain,
% 2.02/2.20 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), z)) | (~b(z, s(z))) | (~b(s(s(z)), z)) | (~b(s(s(z)), s(z)))),
% 2.02/2.20 inference(modus_ponens,[status(thm)],[3857, 3856])).
% 2.02/2.20 tff(3859,plain,
% 2.02/2.20 ($false),
% 2.02/2.20 inference(unit_resolution,[status(thm)],[3858, 166, 241, 118, 121, 156, 122])).
% 2.02/2.20 tff(3860,plain,((~b(s(z), s(s(s(elem!1))))) | (~b(z, s(z))) | (~b(s(s(s(elem!1))), z)) | (~b(s(s(z)), s(z))) | (~b(s(s(z)), z))), inference(lemma,lemma(discharge,[]))).
% 2.02/2.20 tff(3861,plain,
% 2.02/2.20 (~b(s(z), s(s(s(elem!1))))),
% 2.02/2.20 inference(unit_resolution,[status(thm)],[3860, 3635, 121, 156, 118])).
% 2.02/2.20 tff(3862,plain,
% 2.02/2.20 (r(s(z), s(s(s(elem!1))))),
% 2.02/2.20 inference(unit_resolution,[status(thm)],[116, 3861])).
% 2.02/2.20 tff(3863,plain,
% 2.02/2.20 (~r(s(s(elem!1)), s(s(s(elem!1))))),
% 2.02/2.20 inference(unit_resolution,[status(thm)],[764, 3862, 350, 311])).
% 2.02/2.20 tff(3864,plain,
% 2.02/2.20 (b(s(s(elem!1)), s(s(s(elem!1))))),
% 2.02/2.20 inference(unit_resolution,[status(thm)],[461, 3863, 45])).
% 2.02/2.20 tff(3865,plain,
% 2.02/2.20 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), s(z))) | (~r(s(z), z)) | (~r(s(z), s(s(s(elem!1))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), s(z))) | (~r(s(z), z)) | (~r(s(z), s(s(s(elem!1))))))),
% 2.02/2.20 inference(rewrite,[status(thm)],[])).
% 2.02/2.21 tff(3866,plain,
% 2.02/2.21 (((~r(s(s(s(elem!1))), s(z))) | (~r(z, s(s(s(elem!1))))) | (~r(s(z), s(s(s(elem!1))))) | (~r(s(z), z))) <=> ((~r(z, s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), s(z))) | (~r(s(z), z)) | (~r(s(z), s(s(s(elem!1))))))),
% 2.02/2.21 inference(rewrite,[status(thm)],[])).
% 2.02/2.21 tff(3867,plain,
% 2.02/2.21 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), s(z))) | (~r(z, s(s(s(elem!1))))) | (~r(s(z), s(s(s(elem!1))))) | (~r(s(z), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), s(z))) | (~r(s(z), z)) | (~r(s(z), s(s(s(elem!1)))))))),
% 2.02/2.21 inference(monotonicity,[status(thm)],[3866])).
% 2.02/2.21 tff(3868,plain,
% 2.02/2.21 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), s(z))) | (~r(z, s(s(s(elem!1))))) | (~r(s(z), s(s(s(elem!1))))) | (~r(s(z), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), s(z))) | (~r(s(z), z)) | (~r(s(z), s(s(s(elem!1))))))),
% 2.02/2.21 inference(transitivity,[status(thm)],[3867, 3865])).
% 2.02/2.21 tff(3869,plain,
% 2.02/2.21 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), s(z))) | (~r(z, s(s(s(elem!1))))) | (~r(s(z), s(s(s(elem!1))))) | (~r(s(z), z)))),
% 2.02/2.21 inference(quant_inst,[status(thm)],[])).
% 2.02/2.21 tff(3870,plain,
% 2.02/2.21 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), s(z))) | (~r(s(z), z)) | (~r(s(z), s(s(s(elem!1)))))),
% 2.02/2.21 inference(modus_ponens,[status(thm)],[3869, 3868])).
% 2.02/2.21 tff(3871,plain,
% 2.02/2.21 ($false),
% 2.02/2.21 inference(unit_resolution,[status(thm)],[3870, 197, 350, 97, 119, 282])).
% 2.02/2.21 tff(3872,plain,((~r(z, s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), s(z))) | (~r(s(z), z)) | (~r(s(z), s(s(s(elem!1)))))), inference(lemma,lemma(discharge,[]))).
% 2.02/2.21 tff(3873,plain,
% 2.02/2.21 (~r(z, s(s(s(elem!1))))),
% 2.02/2.21 inference(unit_resolution,[status(thm)],[3872, 3862, 350, 97])).
% 2.02/2.21 tff(3874,plain,
% 2.02/2.21 (b(z, s(s(s(elem!1))))),
% 2.02/2.21 inference(unit_resolution,[status(thm)],[261, 3873])).
% 2.02/2.21 tff(3875,plain,
% 2.02/2.21 ($false),
% 2.02/2.21 inference(unit_resolution,[status(thm)],[600, 3874, 3864, 121, 3532])).
% 2.02/2.21 tff(3876,plain,((~r(s(z), z)) | (~b(s(s(s(elem!1))), z)) | (s(s(elem!1)) = s(s(s(elem!1)))) | (~r(s(s(s(elem!1))), s(z))) | (~r(s(z), s(s(elem!1)))) | (~b(s(s(z)), s(z))) | (~b(z, s(z))) | (~r(z, s(s(z)))) | (~r(s(z), s(s(z))))), inference(lemma,lemma(discharge,[]))).
% 2.02/2.21 tff(3877,plain,
% 2.02/2.21 (~r(s(z), z)),
% 2.02/2.21 inference(unit_resolution,[status(thm)],[3876, 3852, 3850, 3842, 311, 156, 3338, 152, 120])).
% 2.02/2.21 tff(3878,plain,
% 2.02/2.21 (b(s(z), z)),
% 2.02/2.21 inference(unit_resolution,[status(thm)],[230, 3877])).
% 2.02/2.21 tff(3879,plain,
% 2.02/2.21 (s(s(z)) = s(s(elem!1))),
% 2.02/2.21 inference(unit_resolution,[status(thm)],[3500, 3878, 152, 3338, 310, 156])).
% 2.02/2.21 tff(3880,plain,
% 2.02/2.21 ((s(s(s(s(elem!1)))) = s(s(z))) <=> (s(s(s(s(elem!1)))) = s(s(elem!1)))),
% 2.02/2.21 inference(monotonicity,[status(thm)],[3879])).
% 2.02/2.21 tff(3881,plain,
% 2.02/2.21 ((s(s(s(s(elem!1)))) = s(s(z))) <=> (s(s(elem!1)) = s(s(s(s(elem!1)))))),
% 2.02/2.21 inference(transitivity,[status(thm)],[3880, 123])).
% 2.02/2.21 tff(3882,plain,
% 2.02/2.21 ((s(s(s(s(elem!1)))) = s(s(z))) <=> (s(s(s(s(elem!1)))) = s(s(elem!1)))),
% 2.02/2.21 inference(transitivity,[status(thm)],[3881, 124])).
% 2.02/2.21 tff(3883,plain,
% 2.02/2.21 ((~(s(s(s(s(elem!1)))) = s(s(z)))) <=> (~(s(s(s(s(elem!1)))) = s(s(elem!1))))),
% 2.02/2.21 inference(monotonicity,[status(thm)],[3882])).
% 2.02/2.21 tff(3884,plain,
% 2.02/2.21 (~(s(s(s(s(elem!1)))) = s(s(elem!1)))),
% 2.02/2.21 inference(modus_ponens,[status(thm)],[733, 3883])).
% 2.02/2.21 tff(3885,plain,
% 2.02/2.21 (s(elem!1) = s(z)),
% 2.02/2.21 inference(unit_resolution,[status(thm)],[43, 3879])).
% 2.02/2.21 tff(3886,plain,
% 2.02/2.21 (z = elem!1),
% 2.02/2.21 inference(unit_resolution,[status(thm)],[30, 3885])).
% 2.02/2.21 tff(3887,plain,
% 2.02/2.21 (r(z, s(s(elem!1))) <=> r(elem!1, s(s(elem!1)))),
% 2.02/2.21 inference(monotonicity,[status(thm)],[3886])).
% 2.02/2.21 tff(3888,plain,
% 2.02/2.21 (~b(z, s(s(elem!1)))),
% 2.02/2.21 inference(unit_resolution,[status(thm)],[3358, 3878, 310, 3338])).
% 2.02/2.21 tff(3889,plain,
% 2.02/2.21 (r(z, s(s(elem!1)))),
% 2.02/2.21 inference(unit_resolution,[status(thm)],[1795, 3888])).
% 2.02/2.21 tff(3890,plain,
% 2.02/2.21 (r(elem!1, s(s(elem!1)))),
% 2.02/2.21 inference(modus_ponens,[status(thm)],[3889, 3887])).
% 2.02/2.21 tff(3891,plain,
% 2.02/2.21 (r(s(s(elem!1)), z) <=> r(s(s(elem!1)), elem!1)),
% 2.02/2.21 inference(monotonicity,[status(thm)],[3886])).
% 2.02/2.21 tff(3892,plain,
% 2.02/2.21 (r(s(s(z)), z) <=> r(s(s(elem!1)), z)),
% 2.02/2.21 inference(monotonicity,[status(thm)],[3879])).
% 2.02/2.21 tff(3893,plain,
% 2.02/2.21 (~b(s(s(z)), z)),
% 2.02/2.21 inference(unit_resolution,[status(thm)],[181, 3878, 156, 3338])).
% 2.02/2.21 tff(3894,plain,
% 2.02/2.21 (r(s(s(z)), z)),
% 2.02/2.21 inference(unit_resolution,[status(thm)],[186, 3893])).
% 2.02/2.21 tff(3895,plain,
% 2.02/2.21 (r(s(s(elem!1)), z)),
% 2.02/2.21 inference(modus_ponens,[status(thm)],[3894, 3892])).
% 2.02/2.21 tff(3896,plain,
% 2.02/2.21 (r(s(s(elem!1)), elem!1)),
% 2.02/2.21 inference(modus_ponens,[status(thm)],[3895, 3891])).
% 2.02/2.21 tff(3897,plain,
% 2.02/2.21 ((s(s(s(s(elem!1)))) = z) <=> (s(s(s(s(elem!1)))) = elem!1)),
% 2.02/2.21 inference(monotonicity,[status(thm)],[3886])).
% 2.02/2.21 tff(3898,plain,
% 2.02/2.21 ((s(s(s(s(elem!1)))) = z) <=> (elem!1 = s(s(s(s(elem!1)))))),
% 2.02/2.21 inference(transitivity,[status(thm)],[3897, 2287])).
% 2.02/2.21 tff(3899,plain,
% 2.02/2.21 ((~(s(s(s(s(elem!1)))) = z)) <=> (~(elem!1 = s(s(s(s(elem!1))))))),
% 2.02/2.21 inference(monotonicity,[status(thm)],[3898])).
% 2.02/2.21 tff(3900,plain,
% 2.02/2.21 (~(elem!1 = s(s(s(s(elem!1)))))),
% 2.02/2.21 inference(modus_ponens,[status(thm)],[626, 3899])).
% 2.02/2.21 tff(3901,plain,
% 2.02/2.21 (b(z, s(z)) <=> b(elem!1, s(z))),
% 2.02/2.21 inference(monotonicity,[status(thm)],[3886])).
% 2.02/2.21 tff(3902,plain,
% 2.02/2.21 (b(elem!1, s(z))),
% 2.02/2.21 inference(modus_ponens,[status(thm)],[3338, 3901])).
% 2.02/2.21 tff(3903,plain,
% 2.02/2.21 (b(s(z), z) <=> b(s(z), elem!1)),
% 2.02/2.21 inference(monotonicity,[status(thm)],[3886])).
% 2.02/2.21 tff(3904,plain,
% 2.02/2.21 (b(s(z), elem!1)),
% 2.02/2.21 inference(modus_ponens,[status(thm)],[3878, 3903])).
% 2.02/2.21 tff(3905,plain,
% 2.02/2.21 (~r(s(s(s(s(elem!1)))), s(s(elem!1)))),
% 2.02/2.21 inference(unit_resolution,[status(thm)],[3432, 3904, 3902, 3900, 3896, 3890, 311])).
% 2.02/2.21 tff(3906,plain,
% 2.02/2.21 (b(s(s(s(s(elem!1)))), s(s(elem!1)))),
% 2.02/2.21 inference(unit_resolution,[status(thm)],[813, 3905, 3884])).
% 2.02/2.21 tff(3907,plain,
% 2.02/2.21 (~(s(s(s(elem!1))) = s(s(s(s(elem!1)))))),
% 2.02/2.21 inference(unit_resolution,[status(thm)],[357, 3850])).
% 2.02/2.21 tff(3908,plain,
% 2.02/2.21 (~(s(s(s(elem!1))) = s(s(elem!1)))),
% 2.02/2.21 inference(unit_resolution,[status(thm)],[50, 3850])).
% 2.02/2.21 tff(3909,plain,
% 2.02/2.21 (~r(s(s(s(elem!1))), s(s(z)))),
% 2.02/2.21 inference(unit_resolution,[status(thm)],[874, 3894, 3842, 120])).
% 2.02/2.21 tff(3910,plain,
% 2.02/2.21 (~r(s(s(s(elem!1))), s(s(elem!1)))),
% 2.02/2.21 inference(unit_resolution,[status(thm)],[3454, 3909, 3879])).
% 2.02/2.21 tff(3911,plain,
% 2.02/2.21 (b(s(s(s(elem!1))), s(s(elem!1)))),
% 2.02/2.21 inference(unit_resolution,[status(thm)],[889, 3910, 3908])).
% 2.02/2.21 tff(3912,plain,
% 2.02/2.21 (b(s(s(s(elem!1))), elem!1)),
% 2.02/2.21 inference(unit_resolution,[status(thm)],[634, 3886, 3852])).
% 2.02/2.21 tff(3913,plain,
% 2.02/2.21 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(z))) | (~b(s(z), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(z), elem!1)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(z))) | (~b(s(z), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(z), elem!1)))),
% 2.02/2.21 inference(rewrite,[status(thm)],[])).
% 2.02/2.21 tff(3914,plain,
% 2.02/2.21 (((~b(s(z), elem!1)) | (~b(s(z), elem!1)) | (~b(elem!1, s(z))) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(z), elem!1)) | (~b(s(z), s(s(s(elem!1)))))) <=> ((~b(elem!1, s(z))) | (~b(s(z), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(z), elem!1)))),
% 2.02/2.21 inference(rewrite,[status(thm)],[])).
% 2.02/2.21 tff(3915,plain,
% 2.02/2.21 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), elem!1)) | (~b(s(z), elem!1)) | (~b(elem!1, s(z))) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(z), elem!1)) | (~b(s(z), s(s(s(elem!1))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(z))) | (~b(s(z), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(z), elem!1))))),
% 2.02/2.21 inference(monotonicity,[status(thm)],[3914])).
% 2.02/2.21 tff(3916,plain,
% 2.02/2.21 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), elem!1)) | (~b(s(z), elem!1)) | (~b(elem!1, s(z))) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(z), elem!1)) | (~b(s(z), s(s(s(elem!1))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(z))) | (~b(s(z), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(z), elem!1)))),
% 2.02/2.21 inference(transitivity,[status(thm)],[3915, 3913])).
% 2.02/2.21 tff(3917,plain,
% 2.02/2.21 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), elem!1)) | (~b(s(z), elem!1)) | (~b(elem!1, s(z))) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(z), elem!1)) | (~b(s(z), s(s(s(elem!1))))))),
% 2.02/2.21 inference(quant_inst,[status(thm)],[])).
% 2.02/2.21 tff(3918,plain,
% 2.02/2.21 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(z))) | (~b(s(z), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(z), elem!1))),
% 2.02/2.21 inference(modus_ponens,[status(thm)],[3917, 3916])).
% 2.02/2.21 tff(3919,plain,
% 2.02/2.21 (~b(s(z), s(s(s(elem!1))))),
% 2.02/2.21 inference(unit_resolution,[status(thm)],[3918, 166, 3902, 3904, 3912])).
% 2.02/2.21 tff(3920,plain,
% 2.02/2.21 (r(s(z), s(s(s(elem!1))))),
% 2.02/2.21 inference(unit_resolution,[status(thm)],[116, 3919])).
% 2.02/2.21 tff(3921,plain,
% 2.02/2.21 (~r(s(s(elem!1)), s(s(s(elem!1))))),
% 2.02/2.21 inference(unit_resolution,[status(thm)],[764, 3920, 3842, 311])).
% 2.02/2.21 tff(3922,plain,
% 2.02/2.21 (b(s(s(elem!1)), s(s(s(elem!1))))),
% 2.02/2.21 inference(unit_resolution,[status(thm)],[461, 3921, 3850])).
% 2.02/2.21 tff(3923,plain,
% 2.02/2.21 (~b(s(s(s(elem!1))), s(s(s(s(elem!1)))))),
% 2.02/2.21 inference(unit_resolution,[status(thm)],[3459, 3922, 3906, 3911])).
% 2.02/2.21 tff(3924,plain,
% 2.02/2.21 (r(s(s(s(elem!1))), s(s(s(s(elem!1)))))),
% 2.02/2.21 inference(unit_resolution,[status(thm)],[696, 3923, 3907])).
% 2.02/2.21 tff(3925,plain,
% 2.02/2.21 (~r(s(s(s(s(elem!1)))), s(z))),
% 2.02/2.21 inference(unit_resolution,[status(thm)],[3469, 3924, 3842, 311])).
% 2.02/2.21 tff(3926,plain,
% 2.02/2.21 (b(s(s(s(s(elem!1)))), s(z))),
% 2.02/2.21 inference(unit_resolution,[status(thm)],[661, 3925])).
% 2.02/2.21 tff(3927,plain,
% 2.02/2.21 ($false),
% 2.02/2.21 inference(unit_resolution,[status(thm)],[3477, 166, 3902, 310, 3904, 3926, 3906])).
% 2.02/2.21 tff(3928,plain,((~b(s(s(z)), s(z))) | (~b(s(s(elem!1)), s(z))) | (~r(s(z), s(s(elem!1)))) | (~r(s(z), s(s(z)))) | b(z, s(s(z)))), inference(lemma,lemma(discharge,[]))).
% 2.02/2.21 tff(3929,plain,
% 2.02/2.21 (~b(s(s(z)), s(z))),
% 2.02/2.21 inference(unit_resolution,[status(thm)],[3928, 120, 311, 310, 125])).
% 2.02/2.21 tff(3930,plain,
% 2.02/2.21 (r(s(s(z)), s(z))),
% 2.02/2.21 inference(unit_resolution,[status(thm)],[308, 3929])).
% 2.02/2.21 tff(3931,plain,
% 2.02/2.21 (~r(z, s(z))),
% 2.02/2.21 inference(unit_resolution,[status(thm)],[553, 3930, 120, 152])).
% 2.02/2.21 tff(3932,plain,
% 2.02/2.21 (b(z, s(z))),
% 2.02/2.21 inference(unit_resolution,[status(thm)],[321, 3931])).
% 2.02/2.21 tff(3933,plain,
% 2.02/2.21 (b(s(s(z)), s(z)) <=> b(s(s(elem!1)), s(z))),
% 2.02/2.21 inference(monotonicity,[status(thm)],[34])).
% 2.02/2.21 tff(3934,plain,
% 2.02/2.21 (b(s(s(elem!1)), s(z)) <=> b(s(s(z)), s(z))),
% 2.02/2.21 inference(symmetry,[status(thm)],[3933])).
% 2.02/2.21 tff(3935,plain,
% 2.02/2.21 (b(s(s(z)), s(z))),
% 2.02/2.21 inference(modus_ponens,[status(thm)],[310, 3934])).
% 2.02/2.21 tff(3936,assumption,(~b(s(s(z)), s(z))), introduced(assumption)).
% 2.02/2.21 tff(3937,plain,
% 2.02/2.21 ($false),
% 2.02/2.21 inference(unit_resolution,[status(thm)],[3936, 3935])).
% 2.02/2.21 tff(3938,plain,((~(s(s(z)) = s(s(elem!1)))) | b(s(s(z)), s(z)) | (~b(s(s(elem!1)), s(z)))), inference(lemma,lemma(discharge,[]))).
% 2.02/2.21 tff(3939,plain,
% 2.02/2.21 (~(s(s(z)) = s(s(elem!1)))),
% 2.02/2.21 inference(unit_resolution,[status(thm)],[3938, 3929, 310])).
% 2.02/2.21 tff(3940,plain,
% 2.02/2.21 (~r(z, s(z))),
% 2.02/2.21 inference(unit_resolution,[status(thm)],[553, 392, 120, 155])).
% 2.02/2.21 tff(3941,plain,
% 2.02/2.21 (b(z, s(z))),
% 2.02/2.21 inference(unit_resolution,[status(thm)],[321, 3940])).
% 2.02/2.21 tff(3942,plain,
% 2.02/2.21 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), z)) | (~r(s(s(z)), s(z))) | (~r(s(z), s(s(z)))) | (~r(z, s(s(z)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(z), z)) | (~r(s(s(z)), s(z))) | (~r(s(z), s(s(z)))) | (~r(z, s(s(z)))))),
% 2.02/2.21 inference(rewrite,[status(thm)],[])).
% 2.02/2.21 tff(3943,plain,
% 2.02/2.21 (((~r(s(s(z)), s(z))) | (~r(z, s(s(z)))) | (~r(s(z), s(s(z)))) | (~r(s(z), z))) <=> ((~r(s(z), z)) | (~r(s(s(z)), s(z))) | (~r(s(z), s(s(z)))) | (~r(z, s(s(z)))))),
% 2.02/2.21 inference(rewrite,[status(thm)],[])).
% 2.02/2.21 tff(3944,plain,
% 2.02/2.21 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(z)), s(z))) | (~r(z, s(s(z)))) | (~r(s(z), s(s(z)))) | (~r(s(z), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), z)) | (~r(s(s(z)), s(z))) | (~r(s(z), s(s(z)))) | (~r(z, s(s(z))))))),
% 2.02/2.21 inference(monotonicity,[status(thm)],[3943])).
% 2.02/2.21 tff(3945,plain,
% 2.02/2.21 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(z)), s(z))) | (~r(z, s(s(z)))) | (~r(s(z), s(s(z)))) | (~r(s(z), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(z), z)) | (~r(s(s(z)), s(z))) | (~r(s(z), s(s(z)))) | (~r(z, s(s(z)))))),
% 2.02/2.21 inference(transitivity,[status(thm)],[3944, 3942])).
% 2.02/2.21 tff(3946,plain,
% 2.02/2.21 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(z)), s(z))) | (~r(z, s(s(z)))) | (~r(s(z), s(s(z)))) | (~r(s(z), z)))),
% 2.02/2.21 inference(quant_inst,[status(thm)],[])).
% 2.02/2.21 tff(3947,plain,
% 2.02/2.21 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(z), z)) | (~r(s(s(z)), s(z))) | (~r(s(z), s(s(z)))) | (~r(z, s(s(z))))),
% 2.02/2.21 inference(modus_ponens,[status(thm)],[3946, 3945])).
% 2.02/2.21 tff(3948,plain,
% 2.02/2.21 (~r(s(z), z)),
% 2.02/2.21 inference(unit_resolution,[status(thm)],[3947, 197, 120, 155, 392])).
% 2.02/2.21 tff(3949,plain,
% 2.02/2.21 (b(s(z), z)),
% 2.02/2.21 inference(unit_resolution,[status(thm)],[230, 3948])).
% 2.02/2.21 tff(3950,plain,
% 2.02/2.21 (~b(z, s(s(elem!1)))),
% 2.02/2.21 inference(unit_resolution,[status(thm)],[3358, 3949, 310, 3941])).
% 2.02/2.21 tff(3951,plain,
% 2.02/2.21 (r(z, s(s(elem!1)))),
% 2.02/2.21 inference(unit_resolution,[status(thm)],[1795, 3950])).
% 2.02/2.21 tff(3952,plain,
% 2.02/2.21 (~r(s(s(elem!1)), s(s(z)))),
% 2.02/2.21 inference(unit_resolution,[status(thm)],[401, 3951, 155, 392])).
% 2.02/2.21 tff(3953,plain,
% 2.02/2.21 (r(s(s(s(elem!1))), s(z))),
% 2.02/2.21 inference(unit_resolution,[status(thm)],[1849, 3846])).
% 2.02/2.21 tff(3954,plain,
% 2.02/2.21 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(s(elem!1)))) | (~r(s(s(s(elem!1))), s(z))) | (~r(s(s(z)), s(z))) | (~r(s(s(z)), s(s(s(elem!1))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(z), s(s(elem!1)))) | (~r(s(s(s(elem!1))), s(z))) | (~r(s(s(z)), s(z))) | (~r(s(s(z)), s(s(s(elem!1))))))),
% 2.02/2.21 inference(rewrite,[status(thm)],[])).
% 2.02/2.21 tff(3955,plain,
% 2.02/2.21 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(s(elem!1)))) | (~r(s(s(s(elem!1))), s(z))) | (~r(s(s(z)), s(z))) | (~r(s(s(z)), s(s(s(elem!1))))))),
% 2.02/2.21 inference(quant_inst,[status(thm)],[])).
% 2.02/2.21 tff(3956,plain,
% 2.02/2.21 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(z), s(s(elem!1)))) | (~r(s(s(s(elem!1))), s(z))) | (~r(s(s(z)), s(z))) | (~r(s(s(z)), s(s(s(elem!1)))))),
% 2.02/2.21 inference(modus_ponens,[status(thm)],[3955, 3954])).
% 2.02/2.21 tff(3957,plain,
% 2.02/2.21 ($false),
% 2.02/2.21 inference(unit_resolution,[status(thm)],[3956, 197, 311, 350, 392, 281])).
% 2.02/2.21 tff(3958,plain,((~r(s(s(s(elem!1))), s(z))) | (~r(s(z), s(s(elem!1)))) | (~r(s(s(z)), s(z))) | (~r(s(s(z)), s(s(s(elem!1)))))), inference(lemma,lemma(discharge,[]))).
% 2.02/2.21 tff(3959,plain,
% 2.02/2.21 (~r(s(s(z)), s(s(s(elem!1))))),
% 2.02/2.21 inference(unit_resolution,[status(thm)],[3958, 3953, 392, 311])).
% 2.02/2.21 tff(3960,plain,
% 2.02/2.21 (~r(s(s(s(elem!1))), s(s(z)))),
% 2.02/2.21 inference(unit_resolution,[status(thm)],[483, 3953, 392, 120])).
% 2.02/2.21 tff(3961,plain,
% 2.02/2.21 (~(s(s(elem!1)) = s(s(s(elem!1))))),
% 2.02/2.21 inference(unit_resolution,[status(thm)],[3849, 3846, 310])).
% 2.02/2.21 tff(3962,plain,
% 2.02/2.21 (b(s(s(s(elem!1))), s(s(z)))),
% 2.02/2.21 inference(unit_resolution,[status(thm)],[218, 213])).
% 2.02/2.21 tff(3963,assumption,(~r(s(s(elem!1)), s(s(z)))), introduced(assumption)).
% 2.02/2.21 tff(3964,plain,
% 2.02/2.21 (b(s(s(elem!1)), s(s(z)))),
% 2.02/2.21 inference(unit_resolution,[status(thm)],[441, 132, 3963])).
% 2.02/2.21 tff(3965,plain,
% 2.02/2.21 (~b(s(s(elem!1)), s(s(s(elem!1))))),
% 2.02/2.21 inference(unit_resolution,[status(thm)],[501, 3964, 213, 273])).
% 2.02/2.21 tff(3966,plain,
% 2.02/2.21 (r(s(s(elem!1)), s(s(s(elem!1))))),
% 2.02/2.21 inference(unit_resolution,[status(thm)],[461, 3965, 45])).
% 2.02/2.21 tff(3967,plain,
% 2.02/2.21 (~r(s(s(z)), s(s(elem!1)))),
% 2.02/2.21 inference(unit_resolution,[status(thm)],[385, 3966, 155, 365])).
% 2.02/2.21 tff(3968,plain,
% 2.02/2.21 (b(s(s(z)), s(s(elem!1)))),
% 2.02/2.21 inference(unit_resolution,[status(thm)],[390, 3967, 52])).
% 2.02/2.21 tff(3969,plain,
% 2.02/2.21 (~r(s(s(s(elem!1))), s(s(elem!1)))),
% 2.02/2.21 inference(unit_resolution,[status(thm)],[2627, 3966, 350, 311])).
% 2.02/2.21 tff(3970,plain,
% 2.02/2.21 (b(s(s(s(elem!1))), s(s(elem!1)))),
% 2.02/2.21 inference(unit_resolution,[status(thm)],[889, 3969, 51])).
% 2.02/2.21 tff(3971,plain,
% 2.02/2.21 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(s(s(elem!1))), s(s(z)))) | (~b(s(s(elem!1)), s(s(z)))) | (~b(s(s(z)), s(s(elem!1)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(s(s(elem!1))), s(s(z)))) | (~b(s(s(elem!1)), s(s(z)))) | (~b(s(s(z)), s(s(elem!1)))))),
% 2.02/2.21 inference(rewrite,[status(thm)],[])).
% 2.02/2.21 tff(3972,plain,
% 2.02/2.21 (((~b(s(s(elem!1)), s(s(z)))) | (~b(s(s(s(elem!1))), s(s(z)))) | (~b(s(s(z)), s(s(elem!1)))) | (~b(s(s(elem!1)), s(s(z)))) | (~b(s(s(s(elem!1))), s(s(z)))) | (~b(s(s(s(elem!1))), s(s(elem!1))))) <=> ((~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(s(s(elem!1))), s(s(z)))) | (~b(s(s(elem!1)), s(s(z)))) | (~b(s(s(z)), s(s(elem!1)))))),
% 2.02/2.21 inference(rewrite,[status(thm)],[])).
% 2.02/2.21 tff(3973,plain,
% 2.02/2.21 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), s(s(z)))) | (~b(s(s(s(elem!1))), s(s(z)))) | (~b(s(s(z)), s(s(elem!1)))) | (~b(s(s(elem!1)), s(s(z)))) | (~b(s(s(s(elem!1))), s(s(z)))) | (~b(s(s(s(elem!1))), s(s(elem!1)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(s(s(elem!1))), s(s(z)))) | (~b(s(s(elem!1)), s(s(z)))) | (~b(s(s(z)), s(s(elem!1))))))),
% 2.02/2.21 inference(monotonicity,[status(thm)],[3972])).
% 2.02/2.21 tff(3974,plain,
% 2.02/2.21 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), s(s(z)))) | (~b(s(s(s(elem!1))), s(s(z)))) | (~b(s(s(z)), s(s(elem!1)))) | (~b(s(s(elem!1)), s(s(z)))) | (~b(s(s(s(elem!1))), s(s(z)))) | (~b(s(s(s(elem!1))), s(s(elem!1)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(s(s(elem!1))), s(s(z)))) | (~b(s(s(elem!1)), s(s(z)))) | (~b(s(s(z)), s(s(elem!1)))))),
% 2.02/2.21 inference(transitivity,[status(thm)],[3973, 3971])).
% 2.02/2.21 tff(3975,plain,
% 2.02/2.21 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), s(s(z)))) | (~b(s(s(s(elem!1))), s(s(z)))) | (~b(s(s(z)), s(s(elem!1)))) | (~b(s(s(elem!1)), s(s(z)))) | (~b(s(s(s(elem!1))), s(s(z)))) | (~b(s(s(s(elem!1))), s(s(elem!1)))))),
% 2.02/2.21 inference(quant_inst,[status(thm)],[])).
% 2.02/2.21 tff(3976,plain,
% 2.02/2.21 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(s(s(elem!1))), s(s(z)))) | (~b(s(s(elem!1)), s(s(z)))) | (~b(s(s(z)), s(s(elem!1))))),
% 2.02/2.21 inference(modus_ponens,[status(thm)],[3975, 3974])).
% 2.02/2.21 tff(3977,plain,
% 2.02/2.21 ($false),
% 2.02/2.21 inference(unit_resolution,[status(thm)],[3976, 166, 3970, 3964, 3968, 3962])).
% 2.02/2.21 tff(3978,plain,((s(s(z)) = s(s(elem!1))) | (~r(s(s(s(elem!1))), s(z))) | (~r(s(z), s(s(elem!1)))) | (~r(z, s(s(z)))) | (~r(z, s(s(elem!1)))) | (s(s(elem!1)) = s(s(s(elem!1)))) | r(s(s(s(elem!1))), s(s(z))) | r(s(s(z)), s(s(s(elem!1)))) | r(s(s(elem!1)), s(s(z)))), inference(lemma,lemma(discharge,[]))).
% 2.02/2.21 tff(3979,plain,
% 2.02/2.21 ($false),
% 2.02/2.21 inference(unit_resolution,[status(thm)],[3978, 3961, 3953, 311, 155, 3951, 52, 3960, 3959, 3952])).
% 2.02/2.21 tff(3980,plain,(b(s(s(s(elem!1))), s(z)) | (~r(s(z), s(s(elem!1)))) | (~r(z, s(s(z)))) | (s(s(z)) = s(s(elem!1))) | (~r(s(s(z)), s(z))) | (~r(s(z), s(s(z)))) | (~b(s(s(elem!1)), s(z)))), inference(lemma,lemma(discharge,[]))).
% 2.02/2.21 tff(3981,plain,
% 2.02/2.21 (b(s(s(s(elem!1))), s(z))),
% 2.02/2.21 inference(unit_resolution,[status(thm)],[3980, 3939, 152, 311, 3930, 120, 310])).
% 2.02/2.21 tff(3982,plain,
% 2.02/2.21 (~r(s(z), z)),
% 2.02/2.21 inference(unit_resolution,[status(thm)],[3947, 197, 120, 152, 3930])).
% 2.02/2.21 tff(3983,plain,
% 2.02/2.21 (b(s(z), z)),
% 2.02/2.21 inference(unit_resolution,[status(thm)],[230, 3982])).
% 2.02/2.21 tff(3984,plain,
% 2.02/2.21 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(s(elem!1))))) | (~b(s(z), z)) | (~b(s(s(s(elem!1))), s(z))) | (~b(z, s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(s(s(elem!1))))) | (~b(s(z), z)) | (~b(s(s(s(elem!1))), s(z))) | (~b(z, s(z))))),
% 2.02/2.21 inference(rewrite,[status(thm)],[])).
% 2.02/2.21 tff(3985,plain,
% 2.02/2.21 (((~b(z, s(z))) | (~b(z, s(z))) | (~b(s(z), z)) | (~b(s(s(s(elem!1))), s(z))) | (~b(z, s(z))) | (~b(z, s(s(s(elem!1)))))) <=> ((~b(z, s(s(s(elem!1))))) | (~b(s(z), z)) | (~b(s(s(s(elem!1))), s(z))) | (~b(z, s(z))))),
% 2.02/2.21 inference(rewrite,[status(thm)],[])).
% 2.02/2.21 tff(3986,plain,
% 2.02/2.21 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(z))) | (~b(z, s(z))) | (~b(s(z), z)) | (~b(s(s(s(elem!1))), s(z))) | (~b(z, s(z))) | (~b(z, s(s(s(elem!1))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(s(elem!1))))) | (~b(s(z), z)) | (~b(s(s(s(elem!1))), s(z))) | (~b(z, s(z)))))),
% 2.02/2.21 inference(monotonicity,[status(thm)],[3985])).
% 2.02/2.21 tff(3987,plain,
% 2.02/2.21 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(z))) | (~b(z, s(z))) | (~b(s(z), z)) | (~b(s(s(s(elem!1))), s(z))) | (~b(z, s(z))) | (~b(z, s(s(s(elem!1))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(s(s(elem!1))))) | (~b(s(z), z)) | (~b(s(s(s(elem!1))), s(z))) | (~b(z, s(z))))),
% 2.02/2.21 inference(transitivity,[status(thm)],[3986, 3984])).
% 2.02/2.21 tff(3988,plain,
% 2.02/2.21 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(z))) | (~b(z, s(z))) | (~b(s(z), z)) | (~b(s(s(s(elem!1))), s(z))) | (~b(z, s(z))) | (~b(z, s(s(s(elem!1))))))),
% 2.02/2.21 inference(quant_inst,[status(thm)],[])).
% 2.02/2.21 tff(3989,plain,
% 2.02/2.21 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(s(s(elem!1))))) | (~b(s(z), z)) | (~b(s(s(s(elem!1))), s(z))) | (~b(z, s(z)))),
% 2.02/2.21 inference(modus_ponens,[status(thm)],[3988, 3987])).
% 2.02/2.21 tff(3990,plain,
% 2.02/2.22 (~b(z, s(s(s(elem!1))))),
% 2.02/2.22 inference(unit_resolution,[status(thm)],[3989, 166, 3983, 3981, 3932])).
% 2.02/2.22 tff(3991,plain,
% 2.02/2.22 (r(z, s(s(s(elem!1))))),
% 2.02/2.22 inference(unit_resolution,[status(thm)],[261, 3990])).
% 2.02/2.22 tff(3992,plain,
% 2.02/2.22 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), z)) | (~b(s(s(s(elem!1))), z)) | (~b(s(s(s(elem!1))), s(z))) | (~b(z, s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), z)) | (~b(s(s(s(elem!1))), z)) | (~b(s(s(s(elem!1))), s(z))) | (~b(z, s(z))))),
% 2.02/2.22 inference(rewrite,[status(thm)],[])).
% 2.02/2.22 tff(3993,plain,
% 2.02/2.22 (((~b(z, s(z))) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(z), z)) | (~b(z, s(z))) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(s(s(elem!1))), z))) <=> ((~b(s(z), z)) | (~b(s(s(s(elem!1))), z)) | (~b(s(s(s(elem!1))), s(z))) | (~b(z, s(z))))),
% 2.02/2.22 inference(rewrite,[status(thm)],[])).
% 2.02/2.22 tff(3994,plain,
% 2.02/2.22 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(z))) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(z), z)) | (~b(z, s(z))) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(s(s(elem!1))), z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), z)) | (~b(s(s(s(elem!1))), z)) | (~b(s(s(s(elem!1))), s(z))) | (~b(z, s(z)))))),
% 2.02/2.22 inference(monotonicity,[status(thm)],[3993])).
% 2.02/2.22 tff(3995,plain,
% 2.02/2.22 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(z))) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(z), z)) | (~b(z, s(z))) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(s(s(elem!1))), z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), z)) | (~b(s(s(s(elem!1))), z)) | (~b(s(s(s(elem!1))), s(z))) | (~b(z, s(z))))),
% 2.02/2.22 inference(transitivity,[status(thm)],[3994, 3992])).
% 2.02/2.22 tff(3996,plain,
% 2.02/2.22 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(z))) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(z), z)) | (~b(z, s(z))) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(s(s(elem!1))), z)))),
% 2.02/2.22 inference(quant_inst,[status(thm)],[])).
% 2.02/2.22 tff(3997,plain,
% 2.02/2.22 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), z)) | (~b(s(s(s(elem!1))), z)) | (~b(s(s(s(elem!1))), s(z))) | (~b(z, s(z)))),
% 2.02/2.22 inference(modus_ponens,[status(thm)],[3996, 3995])).
% 2.02/2.22 tff(3998,plain,
% 2.02/2.22 (~b(s(s(s(elem!1))), z)),
% 2.02/2.22 inference(unit_resolution,[status(thm)],[3997, 166, 3983, 3981, 3932])).
% 2.02/2.22 tff(3999,plain,
% 2.02/2.22 (r(s(s(s(elem!1))), z)),
% 2.02/2.22 inference(unit_resolution,[status(thm)],[94, 3998])).
% 2.02/2.22 tff(4000,plain,
% 2.02/2.22 (~r(s(s(z)), s(s(s(elem!1))))),
% 2.02/2.22 inference(unit_resolution,[status(thm)],[290, 3999, 152, 3991])).
% 2.02/2.22 tff(4001,plain,
% 2.02/2.22 (b(s(s(z)), s(s(s(elem!1))))),
% 2.02/2.22 inference(unit_resolution,[status(thm)],[279, 4000])).
% 2.02/2.22 tff(4002,plain,
% 2.02/2.22 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(s(z), z)) | (~b(s(s(s(elem!1))), s(z))) | (~b(z, s(z))) | (~b(s(s(elem!1)), s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(s(z), z)) | (~b(s(s(s(elem!1))), s(z))) | (~b(z, s(z))) | (~b(s(s(elem!1)), s(z))))),
% 2.02/2.22 inference(rewrite,[status(thm)],[])).
% 2.02/2.22 tff(4003,plain,
% 2.02/2.22 (((~b(z, s(z))) | (~b(s(s(elem!1)), s(z))) | (~b(s(z), z)) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(s(elem!1)), s(z))) | (~b(s(s(elem!1)), s(s(s(elem!1)))))) <=> ((~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(s(z), z)) | (~b(s(s(s(elem!1))), s(z))) | (~b(z, s(z))) | (~b(s(s(elem!1)), s(z))))),
% 2.02/2.22 inference(rewrite,[status(thm)],[])).
% 2.02/2.22 tff(4004,plain,
% 2.02/2.22 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(z))) | (~b(s(s(elem!1)), s(z))) | (~b(s(z), z)) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(s(elem!1)), s(z))) | (~b(s(s(elem!1)), s(s(s(elem!1))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(s(z), z)) | (~b(s(s(s(elem!1))), s(z))) | (~b(z, s(z))) | (~b(s(s(elem!1)), s(z)))))),
% 2.02/2.22 inference(monotonicity,[status(thm)],[4003])).
% 2.02/2.22 tff(4005,plain,
% 2.02/2.22 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(z))) | (~b(s(s(elem!1)), s(z))) | (~b(s(z), z)) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(s(elem!1)), s(z))) | (~b(s(s(elem!1)), s(s(s(elem!1))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(s(z), z)) | (~b(s(s(s(elem!1))), s(z))) | (~b(z, s(z))) | (~b(s(s(elem!1)), s(z))))),
% 2.02/2.22 inference(transitivity,[status(thm)],[4004, 4002])).
% 2.02/2.22 tff(4006,plain,
% 2.02/2.22 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(z))) | (~b(s(s(elem!1)), s(z))) | (~b(s(z), z)) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(s(elem!1)), s(z))) | (~b(s(s(elem!1)), s(s(s(elem!1))))))),
% 2.02/2.22 inference(quant_inst,[status(thm)],[])).
% 2.02/2.22 tff(4007,plain,
% 2.02/2.22 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(s(z), z)) | (~b(s(s(s(elem!1))), s(z))) | (~b(z, s(z))) | (~b(s(s(elem!1)), s(z)))),
% 2.02/2.22 inference(modus_ponens,[status(thm)],[4006, 4005])).
% 2.02/2.22 tff(4008,plain,
% 2.02/2.22 (~b(s(s(elem!1)), s(s(s(elem!1))))),
% 2.02/2.22 inference(unit_resolution,[status(thm)],[4007, 166, 3983, 3981, 3932, 310])).
% 2.02/2.22 tff(4009,plain,
% 2.02/2.22 (~b(s(s(elem!1)), z)),
% 2.02/2.22 inference(unit_resolution,[status(thm)],[3390, 166, 3983, 3932, 310])).
% 2.02/2.22 tff(4010,plain,
% 2.02/2.22 (r(s(s(elem!1)), z)),
% 2.02/2.22 inference(unit_resolution,[status(thm)],[608, 4009])).
% 2.02/2.22 tff(4011,plain,
% 2.02/2.22 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), z)) | (~r(z, s(s(s(elem!1))))) | (~r(s(s(elem!1)), z)) | (~r(s(s(elem!1)), s(s(s(elem!1))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(elem!1))), z)) | (~r(z, s(s(s(elem!1))))) | (~r(s(s(elem!1)), z)) | (~r(s(s(elem!1)), s(s(s(elem!1))))))),
% 2.02/2.22 inference(rewrite,[status(thm)],[])).
% 2.02/2.22 tff(4012,plain,
% 2.02/2.22 (((~r(s(s(s(elem!1))), z)) | (~r(z, s(s(s(elem!1))))) | (~r(s(s(elem!1)), s(s(s(elem!1))))) | (~r(s(s(elem!1)), z))) <=> ((~r(s(s(s(elem!1))), z)) | (~r(z, s(s(s(elem!1))))) | (~r(s(s(elem!1)), z)) | (~r(s(s(elem!1)), s(s(s(elem!1))))))),
% 2.02/2.22 inference(rewrite,[status(thm)],[])).
% 2.02/2.22 tff(4013,plain,
% 2.02/2.22 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), z)) | (~r(z, s(s(s(elem!1))))) | (~r(s(s(elem!1)), s(s(s(elem!1))))) | (~r(s(s(elem!1)), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), z)) | (~r(z, s(s(s(elem!1))))) | (~r(s(s(elem!1)), z)) | (~r(s(s(elem!1)), s(s(s(elem!1)))))))),
% 2.02/2.22 inference(monotonicity,[status(thm)],[4012])).
% 2.02/2.22 tff(4014,plain,
% 2.02/2.22 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), z)) | (~r(z, s(s(s(elem!1))))) | (~r(s(s(elem!1)), s(s(s(elem!1))))) | (~r(s(s(elem!1)), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(elem!1))), z)) | (~r(z, s(s(s(elem!1))))) | (~r(s(s(elem!1)), z)) | (~r(s(s(elem!1)), s(s(s(elem!1))))))),
% 2.02/2.22 inference(transitivity,[status(thm)],[4013, 4011])).
% 2.02/2.22 tff(4015,plain,
% 2.02/2.22 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), z)) | (~r(z, s(s(s(elem!1))))) | (~r(s(s(elem!1)), s(s(s(elem!1))))) | (~r(s(s(elem!1)), z)))),
% 2.02/2.22 inference(quant_inst,[status(thm)],[])).
% 2.02/2.22 tff(4016,plain,
% 2.02/2.22 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(elem!1))), z)) | (~r(z, s(s(s(elem!1))))) | (~r(s(s(elem!1)), z)) | (~r(s(s(elem!1)), s(s(s(elem!1)))))),
% 2.02/2.22 inference(modus_ponens,[status(thm)],[4015, 4014])).
% 2.02/2.22 tff(4017,plain,
% 2.02/2.22 ($false),
% 2.02/2.22 inference(unit_resolution,[status(thm)],[4016, 197, 154, 377, 282, 1970])).
% 2.02/2.22 tff(4018,plain,((~r(s(s(s(elem!1))), z)) | (~r(s(s(elem!1)), s(s(s(elem!1))))) | (~r(z, s(s(s(elem!1))))) | (~r(s(s(elem!1)), z))), inference(lemma,lemma(discharge,[]))).
% 2.02/2.22 tff(4019,plain,
% 2.02/2.22 (~r(s(s(elem!1)), s(s(s(elem!1))))),
% 2.02/2.22 inference(unit_resolution,[status(thm)],[4018, 3991, 4010, 3999])).
% 2.02/2.22 tff(4020,plain,
% 2.02/2.22 (s(s(elem!1)) = s(s(s(elem!1)))),
% 2.02/2.22 inference(unit_resolution,[status(thm)],[461, 4019, 4008])).
% 2.02/2.22 tff(4021,plain,
% 2.02/2.22 (r(s(z), s(s(elem!1))) <=> r(s(z), s(s(s(elem!1))))),
% 2.02/2.22 inference(monotonicity,[status(thm)],[4020])).
% 2.02/2.22 tff(4022,plain,
% 2.02/2.22 (r(s(z), s(s(s(elem!1))))),
% 2.02/2.22 inference(modus_ponens,[status(thm)],[311, 4021])).
% 2.02/2.22 tff(4023,plain,
% 2.02/2.22 (r(s(s(s(z))), s(s(s(elem!1)))) <=> r(s(s(s(z))), s(s(elem!1)))),
% 2.02/2.22 inference(monotonicity,[status(thm)],[2591])).
% 2.02/2.22 tff(4024,plain,
% 2.02/2.22 (r(s(s(s(z))), s(s(elem!1))) <=> r(s(s(s(z))), s(s(s(elem!1))))),
% 2.02/2.22 inference(symmetry,[status(thm)],[4023])).
% 2.02/2.22 tff(4025,plain,
% 2.02/2.22 (elem!1 = s(s(elem!1))),
% 2.02/2.22 inference(transitivity,[status(thm)],[1170, 3117, 104])).
% 2.02/2.22 tff(4026,plain,
% 2.02/2.22 (r(s(s(s(z))), elem!1) <=> r(s(s(s(z))), s(s(elem!1)))),
% 2.02/2.22 inference(monotonicity,[status(thm)],[4025])).
% 2.02/2.22 tff(4027,plain,
% 2.02/2.22 (~(s(s(s(z))) = elem!1)),
% 2.02/2.22 inference(unit_resolution,[status(thm)],[3122, 334])).
% 2.02/2.22 tff(4028,plain,
% 2.02/2.22 (s(s(s(elem!1))) = s(s(elem!1))),
% 2.02/2.22 inference(modus_ponens,[status(thm)],[334, 3341])).
% 2.02/2.22 tff(4029,plain,
% 2.02/2.22 ($false),
% 2.02/2.22 inference(unit_resolution,[status(thm)],[1863, 4028])).
% 2.02/2.22 tff(4030,plain,((~(s(s(elem!1)) = s(s(s(elem!1))))) | (s(s(s(elem!1))) = s(s(elem!1)))), inference(lemma,lemma(discharge,[]))).
% 2.02/2.22 tff(4031,plain,
% 2.02/2.22 (s(s(s(elem!1))) = s(s(elem!1))),
% 2.02/2.22 inference(unit_resolution,[status(thm)],[4030, 334])).
% 2.02/2.22 tff(4032,plain,
% 2.02/2.22 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), z)) | (~b(z, s(z))) | (~b(s(s(s(z))), z)) | (~b(s(z), s(s(s(z))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), z)) | (~b(z, s(z))) | (~b(s(s(s(z))), z)) | (~b(s(z), s(s(s(z))))))),
% 2.02/2.22 inference(rewrite,[status(thm)],[])).
% 2.02/2.22 tff(4033,plain,
% 2.02/2.22 (((~b(s(z), z)) | (~b(s(z), z)) | (~b(z, s(z))) | (~b(s(s(s(z))), z)) | (~b(s(z), z)) | (~b(s(z), s(s(s(z)))))) <=> ((~b(s(z), z)) | (~b(z, s(z))) | (~b(s(s(s(z))), z)) | (~b(s(z), s(s(s(z))))))),
% 2.02/2.22 inference(rewrite,[status(thm)],[])).
% 2.02/2.22 tff(4034,plain,
% 2.02/2.22 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), z)) | (~b(s(z), z)) | (~b(z, s(z))) | (~b(s(s(s(z))), z)) | (~b(s(z), z)) | (~b(s(z), s(s(s(z))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), z)) | (~b(z, s(z))) | (~b(s(s(s(z))), z)) | (~b(s(z), s(s(s(z)))))))),
% 2.02/2.22 inference(monotonicity,[status(thm)],[4033])).
% 2.02/2.22 tff(4035,plain,
% 2.02/2.22 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), z)) | (~b(s(z), z)) | (~b(z, s(z))) | (~b(s(s(s(z))), z)) | (~b(s(z), z)) | (~b(s(z), s(s(s(z))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), z)) | (~b(z, s(z))) | (~b(s(s(s(z))), z)) | (~b(s(z), s(s(s(z))))))),
% 2.02/2.22 inference(transitivity,[status(thm)],[4034, 4032])).
% 2.02/2.22 tff(4036,plain,
% 2.02/2.22 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), z)) | (~b(s(z), z)) | (~b(z, s(z))) | (~b(s(s(s(z))), z)) | (~b(s(z), z)) | (~b(s(z), s(s(s(z))))))),
% 2.02/2.22 inference(quant_inst,[status(thm)],[])).
% 2.02/2.22 tff(4037,plain,
% 2.02/2.22 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), z)) | (~b(z, s(z))) | (~b(s(s(s(z))), z)) | (~b(s(z), s(s(s(z)))))),
% 2.02/2.22 inference(modus_ponens,[status(thm)],[4036, 4035])).
% 2.02/2.22 tff(4038,plain,
% 2.02/2.22 (~b(s(z), s(s(s(z))))),
% 2.02/2.22 inference(unit_resolution,[status(thm)],[4037, 166, 53, 118, 1699])).
% 2.02/2.22 tff(4039,plain,
% 2.02/2.22 (r(s(z), s(s(s(z))))),
% 2.02/2.22 inference(unit_resolution,[status(thm)],[1674, 4038])).
% 2.02/2.22 tff(4040,plain,
% 2.02/2.22 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), z)) | (~b(z, s(z))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(z))), z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), z)) | (~b(z, s(z))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(z))), z)))),
% 2.02/2.22 inference(rewrite,[status(thm)],[])).
% 2.02/2.22 tff(4041,plain,
% 2.02/2.22 (((~b(s(z), z)) | (~b(s(s(s(z))), z)) | (~b(z, s(z))) | (~b(s(z), z)) | (~b(s(s(s(z))), z)) | (~b(s(s(s(z))), s(z)))) <=> ((~b(s(z), z)) | (~b(z, s(z))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(z))), z)))),
% 2.02/2.22 inference(rewrite,[status(thm)],[])).
% 2.02/2.22 tff(4042,plain,
% 2.02/2.22 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), z)) | (~b(s(s(s(z))), z)) | (~b(z, s(z))) | (~b(s(z), z)) | (~b(s(s(s(z))), z)) | (~b(s(s(s(z))), s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), z)) | (~b(z, s(z))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(z))), z))))),
% 2.02/2.22 inference(monotonicity,[status(thm)],[4041])).
% 2.02/2.22 tff(4043,plain,
% 2.02/2.22 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), z)) | (~b(s(s(s(z))), z)) | (~b(z, s(z))) | (~b(s(z), z)) | (~b(s(s(s(z))), z)) | (~b(s(s(s(z))), s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), z)) | (~b(z, s(z))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(z))), z)))),
% 2.02/2.22 inference(transitivity,[status(thm)],[4042, 4040])).
% 2.02/2.22 tff(4044,plain,
% 2.02/2.22 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), z)) | (~b(s(s(s(z))), z)) | (~b(z, s(z))) | (~b(s(z), z)) | (~b(s(s(s(z))), z)) | (~b(s(s(s(z))), s(z))))),
% 2.02/2.22 inference(quant_inst,[status(thm)],[])).
% 2.02/2.22 tff(4045,plain,
% 2.02/2.22 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), z)) | (~b(z, s(z))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(z))), z))),
% 2.02/2.22 inference(modus_ponens,[status(thm)],[4044, 4043])).
% 2.02/2.22 tff(4046,plain,
% 2.02/2.22 (~b(s(s(s(z))), s(z))),
% 2.02/2.22 inference(unit_resolution,[status(thm)],[4045, 166, 53, 118, 1699])).
% 2.02/2.22 tff(4047,plain,
% 2.02/2.22 (r(s(s(s(z))), s(z))),
% 2.02/2.22 inference(unit_resolution,[status(thm)],[1763, 4046])).
% 2.02/2.22 tff(4048,plain,
% 2.02/2.22 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(z)), s(z))) | (~r(s(z), s(s(s(z))))) | (~r(s(s(s(z))), s(s(z)))) | (~r(s(s(s(z))), s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(z)), s(z))) | (~r(s(z), s(s(s(z))))) | (~r(s(s(s(z))), s(s(z)))) | (~r(s(s(s(z))), s(z))))),
% 2.02/2.23 inference(rewrite,[status(thm)],[])).
% 2.02/2.23 tff(4049,plain,
% 2.02/2.23 (((~r(s(z), s(s(s(z))))) | (~r(s(s(z)), s(z))) | (~r(s(s(s(z))), s(z))) | (~r(s(s(s(z))), s(s(z))))) <=> ((~r(s(s(z)), s(z))) | (~r(s(z), s(s(s(z))))) | (~r(s(s(s(z))), s(s(z)))) | (~r(s(s(s(z))), s(z))))),
% 2.02/2.23 inference(rewrite,[status(thm)],[])).
% 2.02/2.23 tff(4050,plain,
% 2.02/2.23 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(s(s(z))))) | (~r(s(s(z)), s(z))) | (~r(s(s(s(z))), s(z))) | (~r(s(s(s(z))), s(s(z)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(z)), s(z))) | (~r(s(z), s(s(s(z))))) | (~r(s(s(s(z))), s(s(z)))) | (~r(s(s(s(z))), s(z)))))),
% 2.02/2.23 inference(monotonicity,[status(thm)],[4049])).
% 2.02/2.23 tff(4051,plain,
% 2.02/2.23 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(s(s(z))))) | (~r(s(s(z)), s(z))) | (~r(s(s(s(z))), s(z))) | (~r(s(s(s(z))), s(s(z)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(z)), s(z))) | (~r(s(z), s(s(s(z))))) | (~r(s(s(s(z))), s(s(z)))) | (~r(s(s(s(z))), s(z))))),
% 2.02/2.23 inference(transitivity,[status(thm)],[4050, 4048])).
% 2.02/2.23 tff(4052,plain,
% 2.02/2.23 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(s(s(z))))) | (~r(s(s(z)), s(z))) | (~r(s(s(s(z))), s(z))) | (~r(s(s(s(z))), s(s(z)))))),
% 2.02/2.23 inference(quant_inst,[status(thm)],[])).
% 2.02/2.23 tff(4053,plain,
% 2.02/2.23 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(z)), s(z))) | (~r(s(z), s(s(s(z))))) | (~r(s(s(s(z))), s(s(z)))) | (~r(s(s(s(z))), s(z)))),
% 2.02/2.23 inference(modus_ponens,[status(thm)],[4052, 4051])).
% 2.02/2.23 tff(4054,plain,
% 2.02/2.23 (~r(s(s(s(z))), s(s(z)))),
% 2.02/2.23 inference(unit_resolution,[status(thm)],[4053, 197, 392, 4047, 4039])).
% 2.02/2.23 tff(4055,plain,
% 2.02/2.23 (b(s(s(s(z))), s(s(z)))),
% 2.02/2.23 inference(unit_resolution,[status(thm)],[1010, 4054])).
% 2.02/2.23 tff(4056,plain,
% 2.02/2.23 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), z)) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(s(z)), s(s(s(elem!1))))) | (~b(s(s(s(z))), z)) | (~b(s(s(s(z))), s(s(s(elem!1))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), z)) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(s(z)), s(s(s(elem!1))))) | (~b(s(s(s(z))), z)) | (~b(s(s(s(z))), s(s(s(elem!1))))))),
% 2.02/2.23 inference(rewrite,[status(thm)],[])).
% 2.02/2.23 tff(4057,plain,
% 2.02/2.23 (((~b(s(z), z)) | (~b(s(s(s(z))), z)) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(s(z)), s(s(s(elem!1))))) | (~b(s(s(s(z))), s(s(s(elem!1))))) | (~b(s(s(s(z))), s(s(z))))) <=> ((~b(s(z), z)) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(s(z)), s(s(s(elem!1))))) | (~b(s(s(s(z))), z)) | (~b(s(s(s(z))), s(s(s(elem!1))))))),
% 2.02/2.23 inference(rewrite,[status(thm)],[])).
% 2.02/2.23 tff(4058,plain,
% 2.02/2.23 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), z)) | (~b(s(s(s(z))), z)) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(s(z)), s(s(s(elem!1))))) | (~b(s(s(s(z))), s(s(s(elem!1))))) | (~b(s(s(s(z))), s(s(z)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), z)) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(s(z)), s(s(s(elem!1))))) | (~b(s(s(s(z))), z)) | (~b(s(s(s(z))), s(s(s(elem!1)))))))),
% 2.02/2.23 inference(monotonicity,[status(thm)],[4057])).
% 2.02/2.23 tff(4059,plain,
% 2.02/2.23 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), z)) | (~b(s(s(s(z))), z)) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(s(z)), s(s(s(elem!1))))) | (~b(s(s(s(z))), s(s(s(elem!1))))) | (~b(s(s(s(z))), s(s(z)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), z)) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(s(z)), s(s(s(elem!1))))) | (~b(s(s(s(z))), z)) | (~b(s(s(s(z))), s(s(s(elem!1))))))),
% 2.02/2.23 inference(transitivity,[status(thm)],[4058, 4056])).
% 2.02/2.23 tff(4060,plain,
% 2.02/2.23 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), z)) | (~b(s(s(s(z))), z)) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(s(z)), s(s(s(elem!1))))) | (~b(s(s(s(z))), s(s(s(elem!1))))) | (~b(s(s(s(z))), s(s(z)))))),
% 2.02/2.23 inference(quant_inst,[status(thm)],[])).
% 2.02/2.23 tff(4061,plain,
% 2.02/2.23 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), z)) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(s(z)), s(s(s(elem!1))))) | (~b(s(s(s(z))), z)) | (~b(s(s(s(z))), s(s(s(elem!1)))))),
% 2.02/2.23 inference(modus_ponens,[status(thm)],[4060, 4059])).
% 2.02/2.23 tff(4062,plain,
% 2.02/2.23 ((~b(s(s(s(z))), s(s(z)))) | (~b(s(s(s(z))), s(s(s(elem!1)))))),
% 2.02/2.23 inference(unit_resolution,[status(thm)],[4061, 166, 53, 96, 263, 1699])).
% 2.02/2.23 tff(4063,plain,
% 2.02/2.23 (~b(s(s(s(z))), s(s(s(elem!1))))),
% 2.02/2.23 inference(unit_resolution,[status(thm)],[4062, 4055])).
% 2.02/2.23 tff(4064,plain,
% 2.02/2.23 (b(s(s(s(z))), s(s(s(elem!1)))) <=> b(s(s(s(z))), s(s(elem!1)))),
% 2.02/2.23 inference(monotonicity,[status(thm)],[47])).
% 2.02/2.23 tff(4065,plain,
% 2.02/2.23 (b(s(s(s(z))), s(s(elem!1))) <=> b(s(s(s(z))), s(s(s(elem!1))))),
% 2.02/2.23 inference(symmetry,[status(thm)],[4064])).
% 2.02/2.23 tff(4066,plain,
% 2.02/2.23 (s(s(elem!1)) = s(s(s(elem!1)))),
% 2.02/2.23 inference(unit_resolution,[status(thm)],[50, 47])).
% 2.02/2.23 tff(4067,plain,
% 2.02/2.23 (s(s(s(elem!1))) = s(elem!1)),
% 2.02/2.23 inference(unit_resolution,[status(thm)],[2594, 4066])).
% 2.02/2.23 tff(4068,plain,
% 2.02/2.23 (s(elem!1) = s(s(s(elem!1)))),
% 2.02/2.23 inference(symmetry,[status(thm)],[4067])).
% 2.02/2.23 tff(4069,plain,
% 2.02/2.23 (s(elem!1) = s(s(elem!1))),
% 2.02/2.23 inference(transitivity,[status(thm)],[4068, 47])).
% 2.02/2.23 tff(4070,plain,
% 2.02/2.23 (inj_0(s(elem!1)) = inj_0(s(s(elem!1)))),
% 2.02/2.23 inference(monotonicity,[status(thm)],[4069])).
% 2.02/2.23 tff(4071,plain,
% 2.02/2.23 (elem!1 = s(s(elem!1))),
% 2.02/2.23 inference(transitivity,[status(thm)],[1170, 4070, 38, 4068, 47])).
% 2.02/2.23 tff(4072,plain,
% 2.02/2.23 (b(s(s(s(z))), elem!1) <=> b(s(s(s(z))), s(s(elem!1)))),
% 2.02/2.23 inference(monotonicity,[status(thm)],[4071])).
% 2.02/2.23 tff(4073,plain,
% 2.02/2.23 (b(s(s(s(z))), elem!1) <=> b(s(s(s(z))), s(s(s(elem!1))))),
% 2.02/2.23 inference(transitivity,[status(thm)],[4072, 4065])).
% 2.02/2.23 tff(4074,assumption,(b(s(s(s(z))), elem!1)), introduced(assumption)).
% 2.02/2.23 tff(4075,plain,
% 2.02/2.23 (b(s(s(s(z))), s(s(s(elem!1))))),
% 2.02/2.23 inference(modus_ponens,[status(thm)],[4074, 4073])).
% 2.02/2.23 tff(4076,assumption,(~b(s(s(s(z))), s(s(s(elem!1))))), introduced(assumption)).
% 2.02/2.23 tff(4077,plain,
% 2.02/2.23 ($false),
% 2.02/2.23 inference(unit_resolution,[status(thm)],[4076, 4075])).
% 2.02/2.23 tff(4078,plain,((~b(s(s(s(z))), elem!1)) | b(s(s(s(z))), s(s(s(elem!1)))) | (~(s(s(s(elem!1))) = s(s(elem!1))))), inference(lemma,lemma(discharge,[]))).
% 2.02/2.23 tff(4079,plain,
% 2.02/2.23 (~b(s(s(s(z))), elem!1)),
% 2.02/2.23 inference(unit_resolution,[status(thm)],[4078, 4063, 4031])).
% 2.02/2.23 tff(4080,plain,
% 2.02/2.23 (r(s(s(s(z))), elem!1)),
% 2.02/2.23 inference(unit_resolution,[status(thm)],[2826, 4079, 4027])).
% 2.02/2.23 tff(4081,plain,
% 2.02/2.23 (r(s(s(s(z))), s(s(elem!1)))),
% 2.02/2.23 inference(modus_ponens,[status(thm)],[4080, 4026])).
% 2.02/2.23 tff(4082,plain,
% 2.02/2.23 (r(s(s(s(z))), s(s(s(elem!1))))),
% 2.02/2.23 inference(modus_ponens,[status(thm)],[4081, 4024])).
% 2.02/2.23 tff(4083,plain,
% 2.02/2.23 (~b(s(s(s(elem!1))), z)),
% 2.02/2.23 inference(unit_resolution,[status(thm)],[3997, 166, 53, 96, 118])).
% 2.02/2.23 tff(4084,plain,
% 2.02/2.23 (r(s(s(s(elem!1))), z)),
% 2.02/2.23 inference(unit_resolution,[status(thm)],[94, 4083])).
% 2.02/2.23 tff(4085,plain,
% 2.02/2.23 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(z))), s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), z)) | (~r(s(z), s(s(s(elem!1))))) | (~r(s(s(s(z))), s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(z))), s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), z)) | (~r(s(z), s(s(s(elem!1))))) | (~r(s(s(s(z))), s(z))))),
% 2.02/2.23 inference(rewrite,[status(thm)],[])).
% 2.02/2.23 tff(4086,plain,
% 2.02/2.23 (((~r(s(s(s(elem!1))), z)) | (~r(s(z), s(s(s(elem!1))))) | (~r(s(s(s(z))), s(s(s(elem!1))))) | (~r(s(s(s(z))), s(z)))) <=> ((~r(s(s(s(z))), s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), z)) | (~r(s(z), s(s(s(elem!1))))) | (~r(s(s(s(z))), s(z))))),
% 2.02/2.23 inference(rewrite,[status(thm)],[])).
% 2.02/2.23 tff(4087,plain,
% 2.02/2.23 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), z)) | (~r(s(z), s(s(s(elem!1))))) | (~r(s(s(s(z))), s(s(s(elem!1))))) | (~r(s(s(s(z))), s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(z))), s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), z)) | (~r(s(z), s(s(s(elem!1))))) | (~r(s(s(s(z))), s(z)))))),
% 2.02/2.23 inference(monotonicity,[status(thm)],[4086])).
% 2.02/2.23 tff(4088,plain,
% 2.02/2.23 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), z)) | (~r(s(z), s(s(s(elem!1))))) | (~r(s(s(s(z))), s(s(s(elem!1))))) | (~r(s(s(s(z))), s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(z))), s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), z)) | (~r(s(z), s(s(s(elem!1))))) | (~r(s(s(s(z))), s(z))))),
% 2.02/2.23 inference(transitivity,[status(thm)],[4087, 4085])).
% 2.02/2.23 tff(4089,plain,
% 2.02/2.23 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), z)) | (~r(s(z), s(s(s(elem!1))))) | (~r(s(s(s(z))), s(s(s(elem!1))))) | (~r(s(s(s(z))), s(z))))),
% 2.02/2.23 inference(quant_inst,[status(thm)],[])).
% 2.02/2.23 tff(4090,plain,
% 2.02/2.23 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(z))), s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), z)) | (~r(s(z), s(s(s(elem!1))))) | (~r(s(s(s(z))), s(z)))),
% 2.02/2.23 inference(modus_ponens,[status(thm)],[4089, 4088])).
% 2.02/2.23 tff(4091,plain,
% 2.02/2.23 (~r(s(s(s(z))), s(s(s(elem!1))))),
% 2.02/2.23 inference(unit_resolution,[status(thm)],[4090, 197, 4084, 119, 4047])).
% 2.02/2.23 tff(4092,plain,
% 2.02/2.23 ($false),
% 2.02/2.23 inference(unit_resolution,[status(thm)],[4091, 4082])).
% 2.02/2.23 tff(4093,plain,((~b(s(s(s(z))), z)) | (~(s(s(elem!1)) = s(s(s(elem!1))))) | (~r(s(z), s(s(s(elem!1))))) | (~b(s(z), z)) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(s(z)), s(s(s(elem!1))))) | (~r(s(s(z)), s(z))) | (~b(z, s(z)))), inference(lemma,lemma(discharge,[]))).
% 2.02/2.23 tff(4094,plain,
% 2.02/2.23 (~b(s(s(s(z))), z)),
% 2.02/2.23 inference(unit_resolution,[status(thm)],[4093, 4020, 4022, 3983, 3981, 4001, 3930, 3932])).
% 2.02/2.23 tff(4095,plain,
% 2.02/2.23 (r(s(s(s(z))), z)),
% 2.02/2.23 inference(unit_resolution,[status(thm)],[1713, 4094])).
% 2.02/2.23 tff(4096,plain,
% 2.02/2.23 (~(s(s(elem!1)) = s(s(z)))),
% 2.02/2.23 inference(unit_resolution,[status(thm)],[131, 3939])).
% 2.02/2.23 tff(4097,plain,
% 2.02/2.23 (~(s(s(s(elem!1))) = s(s(s(z))))),
% 2.02/2.23 inference(unit_resolution,[status(thm)],[139, 4096])).
% 2.02/2.23 tff(4098,plain,
% 2.02/2.23 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), z)) | (~r(s(s(s(elem!1))), s(s(s(z))))) | (~r(z, s(s(z)))) | (~r(s(s(s(z))), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(elem!1))), z)) | (~r(s(s(s(elem!1))), s(s(s(z))))) | (~r(z, s(s(z)))) | (~r(s(s(s(z))), z)))),
% 2.02/2.23 inference(rewrite,[status(thm)],[])).
% 2.02/2.23 tff(4099,plain,
% 2.02/2.23 (((~r(z, s(s(z)))) | (~r(s(s(s(z))), z)) | (~r(s(s(s(elem!1))), z)) | (~r(s(s(s(elem!1))), s(s(s(z)))))) <=> ((~r(s(s(s(elem!1))), z)) | (~r(s(s(s(elem!1))), s(s(s(z))))) | (~r(z, s(s(z)))) | (~r(s(s(s(z))), z)))),
% 2.02/2.23 inference(rewrite,[status(thm)],[])).
% 2.02/2.23 tff(4100,plain,
% 2.02/2.23 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(z)))) | (~r(s(s(s(z))), z)) | (~r(s(s(s(elem!1))), z)) | (~r(s(s(s(elem!1))), s(s(s(z))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), z)) | (~r(s(s(s(elem!1))), s(s(s(z))))) | (~r(z, s(s(z)))) | (~r(s(s(s(z))), z))))),
% 2.02/2.23 inference(monotonicity,[status(thm)],[4099])).
% 2.02/2.23 tff(4101,plain,
% 2.02/2.23 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(z)))) | (~r(s(s(s(z))), z)) | (~r(s(s(s(elem!1))), z)) | (~r(s(s(s(elem!1))), s(s(s(z))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(elem!1))), z)) | (~r(s(s(s(elem!1))), s(s(s(z))))) | (~r(z, s(s(z)))) | (~r(s(s(s(z))), z)))),
% 2.02/2.23 inference(transitivity,[status(thm)],[4100, 4098])).
% 2.02/2.23 tff(4102,plain,
% 2.02/2.23 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(z)))) | (~r(s(s(s(z))), z)) | (~r(s(s(s(elem!1))), z)) | (~r(s(s(s(elem!1))), s(s(s(z))))))),
% 2.02/2.23 inference(quant_inst,[status(thm)],[])).
% 2.02/2.23 tff(4103,plain,
% 2.02/2.23 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(elem!1))), z)) | (~r(s(s(s(elem!1))), s(s(s(z))))) | (~r(z, s(s(z)))) | (~r(s(s(s(z))), z))),
% 2.02/2.23 inference(modus_ponens,[status(thm)],[4102, 4101])).
% 2.02/2.23 tff(4104,plain,
% 2.02/2.23 (~r(s(s(s(elem!1))), s(s(s(z))))),
% 2.02/2.23 inference(unit_resolution,[status(thm)],[4103, 197, 3999, 152, 4095])).
% 2.02/2.23 tff(4105,plain,
% 2.02/2.23 (b(s(s(s(elem!1))), s(s(s(z))))),
% 2.02/2.23 inference(unit_resolution,[status(thm)],[3574, 4104, 4097])).
% 2.02/2.23 tff(4106,plain,
% 2.02/2.23 (s(s(s(elem!1))) = s(s(elem!1))),
% 2.02/2.23 inference(unit_resolution,[status(thm)],[4030, 4020])).
% 2.02/2.23 tff(4107,plain,
% 2.02/2.23 (~(s(s(s(z))) = elem!1)),
% 2.02/2.23 inference(unit_resolution,[status(thm)],[3122, 4020])).
% 2.02/2.23 tff(4108,plain,
% 2.02/2.23 (s(s(s(elem!1))) = s(elem!1)),
% 2.02/2.23 inference(unit_resolution,[status(thm)],[2594, 4020])).
% 2.02/2.23 tff(4109,plain,
% 2.02/2.23 (s(elem!1) = s(s(s(elem!1)))),
% 2.02/2.23 inference(symmetry,[status(thm)],[4108])).
% 2.02/2.23 tff(4110,plain,
% 2.02/2.23 (inj_0(s(elem!1)) = inj_0(s(s(s(elem!1))))),
% 2.02/2.23 inference(monotonicity,[status(thm)],[4109])).
% 2.02/2.23 tff(4111,plain,
% 2.02/2.23 (elem!1 = s(s(elem!1))),
% 2.02/2.23 inference(transitivity,[status(thm)],[1170, 4110, 104])).
% 2.02/2.23 tff(4112,plain,
% 2.02/2.23 (r(s(s(s(z))), elem!1) <=> r(s(s(s(z))), s(s(elem!1)))),
% 2.02/2.23 inference(monotonicity,[status(thm)],[4111])).
% 2.02/2.23 tff(4113,plain,
% 2.02/2.23 (r(s(s(s(z))), s(s(elem!1))) <=> r(s(s(s(z))), elem!1)),
% 2.02/2.23 inference(symmetry,[status(thm)],[4112])).
% 2.02/2.23 tff(4114,plain,
% 2.02/2.23 (s(s(s(elem!1))) = s(s(elem!1))),
% 2.02/2.23 inference(symmetry,[status(thm)],[4020])).
% 2.02/2.23 tff(4115,plain,
% 2.02/2.23 (r(s(s(s(z))), s(s(s(elem!1)))) <=> r(s(s(s(z))), s(s(elem!1)))),
% 2.02/2.23 inference(monotonicity,[status(thm)],[4114])).
% 2.02/2.23 tff(4116,plain,
% 2.02/2.23 (r(s(s(s(z))), s(s(s(elem!1)))) <=> r(s(s(s(z))), elem!1)),
% 2.02/2.23 inference(transitivity,[status(thm)],[4115, 4113])).
% 2.02/2.23 tff(4117,plain,
% 2.02/2.23 ((~r(s(s(s(z))), s(s(s(elem!1))))) <=> (~r(s(s(s(z))), elem!1))),
% 2.02/2.23 inference(monotonicity,[status(thm)],[4116])).
% 2.02/2.23 tff(4118,plain,
% 2.02/2.23 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(z)))) | (~r(s(s(s(elem!1))), z)) | (~r(s(s(s(z))), z)) | (~r(s(s(s(z))), s(s(s(elem!1))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, s(s(z)))) | (~r(s(s(s(elem!1))), z)) | (~r(s(s(s(z))), z)) | (~r(s(s(s(z))), s(s(s(elem!1))))))),
% 2.02/2.23 inference(rewrite,[status(thm)],[])).
% 2.02/2.23 tff(4119,plain,
% 2.02/2.23 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(z)))) | (~r(s(s(s(elem!1))), z)) | (~r(s(s(s(z))), z)) | (~r(s(s(s(z))), s(s(s(elem!1))))))),
% 2.02/2.23 inference(quant_inst,[status(thm)],[])).
% 2.02/2.23 tff(4120,plain,
% 2.02/2.23 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, s(s(z)))) | (~r(s(s(s(elem!1))), z)) | (~r(s(s(s(z))), z)) | (~r(s(s(s(z))), s(s(s(elem!1)))))),
% 2.02/2.23 inference(modus_ponens,[status(thm)],[4119, 4118])).
% 2.02/2.23 tff(4121,plain,
% 2.02/2.23 (~r(s(s(s(z))), s(s(s(elem!1))))),
% 2.02/2.23 inference(unit_resolution,[status(thm)],[4120, 197, 3999, 152, 4095])).
% 2.02/2.23 tff(4122,plain,
% 2.02/2.23 (~r(s(s(s(z))), elem!1)),
% 2.02/2.23 inference(modus_ponens,[status(thm)],[4121, 4117])).
% 2.02/2.23 tff(4123,plain,
% 2.02/2.23 (b(s(s(s(z))), elem!1)),
% 2.02/2.23 inference(unit_resolution,[status(thm)],[2826, 4122, 4107])).
% 2.02/2.23 tff(4124,plain,
% 2.02/2.23 (b(s(s(s(z))), s(s(s(elem!1))))),
% 2.02/2.23 inference(unit_resolution,[status(thm)],[4078, 4123, 4106])).
% 2.02/2.23 tff(4125,plain,
% 2.02/2.23 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), s(s(z)))) | (~b(s(s(z)), s(s(s(elem!1))))) | (~b(s(s(s(z))), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(s(s(z))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(s(z)), s(s(s(elem!1))))) | (~b(s(s(s(z))), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(s(s(z))))))),
% 2.02/2.23 inference(rewrite,[status(thm)],[])).
% 2.02/2.23 tff(4126,plain,
% 2.02/2.23 (((~b(s(s(s(z))), s(s(s(elem!1))))) | (~b(s(s(s(z))), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(s(s(z))))) | (~b(s(s(z)), s(s(s(elem!1))))) | (~b(s(s(s(z))), s(s(s(elem!1))))) | (~b(s(s(s(z))), s(s(z))))) <=> ((~b(s(s(s(z))), s(s(z)))) | (~b(s(s(z)), s(s(s(elem!1))))) | (~b(s(s(s(z))), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(s(s(z))))))),
% 2.02/2.23 inference(rewrite,[status(thm)],[])).
% 2.02/2.23 tff(4127,plain,
% 2.02/2.23 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), s(s(s(elem!1))))) | (~b(s(s(s(z))), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(s(s(z))))) | (~b(s(s(z)), s(s(s(elem!1))))) | (~b(s(s(s(z))), s(s(s(elem!1))))) | (~b(s(s(s(z))), s(s(z)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), s(s(z)))) | (~b(s(s(z)), s(s(s(elem!1))))) | (~b(s(s(s(z))), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(s(s(z)))))))),
% 2.02/2.23 inference(monotonicity,[status(thm)],[4126])).
% 2.02/2.23 tff(4128,plain,
% 2.02/2.23 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), s(s(s(elem!1))))) | (~b(s(s(s(z))), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(s(s(z))))) | (~b(s(s(z)), s(s(s(elem!1))))) | (~b(s(s(s(z))), s(s(s(elem!1))))) | (~b(s(s(s(z))), s(s(z)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(s(z)), s(s(s(elem!1))))) | (~b(s(s(s(z))), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(s(s(z))))))),
% 2.02/2.23 inference(transitivity,[status(thm)],[4127, 4125])).
% 2.02/2.23 tff(4129,plain,
% 2.02/2.23 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), s(s(s(elem!1))))) | (~b(s(s(s(z))), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(s(s(z))))) | (~b(s(s(z)), s(s(s(elem!1))))) | (~b(s(s(s(z))), s(s(s(elem!1))))) | (~b(s(s(s(z))), s(s(z)))))),
% 2.02/2.23 inference(quant_inst,[status(thm)],[])).
% 2.02/2.23 tff(4130,plain,
% 2.02/2.23 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(s(z)), s(s(s(elem!1))))) | (~b(s(s(s(z))), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(s(s(z)))))),
% 2.02/2.23 inference(modus_ponens,[status(thm)],[4129, 4128])).
% 2.02/2.23 tff(4131,plain,
% 2.02/2.23 (~b(s(s(s(z))), s(s(z)))),
% 2.02/2.23 inference(unit_resolution,[status(thm)],[4130, 166, 4001, 4124, 4105])).
% 2.02/2.23 tff(4132,plain,
% 2.02/2.23 (r(s(s(s(z))), s(s(z)))),
% 2.02/2.23 inference(unit_resolution,[status(thm)],[1010, 4131])).
% 2.02/2.24 tff(4133,plain,
% 2.02/2.24 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(z)), s(z))) | (~r(z, s(s(z)))) | (~r(s(s(s(z))), z)) | (~r(s(s(s(z))), s(s(z)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(z)), s(z))) | (~r(z, s(s(z)))) | (~r(s(s(s(z))), z)) | (~r(s(s(s(z))), s(s(z)))))),
% 2.02/2.24 inference(rewrite,[status(thm)],[])).
% 2.02/2.24 tff(4134,plain,
% 2.02/2.24 (((~r(s(s(z)), s(z))) | (~r(z, s(s(z)))) | (~r(s(s(s(z))), s(s(z)))) | (~r(s(s(s(z))), z))) <=> ((~r(s(s(z)), s(z))) | (~r(z, s(s(z)))) | (~r(s(s(s(z))), z)) | (~r(s(s(s(z))), s(s(z)))))),
% 2.02/2.24 inference(rewrite,[status(thm)],[])).
% 2.02/2.24 tff(4135,plain,
% 2.02/2.24 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(z)), s(z))) | (~r(z, s(s(z)))) | (~r(s(s(s(z))), s(s(z)))) | (~r(s(s(s(z))), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(z)), s(z))) | (~r(z, s(s(z)))) | (~r(s(s(s(z))), z)) | (~r(s(s(s(z))), s(s(z))))))),
% 2.02/2.24 inference(monotonicity,[status(thm)],[4134])).
% 2.02/2.24 tff(4136,plain,
% 2.02/2.24 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(z)), s(z))) | (~r(z, s(s(z)))) | (~r(s(s(s(z))), s(s(z)))) | (~r(s(s(s(z))), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(z)), s(z))) | (~r(z, s(s(z)))) | (~r(s(s(s(z))), z)) | (~r(s(s(s(z))), s(s(z)))))),
% 2.02/2.24 inference(transitivity,[status(thm)],[4135, 4133])).
% 2.02/2.24 tff(4137,plain,
% 2.02/2.24 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(z)), s(z))) | (~r(z, s(s(z)))) | (~r(s(s(s(z))), s(s(z)))) | (~r(s(s(s(z))), z)))),
% 2.02/2.24 inference(quant_inst,[status(thm)],[])).
% 2.02/2.24 tff(4138,plain,
% 2.02/2.24 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(z)), s(z))) | (~r(z, s(s(z)))) | (~r(s(s(s(z))), z)) | (~r(s(s(s(z))), s(s(z))))),
% 2.02/2.24 inference(modus_ponens,[status(thm)],[4137, 4136])).
% 2.02/2.24 tff(4139,plain,
% 2.02/2.24 ($false),
% 2.02/2.24 inference(unit_resolution,[status(thm)],[4138, 197, 152, 3930, 4132, 4095])).
% 2.02/2.24 tff(4140,plain,((~r(s(z), s(s(z)))) | (~r(s(z), s(s(elem!1)))) | (~b(s(s(elem!1)), s(z))) | b(z, s(s(z)))), inference(lemma,lemma(discharge,[]))).
% 2.02/2.24 tff(4141,plain,
% 2.02/2.24 (~r(s(z), s(s(z)))),
% 2.02/2.24 inference(unit_resolution,[status(thm)],[4140, 310, 85, 125])).
% 2.02/2.24 tff(4142,plain,
% 2.02/2.24 (b(s(z), s(s(z)))),
% 2.02/2.24 inference(unit_resolution,[status(thm)],[427, 4141])).
% 2.02/2.24 tff(4143,plain,
% 2.02/2.24 (r(s(s(z)), s(z))),
% 2.02/2.24 inference(unit_resolution,[status(thm)],[308, 3936])).
% 2.02/2.24 tff(4144,plain,
% 2.02/2.24 (~(s(s(z)) = s(s(elem!1)))),
% 2.02/2.24 inference(unit_resolution,[status(thm)],[3938, 3936, 310])).
% 2.02/2.24 tff(4145,plain,
% 2.02/2.24 (~(s(s(elem!1)) = s(s(z)))),
% 2.02/2.24 inference(unit_resolution,[status(thm)],[131, 4144])).
% 2.02/2.24 tff(4146,plain,
% 2.02/2.24 (~(z = elem!1)),
% 2.02/2.24 inference(unit_resolution,[status(thm)],[17, 4145])).
% 2.02/2.24 tff(4147,plain,
% 2.02/2.24 (~(s(elem!1) = s(z))),
% 2.02/2.24 inference(unit_resolution,[status(thm)],[30, 4146])).
% 2.02/2.24 tff(4148,plain,
% 2.02/2.24 ((s(z) = s(elem!1)) <=> (s(elem!1) = s(z))),
% 2.02/2.24 inference(commutativity,[status(thm)],[])).
% 2.02/2.24 tff(4149,assumption,(s(z) = s(elem!1)), introduced(assumption)).
% 2.02/2.24 tff(4150,plain,
% 2.02/2.24 (s(elem!1) = s(z)),
% 2.02/2.24 inference(modus_ponens,[status(thm)],[4149, 4148])).
% 2.02/2.24 tff(4151,plain,
% 2.02/2.24 ($false),
% 2.02/2.24 inference(unit_resolution,[status(thm)],[41, 4150])).
% 2.02/2.24 tff(4152,plain,((~(s(z) = s(elem!1))) | (s(elem!1) = s(z))), inference(lemma,lemma(discharge,[]))).
% 2.02/2.24 tff(4153,plain,
% 2.02/2.24 (~(s(z) = s(elem!1))),
% 2.02/2.24 inference(unit_resolution,[status(thm)],[4152, 4147])).
% 2.02/2.24 tff(4154,plain,
% 2.02/2.24 (~r(s(z), z)),
% 2.02/2.24 inference(unit_resolution,[status(thm)],[2680, 323, 155, 392])).
% 2.02/2.24 tff(4155,plain,
% 2.02/2.24 (b(s(z), z)),
% 2.02/2.24 inference(unit_resolution,[status(thm)],[230, 4154])).
% 2.02/2.24 tff(4156,plain,
% 2.02/2.24 (s(s(elem!1)) = s(s(s(elem!1)))),
% 2.02/2.24 inference(unit_resolution,[status(thm)],[2253, 4155, 155, 310, 323])).
% 2.02/2.24 tff(4157,plain,
% 2.02/2.24 (s(s(s(elem!1))) = s(elem!1)),
% 2.02/2.24 inference(unit_resolution,[status(thm)],[2594, 4156])).
% 2.02/2.24 tff(4158,plain,
% 2.02/2.24 (s(elem!1) = s(s(s(elem!1)))),
% 2.02/2.24 inference(symmetry,[status(thm)],[4157])).
% 2.02/2.24 tff(4159,plain,
% 2.02/2.24 (b(s(z), s(elem!1)) <=> b(s(z), s(s(s(elem!1))))),
% 2.02/2.24 inference(monotonicity,[status(thm)],[4158])).
% 2.02/2.24 tff(4160,plain,
% 2.02/2.24 (b(s(z), s(s(s(elem!1)))) <=> b(s(z), s(elem!1))),
% 2.02/2.24 inference(symmetry,[status(thm)],[4159])).
% 2.02/2.24 tff(4161,plain,
% 2.02/2.24 ((~b(s(z), s(s(s(elem!1))))) <=> (~b(s(z), s(elem!1)))),
% 2.02/2.24 inference(monotonicity,[status(thm)],[4160])).
% 2.02/2.24 tff(4162,plain,
% 2.02/2.24 (b(s(z), s(s(elem!1))) <=> b(s(z), s(s(s(elem!1))))),
% 2.02/2.24 inference(monotonicity,[status(thm)],[4156])).
% 2.02/2.24 tff(4163,plain,
% 2.02/2.24 ((~b(s(z), s(s(elem!1)))) <=> (~b(s(z), s(s(s(elem!1)))))),
% 2.02/2.24 inference(monotonicity,[status(thm)],[4162])).
% 2.02/2.24 tff(4164,plain,
% 2.02/2.24 (~b(s(z), s(s(s(elem!1))))),
% 2.02/2.24 inference(modus_ponens,[status(thm)],[54, 4163])).
% 2.02/2.24 tff(4165,plain,
% 2.02/2.24 (~b(s(z), s(elem!1))),
% 2.02/2.24 inference(modus_ponens,[status(thm)],[4164, 4161])).
% 2.02/2.24 tff(4166,assumption,(~(s(z) = s(elem!1))), introduced(assumption)).
% 2.02/2.24 tff(4167,plain,
% 2.02/2.24 (~r(s(z), s(elem!1))),
% 2.02/2.24 inference(unit_resolution,[status(thm)],[2095, 323, 392, 155])).
% 2.02/2.24 tff(4168,plain,
% 2.02/2.24 (((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((s(z) = s(elem!1)) | b(s(z), s(elem!1)) | r(s(z), s(elem!1)))) <=> ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (s(z) = s(elem!1)) | b(s(z), s(elem!1)) | r(s(z), s(elem!1)))),
% 2.02/2.24 inference(rewrite,[status(thm)],[])).
% 2.02/2.24 tff(4169,plain,
% 2.02/2.24 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((s(z) = s(elem!1)) | b(s(z), s(elem!1)) | r(s(z), s(elem!1)))),
% 2.02/2.24 inference(quant_inst,[status(thm)],[])).
% 2.02/2.24 tff(4170,plain,
% 2.02/2.24 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (s(z) = s(elem!1)) | b(s(z), s(elem!1)) | r(s(z), s(elem!1))),
% 2.02/2.24 inference(modus_ponens,[status(thm)],[4169, 4168])).
% 2.02/2.24 tff(4171,plain,
% 2.02/2.24 ((s(z) = s(elem!1)) | b(s(z), s(elem!1)) | r(s(z), s(elem!1))),
% 2.02/2.24 inference(unit_resolution,[status(thm)],[4170, 79])).
% 2.02/2.24 tff(4172,plain,
% 2.02/2.24 (b(s(z), s(elem!1))),
% 2.02/2.24 inference(unit_resolution,[status(thm)],[4171, 4167, 4166])).
% 2.02/2.24 tff(4173,plain,
% 2.02/2.24 ($false),
% 2.02/2.24 inference(unit_resolution,[status(thm)],[4172, 4165])).
% 2.02/2.24 tff(4174,plain,((~r(z, s(z))) | b(s(z), s(s(elem!1))) | (~r(z, s(s(z)))) | (~b(s(s(elem!1)), s(z))) | (s(z) = s(elem!1)) | (~r(s(s(z)), s(z)))), inference(lemma,lemma(discharge,[]))).
% 2.02/2.24 tff(4175,plain,
% 2.02/2.24 (~r(z, s(z))),
% 2.02/2.24 inference(unit_resolution,[status(thm)],[4174, 4153, 155, 310, 54, 4143])).
% 2.02/2.24 tff(4176,plain,
% 2.02/2.24 (b(z, s(z))),
% 2.02/2.24 inference(unit_resolution,[status(thm)],[321, 4175])).
% 2.02/2.24 tff(4177,plain,
% 2.02/2.24 (~r(s(s(s(elem!1))), s(s(z)))),
% 2.02/2.24 inference(unit_resolution,[status(thm)],[854, 3953, 392, 311])).
% 2.02/2.24 tff(4178,plain,
% 2.02/2.24 (b(s(s(s(elem!1))), s(s(z)))),
% 2.02/2.24 inference(unit_resolution,[status(thm)],[218, 4177])).
% 2.02/2.24 tff(4179,plain,
% 2.02/2.24 (b(s(s(z)), s(s(s(elem!1))))),
% 2.02/2.24 inference(unit_resolution,[status(thm)],[279, 3959])).
% 2.02/2.24 tff(4180,plain,
% 2.02/2.24 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(s(z)))) | (~b(s(z), s(s(z)))) | (~b(s(s(z)), s(s(s(elem!1))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(s(z)))) | (~b(s(z), s(s(z)))) | (~b(s(s(z)), s(s(s(elem!1))))))),
% 2.02/2.24 inference(rewrite,[status(thm)],[])).
% 2.02/2.24 tff(4181,plain,
% 2.02/2.24 (((~b(s(s(s(elem!1))), s(s(z)))) | (~b(s(z), s(s(z)))) | (~b(s(s(z)), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(s(z)))) | (~b(s(z), s(s(z)))) | (~b(s(z), s(s(s(elem!1)))))) <=> ((~b(s(z), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(s(z)))) | (~b(s(z), s(s(z)))) | (~b(s(s(z)), s(s(s(elem!1))))))),
% 2.02/2.24 inference(rewrite,[status(thm)],[])).
% 2.02/2.24 tff(4182,plain,
% 2.02/2.24 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), s(s(z)))) | (~b(s(z), s(s(z)))) | (~b(s(s(z)), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(s(z)))) | (~b(s(z), s(s(z)))) | (~b(s(z), s(s(s(elem!1))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(s(z)))) | (~b(s(z), s(s(z)))) | (~b(s(s(z)), s(s(s(elem!1)))))))),
% 2.02/2.24 inference(monotonicity,[status(thm)],[4181])).
% 2.02/2.24 tff(4183,plain,
% 2.02/2.24 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), s(s(z)))) | (~b(s(z), s(s(z)))) | (~b(s(s(z)), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(s(z)))) | (~b(s(z), s(s(z)))) | (~b(s(z), s(s(s(elem!1))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(s(z)))) | (~b(s(z), s(s(z)))) | (~b(s(s(z)), s(s(s(elem!1))))))),
% 2.02/2.24 inference(transitivity,[status(thm)],[4182, 4180])).
% 2.02/2.24 tff(4184,plain,
% 2.02/2.24 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), s(s(z)))) | (~b(s(z), s(s(z)))) | (~b(s(s(z)), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(s(z)))) | (~b(s(z), s(s(z)))) | (~b(s(z), s(s(s(elem!1))))))),
% 2.02/2.24 inference(quant_inst,[status(thm)],[])).
% 2.02/2.24 tff(4185,plain,
% 2.02/2.24 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(s(z)))) | (~b(s(z), s(s(z)))) | (~b(s(s(z)), s(s(s(elem!1)))))),
% 2.02/2.24 inference(modus_ponens,[status(thm)],[4184, 4183])).
% 2.02/2.24 tff(4186,plain,
% 2.02/2.24 (~b(s(z), s(s(s(elem!1))))),
% 2.02/2.24 inference(unit_resolution,[status(thm)],[4185, 166, 556, 4179, 4178])).
% 2.02/2.24 tff(4187,plain,
% 2.02/2.24 (r(s(z), s(s(s(elem!1))))),
% 2.02/2.24 inference(unit_resolution,[status(thm)],[116, 4186])).
% 2.02/2.24 tff(4188,plain,
% 2.02/2.24 (~r(s(s(elem!1)), s(s(s(elem!1))))),
% 2.02/2.24 inference(unit_resolution,[status(thm)],[764, 4187, 3953, 311])).
% 2.02/2.24 tff(4189,plain,
% 2.02/2.24 (b(s(s(elem!1)), s(s(s(elem!1))))),
% 2.02/2.24 inference(unit_resolution,[status(thm)],[461, 4188, 3961])).
% 2.02/2.24 tff(4190,plain,
% 2.02/2.24 (~b(s(s(elem!1)), s(s(z)))),
% 2.02/2.24 inference(unit_resolution,[status(thm)],[501, 4189, 4177, 3959])).
% 2.02/2.24 tff(4191,plain,
% 2.02/2.24 (r(s(s(elem!1)), s(s(z)))),
% 2.02/2.24 inference(unit_resolution,[status(thm)],[441, 4190, 11])).
% 2.02/2.24 tff(4192,plain,
% 2.02/2.24 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), s(s(elem!1)))) | (~r(s(z), s(s(elem!1)))) | (~r(s(s(s(elem!1))), s(z))) | (~r(s(s(elem!1)), s(s(z)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(elem!1))), s(s(elem!1)))) | (~r(s(z), s(s(elem!1)))) | (~r(s(s(s(elem!1))), s(z))) | (~r(s(s(elem!1)), s(s(z)))))),
% 2.02/2.24 inference(rewrite,[status(thm)],[])).
% 2.02/2.24 tff(4193,plain,
% 2.02/2.24 (((~r(s(s(elem!1)), s(s(z)))) | (~r(s(z), s(s(elem!1)))) | (~r(s(s(s(elem!1))), s(s(elem!1)))) | (~r(s(s(s(elem!1))), s(z)))) <=> ((~r(s(s(s(elem!1))), s(s(elem!1)))) | (~r(s(z), s(s(elem!1)))) | (~r(s(s(s(elem!1))), s(z))) | (~r(s(s(elem!1)), s(s(z)))))),
% 2.02/2.24 inference(rewrite,[status(thm)],[])).
% 2.02/2.24 tff(4194,plain,
% 2.02/2.24 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(elem!1)), s(s(z)))) | (~r(s(z), s(s(elem!1)))) | (~r(s(s(s(elem!1))), s(s(elem!1)))) | (~r(s(s(s(elem!1))), s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), s(s(elem!1)))) | (~r(s(z), s(s(elem!1)))) | (~r(s(s(s(elem!1))), s(z))) | (~r(s(s(elem!1)), s(s(z))))))),
% 2.02/2.24 inference(monotonicity,[status(thm)],[4193])).
% 2.02/2.24 tff(4195,plain,
% 2.02/2.24 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(elem!1)), s(s(z)))) | (~r(s(z), s(s(elem!1)))) | (~r(s(s(s(elem!1))), s(s(elem!1)))) | (~r(s(s(s(elem!1))), s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(elem!1))), s(s(elem!1)))) | (~r(s(z), s(s(elem!1)))) | (~r(s(s(s(elem!1))), s(z))) | (~r(s(s(elem!1)), s(s(z)))))),
% 2.02/2.24 inference(transitivity,[status(thm)],[4194, 4192])).
% 2.02/2.24 tff(4196,plain,
% 2.02/2.24 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(elem!1)), s(s(z)))) | (~r(s(z), s(s(elem!1)))) | (~r(s(s(s(elem!1))), s(s(elem!1)))) | (~r(s(s(s(elem!1))), s(z))))),
% 2.02/2.24 inference(quant_inst,[status(thm)],[])).
% 2.02/2.24 tff(4197,plain,
% 2.02/2.24 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(elem!1))), s(s(elem!1)))) | (~r(s(z), s(s(elem!1)))) | (~r(s(s(s(elem!1))), s(z))) | (~r(s(s(elem!1)), s(s(z))))),
% 2.02/2.24 inference(modus_ponens,[status(thm)],[4196, 4195])).
% 2.02/2.24 tff(4198,plain,
% 2.02/2.24 ($false),
% 2.02/2.24 inference(unit_resolution,[status(thm)],[4197, 197, 311, 393, 350, 905])).
% 2.02/2.24 tff(4199,plain,((~r(s(s(s(elem!1))), s(s(elem!1)))) | (~r(s(z), s(s(elem!1)))) | (~r(s(s(elem!1)), s(s(z)))) | (~r(s(s(s(elem!1))), s(z)))), inference(lemma,lemma(discharge,[]))).
% 2.02/2.24 tff(4200,plain,
% 2.02/2.24 (~r(s(s(s(elem!1))), s(s(elem!1)))),
% 2.02/2.24 inference(unit_resolution,[status(thm)],[4199, 4191, 311, 3953])).
% 2.02/2.24 tff(4201,plain,
% 2.02/2.24 (~r(z, s(s(elem!1)))),
% 2.02/2.24 inference(unit_resolution,[status(thm)],[401, 4191, 155, 392])).
% 2.02/2.24 tff(4202,plain,
% 2.02/2.24 (b(z, s(s(elem!1)))),
% 2.02/2.24 inference(unit_resolution,[status(thm)],[1795, 4201])).
% 2.02/2.24 tff(4203,plain,
% 2.02/2.24 (~b(z, s(s(s(elem!1))))),
% 2.02/2.24 inference(unit_resolution,[status(thm)],[1834, 4202, 3961, 4200, 4188])).
% 2.02/2.24 tff(4204,plain,
% 2.02/2.24 (r(z, s(s(s(elem!1))))),
% 2.02/2.24 inference(unit_resolution,[status(thm)],[261, 4203])).
% 2.02/2.24 tff(4205,plain,
% 2.02/2.24 (~r(z, s(z))),
% 2.02/2.24 inference(unit_resolution,[status(thm)],[1524, 4204, 311, 3953])).
% 2.02/2.24 tff(4206,plain,
% 2.02/2.24 (~(s(s(s(elem!1))) = s(s(elem!1)))),
% 2.02/2.24 inference(unit_resolution,[status(thm)],[50, 3961])).
% 2.02/2.24 tff(4207,plain,
% 2.02/2.24 (b(s(s(s(elem!1))), s(s(elem!1)))),
% 2.02/2.24 inference(unit_resolution,[status(thm)],[889, 4200, 4206])).
% 2.02/2.24 tff(4208,plain,
% 2.02/2.24 (~r(s(z), z)),
% 2.02/2.24 inference(unit_resolution,[status(thm)],[2349, 4207, 4189, 4202, 4187])).
% 2.02/2.24 tff(4209,plain,
% 2.02/2.24 (b(s(z), z)),
% 2.02/2.24 inference(unit_resolution,[status(thm)],[230, 4208])).
% 2.02/2.24 tff(4210,plain,
% 2.02/2.24 (~b(z, s(z))),
% 2.02/2.24 inference(unit_resolution,[status(thm)],[3358, 4209, 310, 4202])).
% 2.02/2.24 tff(4211,plain,
% 2.02/2.24 ($false),
% 2.02/2.24 inference(unit_resolution,[status(thm)],[321, 4210, 4205])).
% 2.02/2.24 tff(4212,plain,(b(s(s(s(elem!1))), s(z)) | (~b(s(s(elem!1)), s(z))) | (~r(s(z), s(s(elem!1)))) | (~r(z, s(s(z)))) | (~r(s(s(z)), s(z))) | (s(s(elem!1)) = s(s(z))) | (~b(s(z), s(s(z))))), inference(lemma,lemma(discharge,[]))).
% 2.02/2.24 tff(4213,plain,
% 2.02/2.24 (b(s(s(s(elem!1))), s(z))),
% 2.02/2.24 inference(unit_resolution,[status(thm)],[4212, 4143, 85, 155, 310, 4145, 556])).
% 2.02/2.24 tff(4214,plain,
% 2.02/2.24 (b(s(s(s(elem!1))), s(z))),
% 2.02/2.24 inference(unit_resolution,[status(thm)],[4212, 392, 311, 155, 310, 132, 556])).
% 2.02/2.24 tff(4215,plain,
% 2.02/2.24 (~b(z, s(s(s(elem!1))))),
% 2.02/2.24 inference(unit_resolution,[status(thm)],[249, 241, 118, 4214])).
% 2.02/2.24 tff(4216,plain,
% 2.02/2.24 (r(z, s(s(s(elem!1))))),
% 2.02/2.24 inference(unit_resolution,[status(thm)],[261, 4215])).
% 2.02/2.24 tff(4217,plain,
% 2.02/2.24 (~r(s(s(s(elem!1))), s(s(z)))),
% 2.02/2.24 inference(unit_resolution,[status(thm)],[1588, 4216, 155, 392])).
% 2.02/2.24 tff(4218,plain,
% 2.02/2.24 (b(s(s(s(elem!1))), s(s(z)))),
% 2.02/2.24 inference(unit_resolution,[status(thm)],[218, 4217])).
% 2.02/2.24 tff(4219,plain,
% 2.02/2.24 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), s(s(z)))) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(s(elem!1)), s(z))) | (~b(s(z), s(s(z)))) | (~b(s(s(z)), s(s(elem!1)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(elem!1))), s(s(z)))) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(s(elem!1)), s(z))) | (~b(s(z), s(s(z)))) | (~b(s(s(z)), s(s(elem!1)))))),
% 2.02/2.24 inference(rewrite,[status(thm)],[])).
% 2.02/2.24 tff(4220,plain,
% 2.02/2.24 (((~b(s(s(elem!1)), s(z))) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(s(z)), s(s(elem!1)))) | (~b(s(z), s(s(z)))) | (~b(s(s(s(elem!1))), s(s(z)))) | (~b(s(s(s(elem!1))), s(z)))) <=> ((~b(s(s(s(elem!1))), s(s(z)))) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(s(elem!1)), s(z))) | (~b(s(z), s(s(z)))) | (~b(s(s(z)), s(s(elem!1)))))),
% 2.02/2.24 inference(rewrite,[status(thm)],[])).
% 2.02/2.24 tff(4221,plain,
% 2.02/2.24 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), s(z))) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(s(z)), s(s(elem!1)))) | (~b(s(z), s(s(z)))) | (~b(s(s(s(elem!1))), s(s(z)))) | (~b(s(s(s(elem!1))), s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), s(s(z)))) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(s(elem!1)), s(z))) | (~b(s(z), s(s(z)))) | (~b(s(s(z)), s(s(elem!1))))))),
% 2.02/2.24 inference(monotonicity,[status(thm)],[4220])).
% 2.02/2.24 tff(4222,plain,
% 2.02/2.24 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), s(z))) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(s(z)), s(s(elem!1)))) | (~b(s(z), s(s(z)))) | (~b(s(s(s(elem!1))), s(s(z)))) | (~b(s(s(s(elem!1))), s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(elem!1))), s(s(z)))) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(s(elem!1)), s(z))) | (~b(s(z), s(s(z)))) | (~b(s(s(z)), s(s(elem!1)))))),
% 2.02/2.24 inference(transitivity,[status(thm)],[4221, 4219])).
% 2.02/2.24 tff(4223,plain,
% 2.02/2.24 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), s(z))) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(s(z)), s(s(elem!1)))) | (~b(s(z), s(s(z)))) | (~b(s(s(s(elem!1))), s(s(z)))) | (~b(s(s(s(elem!1))), s(z))))),
% 2.02/2.24 inference(quant_inst,[status(thm)],[])).
% 2.02/2.24 tff(4224,plain,
% 2.02/2.24 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(elem!1))), s(s(z)))) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(s(elem!1)), s(z))) | (~b(s(z), s(s(z)))) | (~b(s(s(z)), s(s(elem!1))))),
% 2.02/2.24 inference(modus_ponens,[status(thm)],[4223, 4222])).
% 2.02/2.24 tff(4225,plain,
% 2.02/2.24 ($false),
% 2.02/2.24 inference(unit_resolution,[status(thm)],[4224, 166, 556, 96, 310, 446, 2060])).
% 2.02/2.24 tff(4226,plain,((~b(s(z), s(s(z)))) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(s(elem!1)), s(z))) | (~b(s(s(z)), s(s(elem!1)))) | (~b(s(s(s(elem!1))), s(s(z))))), inference(lemma,lemma(discharge,[]))).
% 2.02/2.24 tff(4227,plain,
% 2.02/2.24 (~b(s(s(z)), s(s(elem!1)))),
% 2.02/2.24 inference(unit_resolution,[status(thm)],[4226, 4218, 310, 556, 4214])).
% 2.02/2.24 tff(4228,plain,
% 2.02/2.24 (~b(s(s(elem!1)), s(s(s(elem!1))))),
% 2.02/2.24 inference(unit_resolution,[status(thm)],[1994, 241, 310, 4214])).
% 2.02/2.24 tff(4229,plain,
% 2.02/2.24 (r(s(s(elem!1)), s(s(s(elem!1))))),
% 2.02/2.24 inference(unit_resolution,[status(thm)],[461, 4228, 45])).
% 2.02/2.24 tff(4230,plain,
% 2.02/2.24 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(s(elem!1)))) | (~r(s(s(elem!1)), s(s(s(elem!1))))) | (~r(s(s(z)), s(s(elem!1)))) | (~r(s(s(z)), s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(z), s(s(elem!1)))) | (~r(s(s(elem!1)), s(s(s(elem!1))))) | (~r(s(s(z)), s(s(elem!1)))) | (~r(s(s(z)), s(z))))),
% 2.02/2.24 inference(rewrite,[status(thm)],[])).
% 2.02/2.24 tff(4231,plain,
% 2.02/2.24 (((~r(s(s(elem!1)), s(s(s(elem!1))))) | (~r(s(z), s(s(elem!1)))) | (~r(s(s(z)), s(s(elem!1)))) | (~r(s(s(z)), s(z)))) <=> ((~r(s(z), s(s(elem!1)))) | (~r(s(s(elem!1)), s(s(s(elem!1))))) | (~r(s(s(z)), s(s(elem!1)))) | (~r(s(s(z)), s(z))))),
% 2.02/2.24 inference(rewrite,[status(thm)],[])).
% 2.02/2.24 tff(4232,plain,
% 2.02/2.24 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(elem!1)), s(s(s(elem!1))))) | (~r(s(z), s(s(elem!1)))) | (~r(s(s(z)), s(s(elem!1)))) | (~r(s(s(z)), s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(s(elem!1)))) | (~r(s(s(elem!1)), s(s(s(elem!1))))) | (~r(s(s(z)), s(s(elem!1)))) | (~r(s(s(z)), s(z)))))),
% 2.02/2.25 inference(monotonicity,[status(thm)],[4231])).
% 2.02/2.25 tff(4233,plain,
% 2.02/2.25 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(elem!1)), s(s(s(elem!1))))) | (~r(s(z), s(s(elem!1)))) | (~r(s(s(z)), s(s(elem!1)))) | (~r(s(s(z)), s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(z), s(s(elem!1)))) | (~r(s(s(elem!1)), s(s(s(elem!1))))) | (~r(s(s(z)), s(s(elem!1)))) | (~r(s(s(z)), s(z))))),
% 2.02/2.25 inference(transitivity,[status(thm)],[4232, 4230])).
% 2.02/2.25 tff(4234,plain,
% 2.02/2.25 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(elem!1)), s(s(s(elem!1))))) | (~r(s(z), s(s(elem!1)))) | (~r(s(s(z)), s(s(elem!1)))) | (~r(s(s(z)), s(z))))),
% 2.02/2.25 inference(quant_inst,[status(thm)],[])).
% 2.02/2.25 tff(4235,plain,
% 2.02/2.25 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(z), s(s(elem!1)))) | (~r(s(s(elem!1)), s(s(s(elem!1))))) | (~r(s(s(z)), s(s(elem!1)))) | (~r(s(s(z)), s(z)))),
% 2.02/2.25 inference(modus_ponens,[status(thm)],[4234, 4233])).
% 2.02/2.25 tff(4236,plain,
% 2.02/2.25 (~r(s(s(z)), s(z))),
% 2.02/2.25 inference(unit_resolution,[status(thm)],[4235, 197, 311, 377, 333])).
% 2.02/2.25 tff(4237,plain,
% 2.02/2.25 (b(s(s(z)), s(z))),
% 2.02/2.25 inference(unit_resolution,[status(thm)],[308, 4236])).
% 2.02/2.25 tff(4238,plain,
% 2.02/2.25 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(s(elem!1)))) | (~r(s(s(elem!1)), s(s(s(elem!1))))) | (~r(s(s(z)), s(s(elem!1)))) | (~r(s(z), s(s(z)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(z), s(s(elem!1)))) | (~r(s(s(elem!1)), s(s(s(elem!1))))) | (~r(s(s(z)), s(s(elem!1)))) | (~r(s(z), s(s(z)))))),
% 2.02/2.25 inference(rewrite,[status(thm)],[])).
% 2.02/2.25 tff(4239,plain,
% 2.02/2.25 (((~r(s(s(elem!1)), s(s(s(elem!1))))) | (~r(s(s(z)), s(s(elem!1)))) | (~r(s(z), s(s(elem!1)))) | (~r(s(z), s(s(z))))) <=> ((~r(s(z), s(s(elem!1)))) | (~r(s(s(elem!1)), s(s(s(elem!1))))) | (~r(s(s(z)), s(s(elem!1)))) | (~r(s(z), s(s(z)))))),
% 2.02/2.25 inference(rewrite,[status(thm)],[])).
% 2.02/2.25 tff(4240,plain,
% 2.02/2.25 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(elem!1)), s(s(s(elem!1))))) | (~r(s(s(z)), s(s(elem!1)))) | (~r(s(z), s(s(elem!1)))) | (~r(s(z), s(s(z)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(s(elem!1)))) | (~r(s(s(elem!1)), s(s(s(elem!1))))) | (~r(s(s(z)), s(s(elem!1)))) | (~r(s(z), s(s(z))))))),
% 2.02/2.25 inference(monotonicity,[status(thm)],[4239])).
% 2.02/2.25 tff(4241,plain,
% 2.02/2.25 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(elem!1)), s(s(s(elem!1))))) | (~r(s(s(z)), s(s(elem!1)))) | (~r(s(z), s(s(elem!1)))) | (~r(s(z), s(s(z)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(z), s(s(elem!1)))) | (~r(s(s(elem!1)), s(s(s(elem!1))))) | (~r(s(s(z)), s(s(elem!1)))) | (~r(s(z), s(s(z)))))),
% 2.02/2.25 inference(transitivity,[status(thm)],[4240, 4238])).
% 2.02/2.25 tff(4242,plain,
% 2.02/2.25 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(elem!1)), s(s(s(elem!1))))) | (~r(s(s(z)), s(s(elem!1)))) | (~r(s(z), s(s(elem!1)))) | (~r(s(z), s(s(z)))))),
% 2.02/2.25 inference(quant_inst,[status(thm)],[])).
% 2.02/2.25 tff(4243,plain,
% 2.02/2.25 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(z), s(s(elem!1)))) | (~r(s(s(elem!1)), s(s(s(elem!1))))) | (~r(s(s(z)), s(s(elem!1)))) | (~r(s(z), s(s(z))))),
% 2.02/2.25 inference(modus_ponens,[status(thm)],[4242, 4241])).
% 2.02/2.25 tff(4244,plain,
% 2.02/2.25 (~r(s(z), s(s(z)))),
% 2.02/2.25 inference(unit_resolution,[status(thm)],[4243, 197, 311, 377, 333])).
% 2.02/2.25 tff(4245,plain,
% 2.02/2.25 (b(s(z), s(s(z)))),
% 2.02/2.25 inference(unit_resolution,[status(thm)],[427, 4244])).
% 2.02/2.25 tff(4246,plain,
% 2.02/2.25 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), s(s(z)))) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(z), s(s(z)))) | (~b(s(s(z)), s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(elem!1))), s(s(z)))) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(z), s(s(z)))) | (~b(s(s(z)), s(z))))),
% 2.02/2.25 inference(rewrite,[status(thm)],[])).
% 2.02/2.25 tff(4247,plain,
% 2.02/2.25 (((~b(s(s(z)), s(z))) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(z), s(s(z)))) | (~b(s(s(z)), s(z))) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(s(s(elem!1))), s(s(z))))) <=> ((~b(s(s(s(elem!1))), s(s(z)))) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(z), s(s(z)))) | (~b(s(s(z)), s(z))))),
% 2.02/2.25 inference(rewrite,[status(thm)],[])).
% 2.02/2.25 tff(4248,plain,
% 2.02/2.25 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), s(z))) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(z), s(s(z)))) | (~b(s(s(z)), s(z))) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(s(s(elem!1))), s(s(z)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), s(s(z)))) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(z), s(s(z)))) | (~b(s(s(z)), s(z)))))),
% 2.02/2.25 inference(monotonicity,[status(thm)],[4247])).
% 2.02/2.25 tff(4249,plain,
% 2.02/2.25 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), s(z))) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(z), s(s(z)))) | (~b(s(s(z)), s(z))) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(s(s(elem!1))), s(s(z)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(elem!1))), s(s(z)))) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(z), s(s(z)))) | (~b(s(s(z)), s(z))))),
% 2.02/2.25 inference(transitivity,[status(thm)],[4248, 4246])).
% 2.02/2.25 tff(4250,plain,
% 2.02/2.25 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), s(z))) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(z), s(s(z)))) | (~b(s(s(z)), s(z))) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(s(s(elem!1))), s(s(z)))))),
% 2.02/2.25 inference(quant_inst,[status(thm)],[])).
% 2.02/2.25 tff(4251,plain,
% 2.02/2.25 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(elem!1))), s(s(z)))) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(z), s(s(z)))) | (~b(s(s(z)), s(z)))),
% 2.02/2.25 inference(modus_ponens,[status(thm)],[4250, 4249])).
% 2.02/2.25 tff(4252,plain,
% 2.02/2.25 ($false),
% 2.02/2.25 inference(unit_resolution,[status(thm)],[4251, 166, 4245, 96, 4237, 2060])).
% 2.02/2.25 tff(4253,plain,((~r(s(s(z)), s(s(elem!1)))) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(s(s(elem!1))), s(s(z)))) | (~r(s(z), s(s(elem!1)))) | (~r(s(s(elem!1)), s(s(s(elem!1)))))), inference(lemma,lemma(discharge,[]))).
% 2.02/2.25 tff(4254,plain,
% 2.02/2.25 (~r(s(s(z)), s(s(elem!1)))),
% 2.02/2.25 inference(unit_resolution,[status(thm)],[4253, 4218, 4214, 4229, 311])).
% 2.02/2.25 tff(4255,plain,
% 2.02/2.25 ($false),
% 2.02/2.25 inference(unit_resolution,[status(thm)],[390, 4254, 4227, 52])).
% 2.02/2.25 tff(4256,plain,((~b(s(z), s(s(s(elem!1))))) | (s(s(z)) = s(s(elem!1))) | (~r(s(z), s(s(elem!1)))) | (~b(s(s(elem!1)), s(z))) | (~b(s(z), s(s(z)))) | (~r(z, s(s(z)))) | (~r(s(s(z)), s(z))) | (s(s(elem!1)) = s(s(s(elem!1)))) | (~b(z, s(z)))), inference(lemma,lemma(discharge,[]))).
% 2.02/2.25 tff(4257,plain,
% 2.02/2.25 (~b(s(z), s(s(s(elem!1))))),
% 2.02/2.25 inference(unit_resolution,[status(thm)],[4256, 45, 311, 310, 556, 155, 392, 52, 118])).
% 2.02/2.25 tff(4258,plain,
% 2.02/2.25 (r(s(z), s(s(s(elem!1))))),
% 2.02/2.25 inference(unit_resolution,[status(thm)],[116, 4257])).
% 2.02/2.25 tff(4259,plain,
% 2.02/2.25 (~r(s(s(s(elem!1))), s(s(z)))),
% 2.02/2.25 inference(unit_resolution,[status(thm)],[2939, 377, 119, 311])).
% 2.02/2.25 tff(4260,plain,
% 2.02/2.25 (b(s(s(s(elem!1))), s(s(z)))),
% 2.02/2.25 inference(unit_resolution,[status(thm)],[218, 4259])).
% 2.02/2.25 tff(4261,plain,
% 2.02/2.25 (~b(s(s(z)), s(s(elem!1)))),
% 2.02/2.25 inference(unit_resolution,[status(thm)],[4226, 4260, 310, 556, 96])).
% 2.02/2.25 tff(4262,plain,
% 2.02/2.25 (~r(s(s(z)), s(s(elem!1)))),
% 2.02/2.25 inference(unit_resolution,[status(thm)],[4253, 4260, 96, 377, 311])).
% 2.02/2.25 tff(4263,plain,
% 2.02/2.25 ($false),
% 2.02/2.25 inference(unit_resolution,[status(thm)],[390, 4262, 4261, 52])).
% 2.02/2.25 tff(4264,plain,((~r(s(s(elem!1)), s(s(s(elem!1))))) | (s(s(z)) = s(s(elem!1))) | (~b(s(s(s(elem!1))), s(z))) | (~r(s(z), s(s(elem!1)))) | (~b(s(s(elem!1)), s(z))) | (~b(s(z), s(s(z)))) | (~r(s(z), s(s(s(elem!1)))))), inference(lemma,lemma(discharge,[]))).
% 2.02/2.25 tff(4265,plain,
% 2.02/2.25 (~r(s(s(elem!1)), s(s(s(elem!1))))),
% 2.02/2.25 inference(unit_resolution,[status(thm)],[4264, 4258, 4214, 311, 310, 556, 52])).
% 2.02/2.25 tff(4266,plain,
% 2.02/2.25 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(z), z)) | (~b(s(s(s(elem!1))), s(z))) | (~b(z, s(z))) | (~b(s(s(elem!1)), s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(z), z)) | (~b(s(s(s(elem!1))), s(z))) | (~b(z, s(z))) | (~b(s(s(elem!1)), s(z))))),
% 2.02/2.25 inference(rewrite,[status(thm)],[])).
% 2.02/2.25 tff(4267,plain,
% 2.02/2.25 (((~b(z, s(z))) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(z), z)) | (~b(s(s(elem!1)), s(z))) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(s(s(elem!1))), s(s(elem!1))))) <=> ((~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(z), z)) | (~b(s(s(s(elem!1))), s(z))) | (~b(z, s(z))) | (~b(s(s(elem!1)), s(z))))),
% 2.02/2.25 inference(rewrite,[status(thm)],[])).
% 2.02/2.25 tff(4268,plain,
% 2.02/2.25 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(z))) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(z), z)) | (~b(s(s(elem!1)), s(z))) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(s(s(elem!1))), s(s(elem!1)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(z), z)) | (~b(s(s(s(elem!1))), s(z))) | (~b(z, s(z))) | (~b(s(s(elem!1)), s(z)))))),
% 2.02/2.25 inference(monotonicity,[status(thm)],[4267])).
% 2.02/2.25 tff(4269,plain,
% 2.02/2.25 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(z))) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(z), z)) | (~b(s(s(elem!1)), s(z))) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(s(s(elem!1))), s(s(elem!1)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(z), z)) | (~b(s(s(s(elem!1))), s(z))) | (~b(z, s(z))) | (~b(s(s(elem!1)), s(z))))),
% 2.02/2.25 inference(transitivity,[status(thm)],[4268, 4266])).
% 2.02/2.25 tff(4270,plain,
% 2.02/2.25 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(z))) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(z), z)) | (~b(s(s(elem!1)), s(z))) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(s(s(elem!1))), s(s(elem!1)))))),
% 2.02/2.25 inference(quant_inst,[status(thm)],[])).
% 2.02/2.25 tff(4271,plain,
% 2.02/2.25 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(z), z)) | (~b(s(s(s(elem!1))), s(z))) | (~b(z, s(z))) | (~b(s(s(elem!1)), s(z)))),
% 2.02/2.25 inference(modus_ponens,[status(thm)],[4270, 4269])).
% 2.02/2.25 tff(4272,plain,
% 2.02/2.25 (~b(s(s(s(elem!1))), s(s(elem!1)))),
% 2.02/2.25 inference(unit_resolution,[status(thm)],[4271, 166, 53, 96, 118, 310])).
% 2.02/2.25 tff(4273,plain,
% 2.02/2.25 (r(s(s(s(elem!1))), s(s(elem!1)))),
% 2.02/2.25 inference(unit_resolution,[status(thm)],[889, 4272, 51])).
% 2.02/2.25 tff(4274,plain,
% 2.02/2.25 (~b(s(s(elem!1)), s(s(s(elem!1))))),
% 2.02/2.25 inference(unit_resolution,[status(thm)],[4007, 166, 53, 96, 118, 310])).
% 2.02/2.25 tff(4275,plain,
% 2.02/2.25 (r(s(s(elem!1)), s(s(s(elem!1))))),
% 2.02/2.25 inference(unit_resolution,[status(thm)],[461, 4274, 45])).
% 2.02/2.25 tff(4276,plain,
% 2.02/2.25 ($false),
% 2.02/2.25 inference(unit_resolution,[status(thm)],[1386, 4275, 4273, 4084, 3496])).
% 2.02/2.25 tff(4277,plain,((~b(s(z), z)) | (s(s(elem!1)) = s(s(s(elem!1)))) | (~b(s(s(s(elem!1))), s(z))) | (~b(z, s(z))) | (~b(s(s(elem!1)), s(z)))), inference(lemma,lemma(discharge,[]))).
% 2.02/2.25 tff(4278,plain,
% 2.02/2.25 (~b(s(z), z)),
% 2.02/2.25 inference(unit_resolution,[status(thm)],[4277, 45, 4214, 118, 310])).
% 2.02/2.25 tff(4279,plain,
% 2.02/2.25 (r(s(z), z)),
% 2.02/2.25 inference(unit_resolution,[status(thm)],[230, 4278])).
% 2.02/2.25 tff(4280,plain,
% 2.02/2.25 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), z)) | (~r(s(s(z)), s(z))) | (~r(s(s(z)), z)) | (~r(z, s(s(z)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(z), z)) | (~r(s(s(z)), s(z))) | (~r(s(s(z)), z)) | (~r(z, s(s(z)))))),
% 2.02/2.25 inference(rewrite,[status(thm)],[])).
% 2.02/2.25 tff(4281,plain,
% 2.02/2.25 (((~r(z, s(s(z)))) | (~r(s(z), z)) | (~r(s(s(z)), z)) | (~r(s(s(z)), s(z)))) <=> ((~r(s(z), z)) | (~r(s(s(z)), s(z))) | (~r(s(s(z)), z)) | (~r(z, s(s(z)))))),
% 2.02/2.25 inference(rewrite,[status(thm)],[])).
% 2.02/2.25 tff(4282,plain,
% 2.02/2.25 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(z)))) | (~r(s(z), z)) | (~r(s(s(z)), z)) | (~r(s(s(z)), s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), z)) | (~r(s(s(z)), s(z))) | (~r(s(s(z)), z)) | (~r(z, s(s(z))))))),
% 2.02/2.25 inference(monotonicity,[status(thm)],[4281])).
% 2.02/2.25 tff(4283,plain,
% 2.02/2.25 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(z)))) | (~r(s(z), z)) | (~r(s(s(z)), z)) | (~r(s(s(z)), s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(z), z)) | (~r(s(s(z)), s(z))) | (~r(s(s(z)), z)) | (~r(z, s(s(z)))))),
% 2.02/2.25 inference(transitivity,[status(thm)],[4282, 4280])).
% 2.02/2.25 tff(4284,plain,
% 2.02/2.25 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(z)))) | (~r(s(z), z)) | (~r(s(s(z)), z)) | (~r(s(s(z)), s(z))))),
% 2.02/2.25 inference(quant_inst,[status(thm)],[])).
% 2.02/2.25 tff(4285,plain,
% 2.02/2.25 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(z), z)) | (~r(s(s(z)), s(z))) | (~r(s(s(z)), z)) | (~r(z, s(s(z))))),
% 2.02/2.25 inference(modus_ponens,[status(thm)],[4284, 4283])).
% 2.02/2.25 tff(4286,plain,
% 2.02/2.25 ($false),
% 2.02/2.25 inference(unit_resolution,[status(thm)],[4285, 197, 155, 97, 392, 866])).
% 2.02/2.25 tff(4287,plain,((~r(s(s(z)), z)) | (~r(z, s(s(z)))) | (~r(s(z), z)) | (~r(s(s(z)), s(z)))), inference(lemma,lemma(discharge,[]))).
% 2.02/2.25 tff(4288,plain,
% 2.02/2.25 (~r(s(s(z)), z)),
% 2.02/2.25 inference(unit_resolution,[status(thm)],[4287, 4279, 155, 392])).
% 2.02/2.25 tff(4289,plain,
% 2.02/2.25 (b(s(s(z)), z)),
% 2.02/2.25 inference(unit_resolution,[status(thm)],[186, 4288])).
% 2.02/2.25 tff(4290,plain,
% 2.02/2.25 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), s(s(z)))) | (~b(z, s(z))) | (~b(s(s(elem!1)), s(z))) | (~b(s(z), s(s(z)))) | (~b(s(s(z)), z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(elem!1)), s(s(z)))) | (~b(z, s(z))) | (~b(s(s(elem!1)), s(z))) | (~b(s(z), s(s(z)))) | (~b(s(s(z)), z)))),
% 2.02/2.25 inference(rewrite,[status(thm)],[])).
% 2.02/2.25 tff(4291,plain,
% 2.02/2.25 (((~b(z, s(z))) | (~b(s(s(elem!1)), s(z))) | (~b(s(s(z)), z)) | (~b(s(z), s(s(z)))) | (~b(s(s(elem!1)), s(s(z)))) | (~b(s(s(elem!1)), s(z)))) <=> ((~b(s(s(elem!1)), s(s(z)))) | (~b(z, s(z))) | (~b(s(s(elem!1)), s(z))) | (~b(s(z), s(s(z)))) | (~b(s(s(z)), z)))),
% 2.02/2.25 inference(rewrite,[status(thm)],[])).
% 2.02/2.25 tff(4292,plain,
% 2.02/2.25 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(z))) | (~b(s(s(elem!1)), s(z))) | (~b(s(s(z)), z)) | (~b(s(z), s(s(z)))) | (~b(s(s(elem!1)), s(s(z)))) | (~b(s(s(elem!1)), s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), s(s(z)))) | (~b(z, s(z))) | (~b(s(s(elem!1)), s(z))) | (~b(s(z), s(s(z)))) | (~b(s(s(z)), z))))),
% 2.02/2.25 inference(monotonicity,[status(thm)],[4291])).
% 2.02/2.25 tff(4293,plain,
% 2.02/2.25 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(z))) | (~b(s(s(elem!1)), s(z))) | (~b(s(s(z)), z)) | (~b(s(z), s(s(z)))) | (~b(s(s(elem!1)), s(s(z)))) | (~b(s(s(elem!1)), s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(elem!1)), s(s(z)))) | (~b(z, s(z))) | (~b(s(s(elem!1)), s(z))) | (~b(s(z), s(s(z)))) | (~b(s(s(z)), z)))),
% 2.02/2.25 inference(transitivity,[status(thm)],[4292, 4290])).
% 2.02/2.25 tff(4294,plain,
% 2.02/2.25 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(z))) | (~b(s(s(elem!1)), s(z))) | (~b(s(s(z)), z)) | (~b(s(z), s(s(z)))) | (~b(s(s(elem!1)), s(s(z)))) | (~b(s(s(elem!1)), s(z))))),
% 2.02/2.25 inference(quant_inst,[status(thm)],[])).
% 2.02/2.25 tff(4295,plain,
% 2.02/2.25 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(elem!1)), s(s(z)))) | (~b(z, s(z))) | (~b(s(s(elem!1)), s(z))) | (~b(s(z), s(s(z)))) | (~b(s(s(z)), z))),
% 2.02/2.25 inference(modus_ponens,[status(thm)],[4294, 4293])).
% 2.02/2.25 tff(4296,plain,
% 2.02/2.25 (~b(s(s(elem!1)), s(s(z)))),
% 2.02/2.25 inference(unit_resolution,[status(thm)],[4295, 166, 556, 118, 310, 4289])).
% 2.02/2.25 tff(4297,plain,
% 2.02/2.25 (r(s(s(elem!1)), s(s(z)))),
% 2.02/2.25 inference(unit_resolution,[status(thm)],[441, 4296, 132])).
% 2.02/2.25 tff(4298,plain,
% 2.02/2.25 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), s(s(z)))) | (~b(s(s(s(elem!1))), s(z))) | (~b(z, s(z))) | (~b(s(z), s(s(z)))) | (~b(s(s(z)), z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(elem!1))), s(s(z)))) | (~b(s(s(s(elem!1))), s(z))) | (~b(z, s(z))) | (~b(s(z), s(s(z)))) | (~b(s(s(z)), z)))),
% 2.02/2.25 inference(rewrite,[status(thm)],[])).
% 2.02/2.25 tff(4299,plain,
% 2.02/2.25 (((~b(z, s(z))) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(s(z)), z)) | (~b(s(z), s(s(z)))) | (~b(s(s(s(elem!1))), s(s(z)))) | (~b(s(s(s(elem!1))), s(z)))) <=> ((~b(s(s(s(elem!1))), s(s(z)))) | (~b(s(s(s(elem!1))), s(z))) | (~b(z, s(z))) | (~b(s(z), s(s(z)))) | (~b(s(s(z)), z)))),
% 2.02/2.25 inference(rewrite,[status(thm)],[])).
% 2.02/2.25 tff(4300,plain,
% 2.02/2.25 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(z))) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(s(z)), z)) | (~b(s(z), s(s(z)))) | (~b(s(s(s(elem!1))), s(s(z)))) | (~b(s(s(s(elem!1))), s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), s(s(z)))) | (~b(s(s(s(elem!1))), s(z))) | (~b(z, s(z))) | (~b(s(z), s(s(z)))) | (~b(s(s(z)), z))))),
% 2.02/2.25 inference(monotonicity,[status(thm)],[4299])).
% 2.02/2.25 tff(4301,plain,
% 2.02/2.25 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(z))) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(s(z)), z)) | (~b(s(z), s(s(z)))) | (~b(s(s(s(elem!1))), s(s(z)))) | (~b(s(s(s(elem!1))), s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(elem!1))), s(s(z)))) | (~b(s(s(s(elem!1))), s(z))) | (~b(z, s(z))) | (~b(s(z), s(s(z)))) | (~b(s(s(z)), z)))),
% 2.02/2.26 inference(transitivity,[status(thm)],[4300, 4298])).
% 2.02/2.26 tff(4302,plain,
% 2.02/2.26 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(z))) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(s(z)), z)) | (~b(s(z), s(s(z)))) | (~b(s(s(s(elem!1))), s(s(z)))) | (~b(s(s(s(elem!1))), s(z))))),
% 2.02/2.26 inference(quant_inst,[status(thm)],[])).
% 2.02/2.26 tff(4303,plain,
% 2.02/2.26 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(elem!1))), s(s(z)))) | (~b(s(s(s(elem!1))), s(z))) | (~b(z, s(z))) | (~b(s(z), s(s(z)))) | (~b(s(s(z)), z))),
% 2.02/2.26 inference(modus_ponens,[status(thm)],[4302, 4301])).
% 2.02/2.26 tff(4304,plain,
% 2.02/2.26 (~b(s(s(s(elem!1))), s(s(z)))),
% 2.02/2.26 inference(unit_resolution,[status(thm)],[4303, 166, 556, 4214, 118, 4289])).
% 2.02/2.26 tff(4305,plain,
% 2.02/2.26 (r(s(s(s(elem!1))), s(s(z)))),
% 2.02/2.26 inference(unit_resolution,[status(thm)],[218, 4304])).
% 2.02/2.26 tff(4306,plain,
% 2.02/2.26 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), s(s(elem!1)))) | (~r(s(s(z)), s(z))) | (~r(s(s(elem!1)), s(s(z)))) | (~r(s(s(s(elem!1))), s(s(z)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(elem!1))), s(s(elem!1)))) | (~r(s(s(z)), s(z))) | (~r(s(s(elem!1)), s(s(z)))) | (~r(s(s(s(elem!1))), s(s(z)))))),
% 2.02/2.26 inference(rewrite,[status(thm)],[])).
% 2.02/2.26 tff(4307,plain,
% 2.02/2.26 (((~r(s(s(z)), s(z))) | (~r(s(s(elem!1)), s(s(z)))) | (~r(s(s(s(elem!1))), s(s(z)))) | (~r(s(s(s(elem!1))), s(s(elem!1))))) <=> ((~r(s(s(s(elem!1))), s(s(elem!1)))) | (~r(s(s(z)), s(z))) | (~r(s(s(elem!1)), s(s(z)))) | (~r(s(s(s(elem!1))), s(s(z)))))),
% 2.02/2.26 inference(rewrite,[status(thm)],[])).
% 2.02/2.26 tff(4308,plain,
% 2.02/2.26 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(z)), s(z))) | (~r(s(s(elem!1)), s(s(z)))) | (~r(s(s(s(elem!1))), s(s(z)))) | (~r(s(s(s(elem!1))), s(s(elem!1)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), s(s(elem!1)))) | (~r(s(s(z)), s(z))) | (~r(s(s(elem!1)), s(s(z)))) | (~r(s(s(s(elem!1))), s(s(z))))))),
% 2.02/2.26 inference(monotonicity,[status(thm)],[4307])).
% 2.02/2.26 tff(4309,plain,
% 2.02/2.26 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(z)), s(z))) | (~r(s(s(elem!1)), s(s(z)))) | (~r(s(s(s(elem!1))), s(s(z)))) | (~r(s(s(s(elem!1))), s(s(elem!1)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(elem!1))), s(s(elem!1)))) | (~r(s(s(z)), s(z))) | (~r(s(s(elem!1)), s(s(z)))) | (~r(s(s(s(elem!1))), s(s(z)))))),
% 2.02/2.26 inference(transitivity,[status(thm)],[4308, 4306])).
% 2.02/2.26 tff(4310,plain,
% 2.02/2.26 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(z)), s(z))) | (~r(s(s(elem!1)), s(s(z)))) | (~r(s(s(s(elem!1))), s(s(z)))) | (~r(s(s(s(elem!1))), s(s(elem!1)))))),
% 2.02/2.26 inference(quant_inst,[status(thm)],[])).
% 2.02/2.26 tff(4311,plain,
% 2.02/2.26 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(elem!1))), s(s(elem!1)))) | (~r(s(s(z)), s(z))) | (~r(s(s(elem!1)), s(s(z)))) | (~r(s(s(s(elem!1))), s(s(z))))),
% 2.02/2.26 inference(modus_ponens,[status(thm)],[4310, 4309])).
% 2.02/2.26 tff(4312,plain,
% 2.02/2.26 ($false),
% 2.02/2.26 inference(unit_resolution,[status(thm)],[4311, 197, 393, 392, 905, 464])).
% 2.02/2.26 tff(4313,plain,((~r(s(s(elem!1)), s(s(z)))) | (~r(s(s(z)), s(z))) | (~r(s(s(s(elem!1))), s(s(elem!1)))) | (~r(s(s(s(elem!1))), s(s(z))))), inference(lemma,lemma(discharge,[]))).
% 2.02/2.26 tff(4314,plain,
% 2.02/2.26 (~r(s(s(s(elem!1))), s(s(elem!1)))),
% 2.02/2.26 inference(unit_resolution,[status(thm)],[4313, 4305, 392, 4297])).
% 2.02/2.26 tff(4315,plain,
% 2.02/2.26 (~r(z, s(s(s(elem!1))))),
% 2.02/2.26 inference(unit_resolution,[status(thm)],[1588, 4305, 155, 392])).
% 2.02/2.26 tff(4316,plain,
% 2.02/2.26 (b(z, s(s(s(elem!1))))),
% 2.02/2.26 inference(unit_resolution,[status(thm)],[261, 4315])).
% 2.02/2.26 tff(4317,plain,
% 2.02/2.26 (~r(z, s(s(elem!1)))),
% 2.02/2.26 inference(unit_resolution,[status(thm)],[401, 4297, 155, 392])).
% 2.02/2.26 tff(4318,plain,
% 2.02/2.26 (b(z, s(s(elem!1)))),
% 2.02/2.26 inference(unit_resolution,[status(thm)],[1795, 4317])).
% 2.02/2.26 tff(4319,plain,
% 2.02/2.26 ($false),
% 2.02/2.26 inference(unit_resolution,[status(thm)],[1834, 4318, 4316, 45, 4314, 4265])).
% 2.02/2.26 tff(4320,plain,((s(s(elem!1)) = s(s(s(elem!1)))) | (~r(z, s(s(z)))) | (~r(s(s(z)), s(z))) | (~b(s(z), s(s(z)))) | (~b(z, s(z))) | (~b(s(s(elem!1)), s(z))) | (~r(s(z), s(s(elem!1)))) | (s(s(z)) = s(s(elem!1)))), inference(lemma,lemma(discharge,[]))).
% 2.02/2.26 tff(4321,plain,
% 2.02/2.26 (s(s(elem!1)) = s(s(s(elem!1)))),
% 2.02/2.26 inference(unit_resolution,[status(thm)],[4320, 4143, 155, 556, 4176, 310, 85, 4144])).
% 2.02/2.26 tff(4322,plain,
% 2.02/2.26 (b(s(s(elem!1)), z) <=> b(s(s(s(elem!1))), z)),
% 2.02/2.26 inference(monotonicity,[status(thm)],[334])).
% 2.02/2.26 tff(4323,plain,
% 2.02/2.26 (b(s(s(s(elem!1))), z) <=> b(s(s(elem!1)), z)),
% 2.02/2.26 inference(symmetry,[status(thm)],[4322])).
% 2.02/2.26 tff(4324,plain,
% 2.02/2.26 (b(s(elem!1), z) <=> b(s(s(s(elem!1))), z)),
% 2.02/2.26 inference(monotonicity,[status(thm)],[3116])).
% 2.02/2.26 tff(4325,plain,
% 2.02/2.26 (b(s(elem!1), z) <=> b(s(s(elem!1)), z)),
% 2.02/2.26 inference(transitivity,[status(thm)],[4324, 4323])).
% 2.02/2.26 tff(4326,plain,
% 2.02/2.26 ((~b(s(elem!1), z)) <=> (~b(s(s(elem!1)), z))),
% 2.02/2.26 inference(monotonicity,[status(thm)],[4325])).
% 2.02/2.26 tff(4327,plain,
% 2.02/2.26 (b(s(elem!1), s(z)) <=> b(s(s(s(elem!1))), s(z))),
% 2.02/2.26 inference(monotonicity,[status(thm)],[3116])).
% 2.02/2.26 tff(4328,plain,
% 2.02/2.26 (b(s(s(s(elem!1))), s(z)) <=> b(s(elem!1), s(z))),
% 2.02/2.26 inference(symmetry,[status(thm)],[4327])).
% 2.02/2.26 tff(4329,plain,
% 2.02/2.26 (b(s(elem!1), s(z))),
% 2.02/2.26 inference(modus_ponens,[status(thm)],[96, 4328])).
% 2.02/2.26 tff(4330,assumption,(b(s(elem!1), s(z))), introduced(assumption)).
% 2.02/2.26 tff(4331,plain,
% 2.02/2.26 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), z)) | (~b(s(z), z)) | (~b(s(elem!1), s(z))) | (~b(z, s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(elem!1), z)) | (~b(s(z), z)) | (~b(s(elem!1), s(z))) | (~b(z, s(z))))),
% 2.02/2.26 inference(rewrite,[status(thm)],[])).
% 2.02/2.26 tff(4332,plain,
% 2.02/2.26 (((~b(z, s(z))) | (~b(s(elem!1), s(z))) | (~b(s(z), z)) | (~b(z, s(z))) | (~b(s(elem!1), s(z))) | (~b(s(elem!1), z))) <=> ((~b(s(elem!1), z)) | (~b(s(z), z)) | (~b(s(elem!1), s(z))) | (~b(z, s(z))))),
% 2.02/2.26 inference(rewrite,[status(thm)],[])).
% 2.02/2.26 tff(4333,plain,
% 2.02/2.26 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(z))) | (~b(s(elem!1), s(z))) | (~b(s(z), z)) | (~b(z, s(z))) | (~b(s(elem!1), s(z))) | (~b(s(elem!1), z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), z)) | (~b(s(z), z)) | (~b(s(elem!1), s(z))) | (~b(z, s(z)))))),
% 2.02/2.26 inference(monotonicity,[status(thm)],[4332])).
% 2.02/2.26 tff(4334,plain,
% 2.02/2.26 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(z))) | (~b(s(elem!1), s(z))) | (~b(s(z), z)) | (~b(z, s(z))) | (~b(s(elem!1), s(z))) | (~b(s(elem!1), z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(elem!1), z)) | (~b(s(z), z)) | (~b(s(elem!1), s(z))) | (~b(z, s(z))))),
% 2.02/2.26 inference(transitivity,[status(thm)],[4333, 4331])).
% 2.02/2.26 tff(4335,plain,
% 2.02/2.26 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(z))) | (~b(s(elem!1), s(z))) | (~b(s(z), z)) | (~b(z, s(z))) | (~b(s(elem!1), s(z))) | (~b(s(elem!1), z)))),
% 2.02/2.26 inference(quant_inst,[status(thm)],[])).
% 2.02/2.26 tff(4336,plain,
% 2.02/2.26 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(elem!1), z)) | (~b(s(z), z)) | (~b(s(elem!1), s(z))) | (~b(z, s(z)))),
% 2.02/2.26 inference(modus_ponens,[status(thm)],[4335, 4334])).
% 2.02/2.26 tff(4337,plain,
% 2.02/2.26 ($false),
% 2.02/2.26 inference(unit_resolution,[status(thm)],[4336, 166, 4330, 2747, 53, 118])).
% 2.02/2.26 tff(4338,plain,((~b(s(z), z)) | (~b(s(elem!1), s(z))) | (~b(s(elem!1), z)) | (~b(z, s(z)))), inference(lemma,lemma(discharge,[]))).
% 2.02/2.26 tff(4339,plain,
% 2.02/2.26 (~b(s(elem!1), z)),
% 2.02/2.26 inference(unit_resolution,[status(thm)],[4338, 53, 118, 4329])).
% 2.02/2.26 tff(4340,plain,
% 2.02/2.26 (~b(s(s(elem!1)), z)),
% 2.02/2.26 inference(modus_ponens,[status(thm)],[4339, 4326])).
% 2.02/2.26 tff(4341,plain,
% 2.02/2.26 (b(z, s(s(elem!1))) <=> b(z, s(s(s(elem!1))))),
% 2.02/2.26 inference(monotonicity,[status(thm)],[334])).
% 2.02/2.26 tff(4342,plain,
% 2.02/2.26 (b(z, s(s(s(elem!1)))) <=> b(z, s(s(elem!1)))),
% 2.02/2.26 inference(symmetry,[status(thm)],[4341])).
% 2.02/2.26 tff(4343,plain,
% 2.02/2.26 (b(z, s(s(elem!1)))),
% 2.02/2.26 inference(modus_ponens,[status(thm)],[240, 4342])).
% 2.02/2.26 tff(4344,plain,
% 2.02/2.26 ($false),
% 2.02/2.26 inference(unit_resolution,[status(thm)],[1790, 4343])).
% 2.02/2.26 tff(4345,plain,((~(s(s(elem!1)) = s(s(s(elem!1))))) | b(z, s(s(elem!1))) | (~b(z, s(s(s(elem!1)))))), inference(lemma,lemma(discharge,[]))).
% 2.02/2.26 tff(4346,plain,
% 2.02/2.26 (~b(z, s(s(s(elem!1))))),
% 2.02/2.26 inference(unit_resolution,[status(thm)],[4345, 3495, 334])).
% 2.02/2.26 tff(4347,plain,
% 2.02/2.26 (r(z, s(s(s(elem!1))))),
% 2.02/2.26 inference(unit_resolution,[status(thm)],[261, 4346])).
% 2.02/2.26 tff(4348,plain,
% 2.02/2.26 (~r(s(s(s(elem!1))), s(s(z)))),
% 2.02/2.26 inference(unit_resolution,[status(thm)],[1588, 4347, 155, 392])).
% 2.02/2.26 tff(4349,plain,
% 2.02/2.26 (b(s(s(s(elem!1))), s(s(z)))),
% 2.02/2.26 inference(unit_resolution,[status(thm)],[218, 4348])).
% 2.02/2.26 tff(4350,plain,
% 2.02/2.26 (~b(s(s(z)), s(s(elem!1)))),
% 2.02/2.26 inference(unit_resolution,[status(thm)],[4226, 4349, 310, 556, 96])).
% 2.02/2.26 tff(4351,plain,
% 2.02/2.26 (r(s(s(z)), s(s(elem!1)))),
% 2.02/2.26 inference(unit_resolution,[status(thm)],[390, 4350, 52])).
% 2.02/2.26 tff(4352,plain,
% 2.02/2.26 (r(s(s(z)), s(s(s(elem!1))))),
% 2.02/2.26 inference(unit_resolution,[status(thm)],[338, 4351, 334])).
% 2.02/2.26 tff(4353,plain,
% 2.02/2.26 (~r(s(s(s(elem!1))), z)),
% 2.02/2.26 inference(unit_resolution,[status(thm)],[290, 4352, 155, 4347])).
% 2.02/2.26 tff(4354,plain,
% 2.02/2.26 (~r(s(s(elem!1)), z)),
% 2.02/2.26 inference(unit_resolution,[status(thm)],[2974, 4353, 334])).
% 2.02/2.26 tff(4355,plain,
% 2.02/2.26 (b(s(s(elem!1)), z)),
% 2.02/2.26 inference(unit_resolution,[status(thm)],[608, 4354])).
% 2.02/2.26 tff(4356,plain,
% 2.02/2.26 ($false),
% 2.02/2.26 inference(unit_resolution,[status(thm)],[4355, 4340])).
% 2.02/2.26 tff(4357,plain,((~b(s(z), z)) | (~(s(s(elem!1)) = s(s(s(elem!1))))) | (~r(z, s(s(z)))) | (s(s(z)) = s(s(elem!1))) | (~b(s(s(elem!1)), s(z))) | (~b(s(z), s(s(z)))) | (~b(s(s(s(elem!1))), s(z))) | (~r(s(s(z)), s(z))) | (~b(z, s(z)))), inference(lemma,lemma(discharge,[]))).
% 2.02/2.26 tff(4358,plain,
% 2.02/2.26 (~b(s(z), z)),
% 2.02/2.26 inference(unit_resolution,[status(thm)],[4357, 4321, 155, 4144, 310, 556, 4213, 4143, 4176])).
% 2.02/2.26 tff(4359,plain,
% 2.02/2.26 (r(s(z), z)),
% 2.02/2.26 inference(unit_resolution,[status(thm)],[230, 4358])).
% 2.02/2.26 tff(4360,plain,
% 2.02/2.26 (~r(s(s(z)), z)),
% 2.02/2.26 inference(unit_resolution,[status(thm)],[4287, 4359, 155, 4143])).
% 2.02/2.26 tff(4361,plain,
% 2.02/2.26 (b(s(s(z)), z)),
% 2.02/2.26 inference(unit_resolution,[status(thm)],[186, 4360])).
% 2.02/2.26 tff(4362,plain,
% 2.02/2.26 (s(s(s(elem!1))) = s(elem!1)),
% 2.02/2.26 inference(unit_resolution,[status(thm)],[2594, 4321])).
% 2.02/2.26 tff(4363,plain,
% 2.02/2.26 (s(elem!1) = s(s(s(elem!1)))),
% 2.02/2.26 inference(symmetry,[status(thm)],[4362])).
% 2.02/2.26 tff(4364,plain,
% 2.02/2.26 (inj_0(s(elem!1)) = inj_0(s(s(s(elem!1))))),
% 2.02/2.26 inference(monotonicity,[status(thm)],[4363])).
% 2.02/2.26 tff(4365,plain,
% 2.02/2.26 (elem!1 = s(s(s(elem!1)))),
% 2.02/2.26 inference(transitivity,[status(thm)],[1170, 4364, 104, 4321])).
% 2.02/2.26 tff(4366,plain,
% 2.02/2.26 (b(elem!1, z) <=> b(s(s(s(elem!1))), z)),
% 2.02/2.26 inference(monotonicity,[status(thm)],[4365])).
% 2.02/2.26 tff(4367,plain,
% 2.02/2.26 (~(elem!1 = z)),
% 2.02/2.26 inference(unit_resolution,[status(thm)],[1151, 4146])).
% 2.02/2.26 tff(4368,plain,
% 2.02/2.26 (r(s(z), elem!1) <=> r(s(z), s(s(s(elem!1))))),
% 2.02/2.26 inference(monotonicity,[status(thm)],[4365])).
% 2.02/2.26 tff(4369,plain,
% 2.02/2.26 (r(s(z), s(s(s(elem!1)))) <=> r(s(z), elem!1)),
% 2.02/2.26 inference(symmetry,[status(thm)],[4368])).
% 2.02/2.26 tff(4370,plain,
% 2.02/2.26 (r(s(z), s(s(elem!1))) <=> r(s(z), s(s(s(elem!1))))),
% 2.02/2.26 inference(monotonicity,[status(thm)],[4321])).
% 2.02/2.26 tff(4371,plain,
% 2.02/2.26 (r(s(z), s(s(s(elem!1))))),
% 2.02/2.26 inference(modus_ponens,[status(thm)],[85, 4370])).
% 2.02/2.26 tff(4372,plain,
% 2.02/2.26 (r(s(z), elem!1)),
% 2.02/2.26 inference(modus_ponens,[status(thm)],[4371, 4369])).
% 2.02/2.26 tff(4373,plain,
% 2.02/2.26 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, z)) | (~r(s(z), elem!1)) | (~r(s(z), z)) | (~r(z, s(s(z)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(elem!1, z)) | (~r(s(z), elem!1)) | (~r(s(z), z)) | (~r(z, s(s(z)))))),
% 2.02/2.26 inference(rewrite,[status(thm)],[])).
% 2.02/2.26 tff(4374,plain,
% 2.02/2.26 (((~r(z, s(s(z)))) | (~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)) | (~r(z, s(s(z)))))),
% 2.02/2.26 inference(rewrite,[status(thm)],[])).
% 2.02/2.26 tff(4375,plain,
% 2.02/2.26 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(z)))) | (~r(elem!1, z)) | (~r(s(z), z)) | (~r(s(z), elem!1)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, z)) | (~r(s(z), elem!1)) | (~r(s(z), z)) | (~r(z, s(s(z))))))),
% 2.02/2.26 inference(monotonicity,[status(thm)],[4374])).
% 2.02/2.26 tff(4376,plain,
% 2.02/2.26 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(z)))) | (~r(elem!1, z)) | (~r(s(z), z)) | (~r(s(z), elem!1)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(elem!1, z)) | (~r(s(z), elem!1)) | (~r(s(z), z)) | (~r(z, s(s(z)))))),
% 2.02/2.26 inference(transitivity,[status(thm)],[4375, 4373])).
% 2.02/2.26 tff(4377,plain,
% 2.02/2.26 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(z)))) | (~r(elem!1, z)) | (~r(s(z), z)) | (~r(s(z), elem!1)))),
% 2.02/2.26 inference(quant_inst,[status(thm)],[])).
% 2.02/2.26 tff(4378,plain,
% 2.02/2.26 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(elem!1, z)) | (~r(s(z), elem!1)) | (~r(s(z), z)) | (~r(z, s(s(z))))),
% 2.02/2.26 inference(modus_ponens,[status(thm)],[4377, 4376])).
% 2.02/2.26 tff(4379,plain,
% 2.02/2.26 ((~r(elem!1, z)) | (~r(s(z), elem!1)) | (~r(s(z), z)) | (~r(z, s(s(z))))),
% 2.02/2.26 inference(unit_resolution,[status(thm)],[4378, 197])).
% 2.02/2.26 tff(4380,plain,
% 2.02/2.26 (~r(elem!1, z)),
% 2.02/2.26 inference(unit_resolution,[status(thm)],[4379, 4359, 155, 4372])).
% 2.02/2.26 tff(4381,plain,
% 2.02/2.26 (b(elem!1, z)),
% 2.02/2.26 inference(unit_resolution,[status(thm)],[1239, 4380, 4367])).
% 2.02/2.26 tff(4382,plain,
% 2.02/2.26 (b(s(s(s(elem!1))), z)),
% 2.02/2.26 inference(modus_ponens,[status(thm)],[4381, 4366])).
% 2.02/2.26 tff(4383,plain,
% 2.02/2.26 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), z)) | (~b(s(s(s(elem!1))), s(z))) | (~b(z, s(z))) | (~b(s(z), s(s(z)))) | (~b(s(s(z)), z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(elem!1))), z)) | (~b(s(s(s(elem!1))), s(z))) | (~b(z, s(z))) | (~b(s(z), s(s(z)))) | (~b(s(s(z)), z)))),
% 2.02/2.26 inference(rewrite,[status(thm)],[])).
% 2.02/2.26 tff(4384,plain,
% 2.02/2.26 (((~b(s(s(z)), z)) | (~b(s(s(s(elem!1))), z)) | (~b(s(z), s(s(z)))) | (~b(z, s(z))) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(s(s(elem!1))), z))) <=> ((~b(s(s(s(elem!1))), z)) | (~b(s(s(s(elem!1))), s(z))) | (~b(z, s(z))) | (~b(s(z), s(s(z)))) | (~b(s(s(z)), z)))),
% 2.02/2.26 inference(rewrite,[status(thm)],[])).
% 2.02/2.26 tff(4385,plain,
% 2.02/2.26 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), z)) | (~b(s(s(s(elem!1))), z)) | (~b(s(z), s(s(z)))) | (~b(z, s(z))) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(s(s(elem!1))), z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), z)) | (~b(s(s(s(elem!1))), s(z))) | (~b(z, s(z))) | (~b(s(z), s(s(z)))) | (~b(s(s(z)), z))))),
% 2.02/2.26 inference(monotonicity,[status(thm)],[4384])).
% 2.02/2.26 tff(4386,plain,
% 2.02/2.26 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), z)) | (~b(s(s(s(elem!1))), z)) | (~b(s(z), s(s(z)))) | (~b(z, s(z))) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(s(s(elem!1))), z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(elem!1))), z)) | (~b(s(s(s(elem!1))), s(z))) | (~b(z, s(z))) | (~b(s(z), s(s(z)))) | (~b(s(s(z)), z)))),
% 2.02/2.26 inference(transitivity,[status(thm)],[4385, 4383])).
% 2.02/2.26 tff(4387,plain,
% 2.02/2.26 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), z)) | (~b(s(s(s(elem!1))), z)) | (~b(s(z), s(s(z)))) | (~b(z, s(z))) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(s(s(elem!1))), z)))),
% 2.02/2.26 inference(quant_inst,[status(thm)],[])).
% 2.02/2.26 tff(4388,plain,
% 2.02/2.26 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(elem!1))), z)) | (~b(s(s(s(elem!1))), s(z))) | (~b(z, s(z))) | (~b(s(z), s(s(z)))) | (~b(s(s(z)), z))),
% 2.02/2.26 inference(modus_ponens,[status(thm)],[4387, 4386])).
% 2.02/2.26 tff(4389,plain,
% 2.02/2.26 ($false),
% 2.02/2.26 inference(unit_resolution,[status(thm)],[4388, 166, 556, 4213, 4176, 4382, 4361])).
% 2.02/2.26 tff(4390,plain,(b(s(s(z)), s(z)) | (~b(s(z), s(s(z)))) | (~r(z, s(s(z)))) | (~b(s(s(elem!1)), s(z))) | b(s(z), s(s(elem!1)))), inference(lemma,lemma(discharge,[]))).
% 2.02/2.26 tff(4391,plain,
% 2.02/2.26 (b(s(s(z)), s(z))),
% 2.02/2.26 inference(unit_resolution,[status(thm)],[4390, 4142, 152, 310, 54])).
% 2.02/2.26 tff(4392,plain,
% 2.02/2.26 (~b(s(s(z)), s(s(elem!1)))),
% 2.02/2.26 inference(unit_resolution,[status(thm)],[882, 166, 4142, 310, 4391])).
% 2.02/2.26 tff(4393,plain,
% 2.02/2.26 (b(s(z), s(s(z))) <=> b(s(z), s(s(elem!1)))),
% 2.02/2.26 inference(monotonicity,[status(thm)],[34])).
% 2.02/2.26 tff(4394,plain,
% 2.02/2.26 (b(s(z), s(s(elem!1))) <=> b(s(z), s(s(z)))),
% 2.02/2.26 inference(symmetry,[status(thm)],[4393])).
% 2.02/2.26 tff(4395,plain,
% 2.02/2.26 ((~b(s(z), s(s(elem!1)))) <=> (~b(s(z), s(s(z))))),
% 2.02/2.26 inference(monotonicity,[status(thm)],[4394])).
% 2.02/2.26 tff(4396,plain,
% 2.02/2.26 (~b(s(z), s(s(z)))),
% 2.02/2.26 inference(modus_ponens,[status(thm)],[54, 4395])).
% 2.02/2.26 tff(4397,plain,
% 2.02/2.26 ($false),
% 2.02/2.26 inference(unit_resolution,[status(thm)],[556, 4396])).
% 2.02/2.26 tff(4398,plain,((~(s(s(z)) = s(s(elem!1)))) | (~b(s(z), s(s(z)))) | b(s(z), s(s(elem!1)))), inference(lemma,lemma(discharge,[]))).
% 2.02/2.26 tff(4399,plain,
% 2.02/2.26 (~(s(s(z)) = s(s(elem!1)))),
% 2.02/2.26 inference(unit_resolution,[status(thm)],[4398, 4142, 54])).
% 2.02/2.26 tff(4400,plain,
% 2.02/2.26 (r(s(s(z)), s(s(elem!1)))),
% 2.02/2.26 inference(unit_resolution,[status(thm)],[390, 4399, 4392])).
% 2.02/2.26 tff(4401,plain,
% 2.02/2.26 (((~b(s(s(z)), s(z))) | (~b(s(s(elem!1)), s(z))) | (~b(s(z), s(s(z)))) | (~b(s(s(z)), s(z))) | (~b(s(s(elem!1)), s(z))) | (~b(s(s(elem!1)), s(s(z))))) <=> ((~b(s(s(elem!1)), s(s(z)))) | (~b(s(s(elem!1)), s(z))) | (~b(s(z), s(s(z)))) | (~b(s(s(z)), s(z))))),
% 2.02/2.26 inference(rewrite,[status(thm)],[])).
% 2.02/2.26 tff(4402,plain,
% 2.02/2.26 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), s(z))) | (~b(s(s(elem!1)), s(z))) | (~b(s(z), s(s(z)))) | (~b(s(s(z)), s(z))) | (~b(s(s(elem!1)), s(z))) | (~b(s(s(elem!1)), s(s(z)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), s(s(z)))) | (~b(s(s(elem!1)), s(z))) | (~b(s(z), s(s(z)))) | (~b(s(s(z)), s(z)))))),
% 2.02/2.26 inference(monotonicity,[status(thm)],[4401])).
% 2.02/2.27 tff(4403,plain,
% 2.02/2.27 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), s(z))) | (~b(s(s(elem!1)), s(z))) | (~b(s(z), s(s(z)))) | (~b(s(s(z)), s(z))) | (~b(s(s(elem!1)), s(z))) | (~b(s(s(elem!1)), s(s(z)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(elem!1)), s(s(z)))) | (~b(s(s(elem!1)), s(z))) | (~b(s(z), s(s(z)))) | (~b(s(s(z)), s(z))))),
% 2.02/2.27 inference(transitivity,[status(thm)],[4402, 3611])).
% 2.02/2.27 tff(4404,plain,
% 2.02/2.27 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), s(z))) | (~b(s(s(elem!1)), s(z))) | (~b(s(z), s(s(z)))) | (~b(s(s(z)), s(z))) | (~b(s(s(elem!1)), s(z))) | (~b(s(s(elem!1)), s(s(z)))))),
% 2.02/2.27 inference(quant_inst,[status(thm)],[])).
% 2.02/2.27 tff(4405,plain,
% 2.02/2.27 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(elem!1)), s(s(z)))) | (~b(s(s(elem!1)), s(z))) | (~b(s(z), s(s(z)))) | (~b(s(s(z)), s(z)))),
% 2.02/2.27 inference(modus_ponens,[status(thm)],[4404, 4403])).
% 2.02/2.27 tff(4406,plain,
% 2.02/2.27 (~b(s(s(elem!1)), s(s(z)))),
% 2.02/2.27 inference(unit_resolution,[status(thm)],[4405, 166, 4142, 310, 4391])).
% 2.02/2.27 tff(4407,plain,
% 2.02/2.27 (~(s(s(elem!1)) = s(s(z)))),
% 2.02/2.27 inference(unit_resolution,[status(thm)],[131, 4399])).
% 2.02/2.27 tff(4408,plain,
% 2.02/2.27 (r(s(s(elem!1)), s(s(z)))),
% 2.02/2.27 inference(unit_resolution,[status(thm)],[441, 4407, 4406])).
% 2.02/2.27 tff(4409,assumption,(r(s(s(s(z))), s(s(elem!1)))), introduced(assumption)).
% 2.02/2.27 tff(4410,plain,
% 2.02/2.27 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(z)), s(s(elem!1)))) | (~r(s(s(elem!1)), s(s(z)))) | (~r(s(s(z)), s(s(s(z))))) | (~r(s(s(s(z))), s(s(elem!1)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(z)), s(s(elem!1)))) | (~r(s(s(elem!1)), s(s(z)))) | (~r(s(s(z)), s(s(s(z))))) | (~r(s(s(s(z))), s(s(elem!1)))))),
% 2.02/2.27 inference(rewrite,[status(thm)],[])).
% 2.02/2.27 tff(4411,plain,
% 2.02/2.27 (((~r(s(s(elem!1)), s(s(z)))) | (~r(s(s(s(z))), s(s(elem!1)))) | (~r(s(s(z)), s(s(elem!1)))) | (~r(s(s(z)), s(s(s(z)))))) <=> ((~r(s(s(z)), s(s(elem!1)))) | (~r(s(s(elem!1)), s(s(z)))) | (~r(s(s(z)), s(s(s(z))))) | (~r(s(s(s(z))), s(s(elem!1)))))),
% 2.02/2.27 inference(rewrite,[status(thm)],[])).
% 2.02/2.27 tff(4412,plain,
% 2.02/2.27 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(elem!1)), s(s(z)))) | (~r(s(s(s(z))), s(s(elem!1)))) | (~r(s(s(z)), s(s(elem!1)))) | (~r(s(s(z)), s(s(s(z))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(z)), s(s(elem!1)))) | (~r(s(s(elem!1)), s(s(z)))) | (~r(s(s(z)), s(s(s(z))))) | (~r(s(s(s(z))), s(s(elem!1))))))),
% 2.02/2.27 inference(monotonicity,[status(thm)],[4411])).
% 2.02/2.27 tff(4413,plain,
% 2.02/2.27 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(elem!1)), s(s(z)))) | (~r(s(s(s(z))), s(s(elem!1)))) | (~r(s(s(z)), s(s(elem!1)))) | (~r(s(s(z)), s(s(s(z))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(z)), s(s(elem!1)))) | (~r(s(s(elem!1)), s(s(z)))) | (~r(s(s(z)), s(s(s(z))))) | (~r(s(s(s(z))), s(s(elem!1)))))),
% 2.02/2.27 inference(transitivity,[status(thm)],[4412, 4410])).
% 2.02/2.27 tff(4414,plain,
% 2.02/2.27 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(elem!1)), s(s(z)))) | (~r(s(s(s(z))), s(s(elem!1)))) | (~r(s(s(z)), s(s(elem!1)))) | (~r(s(s(z)), s(s(s(z))))))),
% 2.02/2.27 inference(quant_inst,[status(thm)],[])).
% 2.02/2.27 tff(4415,plain,
% 2.02/2.27 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(z)), s(s(elem!1)))) | (~r(s(s(elem!1)), s(s(z)))) | (~r(s(s(z)), s(s(s(z))))) | (~r(s(s(s(z))), s(s(elem!1))))),
% 2.02/2.27 inference(modus_ponens,[status(thm)],[4414, 4413])).
% 2.02/2.27 tff(4416,plain,
% 2.02/2.27 (~r(s(s(z)), s(s(s(z))))),
% 2.02/2.27 inference(unit_resolution,[status(thm)],[4415, 197, 393, 333, 4409])).
% 2.02/2.27 tff(4417,plain,
% 2.02/2.27 (b(s(s(z)), s(s(s(z))))),
% 2.02/2.27 inference(unit_resolution,[status(thm)],[1730, 4416])).
% 2.02/2.27 tff(4418,plain,
% 2.02/2.27 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(s(elem!1)))) | (~r(s(s(elem!1)), s(s(z)))) | (~r(s(s(s(z))), s(z))) | (~r(s(s(s(z))), s(s(elem!1)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(z), s(s(elem!1)))) | (~r(s(s(elem!1)), s(s(z)))) | (~r(s(s(s(z))), s(z))) | (~r(s(s(s(z))), s(s(elem!1)))))),
% 2.02/2.27 inference(rewrite,[status(thm)],[])).
% 2.02/2.27 tff(4419,plain,
% 2.02/2.27 (((~r(s(s(elem!1)), s(s(z)))) | (~r(s(z), s(s(elem!1)))) | (~r(s(s(s(z))), s(s(elem!1)))) | (~r(s(s(s(z))), s(z)))) <=> ((~r(s(z), s(s(elem!1)))) | (~r(s(s(elem!1)), s(s(z)))) | (~r(s(s(s(z))), s(z))) | (~r(s(s(s(z))), s(s(elem!1)))))),
% 2.02/2.27 inference(rewrite,[status(thm)],[])).
% 2.02/2.27 tff(4420,plain,
% 2.02/2.27 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(elem!1)), s(s(z)))) | (~r(s(z), s(s(elem!1)))) | (~r(s(s(s(z))), s(s(elem!1)))) | (~r(s(s(s(z))), s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(s(elem!1)))) | (~r(s(s(elem!1)), s(s(z)))) | (~r(s(s(s(z))), s(z))) | (~r(s(s(s(z))), s(s(elem!1))))))),
% 2.02/2.27 inference(monotonicity,[status(thm)],[4419])).
% 2.02/2.27 tff(4421,plain,
% 2.02/2.27 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(elem!1)), s(s(z)))) | (~r(s(z), s(s(elem!1)))) | (~r(s(s(s(z))), s(s(elem!1)))) | (~r(s(s(s(z))), s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(z), s(s(elem!1)))) | (~r(s(s(elem!1)), s(s(z)))) | (~r(s(s(s(z))), s(z))) | (~r(s(s(s(z))), s(s(elem!1)))))),
% 2.02/2.27 inference(transitivity,[status(thm)],[4420, 4418])).
% 2.02/2.27 tff(4422,plain,
% 2.02/2.27 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(elem!1)), s(s(z)))) | (~r(s(z), s(s(elem!1)))) | (~r(s(s(s(z))), s(s(elem!1)))) | (~r(s(s(s(z))), s(z))))),
% 2.02/2.27 inference(quant_inst,[status(thm)],[])).
% 2.02/2.27 tff(4423,plain,
% 2.02/2.27 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(z), s(s(elem!1)))) | (~r(s(s(elem!1)), s(s(z)))) | (~r(s(s(s(z))), s(z))) | (~r(s(s(s(z))), s(s(elem!1))))),
% 2.02/2.27 inference(modus_ponens,[status(thm)],[4422, 4421])).
% 2.02/2.27 tff(4424,plain,
% 2.02/2.27 (~r(s(s(s(z))), s(z))),
% 2.02/2.27 inference(unit_resolution,[status(thm)],[4423, 197, 311, 393, 4409])).
% 2.02/2.27 tff(4425,plain,
% 2.02/2.27 (b(s(s(s(z))), s(z))),
% 2.02/2.27 inference(unit_resolution,[status(thm)],[1763, 4424])).
% 2.02/2.27 tff(4426,plain,
% 2.02/2.27 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(s(elem!1)))) | (~r(s(s(elem!1)), s(s(z)))) | (~r(s(z), s(s(s(z))))) | (~r(s(s(s(z))), s(s(elem!1)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(z), s(s(elem!1)))) | (~r(s(s(elem!1)), s(s(z)))) | (~r(s(z), s(s(s(z))))) | (~r(s(s(s(z))), s(s(elem!1)))))),
% 2.02/2.27 inference(rewrite,[status(thm)],[])).
% 2.02/2.27 tff(4427,plain,
% 2.02/2.27 (((~r(s(s(elem!1)), s(s(z)))) | (~r(s(s(s(z))), s(s(elem!1)))) | (~r(s(z), s(s(elem!1)))) | (~r(s(z), s(s(s(z)))))) <=> ((~r(s(z), s(s(elem!1)))) | (~r(s(s(elem!1)), s(s(z)))) | (~r(s(z), s(s(s(z))))) | (~r(s(s(s(z))), s(s(elem!1)))))),
% 2.02/2.27 inference(rewrite,[status(thm)],[])).
% 2.02/2.27 tff(4428,plain,
% 2.02/2.27 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(elem!1)), s(s(z)))) | (~r(s(s(s(z))), s(s(elem!1)))) | (~r(s(z), s(s(elem!1)))) | (~r(s(z), s(s(s(z))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(s(elem!1)))) | (~r(s(s(elem!1)), s(s(z)))) | (~r(s(z), s(s(s(z))))) | (~r(s(s(s(z))), s(s(elem!1))))))),
% 2.02/2.27 inference(monotonicity,[status(thm)],[4427])).
% 2.02/2.27 tff(4429,plain,
% 2.02/2.27 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(elem!1)), s(s(z)))) | (~r(s(s(s(z))), s(s(elem!1)))) | (~r(s(z), s(s(elem!1)))) | (~r(s(z), s(s(s(z))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(z), s(s(elem!1)))) | (~r(s(s(elem!1)), s(s(z)))) | (~r(s(z), s(s(s(z))))) | (~r(s(s(s(z))), s(s(elem!1)))))),
% 2.02/2.27 inference(transitivity,[status(thm)],[4428, 4426])).
% 2.02/2.27 tff(4430,plain,
% 2.02/2.27 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(elem!1)), s(s(z)))) | (~r(s(s(s(z))), s(s(elem!1)))) | (~r(s(z), s(s(elem!1)))) | (~r(s(z), s(s(s(z))))))),
% 2.02/2.27 inference(quant_inst,[status(thm)],[])).
% 2.02/2.27 tff(4431,plain,
% 2.02/2.27 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(z), s(s(elem!1)))) | (~r(s(s(elem!1)), s(s(z)))) | (~r(s(z), s(s(s(z))))) | (~r(s(s(s(z))), s(s(elem!1))))),
% 2.02/2.27 inference(modus_ponens,[status(thm)],[4430, 4429])).
% 2.02/2.27 tff(4432,plain,
% 2.02/2.27 (~r(s(z), s(s(s(z))))),
% 2.02/2.27 inference(unit_resolution,[status(thm)],[4431, 197, 311, 393, 4409])).
% 2.02/2.27 tff(4433,plain,
% 2.02/2.27 (b(s(z), s(s(s(z))))),
% 2.02/2.27 inference(unit_resolution,[status(thm)],[1674, 4432])).
% 2.02/2.27 tff(4434,plain,
% 2.02/2.27 ($false),
% 2.02/2.27 inference(unit_resolution,[status(thm)],[3248, 4433, 4425, 156, 4417])).
% 2.02/2.27 tff(4435,plain,((~r(s(s(s(z))), s(s(elem!1)))) | (~b(s(s(z)), s(z))) | (~r(s(s(elem!1)), s(s(z)))) | (~r(s(s(z)), s(s(elem!1)))) | (~r(s(z), s(s(elem!1))))), inference(lemma,lemma(discharge,[]))).
% 2.02/2.27 tff(4436,plain,
% 2.02/2.27 (~r(s(s(s(z))), s(s(elem!1)))),
% 2.02/2.27 inference(unit_resolution,[status(thm)],[4435, 4391, 4408, 4400, 85])).
% 2.02/2.27 tff(4437,plain,
% 2.02/2.27 ((s(s(elem!1)) = s(s(s(z)))) <=> (s(s(s(z))) = s(s(elem!1)))),
% 2.02/2.27 inference(commutativity,[status(thm)],[])).
% 2.02/2.27 tff(4438,plain,
% 2.02/2.27 (~r(s(s(elem!1)), z)),
% 2.02/2.27 inference(unit_resolution,[status(thm)],[2740, 197, 4408, 152, 4400])).
% 2.02/2.27 tff(4439,plain,
% 2.02/2.27 (b(s(s(elem!1)), z)),
% 2.02/2.27 inference(unit_resolution,[status(thm)],[608, 4438])).
% 2.02/2.27 tff(4440,plain,
% 2.02/2.27 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), z)) | (~b(z, s(z))) | (~b(s(s(elem!1)), s(z))) | (~b(s(z), s(s(z)))) | (~b(s(s(z)), s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(elem!1)), z)) | (~b(z, s(z))) | (~b(s(s(elem!1)), s(z))) | (~b(s(z), s(s(z)))) | (~b(s(s(z)), s(z))))),
% 2.02/2.27 inference(rewrite,[status(thm)],[])).
% 2.02/2.27 tff(4441,plain,
% 2.02/2.27 (((~b(s(s(z)), s(z))) | (~b(s(s(elem!1)), s(z))) | (~b(s(z), s(s(z)))) | (~b(z, s(z))) | (~b(s(s(elem!1)), s(z))) | (~b(s(s(elem!1)), z))) <=> ((~b(s(s(elem!1)), z)) | (~b(z, s(z))) | (~b(s(s(elem!1)), s(z))) | (~b(s(z), s(s(z)))) | (~b(s(s(z)), s(z))))),
% 2.02/2.27 inference(rewrite,[status(thm)],[])).
% 2.02/2.27 tff(4442,plain,
% 2.02/2.27 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), s(z))) | (~b(s(s(elem!1)), s(z))) | (~b(s(z), s(s(z)))) | (~b(z, s(z))) | (~b(s(s(elem!1)), s(z))) | (~b(s(s(elem!1)), z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), z)) | (~b(z, s(z))) | (~b(s(s(elem!1)), s(z))) | (~b(s(z), s(s(z)))) | (~b(s(s(z)), s(z)))))),
% 2.02/2.27 inference(monotonicity,[status(thm)],[4441])).
% 2.02/2.27 tff(4443,plain,
% 2.02/2.27 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), s(z))) | (~b(s(s(elem!1)), s(z))) | (~b(s(z), s(s(z)))) | (~b(z, s(z))) | (~b(s(s(elem!1)), s(z))) | (~b(s(s(elem!1)), z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(elem!1)), z)) | (~b(z, s(z))) | (~b(s(s(elem!1)), s(z))) | (~b(s(z), s(s(z)))) | (~b(s(s(z)), s(z))))),
% 2.02/2.27 inference(transitivity,[status(thm)],[4442, 4440])).
% 2.02/2.27 tff(4444,plain,
% 2.02/2.27 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), s(z))) | (~b(s(s(elem!1)), s(z))) | (~b(s(z), s(s(z)))) | (~b(z, s(z))) | (~b(s(s(elem!1)), s(z))) | (~b(s(s(elem!1)), z)))),
% 2.02/2.27 inference(quant_inst,[status(thm)],[])).
% 2.02/2.27 tff(4445,plain,
% 2.02/2.27 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(elem!1)), z)) | (~b(z, s(z))) | (~b(s(s(elem!1)), s(z))) | (~b(s(z), s(s(z)))) | (~b(s(s(z)), s(z)))),
% 2.02/2.27 inference(modus_ponens,[status(thm)],[4444, 4443])).
% 2.02/2.27 tff(4446,plain,
% 2.02/2.27 ($false),
% 2.02/2.27 inference(unit_resolution,[status(thm)],[4445, 166, 556, 118, 310, 592, 156])).
% 2.02/2.27 tff(4447,plain,((~b(z, s(z))) | (~b(s(z), s(s(z)))) | (~b(s(s(elem!1)), s(z))) | (~b(s(s(elem!1)), z)) | (~b(s(s(z)), s(z)))), inference(lemma,lemma(discharge,[]))).
% 2.02/2.27 tff(4448,plain,
% 2.02/2.27 (~b(z, s(z))),
% 2.02/2.27 inference(unit_resolution,[status(thm)],[4447, 4142, 310, 4439, 4391])).
% 2.02/2.27 tff(4449,plain,
% 2.02/2.27 (r(z, s(z))),
% 2.02/2.27 inference(unit_resolution,[status(thm)],[321, 4448])).
% 2.02/2.27 tff(4450,plain,
% 2.02/2.27 (~b(s(z), z)),
% 2.02/2.27 inference(unit_resolution,[status(thm)],[2253, 323, 152, 310, 45])).
% 2.02/2.27 tff(4451,plain,
% 2.02/2.27 (r(s(z), z)),
% 2.02/2.27 inference(unit_resolution,[status(thm)],[230, 4450])).
% 2.02/2.27 tff(4452,plain,
% 2.02/2.27 (~r(s(s(elem!1)), s(s(s(elem!1))))),
% 2.02/2.27 inference(unit_resolution,[status(thm)],[2919, 4451, 310, 125, 350, 358, 323, 51])).
% 2.02/2.27 tff(4453,plain,
% 2.02/2.27 (b(s(s(elem!1)), s(s(s(elem!1))))),
% 2.02/2.27 inference(unit_resolution,[status(thm)],[461, 4452, 45])).
% 2.02/2.27 tff(4454,plain,
% 2.02/2.27 (~r(s(s(s(elem!1))), z)),
% 2.02/2.27 inference(unit_resolution,[status(thm)],[373, 323, 311, 350])).
% 2.02/2.27 tff(4455,plain,
% 2.02/2.27 (b(s(s(s(elem!1))), z)),
% 2.02/2.27 inference(unit_resolution,[status(thm)],[94, 4454])).
% 2.02/2.27 tff(4456,plain,
% 2.02/2.27 (~r(z, s(s(s(elem!1))))),
% 2.02/2.27 inference(unit_resolution,[status(thm)],[1524, 323, 311, 350])).
% 2.02/2.27 tff(4457,plain,
% 2.02/2.27 (b(z, s(s(s(elem!1))))),
% 2.02/2.27 inference(unit_resolution,[status(thm)],[261, 4456])).
% 2.02/2.27 tff(4458,plain,
% 2.02/2.27 (r(z, s(s(elem!1)))),
% 2.02/2.27 inference(unit_resolution,[status(thm)],[1795, 1790])).
% 2.02/2.27 tff(4459,plain,
% 2.02/2.27 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), z)) | (~r(s(s(s(elem!1))), s(z))) | (~r(z, s(s(elem!1)))) | (~r(s(z), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(elem!1))), z)) | (~r(s(s(s(elem!1))), s(z))) | (~r(z, s(s(elem!1)))) | (~r(s(z), z)))),
% 2.02/2.27 inference(rewrite,[status(thm)],[])).
% 2.02/2.27 tff(4460,plain,
% 2.02/2.27 (((~r(z, s(s(elem!1)))) | (~r(s(z), z)) | (~r(s(s(s(elem!1))), z)) | (~r(s(s(s(elem!1))), s(z)))) <=> ((~r(s(s(s(elem!1))), z)) | (~r(s(s(s(elem!1))), s(z))) | (~r(z, s(s(elem!1)))) | (~r(s(z), z)))),
% 2.02/2.27 inference(rewrite,[status(thm)],[])).
% 2.02/2.27 tff(4461,plain,
% 2.02/2.27 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(elem!1)))) | (~r(s(z), z)) | (~r(s(s(s(elem!1))), z)) | (~r(s(s(s(elem!1))), s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), z)) | (~r(s(s(s(elem!1))), s(z))) | (~r(z, s(s(elem!1)))) | (~r(s(z), z))))),
% 2.02/2.27 inference(monotonicity,[status(thm)],[4460])).
% 2.02/2.27 tff(4462,plain,
% 2.02/2.27 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(elem!1)))) | (~r(s(z), z)) | (~r(s(s(s(elem!1))), z)) | (~r(s(s(s(elem!1))), s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(elem!1))), z)) | (~r(s(s(s(elem!1))), s(z))) | (~r(z, s(s(elem!1)))) | (~r(s(z), z)))),
% 2.02/2.27 inference(transitivity,[status(thm)],[4461, 4459])).
% 2.02/2.27 tff(4463,plain,
% 2.02/2.27 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(elem!1)))) | (~r(s(z), z)) | (~r(s(s(s(elem!1))), z)) | (~r(s(s(s(elem!1))), s(z))))),
% 2.02/2.27 inference(quant_inst,[status(thm)],[])).
% 2.02/2.27 tff(4464,plain,
% 2.02/2.27 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(elem!1))), z)) | (~r(s(s(s(elem!1))), s(z))) | (~r(z, s(s(elem!1)))) | (~r(s(z), z))),
% 2.02/2.27 inference(modus_ponens,[status(thm)],[4463, 4462])).
% 2.02/2.27 tff(4465,plain,
% 2.02/2.27 ($false),
% 2.02/2.27 inference(unit_resolution,[status(thm)],[4464, 197, 154, 350, 97, 365])).
% 2.02/2.27 tff(4466,plain,((~r(s(s(s(elem!1))), z)) | (~r(s(s(s(elem!1))), s(z))) | (~r(s(z), z)) | (~r(z, s(s(elem!1))))), inference(lemma,lemma(discharge,[]))).
% 2.02/2.27 tff(4467,plain,
% 2.02/2.27 (~r(s(s(s(elem!1))), z)),
% 2.02/2.27 inference(unit_resolution,[status(thm)],[4466, 4458, 97, 350])).
% 2.02/2.27 tff(4468,plain,
% 2.02/2.27 (b(s(s(s(elem!1))), z)),
% 2.02/2.27 inference(unit_resolution,[status(thm)],[94, 4467])).
% 2.02/2.27 tff(4469,plain,
% 2.02/2.27 (~(s(s(elem!1)) = s(s(s(elem!1))))),
% 2.02/2.27 inference(unit_resolution,[status(thm)],[4345, 1790, 240])).
% 2.02/2.27 tff(4470,plain,
% 2.02/2.27 (b(s(s(elem!1)), s(s(s(elem!1))))),
% 2.02/2.27 inference(unit_resolution,[status(thm)],[461, 4469, 1821])).
% 2.02/2.27 tff(4471,plain,
% 2.02/2.27 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(s(elem!1)))) | (~r(z, s(s(elem!1)))) | (~r(s(s(elem!1)), z)) | (~r(s(z), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(z), s(s(elem!1)))) | (~r(z, s(s(elem!1)))) | (~r(s(s(elem!1)), z)) | (~r(s(z), z)))),
% 2.02/2.27 inference(rewrite,[status(thm)],[])).
% 2.02/2.27 tff(4472,plain,
% 2.02/2.27 (((~r(z, s(s(elem!1)))) | (~r(s(s(elem!1)), z)) | (~r(s(z), z)) | (~r(s(z), s(s(elem!1))))) <=> ((~r(s(z), s(s(elem!1)))) | (~r(z, s(s(elem!1)))) | (~r(s(s(elem!1)), z)) | (~r(s(z), z)))),
% 2.02/2.27 inference(rewrite,[status(thm)],[])).
% 2.02/2.27 tff(4473,plain,
% 2.02/2.27 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(elem!1)))) | (~r(s(s(elem!1)), z)) | (~r(s(z), z)) | (~r(s(z), s(s(elem!1)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(s(elem!1)))) | (~r(z, s(s(elem!1)))) | (~r(s(s(elem!1)), z)) | (~r(s(z), z))))),
% 2.02/2.27 inference(monotonicity,[status(thm)],[4472])).
% 2.02/2.27 tff(4474,plain,
% 2.02/2.27 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(elem!1)))) | (~r(s(s(elem!1)), z)) | (~r(s(z), z)) | (~r(s(z), s(s(elem!1)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(z), s(s(elem!1)))) | (~r(z, s(s(elem!1)))) | (~r(s(s(elem!1)), z)) | (~r(s(z), z)))),
% 2.02/2.27 inference(transitivity,[status(thm)],[4473, 4471])).
% 2.02/2.27 tff(4475,plain,
% 2.02/2.27 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(elem!1)))) | (~r(s(s(elem!1)), z)) | (~r(s(z), z)) | (~r(s(z), s(s(elem!1)))))),
% 2.02/2.27 inference(quant_inst,[status(thm)],[])).
% 2.02/2.27 tff(4476,plain,
% 2.02/2.27 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(z), s(s(elem!1)))) | (~r(z, s(s(elem!1)))) | (~r(s(s(elem!1)), z)) | (~r(s(z), z))),
% 2.02/2.27 inference(modus_ponens,[status(thm)],[4475, 4474])).
% 2.02/2.27 tff(4477,plain,
% 2.02/2.27 ($false),
% 2.02/2.27 inference(unit_resolution,[status(thm)],[4476, 197, 311, 97, 365, 1970])).
% 2.02/2.27 tff(4478,plain,((~r(s(z), z)) | (~r(s(z), s(s(elem!1)))) | (~r(z, s(s(elem!1)))) | (~r(s(s(elem!1)), z))), inference(lemma,lemma(discharge,[]))).
% 2.02/2.27 tff(4479,plain,
% 2.02/2.27 (~r(s(s(elem!1)), z)),
% 2.02/2.27 inference(unit_resolution,[status(thm)],[4478, 4458, 97, 311])).
% 2.02/2.27 tff(4480,plain,
% 2.02/2.27 (b(s(s(elem!1)), z)),
% 2.02/2.27 inference(unit_resolution,[status(thm)],[608, 4479])).
% 2.02/2.27 tff(4481,plain,
% 2.02/2.27 ($false),
% 2.02/2.27 inference(unit_resolution,[status(thm)],[600, 4480, 4470, 240, 4468])).
% 2.02/2.27 tff(4482,plain,(b(z, s(s(elem!1))) | (~b(z, s(s(s(elem!1))))) | r(s(s(elem!1)), s(s(s(elem!1)))) | (~r(s(z), z)) | (~r(s(z), s(s(elem!1)))) | (~r(s(s(s(elem!1))), s(z)))), inference(lemma,lemma(discharge,[]))).
% 2.02/2.28 tff(4483,plain,
% 2.02/2.28 (b(z, s(s(elem!1)))),
% 2.02/2.28 inference(unit_resolution,[status(thm)],[4482, 4457, 311, 350, 4451, 4452])).
% 2.02/2.28 tff(4484,plain,
% 2.02/2.28 (~r(s(s(elem!1)), z)),
% 2.02/2.28 inference(unit_resolution,[status(thm)],[2274, 4451, 152, 311])).
% 2.02/2.28 tff(4485,plain,
% 2.02/2.28 (b(s(s(elem!1)), z)),
% 2.02/2.28 inference(unit_resolution,[status(thm)],[608, 4484])).
% 2.02/2.28 tff(4486,plain,
% 2.02/2.28 ($false),
% 2.02/2.28 inference(unit_resolution,[status(thm)],[3593, 4485, 4483, 4455, 4453])).
% 2.02/2.28 tff(4487,plain,((~r(z, s(z))) | (s(s(elem!1)) = s(s(s(elem!1)))) | (~r(s(z), s(s(elem!1)))) | (~r(s(s(s(elem!1))), s(z))) | (~b(s(s(elem!1)), s(z))) | b(z, s(s(z)))), inference(lemma,lemma(discharge,[]))).
% 2.02/2.28 tff(4488,plain,
% 2.02/2.28 ($false),
% 2.02/2.28 inference(unit_resolution,[status(thm)],[4487, 3961, 3953, 311, 323, 310, 125])).
% 2.02/2.28 tff(4489,plain,(b(s(s(s(elem!1))), s(z)) | (~r(s(z), s(s(elem!1)))) | (~r(z, s(z))) | (~b(s(s(elem!1)), s(z))) | b(z, s(s(z)))), inference(lemma,lemma(discharge,[]))).
% 2.02/2.28 tff(4490,plain,
% 2.02/2.28 (b(s(s(s(elem!1))), s(z))),
% 2.02/2.28 inference(unit_resolution,[status(thm)],[4489, 4449, 85, 310, 125])).
% 2.02/2.28 tff(4491,plain,
% 2.02/2.28 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(s(elem!1)), s(z))) | (~b(s(z), s(s(z)))) | (~b(s(s(z)), s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(s(elem!1)), s(z))) | (~b(s(z), s(s(z)))) | (~b(s(s(z)), s(z))))),
% 2.02/2.28 inference(rewrite,[status(thm)],[])).
% 2.02/2.28 tff(4492,plain,
% 2.02/2.28 (((~b(s(s(z)), s(z))) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(z), s(s(z)))) | (~b(s(s(elem!1)), s(z))) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(s(s(elem!1))), s(s(elem!1))))) <=> ((~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(s(elem!1)), s(z))) | (~b(s(z), s(s(z)))) | (~b(s(s(z)), s(z))))),
% 2.02/2.28 inference(rewrite,[status(thm)],[])).
% 2.02/2.28 tff(4493,plain,
% 2.02/2.28 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), s(z))) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(z), s(s(z)))) | (~b(s(s(elem!1)), s(z))) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(s(s(elem!1))), s(s(elem!1)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(s(elem!1)), s(z))) | (~b(s(z), s(s(z)))) | (~b(s(s(z)), s(z)))))),
% 2.02/2.28 inference(monotonicity,[status(thm)],[4492])).
% 2.02/2.28 tff(4494,plain,
% 2.02/2.28 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), s(z))) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(z), s(s(z)))) | (~b(s(s(elem!1)), s(z))) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(s(s(elem!1))), s(s(elem!1)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(s(elem!1)), s(z))) | (~b(s(z), s(s(z)))) | (~b(s(s(z)), s(z))))),
% 2.02/2.28 inference(transitivity,[status(thm)],[4493, 4491])).
% 2.02/2.28 tff(4495,plain,
% 2.02/2.28 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), s(z))) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(z), s(s(z)))) | (~b(s(s(elem!1)), s(z))) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(s(s(elem!1))), s(s(elem!1)))))),
% 2.02/2.28 inference(quant_inst,[status(thm)],[])).
% 2.02/2.28 tff(4496,plain,
% 2.02/2.28 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(s(elem!1)), s(z))) | (~b(s(z), s(s(z)))) | (~b(s(s(z)), s(z)))),
% 2.02/2.28 inference(modus_ponens,[status(thm)],[4495, 4494])).
% 2.02/2.28 tff(4497,plain,
% 2.02/2.28 (~b(s(s(s(elem!1))), s(s(elem!1)))),
% 2.02/2.28 inference(unit_resolution,[status(thm)],[4496, 166, 4142, 4490, 310, 4391])).
% 2.02/2.28 tff(4498,plain,
% 2.02/2.28 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), s(z))) | (~b(s(z), s(s(z)))) | (~b(s(s(z)), s(z))) | (~b(s(s(z)), s(s(s(elem!1))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(z), s(s(z)))) | (~b(s(s(z)), s(z))) | (~b(s(s(z)), s(s(s(elem!1))))))),
% 2.02/2.28 inference(rewrite,[status(thm)],[])).
% 2.02/2.28 tff(4499,plain,
% 2.02/2.28 (((~b(s(s(z)), s(z))) | (~b(s(s(z)), s(z))) | (~b(s(z), s(s(z)))) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(s(z)), s(z))) | (~b(s(s(z)), s(s(s(elem!1)))))) <=> ((~b(s(s(s(elem!1))), s(z))) | (~b(s(z), s(s(z)))) | (~b(s(s(z)), s(z))) | (~b(s(s(z)), s(s(s(elem!1))))))),
% 2.02/2.28 inference(rewrite,[status(thm)],[])).
% 2.02/2.28 tff(4500,plain,
% 2.02/2.28 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), s(z))) | (~b(s(s(z)), s(z))) | (~b(s(z), s(s(z)))) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(s(z)), s(z))) | (~b(s(s(z)), s(s(s(elem!1))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), s(z))) | (~b(s(z), s(s(z)))) | (~b(s(s(z)), s(z))) | (~b(s(s(z)), s(s(s(elem!1)))))))),
% 2.02/2.28 inference(monotonicity,[status(thm)],[4499])).
% 2.02/2.28 tff(4501,plain,
% 2.02/2.28 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), s(z))) | (~b(s(s(z)), s(z))) | (~b(s(z), s(s(z)))) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(s(z)), s(z))) | (~b(s(s(z)), s(s(s(elem!1))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(z), s(s(z)))) | (~b(s(s(z)), s(z))) | (~b(s(s(z)), s(s(s(elem!1))))))),
% 2.02/2.28 inference(transitivity,[status(thm)],[4500, 4498])).
% 2.02/2.28 tff(4502,plain,
% 2.02/2.28 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), s(z))) | (~b(s(s(z)), s(z))) | (~b(s(z), s(s(z)))) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(s(z)), s(z))) | (~b(s(s(z)), s(s(s(elem!1))))))),
% 2.02/2.28 inference(quant_inst,[status(thm)],[])).
% 2.02/2.28 tff(4503,plain,
% 2.02/2.28 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(z), s(s(z)))) | (~b(s(s(z)), s(z))) | (~b(s(s(z)), s(s(s(elem!1)))))),
% 2.02/2.28 inference(modus_ponens,[status(thm)],[4502, 4501])).
% 2.02/2.28 tff(4504,plain,
% 2.02/2.28 (~b(s(s(z)), s(s(s(elem!1))))),
% 2.02/2.28 inference(unit_resolution,[status(thm)],[4503, 166, 4142, 4490, 4391])).
% 2.02/2.28 tff(4505,plain,
% 2.02/2.28 (r(s(s(z)), s(s(s(elem!1))))),
% 2.02/2.28 inference(unit_resolution,[status(thm)],[279, 4504])).
% 2.02/2.28 tff(4506,plain,
% 2.02/2.28 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), s(s(elem!1)))) | (~r(s(s(z)), s(s(elem!1)))) | (~r(s(s(elem!1)), s(s(z)))) | (~r(s(s(z)), s(s(s(elem!1))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(elem!1))), s(s(elem!1)))) | (~r(s(s(z)), s(s(elem!1)))) | (~r(s(s(elem!1)), s(s(z)))) | (~r(s(s(z)), s(s(s(elem!1))))))),
% 2.02/2.28 inference(rewrite,[status(thm)],[])).
% 2.02/2.28 tff(4507,plain,
% 2.02/2.28 (((~r(s(s(elem!1)), s(s(z)))) | (~r(s(s(s(elem!1))), s(s(elem!1)))) | (~r(s(s(z)), s(s(elem!1)))) | (~r(s(s(z)), s(s(s(elem!1)))))) <=> ((~r(s(s(s(elem!1))), s(s(elem!1)))) | (~r(s(s(z)), s(s(elem!1)))) | (~r(s(s(elem!1)), s(s(z)))) | (~r(s(s(z)), s(s(s(elem!1))))))),
% 2.02/2.28 inference(rewrite,[status(thm)],[])).
% 2.02/2.28 tff(4508,plain,
% 2.02/2.28 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(elem!1)), s(s(z)))) | (~r(s(s(s(elem!1))), s(s(elem!1)))) | (~r(s(s(z)), s(s(elem!1)))) | (~r(s(s(z)), s(s(s(elem!1))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), s(s(elem!1)))) | (~r(s(s(z)), s(s(elem!1)))) | (~r(s(s(elem!1)), s(s(z)))) | (~r(s(s(z)), s(s(s(elem!1)))))))),
% 2.02/2.28 inference(monotonicity,[status(thm)],[4507])).
% 2.02/2.28 tff(4509,plain,
% 2.02/2.28 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(elem!1)), s(s(z)))) | (~r(s(s(s(elem!1))), s(s(elem!1)))) | (~r(s(s(z)), s(s(elem!1)))) | (~r(s(s(z)), s(s(s(elem!1))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(elem!1))), s(s(elem!1)))) | (~r(s(s(z)), s(s(elem!1)))) | (~r(s(s(elem!1)), s(s(z)))) | (~r(s(s(z)), s(s(s(elem!1))))))),
% 2.02/2.28 inference(transitivity,[status(thm)],[4508, 4506])).
% 2.02/2.28 tff(4510,plain,
% 2.02/2.28 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(elem!1)), s(s(z)))) | (~r(s(s(s(elem!1))), s(s(elem!1)))) | (~r(s(s(z)), s(s(elem!1)))) | (~r(s(s(z)), s(s(s(elem!1))))))),
% 2.02/2.28 inference(quant_inst,[status(thm)],[])).
% 2.02/2.28 tff(4511,plain,
% 2.02/2.28 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(elem!1))), s(s(elem!1)))) | (~r(s(s(z)), s(s(elem!1)))) | (~r(s(s(elem!1)), s(s(z)))) | (~r(s(s(z)), s(s(s(elem!1)))))),
% 2.02/2.28 inference(modus_ponens,[status(thm)],[4510, 4509])).
% 2.02/2.28 tff(4512,plain,
% 2.02/2.28 ($false),
% 2.02/2.28 inference(unit_resolution,[status(thm)],[4511, 197, 393, 333, 905, 281])).
% 2.02/2.28 tff(4513,plain,((~r(s(s(s(elem!1))), s(s(elem!1)))) | (~r(s(s(elem!1)), s(s(z)))) | (~r(s(s(z)), s(s(elem!1)))) | (~r(s(s(z)), s(s(s(elem!1)))))), inference(lemma,lemma(discharge,[]))).
% 2.02/2.28 tff(4514,plain,
% 2.02/2.28 (~r(s(s(s(elem!1))), s(s(elem!1)))),
% 2.02/2.28 inference(unit_resolution,[status(thm)],[4513, 4505, 4408, 4400])).
% 2.02/2.28 tff(4515,plain,
% 2.02/2.28 (s(s(s(elem!1))) = s(s(elem!1))),
% 2.02/2.28 inference(unit_resolution,[status(thm)],[889, 4514, 4497])).
% 2.02/2.28 tff(4516,plain,
% 2.02/2.28 ((s(s(s(elem!1))) = s(s(s(z)))) <=> (s(s(elem!1)) = s(s(s(z))))),
% 2.02/2.28 inference(monotonicity,[status(thm)],[4515])).
% 2.02/2.28 tff(4517,plain,
% 2.02/2.28 ((s(s(s(elem!1))) = s(s(s(z)))) <=> (s(s(s(z))) = s(s(elem!1)))),
% 2.02/2.28 inference(transitivity,[status(thm)],[4516, 4437])).
% 2.02/2.28 tff(4518,plain,
% 2.02/2.28 ((~(s(s(s(elem!1))) = s(s(s(z))))) <=> (~(s(s(s(z))) = s(s(elem!1))))),
% 2.02/2.28 inference(monotonicity,[status(thm)],[4517])).
% 2.02/2.28 tff(4519,plain,
% 2.02/2.28 (~(s(s(s(elem!1))) = s(s(s(z))))),
% 2.02/2.28 inference(unit_resolution,[status(thm)],[139, 4407])).
% 2.02/2.28 tff(4520,plain,
% 2.02/2.28 (~(s(s(s(z))) = s(s(elem!1)))),
% 2.02/2.28 inference(modus_ponens,[status(thm)],[4519, 4518])).
% 2.02/2.28 tff(4521,plain,
% 2.02/2.28 (((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((s(s(s(z))) = s(s(elem!1))) | b(s(s(s(z))), s(s(elem!1))) | r(s(s(s(z))), s(s(elem!1))))) <=> ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (s(s(s(z))) = s(s(elem!1))) | b(s(s(s(z))), s(s(elem!1))) | r(s(s(s(z))), s(s(elem!1))))),
% 2.02/2.28 inference(rewrite,[status(thm)],[])).
% 2.02/2.28 tff(4522,plain,
% 2.02/2.28 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((s(s(s(z))) = s(s(elem!1))) | b(s(s(s(z))), s(s(elem!1))) | r(s(s(s(z))), s(s(elem!1))))),
% 2.02/2.28 inference(quant_inst,[status(thm)],[])).
% 2.02/2.28 tff(4523,plain,
% 2.02/2.28 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (s(s(s(z))) = s(s(elem!1))) | b(s(s(s(z))), s(s(elem!1))) | r(s(s(s(z))), s(s(elem!1)))),
% 2.02/2.28 inference(modus_ponens,[status(thm)],[4522, 4521])).
% 2.02/2.28 tff(4524,plain,
% 2.02/2.28 (b(s(s(s(z))), s(s(elem!1)))),
% 2.02/2.28 inference(unit_resolution,[status(thm)],[4523, 79, 4520, 4436])).
% 2.02/2.28 tff(4525,plain,
% 2.02/2.28 (~r(z, s(s(elem!1)))),
% 2.02/2.28 inference(unit_resolution,[status(thm)],[2079, 4399, 152, 4406, 4392])).
% 2.02/2.28 tff(4526,plain,
% 2.02/2.28 (b(z, s(s(elem!1)))),
% 2.02/2.28 inference(unit_resolution,[status(thm)],[1795, 4525])).
% 2.02/2.28 tff(4527,plain,
% 2.02/2.28 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(elem!1)))) | (~b(s(s(elem!1)), z)) | (~b(s(s(s(z))), z)) | (~b(s(s(s(z))), s(s(elem!1)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(s(elem!1)))) | (~b(s(s(elem!1)), z)) | (~b(s(s(s(z))), z)) | (~b(s(s(s(z))), s(s(elem!1)))))),
% 2.02/2.28 inference(rewrite,[status(thm)],[])).
% 2.02/2.28 tff(4528,plain,
% 2.02/2.28 (((~b(z, s(s(elem!1)))) | (~b(s(s(s(z))), s(s(elem!1)))) | (~b(s(s(elem!1)), z)) | (~b(z, s(s(elem!1)))) | (~b(s(s(s(z))), s(s(elem!1)))) | (~b(s(s(s(z))), z))) <=> ((~b(z, s(s(elem!1)))) | (~b(s(s(elem!1)), z)) | (~b(s(s(s(z))), z)) | (~b(s(s(s(z))), s(s(elem!1)))))),
% 2.02/2.28 inference(rewrite,[status(thm)],[])).
% 2.02/2.28 tff(4529,plain,
% 2.02/2.28 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(elem!1)))) | (~b(s(s(s(z))), s(s(elem!1)))) | (~b(s(s(elem!1)), z)) | (~b(z, s(s(elem!1)))) | (~b(s(s(s(z))), s(s(elem!1)))) | (~b(s(s(s(z))), z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(elem!1)))) | (~b(s(s(elem!1)), z)) | (~b(s(s(s(z))), z)) | (~b(s(s(s(z))), s(s(elem!1))))))),
% 2.02/2.28 inference(monotonicity,[status(thm)],[4528])).
% 2.02/2.28 tff(4530,plain,
% 2.02/2.28 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(elem!1)))) | (~b(s(s(s(z))), s(s(elem!1)))) | (~b(s(s(elem!1)), z)) | (~b(z, s(s(elem!1)))) | (~b(s(s(s(z))), s(s(elem!1)))) | (~b(s(s(s(z))), z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(s(elem!1)))) | (~b(s(s(elem!1)), z)) | (~b(s(s(s(z))), z)) | (~b(s(s(s(z))), s(s(elem!1)))))),
% 2.02/2.28 inference(transitivity,[status(thm)],[4529, 4527])).
% 2.02/2.28 tff(4531,plain,
% 2.02/2.28 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(elem!1)))) | (~b(s(s(s(z))), s(s(elem!1)))) | (~b(s(s(elem!1)), z)) | (~b(z, s(s(elem!1)))) | (~b(s(s(s(z))), s(s(elem!1)))) | (~b(s(s(s(z))), z)))),
% 2.02/2.28 inference(quant_inst,[status(thm)],[])).
% 2.02/2.28 tff(4532,plain,
% 2.02/2.28 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(s(elem!1)))) | (~b(s(s(elem!1)), z)) | (~b(s(s(s(z))), z)) | (~b(s(s(s(z))), s(s(elem!1))))),
% 2.02/2.28 inference(modus_ponens,[status(thm)],[4531, 4530])).
% 2.02/2.28 tff(4533,plain,
% 2.02/2.28 (~b(s(s(s(z))), z)),
% 2.02/2.28 inference(unit_resolution,[status(thm)],[4532, 166, 4526, 4439, 4524])).
% 2.02/2.28 tff(4534,plain,
% 2.02/2.28 (r(s(s(s(z))), z)),
% 2.02/2.28 inference(unit_resolution,[status(thm)],[1713, 4533])).
% 2.02/2.28 tff(4535,plain,
% 2.02/2.28 ($false),
% 2.02/2.28 inference(unit_resolution,[status(thm)],[1802, 166, 1820, 53, 310, 592])).
% 2.02/2.28 tff(4536,plain,((~b(s(z), z)) | (~b(z, s(s(elem!1)))) | (~b(s(s(elem!1)), s(z))) | (~b(s(s(elem!1)), z))), inference(lemma,lemma(discharge,[]))).
% 2.02/2.28 tff(4537,plain,
% 2.02/2.28 (~b(s(z), z)),
% 2.02/2.28 inference(unit_resolution,[status(thm)],[4536, 4526, 310, 4439])).
% 2.02/2.28 tff(4538,plain,
% 2.02/2.28 (r(s(z), z)),
% 2.02/2.28 inference(unit_resolution,[status(thm)],[230, 4537])).
% 2.02/2.28 tff(4539,plain,
% 2.02/2.28 (~b(s(s(z)), s(s(s(z))))),
% 2.02/2.28 inference(unit_resolution,[status(thm)],[3528, 4538, 4391, 152, 4534])).
% 2.02/2.28 tff(4540,plain,
% 2.02/2.28 (r(s(s(z)), s(s(s(z))))),
% 2.02/2.28 inference(unit_resolution,[status(thm)],[1730, 4539])).
% 2.02/2.28 tff(4541,plain,
% 2.02/2.28 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(elem!1)))) | (~b(s(s(elem!1)), z)) | (~b(z, s(s(s(z))))) | (~b(s(s(s(z))), s(s(elem!1)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(s(elem!1)))) | (~b(s(s(elem!1)), z)) | (~b(z, s(s(s(z))))) | (~b(s(s(s(z))), s(s(elem!1)))))),
% 2.02/2.29 inference(rewrite,[status(thm)],[])).
% 2.02/2.29 tff(4542,plain,
% 2.02/2.29 (((~b(z, s(s(elem!1)))) | (~b(z, s(s(elem!1)))) | (~b(s(s(elem!1)), z)) | (~b(s(s(s(z))), s(s(elem!1)))) | (~b(z, s(s(elem!1)))) | (~b(z, s(s(s(z)))))) <=> ((~b(z, s(s(elem!1)))) | (~b(s(s(elem!1)), z)) | (~b(z, s(s(s(z))))) | (~b(s(s(s(z))), s(s(elem!1)))))),
% 2.02/2.29 inference(rewrite,[status(thm)],[])).
% 2.02/2.29 tff(4543,plain,
% 2.02/2.29 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(elem!1)))) | (~b(z, s(s(elem!1)))) | (~b(s(s(elem!1)), z)) | (~b(s(s(s(z))), s(s(elem!1)))) | (~b(z, s(s(elem!1)))) | (~b(z, s(s(s(z))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(elem!1)))) | (~b(s(s(elem!1)), z)) | (~b(z, s(s(s(z))))) | (~b(s(s(s(z))), s(s(elem!1))))))),
% 2.02/2.29 inference(monotonicity,[status(thm)],[4542])).
% 2.02/2.29 tff(4544,plain,
% 2.02/2.29 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(elem!1)))) | (~b(z, s(s(elem!1)))) | (~b(s(s(elem!1)), z)) | (~b(s(s(s(z))), s(s(elem!1)))) | (~b(z, s(s(elem!1)))) | (~b(z, s(s(s(z))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(s(elem!1)))) | (~b(s(s(elem!1)), z)) | (~b(z, s(s(s(z))))) | (~b(s(s(s(z))), s(s(elem!1)))))),
% 2.02/2.29 inference(transitivity,[status(thm)],[4543, 4541])).
% 2.02/2.29 tff(4545,plain,
% 2.02/2.29 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(elem!1)))) | (~b(z, s(s(elem!1)))) | (~b(s(s(elem!1)), z)) | (~b(s(s(s(z))), s(s(elem!1)))) | (~b(z, s(s(elem!1)))) | (~b(z, s(s(s(z))))))),
% 2.02/2.29 inference(quant_inst,[status(thm)],[])).
% 2.02/2.29 tff(4546,plain,
% 2.02/2.29 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(s(elem!1)))) | (~b(s(s(elem!1)), z)) | (~b(z, s(s(s(z))))) | (~b(s(s(s(z))), s(s(elem!1))))),
% 2.02/2.29 inference(modus_ponens,[status(thm)],[4545, 4544])).
% 2.02/2.29 tff(4547,plain,
% 2.02/2.29 (~b(z, s(s(s(z))))),
% 2.02/2.29 inference(unit_resolution,[status(thm)],[4546, 166, 4526, 4439, 4524])).
% 2.02/2.29 tff(4548,plain,
% 2.02/2.29 (r(z, s(s(s(z))))),
% 2.02/2.29 inference(unit_resolution,[status(thm)],[1697, 4547])).
% 2.02/2.29 tff(4549,plain,
% 2.02/2.29 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(s(z))))) | (~r(s(s(z)), s(s(s(z))))) | (~r(z, s(s(z)))) | (~r(s(s(s(z))), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, s(s(s(z))))) | (~r(s(s(z)), s(s(s(z))))) | (~r(z, s(s(z)))) | (~r(s(s(s(z))), z)))),
% 2.02/2.29 inference(rewrite,[status(thm)],[])).
% 2.02/2.29 tff(4550,plain,
% 2.02/2.29 (((~r(s(s(s(z))), z)) | (~r(s(s(z)), s(s(s(z))))) | (~r(z, s(s(s(z))))) | (~r(z, s(s(z))))) <=> ((~r(z, s(s(s(z))))) | (~r(s(s(z)), s(s(s(z))))) | (~r(z, s(s(z)))) | (~r(s(s(s(z))), z)))),
% 2.02/2.29 inference(rewrite,[status(thm)],[])).
% 2.02/2.29 tff(4551,plain,
% 2.02/2.29 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(z))), z)) | (~r(s(s(z)), s(s(s(z))))) | (~r(z, s(s(s(z))))) | (~r(z, s(s(z)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(s(z))))) | (~r(s(s(z)), s(s(s(z))))) | (~r(z, s(s(z)))) | (~r(s(s(s(z))), z))))),
% 2.02/2.29 inference(monotonicity,[status(thm)],[4550])).
% 2.02/2.29 tff(4552,plain,
% 2.02/2.29 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(z))), z)) | (~r(s(s(z)), s(s(s(z))))) | (~r(z, s(s(s(z))))) | (~r(z, s(s(z)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, s(s(s(z))))) | (~r(s(s(z)), s(s(s(z))))) | (~r(z, s(s(z)))) | (~r(s(s(s(z))), z)))),
% 2.02/2.29 inference(transitivity,[status(thm)],[4551, 4549])).
% 2.02/2.29 tff(4553,plain,
% 2.02/2.29 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(z))), z)) | (~r(s(s(z)), s(s(s(z))))) | (~r(z, s(s(s(z))))) | (~r(z, s(s(z)))))),
% 2.02/2.29 inference(quant_inst,[status(thm)],[])).
% 2.02/2.29 tff(4554,plain,
% 2.02/2.29 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, s(s(s(z))))) | (~r(s(s(z)), s(s(s(z))))) | (~r(z, s(s(z)))) | (~r(s(s(s(z))), z))),
% 2.02/2.29 inference(modus_ponens,[status(thm)],[4553, 4552])).
% 2.02/2.29 tff(4555,plain,
% 2.02/2.29 ($false),
% 2.02/2.29 inference(unit_resolution,[status(thm)],[4554, 197, 152, 4548, 4534, 4540])).
% 2.02/2.29 tff(4556,plain,((~b(s(s(elem!1)), s(z))) | b(z, s(s(z))) | b(s(z), s(s(elem!1)))), inference(lemma,lemma(discharge,[]))).
% 2.02/2.29 tff(4557,plain,
% 2.02/2.29 (~b(s(s(elem!1)), s(z))),
% 2.02/2.29 inference(unit_resolution,[status(thm)],[4556, 54, 125])).
% 2.02/2.29 tff(4558,plain,
% 2.02/2.29 (r(s(s(elem!1)), s(z))),
% 2.02/2.29 inference(unit_resolution,[status(thm)],[1912, 4557])).
% 2.02/2.29 tff(4559,plain,
% 2.02/2.29 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(s(elem!1)))) | (~r(s(s(elem!1)), s(z))) | (~r(s(s(z)), s(z))) | (~r(s(s(z)), s(s(elem!1)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(z), s(s(elem!1)))) | (~r(s(s(elem!1)), s(z))) | (~r(s(s(z)), s(z))) | (~r(s(s(z)), s(s(elem!1)))))),
% 2.02/2.29 inference(rewrite,[status(thm)],[])).
% 2.02/2.29 tff(4560,plain,
% 2.02/2.29 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(s(elem!1)))) | (~r(s(s(elem!1)), s(z))) | (~r(s(s(z)), s(z))) | (~r(s(s(z)), s(s(elem!1)))))),
% 2.02/2.29 inference(quant_inst,[status(thm)],[])).
% 2.02/2.29 tff(4561,plain,
% 2.02/2.29 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(z), s(s(elem!1)))) | (~r(s(s(elem!1)), s(z))) | (~r(s(s(z)), s(z))) | (~r(s(s(z)), s(s(elem!1))))),
% 2.02/2.29 inference(modus_ponens,[status(thm)],[4560, 4559])).
% 2.02/2.29 tff(4562,plain,
% 2.02/2.29 (~r(s(s(z)), s(s(elem!1)))),
% 2.02/2.29 inference(unit_resolution,[status(thm)],[4561, 197, 85, 4558, 309])).
% 2.02/2.29 tff(4563,plain,
% 2.02/2.29 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(s(elem!1)))) | (~r(s(s(z)), s(z))) | (~r(s(s(elem!1)), s(z))) | (~r(s(s(elem!1)), s(s(z)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(z), s(s(elem!1)))) | (~r(s(s(z)), s(z))) | (~r(s(s(elem!1)), s(z))) | (~r(s(s(elem!1)), s(s(z)))))),
% 2.02/2.29 inference(rewrite,[status(thm)],[])).
% 2.02/2.29 tff(4564,plain,
% 2.02/2.29 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(s(elem!1)))) | (~r(s(s(z)), s(z))) | (~r(s(s(elem!1)), s(z))) | (~r(s(s(elem!1)), s(s(z)))))),
% 2.02/2.29 inference(quant_inst,[status(thm)],[])).
% 2.02/2.29 tff(4565,plain,
% 2.02/2.29 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(z), s(s(elem!1)))) | (~r(s(s(z)), s(z))) | (~r(s(s(elem!1)), s(z))) | (~r(s(s(elem!1)), s(s(z))))),
% 2.02/2.29 inference(modus_ponens,[status(thm)],[4564, 4563])).
% 2.02/2.29 tff(4566,plain,
% 2.02/2.29 (~r(s(s(elem!1)), s(s(z)))),
% 2.02/2.29 inference(unit_resolution,[status(thm)],[4565, 197, 85, 4558, 309])).
% 2.02/2.29 tff(4567,plain,
% 2.02/2.29 (b(s(s(elem!1)), s(z))),
% 2.02/2.29 inference(modus_ponens,[status(thm)],[96, 3844])).
% 2.02/2.29 tff(4568,assumption,(~b(s(s(elem!1)), s(z))), introduced(assumption)).
% 2.02/2.29 tff(4569,plain,
% 2.02/2.29 ($false),
% 2.02/2.29 inference(unit_resolution,[status(thm)],[4568, 4567])).
% 2.02/2.29 tff(4570,plain,((~(s(s(elem!1)) = s(s(s(elem!1))))) | b(s(s(elem!1)), s(z)) | (~b(s(s(s(elem!1))), s(z)))), inference(lemma,lemma(discharge,[]))).
% 2.02/2.29 tff(4571,plain,
% 2.02/2.29 (~(s(s(elem!1)) = s(s(s(elem!1))))),
% 2.02/2.29 inference(unit_resolution,[status(thm)],[4570, 4557, 96])).
% 2.02/2.29 tff(4572,plain,
% 2.02/2.29 (~b(s(s(z)), s(z))),
% 2.02/2.29 inference(unit_resolution,[status(thm)],[292, 96, 155, 118, 153])).
% 2.02/2.29 tff(4573,plain,
% 2.02/2.29 (r(s(s(z)), s(z))),
% 2.02/2.29 inference(unit_resolution,[status(thm)],[308, 4572])).
% 2.02/2.29 tff(4574,plain,
% 2.02/2.29 (~b(z, s(s(s(elem!1))))),
% 2.02/2.29 inference(unit_resolution,[status(thm)],[3989, 166, 53, 96, 118])).
% 2.02/2.29 tff(4575,plain,
% 2.02/2.29 (r(z, s(s(s(elem!1))))),
% 2.02/2.29 inference(unit_resolution,[status(thm)],[261, 4574])).
% 2.02/2.29 tff(4576,plain,
% 2.02/2.29 (~r(s(s(s(elem!1))), s(s(z)))),
% 2.02/2.29 inference(unit_resolution,[status(thm)],[1588, 4575, 155, 4573])).
% 2.02/2.29 tff(4577,assumption,(r(s(s(elem!1)), s(z))), introduced(assumption)).
% 2.02/2.29 tff(4578,plain,
% 2.02/2.29 (~r(s(s(z)), s(s(elem!1)))),
% 2.02/2.29 inference(unit_resolution,[status(thm)],[4561, 197, 311, 4577, 4573])).
% 2.02/2.29 tff(4579,plain,
% 2.02/2.29 (~r(s(s(elem!1)), s(s(z)))),
% 2.02/2.29 inference(unit_resolution,[status(thm)],[4565, 197, 311, 4577, 4573])).
% 2.02/2.29 tff(4580,plain,
% 2.02/2.29 (~r(s(s(s(elem!1))), s(s(s(z))))),
% 2.02/2.29 inference(unit_resolution,[status(thm)],[4103, 197, 154, 155, 1733])).
% 2.02/2.29 tff(4581,plain,
% 2.02/2.29 (~b(s(s(z)), s(z))),
% 2.02/2.29 inference(unit_resolution,[status(thm)],[292, 96, 155, 118, 154])).
% 2.02/2.29 tff(4582,plain,
% 2.02/2.29 (r(s(s(z)), s(z))),
% 2.02/2.29 inference(unit_resolution,[status(thm)],[308, 4581])).
% 2.02/2.29 tff(4583,plain,
% 2.02/2.29 (~r(s(s(s(elem!1))), s(s(z)))),
% 2.02/2.29 inference(unit_resolution,[status(thm)],[1588, 4575, 155, 4582])).
% 2.02/2.29 tff(4584,plain,
% 2.02/2.29 (b(s(s(s(elem!1))), s(s(z)))),
% 2.02/2.29 inference(unit_resolution,[status(thm)],[218, 4583])).
% 2.02/2.29 tff(4585,plain,
% 2.02/2.29 (~r(s(s(z)), s(s(elem!1)))),
% 2.02/2.29 inference(unit_resolution,[status(thm)],[4561, 197, 311, 4577, 4582])).
% 2.02/2.29 tff(4586,plain,
% 2.02/2.29 (~r(s(s(elem!1)), s(s(z)))),
% 2.02/2.29 inference(unit_resolution,[status(thm)],[4565, 197, 311, 4577, 4582])).
% 2.02/2.29 tff(4587,plain,
% 2.02/2.29 (~r(s(s(z)), s(s(s(elem!1))))),
% 2.02/2.29 inference(unit_resolution,[status(thm)],[290, 4575, 155, 154])).
% 2.02/2.29 tff(4588,plain,
% 2.02/2.29 (~b(s(s(elem!1)), s(s(s(elem!1))))),
% 2.02/2.29 inference(unit_resolution,[status(thm)],[501, 3964, 273, 213])).
% 2.02/2.29 tff(4589,plain,
% 2.02/2.29 (r(s(s(elem!1)), s(s(s(elem!1))))),
% 2.02/2.29 inference(unit_resolution,[status(thm)],[461, 4588, 45])).
% 2.02/2.29 tff(4590,plain,
% 2.02/2.29 (~r(s(s(elem!1)), z)),
% 2.02/2.29 inference(unit_resolution,[status(thm)],[4018, 4589, 154, 282])).
% 2.02/2.29 tff(4591,plain,
% 2.02/2.29 (b(s(s(elem!1)), z)),
% 2.02/2.29 inference(unit_resolution,[status(thm)],[608, 4590])).
% 2.02/2.29 tff(4592,plain,
% 2.02/2.29 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), z)) | (~r(z, s(s(s(elem!1))))) | (~r(z, s(s(elem!1)))) | (~r(s(s(elem!1)), s(s(s(elem!1))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(elem!1))), z)) | (~r(z, s(s(s(elem!1))))) | (~r(z, s(s(elem!1)))) | (~r(s(s(elem!1)), s(s(s(elem!1))))))),
% 2.02/2.29 inference(rewrite,[status(thm)],[])).
% 2.02/2.29 tff(4593,plain,
% 2.02/2.29 (((~r(s(s(s(elem!1))), z)) | (~r(s(s(elem!1)), s(s(s(elem!1))))) | (~r(z, s(s(s(elem!1))))) | (~r(z, s(s(elem!1))))) <=> ((~r(s(s(s(elem!1))), z)) | (~r(z, s(s(s(elem!1))))) | (~r(z, s(s(elem!1)))) | (~r(s(s(elem!1)), s(s(s(elem!1))))))),
% 2.02/2.29 inference(rewrite,[status(thm)],[])).
% 2.02/2.29 tff(4594,plain,
% 2.02/2.29 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), z)) | (~r(s(s(elem!1)), s(s(s(elem!1))))) | (~r(z, s(s(s(elem!1))))) | (~r(z, s(s(elem!1)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), z)) | (~r(z, s(s(s(elem!1))))) | (~r(z, s(s(elem!1)))) | (~r(s(s(elem!1)), s(s(s(elem!1)))))))),
% 2.02/2.29 inference(monotonicity,[status(thm)],[4593])).
% 2.02/2.29 tff(4595,plain,
% 2.02/2.29 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), z)) | (~r(s(s(elem!1)), s(s(s(elem!1))))) | (~r(z, s(s(s(elem!1))))) | (~r(z, s(s(elem!1)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(elem!1))), z)) | (~r(z, s(s(s(elem!1))))) | (~r(z, s(s(elem!1)))) | (~r(s(s(elem!1)), s(s(s(elem!1))))))),
% 2.02/2.29 inference(transitivity,[status(thm)],[4594, 4592])).
% 2.02/2.29 tff(4596,plain,
% 2.02/2.29 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), z)) | (~r(s(s(elem!1)), s(s(s(elem!1))))) | (~r(z, s(s(s(elem!1))))) | (~r(z, s(s(elem!1)))))),
% 2.02/2.29 inference(quant_inst,[status(thm)],[])).
% 2.02/2.29 tff(4597,plain,
% 2.02/2.29 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(elem!1))), z)) | (~r(z, s(s(s(elem!1))))) | (~r(z, s(s(elem!1)))) | (~r(s(s(elem!1)), s(s(s(elem!1)))))),
% 2.02/2.29 inference(modus_ponens,[status(thm)],[4596, 4595])).
% 2.02/2.29 tff(4598,plain,
% 2.02/2.29 (~r(z, s(s(elem!1)))),
% 2.02/2.29 inference(unit_resolution,[status(thm)],[4597, 197, 154, 4589, 282])).
% 2.02/2.29 tff(4599,plain,
% 2.02/2.29 (b(z, s(s(elem!1)))),
% 2.02/2.29 inference(unit_resolution,[status(thm)],[1795, 4598])).
% 2.02/2.29 tff(4600,plain,
% 2.02/2.29 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(elem!1)))) | (~b(s(s(elem!1)), z)) | (~b(s(s(z)), s(s(elem!1)))) | (~b(s(s(z)), z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(s(elem!1)))) | (~b(s(s(elem!1)), z)) | (~b(s(s(z)), s(s(elem!1)))) | (~b(s(s(z)), z)))),
% 2.02/2.29 inference(rewrite,[status(thm)],[])).
% 2.02/2.29 tff(4601,plain,
% 2.02/2.29 (((~b(s(s(elem!1)), z)) | (~b(s(s(z)), z)) | (~b(z, s(s(elem!1)))) | (~b(s(s(elem!1)), z)) | (~b(s(s(z)), z)) | (~b(s(s(z)), s(s(elem!1))))) <=> ((~b(z, s(s(elem!1)))) | (~b(s(s(elem!1)), z)) | (~b(s(s(z)), s(s(elem!1)))) | (~b(s(s(z)), z)))),
% 2.02/2.29 inference(rewrite,[status(thm)],[])).
% 2.02/2.29 tff(4602,plain,
% 2.02/2.29 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), z)) | (~b(s(s(z)), z)) | (~b(z, s(s(elem!1)))) | (~b(s(s(elem!1)), z)) | (~b(s(s(z)), z)) | (~b(s(s(z)), s(s(elem!1)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(elem!1)))) | (~b(s(s(elem!1)), z)) | (~b(s(s(z)), s(s(elem!1)))) | (~b(s(s(z)), z))))),
% 2.02/2.29 inference(monotonicity,[status(thm)],[4601])).
% 2.02/2.29 tff(4603,plain,
% 2.02/2.29 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), z)) | (~b(s(s(z)), z)) | (~b(z, s(s(elem!1)))) | (~b(s(s(elem!1)), z)) | (~b(s(s(z)), z)) | (~b(s(s(z)), s(s(elem!1)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(s(elem!1)))) | (~b(s(s(elem!1)), z)) | (~b(s(s(z)), s(s(elem!1)))) | (~b(s(s(z)), z)))),
% 2.02/2.29 inference(transitivity,[status(thm)],[4602, 4600])).
% 2.02/2.29 tff(4604,plain,
% 2.02/2.29 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), z)) | (~b(s(s(z)), z)) | (~b(z, s(s(elem!1)))) | (~b(s(s(elem!1)), z)) | (~b(s(s(z)), z)) | (~b(s(s(z)), s(s(elem!1)))))),
% 2.02/2.29 inference(quant_inst,[status(thm)],[])).
% 2.02/2.29 tff(4605,plain,
% 2.02/2.29 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(s(elem!1)))) | (~b(s(s(elem!1)), z)) | (~b(s(s(z)), s(s(elem!1)))) | (~b(s(s(z)), z))),
% 2.02/2.29 inference(modus_ponens,[status(thm)],[4604, 4603])).
% 2.02/2.29 tff(4606,plain,
% 2.02/2.29 ($false),
% 2.02/2.29 inference(unit_resolution,[status(thm)],[4605, 166, 4599, 4591, 2516, 122])).
% 2.02/2.29 tff(4607,plain,((s(s(z)) = s(s(elem!1))) | (~b(s(s(z)), z)) | (~r(s(s(s(elem!1))), z)) | (~r(z, s(s(s(elem!1))))) | (s(s(elem!1)) = s(s(s(elem!1)))) | r(s(s(z)), s(s(s(elem!1)))) | r(s(s(s(elem!1))), s(s(z))) | r(s(s(elem!1)), s(s(z))) | r(s(s(z)), s(s(elem!1)))), inference(lemma,lemma(discharge,[]))).
% 2.02/2.29 tff(4608,plain,
% 2.02/2.29 (s(s(z)) = s(s(elem!1))),
% 2.02/2.29 inference(unit_resolution,[status(thm)],[4607, 122, 154, 4575, 45, 4587, 4583, 4586, 4585])).
% 2.02/2.29 tff(4609,plain,
% 2.02/2.29 (s(s(s(z))) = s(s(s(elem!1)))),
% 2.02/2.29 inference(monotonicity,[status(thm)],[4608])).
% 2.02/2.29 tff(4610,plain,
% 2.02/2.29 (s(s(s(s(z)))) = s(s(s(s(elem!1))))),
% 2.02/2.29 inference(monotonicity,[status(thm)],[4609])).
% 2.02/2.29 tff(4611,plain,
% 2.02/2.29 (b(s(s(s(s(z)))), elem!1) <=> b(s(s(s(s(elem!1)))), elem!1)),
% 2.02/2.29 inference(monotonicity,[status(thm)],[4610])).
% 2.02/2.29 tff(4612,plain,
% 2.02/2.29 (s(elem!1) = s(z)),
% 2.02/2.29 inference(unit_resolution,[status(thm)],[43, 4608])).
% 2.02/2.29 tff(4613,plain,
% 2.02/2.29 (z = elem!1),
% 2.02/2.29 inference(unit_resolution,[status(thm)],[30, 4612])).
% 2.02/2.29 tff(4614,plain,
% 2.02/2.29 (b(s(s(s(s(z)))), z) <=> b(s(s(s(s(z)))), elem!1)),
% 2.02/2.29 inference(monotonicity,[status(thm)],[4613])).
% 2.02/2.29 tff(4615,plain,
% 2.02/2.29 (b(s(s(s(s(z)))), z) <=> b(s(s(s(s(elem!1)))), elem!1)),
% 2.02/2.29 inference(transitivity,[status(thm)],[4614, 4611])).
% 2.02/2.29 tff(4616,plain,
% 2.02/2.29 (b(s(s(s(s(z)))), s(s(s(z)))) <=> b(s(s(s(s(elem!1)))), s(s(s(elem!1))))),
% 2.02/2.29 inference(monotonicity,[status(thm)],[4610, 4609])).
% 2.02/2.29 tff(4617,plain,
% 2.02/2.29 (b(s(s(s(s(elem!1)))), s(s(s(elem!1)))) <=> b(s(s(s(s(z)))), s(s(s(z))))),
% 2.02/2.29 inference(symmetry,[status(thm)],[4616])).
% 2.02/2.29 tff(4618,plain,
% 2.02/2.29 ((~b(s(s(s(s(elem!1)))), s(s(s(elem!1))))) <=> (~b(s(s(s(s(z)))), s(s(s(z)))))),
% 2.02/2.29 inference(monotonicity,[status(thm)],[4617])).
% 2.02/2.29 tff(4619,plain,
% 2.02/2.29 ((s(s(s(s(elem!1)))) = s(s(z))) <=> (s(s(s(s(elem!1)))) = s(s(elem!1)))),
% 2.02/2.29 inference(monotonicity,[status(thm)],[4608])).
% 2.02/2.29 tff(4620,plain,
% 2.02/2.29 ((s(s(s(s(elem!1)))) = s(s(z))) <=> (s(s(elem!1)) = s(s(s(s(elem!1)))))),
% 2.02/2.29 inference(transitivity,[status(thm)],[4619, 123])).
% 2.02/2.29 tff(4621,plain,
% 2.02/2.29 ((s(s(s(s(elem!1)))) = s(s(z))) <=> (s(s(s(s(elem!1)))) = s(s(elem!1)))),
% 2.02/2.29 inference(transitivity,[status(thm)],[4620, 124])).
% 2.02/2.29 tff(4622,plain,
% 2.02/2.29 ((~(s(s(s(s(elem!1)))) = s(s(z)))) <=> (~(s(s(s(s(elem!1)))) = s(s(elem!1))))),
% 2.02/2.29 inference(monotonicity,[status(thm)],[4621])).
% 2.02/2.29 tff(4623,plain,
% 2.02/2.29 (~(s(s(s(s(elem!1)))) = s(s(elem!1)))),
% 2.02/2.29 inference(modus_ponens,[status(thm)],[733, 4622])).
% 2.02/2.29 tff(4624,plain,
% 2.02/2.29 (b(z, s(z)) <=> b(elem!1, s(z))),
% 2.02/2.29 inference(monotonicity,[status(thm)],[4613])).
% 2.02/2.29 tff(4625,plain,
% 2.02/2.29 (b(elem!1, s(z))),
% 2.02/2.29 inference(modus_ponens,[status(thm)],[118, 4624])).
% 2.02/2.29 tff(4626,plain,
% 2.02/2.29 (b(s(s(s(s(z)))), s(s(s(z)))) <=> b(s(s(s(s(elem!1)))), s(s(s(elem!1))))),
% 2.02/2.29 inference(monotonicity,[status(thm)],[1087, 1086])).
% 2.02/2.29 tff(4627,plain,
% 2.02/2.29 (b(s(s(s(s(elem!1)))), s(s(s(elem!1)))) <=> b(s(s(s(s(z)))), s(s(s(z))))),
% 2.02/2.29 inference(symmetry,[status(thm)],[4626])).
% 2.02/2.29 tff(4628,plain,
% 2.02/2.29 ((~b(s(s(s(s(elem!1)))), s(s(s(elem!1))))) <=> (~b(s(s(s(s(z)))), s(s(s(z)))))),
% 2.02/2.29 inference(monotonicity,[status(thm)],[4627])).
% 2.02/2.29 tff(4629,plain,
% 2.02/2.29 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(s(elem!1)))) | (~r(s(s(elem!1)), s(z))) | (~r(s(z), s(s(s(s(elem!1)))))) | (~r(s(s(s(s(elem!1)))), s(s(elem!1)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(z), s(s(elem!1)))) | (~r(s(s(elem!1)), s(z))) | (~r(s(z), s(s(s(s(elem!1)))))) | (~r(s(s(s(s(elem!1)))), s(s(elem!1)))))),
% 2.02/2.29 inference(rewrite,[status(thm)],[])).
% 2.02/2.29 tff(4630,plain,
% 2.02/2.29 (((~r(s(s(elem!1)), s(z))) | (~r(s(s(s(s(elem!1)))), s(s(elem!1)))) | (~r(s(z), s(s(elem!1)))) | (~r(s(z), s(s(s(s(elem!1))))))) <=> ((~r(s(z), s(s(elem!1)))) | (~r(s(s(elem!1)), s(z))) | (~r(s(z), s(s(s(s(elem!1)))))) | (~r(s(s(s(s(elem!1)))), s(s(elem!1)))))),
% 2.02/2.29 inference(rewrite,[status(thm)],[])).
% 2.02/2.29 tff(4631,plain,
% 2.02/2.29 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(elem!1)), s(z))) | (~r(s(s(s(s(elem!1)))), s(s(elem!1)))) | (~r(s(z), s(s(elem!1)))) | (~r(s(z), s(s(s(s(elem!1)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(s(elem!1)))) | (~r(s(s(elem!1)), s(z))) | (~r(s(z), s(s(s(s(elem!1)))))) | (~r(s(s(s(s(elem!1)))), s(s(elem!1))))))),
% 2.02/2.29 inference(monotonicity,[status(thm)],[4630])).
% 2.02/2.29 tff(4632,plain,
% 2.02/2.29 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(elem!1)), s(z))) | (~r(s(s(s(s(elem!1)))), s(s(elem!1)))) | (~r(s(z), s(s(elem!1)))) | (~r(s(z), s(s(s(s(elem!1)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(z), s(s(elem!1)))) | (~r(s(s(elem!1)), s(z))) | (~r(s(z), s(s(s(s(elem!1)))))) | (~r(s(s(s(s(elem!1)))), s(s(elem!1)))))),
% 2.02/2.29 inference(transitivity,[status(thm)],[4631, 4629])).
% 2.02/2.29 tff(4633,plain,
% 2.02/2.29 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(elem!1)), s(z))) | (~r(s(s(s(s(elem!1)))), s(s(elem!1)))) | (~r(s(z), s(s(elem!1)))) | (~r(s(z), s(s(s(s(elem!1)))))))),
% 2.02/2.29 inference(quant_inst,[status(thm)],[])).
% 2.02/2.29 tff(4634,plain,
% 2.02/2.29 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(z), s(s(elem!1)))) | (~r(s(s(elem!1)), s(z))) | (~r(s(z), s(s(s(s(elem!1)))))) | (~r(s(s(s(s(elem!1)))), s(s(elem!1))))),
% 2.02/2.29 inference(modus_ponens,[status(thm)],[4633, 4632])).
% 2.02/2.29 tff(4635,plain,
% 2.02/2.29 ($false),
% 2.02/2.29 inference(unit_resolution,[status(thm)],[4634, 197, 311, 4577, 699, 3408])).
% 2.02/2.29 tff(4636,plain,((~r(s(s(s(s(elem!1)))), s(s(elem!1)))) | (~r(s(z), s(s(elem!1)))) | (~r(s(s(elem!1)), s(z))) | (~r(s(z), s(s(s(s(elem!1))))))), inference(lemma,lemma(discharge,[]))).
% 2.02/2.29 tff(4637,plain,
% 2.02/2.29 (~r(s(z), s(s(s(s(elem!1)))))),
% 2.02/2.29 inference(unit_resolution,[status(thm)],[4636, 3408, 311, 4577])).
% 2.02/2.29 tff(4638,plain,
% 2.02/2.29 (b(s(z), s(s(s(s(elem!1)))))),
% 2.02/2.29 inference(unit_resolution,[status(thm)],[681, 4637])).
% 2.02/2.29 tff(4639,plain,
% 2.02/2.29 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(s(z)))) | (~r(s(s(elem!1)), s(z))) | (~r(s(s(s(s(elem!1)))), s(z))) | (~r(s(s(s(s(elem!1)))), s(s(elem!1)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(z), s(s(z)))) | (~r(s(s(elem!1)), s(z))) | (~r(s(s(s(s(elem!1)))), s(z))) | (~r(s(s(s(s(elem!1)))), s(s(elem!1)))))),
% 2.02/2.29 inference(rewrite,[status(thm)],[])).
% 2.02/2.29 tff(4640,plain,
% 2.02/2.29 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(s(z)))) | (~r(s(s(elem!1)), s(z))) | (~r(s(s(s(s(elem!1)))), s(z))) | (~r(s(s(s(s(elem!1)))), s(s(elem!1)))))),
% 2.02/2.29 inference(quant_inst,[status(thm)],[])).
% 2.02/2.29 tff(4641,plain,
% 2.02/2.29 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(z), s(s(z)))) | (~r(s(s(elem!1)), s(z))) | (~r(s(s(s(s(elem!1)))), s(z))) | (~r(s(s(s(s(elem!1)))), s(s(elem!1))))),
% 2.02/2.29 inference(modus_ponens,[status(thm)],[4640, 4639])).
% 2.02/2.29 tff(4642,plain,
% 2.02/2.29 ($false),
% 2.02/2.29 inference(unit_resolution,[status(thm)],[4641, 197, 120, 4577, 700, 3408])).
% 2.02/2.29 tff(4643,plain,((~r(s(s(s(s(elem!1)))), s(z))) | (~r(s(z), s(s(z)))) | (~r(s(s(elem!1)), s(z))) | (~r(s(s(s(s(elem!1)))), s(s(elem!1))))), inference(lemma,lemma(discharge,[]))).
% 2.02/2.29 tff(4644,plain,
% 2.02/2.29 (~r(s(s(s(s(elem!1)))), s(z))),
% 2.02/2.29 inference(unit_resolution,[status(thm)],[4643, 3408, 4577, 120])).
% 2.02/2.29 tff(4645,plain,
% 2.02/2.29 (b(s(s(s(s(elem!1)))), s(z))),
% 2.02/2.29 inference(unit_resolution,[status(thm)],[661, 4644])).
% 2.02/2.29 tff(4646,plain,
% 2.02/2.29 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), s(z))) | (~b(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~b(s(s(s(s(elem!1)))), s(z))) | (~b(s(z), s(s(s(s(elem!1)))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~b(s(s(s(s(elem!1)))), s(z))) | (~b(s(z), s(s(s(s(elem!1)))))))),
% 2.02/2.29 inference(rewrite,[status(thm)],[])).
% 2.02/2.29 tff(4647,plain,
% 2.02/2.29 (((~b(s(s(s(s(elem!1)))), s(z))) | (~b(s(s(s(s(elem!1)))), s(z))) | (~b(s(z), s(s(s(s(elem!1)))))) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(s(s(s(elem!1)))), s(z))) | (~b(s(s(s(s(elem!1)))), s(s(s(elem!1)))))) <=> ((~b(s(s(s(elem!1))), s(z))) | (~b(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~b(s(s(s(s(elem!1)))), s(z))) | (~b(s(z), s(s(s(s(elem!1)))))))),
% 2.12/2.30 inference(rewrite,[status(thm)],[])).
% 2.12/2.30 tff(4648,plain,
% 2.12/2.30 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(elem!1)))), s(z))) | (~b(s(s(s(s(elem!1)))), s(z))) | (~b(s(z), s(s(s(s(elem!1)))))) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(s(s(s(elem!1)))), s(z))) | (~b(s(s(s(s(elem!1)))), s(s(s(elem!1))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), s(z))) | (~b(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~b(s(s(s(s(elem!1)))), s(z))) | (~b(s(z), s(s(s(s(elem!1))))))))),
% 2.12/2.30 inference(monotonicity,[status(thm)],[4647])).
% 2.12/2.30 tff(4649,plain,
% 2.12/2.30 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(elem!1)))), s(z))) | (~b(s(s(s(s(elem!1)))), s(z))) | (~b(s(z), s(s(s(s(elem!1)))))) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(s(s(s(elem!1)))), s(z))) | (~b(s(s(s(s(elem!1)))), s(s(s(elem!1))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~b(s(s(s(s(elem!1)))), s(z))) | (~b(s(z), s(s(s(s(elem!1)))))))),
% 2.12/2.30 inference(transitivity,[status(thm)],[4648, 4646])).
% 2.12/2.30 tff(4650,plain,
% 2.12/2.30 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(elem!1)))), s(z))) | (~b(s(s(s(s(elem!1)))), s(z))) | (~b(s(z), s(s(s(s(elem!1)))))) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(s(s(s(elem!1)))), s(z))) | (~b(s(s(s(s(elem!1)))), s(s(s(elem!1))))))),
% 2.12/2.30 inference(quant_inst,[status(thm)],[])).
% 2.12/2.30 tff(4651,plain,
% 2.12/2.30 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~b(s(s(s(s(elem!1)))), s(z))) | (~b(s(z), s(s(s(s(elem!1))))))),
% 2.12/2.30 inference(modus_ponens,[status(thm)],[4650, 4649])).
% 2.12/2.30 tff(4652,plain,
% 2.12/2.30 (~b(s(s(s(s(elem!1)))), s(s(s(elem!1))))),
% 2.12/2.30 inference(unit_resolution,[status(thm)],[4651, 166, 96, 4645, 4638])).
% 2.12/2.30 tff(4653,plain,
% 2.12/2.30 (~b(s(s(s(s(z)))), s(s(s(z))))),
% 2.12/2.30 inference(modus_ponens,[status(thm)],[4652, 4628])).
% 2.12/2.30 tff(4654,plain,
% 2.12/2.30 ((s(s(s(s(z)))) = s(s(s(z)))) <=> (s(s(s(z))) = s(s(s(s(z)))))),
% 2.12/2.30 inference(commutativity,[status(thm)],[])).
% 2.12/2.30 tff(4655,plain,
% 2.12/2.30 ((s(s(s(z))) = s(s(s(s(z))))) <=> (s(s(s(s(z)))) = s(s(s(z))))),
% 2.12/2.30 inference(symmetry,[status(thm)],[4654])).
% 2.12/2.30 tff(4656,plain,
% 2.12/2.30 ((~(s(s(s(z))) = s(s(s(s(z)))))) <=> (~(s(s(s(s(z)))) = s(s(s(z)))))),
% 2.12/2.30 inference(monotonicity,[status(thm)],[4655])).
% 2.12/2.30 tff(4657,plain,
% 2.12/2.30 (~(s(s(s(s(z)))) = s(s(s(z))))),
% 2.12/2.30 inference(modus_ponens,[status(thm)],[2228, 4656])).
% 2.12/2.30 tff(4658,plain,
% 2.12/2.30 (((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((s(s(s(s(z)))) = s(s(s(z)))) | b(s(s(s(s(z)))), s(s(s(z)))) | r(s(s(s(s(z)))), s(s(s(z)))))) <=> ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (s(s(s(s(z)))) = s(s(s(z)))) | b(s(s(s(s(z)))), s(s(s(z)))) | r(s(s(s(s(z)))), s(s(s(z)))))),
% 2.12/2.30 inference(rewrite,[status(thm)],[])).
% 2.12/2.30 tff(4659,plain,
% 2.12/2.30 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((s(s(s(s(z)))) = s(s(s(z)))) | b(s(s(s(s(z)))), s(s(s(z)))) | r(s(s(s(s(z)))), s(s(s(z)))))),
% 2.12/2.30 inference(quant_inst,[status(thm)],[])).
% 2.12/2.30 tff(4660,plain,
% 2.12/2.30 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (s(s(s(s(z)))) = s(s(s(z)))) | b(s(s(s(s(z)))), s(s(s(z)))) | r(s(s(s(s(z)))), s(s(s(z))))),
% 2.12/2.30 inference(modus_ponens,[status(thm)],[4659, 4658])).
% 2.12/2.30 tff(4661,plain,
% 2.12/2.30 ((s(s(s(s(z)))) = s(s(s(z)))) | b(s(s(s(s(z)))), s(s(s(z)))) | r(s(s(s(s(z)))), s(s(s(z))))),
% 2.12/2.30 inference(unit_resolution,[status(thm)],[4660, 79])).
% 2.12/2.30 tff(4662,plain,
% 2.12/2.30 (b(s(s(s(s(z)))), s(s(s(z)))) | r(s(s(s(s(z)))), s(s(s(z))))),
% 2.12/2.30 inference(unit_resolution,[status(thm)],[4661, 4657])).
% 2.12/2.30 tff(4663,plain,
% 2.12/2.30 (r(s(s(s(s(z)))), s(s(s(z))))),
% 2.12/2.30 inference(unit_resolution,[status(thm)],[4662, 4653])).
% 2.12/2.30 tff(4664,plain,
% 2.12/2.30 (b(s(s(s(s(z)))), z) <=> b(s(s(s(s(z)))), elem!1)),
% 2.12/2.30 inference(monotonicity,[status(thm)],[620])).
% 2.12/2.30 tff(4665,plain,
% 2.12/2.30 (b(s(s(s(s(z)))), elem!1) <=> b(s(s(s(s(z)))), z)),
% 2.12/2.30 inference(symmetry,[status(thm)],[4664])).
% 2.12/2.30 tff(4666,plain,
% 2.12/2.30 (b(s(s(s(s(z)))), elem!1) <=> b(s(s(s(s(elem!1)))), elem!1)),
% 2.12/2.30 inference(monotonicity,[status(thm)],[1087])).
% 2.12/2.30 tff(4667,plain,
% 2.12/2.30 (b(s(s(s(s(elem!1)))), elem!1) <=> b(s(s(s(s(z)))), elem!1)),
% 2.12/2.30 inference(symmetry,[status(thm)],[4666])).
% 2.12/2.30 tff(4668,plain,
% 2.12/2.30 (b(s(s(s(s(elem!1)))), elem!1) <=> b(s(s(s(s(z)))), z)),
% 2.12/2.30 inference(transitivity,[status(thm)],[4667, 4665])).
% 2.12/2.30 tff(4669,plain,
% 2.12/2.30 ((~b(s(s(s(s(elem!1)))), elem!1)) <=> (~b(s(s(s(s(z)))), z))),
% 2.12/2.30 inference(monotonicity,[status(thm)],[4668])).
% 2.12/2.30 tff(4670,plain,
% 2.12/2.30 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(z))) | (~b(s(s(s(s(elem!1)))), elem!1)) | (~b(s(s(s(s(elem!1)))), s(z))) | (~b(s(z), s(s(s(s(elem!1)))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(z))) | (~b(s(s(s(s(elem!1)))), elem!1)) | (~b(s(s(s(s(elem!1)))), s(z))) | (~b(s(z), s(s(s(s(elem!1)))))))),
% 2.12/2.30 inference(rewrite,[status(thm)],[])).
% 2.12/2.30 tff(4671,plain,
% 2.12/2.30 (((~b(s(s(s(s(elem!1)))), s(z))) | (~b(s(s(s(s(elem!1)))), s(z))) | (~b(s(z), s(s(s(s(elem!1)))))) | (~b(elem!1, s(z))) | (~b(s(s(s(s(elem!1)))), s(z))) | (~b(s(s(s(s(elem!1)))), elem!1))) <=> ((~b(elem!1, s(z))) | (~b(s(s(s(s(elem!1)))), elem!1)) | (~b(s(s(s(s(elem!1)))), s(z))) | (~b(s(z), s(s(s(s(elem!1)))))))),
% 2.12/2.30 inference(rewrite,[status(thm)],[])).
% 2.12/2.30 tff(4672,plain,
% 2.12/2.30 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(elem!1)))), s(z))) | (~b(s(s(s(s(elem!1)))), s(z))) | (~b(s(z), s(s(s(s(elem!1)))))) | (~b(elem!1, s(z))) | (~b(s(s(s(s(elem!1)))), s(z))) | (~b(s(s(s(s(elem!1)))), elem!1)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(z))) | (~b(s(s(s(s(elem!1)))), elem!1)) | (~b(s(s(s(s(elem!1)))), s(z))) | (~b(s(z), s(s(s(s(elem!1))))))))),
% 2.12/2.30 inference(monotonicity,[status(thm)],[4671])).
% 2.12/2.30 tff(4673,plain,
% 2.12/2.30 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(elem!1)))), s(z))) | (~b(s(s(s(s(elem!1)))), s(z))) | (~b(s(z), s(s(s(s(elem!1)))))) | (~b(elem!1, s(z))) | (~b(s(s(s(s(elem!1)))), s(z))) | (~b(s(s(s(s(elem!1)))), elem!1)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(z))) | (~b(s(s(s(s(elem!1)))), elem!1)) | (~b(s(s(s(s(elem!1)))), s(z))) | (~b(s(z), s(s(s(s(elem!1)))))))),
% 2.12/2.30 inference(transitivity,[status(thm)],[4672, 4670])).
% 2.12/2.30 tff(4674,plain,
% 2.12/2.30 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(elem!1)))), s(z))) | (~b(s(s(s(s(elem!1)))), s(z))) | (~b(s(z), s(s(s(s(elem!1)))))) | (~b(elem!1, s(z))) | (~b(s(s(s(s(elem!1)))), s(z))) | (~b(s(s(s(s(elem!1)))), elem!1)))),
% 2.12/2.30 inference(quant_inst,[status(thm)],[])).
% 2.12/2.30 tff(4675,plain,
% 2.12/2.30 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(z))) | (~b(s(s(s(s(elem!1)))), elem!1)) | (~b(s(s(s(s(elem!1)))), s(z))) | (~b(s(z), s(s(s(s(elem!1))))))),
% 2.12/2.30 inference(modus_ponens,[status(thm)],[4674, 4673])).
% 2.12/2.30 tff(4676,plain,
% 2.12/2.30 (~b(s(s(s(s(elem!1)))), elem!1)),
% 2.12/2.30 inference(unit_resolution,[status(thm)],[4675, 166, 1212, 4645, 4638])).
% 2.12/2.30 tff(4677,plain,
% 2.12/2.30 (~b(s(s(s(s(z)))), z)),
% 2.12/2.30 inference(modus_ponens,[status(thm)],[4676, 4669])).
% 2.12/2.30 tff(4678,plain,
% 2.12/2.30 (r(s(s(s(s(z)))), z)),
% 2.12/2.30 inference(unit_resolution,[status(thm)],[3266, 4677])).
% 2.12/2.30 tff(4679,assumption,(r(s(s(s(s(z)))), z)), introduced(assumption)).
% 2.12/2.30 tff(4680,assumption,(r(s(s(s(s(z)))), s(s(s(z))))), introduced(assumption)).
% 2.12/2.30 tff(4681,plain,
% 2.12/2.30 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(z)))) | (~r(s(s(s(z))), z)) | (~r(s(s(s(s(z)))), z)) | (~r(s(s(s(s(z)))), s(s(s(z))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, s(s(z)))) | (~r(s(s(s(z))), z)) | (~r(s(s(s(s(z)))), z)) | (~r(s(s(s(s(z)))), s(s(s(z))))))),
% 2.12/2.30 inference(rewrite,[status(thm)],[])).
% 2.12/2.30 tff(4682,plain,
% 2.12/2.30 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(z)))) | (~r(s(s(s(z))), z)) | (~r(s(s(s(s(z)))), z)) | (~r(s(s(s(s(z)))), s(s(s(z))))))),
% 2.12/2.30 inference(quant_inst,[status(thm)],[])).
% 2.12/2.30 tff(4683,plain,
% 2.12/2.30 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, s(s(z)))) | (~r(s(s(s(z))), z)) | (~r(s(s(s(s(z)))), z)) | (~r(s(s(s(s(z)))), s(s(s(z)))))),
% 2.12/2.30 inference(modus_ponens,[status(thm)],[4682, 4681])).
% 2.12/2.30 tff(4684,plain,
% 2.12/2.30 ($false),
% 2.12/2.30 inference(unit_resolution,[status(thm)],[4683, 197, 155, 4680, 1733, 4679])).
% 2.12/2.30 tff(4685,plain,((~r(s(s(s(s(z)))), z)) | (~r(z, s(s(z)))) | (~r(s(s(s(s(z)))), s(s(s(z))))) | (~r(s(s(s(z))), z))), inference(lemma,lemma(discharge,[]))).
% 2.12/2.30 tff(4686,plain,
% 2.12/2.30 ($false),
% 2.12/2.30 inference(unit_resolution,[status(thm)],[4685, 4678, 4663, 155, 1733])).
% 2.12/2.30 tff(4687,plain,((~r(s(s(s(s(elem!1)))), s(s(elem!1)))) | (~r(z, s(s(z)))) | (~r(s(s(s(z))), z)) | (~(s(s(z)) = s(s(elem!1)))) | (~b(elem!1, s(z))) | (~b(s(s(s(elem!1))), s(z))) | (~r(s(s(elem!1)), s(z))) | (~r(s(z), s(s(z)))) | (~r(s(z), s(s(elem!1))))), inference(lemma,lemma(discharge,[]))).
% 2.12/2.30 tff(4688,plain,
% 2.12/2.30 (~r(s(s(s(s(elem!1)))), s(s(elem!1)))),
% 2.12/2.30 inference(unit_resolution,[status(thm)],[4687, 4608, 1733, 155, 4625, 96, 4577, 120, 311])).
% 2.12/2.30 tff(4689,plain,
% 2.12/2.30 (b(s(s(s(s(elem!1)))), s(s(elem!1)))),
% 2.12/2.30 inference(unit_resolution,[status(thm)],[813, 4688, 4623])).
% 2.12/2.30 tff(4690,plain,
% 2.12/2.30 (~r(s(s(s(elem!1))), s(s(elem!1)))),
% 2.12/2.30 inference(unit_resolution,[status(thm)],[3454, 4608, 4583])).
% 2.12/2.30 tff(4691,plain,
% 2.12/2.30 (b(s(s(s(elem!1))), s(s(elem!1)))),
% 2.12/2.30 inference(unit_resolution,[status(thm)],[889, 4690, 51])).
% 2.12/2.30 tff(4692,plain,
% 2.12/2.30 (b(s(s(z)), s(s(s(elem!1)))) <=> b(s(s(elem!1)), s(s(s(elem!1))))),
% 2.12/2.30 inference(monotonicity,[status(thm)],[4608])).
% 2.12/2.30 tff(4693,plain,
% 2.12/2.30 (b(s(s(z)), s(s(s(elem!1))))),
% 2.12/2.30 inference(unit_resolution,[status(thm)],[279, 4587])).
% 2.12/2.30 tff(4694,plain,
% 2.12/2.30 (b(s(s(elem!1)), s(s(s(elem!1))))),
% 2.12/2.30 inference(modus_ponens,[status(thm)],[4693, 4692])).
% 2.12/2.30 tff(4695,plain,
% 2.12/2.30 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(s(s(s(elem!1)))), s(s(elem!1)))) | (~b(s(s(s(s(elem!1)))), s(s(s(elem!1))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(s(s(s(elem!1)))), s(s(elem!1)))) | (~b(s(s(s(s(elem!1)))), s(s(s(elem!1))))))),
% 2.12/2.30 inference(rewrite,[status(thm)],[])).
% 2.12/2.30 tff(4696,plain,
% 2.12/2.30 (((~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(s(s(s(elem!1)))), s(s(elem!1)))) | (~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(s(s(s(elem!1)))), s(s(elem!1)))) | (~b(s(s(s(s(elem!1)))), s(s(s(elem!1)))))) <=> ((~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(s(s(s(elem!1)))), s(s(elem!1)))) | (~b(s(s(s(s(elem!1)))), s(s(s(elem!1))))))),
% 2.12/2.30 inference(rewrite,[status(thm)],[])).
% 2.12/2.30 tff(4697,plain,
% 2.12/2.30 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(s(s(s(elem!1)))), s(s(elem!1)))) | (~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(s(s(s(elem!1)))), s(s(elem!1)))) | (~b(s(s(s(s(elem!1)))), s(s(s(elem!1))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(s(s(s(elem!1)))), s(s(elem!1)))) | (~b(s(s(s(s(elem!1)))), s(s(s(elem!1)))))))),
% 2.12/2.30 inference(monotonicity,[status(thm)],[4696])).
% 2.12/2.30 tff(4698,plain,
% 2.12/2.30 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(s(s(s(elem!1)))), s(s(elem!1)))) | (~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(s(s(s(elem!1)))), s(s(elem!1)))) | (~b(s(s(s(s(elem!1)))), s(s(s(elem!1))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(s(s(s(elem!1)))), s(s(elem!1)))) | (~b(s(s(s(s(elem!1)))), s(s(s(elem!1))))))),
% 2.12/2.30 inference(transitivity,[status(thm)],[4697, 4695])).
% 2.12/2.30 tff(4699,plain,
% 2.12/2.30 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(s(s(s(elem!1)))), s(s(elem!1)))) | (~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(s(s(s(elem!1)))), s(s(elem!1)))) | (~b(s(s(s(s(elem!1)))), s(s(s(elem!1))))))),
% 2.12/2.30 inference(quant_inst,[status(thm)],[])).
% 2.12/2.30 tff(4700,plain,
% 2.12/2.30 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(s(s(s(elem!1)))), s(s(elem!1)))) | (~b(s(s(s(s(elem!1)))), s(s(s(elem!1)))))),
% 2.12/2.30 inference(modus_ponens,[status(thm)],[4699, 4698])).
% 2.12/2.30 tff(4701,plain,
% 2.12/2.30 (~b(s(s(s(s(elem!1)))), s(s(s(elem!1))))),
% 2.12/2.30 inference(unit_resolution,[status(thm)],[4700, 166, 4694, 4691, 4689])).
% 2.12/2.30 tff(4702,plain,
% 2.12/2.30 (~b(s(s(s(s(z)))), s(s(s(z))))),
% 2.12/2.30 inference(modus_ponens,[status(thm)],[4701, 4618])).
% 2.12/2.30 tff(4703,plain,
% 2.12/2.30 (r(s(s(s(s(z)))), s(s(s(z))))),
% 2.12/2.30 inference(unit_resolution,[status(thm)],[4662, 4702])).
% 2.12/2.30 tff(4704,plain,
% 2.12/2.30 (~r(s(s(s(s(z)))), z)),
% 2.12/2.30 inference(unit_resolution,[status(thm)],[4685, 4703, 155, 1733])).
% 2.12/2.30 tff(4705,plain,
% 2.12/2.30 (b(s(s(s(s(z)))), z)),
% 2.12/2.30 inference(unit_resolution,[status(thm)],[3266, 4704])).
% 2.12/2.30 tff(4706,plain,
% 2.12/2.30 (b(s(s(s(s(elem!1)))), elem!1)),
% 2.12/2.30 inference(modus_ponens,[status(thm)],[4705, 4615])).
% 2.12/2.30 tff(4707,plain,
% 2.12/2.30 (~b(s(s(s(elem!1))), s(s(s(s(elem!1)))))),
% 2.12/2.30 inference(unit_resolution,[status(thm)],[3459, 4689, 4694, 4691])).
% 2.12/2.30 tff(4708,plain,
% 2.12/2.30 (r(s(s(s(elem!1))), s(s(s(s(elem!1)))))),
% 2.12/2.30 inference(unit_resolution,[status(thm)],[696, 4707, 358])).
% 2.12/2.30 tff(4709,plain,
% 2.12/2.30 (r(s(z), s(s(s(z)))) <=> r(s(z), s(s(s(elem!1))))),
% 2.12/2.30 inference(monotonicity,[status(thm)],[4609])).
% 2.12/2.30 tff(4710,plain,
% 2.12/2.30 (r(s(s(s(z))), s(s(z))) <=> r(s(s(s(elem!1))), s(s(elem!1)))),
% 2.12/2.30 inference(monotonicity,[status(thm)],[1086, 34])).
% 2.12/2.30 tff(4711,plain,
% 2.12/2.30 (r(s(s(s(z))), s(s(z))) <=> r(s(s(s(elem!1))), s(s(z)))),
% 2.12/2.30 inference(transitivity,[status(thm)],[4710, 3451])).
% 2.12/2.30 tff(4712,plain,
% 2.12/2.30 (r(s(s(s(elem!1))), s(s(z)))),
% 2.12/2.30 inference(modus_ponens,[status(thm)],[1676, 4711])).
% 2.12/2.30 tff(4713,plain,
% 2.12/2.30 ($false),
% 2.12/2.30 inference(unit_resolution,[status(thm)],[213, 4712])).
% 2.12/2.30 tff(4714,plain,(r(s(s(s(elem!1))), s(s(z))) | (~r(s(s(s(z))), s(s(z)))) | (~(s(s(z)) = s(s(elem!1))))), inference(lemma,lemma(discharge,[]))).
% 2.12/2.31 tff(4715,plain,
% 2.12/2.31 (~r(s(s(s(z))), s(s(z)))),
% 2.12/2.31 inference(unit_resolution,[status(thm)],[4714, 4608, 4583])).
% 2.12/2.31 tff(4716,plain,
% 2.12/2.31 (b(s(s(s(z))), s(s(z)))),
% 2.12/2.31 inference(unit_resolution,[status(thm)],[1010, 4715])).
% 2.12/2.31 tff(4717,plain,
% 2.12/2.31 (b(s(s(z)), s(s(s(z)))) <=> b(s(s(elem!1)), s(s(s(z))))),
% 2.12/2.31 inference(monotonicity,[status(thm)],[4608])).
% 2.12/2.31 tff(4718,plain,
% 2.12/2.31 (b(s(s(elem!1)), s(s(s(z)))) <=> b(s(s(z)), s(s(s(z))))),
% 2.12/2.31 inference(symmetry,[status(thm)],[4717])).
% 2.12/2.31 tff(4719,plain,
% 2.12/2.31 (b(s(s(elem!1)), s(s(s(z)))) <=> b(s(s(elem!1)), s(s(s(elem!1))))),
% 2.12/2.31 inference(monotonicity,[status(thm)],[4609])).
% 2.12/2.31 tff(4720,plain,
% 2.12/2.31 (b(s(s(elem!1)), s(s(s(elem!1)))) <=> b(s(s(elem!1)), s(s(s(z))))),
% 2.12/2.31 inference(symmetry,[status(thm)],[4719])).
% 2.12/2.31 tff(4721,plain,
% 2.12/2.31 (b(s(s(elem!1)), s(s(s(elem!1)))) <=> b(s(s(z)), s(s(s(z))))),
% 2.12/2.31 inference(transitivity,[status(thm)],[4720, 4718])).
% 2.12/2.31 tff(4722,plain,
% 2.12/2.31 (b(s(s(z)), s(s(s(z))))),
% 2.12/2.31 inference(modus_ponens,[status(thm)],[4694, 4721])).
% 2.12/2.31 tff(4723,plain,
% 2.12/2.31 (b(s(s(s(z))), s(z)) <=> b(s(s(s(elem!1))), s(z))),
% 2.12/2.31 inference(monotonicity,[status(thm)],[4609])).
% 2.12/2.31 tff(4724,plain,
% 2.12/2.31 (b(s(s(s(elem!1))), s(z)) <=> b(s(s(s(z))), s(z))),
% 2.12/2.31 inference(symmetry,[status(thm)],[4723])).
% 2.12/2.31 tff(4725,plain,
% 2.12/2.31 (b(s(s(s(z))), s(z))),
% 2.12/2.31 inference(modus_ponens,[status(thm)],[96, 4724])).
% 2.12/2.31 tff(4726,plain,
% 2.12/2.31 (b(s(z), z) <=> b(s(z), elem!1)),
% 2.12/2.31 inference(monotonicity,[status(thm)],[4613])).
% 2.12/2.31 tff(4727,plain,
% 2.12/2.31 (b(s(z), elem!1)),
% 2.12/2.31 inference(modus_ponens,[status(thm)],[53, 4726])).
% 2.12/2.31 tff(4728,plain,
% 2.12/2.31 (b(s(s(elem!1)), z) <=> b(s(s(elem!1)), elem!1)),
% 2.12/2.31 inference(monotonicity,[status(thm)],[4613])).
% 2.12/2.31 tff(4729,plain,
% 2.12/2.31 (b(s(s(elem!1)), z)),
% 2.12/2.31 inference(unit_resolution,[status(thm)],[2965, 4608, 122])).
% 2.12/2.31 tff(4730,plain,
% 2.12/2.31 (b(s(s(elem!1)), elem!1)),
% 2.12/2.31 inference(modus_ponens,[status(thm)],[4729, 4728])).
% 2.12/2.31 tff(4731,plain,
% 2.12/2.31 (b(s(s(s(s(z)))), z) <=> b(s(s(s(s(elem!1)))), elem!1)),
% 2.12/2.31 inference(transitivity,[status(thm)],[4664, 4666])).
% 2.12/2.31 tff(4732,assumption,(b(s(s(s(s(z)))), s(s(s(z))))), introduced(assumption)).
% 2.12/2.31 tff(4733,assumption,(b(s(s(z)), s(s(s(s(z)))))), introduced(assumption)).
% 2.12/2.31 tff(4734,plain,
% 2.12/2.31 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), s(s(z)))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(z)), s(s(s(s(z)))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(z)), s(s(s(s(z)))))))),
% 2.12/2.31 inference(rewrite,[status(thm)],[])).
% 2.12/2.31 tff(4735,plain,
% 2.12/2.31 (((~b(s(s(z)), s(s(s(z))))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(z)), s(s(s(s(z))))))) <=> ((~b(s(s(s(z))), s(s(z)))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(z)), s(s(s(s(z)))))))),
% 2.12/2.31 inference(rewrite,[status(thm)],[])).
% 2.12/2.31 tff(4736,plain,
% 2.12/2.31 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), s(s(s(z))))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(z)), s(s(s(s(z)))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), s(s(z)))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(z)), s(s(s(s(z))))))))),
% 2.12/2.31 inference(monotonicity,[status(thm)],[4735])).
% 2.12/2.31 tff(4737,plain,
% 2.12/2.31 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), s(s(s(z))))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(z)), s(s(s(s(z)))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(z)), s(s(s(s(z)))))))),
% 2.12/2.31 inference(transitivity,[status(thm)],[4736, 4734])).
% 2.12/2.31 tff(4738,plain,
% 2.12/2.31 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), s(s(s(z))))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(z)), s(s(s(s(z)))))))),
% 2.12/2.31 inference(quant_inst,[status(thm)],[])).
% 2.12/2.31 tff(4739,plain,
% 2.12/2.31 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(z)), s(s(s(s(z))))))),
% 2.12/2.31 inference(modus_ponens,[status(thm)],[4738, 4737])).
% 2.12/2.31 tff(4740,plain,
% 2.12/2.31 ($false),
% 2.12/2.31 inference(unit_resolution,[status(thm)],[4739, 166, 986, 987, 4732, 4733])).
% 2.12/2.31 tff(4741,plain,((~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(s(z)), s(s(s(s(z))))))), inference(lemma,lemma(discharge,[]))).
% 2.12/2.31 tff(4742,plain,
% 2.12/2.31 (~b(s(s(z)), s(s(s(s(z)))))),
% 2.12/2.31 inference(unit_resolution,[status(thm)],[4741, 4732, 987, 986])).
% 2.12/2.31 tff(4743,assumption,(s(s(z)) = s(s(s(s(z))))), introduced(assumption)).
% 2.12/2.31 tff(4744,plain,
% 2.12/2.31 (inj_0(s(s(z))) = inj_0(s(s(s(s(z)))))),
% 2.12/2.31 inference(monotonicity,[status(thm)],[4743])).
% 2.12/2.31 tff(4745,plain,
% 2.12/2.31 (inj_0(s(s(s(s(z))))) = inj_0(s(s(z)))),
% 2.12/2.31 inference(symmetry,[status(thm)],[4744])).
% 2.12/2.31 tff(4746,plain,
% 2.12/2.31 (s(s(s(z))) = s(z)),
% 2.12/2.31 inference(transitivity,[status(thm)],[3277, 4745, 33])).
% 2.12/2.31 tff(4747,plain,
% 2.12/2.31 ($false),
% 2.12/2.31 inference(unit_resolution,[status(thm)],[1758, 4746])).
% 2.12/2.31 tff(4748,plain,(~(s(s(z)) = s(s(s(s(z)))))), inference(lemma,lemma(discharge,[]))).
% 2.12/2.31 tff(4749,plain,
% 2.12/2.31 (((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((s(s(z)) = s(s(s(s(z))))) | b(s(s(z)), s(s(s(s(z))))) | r(s(s(z)), s(s(s(s(z))))))) <=> ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (s(s(z)) = s(s(s(s(z))))) | b(s(s(z)), s(s(s(s(z))))) | r(s(s(z)), s(s(s(s(z))))))),
% 2.12/2.31 inference(rewrite,[status(thm)],[])).
% 2.12/2.31 tff(4750,plain,
% 2.12/2.31 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((s(s(z)) = s(s(s(s(z))))) | b(s(s(z)), s(s(s(s(z))))) | r(s(s(z)), s(s(s(s(z))))))),
% 2.12/2.31 inference(quant_inst,[status(thm)],[])).
% 2.12/2.31 tff(4751,plain,
% 2.12/2.31 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (s(s(z)) = s(s(s(s(z))))) | b(s(s(z)), s(s(s(s(z))))) | r(s(s(z)), s(s(s(s(z)))))),
% 2.12/2.31 inference(modus_ponens,[status(thm)],[4750, 4749])).
% 2.12/2.31 tff(4752,plain,
% 2.12/2.31 ((s(s(z)) = s(s(s(s(z))))) | b(s(s(z)), s(s(s(s(z))))) | r(s(s(z)), s(s(s(s(z)))))),
% 2.12/2.31 inference(unit_resolution,[status(thm)],[4751, 79])).
% 2.12/2.31 tff(4753,plain,
% 2.12/2.31 (b(s(s(z)), s(s(s(s(z))))) | r(s(s(z)), s(s(s(s(z)))))),
% 2.12/2.31 inference(unit_resolution,[status(thm)],[4752, 4748])).
% 2.12/2.31 tff(4754,plain,
% 2.12/2.31 (r(s(s(z)), s(s(s(s(z)))))),
% 2.12/2.31 inference(unit_resolution,[status(thm)],[4753, 4742])).
% 2.12/2.31 tff(4755,plain,
% 2.12/2.31 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), s(s(z)))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(s(z))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(s(z))))))),
% 2.12/2.31 inference(rewrite,[status(thm)],[])).
% 2.12/2.31 tff(4756,plain,
% 2.12/2.31 (((~b(s(s(z)), s(s(s(z))))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(z), s(s(s(z))))) | (~b(s(z), s(s(s(s(z))))))) <=> ((~b(s(s(s(z))), s(s(z)))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(s(z))))))),
% 2.12/2.31 inference(rewrite,[status(thm)],[])).
% 2.12/2.31 tff(4757,plain,
% 2.12/2.31 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), s(s(s(z))))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(z), s(s(s(z))))) | (~b(s(z), s(s(s(s(z)))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), s(s(z)))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(s(z)))))))),
% 2.12/2.31 inference(monotonicity,[status(thm)],[4756])).
% 2.12/2.31 tff(4758,plain,
% 2.12/2.31 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), s(s(s(z))))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(z), s(s(s(z))))) | (~b(s(z), s(s(s(s(z)))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(s(z))))))),
% 2.12/2.31 inference(transitivity,[status(thm)],[4757, 4755])).
% 2.12/2.31 tff(4759,plain,
% 2.12/2.31 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), s(s(s(z))))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(z), s(s(s(z))))) | (~b(s(z), s(s(s(s(z)))))))),
% 2.12/2.31 inference(quant_inst,[status(thm)],[])).
% 2.12/2.31 tff(4760,plain,
% 2.12/2.31 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(s(z)))))),
% 2.12/2.31 inference(modus_ponens,[status(thm)],[4759, 4758])).
% 2.12/2.31 tff(4761,plain,
% 2.12/2.31 (~b(s(z), s(s(s(s(z)))))),
% 2.12/2.31 inference(unit_resolution,[status(thm)],[4760, 166, 988, 986, 987, 4732])).
% 2.12/2.31 tff(4762,plain,
% 2.12/2.31 (r(s(z), s(s(s(s(z)))))),
% 2.12/2.31 inference(unit_resolution,[status(thm)],[3302, 4761])).
% 2.12/2.31 tff(4763,plain,
% 2.12/2.31 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), s(z))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(s(z)))), s(s(s(z))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(z))), s(z))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(s(z)))), s(s(s(z))))))),
% 2.12/2.31 inference(rewrite,[status(thm)],[])).
% 2.12/2.31 tff(4764,plain,
% 2.12/2.31 (((~b(s(z), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(z))), s(z))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(z)))) <=> ((~b(s(s(s(z))), s(z))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(s(z)))), s(s(s(z))))))),
% 2.12/2.31 inference(rewrite,[status(thm)],[])).
% 2.12/2.31 tff(4765,plain,
% 2.12/2.31 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(z))), s(z))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), s(z))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(s(z)))), s(s(s(z)))))))),
% 2.12/2.31 inference(monotonicity,[status(thm)],[4764])).
% 2.12/2.31 tff(4766,plain,
% 2.12/2.31 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(z))), s(z))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(z))), s(z))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(s(z)))), s(s(s(z))))))),
% 2.12/2.31 inference(transitivity,[status(thm)],[4765, 4763])).
% 2.12/2.31 tff(4767,plain,
% 2.12/2.31 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(z))), s(z))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(z))))),
% 2.12/2.31 inference(quant_inst,[status(thm)],[])).
% 2.12/2.31 tff(4768,plain,
% 2.12/2.31 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(z))), s(z))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(s(z)))), s(s(s(z)))))),
% 2.12/2.31 inference(modus_ponens,[status(thm)],[4767, 4766])).
% 2.12/2.31 tff(4769,plain,
% 2.12/2.31 (~b(s(s(s(s(z)))), s(z))),
% 2.12/2.31 inference(unit_resolution,[status(thm)],[4768, 166, 988, 4732, 3240])).
% 2.12/2.31 tff(4770,plain,
% 2.12/2.31 (r(s(s(s(s(z)))), s(z))),
% 2.12/2.31 inference(unit_resolution,[status(thm)],[3285, 4769])).
% 2.12/2.31 tff(4771,plain,
% 2.12/2.31 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(s(z)))) | (~r(s(z), s(s(s(s(z)))))) | (~r(s(s(s(s(z)))), s(z))) | (~r(s(s(z)), s(s(s(s(z)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(z), s(s(z)))) | (~r(s(z), s(s(s(s(z)))))) | (~r(s(s(s(s(z)))), s(z))) | (~r(s(s(z)), s(s(s(s(z)))))))),
% 2.12/2.31 inference(rewrite,[status(thm)],[])).
% 2.12/2.31 tff(4772,plain,
% 2.12/2.31 (((~r(s(s(s(s(z)))), s(z))) | (~r(s(s(z)), s(s(s(s(z)))))) | (~r(s(z), s(s(s(s(z)))))) | (~r(s(z), s(s(z))))) <=> ((~r(s(z), s(s(z)))) | (~r(s(z), s(s(s(s(z)))))) | (~r(s(s(s(s(z)))), s(z))) | (~r(s(s(z)), s(s(s(s(z)))))))),
% 2.12/2.31 inference(rewrite,[status(thm)],[])).
% 2.12/2.31 tff(4773,plain,
% 2.12/2.31 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(z)))), s(z))) | (~r(s(s(z)), s(s(s(s(z)))))) | (~r(s(z), s(s(s(s(z)))))) | (~r(s(z), s(s(z)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(s(z)))) | (~r(s(z), s(s(s(s(z)))))) | (~r(s(s(s(s(z)))), s(z))) | (~r(s(s(z)), s(s(s(s(z))))))))),
% 2.12/2.31 inference(monotonicity,[status(thm)],[4772])).
% 2.12/2.31 tff(4774,plain,
% 2.12/2.31 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(z)))), s(z))) | (~r(s(s(z)), s(s(s(s(z)))))) | (~r(s(z), s(s(s(s(z)))))) | (~r(s(z), s(s(z)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(z), s(s(z)))) | (~r(s(z), s(s(s(s(z)))))) | (~r(s(s(s(s(z)))), s(z))) | (~r(s(s(z)), s(s(s(s(z)))))))),
% 2.12/2.31 inference(transitivity,[status(thm)],[4773, 4771])).
% 2.12/2.31 tff(4775,plain,
% 2.12/2.31 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(z)))), s(z))) | (~r(s(s(z)), s(s(s(s(z)))))) | (~r(s(z), s(s(s(s(z)))))) | (~r(s(z), s(s(z)))))),
% 2.12/2.31 inference(quant_inst,[status(thm)],[])).
% 2.12/2.31 tff(4776,plain,
% 2.12/2.31 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(z), s(s(z)))) | (~r(s(z), s(s(s(s(z)))))) | (~r(s(s(s(s(z)))), s(z))) | (~r(s(s(z)), s(s(s(s(z))))))),
% 2.12/2.31 inference(modus_ponens,[status(thm)],[4775, 4774])).
% 2.12/2.31 tff(4777,plain,
% 2.12/2.31 ($false),
% 2.12/2.31 inference(unit_resolution,[status(thm)],[4776, 197, 120, 4770, 4762, 4754])).
% 2.12/2.31 tff(4778,plain,((~b(s(s(s(s(z)))), s(s(s(z))))) | (~r(s(z), s(s(z)))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(s(z))), s(s(z))))), inference(lemma,lemma(discharge,[]))).
% 2.12/2.31 tff(4779,plain,
% 2.12/2.31 (~b(s(s(s(s(z)))), s(s(s(z))))),
% 2.12/2.31 inference(unit_resolution,[status(thm)],[4778, 988, 120, 3240, 986, 987])).
% 2.12/2.31 tff(4780,plain,
% 2.12/2.31 (r(s(s(s(s(z)))), s(s(s(z))))),
% 2.12/2.31 inference(unit_resolution,[status(thm)],[4662, 4779])).
% 2.12/2.31 tff(4781,plain,
% 2.12/2.31 (~r(s(s(s(s(z)))), z)),
% 2.12/2.31 inference(unit_resolution,[status(thm)],[4685, 4780, 155, 1733])).
% 2.12/2.31 tff(4782,plain,
% 2.12/2.31 (b(s(s(s(s(z)))), z)),
% 2.12/2.31 inference(unit_resolution,[status(thm)],[3266, 4781])).
% 2.12/2.31 tff(4783,plain,
% 2.12/2.31 (b(s(s(s(s(elem!1)))), elem!1)),
% 2.12/2.31 inference(modus_ponens,[status(thm)],[4782, 4731])).
% 2.12/2.31 tff(4784,plain,
% 2.12/2.31 (b(s(z), s(s(s(z)))) <=> b(s(z), s(s(s(elem!1))))),
% 2.12/2.31 inference(monotonicity,[status(thm)],[1086])).
% 2.12/2.31 tff(4785,plain,
% 2.12/2.31 (b(s(z), s(s(s(elem!1))))),
% 2.12/2.31 inference(modus_ponens,[status(thm)],[988, 4784])).
% 2.12/2.31 tff(4786,plain,
% 2.12/2.31 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(z))) | (~b(s(z), s(s(s(elem!1))))) | (~b(s(z), elem!1)) | (~b(s(s(s(s(elem!1)))), elem!1)) | (~b(s(z), s(s(s(s(elem!1)))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(z))) | (~b(s(z), s(s(s(elem!1))))) | (~b(s(z), elem!1)) | (~b(s(s(s(s(elem!1)))), elem!1)) | (~b(s(z), s(s(s(s(elem!1)))))))),
% 2.12/2.31 inference(rewrite,[status(thm)],[])).
% 2.12/2.31 tff(4787,plain,
% 2.12/2.31 (((~b(s(z), s(s(s(elem!1))))) | (~b(s(z), s(s(s(elem!1))))) | (~b(elem!1, s(z))) | (~b(s(s(s(s(elem!1)))), elem!1)) | (~b(s(z), elem!1)) | (~b(s(z), s(s(s(s(elem!1))))))) <=> ((~b(elem!1, s(z))) | (~b(s(z), s(s(s(elem!1))))) | (~b(s(z), elem!1)) | (~b(s(s(s(s(elem!1)))), elem!1)) | (~b(s(z), s(s(s(s(elem!1)))))))),
% 2.12/2.31 inference(rewrite,[status(thm)],[])).
% 2.12/2.31 tff(4788,plain,
% 2.12/2.31 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(s(elem!1))))) | (~b(s(z), s(s(s(elem!1))))) | (~b(elem!1, s(z))) | (~b(s(s(s(s(elem!1)))), elem!1)) | (~b(s(z), elem!1)) | (~b(s(z), s(s(s(s(elem!1)))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(z))) | (~b(s(z), s(s(s(elem!1))))) | (~b(s(z), elem!1)) | (~b(s(s(s(s(elem!1)))), elem!1)) | (~b(s(z), s(s(s(s(elem!1))))))))),
% 2.12/2.31 inference(monotonicity,[status(thm)],[4787])).
% 2.12/2.31 tff(4789,plain,
% 2.12/2.31 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(s(elem!1))))) | (~b(s(z), s(s(s(elem!1))))) | (~b(elem!1, s(z))) | (~b(s(s(s(s(elem!1)))), elem!1)) | (~b(s(z), elem!1)) | (~b(s(z), s(s(s(s(elem!1)))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(z))) | (~b(s(z), s(s(s(elem!1))))) | (~b(s(z), elem!1)) | (~b(s(s(s(s(elem!1)))), elem!1)) | (~b(s(z), s(s(s(s(elem!1)))))))),
% 2.12/2.31 inference(transitivity,[status(thm)],[4788, 4786])).
% 2.12/2.31 tff(4790,plain,
% 2.12/2.31 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(s(elem!1))))) | (~b(s(z), s(s(s(elem!1))))) | (~b(elem!1, s(z))) | (~b(s(s(s(s(elem!1)))), elem!1)) | (~b(s(z), elem!1)) | (~b(s(z), s(s(s(s(elem!1)))))))),
% 2.12/2.31 inference(quant_inst,[status(thm)],[])).
% 2.12/2.31 tff(4791,plain,
% 2.12/2.31 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(z))) | (~b(s(z), s(s(s(elem!1))))) | (~b(s(z), elem!1)) | (~b(s(s(s(s(elem!1)))), elem!1)) | (~b(s(z), s(s(s(s(elem!1))))))),
% 2.12/2.31 inference(modus_ponens,[status(thm)],[4790, 4789])).
% 2.12/2.31 tff(4792,plain,
% 2.12/2.31 (~b(s(z), s(s(s(s(elem!1)))))),
% 2.12/2.31 inference(unit_resolution,[status(thm)],[4791, 166, 4785, 1212, 642, 4783])).
% 2.12/2.32 tff(4793,plain,
% 2.12/2.32 (r(s(z), s(s(s(s(elem!1)))))),
% 2.12/2.32 inference(unit_resolution,[status(thm)],[681, 4792])).
% 2.12/2.32 tff(4794,plain,
% 2.12/2.32 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), elem!1)) | (~b(elem!1, s(z))) | (~b(s(s(s(s(elem!1)))), s(s(elem!1)))) | (~b(s(z), elem!1)) | (~b(s(s(s(s(elem!1)))), elem!1)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(elem!1)), elem!1)) | (~b(elem!1, s(z))) | (~b(s(s(s(s(elem!1)))), s(s(elem!1)))) | (~b(s(z), elem!1)) | (~b(s(s(s(s(elem!1)))), elem!1)))),
% 2.12/2.32 inference(rewrite,[status(thm)],[])).
% 2.12/2.32 tff(4795,plain,
% 2.12/2.32 (((~b(s(z), elem!1)) | (~b(s(s(s(s(elem!1)))), elem!1)) | (~b(elem!1, s(z))) | (~b(s(s(elem!1)), elem!1)) | (~b(s(s(s(s(elem!1)))), elem!1)) | (~b(s(s(s(s(elem!1)))), s(s(elem!1))))) <=> ((~b(s(s(elem!1)), elem!1)) | (~b(elem!1, s(z))) | (~b(s(s(s(s(elem!1)))), s(s(elem!1)))) | (~b(s(z), elem!1)) | (~b(s(s(s(s(elem!1)))), elem!1)))),
% 2.12/2.32 inference(rewrite,[status(thm)],[])).
% 2.12/2.32 tff(4796,plain,
% 2.12/2.32 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), elem!1)) | (~b(s(s(s(s(elem!1)))), elem!1)) | (~b(elem!1, s(z))) | (~b(s(s(elem!1)), elem!1)) | (~b(s(s(s(s(elem!1)))), elem!1)) | (~b(s(s(s(s(elem!1)))), s(s(elem!1)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), elem!1)) | (~b(elem!1, s(z))) | (~b(s(s(s(s(elem!1)))), s(s(elem!1)))) | (~b(s(z), elem!1)) | (~b(s(s(s(s(elem!1)))), elem!1))))),
% 2.12/2.32 inference(monotonicity,[status(thm)],[4795])).
% 2.12/2.32 tff(4797,plain,
% 2.12/2.32 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), elem!1)) | (~b(s(s(s(s(elem!1)))), elem!1)) | (~b(elem!1, s(z))) | (~b(s(s(elem!1)), elem!1)) | (~b(s(s(s(s(elem!1)))), elem!1)) | (~b(s(s(s(s(elem!1)))), s(s(elem!1)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(elem!1)), elem!1)) | (~b(elem!1, s(z))) | (~b(s(s(s(s(elem!1)))), s(s(elem!1)))) | (~b(s(z), elem!1)) | (~b(s(s(s(s(elem!1)))), elem!1)))),
% 2.12/2.32 inference(transitivity,[status(thm)],[4796, 4794])).
% 2.12/2.32 tff(4798,plain,
% 2.12/2.32 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), elem!1)) | (~b(s(s(s(s(elem!1)))), elem!1)) | (~b(elem!1, s(z))) | (~b(s(s(elem!1)), elem!1)) | (~b(s(s(s(s(elem!1)))), elem!1)) | (~b(s(s(s(s(elem!1)))), s(s(elem!1)))))),
% 2.12/2.32 inference(quant_inst,[status(thm)],[])).
% 2.12/2.32 tff(4799,plain,
% 2.12/2.32 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(elem!1)), elem!1)) | (~b(elem!1, s(z))) | (~b(s(s(s(s(elem!1)))), s(s(elem!1)))) | (~b(s(z), elem!1)) | (~b(s(s(s(s(elem!1)))), elem!1))),
% 2.12/2.32 inference(modus_ponens,[status(thm)],[4798, 4797])).
% 2.12/2.32 tff(4800,plain,
% 2.12/2.32 (~b(s(s(s(s(elem!1)))), s(s(elem!1)))),
% 2.12/2.32 inference(unit_resolution,[status(thm)],[4799, 166, 786, 1212, 642, 4783])).
% 2.12/2.32 tff(4801,plain,
% 2.12/2.32 (r(s(s(s(s(elem!1)))), s(s(elem!1)))),
% 2.12/2.32 inference(unit_resolution,[status(thm)],[813, 4800, 734])).
% 2.12/2.32 tff(4802,plain,
% 2.12/2.32 ($false),
% 2.12/2.32 inference(unit_resolution,[status(thm)],[4636, 4801, 4793, 311, 4577])).
% 2.12/2.32 tff(4803,plain,((~b(s(z), s(s(s(z))))) | (~r(s(z), s(s(elem!1)))) | (~r(s(s(elem!1)), s(z))) | (~b(s(s(elem!1)), elem!1)) | (~b(elem!1, s(z))) | (~b(s(z), elem!1)) | (~(s(s(z)) = s(s(elem!1)))) | (~r(z, s(s(z)))) | (~r(s(s(s(z))), z)) | (~r(s(z), s(s(z)))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(s(z))), s(s(z))))), inference(lemma,lemma(discharge,[]))).
% 2.12/2.32 tff(4804,plain,
% 2.12/2.32 (~b(s(z), s(s(s(z))))),
% 2.12/2.32 inference(unit_resolution,[status(thm)],[4803, 4730, 4577, 311, 4625, 4727, 4608, 155, 1733, 120, 4725, 4722, 4716])).
% 2.12/2.32 tff(4805,plain,
% 2.12/2.32 (r(s(z), s(s(s(z))))),
% 2.12/2.32 inference(unit_resolution,[status(thm)],[1674, 4804])).
% 2.12/2.32 tff(4806,plain,
% 2.12/2.32 (r(s(z), s(s(s(elem!1))))),
% 2.12/2.32 inference(modus_ponens,[status(thm)],[4805, 4709])).
% 2.12/2.32 tff(4807,plain,
% 2.12/2.32 (r(s(s(s(s(elem!1)))), s(s(s(elem!1))))),
% 2.12/2.32 inference(unit_resolution,[status(thm)],[1065, 4701, 364])).
% 2.12/2.32 tff(4808,plain,
% 2.12/2.32 (~r(s(z), s(s(s(s(elem!1)))))),
% 2.12/2.32 inference(unit_resolution,[status(thm)],[2125, 4807, 4806, 4708])).
% 2.12/2.32 tff(4809,plain,
% 2.12/2.32 (b(s(z), s(s(s(s(elem!1)))))),
% 2.12/2.32 inference(unit_resolution,[status(thm)],[681, 4808])).
% 2.12/2.32 tff(4810,plain,
% 2.12/2.32 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(z))) | (~b(s(z), elem!1)) | (~b(s(s(s(s(elem!1)))), elem!1)) | (~b(s(z), s(s(s(s(elem!1)))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(z))) | (~b(s(z), elem!1)) | (~b(s(s(s(s(elem!1)))), elem!1)) | (~b(s(z), s(s(s(s(elem!1)))))))),
% 2.12/2.32 inference(rewrite,[status(thm)],[])).
% 2.12/2.32 tff(4811,plain,
% 2.12/2.32 (((~b(s(z), elem!1)) | (~b(s(z), elem!1)) | (~b(elem!1, s(z))) | (~b(s(s(s(s(elem!1)))), elem!1)) | (~b(s(z), elem!1)) | (~b(s(z), s(s(s(s(elem!1))))))) <=> ((~b(elem!1, s(z))) | (~b(s(z), elem!1)) | (~b(s(s(s(s(elem!1)))), elem!1)) | (~b(s(z), s(s(s(s(elem!1)))))))),
% 2.12/2.32 inference(rewrite,[status(thm)],[])).
% 2.12/2.32 tff(4812,plain,
% 2.12/2.32 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), elem!1)) | (~b(s(z), elem!1)) | (~b(elem!1, s(z))) | (~b(s(s(s(s(elem!1)))), elem!1)) | (~b(s(z), elem!1)) | (~b(s(z), s(s(s(s(elem!1)))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(z))) | (~b(s(z), elem!1)) | (~b(s(s(s(s(elem!1)))), elem!1)) | (~b(s(z), s(s(s(s(elem!1))))))))),
% 2.12/2.32 inference(monotonicity,[status(thm)],[4811])).
% 2.12/2.32 tff(4813,plain,
% 2.12/2.32 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), elem!1)) | (~b(s(z), elem!1)) | (~b(elem!1, s(z))) | (~b(s(s(s(s(elem!1)))), elem!1)) | (~b(s(z), elem!1)) | (~b(s(z), s(s(s(s(elem!1)))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(z))) | (~b(s(z), elem!1)) | (~b(s(s(s(s(elem!1)))), elem!1)) | (~b(s(z), s(s(s(s(elem!1)))))))),
% 2.12/2.32 inference(transitivity,[status(thm)],[4812, 4810])).
% 2.12/2.32 tff(4814,plain,
% 2.12/2.32 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), elem!1)) | (~b(s(z), elem!1)) | (~b(elem!1, s(z))) | (~b(s(s(s(s(elem!1)))), elem!1)) | (~b(s(z), elem!1)) | (~b(s(z), s(s(s(s(elem!1)))))))),
% 2.12/2.32 inference(quant_inst,[status(thm)],[])).
% 2.12/2.32 tff(4815,plain,
% 2.12/2.32 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(z))) | (~b(s(z), elem!1)) | (~b(s(s(s(s(elem!1)))), elem!1)) | (~b(s(z), s(s(s(s(elem!1))))))),
% 2.12/2.32 inference(modus_ponens,[status(thm)],[4814, 4813])).
% 2.12/2.32 tff(4816,plain,
% 2.12/2.32 ($false),
% 2.12/2.32 inference(unit_resolution,[status(thm)],[4815, 166, 4625, 4727, 4809, 4706])).
% 2.12/2.32 tff(4817,plain,((~b(s(s(z)), z)) | (~r(z, s(s(z)))) | (~r(s(s(s(z))), z)) | (~b(s(s(s(elem!1))), s(z))) | (~r(s(s(elem!1)), s(z))) | (~r(s(z), s(s(z)))) | (~r(s(z), s(s(elem!1)))) | (~b(z, s(z))) | (~b(s(z), z)) | (~r(s(s(s(elem!1))), z)) | (s(s(elem!1)) = s(s(s(elem!1))))), inference(lemma,lemma(discharge,[]))).
% 2.12/2.32 tff(4818,plain,
% 2.12/2.32 (~b(s(s(z)), z)),
% 2.12/2.32 inference(unit_resolution,[status(thm)],[4817, 1733, 155, 96, 4577, 120, 311, 118, 53, 154, 45])).
% 2.12/2.32 tff(4819,plain,
% 2.12/2.32 (r(s(s(z)), z)),
% 2.12/2.32 inference(unit_resolution,[status(thm)],[186, 4818])).
% 2.12/2.32 tff(4820,plain,
% 2.12/2.32 (~r(s(s(s(z))), s(s(z)))),
% 2.12/2.32 inference(unit_resolution,[status(thm)],[1717, 197, 155, 4819, 1733])).
% 2.12/2.32 tff(4821,plain,
% 2.12/2.32 (b(s(s(s(z))), s(s(z)))),
% 2.12/2.32 inference(unit_resolution,[status(thm)],[1010, 4820])).
% 2.12/2.32 tff(4822,plain,
% 2.12/2.32 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), s(s(z)))) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(s(z)), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(s(s(z))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(elem!1))), s(s(z)))) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(s(z)), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(s(s(z))))))),
% 2.12/2.32 inference(rewrite,[status(thm)],[])).
% 2.12/2.32 tff(4823,plain,
% 2.12/2.32 (((~b(s(s(s(elem!1))), s(z))) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(s(z)), s(s(s(elem!1))))) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(s(s(elem!1))), s(s(z)))) | (~b(s(s(s(elem!1))), s(s(s(z)))))) <=> ((~b(s(s(s(elem!1))), s(s(z)))) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(s(z)), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(s(s(z))))))),
% 2.12/2.32 inference(rewrite,[status(thm)],[])).
% 2.12/2.32 tff(4824,plain,
% 2.12/2.32 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), s(z))) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(s(z)), s(s(s(elem!1))))) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(s(s(elem!1))), s(s(z)))) | (~b(s(s(s(elem!1))), s(s(s(z))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), s(s(z)))) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(s(z)), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(s(s(z)))))))),
% 2.12/2.32 inference(monotonicity,[status(thm)],[4823])).
% 2.12/2.32 tff(4825,plain,
% 2.12/2.32 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), s(z))) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(s(z)), s(s(s(elem!1))))) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(s(s(elem!1))), s(s(z)))) | (~b(s(s(s(elem!1))), s(s(s(z))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(elem!1))), s(s(z)))) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(s(z)), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(s(s(z))))))),
% 2.12/2.32 inference(transitivity,[status(thm)],[4824, 4822])).
% 2.12/2.32 tff(4826,plain,
% 2.12/2.32 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), s(z))) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(s(z)), s(s(s(elem!1))))) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(s(s(elem!1))), s(s(z)))) | (~b(s(s(s(elem!1))), s(s(s(z))))))),
% 2.12/2.32 inference(quant_inst,[status(thm)],[])).
% 2.12/2.32 tff(4827,plain,
% 2.12/2.32 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(elem!1))), s(s(z)))) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(s(z)), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(s(s(z)))))),
% 2.12/2.32 inference(modus_ponens,[status(thm)],[4826, 4825])).
% 2.12/2.32 tff(4828,plain,
% 2.12/2.32 (~b(s(s(s(elem!1))), s(s(s(z))))),
% 2.12/2.32 inference(unit_resolution,[status(thm)],[4827, 166, 96, 4693, 4821, 4584])).
% 2.12/2.32 tff(4829,plain,
% 2.12/2.32 (s(s(s(elem!1))) = s(s(s(z)))),
% 2.12/2.32 inference(unit_resolution,[status(thm)],[3574, 4828, 4580])).
% 2.12/2.32 tff(4830,plain,
% 2.12/2.32 (r(s(s(s(elem!1))), elem!1) <=> r(s(s(s(z))), elem!1)),
% 2.12/2.32 inference(monotonicity,[status(thm)],[4829])).
% 2.12/2.32 tff(4831,plain,
% 2.12/2.32 (s(s(elem!1)) = s(s(z))),
% 2.12/2.32 inference(unit_resolution,[status(thm)],[139, 4829])).
% 2.12/2.32 tff(4832,plain,
% 2.12/2.32 (s(s(z)) = s(s(elem!1))),
% 2.12/2.32 inference(unit_resolution,[status(thm)],[131, 4831])).
% 2.12/2.32 tff(4833,plain,
% 2.12/2.32 (s(elem!1) = s(z)),
% 2.12/2.32 inference(unit_resolution,[status(thm)],[43, 4832])).
% 2.12/2.32 tff(4834,plain,
% 2.12/2.32 (z = elem!1),
% 2.12/2.32 inference(unit_resolution,[status(thm)],[30, 4833])).
% 2.12/2.32 tff(4835,plain,
% 2.12/2.32 (r(s(s(s(elem!1))), elem!1)),
% 2.12/2.32 inference(unit_resolution,[status(thm)],[966, 4834, 154])).
% 2.12/2.32 tff(4836,plain,
% 2.12/2.32 (r(s(s(s(z))), elem!1)),
% 2.12/2.32 inference(modus_ponens,[status(thm)],[4835, 4830])).
% 2.12/2.32 tff(4837,plain,
% 2.12/2.32 (r(z, s(s(s(z)))) <=> r(elem!1, s(s(s(z))))),
% 2.12/2.32 inference(monotonicity,[status(thm)],[4834])).
% 2.12/2.32 tff(4838,plain,
% 2.12/2.32 (b(elem!1, s(s(s(elem!1)))) <=> b(z, s(s(s(elem!1))))),
% 2.12/2.32 inference(symmetry,[status(thm)],[638])).
% 2.12/2.32 tff(4839,plain,
% 2.12/2.32 (b(elem!1, s(s(s(z)))) <=> b(elem!1, s(s(s(elem!1))))),
% 2.12/2.32 inference(monotonicity,[status(thm)],[1086])).
% 2.12/2.32 tff(4840,plain,
% 2.12/2.32 (b(z, s(s(s(z)))) <=> b(elem!1, s(s(s(z))))),
% 2.12/2.32 inference(monotonicity,[status(thm)],[620])).
% 2.12/2.32 tff(4841,plain,
% 2.12/2.32 (b(z, s(s(s(z)))) <=> b(z, s(s(s(elem!1))))),
% 2.12/2.32 inference(transitivity,[status(thm)],[4840, 4839, 4838])).
% 2.12/2.32 tff(4842,plain,
% 2.12/2.32 (b(z, s(s(s(elem!1))))),
% 2.12/2.32 inference(modus_ponens,[status(thm)],[1700, 4841])).
% 2.12/2.32 tff(4843,plain,
% 2.12/2.32 ($false),
% 2.12/2.32 inference(unit_resolution,[status(thm)],[256, 4842])).
% 2.12/2.32 tff(4844,plain,((~b(z, s(s(s(z))))) | b(z, s(s(s(elem!1)))) | (~(s(s(z)) = s(s(elem!1))))), inference(lemma,lemma(discharge,[]))).
% 2.12/2.32 tff(4845,plain,
% 2.12/2.32 (~b(z, s(s(s(z))))),
% 2.12/2.32 inference(unit_resolution,[status(thm)],[4844, 4832, 4574])).
% 2.12/2.32 tff(4846,plain,
% 2.12/2.32 (r(z, s(s(s(z))))),
% 2.12/2.32 inference(unit_resolution,[status(thm)],[1697, 4845])).
% 2.12/2.32 tff(4847,plain,
% 2.12/2.32 (r(elem!1, s(s(s(z))))),
% 2.12/2.32 inference(modus_ponens,[status(thm)],[4846, 4837])).
% 2.12/2.32 tff(4848,plain,
% 2.12/2.32 (elem!1 = z),
% 2.12/2.32 inference(symmetry,[status(thm)],[4834])).
% 2.12/2.32 tff(4849,plain,
% 2.12/2.32 ((s(s(s(s(s(s(s(elem!1))))))) = elem!1) <=> (s(s(s(s(s(s(s(elem!1))))))) = z)),
% 2.12/2.32 inference(monotonicity,[status(thm)],[4848])).
% 2.12/2.32 tff(4850,plain,
% 2.12/2.32 ((s(s(s(s(s(s(s(elem!1))))))) = z) <=> (s(s(s(s(s(s(s(elem!1))))))) = elem!1)),
% 2.12/2.32 inference(symmetry,[status(thm)],[4849])).
% 2.12/2.32 tff(4851,plain,
% 2.12/2.32 ((~(s(s(s(s(s(s(s(elem!1))))))) = z)) <=> (~(s(s(s(s(s(s(s(elem!1))))))) = elem!1))),
% 2.12/2.32 inference(monotonicity,[status(thm)],[4850])).
% 2.12/2.32 tff(4852,plain,
% 2.12/2.32 ((~![X: $i] : (~(s(X) = z))) | (~(s(s(s(s(s(s(s(elem!1))))))) = z))),
% 2.12/2.32 inference(quant_inst,[status(thm)],[])).
% 2.12/2.32 tff(4853,plain,
% 2.12/2.32 (~(s(s(s(s(s(s(s(elem!1))))))) = z)),
% 2.12/2.32 inference(unit_resolution,[status(thm)],[4852, 65])).
% 2.12/2.32 tff(4854,plain,
% 2.12/2.32 (~(s(s(s(s(s(s(s(elem!1))))))) = elem!1)),
% 2.12/2.32 inference(modus_ponens,[status(thm)],[4853, 4851])).
% 2.12/2.32 tff(4855,plain,
% 2.12/2.32 (b(s(s(s(s(z)))), z) <=> b(s(s(s(s(z)))), elem!1)),
% 2.12/2.32 inference(monotonicity,[status(thm)],[4834])).
% 2.12/2.32 tff(4856,plain,
% 2.12/2.32 (s(s(s(s(elem!1)))) = s(s(s(s(z))))),
% 2.12/2.32 inference(monotonicity,[status(thm)],[4829])).
% 2.12/2.32 tff(4857,plain,
% 2.12/2.32 (s(s(s(s(z)))) = s(s(s(s(elem!1))))),
% 2.12/2.32 inference(symmetry,[status(thm)],[4856])).
% 2.12/2.32 tff(4858,plain,
% 2.12/2.32 (b(s(s(s(s(z)))), s(s(z))) <=> b(s(s(s(s(elem!1)))), s(s(z)))),
% 2.12/2.32 inference(monotonicity,[status(thm)],[4857])).
% 2.12/2.32 tff(4859,plain,
% 2.12/2.32 (b(s(s(s(s(elem!1)))), s(s(z))) <=> b(s(s(s(s(z)))), s(s(z)))),
% 2.12/2.32 inference(symmetry,[status(thm)],[4858])).
% 2.12/2.32 tff(4860,plain,
% 2.12/2.32 (b(z, s(z)) <=> b(elem!1, s(z))),
% 2.12/2.32 inference(monotonicity,[status(thm)],[4834])).
% 2.12/2.32 tff(4861,plain,
% 2.12/2.32 (b(elem!1, s(z))),
% 2.12/2.32 inference(modus_ponens,[status(thm)],[118, 4860])).
% 2.12/2.32 tff(4862,plain,
% 2.12/2.32 (~r(s(s(s(s(elem!1)))), s(s(elem!1)))),
% 2.12/2.32 inference(unit_resolution,[status(thm)],[4687, 4861, 1733, 155, 4832, 96, 4577, 120, 311])).
% 2.12/2.32 tff(4863,plain,
% 2.12/2.32 (r(s(s(s(s(elem!1)))), s(s(z))) <=> r(s(s(s(s(elem!1)))), s(s(elem!1)))),
% 2.12/2.32 inference(monotonicity,[status(thm)],[34])).
% 2.12/2.32 tff(4864,plain,
% 2.12/2.32 (r(s(s(s(s(elem!1)))), s(s(elem!1)))),
% 2.12/2.32 inference(modus_ponens,[status(thm)],[2168, 4863])).
% 2.12/2.32 tff(4865,plain,
% 2.12/2.32 ($false),
% 2.12/2.32 inference(unit_resolution,[status(thm)],[808, 4864])).
% 2.12/2.32 tff(4866,plain,((~r(s(s(s(s(elem!1)))), s(s(z)))) | r(s(s(s(s(elem!1)))), s(s(elem!1))) | (~(s(s(z)) = s(s(elem!1))))), inference(lemma,lemma(discharge,[]))).
% 2.12/2.32 tff(4867,plain,
% 2.12/2.32 (~r(s(s(s(s(elem!1)))), s(s(z)))),
% 2.12/2.32 inference(unit_resolution,[status(thm)],[4866, 4862, 4832])).
% 2.12/2.32 tff(4868,plain,
% 2.12/2.32 (b(s(s(s(s(elem!1)))), s(s(z)))),
% 2.12/2.32 inference(unit_resolution,[status(thm)],[1299, 4867])).
% 2.12/2.32 tff(4869,plain,
% 2.12/2.32 (b(s(s(s(s(z)))), s(s(z)))),
% 2.12/2.32 inference(modus_ponens,[status(thm)],[4868, 4859])).
% 2.12/2.32 tff(4870,plain,
% 2.12/2.32 (~r(s(s(z)), s(s(s(z))))),
% 2.12/2.32 inference(unit_resolution,[status(thm)],[1741, 4819, 155, 1733])).
% 2.12/2.32 tff(4871,plain,
% 2.12/2.32 (b(s(s(z)), s(s(s(z))))),
% 2.12/2.32 inference(unit_resolution,[status(thm)],[1730, 4870])).
% 2.12/2.32 tff(4872,plain,
% 2.12/2.32 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), s(s(z)))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(s(s(z)))), s(s(s(z))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(s(s(z)))), s(s(s(z))))))),
% 2.12/2.32 inference(rewrite,[status(thm)],[])).
% 2.12/2.32 tff(4873,plain,
% 2.12/2.32 (((~b(s(s(s(z))), s(s(z)))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(s(s(z)))), s(s(s(z)))))) <=> ((~b(s(s(s(z))), s(s(z)))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(s(s(z)))), s(s(s(z))))))),
% 2.12/2.32 inference(rewrite,[status(thm)],[])).
% 2.12/2.32 tff(4874,plain,
% 2.12/2.32 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), s(s(z)))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(s(s(z)))), s(s(s(z))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), s(s(z)))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(s(s(z)))), s(s(s(z)))))))),
% 2.12/2.32 inference(monotonicity,[status(thm)],[4873])).
% 2.12/2.32 tff(4875,plain,
% 2.12/2.32 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), s(s(z)))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(s(s(z)))), s(s(s(z))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(s(s(z)))), s(s(s(z))))))),
% 2.12/2.32 inference(transitivity,[status(thm)],[4874, 4872])).
% 2.12/2.32 tff(4876,plain,
% 2.12/2.32 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), s(s(z)))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(s(s(z)))), s(s(s(z))))))),
% 2.12/2.32 inference(quant_inst,[status(thm)],[])).
% 2.12/2.32 tff(4877,plain,
% 2.12/2.32 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(s(s(z)))), s(s(s(z)))))),
% 2.12/2.32 inference(modus_ponens,[status(thm)],[4876, 4875])).
% 2.12/2.32 tff(4878,plain,
% 2.12/2.32 (~b(s(s(s(s(z)))), s(s(s(z))))),
% 2.12/2.32 inference(unit_resolution,[status(thm)],[4877, 166, 4871, 4821, 4869])).
% 2.12/2.32 tff(4879,plain,
% 2.12/2.32 (r(s(s(s(s(z)))), s(s(s(z))))),
% 2.12/2.32 inference(unit_resolution,[status(thm)],[4662, 4878])).
% 2.12/2.32 tff(4880,plain,
% 2.12/2.32 (~r(s(s(s(s(z)))), z)),
% 2.12/2.32 inference(unit_resolution,[status(thm)],[4685, 4879, 155, 1733])).
% 2.12/2.32 tff(4881,plain,
% 2.12/2.32 (b(s(s(s(s(z)))), z)),
% 2.12/2.32 inference(unit_resolution,[status(thm)],[3266, 4880])).
% 2.12/2.32 tff(4882,plain,
% 2.12/2.32 (b(s(s(s(s(z)))), elem!1)),
% 2.12/2.32 inference(modus_ponens,[status(thm)],[4881, 4855])).
% 2.12/2.32 tff(4883,plain,
% 2.12/2.32 (b(s(z), z) <=> b(s(z), elem!1)),
% 2.12/2.32 inference(monotonicity,[status(thm)],[4834])).
% 2.12/2.32 tff(4884,plain,
% 2.12/2.32 (b(s(z), elem!1)),
% 2.12/2.32 inference(modus_ponens,[status(thm)],[53, 4883])).
% 2.12/2.32 tff(4885,assumption,(s(s(s(s(s(s(s(elem!1))))))) = s(z)), introduced(assumption)).
% 2.12/2.32 tff(4886,plain,
% 2.12/2.32 (inj_0(s(s(s(s(s(s(s(elem!1)))))))) = inj_0(s(z))),
% 2.12/2.32 inference(monotonicity,[status(thm)],[4885])).
% 2.12/2.32 tff(4887,plain,
% 2.12/2.32 ((~![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)))))))),
% 2.12/2.32 inference(quant_inst,[status(thm)],[])).
% 2.12/2.32 tff(4888,plain,
% 2.12/2.32 (inj_0(s(s(s(s(s(s(s(elem!1)))))))) = s(s(s(s(s(s(elem!1))))))),
% 2.12/2.32 inference(unit_resolution,[status(thm)],[4887, 8])).
% 2.12/2.32 tff(4889,plain,
% 2.12/2.32 (s(s(s(s(s(s(elem!1)))))) = inj_0(s(s(s(s(s(s(s(elem!1))))))))),
% 2.12/2.32 inference(symmetry,[status(thm)],[4888])).
% 2.12/2.32 tff(4890,plain,
% 2.12/2.32 (s(s(s(s(s(s(elem!1)))))) = elem!1),
% 2.12/2.32 inference(transitivity,[status(thm)],[4889, 4886, 25, 12])).
% 2.12/2.32 tff(4891,plain,
% 2.12/2.32 (elem!1 = z),
% 2.12/2.32 inference(symmetry,[status(thm)],[12])).
% 2.12/2.32 tff(4892,assumption,(s(s(s(s(s(s(elem!1)))))) = elem!1), introduced(assumption)).
% 2.12/2.32 tff(4893,plain,
% 2.12/2.32 (s(s(s(s(s(s(elem!1)))))) = z),
% 2.12/2.32 inference(transitivity,[status(thm)],[4892, 4891])).
% 2.12/2.32 tff(4894,plain,
% 2.12/2.32 ((~![X: $i] : (~(s(X) = z))) | (~(s(s(s(s(s(s(elem!1)))))) = z))),
% 2.12/2.32 inference(quant_inst,[status(thm)],[])).
% 2.12/2.32 tff(4895,plain,
% 2.12/2.32 (~(s(s(s(s(s(s(elem!1)))))) = z)),
% 2.12/2.32 inference(unit_resolution,[status(thm)],[4894, 65])).
% 2.12/2.32 tff(4896,plain,
% 2.12/2.32 ($false),
% 2.12/2.32 inference(unit_resolution,[status(thm)],[4895, 4893])).
% 2.12/2.32 tff(4897,plain,((~(s(s(s(s(s(s(elem!1)))))) = elem!1)) | (~(z = elem!1))), inference(lemma,lemma(discharge,[]))).
% 2.12/2.32 tff(4898,plain,
% 2.12/2.32 (~(s(s(s(s(s(s(elem!1)))))) = elem!1)),
% 2.12/2.32 inference(unit_resolution,[status(thm)],[4897, 12])).
% 2.12/2.32 tff(4899,plain,
% 2.12/2.32 ($false),
% 2.12/2.32 inference(unit_resolution,[status(thm)],[4898, 4890])).
% 2.12/2.32 tff(4900,plain,((~(s(s(s(s(s(s(s(elem!1))))))) = s(z))) | (~(z = elem!1))), inference(lemma,lemma(discharge,[]))).
% 2.12/2.32 tff(4901,plain,
% 2.12/2.32 (~(s(s(s(s(s(s(s(elem!1))))))) = s(z))),
% 2.12/2.32 inference(unit_resolution,[status(thm)],[4900, 4834])).
% 2.12/2.32 tff(4902,plain,
% 2.12/2.32 (s(s(s(z))) = s(s(s(elem!1)))),
% 2.12/2.32 inference(symmetry,[status(thm)],[135])).
% 2.12/2.32 tff(4903,assumption,(s(s(s(s(s(s(s(elem!1))))))) = s(s(s(s(z))))), introduced(assumption)).
% 2.12/2.32 tff(4904,plain,
% 2.12/2.32 (inj_0(s(s(s(s(s(s(s(elem!1)))))))) = inj_0(s(s(s(s(z)))))),
% 2.12/2.32 inference(monotonicity,[status(thm)],[4903])).
% 2.12/2.32 tff(4905,plain,
% 2.12/2.32 (s(s(s(s(s(s(elem!1)))))) = s(s(s(elem!1)))),
% 2.12/2.32 inference(transitivity,[status(thm)],[4889, 4904, 2223, 4902])).
% 2.12/2.32 tff(4906,plain,
% 2.12/2.32 (s(s(elem!1)) = s(s(z))),
% 2.12/2.32 inference(unit_resolution,[status(thm)],[139, 135])).
% 2.12/2.32 tff(4907,plain,
% 2.12/2.32 (s(s(z)) = s(s(elem!1))),
% 2.12/2.32 inference(unit_resolution,[status(thm)],[131, 4906])).
% 2.12/2.32 tff(4908,plain,
% 2.12/2.32 (s(elem!1) = s(z)),
% 2.12/2.32 inference(unit_resolution,[status(thm)],[43, 4907])).
% 2.12/2.32 tff(4909,plain,
% 2.12/2.32 ((~![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))))))),
% 2.12/2.32 inference(quant_inst,[status(thm)],[])).
% 2.12/2.32 tff(4910,plain,
% 2.12/2.32 (inj_0(s(s(s(s(s(s(elem!1))))))) = s(s(s(s(s(elem!1)))))),
% 2.12/2.32 inference(unit_resolution,[status(thm)],[4909, 8])).
% 2.12/2.32 tff(4911,assumption,(s(s(s(s(s(s(elem!1)))))) = s(s(s(elem!1)))), introduced(assumption)).
% 2.12/2.32 tff(4912,plain,
% 2.12/2.32 (inj_0(s(s(s(s(s(s(elem!1))))))) = inj_0(s(s(s(elem!1))))),
% 2.12/2.32 inference(monotonicity,[status(thm)],[4911])).
% 2.12/2.32 tff(4913,plain,
% 2.12/2.32 (inj_0(s(s(s(elem!1)))) = inj_0(s(s(s(s(s(s(elem!1)))))))),
% 2.12/2.32 inference(symmetry,[status(thm)],[4912])).
% 2.12/2.32 tff(4914,plain,
% 2.12/2.32 (s(s(elem!1)) = s(s(s(s(s(elem!1)))))),
% 2.12/2.32 inference(transitivity,[status(thm)],[105, 4913, 4910])).
% 2.12/2.32 tff(4915,plain,
% 2.12/2.32 (inj_0(s(s(elem!1))) = inj_0(s(s(s(s(s(elem!1))))))),
% 2.12/2.32 inference(monotonicity,[status(thm)],[4914])).
% 2.12/2.32 tff(4916,plain,
% 2.12/2.32 (inj_0(s(s(s(s(s(elem!1)))))) = inj_0(s(s(elem!1)))),
% 2.12/2.32 inference(symmetry,[status(thm)],[4915])).
% 2.12/2.32 tff(4917,plain,
% 2.12/2.32 ((~![Xk!0: $i] : (inj_0(s(Xk!0)) = Xk!0)) | (inj_0(s(s(s(s(s(elem!1)))))) = s(s(s(s(elem!1)))))),
% 2.12/2.33 inference(quant_inst,[status(thm)],[])).
% 2.12/2.33 tff(4918,plain,
% 2.12/2.33 (inj_0(s(s(s(s(s(elem!1)))))) = s(s(s(s(elem!1))))),
% 2.12/2.33 inference(unit_resolution,[status(thm)],[4917, 8])).
% 2.12/2.33 tff(4919,plain,
% 2.12/2.33 (s(s(s(s(elem!1)))) = inj_0(s(s(s(s(s(elem!1))))))),
% 2.12/2.33 inference(symmetry,[status(thm)],[4918])).
% 2.12/2.33 tff(4920,plain,
% 2.12/2.33 (s(s(s(s(elem!1)))) = s(z)),
% 2.12/2.33 inference(transitivity,[status(thm)],[4919, 4916, 38, 21])).
% 2.12/2.33 tff(4921,plain,
% 2.12/2.33 ($false),
% 2.12/2.33 inference(unit_resolution,[status(thm)],[656, 4920])).
% 2.12/2.33 tff(4922,plain,((~(s(s(s(s(s(s(elem!1)))))) = s(s(s(elem!1))))) | (~(s(elem!1) = s(z)))), inference(lemma,lemma(discharge,[]))).
% 2.12/2.33 tff(4923,plain,
% 2.12/2.33 (~(s(s(s(s(s(s(elem!1)))))) = s(s(s(elem!1))))),
% 2.12/2.33 inference(unit_resolution,[status(thm)],[4922, 4908])).
% 2.12/2.33 tff(4924,plain,
% 2.12/2.33 ($false),
% 2.12/2.33 inference(unit_resolution,[status(thm)],[4923, 4905])).
% 2.12/2.33 tff(4925,plain,((~(s(s(s(s(s(s(s(elem!1))))))) = s(s(s(s(z)))))) | (~(s(s(s(elem!1))) = s(s(s(z)))))), inference(lemma,lemma(discharge,[]))).
% 2.12/2.33 tff(4926,plain,
% 2.12/2.33 (~(s(s(s(s(s(s(s(elem!1))))))) = s(s(s(s(z)))))),
% 2.12/2.33 inference(unit_resolution,[status(thm)],[4925, 4829])).
% 2.12/2.33 tff(4927,assumption,(b(s(s(s(s(s(s(s(elem!1))))))), elem!1)), introduced(assumption)).
% 2.12/2.33 tff(4928,assumption,(b(s(s(s(s(z)))), elem!1)), introduced(assumption)).
% 2.12/2.33 tff(4929,plain,
% 2.12/2.33 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(z))) | (~b(s(z), elem!1)) | (~b(s(s(s(s(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))))))), s(s(s(s(z)))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(z))) | (~b(s(z), elem!1)) | (~b(s(s(s(s(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))))))), s(s(s(s(z)))))))),
% 2.12/2.33 inference(rewrite,[status(thm)],[])).
% 2.12/2.33 tff(4930,plain,
% 2.12/2.33 (((~b(s(z), elem!1)) | (~b(s(s(s(s(s(s(s(elem!1))))))), elem!1)) | (~b(elem!1, s(z))) | (~b(s(s(s(s(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))))))), s(s(s(s(z))))))) <=> ((~b(elem!1, s(z))) | (~b(s(z), elem!1)) | (~b(s(s(s(s(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))))))), s(s(s(s(z)))))))),
% 2.12/2.33 inference(rewrite,[status(thm)],[])).
% 2.12/2.33 tff(4931,plain,
% 2.12/2.33 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), elem!1)) | (~b(s(s(s(s(s(s(s(elem!1))))))), elem!1)) | (~b(elem!1, s(z))) | (~b(s(s(s(s(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))))))), s(s(s(s(z)))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(z))) | (~b(s(z), elem!1)) | (~b(s(s(s(s(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))))))), s(s(s(s(z))))))))),
% 2.12/2.33 inference(monotonicity,[status(thm)],[4930])).
% 2.12/2.33 tff(4932,plain,
% 2.12/2.33 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), elem!1)) | (~b(s(s(s(s(s(s(s(elem!1))))))), elem!1)) | (~b(elem!1, s(z))) | (~b(s(s(s(s(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))))))), s(s(s(s(z)))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(z))) | (~b(s(z), elem!1)) | (~b(s(s(s(s(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))))))), s(s(s(s(z)))))))),
% 2.12/2.33 inference(transitivity,[status(thm)],[4931, 4929])).
% 2.12/2.33 tff(4933,plain,
% 2.12/2.33 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), elem!1)) | (~b(s(s(s(s(s(s(s(elem!1))))))), elem!1)) | (~b(elem!1, s(z))) | (~b(s(s(s(s(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))))))), s(s(s(s(z)))))))),
% 2.12/2.33 inference(quant_inst,[status(thm)],[])).
% 2.12/2.33 tff(4934,plain,
% 2.12/2.33 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(z))) | (~b(s(z), elem!1)) | (~b(s(s(s(s(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))))))), s(s(s(s(z))))))),
% 2.12/2.33 inference(modus_ponens,[status(thm)],[4933, 4932])).
% 2.12/2.33 tff(4935,plain,
% 2.12/2.33 (~b(s(s(s(s(s(s(s(elem!1))))))), s(s(s(s(z)))))),
% 2.12/2.33 inference(unit_resolution,[status(thm)],[4934, 166, 1212, 642, 4928, 4927])).
% 2.12/2.33 tff(4936,assumption,(~(s(s(s(s(s(s(s(elem!1))))))) = s(s(s(s(z)))))), introduced(assumption)).
% 2.12/2.33 tff(4937,plain,
% 2.12/2.33 (((~![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(z))))) | b(s(s(s(s(s(s(s(elem!1))))))), s(s(s(s(z))))) | r(s(s(s(s(s(s(s(elem!1))))))), s(s(s(s(z))))))) <=> ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (s(s(s(s(s(s(s(elem!1))))))) = s(s(s(s(z))))) | b(s(s(s(s(s(s(s(elem!1))))))), s(s(s(s(z))))) | r(s(s(s(s(s(s(s(elem!1))))))), s(s(s(s(z))))))),
% 2.12/2.33 inference(rewrite,[status(thm)],[])).
% 2.12/2.33 tff(4938,plain,
% 2.12/2.33 ((~![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(z))))) | b(s(s(s(s(s(s(s(elem!1))))))), s(s(s(s(z))))) | r(s(s(s(s(s(s(s(elem!1))))))), s(s(s(s(z))))))),
% 2.12/2.33 inference(quant_inst,[status(thm)],[])).
% 2.12/2.33 tff(4939,plain,
% 2.12/2.33 ((~![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(z))))) | b(s(s(s(s(s(s(s(elem!1))))))), s(s(s(s(z))))) | r(s(s(s(s(s(s(s(elem!1))))))), s(s(s(s(z)))))),
% 2.12/2.33 inference(modus_ponens,[status(thm)],[4938, 4937])).
% 2.12/2.33 tff(4940,plain,
% 2.12/2.33 (r(s(s(s(s(s(s(s(elem!1))))))), s(s(s(s(z)))))),
% 2.12/2.33 inference(unit_resolution,[status(thm)],[4939, 79, 4936, 4935])).
% 2.12/2.33 tff(4941,plain,
% 2.12/2.33 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(z))) | (~b(s(z), elem!1)) | (~b(s(s(s(s(s(s(s(elem!1))))))), elem!1)) | (~b(s(s(s(s(s(s(s(elem!1))))))), s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(z))) | (~b(s(z), elem!1)) | (~b(s(s(s(s(s(s(s(elem!1))))))), elem!1)) | (~b(s(s(s(s(s(s(s(elem!1))))))), s(z))))),
% 2.12/2.33 inference(rewrite,[status(thm)],[])).
% 2.12/2.33 tff(4942,plain,
% 2.12/2.33 (((~b(s(z), elem!1)) | (~b(s(s(s(s(s(s(s(elem!1))))))), elem!1)) | (~b(elem!1, s(z))) | (~b(s(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))))))), s(z)))) <=> ((~b(elem!1, s(z))) | (~b(s(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))))))), s(z))))),
% 2.12/2.33 inference(rewrite,[status(thm)],[])).
% 2.12/2.33 tff(4943,plain,
% 2.12/2.33 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), elem!1)) | (~b(s(s(s(s(s(s(s(elem!1))))))), elem!1)) | (~b(elem!1, s(z))) | (~b(s(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))))))), s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(z))) | (~b(s(z), elem!1)) | (~b(s(s(s(s(s(s(s(elem!1))))))), elem!1)) | (~b(s(s(s(s(s(s(s(elem!1))))))), s(z)))))),
% 2.12/2.33 inference(monotonicity,[status(thm)],[4942])).
% 2.12/2.33 tff(4944,plain,
% 2.12/2.33 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), elem!1)) | (~b(s(s(s(s(s(s(s(elem!1))))))), elem!1)) | (~b(elem!1, s(z))) | (~b(s(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))))))), s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(z))) | (~b(s(z), elem!1)) | (~b(s(s(s(s(s(s(s(elem!1))))))), elem!1)) | (~b(s(s(s(s(s(s(s(elem!1))))))), s(z))))),
% 2.12/2.33 inference(transitivity,[status(thm)],[4943, 4941])).
% 2.12/2.33 tff(4945,plain,
% 2.12/2.33 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), elem!1)) | (~b(s(s(s(s(s(s(s(elem!1))))))), elem!1)) | (~b(elem!1, s(z))) | (~b(s(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))))))), s(z))))),
% 2.12/2.33 inference(quant_inst,[status(thm)],[])).
% 2.12/2.33 tff(4946,plain,
% 2.12/2.33 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(z))) | (~b(s(z), elem!1)) | (~b(s(s(s(s(s(s(s(elem!1))))))), elem!1)) | (~b(s(s(s(s(s(s(s(elem!1))))))), s(z)))),
% 2.12/2.33 inference(modus_ponens,[status(thm)],[4945, 4944])).
% 2.12/2.33 tff(4947,plain,
% 2.12/2.33 (~b(s(s(s(s(s(s(s(elem!1))))))), s(z))),
% 2.12/2.33 inference(unit_resolution,[status(thm)],[4946, 166, 1212, 642, 4927])).
% 2.12/2.33 tff(4948,assumption,(~(s(s(s(s(s(s(s(elem!1))))))) = s(z))), introduced(assumption)).
% 2.12/2.33 tff(4949,plain,
% 2.12/2.33 (((~![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)))),
% 2.12/2.33 inference(rewrite,[status(thm)],[])).
% 2.12/2.33 tff(4950,plain,
% 2.12/2.33 ((~![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)))),
% 2.12/2.33 inference(quant_inst,[status(thm)],[])).
% 2.12/2.33 tff(4951,plain,
% 2.12/2.33 ((~![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))),
% 2.12/2.33 inference(modus_ponens,[status(thm)],[4950, 4949])).
% 2.12/2.33 tff(4952,plain,
% 2.12/2.33 (r(s(s(s(s(s(s(s(elem!1))))))), s(z))),
% 2.12/2.33 inference(unit_resolution,[status(thm)],[4951, 79, 4948, 4947])).
% 2.12/2.33 tff(4953,plain,
% 2.12/2.33 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(z))) | (~b(s(z), elem!1)) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), elem!1)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(z))) | (~b(s(z), elem!1)) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), elem!1)))),
% 2.12/2.33 inference(rewrite,[status(thm)],[])).
% 2.12/2.33 tff(4954,plain,
% 2.12/2.33 (((~b(s(z), elem!1)) | (~b(s(z), elem!1)) | (~b(elem!1, s(z))) | (~b(s(s(s(s(z)))), elem!1)) | (~b(s(z), elem!1)) | (~b(s(z), s(s(s(s(z))))))) <=> ((~b(elem!1, s(z))) | (~b(s(z), elem!1)) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), elem!1)))),
% 2.12/2.33 inference(rewrite,[status(thm)],[])).
% 2.12/2.33 tff(4955,plain,
% 2.12/2.33 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), elem!1)) | (~b(s(z), elem!1)) | (~b(elem!1, s(z))) | (~b(s(s(s(s(z)))), elem!1)) | (~b(s(z), elem!1)) | (~b(s(z), s(s(s(s(z)))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(z))) | (~b(s(z), elem!1)) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), elem!1))))),
% 2.12/2.33 inference(monotonicity,[status(thm)],[4954])).
% 2.12/2.33 tff(4956,plain,
% 2.12/2.33 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), elem!1)) | (~b(s(z), elem!1)) | (~b(elem!1, s(z))) | (~b(s(s(s(s(z)))), elem!1)) | (~b(s(z), elem!1)) | (~b(s(z), s(s(s(s(z)))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(z))) | (~b(s(z), elem!1)) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), elem!1)))),
% 2.12/2.33 inference(transitivity,[status(thm)],[4955, 4953])).
% 2.12/2.33 tff(4957,plain,
% 2.12/2.33 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), elem!1)) | (~b(s(z), elem!1)) | (~b(elem!1, s(z))) | (~b(s(s(s(s(z)))), elem!1)) | (~b(s(z), elem!1)) | (~b(s(z), s(s(s(s(z)))))))),
% 2.12/2.33 inference(quant_inst,[status(thm)],[])).
% 2.12/2.33 tff(4958,plain,
% 2.12/2.33 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(z))) | (~b(s(z), elem!1)) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), elem!1))),
% 2.12/2.33 inference(modus_ponens,[status(thm)],[4957, 4956])).
% 2.12/2.33 tff(4959,plain,
% 2.12/2.33 (~b(s(z), s(s(s(s(z)))))),
% 2.12/2.33 inference(unit_resolution,[status(thm)],[4958, 166, 1212, 642, 4928])).
% 2.12/2.33 tff(4960,plain,
% 2.12/2.33 (r(s(z), s(s(s(s(z)))))),
% 2.12/2.33 inference(unit_resolution,[status(thm)],[3302, 4959])).
% 2.12/2.33 tff(4961,plain,
% 2.12/2.33 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(z)))), s(s(s(z))))) | (~r(s(z), s(s(s(s(z)))))) | (~r(s(s(s(s(s(s(s(elem!1))))))), s(s(s(s(z)))))) | (~r(s(s(s(s(s(s(s(elem!1))))))), s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(s(z)))), s(s(s(z))))) | (~r(s(z), s(s(s(s(z)))))) | (~r(s(s(s(s(s(s(s(elem!1))))))), s(s(s(s(z)))))) | (~r(s(s(s(s(s(s(s(elem!1))))))), s(z))))),
% 2.12/2.33 inference(rewrite,[status(thm)],[])).
% 2.12/2.33 tff(4962,plain,
% 2.12/2.33 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(z)))), s(s(s(z))))) | (~r(s(z), s(s(s(s(z)))))) | (~r(s(s(s(s(s(s(s(elem!1))))))), s(s(s(s(z)))))) | (~r(s(s(s(s(s(s(s(elem!1))))))), s(z))))),
% 2.12/2.33 inference(quant_inst,[status(thm)],[])).
% 2.12/2.33 tff(4963,plain,
% 2.12/2.33 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(s(z)))), s(s(s(z))))) | (~r(s(z), s(s(s(s(z)))))) | (~r(s(s(s(s(s(s(s(elem!1))))))), s(s(s(s(z)))))) | (~r(s(s(s(s(s(s(s(elem!1))))))), s(z)))),
% 2.12/2.33 inference(modus_ponens,[status(thm)],[4962, 4961])).
% 2.12/2.33 tff(4964,plain,
% 2.12/2.33 ($false),
% 2.12/2.33 inference(unit_resolution,[status(thm)],[4963, 197, 4680, 4960, 4952, 4940])).
% 2.12/2.33 tff(4965,plain,((~b(s(s(s(s(s(s(s(elem!1))))))), elem!1)) | (~r(s(s(s(s(z)))), s(s(s(z))))) | (s(s(s(s(s(s(s(elem!1))))))) = s(s(s(s(z))))) | (s(s(s(s(s(s(s(elem!1))))))) = s(z)) | (~b(elem!1, s(z))) | (~b(s(z), elem!1)) | (~b(s(s(s(s(z)))), elem!1))), inference(lemma,lemma(discharge,[]))).
% 2.12/2.33 tff(4966,plain,
% 2.12/2.33 (~b(s(s(s(s(s(s(s(elem!1))))))), elem!1)),
% 2.12/2.33 inference(unit_resolution,[status(thm)],[4965, 4879, 4926, 4901, 4861, 4884, 4882])).
% 2.12/2.33 tff(4967,plain,
% 2.12/2.33 (((~![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))),
% 2.12/2.33 inference(rewrite,[status(thm)],[])).
% 2.12/2.33 tff(4968,plain,
% 2.12/2.33 ((~![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))),
% 2.12/2.33 inference(quant_inst,[status(thm)],[])).
% 2.12/2.33 tff(4969,plain,
% 2.12/2.33 ((~![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)),
% 2.12/2.33 inference(modus_ponens,[status(thm)],[4968, 4967])).
% 2.12/2.33 tff(4970,plain,
% 2.12/2.33 ((s(s(s(s(s(s(s(elem!1))))))) = elem!1) | r(s(s(s(s(s(s(s(elem!1))))))), elem!1)),
% 2.12/2.33 inference(unit_resolution,[status(thm)],[4969, 79, 4966])).
% 2.12/2.33 tff(4971,plain,
% 2.12/2.33 (r(s(s(s(s(s(s(s(elem!1))))))), elem!1)),
% 2.12/2.33 inference(unit_resolution,[status(thm)],[4970, 4854])).
% 2.12/2.33 tff(4972,plain,
% 2.12/2.33 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(s(s(s(elem!1))))))), elem!1)) | (~r(elem!1, s(s(s(z))))) | (~r(s(s(s(z))), elem!1)) | (~r(s(s(s(z))), s(s(s(s(s(s(s(elem!1))))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(s(s(s(s(elem!1))))))), elem!1)) | (~r(elem!1, s(s(s(z))))) | (~r(s(s(s(z))), elem!1)) | (~r(s(s(s(z))), s(s(s(s(s(s(s(elem!1))))))))))),
% 2.12/2.33 inference(rewrite,[status(thm)],[])).
% 2.12/2.33 tff(4973,plain,
% 2.12/2.33 (((~r(elem!1, s(s(s(z))))) | (~r(s(s(s(s(s(s(s(elem!1))))))), elem!1)) | (~r(s(s(s(z))), elem!1)) | (~r(s(s(s(z))), s(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(z))))) | (~r(s(s(s(z))), elem!1)) | (~r(s(s(s(z))), s(s(s(s(s(s(s(elem!1))))))))))),
% 2.12/2.33 inference(rewrite,[status(thm)],[])).
% 2.12/2.33 tff(4974,plain,
% 2.12/2.33 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(s(s(z))))) | (~r(s(s(s(s(s(s(s(elem!1))))))), elem!1)) | (~r(s(s(s(z))), elem!1)) | (~r(s(s(s(z))), s(s(s(s(s(s(s(elem!1))))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(s(s(s(elem!1))))))), elem!1)) | (~r(elem!1, s(s(s(z))))) | (~r(s(s(s(z))), elem!1)) | (~r(s(s(s(z))), s(s(s(s(s(s(s(elem!1)))))))))))),
% 2.12/2.33 inference(monotonicity,[status(thm)],[4973])).
% 2.12/2.33 tff(4975,plain,
% 2.12/2.33 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(s(s(z))))) | (~r(s(s(s(s(s(s(s(elem!1))))))), elem!1)) | (~r(s(s(s(z))), elem!1)) | (~r(s(s(s(z))), s(s(s(s(s(s(s(elem!1))))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(s(s(s(s(elem!1))))))), elem!1)) | (~r(elem!1, s(s(s(z))))) | (~r(s(s(s(z))), elem!1)) | (~r(s(s(s(z))), s(s(s(s(s(s(s(elem!1))))))))))),
% 2.12/2.33 inference(transitivity,[status(thm)],[4974, 4972])).
% 2.12/2.33 tff(4976,plain,
% 2.12/2.33 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(s(s(z))))) | (~r(s(s(s(s(s(s(s(elem!1))))))), elem!1)) | (~r(s(s(s(z))), elem!1)) | (~r(s(s(s(z))), s(s(s(s(s(s(s(elem!1))))))))))),
% 2.12/2.33 inference(quant_inst,[status(thm)],[])).
% 2.12/2.33 tff(4977,plain,
% 2.12/2.33 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(s(s(s(s(elem!1))))))), elem!1)) | (~r(elem!1, s(s(s(z))))) | (~r(s(s(s(z))), elem!1)) | (~r(s(s(s(z))), s(s(s(s(s(s(s(elem!1)))))))))),
% 2.12/2.33 inference(modus_ponens,[status(thm)],[4976, 4975])).
% 2.12/2.33 tff(4978,plain,
% 2.12/2.33 (~r(s(s(s(z))), s(s(s(s(s(s(s(elem!1))))))))),
% 2.12/2.33 inference(unit_resolution,[status(thm)],[4977, 197, 4971, 4847, 4836])).
% 2.12/2.33 tff(4979,assumption,(s(s(s(s(s(s(elem!1)))))) = s(s(elem!1))), introduced(assumption)).
% 2.12/2.33 tff(4980,plain,
% 2.12/2.33 (inj_0(s(s(s(s(s(s(elem!1))))))) = inj_0(s(s(elem!1)))),
% 2.12/2.33 inference(monotonicity,[status(thm)],[4979])).
% 2.12/2.33 tff(4981,plain,
% 2.12/2.33 (s(s(s(s(s(elem!1))))) = inj_0(s(s(s(s(s(s(elem!1)))))))),
% 2.12/2.33 inference(symmetry,[status(thm)],[4910])).
% 2.12/2.33 tff(4982,plain,
% 2.12/2.33 (s(s(s(s(s(elem!1))))) = s(z)),
% 2.12/2.33 inference(transitivity,[status(thm)],[4981, 4980, 38, 21])).
% 2.12/2.33 tff(4983,plain,
% 2.12/2.33 (inj_0(s(s(s(s(s(elem!1)))))) = inj_0(s(z))),
% 2.12/2.33 inference(monotonicity,[status(thm)],[4982])).
% 2.12/2.33 tff(4984,plain,
% 2.12/2.33 (s(s(s(s(elem!1)))) = z),
% 2.12/2.33 inference(transitivity,[status(thm)],[4919, 4983, 25])).
% 2.12/2.33 tff(4985,plain,
% 2.12/2.33 ($false),
% 2.12/2.33 inference(unit_resolution,[status(thm)],[626, 4984])).
% 2.12/2.33 tff(4986,plain,((~(s(s(s(s(s(s(elem!1)))))) = s(s(elem!1)))) | (~(s(elem!1) = s(z)))), inference(lemma,lemma(discharge,[]))).
% 2.12/2.33 tff(4987,plain,
% 2.12/2.33 (~(s(s(s(s(s(s(elem!1)))))) = s(s(elem!1)))),
% 2.12/2.33 inference(unit_resolution,[status(thm)],[4986, 4833])).
% 2.12/2.33 tff(4988,plain,
% 2.12/2.33 (s(s(z)) = s(s(elem!1))),
% 2.12/2.33 inference(symmetry,[status(thm)],[128])).
% 2.12/2.33 tff(4989,assumption,(s(s(s(z))) = s(s(s(s(s(s(s(elem!1)))))))), introduced(assumption)).
% 2.12/2.34 tff(4990,plain,
% 2.12/2.34 (s(s(s(s(s(s(s(elem!1))))))) = s(s(s(z)))),
% 2.12/2.34 inference(symmetry,[status(thm)],[4989])).
% 2.12/2.34 tff(4991,plain,
% 2.12/2.34 (inj_0(s(s(s(s(s(s(s(elem!1)))))))) = inj_0(s(s(s(z))))),
% 2.12/2.34 inference(monotonicity,[status(thm)],[4990])).
% 2.12/2.34 tff(4992,plain,
% 2.12/2.34 (s(s(s(s(s(s(elem!1)))))) = s(s(elem!1))),
% 2.12/2.34 inference(transitivity,[status(thm)],[4889, 4991, 134, 4988])).
% 2.12/2.34 tff(4993,assumption,(~(s(s(s(s(s(s(elem!1)))))) = s(s(elem!1)))), introduced(assumption)).
% 2.12/2.34 tff(4994,plain,
% 2.12/2.34 ($false),
% 2.12/2.34 inference(unit_resolution,[status(thm)],[4993, 4992])).
% 2.12/2.34 tff(4995,plain,((~(s(s(s(z))) = s(s(s(s(s(s(s(elem!1))))))))) | (s(s(s(s(s(s(elem!1)))))) = s(s(elem!1))) | (~(s(s(elem!1)) = s(s(z))))), inference(lemma,lemma(discharge,[]))).
% 2.12/2.34 tff(4996,plain,
% 2.12/2.34 (~(s(s(s(z))) = s(s(s(s(s(s(s(elem!1))))))))),
% 2.12/2.34 inference(unit_resolution,[status(thm)],[4995, 4987, 4831])).
% 2.12/2.34 tff(4997,plain,
% 2.12/2.34 (((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((s(s(s(z))) = s(s(s(s(s(s(s(elem!1)))))))) | b(s(s(s(z))), s(s(s(s(s(s(s(elem!1)))))))) | r(s(s(s(z))), s(s(s(s(s(s(s(elem!1)))))))))) <=> ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (s(s(s(z))) = s(s(s(s(s(s(s(elem!1)))))))) | b(s(s(s(z))), s(s(s(s(s(s(s(elem!1)))))))) | r(s(s(s(z))), s(s(s(s(s(s(s(elem!1)))))))))),
% 2.12/2.34 inference(rewrite,[status(thm)],[])).
% 2.12/2.34 tff(4998,plain,
% 2.12/2.34 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((s(s(s(z))) = s(s(s(s(s(s(s(elem!1)))))))) | b(s(s(s(z))), s(s(s(s(s(s(s(elem!1)))))))) | r(s(s(s(z))), s(s(s(s(s(s(s(elem!1)))))))))),
% 2.12/2.34 inference(quant_inst,[status(thm)],[])).
% 2.12/2.34 tff(4999,plain,
% 2.12/2.34 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (s(s(s(z))) = s(s(s(s(s(s(s(elem!1)))))))) | b(s(s(s(z))), s(s(s(s(s(s(s(elem!1)))))))) | r(s(s(s(z))), s(s(s(s(s(s(s(elem!1))))))))),
% 2.12/2.34 inference(modus_ponens,[status(thm)],[4998, 4997])).
% 2.12/2.34 tff(5000,plain,
% 2.12/2.34 (b(s(s(s(z))), s(s(s(s(s(s(s(elem!1))))))))),
% 2.12/2.34 inference(unit_resolution,[status(thm)],[4999, 79, 4996, 4978])).
% 2.12/2.34 tff(5001,plain,
% 2.12/2.34 ((s(s(s(s(s(s(s(elem!1))))))) = s(s(z))) <=> (s(s(z)) = s(s(s(s(s(s(s(elem!1))))))))),
% 2.12/2.34 inference(commutativity,[status(thm)],[])).
% 2.12/2.34 tff(5002,plain,
% 2.12/2.34 ((s(s(z)) = s(s(s(s(s(s(s(elem!1)))))))) <=> (s(s(s(s(s(s(s(elem!1))))))) = s(s(z)))),
% 2.12/2.34 inference(symmetry,[status(thm)],[5001])).
% 2.12/2.34 tff(5003,plain,
% 2.12/2.34 ((~(s(s(z)) = s(s(s(s(s(s(s(elem!1))))))))) <=> (~(s(s(s(s(s(s(s(elem!1))))))) = s(s(z))))),
% 2.12/2.34 inference(monotonicity,[status(thm)],[5002])).
% 2.12/2.34 tff(5004,assumption,(s(s(z)) = s(s(s(s(s(s(s(elem!1)))))))), introduced(assumption)).
% 2.12/2.34 tff(5005,plain,
% 2.12/2.34 (s(s(s(s(s(s(s(elem!1))))))) = s(s(z))),
% 2.12/2.34 inference(symmetry,[status(thm)],[5004])).
% 2.12/2.34 tff(5006,plain,
% 2.12/2.34 (inj_0(s(s(s(s(s(s(s(elem!1)))))))) = inj_0(s(s(z)))),
% 2.12/2.34 inference(monotonicity,[status(thm)],[5005])).
% 2.12/2.34 tff(5007,plain,
% 2.12/2.34 (s(s(s(s(s(s(elem!1)))))) = s(z)),
% 2.12/2.34 inference(transitivity,[status(thm)],[4889, 5006, 33])).
% 2.12/2.34 tff(5008,assumption,(s(s(s(s(s(s(elem!1)))))) = s(z)), introduced(assumption)).
% 2.12/2.34 tff(5009,plain,
% 2.12/2.34 (inj_0(s(s(s(s(s(s(elem!1))))))) = inj_0(s(z))),
% 2.12/2.34 inference(monotonicity,[status(thm)],[5008])).
% 2.12/2.34 tff(5010,plain,
% 2.12/2.34 (s(s(s(s(s(elem!1))))) = z),
% 2.12/2.34 inference(transitivity,[status(thm)],[4981, 5009, 25])).
% 2.12/2.34 tff(5011,plain,
% 2.12/2.34 ((~![X: $i] : (~(s(X) = z))) | (~(s(s(s(s(s(elem!1))))) = z))),
% 2.12/2.34 inference(quant_inst,[status(thm)],[])).
% 2.12/2.34 tff(5012,plain,
% 2.12/2.34 (~(s(s(s(s(s(elem!1))))) = z)),
% 2.12/2.34 inference(unit_resolution,[status(thm)],[5011, 65])).
% 2.12/2.34 tff(5013,plain,
% 2.12/2.34 ($false),
% 2.12/2.34 inference(unit_resolution,[status(thm)],[5012, 5010])).
% 2.12/2.34 tff(5014,plain,(~(s(s(s(s(s(s(elem!1)))))) = s(z))), inference(lemma,lemma(discharge,[]))).
% 2.12/2.34 tff(5015,plain,
% 2.12/2.34 ($false),
% 2.12/2.34 inference(unit_resolution,[status(thm)],[5014, 5007])).
% 2.12/2.34 tff(5016,plain,(~(s(s(z)) = s(s(s(s(s(s(s(elem!1))))))))), inference(lemma,lemma(discharge,[]))).
% 2.12/2.34 tff(5017,plain,
% 2.12/2.34 (~(s(s(s(s(s(s(s(elem!1))))))) = s(s(z)))),
% 2.12/2.34 inference(modus_ponens,[status(thm)],[5016, 5003])).
% 2.12/2.34 tff(5018,plain,
% 2.12/2.34 (r(s(s(z)), z) <=> r(s(s(z)), elem!1)),
% 2.12/2.34 inference(monotonicity,[status(thm)],[4834])).
% 2.12/2.34 tff(5019,plain,
% 2.12/2.34 (r(s(s(z)), elem!1)),
% 2.12/2.34 inference(modus_ponens,[status(thm)],[4819, 5018])).
% 2.12/2.34 tff(5020,plain,
% 2.12/2.34 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(z)), elem!1)) | (~r(s(s(s(s(s(s(s(elem!1))))))), elem!1)) | (~r(elem!1, s(s(s(z))))) | (~r(s(s(s(s(s(s(s(elem!1))))))), s(s(z)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(z)), elem!1)) | (~r(s(s(s(s(s(s(s(elem!1))))))), elem!1)) | (~r(elem!1, s(s(s(z))))) | (~r(s(s(s(s(s(s(s(elem!1))))))), s(s(z)))))),
% 2.12/2.34 inference(rewrite,[status(thm)],[])).
% 2.12/2.34 tff(5021,plain,
% 2.12/2.34 (((~r(elem!1, s(s(s(z))))) | (~r(s(s(z)), 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(z))))) <=> ((~r(s(s(z)), elem!1)) | (~r(s(s(s(s(s(s(s(elem!1))))))), elem!1)) | (~r(elem!1, s(s(s(z))))) | (~r(s(s(s(s(s(s(s(elem!1))))))), s(s(z)))))),
% 2.12/2.34 inference(rewrite,[status(thm)],[])).
% 2.12/2.34 tff(5022,plain,
% 2.12/2.34 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(s(s(z))))) | (~r(s(s(z)), 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(z)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(z)), elem!1)) | (~r(s(s(s(s(s(s(s(elem!1))))))), elem!1)) | (~r(elem!1, s(s(s(z))))) | (~r(s(s(s(s(s(s(s(elem!1))))))), s(s(z))))))),
% 2.12/2.34 inference(monotonicity,[status(thm)],[5021])).
% 2.12/2.34 tff(5023,plain,
% 2.12/2.34 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(s(s(z))))) | (~r(s(s(z)), 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(z)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(z)), elem!1)) | (~r(s(s(s(s(s(s(s(elem!1))))))), elem!1)) | (~r(elem!1, s(s(s(z))))) | (~r(s(s(s(s(s(s(s(elem!1))))))), s(s(z)))))),
% 2.12/2.34 inference(transitivity,[status(thm)],[5022, 5020])).
% 2.12/2.34 tff(5024,plain,
% 2.12/2.34 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(s(s(z))))) | (~r(s(s(z)), 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(z)))))),
% 2.12/2.34 inference(quant_inst,[status(thm)],[])).
% 2.12/2.34 tff(5025,plain,
% 2.12/2.34 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(z)), elem!1)) | (~r(s(s(s(s(s(s(s(elem!1))))))), elem!1)) | (~r(elem!1, s(s(s(z))))) | (~r(s(s(s(s(s(s(s(elem!1))))))), s(s(z))))),
% 2.12/2.34 inference(modus_ponens,[status(thm)],[5024, 5023])).
% 2.12/2.34 tff(5026,plain,
% 2.12/2.34 (~r(s(s(s(s(s(s(s(elem!1))))))), s(s(z)))),
% 2.12/2.34 inference(unit_resolution,[status(thm)],[5025, 197, 5019, 4971, 4847])).
% 2.12/2.34 tff(5027,plain,
% 2.12/2.34 (((~![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))))),
% 2.12/2.34 inference(rewrite,[status(thm)],[])).
% 2.12/2.34 tff(5028,plain,
% 2.12/2.34 ((~![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))))),
% 2.12/2.34 inference(quant_inst,[status(thm)],[])).
% 2.12/2.34 tff(5029,plain,
% 2.12/2.34 ((~![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)))),
% 2.12/2.34 inference(modus_ponens,[status(thm)],[5028, 5027])).
% 2.12/2.34 tff(5030,plain,
% 2.12/2.34 ((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)))),
% 2.12/2.34 inference(unit_resolution,[status(thm)],[5029, 79, 5026])).
% 2.12/2.34 tff(5031,plain,
% 2.12/2.34 (b(s(s(s(s(s(s(s(elem!1))))))), s(s(z)))),
% 2.12/2.34 inference(unit_resolution,[status(thm)],[5030, 5017])).
% 2.12/2.34 tff(5032,plain,
% 2.12/2.34 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), s(s(z)))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(s(s(s(s(s(elem!1))))))), s(s(z)))) | (~b(s(s(s(z))), s(s(s(s(s(s(s(elem!1))))))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(s(s(s(s(s(elem!1))))))), s(s(z)))) | (~b(s(s(s(z))), s(s(s(s(s(s(s(elem!1))))))))))),
% 2.12/2.34 inference(rewrite,[status(thm)],[])).
% 2.12/2.34 tff(5033,plain,
% 2.12/2.34 (((~b(s(s(s(z))), s(s(z)))) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(s(s(s(s(s(elem!1))))))), s(s(z)))) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(s(s(z))), s(s(s(s(s(s(s(elem!1)))))))))) <=> ((~b(s(s(s(z))), s(s(z)))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(s(s(s(s(s(elem!1))))))), s(s(z)))) | (~b(s(s(s(z))), s(s(s(s(s(s(s(elem!1))))))))))),
% 2.12/2.34 inference(rewrite,[status(thm)],[])).
% 2.12/2.34 tff(5034,plain,
% 2.12/2.34 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), s(s(z)))) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(s(s(s(s(s(elem!1))))))), s(s(z)))) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(s(s(z))), s(s(s(s(s(s(s(elem!1))))))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), s(s(z)))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(s(s(s(s(s(elem!1))))))), s(s(z)))) | (~b(s(s(s(z))), s(s(s(s(s(s(s(elem!1)))))))))))),
% 2.12/2.34 inference(monotonicity,[status(thm)],[5033])).
% 2.12/2.34 tff(5035,plain,
% 2.12/2.34 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), s(s(z)))) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(s(s(s(s(s(elem!1))))))), s(s(z)))) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(s(s(z))), s(s(s(s(s(s(s(elem!1))))))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(s(s(s(s(s(elem!1))))))), s(s(z)))) | (~b(s(s(s(z))), s(s(s(s(s(s(s(elem!1))))))))))),
% 2.12/2.34 inference(transitivity,[status(thm)],[5034, 5032])).
% 2.12/2.34 tff(5036,plain,
% 2.12/2.34 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), s(s(z)))) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(s(s(s(s(s(elem!1))))))), s(s(z)))) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(s(s(z))), s(s(s(s(s(s(s(elem!1))))))))))),
% 2.12/2.34 inference(quant_inst,[status(thm)],[])).
% 2.12/2.34 tff(5037,plain,
% 2.12/2.34 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(s(s(s(s(s(elem!1))))))), s(s(z)))) | (~b(s(s(s(z))), s(s(s(s(s(s(s(elem!1)))))))))),
% 2.12/2.34 inference(modus_ponens,[status(thm)],[5036, 5035])).
% 2.12/2.34 tff(5038,plain,
% 2.12/2.34 ($false),
% 2.12/2.34 inference(unit_resolution,[status(thm)],[5037, 166, 4871, 4821, 5031, 5000])).
% 2.12/2.34 tff(5039,plain,((~r(s(s(s(z))), z)) | (~r(z, s(s(z)))) | (~b(s(s(s(elem!1))), s(z))) | (~r(s(s(elem!1)), s(z))) | (~r(s(z), s(s(z)))) | (~r(s(z), s(s(elem!1)))) | (~b(z, s(z))) | (~b(s(z), z)) | (~r(s(s(s(elem!1))), z)) | (s(s(elem!1)) = s(s(s(elem!1))))), inference(lemma,lemma(discharge,[]))).
% 2.12/2.34 tff(5040,plain,
% 2.12/2.34 (~r(s(s(s(z))), z)),
% 2.12/2.34 inference(unit_resolution,[status(thm)],[5039, 120, 96, 4577, 155, 311, 118, 53, 153, 45])).
% 2.12/2.34 tff(5041,plain,
% 2.12/2.34 (b(s(s(s(z))), z)),
% 2.12/2.34 inference(unit_resolution,[status(thm)],[1713, 5040])).
% 2.12/2.34 tff(5042,plain,
% 2.12/2.34 (b(s(s(s(elem!1))), s(s(z)))),
% 2.12/2.34 inference(unit_resolution,[status(thm)],[218, 4576])).
% 2.12/2.34 tff(5043,plain,
% 2.12/2.34 (~b(s(z), s(s(s(z))))),
% 2.12/2.34 inference(unit_resolution,[status(thm)],[4037, 166, 53, 118, 5041])).
% 2.12/2.34 tff(5044,plain,
% 2.12/2.34 (r(s(z), s(s(s(z))))),
% 2.12/2.34 inference(unit_resolution,[status(thm)],[1674, 5043])).
% 2.12/2.34 tff(5045,plain,
% 2.12/2.34 (~b(s(s(s(z))), s(z))),
% 2.12/2.34 inference(unit_resolution,[status(thm)],[4045, 166, 53, 118, 5041])).
% 2.12/2.34 tff(5046,plain,
% 2.12/2.34 (r(s(s(s(z))), s(z))),
% 2.12/2.34 inference(unit_resolution,[status(thm)],[1763, 5045])).
% 2.12/2.34 tff(5047,plain,
% 2.12/2.34 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(z)), s(z))) | (~r(s(s(z)), s(s(s(z))))) | (~r(s(z), s(s(s(z))))) | (~r(s(s(s(z))), s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(z)), s(z))) | (~r(s(s(z)), s(s(s(z))))) | (~r(s(z), s(s(s(z))))) | (~r(s(s(s(z))), s(z))))),
% 2.12/2.34 inference(rewrite,[status(thm)],[])).
% 2.12/2.34 tff(5048,plain,
% 2.12/2.34 (((~r(s(z), s(s(s(z))))) | (~r(s(s(s(z))), s(z))) | (~r(s(s(z)), s(z))) | (~r(s(s(z)), s(s(s(z)))))) <=> ((~r(s(s(z)), s(z))) | (~r(s(s(z)), s(s(s(z))))) | (~r(s(z), s(s(s(z))))) | (~r(s(s(s(z))), s(z))))),
% 2.12/2.34 inference(rewrite,[status(thm)],[])).
% 2.12/2.34 tff(5049,plain,
% 2.12/2.34 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(s(s(z))))) | (~r(s(s(s(z))), s(z))) | (~r(s(s(z)), s(z))) | (~r(s(s(z)), s(s(s(z))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(z)), s(z))) | (~r(s(s(z)), s(s(s(z))))) | (~r(s(z), s(s(s(z))))) | (~r(s(s(s(z))), s(z)))))),
% 2.12/2.34 inference(monotonicity,[status(thm)],[5048])).
% 2.12/2.34 tff(5050,plain,
% 2.12/2.34 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(s(s(z))))) | (~r(s(s(s(z))), s(z))) | (~r(s(s(z)), s(z))) | (~r(s(s(z)), s(s(s(z))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(z)), s(z))) | (~r(s(s(z)), s(s(s(z))))) | (~r(s(z), s(s(s(z))))) | (~r(s(s(s(z))), s(z))))),
% 2.12/2.34 inference(transitivity,[status(thm)],[5049, 5047])).
% 2.12/2.34 tff(5051,plain,
% 2.12/2.34 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(s(s(z))))) | (~r(s(s(s(z))), s(z))) | (~r(s(s(z)), s(z))) | (~r(s(s(z)), s(s(s(z))))))),
% 2.12/2.34 inference(quant_inst,[status(thm)],[])).
% 2.12/2.34 tff(5052,plain,
% 2.12/2.34 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(z)), s(z))) | (~r(s(s(z)), s(s(s(z))))) | (~r(s(z), s(s(s(z))))) | (~r(s(s(s(z))), s(z)))),
% 2.12/2.34 inference(modus_ponens,[status(thm)],[5051, 5050])).
% 2.12/2.34 tff(5053,plain,
% 2.12/2.34 (~r(s(s(z)), s(s(s(z))))),
% 2.12/2.34 inference(unit_resolution,[status(thm)],[5052, 197, 4573, 5046, 5044])).
% 2.12/2.34 tff(5054,plain,
% 2.12/2.34 (b(s(s(z)), s(s(s(z))))),
% 2.12/2.34 inference(unit_resolution,[status(thm)],[1730, 5053])).
% 2.12/2.34 tff(5055,plain,
% 2.12/2.34 (~b(s(s(s(elem!1))), s(s(s(z))))),
% 2.12/2.34 inference(unit_resolution,[status(thm)],[3565, 5054, 118, 5042, 5041, 96])).
% 2.12/2.34 tff(5056,plain,
% 2.12/2.34 (~r(s(s(z)), s(s(s(elem!1))))),
% 2.12/2.34 inference(unit_resolution,[status(thm)],[290, 4575, 155, 153])).
% 2.12/2.34 tff(5057,plain,
% 2.12/2.34 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(elem!1)), s(z))) | (~r(s(z), s(s(s(z))))) | (~r(s(s(s(z))), s(z))) | (~r(s(s(elem!1)), s(s(s(z))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(elem!1)), s(z))) | (~r(s(z), s(s(s(z))))) | (~r(s(s(s(z))), s(z))) | (~r(s(s(elem!1)), s(s(s(z))))))),
% 2.12/2.34 inference(rewrite,[status(thm)],[])).
% 2.12/2.34 tff(5058,plain,
% 2.12/2.34 (((~r(s(z), s(s(s(z))))) | (~r(s(s(s(z))), s(z))) | (~r(s(s(elem!1)), s(z))) | (~r(s(s(elem!1)), s(s(s(z)))))) <=> ((~r(s(s(elem!1)), s(z))) | (~r(s(z), s(s(s(z))))) | (~r(s(s(s(z))), s(z))) | (~r(s(s(elem!1)), s(s(s(z))))))),
% 2.12/2.34 inference(rewrite,[status(thm)],[])).
% 2.12/2.34 tff(5059,plain,
% 2.12/2.34 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(s(s(z))))) | (~r(s(s(s(z))), s(z))) | (~r(s(s(elem!1)), s(z))) | (~r(s(s(elem!1)), s(s(s(z))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(elem!1)), s(z))) | (~r(s(z), s(s(s(z))))) | (~r(s(s(s(z))), s(z))) | (~r(s(s(elem!1)), s(s(s(z)))))))),
% 2.12/2.34 inference(monotonicity,[status(thm)],[5058])).
% 2.12/2.34 tff(5060,plain,
% 2.12/2.34 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(s(s(z))))) | (~r(s(s(s(z))), s(z))) | (~r(s(s(elem!1)), s(z))) | (~r(s(s(elem!1)), s(s(s(z))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(elem!1)), s(z))) | (~r(s(z), s(s(s(z))))) | (~r(s(s(s(z))), s(z))) | (~r(s(s(elem!1)), s(s(s(z))))))),
% 2.12/2.34 inference(transitivity,[status(thm)],[5059, 5057])).
% 2.12/2.34 tff(5061,plain,
% 2.12/2.34 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(s(s(z))))) | (~r(s(s(s(z))), s(z))) | (~r(s(s(elem!1)), s(z))) | (~r(s(s(elem!1)), s(s(s(z))))))),
% 2.12/2.34 inference(quant_inst,[status(thm)],[])).
% 2.12/2.34 tff(5062,plain,
% 2.12/2.34 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(elem!1)), s(z))) | (~r(s(z), s(s(s(z))))) | (~r(s(s(s(z))), s(z))) | (~r(s(s(elem!1)), s(s(s(z)))))),
% 2.12/2.34 inference(modus_ponens,[status(thm)],[5061, 5060])).
% 2.12/2.34 tff(5063,plain,
% 2.12/2.34 (~r(s(s(elem!1)), s(s(s(z))))),
% 2.12/2.34 inference(unit_resolution,[status(thm)],[5062, 197, 4577, 5046, 5044])).
% 2.12/2.34 tff(5064,plain,
% 2.12/2.34 (~r(s(s(s(z))), s(s(z)))),
% 2.12/2.34 inference(unit_resolution,[status(thm)],[4053, 197, 4573, 5046, 5044])).
% 2.12/2.34 tff(5065,plain,
% 2.12/2.34 (b(s(s(s(z))), s(s(z)))),
% 2.12/2.34 inference(unit_resolution,[status(thm)],[1010, 5064])).
% 2.12/2.34 tff(5066,plain,
% 2.12/2.34 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), z)) | (~b(z, s(z))) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(s(z)), z)) | (~b(s(s(s(z))), z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), z)) | (~b(z, s(z))) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(s(z)), z)) | (~b(s(s(s(z))), z)))),
% 2.12/2.34 inference(rewrite,[status(thm)],[])).
% 2.12/2.34 tff(5067,plain,
% 2.12/2.34 (((~b(s(z), z)) | (~b(s(s(s(z))), z)) | (~b(z, s(z))) | (~b(s(s(z)), z)) | (~b(s(s(s(z))), z)) | (~b(s(s(s(z))), s(s(z))))) <=> ((~b(s(z), z)) | (~b(z, s(z))) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(s(z)), z)) | (~b(s(s(s(z))), z)))),
% 2.12/2.34 inference(rewrite,[status(thm)],[])).
% 2.12/2.34 tff(5068,plain,
% 2.12/2.34 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), z)) | (~b(s(s(s(z))), z)) | (~b(z, s(z))) | (~b(s(s(z)), z)) | (~b(s(s(s(z))), z)) | (~b(s(s(s(z))), s(s(z)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), z)) | (~b(z, s(z))) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(s(z)), z)) | (~b(s(s(s(z))), z))))),
% 2.12/2.34 inference(monotonicity,[status(thm)],[5067])).
% 2.12/2.34 tff(5069,plain,
% 2.12/2.34 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), z)) | (~b(s(s(s(z))), z)) | (~b(z, s(z))) | (~b(s(s(z)), z)) | (~b(s(s(s(z))), z)) | (~b(s(s(s(z))), s(s(z)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), z)) | (~b(z, s(z))) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(s(z)), z)) | (~b(s(s(s(z))), z)))),
% 2.12/2.34 inference(transitivity,[status(thm)],[5068, 5066])).
% 2.12/2.34 tff(5070,plain,
% 2.12/2.34 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), z)) | (~b(s(s(s(z))), z)) | (~b(z, s(z))) | (~b(s(s(z)), z)) | (~b(s(s(s(z))), z)) | (~b(s(s(s(z))), s(s(z)))))),
% 2.12/2.34 inference(quant_inst,[status(thm)],[])).
% 2.12/2.35 tff(5071,plain,
% 2.12/2.35 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), z)) | (~b(z, s(z))) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(s(z)), z)) | (~b(s(s(s(z))), z))),
% 2.12/2.35 inference(modus_ponens,[status(thm)],[5070, 5069])).
% 2.12/2.35 tff(5072,plain,
% 2.12/2.35 (~b(s(s(s(z))), s(s(z)))),
% 2.12/2.35 inference(unit_resolution,[status(thm)],[5071, 166, 53, 118, 122, 1699])).
% 2.12/2.35 tff(5073,plain,
% 2.12/2.35 (r(s(s(s(z))), s(s(z)))),
% 2.12/2.35 inference(unit_resolution,[status(thm)],[1010, 5072])).
% 2.12/2.35 tff(5074,plain,
% 2.12/2.35 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(s(z)))) | (~r(s(s(z)), s(z))) | (~r(s(s(s(z))), s(z))) | (~r(s(s(s(z))), s(s(z)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(z), s(s(z)))) | (~r(s(s(z)), s(z))) | (~r(s(s(s(z))), s(z))) | (~r(s(s(s(z))), s(s(z)))))),
% 2.12/2.35 inference(rewrite,[status(thm)],[])).
% 2.12/2.35 tff(5075,plain,
% 2.12/2.35 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(s(z)))) | (~r(s(s(z)), s(z))) | (~r(s(s(s(z))), s(z))) | (~r(s(s(s(z))), s(s(z)))))),
% 2.12/2.35 inference(quant_inst,[status(thm)],[])).
% 2.12/2.35 tff(5076,plain,
% 2.12/2.35 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(z), s(s(z)))) | (~r(s(s(z)), s(z))) | (~r(s(s(s(z))), s(z))) | (~r(s(s(s(z))), s(s(z))))),
% 2.12/2.35 inference(modus_ponens,[status(thm)],[5075, 5074])).
% 2.12/2.35 tff(5077,plain,
% 2.12/2.35 ($false),
% 2.12/2.35 inference(unit_resolution,[status(thm)],[5076, 197, 120, 392, 5073, 4047])).
% 2.12/2.35 tff(5078,plain,((~b(s(s(s(z))), z)) | (~r(s(z), s(s(z)))) | (~r(s(s(z)), s(z))) | (~b(s(z), z)) | (~b(z, s(z))) | (~b(s(s(z)), z))), inference(lemma,lemma(discharge,[]))).
% 2.12/2.35 tff(5079,plain,
% 2.12/2.35 (~b(s(s(z)), z)),
% 2.12/2.35 inference(unit_resolution,[status(thm)],[5078, 5041, 4573, 118, 53, 120])).
% 2.12/2.35 tff(5080,plain,
% 2.12/2.35 (r(s(s(z)), z)),
% 2.12/2.35 inference(unit_resolution,[status(thm)],[186, 5079])).
% 2.12/2.35 tff(5081,plain,
% 2.12/2.35 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), s(s(z)))) | (~b(s(s(z)), s(s(elem!1)))) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(s(elem!1)), s(s(s(z))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(elem!1)), s(s(z)))) | (~b(s(s(z)), s(s(elem!1)))) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(s(elem!1)), s(s(s(z))))))),
% 2.12/2.35 inference(rewrite,[status(thm)],[])).
% 2.12/2.35 tff(5082,plain,
% 2.12/2.35 (((~b(s(s(elem!1)), s(s(z)))) | (~b(s(s(elem!1)), s(s(z)))) | (~b(s(s(z)), s(s(elem!1)))) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(s(elem!1)), s(s(z)))) | (~b(s(s(elem!1)), s(s(s(z)))))) <=> ((~b(s(s(elem!1)), s(s(z)))) | (~b(s(s(z)), s(s(elem!1)))) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(s(elem!1)), s(s(s(z))))))),
% 2.12/2.35 inference(rewrite,[status(thm)],[])).
% 2.12/2.35 tff(5083,plain,
% 2.12/2.35 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), s(s(z)))) | (~b(s(s(elem!1)), s(s(z)))) | (~b(s(s(z)), s(s(elem!1)))) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(s(elem!1)), s(s(z)))) | (~b(s(s(elem!1)), s(s(s(z))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), s(s(z)))) | (~b(s(s(z)), s(s(elem!1)))) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(s(elem!1)), s(s(s(z)))))))),
% 2.12/2.35 inference(monotonicity,[status(thm)],[5082])).
% 2.12/2.35 tff(5084,plain,
% 2.12/2.35 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), s(s(z)))) | (~b(s(s(elem!1)), s(s(z)))) | (~b(s(s(z)), s(s(elem!1)))) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(s(elem!1)), s(s(z)))) | (~b(s(s(elem!1)), s(s(s(z))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(elem!1)), s(s(z)))) | (~b(s(s(z)), s(s(elem!1)))) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(s(elem!1)), s(s(s(z))))))),
% 2.12/2.35 inference(transitivity,[status(thm)],[5083, 5081])).
% 2.12/2.35 tff(5085,plain,
% 2.12/2.35 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), s(s(z)))) | (~b(s(s(elem!1)), s(s(z)))) | (~b(s(s(z)), s(s(elem!1)))) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(s(elem!1)), s(s(z)))) | (~b(s(s(elem!1)), s(s(s(z))))))),
% 2.12/2.35 inference(quant_inst,[status(thm)],[])).
% 2.12/2.35 tff(5086,plain,
% 2.12/2.35 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(elem!1)), s(s(z)))) | (~b(s(s(z)), s(s(elem!1)))) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(s(elem!1)), s(s(s(z)))))),
% 2.12/2.35 inference(modus_ponens,[status(thm)],[5085, 5084])).
% 2.12/2.35 tff(5087,plain,
% 2.12/2.35 (~b(s(s(elem!1)), s(s(s(z))))),
% 2.12/2.35 inference(unit_resolution,[status(thm)],[5086, 166, 3964, 2516, 987])).
% 2.12/2.35 tff(5088,assumption,(~r(s(s(elem!1)), s(s(s(z))))), introduced(assumption)).
% 2.12/2.35 tff(5089,plain,
% 2.12/2.35 (((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((s(s(elem!1)) = s(s(s(z)))) | b(s(s(elem!1)), s(s(s(z)))) | r(s(s(elem!1)), s(s(s(z)))))) <=> ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (s(s(elem!1)) = s(s(s(z)))) | b(s(s(elem!1)), s(s(s(z)))) | r(s(s(elem!1)), s(s(s(z)))))),
% 2.12/2.35 inference(rewrite,[status(thm)],[])).
% 2.12/2.35 tff(5090,plain,
% 2.12/2.35 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((s(s(elem!1)) = s(s(s(z)))) | b(s(s(elem!1)), s(s(s(z)))) | r(s(s(elem!1)), s(s(s(z)))))),
% 2.12/2.35 inference(quant_inst,[status(thm)],[])).
% 2.12/2.35 tff(5091,plain,
% 2.12/2.35 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (s(s(elem!1)) = s(s(s(z)))) | b(s(s(elem!1)), s(s(s(z)))) | r(s(s(elem!1)), s(s(s(z))))),
% 2.12/2.35 inference(modus_ponens,[status(thm)],[5090, 5089])).
% 2.12/2.35 tff(5092,plain,
% 2.12/2.35 ((s(s(elem!1)) = s(s(s(z)))) | b(s(s(elem!1)), s(s(s(z))))),
% 2.12/2.35 inference(unit_resolution,[status(thm)],[5091, 79, 5088])).
% 2.12/2.35 tff(5093,plain,
% 2.12/2.35 (s(s(elem!1)) = s(s(s(z)))),
% 2.12/2.35 inference(unit_resolution,[status(thm)],[5092, 5087])).
% 2.12/2.35 tff(5094,plain,
% 2.12/2.35 (s(s(s(elem!1))) = s(s(s(s(z))))),
% 2.12/2.35 inference(monotonicity,[status(thm)],[5093])).
% 2.12/2.35 tff(5095,plain,
% 2.12/2.35 (s(s(s(s(elem!1)))) = s(s(s(s(s(z)))))),
% 2.12/2.35 inference(monotonicity,[status(thm)],[5094])).
% 2.12/2.35 tff(5096,plain,
% 2.12/2.35 (s(s(s(s(s(z))))) = s(s(s(s(elem!1))))),
% 2.12/2.35 inference(symmetry,[status(thm)],[5095])).
% 2.12/2.35 tff(5097,plain,
% 2.12/2.35 ((s(s(z)) = s(s(s(s(s(z)))))) <=> (s(s(z)) = s(s(s(s(elem!1)))))),
% 2.12/2.35 inference(monotonicity,[status(thm)],[5096])).
% 2.12/2.35 tff(5098,plain,
% 2.12/2.35 ((s(s(z)) = s(s(s(s(s(z)))))) <=> (s(s(s(s(elem!1)))) = s(s(z)))),
% 2.12/2.35 inference(transitivity,[status(thm)],[5097, 1275])).
% 2.12/2.35 tff(5099,plain,
% 2.12/2.35 ((s(s(s(s(elem!1)))) = s(s(z))) <=> (s(s(z)) = s(s(s(s(s(z))))))),
% 2.12/2.35 inference(symmetry,[status(thm)],[5098])).
% 2.12/2.35 tff(5100,plain,
% 2.12/2.35 ((~(s(s(s(s(elem!1)))) = s(s(z)))) <=> (~(s(s(z)) = s(s(s(s(s(z)))))))),
% 2.12/2.35 inference(monotonicity,[status(thm)],[5099])).
% 2.12/2.35 tff(5101,plain,
% 2.12/2.35 (~(s(s(z)) = s(s(s(s(s(z))))))),
% 2.12/2.35 inference(modus_ponens,[status(thm)],[733, 5100])).
% 2.12/2.35 tff(5102,plain,
% 2.12/2.35 (s(s(s(z))) = s(s(elem!1))),
% 2.12/2.35 inference(symmetry,[status(thm)],[5093])).
% 2.12/2.35 tff(5103,plain,
% 2.12/2.35 ((s(s(s(s(elem!1)))) = s(s(s(z)))) <=> (s(s(s(s(elem!1)))) = s(s(elem!1)))),
% 2.12/2.35 inference(monotonicity,[status(thm)],[5102])).
% 2.12/2.35 tff(5104,plain,
% 2.12/2.35 ((s(s(s(s(elem!1)))) = s(s(s(z)))) <=> (s(s(elem!1)) = s(s(s(s(elem!1)))))),
% 2.12/2.35 inference(transitivity,[status(thm)],[5103, 123])).
% 2.12/2.35 tff(5105,plain,
% 2.12/2.35 ((s(s(s(s(elem!1)))) = s(s(s(z)))) <=> (s(s(s(s(elem!1)))) = s(s(elem!1)))),
% 2.12/2.35 inference(transitivity,[status(thm)],[5104, 124])).
% 2.12/2.35 tff(5106,plain,
% 2.12/2.35 ((~(s(s(s(s(elem!1)))) = s(s(s(z))))) <=> (~(s(s(s(s(elem!1)))) = s(s(elem!1))))),
% 2.12/2.35 inference(monotonicity,[status(thm)],[5105])).
% 2.12/2.35 tff(5107,assumption,(s(s(s(s(elem!1)))) = s(s(s(z)))), introduced(assumption)).
% 2.12/2.35 tff(5108,plain,
% 2.12/2.35 (inj_0(s(s(s(s(elem!1))))) = inj_0(s(s(s(z))))),
% 2.12/2.35 inference(monotonicity,[status(thm)],[5107])).
% 2.12/2.35 tff(5109,plain,
% 2.12/2.35 (inj_0(s(s(s(z)))) = inj_0(s(s(s(s(elem!1)))))),
% 2.12/2.35 inference(symmetry,[status(thm)],[5108])).
% 2.12/2.35 tff(5110,plain,
% 2.12/2.35 (s(s(z)) = s(s(s(elem!1)))),
% 2.12/2.35 inference(transitivity,[status(thm)],[1666, 5109, 352])).
% 2.12/2.35 tff(5111,plain,
% 2.12/2.35 ($false),
% 2.12/2.35 inference(unit_resolution,[status(thm)],[209, 5110])).
% 2.12/2.35 tff(5112,plain,(~(s(s(s(s(elem!1)))) = s(s(s(z))))), inference(lemma,lemma(discharge,[]))).
% 2.12/2.35 tff(5113,plain,
% 2.12/2.35 (~(s(s(s(s(elem!1)))) = s(s(elem!1)))),
% 2.12/2.35 inference(modus_ponens,[status(thm)],[5112, 5106])).
% 2.12/2.35 tff(5114,plain,
% 2.12/2.35 (r(s(s(s(elem!1))), s(s(s(z))))),
% 2.12/2.35 inference(unit_resolution,[status(thm)],[3574, 140, 3569])).
% 2.12/2.35 tff(5115,plain,
% 2.12/2.35 (~r(s(z), s(s(s(elem!1))))),
% 2.12/2.35 inference(unit_resolution,[status(thm)],[3583, 4589, 311, 5114])).
% 2.12/2.35 tff(5116,plain,
% 2.12/2.35 (b(s(z), s(s(s(elem!1))))),
% 2.12/2.35 inference(unit_resolution,[status(thm)],[116, 5115])).
% 2.12/2.35 tff(5117,plain,
% 2.12/2.35 (~b(s(s(s(elem!1))), s(s(elem!1)))),
% 2.12/2.35 inference(unit_resolution,[status(thm)],[3976, 166, 3964, 2516, 3962])).
% 2.12/2.35 tff(5118,plain,
% 2.12/2.35 (r(s(s(s(elem!1))), s(s(elem!1)))),
% 2.12/2.35 inference(unit_resolution,[status(thm)],[889, 5117, 51])).
% 2.12/2.35 tff(5119,plain,
% 2.12/2.35 ((~(s(s(s(s(elem!1)))) = s(s(s(z))))) <=> (~(s(s(elem!1)) = s(s(s(s(elem!1))))))),
% 2.12/2.35 inference(monotonicity,[status(thm)],[5104])).
% 2.12/2.35 tff(5120,plain,
% 2.12/2.35 (~(s(s(elem!1)) = s(s(s(s(elem!1)))))),
% 2.12/2.35 inference(modus_ponens,[status(thm)],[5112, 5119])).
% 2.12/2.35 tff(5121,plain,
% 2.12/2.35 (~r(s(z), s(s(s(s(elem!1)))))),
% 2.12/2.35 inference(unit_resolution,[status(thm)],[4636, 3408, 4577, 311])).
% 2.12/2.35 tff(5122,plain,
% 2.12/2.35 (b(s(z), s(s(s(s(elem!1)))))),
% 2.12/2.35 inference(unit_resolution,[status(thm)],[681, 5121])).
% 2.12/2.35 tff(5123,plain,
% 2.12/2.35 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(s(s(elem!1))), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(s(s(elem!1))), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), s(z))))),
% 2.12/2.35 inference(rewrite,[status(thm)],[])).
% 2.12/2.35 tff(5124,plain,
% 2.12/2.35 (((~b(s(s(s(elem!1))), s(z))) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(z), s(s(s(elem!1))))) | (~b(s(s(s(s(elem!1)))), s(z))) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(s(s(elem!1))), s(s(s(s(elem!1))))))) <=> ((~b(s(z), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(s(s(elem!1))), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), s(z))))),
% 2.12/2.35 inference(rewrite,[status(thm)],[])).
% 2.12/2.35 tff(5125,plain,
% 2.12/2.35 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), s(z))) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(z), s(s(s(elem!1))))) | (~b(s(s(s(s(elem!1)))), s(z))) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(s(s(elem!1))), s(s(s(s(elem!1)))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(s(s(elem!1))), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), s(z)))))),
% 2.12/2.35 inference(monotonicity,[status(thm)],[5124])).
% 2.12/2.35 tff(5126,plain,
% 2.12/2.35 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), s(z))) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(z), s(s(s(elem!1))))) | (~b(s(s(s(s(elem!1)))), s(z))) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(s(s(elem!1))), s(s(s(s(elem!1)))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(s(s(elem!1))), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), s(z))))),
% 2.12/2.35 inference(transitivity,[status(thm)],[5125, 5123])).
% 2.12/2.35 tff(5127,plain,
% 2.12/2.35 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), s(z))) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(z), s(s(s(elem!1))))) | (~b(s(s(s(s(elem!1)))), s(z))) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(s(s(elem!1))), s(s(s(s(elem!1)))))))),
% 2.12/2.35 inference(quant_inst,[status(thm)],[])).
% 2.12/2.35 tff(5128,plain,
% 2.12/2.35 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(s(s(elem!1))), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), s(z)))),
% 2.12/2.35 inference(modus_ponens,[status(thm)],[5127, 5126])).
% 2.12/2.35 tff(5129,plain,
% 2.12/2.35 ($false),
% 2.12/2.35 inference(unit_resolution,[status(thm)],[5128, 166, 241, 96, 1402, 1311])).
% 2.12/2.35 tff(5130,plain,((~b(s(s(s(s(elem!1)))), s(z))) | (~b(s(z), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(s(s(elem!1))), s(s(s(s(elem!1))))))), inference(lemma,lemma(discharge,[]))).
% 2.12/2.35 tff(5131,plain,
% 2.12/2.35 (~b(s(s(s(s(elem!1)))), s(z))),
% 2.12/2.35 inference(unit_resolution,[status(thm)],[5130, 1311, 96, 241])).
% 2.12/2.35 tff(5132,plain,
% 2.12/2.35 (r(s(s(s(s(elem!1)))), s(z))),
% 2.12/2.35 inference(unit_resolution,[status(thm)],[661, 5131])).
% 2.12/2.35 tff(5133,plain,
% 2.12/2.35 (~r(s(s(s(s(elem!1)))), s(s(elem!1)))),
% 2.12/2.35 inference(unit_resolution,[status(thm)],[4643, 5132, 4577, 120])).
% 2.12/2.35 tff(5134,plain,
% 2.12/2.35 (b(s(s(s(s(elem!1)))), s(s(elem!1)))),
% 2.12/2.35 inference(unit_resolution,[status(thm)],[813, 5133, 806])).
% 2.12/2.35 tff(5135,plain,
% 2.12/2.35 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(s(elem!1)))) | (~r(s(s(elem!1)), s(z))) | (~r(s(s(s(s(elem!1)))), s(z))) | (~r(s(s(elem!1)), s(s(s(s(elem!1)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(z), s(s(elem!1)))) | (~r(s(s(elem!1)), s(z))) | (~r(s(s(s(s(elem!1)))), s(z))) | (~r(s(s(elem!1)), s(s(s(s(elem!1)))))))),
% 2.12/2.35 inference(rewrite,[status(thm)],[])).
% 2.12/2.35 tff(5136,plain,
% 2.12/2.35 (((~r(s(z), s(s(elem!1)))) | (~r(s(s(s(s(elem!1)))), s(z))) | (~r(s(s(elem!1)), s(z))) | (~r(s(s(elem!1)), s(s(s(s(elem!1))))))) <=> ((~r(s(z), s(s(elem!1)))) | (~r(s(s(elem!1)), s(z))) | (~r(s(s(s(s(elem!1)))), s(z))) | (~r(s(s(elem!1)), s(s(s(s(elem!1)))))))),
% 2.12/2.35 inference(rewrite,[status(thm)],[])).
% 2.12/2.35 tff(5137,plain,
% 2.12/2.35 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(s(elem!1)))) | (~r(s(s(s(s(elem!1)))), s(z))) | (~r(s(s(elem!1)), s(z))) | (~r(s(s(elem!1)), s(s(s(s(elem!1)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(s(elem!1)))) | (~r(s(s(elem!1)), s(z))) | (~r(s(s(s(s(elem!1)))), s(z))) | (~r(s(s(elem!1)), s(s(s(s(elem!1))))))))),
% 2.12/2.35 inference(monotonicity,[status(thm)],[5136])).
% 2.12/2.35 tff(5138,plain,
% 2.12/2.35 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(s(elem!1)))) | (~r(s(s(s(s(elem!1)))), s(z))) | (~r(s(s(elem!1)), s(z))) | (~r(s(s(elem!1)), s(s(s(s(elem!1)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(z), s(s(elem!1)))) | (~r(s(s(elem!1)), s(z))) | (~r(s(s(s(s(elem!1)))), s(z))) | (~r(s(s(elem!1)), s(s(s(s(elem!1)))))))),
% 2.12/2.35 inference(transitivity,[status(thm)],[5137, 5135])).
% 2.12/2.35 tff(5139,plain,
% 2.12/2.35 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(s(elem!1)))) | (~r(s(s(s(s(elem!1)))), s(z))) | (~r(s(s(elem!1)), s(z))) | (~r(s(s(elem!1)), s(s(s(s(elem!1)))))))),
% 2.12/2.35 inference(quant_inst,[status(thm)],[])).
% 2.12/2.35 tff(5140,plain,
% 2.12/2.35 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(z), s(s(elem!1)))) | (~r(s(s(elem!1)), s(z))) | (~r(s(s(s(s(elem!1)))), s(z))) | (~r(s(s(elem!1)), s(s(s(s(elem!1))))))),
% 2.12/2.35 inference(modus_ponens,[status(thm)],[5139, 5138])).
% 2.12/2.35 tff(5141,plain,
% 2.12/2.35 (~r(s(s(elem!1)), s(s(s(s(elem!1)))))),
% 2.12/2.35 inference(unit_resolution,[status(thm)],[5140, 197, 311, 4577, 5132])).
% 2.12/2.35 tff(5142,plain,
% 2.12/2.35 (b(s(s(elem!1)), s(s(s(s(elem!1)))))),
% 2.12/2.35 inference(unit_resolution,[status(thm)],[827, 5141, 2395])).
% 2.12/2.35 tff(5143,plain,
% 2.12/2.35 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(s(elem!1))))) | (~b(s(s(s(s(elem!1)))), s(s(elem!1)))) | (~b(s(s(elem!1)), s(s(s(s(elem!1)))))) | (~b(s(s(s(elem!1))), s(s(s(s(elem!1)))))) | (~b(s(z), s(s(s(s(elem!1)))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), s(s(s(elem!1))))) | (~b(s(s(s(s(elem!1)))), s(s(elem!1)))) | (~b(s(s(elem!1)), s(s(s(s(elem!1)))))) | (~b(s(s(s(elem!1))), s(s(s(s(elem!1)))))) | (~b(s(z), s(s(s(s(elem!1)))))))),
% 2.12/2.35 inference(rewrite,[status(thm)],[])).
% 2.12/2.35 tff(5144,plain,
% 2.12/2.35 (((~b(s(s(elem!1)), s(s(s(s(elem!1)))))) | (~b(s(z), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), s(s(elem!1)))) | (~b(s(s(s(elem!1))), s(s(s(s(elem!1)))))) | (~b(s(z), s(s(s(s(elem!1)))))) | (~b(s(z), s(s(s(elem!1)))))) <=> ((~b(s(z), s(s(s(elem!1))))) | (~b(s(s(s(s(elem!1)))), s(s(elem!1)))) | (~b(s(s(elem!1)), s(s(s(s(elem!1)))))) | (~b(s(s(s(elem!1))), s(s(s(s(elem!1)))))) | (~b(s(z), s(s(s(s(elem!1)))))))),
% 2.12/2.35 inference(rewrite,[status(thm)],[])).
% 2.12/2.35 tff(5145,plain,
% 2.12/2.35 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), s(s(s(s(elem!1)))))) | (~b(s(z), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), s(s(elem!1)))) | (~b(s(s(s(elem!1))), s(s(s(s(elem!1)))))) | (~b(s(z), s(s(s(s(elem!1)))))) | (~b(s(z), s(s(s(elem!1))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(s(elem!1))))) | (~b(s(s(s(s(elem!1)))), s(s(elem!1)))) | (~b(s(s(elem!1)), s(s(s(s(elem!1)))))) | (~b(s(s(s(elem!1))), s(s(s(s(elem!1)))))) | (~b(s(z), s(s(s(s(elem!1))))))))),
% 2.12/2.35 inference(monotonicity,[status(thm)],[5144])).
% 2.12/2.35 tff(5146,plain,
% 2.12/2.35 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), s(s(s(s(elem!1)))))) | (~b(s(z), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), s(s(elem!1)))) | (~b(s(s(s(elem!1))), s(s(s(s(elem!1)))))) | (~b(s(z), s(s(s(s(elem!1)))))) | (~b(s(z), s(s(s(elem!1))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), s(s(s(elem!1))))) | (~b(s(s(s(s(elem!1)))), s(s(elem!1)))) | (~b(s(s(elem!1)), s(s(s(s(elem!1)))))) | (~b(s(s(s(elem!1))), s(s(s(s(elem!1)))))) | (~b(s(z), s(s(s(s(elem!1)))))))),
% 2.12/2.35 inference(transitivity,[status(thm)],[5145, 5143])).
% 2.12/2.35 tff(5147,plain,
% 2.12/2.35 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), s(s(s(s(elem!1)))))) | (~b(s(z), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), s(s(elem!1)))) | (~b(s(s(s(elem!1))), s(s(s(s(elem!1)))))) | (~b(s(z), s(s(s(s(elem!1)))))) | (~b(s(z), s(s(s(elem!1))))))),
% 2.12/2.35 inference(quant_inst,[status(thm)],[])).
% 2.12/2.35 tff(5148,plain,
% 2.12/2.35 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), s(s(s(elem!1))))) | (~b(s(s(s(s(elem!1)))), s(s(elem!1)))) | (~b(s(s(elem!1)), s(s(s(s(elem!1)))))) | (~b(s(s(s(elem!1))), s(s(s(s(elem!1)))))) | (~b(s(z), s(s(s(s(elem!1))))))),
% 2.12/2.35 inference(modus_ponens,[status(thm)],[5147, 5146])).
% 2.12/2.35 tff(5149,plain,
% 2.12/2.35 ($false),
% 2.12/2.35 inference(unit_resolution,[status(thm)],[5148, 166, 241, 5142, 1327, 5134, 1311])).
% 2.12/2.35 tff(5150,plain,((~b(s(s(s(elem!1))), s(s(s(s(elem!1)))))) | (~b(s(z), s(s(s(elem!1))))) | (~b(s(z), s(s(s(s(elem!1)))))) | (s(s(elem!1)) = s(s(s(s(elem!1))))) | (~r(s(z), s(s(elem!1)))) | (~r(s(s(elem!1)), s(z))) | (s(s(s(s(elem!1)))) = s(s(elem!1))) | (~r(s(z), s(s(z)))) | (~b(s(s(s(elem!1))), s(z)))), inference(lemma,lemma(discharge,[]))).
% 2.12/2.36 tff(5151,plain,
% 2.12/2.36 (~b(s(s(s(elem!1))), s(s(s(s(elem!1)))))),
% 2.12/2.36 inference(unit_resolution,[status(thm)],[5150, 5122, 241, 2395, 311, 4577, 806, 120, 96])).
% 2.12/2.36 tff(5152,plain,
% 2.12/2.36 (r(s(s(s(elem!1))), s(s(s(s(elem!1)))))),
% 2.12/2.36 inference(unit_resolution,[status(thm)],[696, 5151, 361])).
% 2.12/2.36 tff(5153,plain,
% 2.12/2.36 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), s(s(elem!1)))) | (~r(s(s(elem!1)), s(z))) | (~r(s(s(s(elem!1))), s(s(s(s(elem!1)))))) | (~r(s(s(s(s(elem!1)))), s(s(elem!1)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(elem!1))), s(s(elem!1)))) | (~r(s(s(elem!1)), s(z))) | (~r(s(s(s(elem!1))), s(s(s(s(elem!1)))))) | (~r(s(s(s(s(elem!1)))), s(s(elem!1)))))),
% 2.12/2.36 inference(rewrite,[status(thm)],[])).
% 2.12/2.36 tff(5154,plain,
% 2.12/2.36 (((~r(s(s(elem!1)), s(z))) | (~r(s(s(s(s(elem!1)))), s(s(elem!1)))) | (~r(s(s(s(elem!1))), s(s(elem!1)))) | (~r(s(s(s(elem!1))), s(s(s(s(elem!1))))))) <=> ((~r(s(s(s(elem!1))), s(s(elem!1)))) | (~r(s(s(elem!1)), s(z))) | (~r(s(s(s(elem!1))), s(s(s(s(elem!1)))))) | (~r(s(s(s(s(elem!1)))), s(s(elem!1)))))),
% 2.12/2.36 inference(rewrite,[status(thm)],[])).
% 2.12/2.36 tff(5155,plain,
% 2.12/2.36 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(elem!1)), s(z))) | (~r(s(s(s(s(elem!1)))), s(s(elem!1)))) | (~r(s(s(s(elem!1))), s(s(elem!1)))) | (~r(s(s(s(elem!1))), s(s(s(s(elem!1)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), s(s(elem!1)))) | (~r(s(s(elem!1)), s(z))) | (~r(s(s(s(elem!1))), s(s(s(s(elem!1)))))) | (~r(s(s(s(s(elem!1)))), s(s(elem!1))))))),
% 2.12/2.36 inference(monotonicity,[status(thm)],[5154])).
% 2.12/2.36 tff(5156,plain,
% 2.12/2.36 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(elem!1)), s(z))) | (~r(s(s(s(s(elem!1)))), s(s(elem!1)))) | (~r(s(s(s(elem!1))), s(s(elem!1)))) | (~r(s(s(s(elem!1))), s(s(s(s(elem!1)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(elem!1))), s(s(elem!1)))) | (~r(s(s(elem!1)), s(z))) | (~r(s(s(s(elem!1))), s(s(s(s(elem!1)))))) | (~r(s(s(s(s(elem!1)))), s(s(elem!1)))))),
% 2.12/2.36 inference(transitivity,[status(thm)],[5155, 5153])).
% 2.12/2.36 tff(5157,plain,
% 2.12/2.36 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(elem!1)), s(z))) | (~r(s(s(s(s(elem!1)))), s(s(elem!1)))) | (~r(s(s(s(elem!1))), s(s(elem!1)))) | (~r(s(s(s(elem!1))), s(s(s(s(elem!1)))))))),
% 2.12/2.36 inference(quant_inst,[status(thm)],[])).
% 2.12/2.36 tff(5158,plain,
% 2.12/2.36 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(elem!1))), s(s(elem!1)))) | (~r(s(s(elem!1)), s(z))) | (~r(s(s(s(elem!1))), s(s(s(s(elem!1)))))) | (~r(s(s(s(s(elem!1)))), s(s(elem!1))))),
% 2.12/2.36 inference(modus_ponens,[status(thm)],[5157, 5156])).
% 2.12/2.36 tff(5159,plain,
% 2.12/2.36 ($false),
% 2.12/2.36 inference(unit_resolution,[status(thm)],[5158, 197, 4577, 905, 3408, 5152])).
% 2.12/2.36 tff(5160,plain,((~r(s(s(s(s(elem!1)))), s(s(elem!1)))) | (~r(s(s(elem!1)), s(z))) | (~r(s(s(s(elem!1))), s(s(elem!1)))) | (s(s(s(elem!1))) = s(s(s(s(elem!1))))) | (~b(s(z), s(s(s(elem!1))))) | (s(s(elem!1)) = s(s(s(s(elem!1))))) | (~r(s(z), s(s(elem!1)))) | (s(s(s(s(elem!1)))) = s(s(elem!1))) | (~r(s(z), s(s(z)))) | (~b(s(s(s(elem!1))), s(z)))), inference(lemma,lemma(discharge,[]))).
% 2.12/2.36 tff(5161,plain,
% 2.12/2.36 (~r(s(s(s(s(elem!1)))), s(s(elem!1)))),
% 2.12/2.36 inference(unit_resolution,[status(thm)],[5160, 5120, 311, 4577, 358, 5118, 5116, 5113, 120, 96])).
% 2.12/2.36 tff(5162,plain,
% 2.12/2.36 (b(s(s(s(s(elem!1)))), s(s(elem!1)))),
% 2.12/2.36 inference(unit_resolution,[status(thm)],[813, 5161, 5113])).
% 2.12/2.36 tff(5163,assumption,(s(s(elem!1)) = s(s(s(z)))), introduced(assumption)).
% 2.12/2.36 tff(5164,plain,
% 2.12/2.36 (b(s(s(s(s(elem!1)))), s(s(elem!1))) <=> b(s(s(s(s(elem!1)))), s(s(s(z))))),
% 2.12/2.36 inference(monotonicity,[status(thm)],[5163])).
% 2.12/2.36 tff(5165,plain,
% 2.12/2.36 (b(s(s(s(s(elem!1)))), s(s(s(z)))) <=> b(s(s(s(s(elem!1)))), s(s(elem!1)))),
% 2.12/2.36 inference(symmetry,[status(thm)],[5164])).
% 2.12/2.36 tff(5166,plain,
% 2.12/2.36 (s(s(s(elem!1))) = s(s(s(s(z))))),
% 2.12/2.36 inference(monotonicity,[status(thm)],[5163])).
% 2.12/2.36 tff(5167,plain,
% 2.12/2.36 (s(s(s(s(elem!1)))) = s(s(s(s(s(z)))))),
% 2.12/2.36 inference(monotonicity,[status(thm)],[5166])).
% 2.12/2.36 tff(5168,plain,
% 2.12/2.36 (s(s(s(s(s(z))))) = s(s(s(s(elem!1))))),
% 2.12/2.36 inference(symmetry,[status(thm)],[5167])).
% 2.12/2.36 tff(5169,plain,
% 2.12/2.36 (b(s(s(s(s(s(z))))), s(s(s(z)))) <=> b(s(s(s(s(elem!1)))), s(s(s(z))))),
% 2.12/2.36 inference(monotonicity,[status(thm)],[5168])).
% 2.12/2.36 tff(5170,plain,
% 2.12/2.36 (b(s(s(s(s(s(z))))), s(s(s(z)))) <=> b(s(s(s(s(elem!1)))), s(s(elem!1)))),
% 2.12/2.36 inference(transitivity,[status(thm)],[5169, 5165])).
% 2.12/2.36 tff(5171,plain,
% 2.12/2.36 ((~b(s(s(s(s(s(z))))), s(s(s(z))))) <=> (~b(s(s(s(s(elem!1)))), s(s(elem!1))))),
% 2.12/2.36 inference(monotonicity,[status(thm)],[5170])).
% 2.12/2.36 tff(5172,assumption,(~b(s(s(s(s(s(z))))), s(s(s(z))))), introduced(assumption)).
% 2.12/2.36 tff(5173,plain,
% 2.12/2.36 (~b(s(s(s(s(elem!1)))), s(s(elem!1)))),
% 2.12/2.36 inference(modus_ponens,[status(thm)],[5172, 5171])).
% 2.12/2.36 tff(5174,plain,
% 2.12/2.36 ($false),
% 2.12/2.36 inference(unit_resolution,[status(thm)],[3457, 5173])).
% 2.12/2.36 tff(5175,plain,(b(s(s(s(s(s(z))))), s(s(s(z)))) | (~b(s(s(s(s(elem!1)))), s(s(elem!1)))) | (~(s(s(elem!1)) = s(s(s(z)))))), inference(lemma,lemma(discharge,[]))).
% 2.12/2.36 tff(5176,plain,
% 2.12/2.36 (b(s(s(s(s(s(z))))), s(s(s(z))))),
% 2.12/2.36 inference(unit_resolution,[status(thm)],[5175, 5162, 5093])).
% 2.12/2.36 tff(5177,plain,
% 2.12/2.36 (b(z, s(s(elem!1))) <=> b(z, s(s(s(z))))),
% 2.12/2.36 inference(monotonicity,[status(thm)],[5093])).
% 2.12/2.36 tff(5178,plain,
% 2.12/2.36 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), s(s(s(z))))) | (~r(z, s(s(s(elem!1))))) | (~r(z, s(s(elem!1)))) | (~r(s(s(elem!1)), s(s(s(elem!1))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(elem!1))), s(s(s(z))))) | (~r(z, s(s(s(elem!1))))) | (~r(z, s(s(elem!1)))) | (~r(s(s(elem!1)), s(s(s(elem!1))))))),
% 2.12/2.36 inference(rewrite,[status(thm)],[])).
% 2.12/2.36 tff(5179,plain,
% 2.12/2.36 (((~r(s(s(s(elem!1))), s(s(s(z))))) | (~r(s(s(elem!1)), s(s(s(elem!1))))) | (~r(z, s(s(s(elem!1))))) | (~r(z, s(s(elem!1))))) <=> ((~r(s(s(s(elem!1))), s(s(s(z))))) | (~r(z, s(s(s(elem!1))))) | (~r(z, s(s(elem!1)))) | (~r(s(s(elem!1)), s(s(s(elem!1))))))),
% 2.12/2.36 inference(rewrite,[status(thm)],[])).
% 2.12/2.36 tff(5180,plain,
% 2.12/2.36 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), s(s(s(z))))) | (~r(s(s(elem!1)), s(s(s(elem!1))))) | (~r(z, s(s(s(elem!1))))) | (~r(z, s(s(elem!1)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), s(s(s(z))))) | (~r(z, s(s(s(elem!1))))) | (~r(z, s(s(elem!1)))) | (~r(s(s(elem!1)), s(s(s(elem!1)))))))),
% 2.12/2.36 inference(monotonicity,[status(thm)],[5179])).
% 2.12/2.36 tff(5181,plain,
% 2.12/2.36 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), s(s(s(z))))) | (~r(s(s(elem!1)), s(s(s(elem!1))))) | (~r(z, s(s(s(elem!1))))) | (~r(z, s(s(elem!1)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(elem!1))), s(s(s(z))))) | (~r(z, s(s(s(elem!1))))) | (~r(z, s(s(elem!1)))) | (~r(s(s(elem!1)), s(s(s(elem!1))))))),
% 2.12/2.36 inference(transitivity,[status(thm)],[5180, 5178])).
% 2.12/2.36 tff(5182,plain,
% 2.12/2.36 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), s(s(s(z))))) | (~r(s(s(elem!1)), s(s(s(elem!1))))) | (~r(z, s(s(s(elem!1))))) | (~r(z, s(s(elem!1)))))),
% 2.12/2.36 inference(quant_inst,[status(thm)],[])).
% 2.12/2.36 tff(5183,plain,
% 2.12/2.36 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(elem!1))), s(s(s(z))))) | (~r(z, s(s(s(elem!1))))) | (~r(z, s(s(elem!1)))) | (~r(s(s(elem!1)), s(s(s(elem!1)))))),
% 2.12/2.36 inference(modus_ponens,[status(thm)],[5182, 5181])).
% 2.12/2.36 tff(5184,plain,
% 2.12/2.36 (~r(z, s(s(elem!1)))),
% 2.12/2.36 inference(unit_resolution,[status(thm)],[5183, 197, 4589, 282, 5114])).
% 2.12/2.36 tff(5185,plain,
% 2.12/2.36 (b(z, s(s(elem!1)))),
% 2.12/2.36 inference(unit_resolution,[status(thm)],[1795, 5184])).
% 2.12/2.36 tff(5186,plain,
% 2.12/2.36 (b(z, s(s(s(z))))),
% 2.12/2.36 inference(modus_ponens,[status(thm)],[5185, 5177])).
% 2.12/2.36 tff(5187,plain,
% 2.12/2.36 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), s(s(z)))) | (~b(z, s(s(s(z))))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(s(s(s(z))))), z)) | (~b(s(s(s(s(s(z))))), s(s(s(z))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(z))), s(s(z)))) | (~b(z, s(s(s(z))))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(s(s(s(z))))), z)) | (~b(s(s(s(s(s(z))))), s(s(s(z))))))),
% 2.12/2.36 inference(rewrite,[status(thm)],[])).
% 2.12/2.36 tff(5188,plain,
% 2.12/2.36 (((~b(s(s(z)), s(s(s(z))))) | (~b(s(s(s(s(s(z))))), s(s(s(z))))) | (~b(s(s(s(z))), s(s(z)))) | (~b(z, s(s(s(z))))) | (~b(s(s(s(s(s(z))))), s(s(s(z))))) | (~b(s(s(s(s(s(z))))), z))) <=> ((~b(s(s(s(z))), s(s(z)))) | (~b(z, s(s(s(z))))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(s(s(s(z))))), z)) | (~b(s(s(s(s(s(z))))), s(s(s(z))))))),
% 2.12/2.36 inference(rewrite,[status(thm)],[])).
% 2.12/2.36 tff(5189,plain,
% 2.12/2.36 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), s(s(s(z))))) | (~b(s(s(s(s(s(z))))), s(s(s(z))))) | (~b(s(s(s(z))), s(s(z)))) | (~b(z, s(s(s(z))))) | (~b(s(s(s(s(s(z))))), s(s(s(z))))) | (~b(s(s(s(s(s(z))))), z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), s(s(z)))) | (~b(z, s(s(s(z))))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(s(s(s(z))))), z)) | (~b(s(s(s(s(s(z))))), s(s(s(z)))))))),
% 2.12/2.36 inference(monotonicity,[status(thm)],[5188])).
% 2.12/2.36 tff(5190,plain,
% 2.12/2.36 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), s(s(s(z))))) | (~b(s(s(s(s(s(z))))), s(s(s(z))))) | (~b(s(s(s(z))), s(s(z)))) | (~b(z, s(s(s(z))))) | (~b(s(s(s(s(s(z))))), s(s(s(z))))) | (~b(s(s(s(s(s(z))))), z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(z))), s(s(z)))) | (~b(z, s(s(s(z))))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(s(s(s(z))))), z)) | (~b(s(s(s(s(s(z))))), s(s(s(z))))))),
% 2.12/2.36 inference(transitivity,[status(thm)],[5189, 5187])).
% 2.12/2.36 tff(5191,plain,
% 2.12/2.36 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), s(s(s(z))))) | (~b(s(s(s(s(s(z))))), s(s(s(z))))) | (~b(s(s(s(z))), s(s(z)))) | (~b(z, s(s(s(z))))) | (~b(s(s(s(s(s(z))))), s(s(s(z))))) | (~b(s(s(s(s(s(z))))), z)))),
% 2.12/2.36 inference(quant_inst,[status(thm)],[])).
% 2.12/2.36 tff(5192,plain,
% 2.12/2.36 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(z))), s(s(z)))) | (~b(z, s(s(s(z))))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(s(s(s(z))))), z)) | (~b(s(s(s(s(s(z))))), s(s(s(z)))))),
% 2.12/2.36 inference(modus_ponens,[status(thm)],[5191, 5190])).
% 2.12/2.36 tff(5193,plain,
% 2.12/2.36 (~b(s(s(s(s(s(z))))), z)),
% 2.12/2.36 inference(unit_resolution,[status(thm)],[5192, 166, 986, 987, 5186, 5176])).
% 2.12/2.36 tff(5194,plain,
% 2.12/2.36 ((~![X: $i] : (~(s(X) = z))) | (~(s(s(s(s(s(z))))) = z))),
% 2.12/2.36 inference(quant_inst,[status(thm)],[])).
% 2.12/2.36 tff(5195,plain,
% 2.12/2.36 (~(s(s(s(s(s(z))))) = z)),
% 2.12/2.36 inference(unit_resolution,[status(thm)],[5194, 65])).
% 2.12/2.36 tff(5196,plain,
% 2.12/2.36 (((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((s(s(s(s(s(z))))) = z) | b(s(s(s(s(s(z))))), z) | r(s(s(s(s(s(z))))), z))) <=> ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (s(s(s(s(s(z))))) = z) | b(s(s(s(s(s(z))))), z) | r(s(s(s(s(s(z))))), z))),
% 2.12/2.36 inference(rewrite,[status(thm)],[])).
% 2.12/2.36 tff(5197,plain,
% 2.12/2.36 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((s(s(s(s(s(z))))) = z) | b(s(s(s(s(s(z))))), z) | r(s(s(s(s(s(z))))), z))),
% 2.12/2.36 inference(quant_inst,[status(thm)],[])).
% 2.12/2.36 tff(5198,plain,
% 2.12/2.36 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (s(s(s(s(s(z))))) = z) | b(s(s(s(s(s(z))))), z) | r(s(s(s(s(s(z))))), z)),
% 2.12/2.36 inference(modus_ponens,[status(thm)],[5197, 5196])).
% 2.12/2.36 tff(5199,plain,
% 2.12/2.36 (r(s(s(s(s(s(z))))), z)),
% 2.12/2.36 inference(unit_resolution,[status(thm)],[5198, 79, 5195, 5193])).
% 2.12/2.36 tff(5200,plain,
% 2.12/2.36 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(z)), z)) | (~r(z, s(s(z)))) | (~r(s(s(z)), s(s(s(s(s(z))))))) | (~r(s(s(s(s(s(z))))), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(z)), z)) | (~r(z, s(s(z)))) | (~r(s(s(z)), s(s(s(s(s(z))))))) | (~r(s(s(s(s(s(z))))), z)))),
% 2.12/2.36 inference(rewrite,[status(thm)],[])).
% 2.12/2.36 tff(5201,plain,
% 2.12/2.36 (((~r(z, s(s(z)))) | (~r(s(s(s(s(s(z))))), z)) | (~r(s(s(z)), z)) | (~r(s(s(z)), s(s(s(s(s(z)))))))) <=> ((~r(s(s(z)), z)) | (~r(z, s(s(z)))) | (~r(s(s(z)), s(s(s(s(s(z))))))) | (~r(s(s(s(s(s(z))))), z)))),
% 2.12/2.36 inference(rewrite,[status(thm)],[])).
% 2.12/2.36 tff(5202,plain,
% 2.12/2.36 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(z)))) | (~r(s(s(s(s(s(z))))), z)) | (~r(s(s(z)), z)) | (~r(s(s(z)), s(s(s(s(s(z))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(z)), z)) | (~r(z, s(s(z)))) | (~r(s(s(z)), s(s(s(s(s(z))))))) | (~r(s(s(s(s(s(z))))), z))))),
% 2.12/2.36 inference(monotonicity,[status(thm)],[5201])).
% 2.12/2.36 tff(5203,plain,
% 2.12/2.36 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(z)))) | (~r(s(s(s(s(s(z))))), z)) | (~r(s(s(z)), z)) | (~r(s(s(z)), s(s(s(s(s(z))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(z)), z)) | (~r(z, s(s(z)))) | (~r(s(s(z)), s(s(s(s(s(z))))))) | (~r(s(s(s(s(s(z))))), z)))),
% 2.12/2.36 inference(transitivity,[status(thm)],[5202, 5200])).
% 2.12/2.36 tff(5204,plain,
% 2.12/2.36 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(z)))) | (~r(s(s(s(s(s(z))))), z)) | (~r(s(s(z)), z)) | (~r(s(s(z)), s(s(s(s(s(z))))))))),
% 2.12/2.36 inference(quant_inst,[status(thm)],[])).
% 2.12/2.36 tff(5205,plain,
% 2.12/2.36 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(z)), z)) | (~r(z, s(s(z)))) | (~r(s(s(z)), s(s(s(s(s(z))))))) | (~r(s(s(s(s(s(z))))), z))),
% 2.12/2.36 inference(modus_ponens,[status(thm)],[5204, 5203])).
% 2.12/2.36 tff(5206,plain,
% 2.12/2.36 (~r(s(s(z)), s(s(s(s(s(z))))))),
% 2.12/2.36 inference(unit_resolution,[status(thm)],[5205, 197, 155, 866, 5199])).
% 2.12/2.36 tff(5207,plain,
% 2.12/2.36 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), s(s(z)))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(z)), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), s(s(s(z))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(z)), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), s(s(s(z))))))),
% 2.12/2.36 inference(rewrite,[status(thm)],[])).
% 2.12/2.36 tff(5208,plain,
% 2.12/2.36 (((~b(s(s(z)), s(s(s(z))))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(s(s(s(s(z))))), s(s(s(z))))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(z)), s(s(s(s(s(z)))))))) <=> ((~b(s(s(s(z))), s(s(z)))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(z)), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), s(s(s(z))))))),
% 2.12/2.36 inference(rewrite,[status(thm)],[])).
% 2.12/2.37 tff(5209,plain,
% 2.12/2.37 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), s(s(s(z))))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(s(s(s(s(z))))), s(s(s(z))))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(z)), s(s(s(s(s(z))))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), s(s(z)))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(z)), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), s(s(s(z)))))))),
% 2.12/2.37 inference(monotonicity,[status(thm)],[5208])).
% 2.12/2.37 tff(5210,plain,
% 2.12/2.37 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), s(s(s(z))))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(s(s(s(s(z))))), s(s(s(z))))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(z)), s(s(s(s(s(z))))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(z)), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), s(s(s(z))))))),
% 2.12/2.37 inference(transitivity,[status(thm)],[5209, 5207])).
% 2.12/2.37 tff(5211,plain,
% 2.12/2.37 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), s(s(s(z))))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(s(s(s(s(z))))), s(s(s(z))))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(z)), s(s(s(s(s(z))))))))),
% 2.12/2.37 inference(quant_inst,[status(thm)],[])).
% 2.12/2.37 tff(5212,plain,
% 2.12/2.37 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(z)), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), s(s(s(z)))))),
% 2.12/2.37 inference(modus_ponens,[status(thm)],[5211, 5210])).
% 2.12/2.37 tff(5213,plain,
% 2.12/2.37 (~b(s(s(z)), s(s(s(s(s(z))))))),
% 2.12/2.37 inference(unit_resolution,[status(thm)],[5212, 166, 986, 987, 5176])).
% 2.12/2.37 tff(5214,plain,
% 2.12/2.37 (((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((s(s(z)) = s(s(s(s(s(z)))))) | b(s(s(z)), s(s(s(s(s(z)))))) | r(s(s(z)), s(s(s(s(s(z)))))))) <=> ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (s(s(z)) = s(s(s(s(s(z)))))) | b(s(s(z)), s(s(s(s(s(z)))))) | r(s(s(z)), s(s(s(s(s(z)))))))),
% 2.12/2.37 inference(rewrite,[status(thm)],[])).
% 2.12/2.37 tff(5215,plain,
% 2.12/2.37 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((s(s(z)) = s(s(s(s(s(z)))))) | b(s(s(z)), s(s(s(s(s(z)))))) | r(s(s(z)), s(s(s(s(s(z)))))))),
% 2.12/2.37 inference(quant_inst,[status(thm)],[])).
% 2.12/2.37 tff(5216,plain,
% 2.12/2.37 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (s(s(z)) = s(s(s(s(s(z)))))) | b(s(s(z)), s(s(s(s(s(z)))))) | r(s(s(z)), s(s(s(s(s(z))))))),
% 2.12/2.37 inference(modus_ponens,[status(thm)],[5215, 5214])).
% 2.12/2.37 tff(5217,plain,
% 2.12/2.37 ((s(s(z)) = s(s(s(s(s(z)))))) | r(s(s(z)), s(s(s(s(s(z))))))),
% 2.12/2.37 inference(unit_resolution,[status(thm)],[5216, 79, 5213])).
% 2.12/2.37 tff(5218,plain,
% 2.12/2.37 ($false),
% 2.12/2.37 inference(unit_resolution,[status(thm)],[5217, 5206, 5101])).
% 2.12/2.37 tff(5219,plain,((s(s(z)) = s(s(elem!1))) | (~r(z, s(s(z)))) | (~r(s(s(z)), z)) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(s(z))), s(s(z)))) | (~r(s(z), s(s(elem!1)))) | (~r(s(s(elem!1)), s(z))) | (~r(s(z), s(s(z)))) | (~b(s(s(s(elem!1))), s(z))) | r(s(s(elem!1)), s(s(s(z)))) | (~r(z, s(s(s(elem!1))))) | (s(s(elem!1)) = s(s(s(elem!1)))) | r(s(s(z)), s(s(s(elem!1)))) | r(s(s(s(elem!1))), s(s(z))) | b(s(s(s(elem!1))), s(s(s(z)))) | r(s(s(elem!1)), s(s(z))) | r(s(s(z)), s(s(elem!1)))), inference(lemma,lemma(discharge,[]))).
% 2.12/2.37 tff(5220,plain,
% 2.12/2.37 (s(s(z)) = s(s(elem!1))),
% 2.12/2.37 inference(unit_resolution,[status(thm)],[5219, 5080, 155, 5054, 5065, 311, 4577, 120, 96, 5063, 4575, 45, 5056, 4576, 5055, 4579, 4578])).
% 2.12/2.37 tff(5221,plain,
% 2.12/2.37 (s(s(s(z))) = s(s(s(elem!1)))),
% 2.12/2.37 inference(monotonicity,[status(thm)],[5220])).
% 2.12/2.37 tff(5222,plain,
% 2.12/2.37 (b(s(s(s(z))), elem!1) <=> b(s(s(s(elem!1))), elem!1)),
% 2.12/2.37 inference(monotonicity,[status(thm)],[5221])).
% 2.12/2.37 tff(5223,plain,
% 2.12/2.37 (b(s(s(s(elem!1))), elem!1) <=> b(s(s(s(z))), elem!1)),
% 2.12/2.37 inference(symmetry,[status(thm)],[5222])).
% 2.12/2.37 tff(5224,plain,
% 2.12/2.37 ((~b(s(s(s(elem!1))), elem!1)) <=> (~b(s(s(s(z))), elem!1))),
% 2.12/2.37 inference(monotonicity,[status(thm)],[5223])).
% 2.12/2.37 tff(5225,plain,
% 2.12/2.37 (s(elem!1) = s(z)),
% 2.12/2.37 inference(unit_resolution,[status(thm)],[43, 5220])).
% 2.12/2.37 tff(5226,plain,
% 2.12/2.37 (z = elem!1),
% 2.12/2.37 inference(unit_resolution,[status(thm)],[30, 5225])).
% 2.12/2.37 tff(5227,plain,
% 2.12/2.37 (b(s(s(s(elem!1))), z) <=> b(s(s(s(elem!1))), elem!1)),
% 2.12/2.37 inference(monotonicity,[status(thm)],[5226])).
% 2.12/2.37 tff(5228,plain,
% 2.12/2.37 ((~b(s(s(s(elem!1))), z)) <=> (~b(s(s(s(elem!1))), elem!1))),
% 2.12/2.37 inference(monotonicity,[status(thm)],[5227])).
% 2.12/2.37 tff(5229,plain,
% 2.12/2.37 (~b(s(s(s(elem!1))), elem!1)),
% 2.12/2.37 inference(modus_ponens,[status(thm)],[87, 5228])).
% 2.12/2.37 tff(5230,plain,
% 2.12/2.37 (~b(s(s(s(z))), elem!1)),
% 2.12/2.37 inference(modus_ponens,[status(thm)],[5229, 5224])).
% 2.12/2.37 tff(5231,plain,
% 2.12/2.37 (b(s(s(s(z))), z) <=> b(s(s(s(z))), elem!1)),
% 2.12/2.37 inference(monotonicity,[status(thm)],[5226])).
% 2.12/2.37 tff(5232,plain,
% 2.12/2.37 (b(s(s(s(z))), elem!1)),
% 2.12/2.37 inference(modus_ponens,[status(thm)],[5041, 5231])).
% 2.12/2.37 tff(5233,plain,
% 2.12/2.37 ($false),
% 2.12/2.37 inference(unit_resolution,[status(thm)],[5232, 5230])).
% 2.12/2.37 tff(5234,plain,((~r(s(z), s(s(z)))) | b(s(s(s(elem!1))), z) | (~r(z, s(s(z)))) | (~r(s(z), s(s(elem!1)))) | (~r(s(s(elem!1)), s(z))) | (~b(s(s(s(elem!1))), s(z))) | (s(s(elem!1)) = s(s(s(elem!1)))) | (~b(z, s(z))) | (~b(s(z), z))), inference(lemma,lemma(discharge,[]))).
% 2.12/2.37 tff(5235,plain,
% 2.12/2.37 (~r(s(z), s(s(z)))),
% 2.12/2.37 inference(unit_resolution,[status(thm)],[5234, 53, 155, 85, 4577, 96, 45, 118, 87])).
% 2.12/2.37 tff(5236,plain,
% 2.12/2.37 (b(s(z), s(s(z)))),
% 2.12/2.37 inference(unit_resolution,[status(thm)],[427, 5235])).
% 2.12/2.37 tff(5237,plain,
% 2.12/2.37 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), z)) | (~r(z, s(s(s(elem!1))))) | (~r(s(s(z)), z)) | (~r(s(s(z)), s(s(s(elem!1))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(elem!1))), z)) | (~r(z, s(s(s(elem!1))))) | (~r(s(s(z)), z)) | (~r(s(s(z)), s(s(s(elem!1))))))),
% 2.12/2.37 inference(rewrite,[status(thm)],[])).
% 2.12/2.37 tff(5238,plain,
% 2.12/2.37 (((~r(z, s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), z)) | (~r(s(s(z)), z)) | (~r(s(s(z)), s(s(s(elem!1)))))) <=> ((~r(s(s(s(elem!1))), z)) | (~r(z, s(s(s(elem!1))))) | (~r(s(s(z)), z)) | (~r(s(s(z)), s(s(s(elem!1))))))),
% 2.12/2.37 inference(rewrite,[status(thm)],[])).
% 2.12/2.37 tff(5239,plain,
% 2.12/2.37 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), z)) | (~r(s(s(z)), z)) | (~r(s(s(z)), s(s(s(elem!1))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), z)) | (~r(z, s(s(s(elem!1))))) | (~r(s(s(z)), z)) | (~r(s(s(z)), s(s(s(elem!1)))))))),
% 2.12/2.37 inference(monotonicity,[status(thm)],[5238])).
% 2.12/2.37 tff(5240,plain,
% 2.12/2.37 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), z)) | (~r(s(s(z)), z)) | (~r(s(s(z)), s(s(s(elem!1))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(elem!1))), z)) | (~r(z, s(s(s(elem!1))))) | (~r(s(s(z)), z)) | (~r(s(s(z)), s(s(s(elem!1))))))),
% 2.12/2.37 inference(transitivity,[status(thm)],[5239, 5237])).
% 2.12/2.37 tff(5241,plain,
% 2.12/2.37 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), z)) | (~r(s(s(z)), z)) | (~r(s(s(z)), s(s(s(elem!1))))))),
% 2.12/2.37 inference(quant_inst,[status(thm)],[])).
% 2.12/2.37 tff(5242,plain,
% 2.12/2.37 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(elem!1))), z)) | (~r(z, s(s(s(elem!1))))) | (~r(s(s(z)), z)) | (~r(s(s(z)), s(s(s(elem!1)))))),
% 2.12/2.37 inference(modus_ponens,[status(thm)],[5241, 5240])).
% 2.12/2.37 tff(5243,plain,
% 2.12/2.37 (~r(s(s(z)), s(s(s(elem!1))))),
% 2.12/2.37 inference(unit_resolution,[status(thm)],[5242, 197, 154, 4575, 866])).
% 2.12/2.37 tff(5244,plain,
% 2.12/2.37 (b(s(s(z)), s(s(s(elem!1))))),
% 2.12/2.37 inference(unit_resolution,[status(thm)],[277, 79, 5243, 209])).
% 2.12/2.37 tff(5245,plain,
% 2.12/2.37 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), s(s(z)))) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(z), s(s(z)))) | (~b(s(s(z)), s(s(s(elem!1))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(elem!1))), s(s(z)))) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(z), s(s(z)))) | (~b(s(s(z)), s(s(s(elem!1))))))),
% 2.12/2.37 inference(rewrite,[status(thm)],[])).
% 2.12/2.37 tff(5246,plain,
% 2.12/2.37 (((~b(s(s(s(elem!1))), s(z))) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(s(z)), s(s(s(elem!1))))) | (~b(s(z), s(s(z)))) | (~b(s(s(s(elem!1))), s(s(z)))) | (~b(s(s(s(elem!1))), s(z)))) <=> ((~b(s(s(s(elem!1))), s(s(z)))) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(z), s(s(z)))) | (~b(s(s(z)), s(s(s(elem!1))))))),
% 2.12/2.37 inference(rewrite,[status(thm)],[])).
% 2.12/2.37 tff(5247,plain,
% 2.12/2.37 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), s(z))) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(s(z)), s(s(s(elem!1))))) | (~b(s(z), s(s(z)))) | (~b(s(s(s(elem!1))), s(s(z)))) | (~b(s(s(s(elem!1))), s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), s(s(z)))) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(z), s(s(z)))) | (~b(s(s(z)), s(s(s(elem!1)))))))),
% 2.12/2.37 inference(monotonicity,[status(thm)],[5246])).
% 2.12/2.37 tff(5248,plain,
% 2.12/2.37 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), s(z))) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(s(z)), s(s(s(elem!1))))) | (~b(s(z), s(s(z)))) | (~b(s(s(s(elem!1))), s(s(z)))) | (~b(s(s(s(elem!1))), s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(elem!1))), s(s(z)))) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(z), s(s(z)))) | (~b(s(s(z)), s(s(s(elem!1))))))),
% 2.12/2.37 inference(transitivity,[status(thm)],[5247, 5245])).
% 2.12/2.37 tff(5249,plain,
% 2.12/2.37 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), s(z))) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(s(z)), s(s(s(elem!1))))) | (~b(s(z), s(s(z)))) | (~b(s(s(s(elem!1))), s(s(z)))) | (~b(s(s(s(elem!1))), s(z))))),
% 2.12/2.37 inference(quant_inst,[status(thm)],[])).
% 2.12/2.37 tff(5250,plain,
% 2.12/2.37 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(elem!1))), s(s(z)))) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(z), s(s(z)))) | (~b(s(s(z)), s(s(s(elem!1)))))),
% 2.12/2.37 inference(modus_ponens,[status(thm)],[5249, 5248])).
% 2.12/2.37 tff(5251,plain,
% 2.12/2.37 (~b(s(s(s(elem!1))), s(s(z)))),
% 2.12/2.37 inference(unit_resolution,[status(thm)],[5250, 166, 556, 96, 5244])).
% 2.12/2.37 tff(5252,plain,
% 2.12/2.37 ($false),
% 2.12/2.37 inference(unit_resolution,[status(thm)],[491, 5251, 490])).
% 2.12/2.37 tff(5253,plain,((~b(s(s(s(elem!1))), s(z))) | r(s(s(s(elem!1))), s(s(z))) | (~b(s(z), s(s(z)))) | (~r(s(s(s(elem!1))), z)) | (~r(s(s(z)), z)) | (~b(s(z), z)) | (~b(z, s(z)))), inference(lemma,lemma(discharge,[]))).
% 2.12/2.37 tff(5254,plain,
% 2.12/2.37 (~r(s(s(z)), z)),
% 2.12/2.37 inference(unit_resolution,[status(thm)],[5253, 5236, 118, 53, 4576, 96, 153])).
% 2.12/2.37 tff(5255,plain,
% 2.12/2.37 (~r(s(s(z)), s(s(elem!1)))),
% 2.12/2.37 inference(unit_resolution,[status(thm)],[4561, 197, 85, 4577, 4573])).
% 2.12/2.37 tff(5256,plain,
% 2.12/2.37 (~r(s(s(elem!1)), s(s(z)))),
% 2.12/2.37 inference(unit_resolution,[status(thm)],[4565, 197, 85, 4577, 4573])).
% 2.12/2.37 tff(5257,plain,
% 2.12/2.37 (~(s(s(z)) = s(s(elem!1)))),
% 2.12/2.37 inference(unit_resolution,[status(thm)],[4398, 5236, 54])).
% 2.12/2.37 tff(5258,plain,
% 2.12/2.37 (~b(s(s(z)), z)),
% 2.12/2.37 inference(unit_resolution,[status(thm)],[4607, 5257, 153, 4575, 45, 5056, 4576, 5256, 5255])).
% 2.12/2.37 tff(5259,plain,
% 2.12/2.37 ($false),
% 2.12/2.37 inference(unit_resolution,[status(thm)],[186, 5258, 5254])).
% 2.12/2.37 tff(5260,plain,((~b(s(z), z)) | (s(s(elem!1)) = s(s(s(elem!1)))) | (~b(z, s(z))) | (~b(s(s(s(elem!1))), s(z))) | b(s(z), s(s(elem!1))) | (~r(z, s(s(z)))) | (~r(s(s(elem!1)), s(z))) | b(s(s(s(elem!1))), z)), inference(lemma,lemma(discharge,[]))).
% 2.12/2.37 tff(5261,plain,
% 2.12/2.37 (~b(s(z), z)),
% 2.12/2.37 inference(unit_resolution,[status(thm)],[5260, 4571, 118, 96, 54, 152, 4558, 87])).
% 2.12/2.37 tff(5262,plain,
% 2.12/2.37 (r(s(z), z)),
% 2.12/2.37 inference(unit_resolution,[status(thm)],[230, 5261])).
% 2.12/2.37 tff(5263,plain,
% 2.12/2.37 (~r(s(z), s(s(s(elem!1))))),
% 2.12/2.37 inference(unit_resolution,[status(thm)],[237, 197, 153, 152, 5262])).
% 2.12/2.37 tff(5264,plain,
% 2.12/2.37 (b(s(z), s(s(s(elem!1))))),
% 2.12/2.37 inference(unit_resolution,[status(thm)],[116, 5263])).
% 2.12/2.37 tff(5265,plain,
% 2.12/2.37 (~b(z, s(s(s(elem!1))))),
% 2.12/2.37 inference(unit_resolution,[status(thm)],[249, 5264, 118, 96])).
% 2.12/2.37 tff(5266,plain,
% 2.12/2.37 (r(z, s(s(s(elem!1))))),
% 2.12/2.37 inference(unit_resolution,[status(thm)],[261, 5265])).
% 2.12/2.37 tff(5267,plain,
% 2.12/2.37 (~r(s(s(s(elem!1))), s(s(z)))),
% 2.12/2.37 inference(unit_resolution,[status(thm)],[1588, 5266, 152, 309])).
% 2.12/2.37 tff(5268,plain,
% 2.12/2.37 (~r(s(s(z)), s(s(s(elem!1))))),
% 2.12/2.37 inference(unit_resolution,[status(thm)],[290, 5266, 152, 153])).
% 2.12/2.37 tff(5269,plain,
% 2.12/2.37 (~r(s(s(z)), z)),
% 2.12/2.37 inference(unit_resolution,[status(thm)],[4287, 5262, 152, 309])).
% 2.12/2.37 tff(5270,plain,
% 2.12/2.37 (b(s(s(z)), z)),
% 2.12/2.37 inference(unit_resolution,[status(thm)],[186, 5269])).
% 2.12/2.37 tff(5271,plain,
% 2.12/2.37 (s(s(z)) = s(s(elem!1))),
% 2.12/2.37 inference(unit_resolution,[status(thm)],[4607, 5266, 153, 5270, 4571, 5268, 5267, 4566, 4562])).
% 2.12/2.37 tff(5272,plain,
% 2.12/2.37 (s(elem!1) = s(z)),
% 2.12/2.37 inference(unit_resolution,[status(thm)],[43, 5271])).
% 2.12/2.37 tff(5273,plain,
% 2.12/2.37 (z = elem!1),
% 2.12/2.37 inference(unit_resolution,[status(thm)],[30, 5272])).
% 2.12/2.37 tff(5274,plain,
% 2.12/2.37 (r(z, s(s(elem!1))) <=> r(elem!1, s(s(elem!1)))),
% 2.12/2.37 inference(monotonicity,[status(thm)],[5273])).
% 2.12/2.37 tff(5275,plain,
% 2.12/2.37 (~b(z, s(s(elem!1)))),
% 2.12/2.37 inference(unit_resolution,[status(thm)],[2261, 5271, 125])).
% 2.12/2.37 tff(5276,plain,
% 2.12/2.37 (r(z, s(s(elem!1)))),
% 2.12/2.37 inference(unit_resolution,[status(thm)],[1795, 5275])).
% 2.12/2.37 tff(5277,plain,
% 2.12/2.37 (r(elem!1, s(s(elem!1)))),
% 2.12/2.37 inference(modus_ponens,[status(thm)],[5276, 5274])).
% 2.12/2.37 tff(5278,plain,
% 2.12/2.37 (r(s(z), z) <=> r(s(z), elem!1)),
% 2.12/2.37 inference(monotonicity,[status(thm)],[5273])).
% 2.12/2.37 tff(5279,plain,
% 2.12/2.37 (r(s(z), elem!1)),
% 2.12/2.37 inference(modus_ponens,[status(thm)],[5262, 5278])).
% 2.12/2.37 tff(5280,plain,
% 2.12/2.37 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(s(elem!1)))) | (~r(s(z), s(s(elem!1)))) | (~r(s(z), elem!1)) | (~r(s(s(elem!1)), s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(elem!1, s(s(elem!1)))) | (~r(s(z), s(s(elem!1)))) | (~r(s(z), elem!1)) | (~r(s(s(elem!1)), s(z))))),
% 2.12/2.37 inference(rewrite,[status(thm)],[])).
% 2.12/2.37 tff(5281,plain,
% 2.12/2.37 (((~r(s(s(elem!1)), s(z))) | (~r(elem!1, s(s(elem!1)))) | (~r(s(z), s(s(elem!1)))) | (~r(s(z), elem!1))) <=> ((~r(elem!1, s(s(elem!1)))) | (~r(s(z), s(s(elem!1)))) | (~r(s(z), elem!1)) | (~r(s(s(elem!1)), s(z))))),
% 2.12/2.37 inference(rewrite,[status(thm)],[])).
% 2.12/2.37 tff(5282,plain,
% 2.12/2.37 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(elem!1)), s(z))) | (~r(elem!1, s(s(elem!1)))) | (~r(s(z), s(s(elem!1)))) | (~r(s(z), elem!1)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(s(elem!1)))) | (~r(s(z), s(s(elem!1)))) | (~r(s(z), elem!1)) | (~r(s(s(elem!1)), s(z)))))),
% 2.12/2.37 inference(monotonicity,[status(thm)],[5281])).
% 2.12/2.37 tff(5283,plain,
% 2.12/2.37 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(elem!1)), s(z))) | (~r(elem!1, s(s(elem!1)))) | (~r(s(z), s(s(elem!1)))) | (~r(s(z), elem!1)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(elem!1, s(s(elem!1)))) | (~r(s(z), s(s(elem!1)))) | (~r(s(z), elem!1)) | (~r(s(s(elem!1)), s(z))))),
% 2.12/2.37 inference(transitivity,[status(thm)],[5282, 5280])).
% 2.12/2.37 tff(5284,plain,
% 2.12/2.37 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(elem!1)), s(z))) | (~r(elem!1, s(s(elem!1)))) | (~r(s(z), s(s(elem!1)))) | (~r(s(z), elem!1)))),
% 2.12/2.37 inference(quant_inst,[status(thm)],[])).
% 2.12/2.37 tff(5285,plain,
% 2.12/2.37 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(elem!1, s(s(elem!1)))) | (~r(s(z), s(s(elem!1)))) | (~r(s(z), elem!1)) | (~r(s(s(elem!1)), s(z)))),
% 2.12/2.37 inference(modus_ponens,[status(thm)],[5284, 5283])).
% 2.12/2.37 tff(5286,plain,
% 2.12/2.37 ($false),
% 2.12/2.37 inference(unit_resolution,[status(thm)],[5285, 197, 85, 4558, 5279, 5277])).
% 2.12/2.37 tff(5287,plain,(b(s(z), s(s(elem!1))) | b(z, s(s(z))) | (~b(z, s(z))) | (~b(s(s(s(elem!1))), s(z))) | b(s(s(s(elem!1))), z)), inference(lemma,lemma(discharge,[]))).
% 2.12/2.37 tff(5288,plain,
% 2.12/2.37 (b(s(z), s(s(elem!1)))),
% 2.12/2.37 inference(unit_resolution,[status(thm)],[5287, 96, 118, 125, 87])).
% 2.12/2.37 tff(5289,plain,
% 2.12/2.37 (~r(s(z), z)),
% 2.12/2.37 inference(unit_resolution,[status(thm)],[4287, 866, 155, 4582])).
% 2.12/2.37 tff(5290,plain,
% 2.12/2.37 (b(s(z), z)),
% 2.12/2.37 inference(unit_resolution,[status(thm)],[230, 5289])).
% 2.12/2.37 tff(5291,plain,
% 2.12/2.37 (~b(s(s(elem!1)), s(z))),
% 2.12/2.37 inference(unit_resolution,[status(thm)],[4277, 5290, 96, 118, 45])).
% 2.12/2.37 tff(5292,plain,
% 2.12/2.37 (r(s(s(elem!1)), s(z))),
% 2.12/2.37 inference(unit_resolution,[status(thm)],[1912, 5291])).
% 2.12/2.37 tff(5293,plain,
% 2.12/2.37 (r(s(s(s(elem!1))), s(s(z)))),
% 2.12/2.37 inference(unit_resolution,[status(thm)],[5253, 5290, 118, 556, 866, 96, 154])).
% 2.12/2.37 tff(5294,plain,
% 2.12/2.37 (~r(z, s(s(s(elem!1))))),
% 2.12/2.37 inference(unit_resolution,[status(thm)],[1588, 5293, 155, 4582])).
% 2.12/2.37 tff(5295,plain,
% 2.12/2.37 (b(z, s(s(s(elem!1))))),
% 2.12/2.37 inference(unit_resolution,[status(thm)],[261, 5294])).
% 2.12/2.37 tff(5296,plain,
% 2.12/2.37 (~b(s(z), s(s(s(elem!1))))),
% 2.12/2.37 inference(unit_resolution,[status(thm)],[249, 5295, 118, 96])).
% 2.12/2.37 tff(5297,plain,
% 2.12/2.37 (r(s(z), s(s(s(elem!1))))),
% 2.12/2.37 inference(unit_resolution,[status(thm)],[116, 5296])).
% 2.12/2.37 tff(5298,plain,
% 2.12/2.37 (~r(s(s(z)), s(s(elem!1)))),
% 2.12/2.37 inference(unit_resolution,[status(thm)],[526, 5293, 155, 154])).
% 2.12/2.37 tff(5299,plain,
% 2.12/2.37 ($false),
% 2.12/2.37 inference(unit_resolution,[status(thm)],[558, 3964, 2516, 376, 556])).
% 2.12/2.37 tff(5300,plain,((s(s(z)) = s(s(elem!1))) | (~b(s(z), s(s(elem!1)))) | (~b(s(z), s(s(z)))) | r(s(s(elem!1)), s(s(z))) | r(s(s(z)), s(s(elem!1)))), inference(lemma,lemma(discharge,[]))).
% 2.12/2.37 tff(5301,plain,
% 2.12/2.37 (r(s(s(elem!1)), s(s(z)))),
% 2.12/2.37 inference(unit_resolution,[status(thm)],[5300, 5298, 376, 52, 556])).
% 2.12/2.37 tff(5302,plain,
% 2.12/2.37 (~r(s(s(s(elem!1))), s(s(elem!1)))),
% 2.12/2.37 inference(unit_resolution,[status(thm)],[4313, 5301, 4582, 5293])).
% 2.12/2.37 tff(5303,plain,
% 2.12/2.37 (~r(z, s(s(elem!1)))),
% 2.12/2.37 inference(unit_resolution,[status(thm)],[401, 5301, 155, 4582])).
% 2.12/2.37 tff(5304,plain,
% 2.12/2.37 (b(z, s(s(elem!1)))),
% 2.12/2.37 inference(unit_resolution,[status(thm)],[1795, 5303])).
% 2.12/2.37 tff(5305,plain,
% 2.12/2.37 (r(s(s(elem!1)), s(s(s(elem!1))))),
% 2.12/2.37 inference(unit_resolution,[status(thm)],[1834, 5304, 45, 5302, 5295])).
% 2.12/2.37 tff(5306,plain,
% 2.12/2.37 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), z)) | (~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, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(elem!1))), z)) | (~r(s(z), s(s(s(elem!1))))) | (~r(s(s(elem!1)), s(s(s(elem!1))))) | (~r(s(s(elem!1)), s(z))))),
% 2.12/2.37 inference(rewrite,[status(thm)],[])).
% 2.12/2.37 tff(5307,plain,
% 2.12/2.37 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), z)) | (~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))))),
% 2.12/2.37 inference(quant_inst,[status(thm)],[])).
% 2.12/2.37 tff(5308,plain,
% 2.12/2.38 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(elem!1))), z)) | (~r(s(z), s(s(s(elem!1))))) | (~r(s(s(elem!1)), s(s(s(elem!1))))) | (~r(s(s(elem!1)), s(z)))),
% 2.12/2.38 inference(modus_ponens,[status(thm)],[5307, 5306])).
% 2.12/2.38 tff(5309,plain,
% 2.12/2.38 ($false),
% 2.12/2.38 inference(unit_resolution,[status(thm)],[5308, 197, 154, 4577, 377, 119])).
% 2.12/2.38 tff(5310,plain,((~r(s(z), s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), z)) | (~r(s(s(elem!1)), s(z))) | (~r(s(s(elem!1)), s(s(s(elem!1)))))), inference(lemma,lemma(discharge,[]))).
% 2.12/2.38 tff(5311,plain,
% 2.12/2.38 ($false),
% 2.12/2.38 inference(unit_resolution,[status(thm)],[5310, 5305, 5297, 154, 5292])).
% 2.12/2.38 tff(5312,plain,((~r(s(s(z)), z)) | (~r(s(s(s(elem!1))), z)) | (s(s(elem!1)) = s(s(s(elem!1)))) | (~b(z, s(z))) | (~b(s(s(s(elem!1))), s(z))) | (~r(z, s(s(z)))) | (~b(s(z), s(s(elem!1)))) | (s(s(z)) = s(s(elem!1))) | (~b(s(z), s(s(z))))), inference(lemma,lemma(discharge,[]))).
% 2.12/2.38 tff(5313,plain,
% 2.12/2.38 (~r(s(s(z)), z)),
% 2.12/2.38 inference(unit_resolution,[status(thm)],[5312, 556, 45, 118, 96, 155, 376, 52, 154])).
% 2.12/2.38 tff(5314,plain,
% 2.12/2.38 (b(s(s(z)), z)),
% 2.12/2.38 inference(unit_resolution,[status(thm)],[186, 5313])).
% 2.12/2.38 tff(5315,plain,
% 2.12/2.38 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), z)) | (~b(s(z), s(s(elem!1)))) | (~b(z, s(z))) | (~b(s(z), s(s(z)))) | (~b(s(s(z)), z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), z)) | (~b(s(z), s(s(elem!1)))) | (~b(z, s(z))) | (~b(s(z), s(s(z)))) | (~b(s(s(z)), z)))),
% 2.12/2.38 inference(rewrite,[status(thm)],[])).
% 2.12/2.38 tff(5316,plain,
% 2.12/2.38 (((~b(s(z), s(s(elem!1)))) | (~b(s(z), s(s(elem!1)))) | (~b(z, s(z))) | (~b(s(s(z)), z)) | (~b(s(z), z)) | (~b(s(z), s(s(z))))) <=> ((~b(s(z), z)) | (~b(s(z), s(s(elem!1)))) | (~b(z, s(z))) | (~b(s(z), s(s(z)))) | (~b(s(s(z)), z)))),
% 2.12/2.38 inference(rewrite,[status(thm)],[])).
% 2.12/2.38 tff(5317,plain,
% 2.12/2.38 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(elem!1)))) | (~b(s(z), s(s(elem!1)))) | (~b(z, s(z))) | (~b(s(s(z)), z)) | (~b(s(z), z)) | (~b(s(z), s(s(z)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), z)) | (~b(s(z), s(s(elem!1)))) | (~b(z, s(z))) | (~b(s(z), s(s(z)))) | (~b(s(s(z)), z))))),
% 2.12/2.38 inference(monotonicity,[status(thm)],[5316])).
% 2.12/2.38 tff(5318,plain,
% 2.12/2.38 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(elem!1)))) | (~b(s(z), s(s(elem!1)))) | (~b(z, s(z))) | (~b(s(s(z)), z)) | (~b(s(z), z)) | (~b(s(z), s(s(z)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), z)) | (~b(s(z), s(s(elem!1)))) | (~b(z, s(z))) | (~b(s(z), s(s(z)))) | (~b(s(s(z)), z)))),
% 2.12/2.38 inference(transitivity,[status(thm)],[5317, 5315])).
% 2.12/2.38 tff(5319,plain,
% 2.12/2.38 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(elem!1)))) | (~b(s(z), s(s(elem!1)))) | (~b(z, s(z))) | (~b(s(s(z)), z)) | (~b(s(z), z)) | (~b(s(z), s(s(z)))))),
% 2.12/2.38 inference(quant_inst,[status(thm)],[])).
% 2.12/2.38 tff(5320,plain,
% 2.12/2.38 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), z)) | (~b(s(z), s(s(elem!1)))) | (~b(z, s(z))) | (~b(s(z), s(s(z)))) | (~b(s(s(z)), z))),
% 2.12/2.38 inference(modus_ponens,[status(thm)],[5319, 5318])).
% 2.12/2.38 tff(5321,plain,
% 2.12/2.38 (~b(s(z), z)),
% 2.12/2.38 inference(unit_resolution,[status(thm)],[5320, 166, 376, 556, 118, 5314])).
% 2.12/2.38 tff(5322,plain,
% 2.12/2.38 (r(s(z), z)),
% 2.12/2.38 inference(unit_resolution,[status(thm)],[230, 5321])).
% 2.12/2.38 tff(5323,plain,
% 2.12/2.38 (~b(s(s(s(elem!1))), s(s(z)))),
% 2.12/2.38 inference(unit_resolution,[status(thm)],[4303, 166, 556, 96, 118, 5314])).
% 2.12/2.38 tff(5324,plain,
% 2.12/2.38 (r(s(s(s(elem!1))), s(s(z)))),
% 2.12/2.38 inference(unit_resolution,[status(thm)],[218, 5323])).
% 2.12/2.38 tff(5325,plain,
% 2.12/2.38 (~r(s(s(z)), s(s(elem!1)))),
% 2.12/2.38 inference(unit_resolution,[status(thm)],[526, 5324, 155, 154])).
% 2.12/2.38 tff(5326,plain,
% 2.12/2.38 (r(s(s(elem!1)), s(s(z)))),
% 2.12/2.38 inference(unit_resolution,[status(thm)],[5300, 5325, 376, 52, 556])).
% 2.12/2.38 tff(5327,plain,
% 2.12/2.38 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), z)) | (~r(s(s(z)), s(z))) | (~r(s(s(elem!1)), s(z))) | (~r(s(s(elem!1)), s(s(z)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(z), z)) | (~r(s(s(z)), s(z))) | (~r(s(s(elem!1)), s(z))) | (~r(s(s(elem!1)), s(s(z)))))),
% 2.12/2.38 inference(rewrite,[status(thm)],[])).
% 2.12/2.38 tff(5328,plain,
% 2.12/2.38 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), z)) | (~r(s(s(z)), s(z))) | (~r(s(s(elem!1)), s(z))) | (~r(s(s(elem!1)), s(s(z)))))),
% 2.12/2.38 inference(quant_inst,[status(thm)],[])).
% 2.12/2.38 tff(5329,plain,
% 2.12/2.38 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(z), z)) | (~r(s(s(z)), s(z))) | (~r(s(s(elem!1)), s(z))) | (~r(s(s(elem!1)), s(s(z))))),
% 2.12/2.38 inference(modus_ponens,[status(thm)],[5328, 5327])).
% 2.12/2.38 tff(5330,plain,
% 2.12/2.38 ($false),
% 2.12/2.38 inference(unit_resolution,[status(thm)],[5329, 197, 393, 4577, 97, 392])).
% 2.12/2.38 tff(5331,plain,((~r(s(s(z)), s(z))) | (~r(s(s(elem!1)), s(s(z)))) | (~r(s(s(elem!1)), s(z))) | (~r(s(z), z))), inference(lemma,lemma(discharge,[]))).
% 2.12/2.38 tff(5332,plain,
% 2.12/2.38 (~r(s(s(elem!1)), s(z))),
% 2.12/2.38 inference(unit_resolution,[status(thm)],[5331, 5326, 4582, 5322])).
% 2.12/2.38 tff(5333,plain,
% 2.12/2.38 (b(s(s(elem!1)), s(z))),
% 2.12/2.38 inference(unit_resolution,[status(thm)],[1912, 5332])).
% 2.12/2.38 tff(5334,plain,
% 2.12/2.38 (~r(z, s(s(elem!1)))),
% 2.12/2.38 inference(unit_resolution,[status(thm)],[401, 5326, 155, 4582])).
% 2.12/2.38 tff(5335,plain,
% 2.12/2.38 (b(z, s(s(elem!1)))),
% 2.12/2.38 inference(unit_resolution,[status(thm)],[1795, 5334])).
% 2.12/2.38 tff(5336,plain,
% 2.12/2.38 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(elem!1)))) | (~b(s(z), s(s(elem!1)))) | (~b(z, s(z))) | (~b(s(s(elem!1)), s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(s(elem!1)))) | (~b(s(z), s(s(elem!1)))) | (~b(z, s(z))) | (~b(s(s(elem!1)), s(z))))),
% 2.12/2.38 inference(rewrite,[status(thm)],[])).
% 2.12/2.38 tff(5337,plain,
% 2.12/2.38 (((~b(s(s(elem!1)), s(z))) | (~b(z, s(z))) | (~b(s(z), s(s(elem!1)))) | (~b(s(s(elem!1)), s(z))) | (~b(z, s(z))) | (~b(z, s(s(elem!1))))) <=> ((~b(z, s(s(elem!1)))) | (~b(s(z), s(s(elem!1)))) | (~b(z, s(z))) | (~b(s(s(elem!1)), s(z))))),
% 2.12/2.38 inference(rewrite,[status(thm)],[])).
% 2.12/2.38 tff(5338,plain,
% 2.12/2.38 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), s(z))) | (~b(z, s(z))) | (~b(s(z), s(s(elem!1)))) | (~b(s(s(elem!1)), s(z))) | (~b(z, s(z))) | (~b(z, s(s(elem!1)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(elem!1)))) | (~b(s(z), s(s(elem!1)))) | (~b(z, s(z))) | (~b(s(s(elem!1)), s(z)))))),
% 2.12/2.38 inference(monotonicity,[status(thm)],[5337])).
% 2.12/2.38 tff(5339,plain,
% 2.12/2.38 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), s(z))) | (~b(z, s(z))) | (~b(s(z), s(s(elem!1)))) | (~b(s(s(elem!1)), s(z))) | (~b(z, s(z))) | (~b(z, s(s(elem!1)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(s(elem!1)))) | (~b(s(z), s(s(elem!1)))) | (~b(z, s(z))) | (~b(s(s(elem!1)), s(z))))),
% 2.12/2.38 inference(transitivity,[status(thm)],[5338, 5336])).
% 2.12/2.38 tff(5340,plain,
% 2.12/2.38 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), s(z))) | (~b(z, s(z))) | (~b(s(z), s(s(elem!1)))) | (~b(s(s(elem!1)), s(z))) | (~b(z, s(z))) | (~b(z, s(s(elem!1)))))),
% 2.12/2.38 inference(quant_inst,[status(thm)],[])).
% 2.12/2.38 tff(5341,plain,
% 2.12/2.38 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(s(elem!1)))) | (~b(s(z), s(s(elem!1)))) | (~b(z, s(z))) | (~b(s(s(elem!1)), s(z)))),
% 2.12/2.38 inference(modus_ponens,[status(thm)],[5340, 5339])).
% 2.12/2.38 tff(5342,plain,
% 2.12/2.38 ($false),
% 2.12/2.38 inference(unit_resolution,[status(thm)],[5341, 166, 376, 1820, 118, 310])).
% 2.12/2.38 tff(5343,plain,((~b(s(s(elem!1)), s(z))) | (~b(s(z), s(s(elem!1)))) | (~b(z, s(s(elem!1)))) | (~b(z, s(z)))), inference(lemma,lemma(discharge,[]))).
% 2.12/2.38 tff(5344,plain,
% 2.12/2.38 ($false),
% 2.12/2.38 inference(unit_resolution,[status(thm)],[5343, 5335, 5333, 118, 376])).
% 2.12/2.38 tff(5345,plain,((~b(s(z), s(s(z)))) | (~b(z, s(z))) | (~b(s(z), s(s(elem!1)))) | (~r(z, s(s(z)))) | (s(s(z)) = s(s(elem!1))) | (~r(s(s(s(elem!1))), z)) | (~b(s(s(s(elem!1))), s(z))) | (s(s(elem!1)) = s(s(s(elem!1))))), inference(lemma,lemma(discharge,[]))).
% 2.12/2.38 tff(5346,plain,
% 2.12/2.38 (~b(s(z), s(s(z)))),
% 2.12/2.38 inference(unit_resolution,[status(thm)],[5345, 52, 376, 155, 118, 154, 96, 45])).
% 2.12/2.38 tff(5347,plain,
% 2.12/2.38 (r(s(z), s(s(z)))),
% 2.12/2.38 inference(unit_resolution,[status(thm)],[427, 5346])).
% 2.12/2.38 tff(5348,plain,
% 2.12/2.38 (~r(s(z), z)),
% 2.12/2.38 inference(unit_resolution,[status(thm)],[3947, 197, 5347, 155, 4582])).
% 2.12/2.38 tff(5349,plain,
% 2.12/2.38 (b(s(z), z)),
% 2.12/2.38 inference(unit_resolution,[status(thm)],[230, 5348])).
% 2.12/2.38 tff(5350,plain,
% 2.12/2.38 (~b(z, s(s(s(elem!1))))),
% 2.12/2.38 inference(unit_resolution,[status(thm)],[3989, 166, 5349, 96, 118])).
% 2.12/2.38 tff(5351,plain,
% 2.12/2.38 (r(z, s(s(s(elem!1))))),
% 2.12/2.38 inference(unit_resolution,[status(thm)],[261, 5350])).
% 2.12/2.38 tff(5352,plain,
% 2.12/2.38 (~r(s(s(s(elem!1))), s(s(z)))),
% 2.12/2.38 inference(unit_resolution,[status(thm)],[1588, 5351, 155, 4582])).
% 2.12/2.38 tff(5353,plain,
% 2.12/2.38 (~b(s(s(elem!1)), s(z))),
% 2.12/2.38 inference(unit_resolution,[status(thm)],[4277, 5349, 96, 118, 45])).
% 2.12/2.38 tff(5354,plain,
% 2.12/2.38 (r(s(s(elem!1)), s(z))),
% 2.12/2.38 inference(unit_resolution,[status(thm)],[1912, 5353])).
% 2.12/2.38 tff(5355,plain,
% 2.12/2.38 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(z)), s(z))) | (~r(s(s(elem!1)), s(z))) | (~r(s(z), s(s(z)))) | (~r(s(s(elem!1)), s(s(z)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(z)), s(z))) | (~r(s(s(elem!1)), s(z))) | (~r(s(z), s(s(z)))) | (~r(s(s(elem!1)), s(s(z)))))),
% 2.12/2.38 inference(rewrite,[status(thm)],[])).
% 2.12/2.38 tff(5356,plain,
% 2.12/2.38 (((~r(s(z), s(s(z)))) | (~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(z))) | (~r(s(z), s(s(z)))) | (~r(s(s(elem!1)), s(s(z)))))),
% 2.12/2.38 inference(rewrite,[status(thm)],[])).
% 2.12/2.38 tff(5357,plain,
% 2.12/2.38 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(s(z)))) | (~r(s(s(z)), s(z))) | (~r(s(s(elem!1)), s(z))) | (~r(s(s(elem!1)), s(s(z)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(z)), s(z))) | (~r(s(s(elem!1)), s(z))) | (~r(s(z), s(s(z)))) | (~r(s(s(elem!1)), s(s(z))))))),
% 2.12/2.38 inference(monotonicity,[status(thm)],[5356])).
% 2.12/2.38 tff(5358,plain,
% 2.12/2.38 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(s(z)))) | (~r(s(s(z)), s(z))) | (~r(s(s(elem!1)), s(z))) | (~r(s(s(elem!1)), s(s(z)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(z)), s(z))) | (~r(s(s(elem!1)), s(z))) | (~r(s(z), s(s(z)))) | (~r(s(s(elem!1)), s(s(z)))))),
% 2.12/2.38 inference(transitivity,[status(thm)],[5357, 5355])).
% 2.12/2.38 tff(5359,plain,
% 2.12/2.38 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(s(z)))) | (~r(s(s(z)), s(z))) | (~r(s(s(elem!1)), s(z))) | (~r(s(s(elem!1)), s(s(z)))))),
% 2.12/2.38 inference(quant_inst,[status(thm)],[])).
% 2.12/2.38 tff(5360,plain,
% 2.12/2.38 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(z)), s(z))) | (~r(s(s(elem!1)), s(z))) | (~r(s(z), s(s(z)))) | (~r(s(s(elem!1)), s(s(z))))),
% 2.12/2.38 inference(modus_ponens,[status(thm)],[5359, 5358])).
% 2.12/2.38 tff(5361,plain,
% 2.12/2.38 ($false),
% 2.12/2.38 inference(unit_resolution,[status(thm)],[5360, 197, 393, 120, 4577, 392])).
% 2.12/2.38 tff(5362,plain,((~r(s(s(z)), s(z))) | (~r(s(s(elem!1)), s(s(z)))) | (~r(s(z), s(s(z)))) | (~r(s(s(elem!1)), s(z)))), inference(lemma,lemma(discharge,[]))).
% 2.12/2.38 tff(5363,plain,
% 2.12/2.38 (~r(s(s(elem!1)), s(s(z)))),
% 2.12/2.38 inference(unit_resolution,[status(thm)],[5362, 5354, 5347, 4582])).
% 2.12/2.38 tff(5364,plain,
% 2.12/2.38 (b(s(s(elem!1)), s(s(z)))),
% 2.12/2.38 inference(unit_resolution,[status(thm)],[441, 5363, 132])).
% 2.12/2.38 tff(5365,plain,
% 2.12/2.38 (~r(s(s(z)), s(s(s(elem!1))))),
% 2.12/2.38 inference(unit_resolution,[status(thm)],[290, 5351, 155, 154])).
% 2.12/2.38 tff(5366,plain,
% 2.12/2.38 (~b(s(s(elem!1)), s(s(s(elem!1))))),
% 2.12/2.38 inference(unit_resolution,[status(thm)],[501, 5365, 5364, 5352])).
% 2.12/2.38 tff(5367,plain,
% 2.12/2.38 (r(s(s(elem!1)), s(s(s(elem!1))))),
% 2.12/2.38 inference(unit_resolution,[status(thm)],[461, 5366, 45])).
% 2.12/2.38 tff(5368,plain,
% 2.12/2.38 (~r(s(s(elem!1)), z)),
% 2.12/2.38 inference(unit_resolution,[status(thm)],[4018, 5367, 154, 5351])).
% 2.12/2.38 tff(5369,plain,
% 2.12/2.38 (b(s(s(elem!1)), z)),
% 2.12/2.38 inference(unit_resolution,[status(thm)],[608, 5368])).
% 2.12/2.38 tff(5370,plain,
% 2.12/2.38 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(elem!1)))) | (~b(s(z), z)) | (~b(s(s(elem!1)), z)) | (~b(s(z), s(s(elem!1)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(s(elem!1)))) | (~b(s(z), z)) | (~b(s(s(elem!1)), z)) | (~b(s(z), s(s(elem!1)))))),
% 2.12/2.38 inference(rewrite,[status(thm)],[])).
% 2.12/2.38 tff(5371,plain,
% 2.12/2.38 (((~b(z, s(s(elem!1)))) | (~b(s(z), s(s(elem!1)))) | (~b(s(s(elem!1)), z)) | (~b(z, s(s(elem!1)))) | (~b(s(z), s(s(elem!1)))) | (~b(s(z), z))) <=> ((~b(z, s(s(elem!1)))) | (~b(s(z), z)) | (~b(s(s(elem!1)), z)) | (~b(s(z), s(s(elem!1)))))),
% 2.12/2.38 inference(rewrite,[status(thm)],[])).
% 2.12/2.38 tff(5372,plain,
% 2.12/2.38 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(elem!1)))) | (~b(s(z), s(s(elem!1)))) | (~b(s(s(elem!1)), z)) | (~b(z, s(s(elem!1)))) | (~b(s(z), s(s(elem!1)))) | (~b(s(z), z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(elem!1)))) | (~b(s(z), z)) | (~b(s(s(elem!1)), z)) | (~b(s(z), s(s(elem!1))))))),
% 2.12/2.38 inference(monotonicity,[status(thm)],[5371])).
% 2.12/2.38 tff(5373,plain,
% 2.12/2.38 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(elem!1)))) | (~b(s(z), s(s(elem!1)))) | (~b(s(s(elem!1)), z)) | (~b(z, s(s(elem!1)))) | (~b(s(z), s(s(elem!1)))) | (~b(s(z), z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(s(elem!1)))) | (~b(s(z), z)) | (~b(s(s(elem!1)), z)) | (~b(s(z), s(s(elem!1)))))),
% 2.12/2.38 inference(transitivity,[status(thm)],[5372, 5370])).
% 2.12/2.38 tff(5374,plain,
% 2.12/2.38 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(elem!1)))) | (~b(s(z), s(s(elem!1)))) | (~b(s(s(elem!1)), z)) | (~b(z, s(s(elem!1)))) | (~b(s(z), s(s(elem!1)))) | (~b(s(z), z)))),
% 2.12/2.38 inference(quant_inst,[status(thm)],[])).
% 2.12/2.38 tff(5375,plain,
% 2.12/2.38 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(s(elem!1)))) | (~b(s(z), z)) | (~b(s(s(elem!1)), z)) | (~b(s(z), s(s(elem!1))))),
% 2.12/2.38 inference(modus_ponens,[status(thm)],[5374, 5373])).
% 2.12/2.38 tff(5376,plain,
% 2.12/2.38 ($false),
% 2.12/2.38 inference(unit_resolution,[status(thm)],[5375, 166, 376, 1820, 53, 592])).
% 2.12/2.38 tff(5377,plain,((~b(s(s(elem!1)), z)) | (~b(s(z), s(s(elem!1)))) | (~b(z, s(s(elem!1)))) | (~b(s(z), z))), inference(lemma,lemma(discharge,[]))).
% 2.12/2.38 tff(5378,plain,
% 2.12/2.38 (~b(z, s(s(elem!1)))),
% 2.12/2.38 inference(unit_resolution,[status(thm)],[5377, 5369, 376, 5349])).
% 2.12/2.38 tff(5379,plain,
% 2.12/2.38 (r(z, s(s(elem!1)))),
% 2.12/2.38 inference(unit_resolution,[status(thm)],[1795, 5378])).
% 2.12/2.38 tff(5380,plain,
% 2.12/2.38 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(s(z)))) | (~r(s(s(elem!1)), s(z))) | (~r(s(s(z)), s(z))) | (~r(s(s(z)), s(s(elem!1)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(z), s(s(z)))) | (~r(s(s(elem!1)), s(z))) | (~r(s(s(z)), s(z))) | (~r(s(s(z)), s(s(elem!1)))))),
% 2.12/2.38 inference(rewrite,[status(thm)],[])).
% 2.12/2.38 tff(5381,plain,
% 2.12/2.38 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(s(z)))) | (~r(s(s(elem!1)), s(z))) | (~r(s(s(z)), s(z))) | (~r(s(s(z)), s(s(elem!1)))))),
% 2.12/2.38 inference(quant_inst,[status(thm)],[])).
% 2.12/2.38 tff(5382,plain,
% 2.12/2.38 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(z), s(s(z)))) | (~r(s(s(elem!1)), s(z))) | (~r(s(s(z)), s(z))) | (~r(s(s(z)), s(s(elem!1))))),
% 2.12/2.38 inference(modus_ponens,[status(thm)],[5381, 5380])).
% 2.12/2.38 tff(5383,plain,
% 2.12/2.38 ($false),
% 2.12/2.38 inference(unit_resolution,[status(thm)],[5382, 197, 120, 4577, 333, 392])).
% 2.12/2.38 tff(5384,plain,((~r(s(z), s(s(z)))) | (~r(s(s(elem!1)), s(z))) | (~r(s(s(z)), s(s(elem!1)))) | (~r(s(s(z)), s(z)))), inference(lemma,lemma(discharge,[]))).
% 2.12/2.38 tff(5385,plain,
% 2.12/2.38 (~r(s(s(z)), s(s(elem!1)))),
% 2.12/2.38 inference(unit_resolution,[status(thm)],[5384, 5354, 5347, 4582])).
% 2.12/2.38 tff(5386,plain,
% 2.12/2.38 (b(s(s(z)), s(s(elem!1)))),
% 2.12/2.38 inference(unit_resolution,[status(thm)],[390, 5385, 52])).
% 2.12/2.38 tff(5387,plain,
% 2.12/2.38 (~r(s(z), s(s(s(elem!1))))),
% 2.12/2.38 inference(unit_resolution,[status(thm)],[5310, 5367, 154, 5354])).
% 2.12/2.38 tff(5388,plain,
% 2.12/2.38 (b(s(z), s(s(s(elem!1))))),
% 2.12/2.38 inference(unit_resolution,[status(thm)],[116, 5387])).
% 2.12/2.38 tff(5389,plain,
% 2.12/2.38 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(z), s(s(s(elem!1))))) | (~b(s(z), s(s(elem!1)))) | (~b(s(s(elem!1)), s(s(z)))) | (~b(s(s(z)), s(s(elem!1)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(z), s(s(s(elem!1))))) | (~b(s(z), s(s(elem!1)))) | (~b(s(s(elem!1)), s(s(z)))) | (~b(s(s(z)), s(s(elem!1)))))),
% 2.12/2.38 inference(rewrite,[status(thm)],[])).
% 2.12/2.38 tff(5390,plain,
% 2.12/2.38 (((~b(s(s(z)), s(s(elem!1)))) | (~b(s(z), s(s(elem!1)))) | (~b(s(s(elem!1)), s(s(z)))) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(z), s(s(elem!1)))) | (~b(s(z), s(s(s(elem!1)))))) <=> ((~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(z), s(s(s(elem!1))))) | (~b(s(z), s(s(elem!1)))) | (~b(s(s(elem!1)), s(s(z)))) | (~b(s(s(z)), s(s(elem!1)))))),
% 2.12/2.38 inference(rewrite,[status(thm)],[])).
% 2.12/2.38 tff(5391,plain,
% 2.12/2.38 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), s(s(elem!1)))) | (~b(s(z), s(s(elem!1)))) | (~b(s(s(elem!1)), s(s(z)))) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(z), s(s(elem!1)))) | (~b(s(z), s(s(s(elem!1))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(z), s(s(s(elem!1))))) | (~b(s(z), s(s(elem!1)))) | (~b(s(s(elem!1)), s(s(z)))) | (~b(s(s(z)), s(s(elem!1))))))),
% 2.12/2.39 inference(monotonicity,[status(thm)],[5390])).
% 2.12/2.39 tff(5392,plain,
% 2.12/2.39 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), s(s(elem!1)))) | (~b(s(z), s(s(elem!1)))) | (~b(s(s(elem!1)), s(s(z)))) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(z), s(s(elem!1)))) | (~b(s(z), s(s(s(elem!1))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(z), s(s(s(elem!1))))) | (~b(s(z), s(s(elem!1)))) | (~b(s(s(elem!1)), s(s(z)))) | (~b(s(s(z)), s(s(elem!1)))))),
% 2.12/2.39 inference(transitivity,[status(thm)],[5391, 5389])).
% 2.12/2.39 tff(5393,plain,
% 2.12/2.39 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), s(s(elem!1)))) | (~b(s(z), s(s(elem!1)))) | (~b(s(s(elem!1)), s(s(z)))) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(z), s(s(elem!1)))) | (~b(s(z), s(s(s(elem!1))))))),
% 2.12/2.39 inference(quant_inst,[status(thm)],[])).
% 2.12/2.39 tff(5394,plain,
% 2.12/2.39 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(z), s(s(s(elem!1))))) | (~b(s(z), s(s(elem!1)))) | (~b(s(s(elem!1)), s(s(z)))) | (~b(s(s(z)), s(s(elem!1))))),
% 2.12/2.39 inference(modus_ponens,[status(thm)],[5393, 5392])).
% 2.12/2.39 tff(5395,plain,
% 2.12/2.39 ($false),
% 2.12/2.39 inference(unit_resolution,[status(thm)],[5394, 166, 376, 839, 241, 405, 446])).
% 2.12/2.39 tff(5396,plain,((~b(s(s(elem!1)), s(s(z)))) | (~b(s(z), s(s(elem!1)))) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(z), s(s(s(elem!1))))) | (~b(s(s(z)), s(s(elem!1))))), inference(lemma,lemma(discharge,[]))).
% 2.12/2.39 tff(5397,plain,
% 2.12/2.39 (~b(s(s(s(elem!1))), s(s(elem!1)))),
% 2.12/2.39 inference(unit_resolution,[status(thm)],[5396, 5388, 376, 5364, 5386])).
% 2.12/2.39 tff(5398,plain,
% 2.12/2.39 (r(s(s(s(elem!1))), s(s(elem!1)))),
% 2.12/2.39 inference(unit_resolution,[status(thm)],[889, 5397, 51])).
% 2.12/2.39 tff(5399,plain,
% 2.12/2.39 ($false),
% 2.12/2.39 inference(unit_resolution,[status(thm)],[1386, 5398, 5379, 154, 5367])).
% 2.12/2.39 tff(5400,plain,((s(s(z)) = s(s(elem!1))) | (~r(s(s(s(elem!1))), z)) | (~b(s(z), s(s(elem!1)))) | (s(s(elem!1)) = s(s(s(elem!1)))) | (~r(z, s(s(z)))) | (~b(s(s(s(elem!1))), s(z))) | (~b(z, s(z)))), inference(lemma,lemma(discharge,[]))).
% 2.12/2.39 tff(5401,plain,
% 2.12/2.39 (s(s(z)) = s(s(elem!1))),
% 2.12/2.39 inference(unit_resolution,[status(thm)],[5400, 45, 376, 154, 155, 96, 118])).
% 2.12/2.39 tff(5402,plain,
% 2.12/2.39 (s(elem!1) = s(z)),
% 2.12/2.39 inference(unit_resolution,[status(thm)],[43, 5401])).
% 2.12/2.39 tff(5403,plain,
% 2.12/2.39 (z = elem!1),
% 2.12/2.39 inference(unit_resolution,[status(thm)],[30, 5402])).
% 2.12/2.39 tff(5404,plain,
% 2.12/2.39 (b(z, s(z)) <=> b(elem!1, s(z))),
% 2.12/2.39 inference(monotonicity,[status(thm)],[5403])).
% 2.12/2.39 tff(5405,plain,
% 2.12/2.39 (b(elem!1, s(z))),
% 2.12/2.39 inference(modus_ponens,[status(thm)],[118, 5404])).
% 2.12/2.39 tff(5406,plain,
% 2.12/2.39 ((s(s(s(elem!1))) = elem!1) <=> (elem!1 = s(s(s(elem!1))))),
% 2.12/2.39 inference(commutativity,[status(thm)],[])).
% 2.12/2.39 tff(5407,plain,
% 2.12/2.39 ((s(s(s(elem!1))) = z) <=> (s(s(s(elem!1))) = elem!1)),
% 2.12/2.39 inference(monotonicity,[status(thm)],[5403])).
% 2.12/2.39 tff(5408,plain,
% 2.12/2.39 ((s(s(s(elem!1))) = z) <=> (elem!1 = s(s(s(elem!1))))),
% 2.12/2.39 inference(transitivity,[status(thm)],[5407, 5406])).
% 2.12/2.39 tff(5409,plain,
% 2.12/2.39 ((~(s(s(s(elem!1))) = z)) <=> (~(elem!1 = s(s(s(elem!1)))))),
% 2.12/2.39 inference(monotonicity,[status(thm)],[5408])).
% 2.12/2.39 tff(5410,plain,
% 2.12/2.39 (~(elem!1 = s(s(s(elem!1))))),
% 2.12/2.39 inference(modus_ponens,[status(thm)],[89, 5409])).
% 2.12/2.39 tff(5411,plain,
% 2.12/2.39 (b(s(s(elem!1)), z) <=> b(s(s(z)), z)),
% 2.12/2.39 inference(symmetry,[status(thm)],[2962])).
% 2.12/2.39 tff(5412,plain,
% 2.12/2.39 (b(s(s(elem!1)), z) <=> b(s(s(elem!1)), elem!1)),
% 2.12/2.39 inference(monotonicity,[status(thm)],[620])).
% 2.12/2.39 tff(5413,plain,
% 2.12/2.39 (b(s(s(elem!1)), elem!1) <=> b(s(s(elem!1)), z)),
% 2.12/2.39 inference(symmetry,[status(thm)],[5412])).
% 2.12/2.39 tff(5414,plain,
% 2.12/2.39 (b(s(s(elem!1)), elem!1) <=> b(s(s(z)), z)),
% 2.12/2.39 inference(transitivity,[status(thm)],[5413, 5411])).
% 2.12/2.39 tff(5415,plain,
% 2.12/2.39 ((~b(s(s(elem!1)), elem!1)) <=> (~b(s(s(z)), z))),
% 2.12/2.39 inference(monotonicity,[status(thm)],[5414])).
% 2.12/2.39 tff(5416,plain,
% 2.12/2.39 (b(z, s(z)) <=> b(elem!1, s(z))),
% 2.12/2.39 inference(monotonicity,[status(thm)],[620])).
% 2.12/2.39 tff(5417,plain,
% 2.12/2.39 (b(elem!1, s(z))),
% 2.12/2.39 inference(modus_ponens,[status(thm)],[118, 5416])).
% 2.12/2.39 tff(5418,plain,
% 2.12/2.39 (~r(s(s(s(elem!1))), s(s(elem!1)))),
% 2.12/2.39 inference(unit_resolution,[status(thm)],[3454, 213, 34])).
% 2.12/2.39 tff(5419,plain,
% 2.12/2.39 (b(s(s(s(elem!1))), s(s(elem!1)))),
% 2.12/2.39 inference(unit_resolution,[status(thm)],[889, 5418, 1863])).
% 2.12/2.39 tff(5420,plain,
% 2.12/2.39 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), elem!1)) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(elem!1, s(z))) | (~b(s(z), s(s(elem!1)))) | (~b(s(s(s(elem!1))), s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(elem!1)), elem!1)) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(elem!1, s(z))) | (~b(s(z), s(s(elem!1)))) | (~b(s(s(s(elem!1))), s(z))))),
% 2.12/2.39 inference(rewrite,[status(thm)],[])).
% 2.12/2.39 tff(5421,plain,
% 2.12/2.39 (((~b(elem!1, s(z))) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(s(elem!1)), elem!1)) | (~b(s(z), s(s(elem!1)))) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(s(s(elem!1))), s(z)))) <=> ((~b(s(s(elem!1)), elem!1)) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(elem!1, s(z))) | (~b(s(z), s(s(elem!1)))) | (~b(s(s(s(elem!1))), s(z))))),
% 2.12/2.39 inference(rewrite,[status(thm)],[])).
% 2.12/2.39 tff(5422,plain,
% 2.12/2.39 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(z))) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(s(elem!1)), elem!1)) | (~b(s(z), s(s(elem!1)))) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(s(s(elem!1))), s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), elem!1)) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(elem!1, s(z))) | (~b(s(z), s(s(elem!1)))) | (~b(s(s(s(elem!1))), s(z)))))),
% 2.12/2.39 inference(monotonicity,[status(thm)],[5421])).
% 2.12/2.39 tff(5423,plain,
% 2.12/2.39 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(z))) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(s(elem!1)), elem!1)) | (~b(s(z), s(s(elem!1)))) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(s(s(elem!1))), s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(elem!1)), elem!1)) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(elem!1, s(z))) | (~b(s(z), s(s(elem!1)))) | (~b(s(s(s(elem!1))), s(z))))),
% 2.12/2.39 inference(transitivity,[status(thm)],[5422, 5420])).
% 2.12/2.39 tff(5424,plain,
% 2.12/2.39 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(z))) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(s(elem!1)), elem!1)) | (~b(s(z), s(s(elem!1)))) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(s(s(elem!1))), s(z))))),
% 2.12/2.39 inference(quant_inst,[status(thm)],[])).
% 2.12/2.39 tff(5425,plain,
% 2.12/2.39 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(elem!1)), elem!1)) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(elem!1, s(z))) | (~b(s(z), s(s(elem!1)))) | (~b(s(s(s(elem!1))), s(z)))),
% 2.12/2.39 inference(modus_ponens,[status(thm)],[5424, 5423])).
% 2.12/2.39 tff(5426,plain,
% 2.12/2.39 ($false),
% 2.12/2.39 inference(unit_resolution,[status(thm)],[5425, 166, 376, 786, 839, 96, 1212])).
% 2.12/2.39 tff(5427,plain,((~b(s(s(elem!1)), elem!1)) | (~b(s(z), s(s(elem!1)))) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(s(s(elem!1))), s(z))) | (~b(elem!1, s(z)))), inference(lemma,lemma(discharge,[]))).
% 2.12/2.39 tff(5428,plain,
% 2.12/2.39 (~b(s(s(elem!1)), elem!1)),
% 2.12/2.39 inference(unit_resolution,[status(thm)],[5427, 5419, 376, 96, 5417])).
% 2.12/2.39 tff(5429,plain,
% 2.12/2.39 (~b(s(s(z)), z)),
% 2.12/2.39 inference(modus_ponens,[status(thm)],[5428, 5415])).
% 2.12/2.39 tff(5430,plain,
% 2.12/2.39 (r(s(s(z)), z)),
% 2.12/2.39 inference(unit_resolution,[status(thm)],[186, 5429])).
% 2.12/2.39 tff(5431,plain,
% 2.12/2.39 (~r(s(z), z)),
% 2.12/2.39 inference(unit_resolution,[status(thm)],[4287, 5430, 155, 4582])).
% 2.12/2.39 tff(5432,plain,
% 2.12/2.39 (b(s(z), s(s(z)))),
% 2.12/2.39 inference(modus_ponens,[status(thm)],[376, 4394])).
% 2.12/2.39 tff(5433,assumption,(~b(s(z), s(s(z)))), introduced(assumption)).
% 2.12/2.39 tff(5434,plain,
% 2.12/2.39 ($false),
% 2.12/2.39 inference(unit_resolution,[status(thm)],[5433, 5432])).
% 2.12/2.39 tff(5435,plain,((~(s(s(z)) = s(s(elem!1)))) | b(s(z), s(s(z))) | (~b(s(z), s(s(elem!1))))), inference(lemma,lemma(discharge,[]))).
% 2.12/2.39 tff(5436,plain,
% 2.12/2.39 (b(s(z), s(s(z)))),
% 2.12/2.39 inference(unit_resolution,[status(thm)],[5435, 34, 376])).
% 2.12/2.39 tff(5437,plain,
% 2.12/2.39 (~b(s(z), z)),
% 2.12/2.39 inference(unit_resolution,[status(thm)],[5253, 5430, 118, 5436, 213, 96, 154])).
% 2.12/2.39 tff(5438,plain,
% 2.12/2.39 ($false),
% 2.12/2.39 inference(unit_resolution,[status(thm)],[230, 5437, 5431])).
% 2.12/2.39 tff(5439,plain,(r(s(s(s(elem!1))), s(s(z))) | (~b(z, s(z))) | (~b(s(s(s(elem!1))), s(z))) | (~r(s(s(s(elem!1))), z)) | (~r(z, s(s(z)))) | (~(s(s(z)) = s(s(elem!1)))) | (~b(s(z), s(s(elem!1)))) | (s(s(s(elem!1))) = s(s(elem!1)))), inference(lemma,lemma(discharge,[]))).
% 2.12/2.39 tff(5440,plain,
% 2.12/2.39 (r(s(s(s(elem!1))), s(s(z)))),
% 2.12/2.39 inference(unit_resolution,[status(thm)],[5439, 5401, 96, 154, 155, 118, 376, 51])).
% 2.12/2.39 tff(5441,plain,
% 2.12/2.39 (~r(z, s(s(s(elem!1))))),
% 2.12/2.39 inference(unit_resolution,[status(thm)],[1588, 5440, 155, 4582])).
% 2.12/2.39 tff(5442,plain,
% 2.12/2.39 (r(z, s(s(s(elem!1)))) <=> r(elem!1, s(s(s(elem!1))))),
% 2.12/2.39 inference(monotonicity,[status(thm)],[12])).
% 2.12/2.39 tff(5443,plain,
% 2.12/2.39 (r(elem!1, s(s(s(elem!1)))) <=> r(z, s(s(s(elem!1))))),
% 2.12/2.39 inference(symmetry,[status(thm)],[5442])).
% 2.12/2.39 tff(5444,plain,
% 2.12/2.39 (r(z, s(s(s(elem!1))))),
% 2.12/2.39 inference(modus_ponens,[status(thm)],[942, 5443])).
% 2.12/2.39 tff(5445,plain,
% 2.12/2.39 ($false),
% 2.12/2.39 inference(unit_resolution,[status(thm)],[255, 5444])).
% 2.12/2.39 tff(5446,plain,((~r(elem!1, s(s(s(elem!1))))) | r(z, s(s(s(elem!1)))) | (~(z = elem!1))), inference(lemma,lemma(discharge,[]))).
% 2.12/2.39 tff(5447,plain,
% 2.12/2.39 (~r(elem!1, s(s(s(elem!1))))),
% 2.12/2.39 inference(unit_resolution,[status(thm)],[5446, 5441, 5403])).
% 2.12/2.39 tff(5448,plain,
% 2.12/2.39 (((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((elem!1 = s(s(s(elem!1)))) | b(elem!1, s(s(s(elem!1)))) | r(elem!1, s(s(s(elem!1)))))) <=> ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (elem!1 = s(s(s(elem!1)))) | b(elem!1, s(s(s(elem!1)))) | r(elem!1, s(s(s(elem!1)))))),
% 2.12/2.39 inference(rewrite,[status(thm)],[])).
% 2.12/2.39 tff(5449,plain,
% 2.12/2.39 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((elem!1 = s(s(s(elem!1)))) | b(elem!1, s(s(s(elem!1)))) | r(elem!1, s(s(s(elem!1)))))),
% 2.12/2.39 inference(quant_inst,[status(thm)],[])).
% 2.12/2.39 tff(5450,plain,
% 2.12/2.39 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (elem!1 = s(s(s(elem!1)))) | b(elem!1, s(s(s(elem!1)))) | r(elem!1, s(s(s(elem!1))))),
% 2.12/2.39 inference(modus_ponens,[status(thm)],[5449, 5448])).
% 2.12/2.39 tff(5451,plain,
% 2.12/2.39 ((elem!1 = s(s(s(elem!1)))) | b(elem!1, s(s(s(elem!1)))) | r(elem!1, s(s(s(elem!1))))),
% 2.12/2.39 inference(unit_resolution,[status(thm)],[5450, 79])).
% 2.12/2.39 tff(5452,plain,
% 2.12/2.39 (b(elem!1, s(s(s(elem!1))))),
% 2.12/2.39 inference(unit_resolution,[status(thm)],[5451, 5447, 5410])).
% 2.12/2.39 tff(5453,plain,
% 2.12/2.39 (~b(s(s(elem!1)), s(z))),
% 2.12/2.39 inference(unit_resolution,[status(thm)],[3938, 5401, 4581])).
% 2.12/2.39 tff(5454,plain,
% 2.12/2.39 (r(s(s(elem!1)), s(z))),
% 2.12/2.39 inference(unit_resolution,[status(thm)],[1912, 5453])).
% 2.12/2.39 tff(5455,plain,
% 2.12/2.39 (b(z, s(s(s(elem!1))))),
% 2.12/2.39 inference(unit_resolution,[status(thm)],[261, 5441])).
% 2.12/2.39 tff(5456,plain,
% 2.12/2.39 (~b(s(z), s(s(s(elem!1))))),
% 2.12/2.39 inference(unit_resolution,[status(thm)],[249, 5455, 118, 96])).
% 2.12/2.39 tff(5457,plain,
% 2.12/2.39 (r(s(z), s(s(s(elem!1))))),
% 2.12/2.39 inference(unit_resolution,[status(thm)],[116, 5456])).
% 2.12/2.39 tff(5458,plain,
% 2.12/2.39 (~r(s(s(elem!1)), s(s(s(elem!1))))),
% 2.12/2.39 inference(unit_resolution,[status(thm)],[5310, 5457, 154, 5454])).
% 2.12/2.39 tff(5459,plain,
% 2.12/2.39 (b(s(s(elem!1)), s(s(s(elem!1))))),
% 2.12/2.39 inference(unit_resolution,[status(thm)],[461, 5458, 45])).
% 2.12/2.39 tff(5460,plain,
% 2.12/2.39 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(elem!1, s(z))) | (~b(elem!1, s(s(s(elem!1))))) | (~b(s(z), s(s(elem!1)))) | (~b(s(s(s(elem!1))), s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(elem!1, s(z))) | (~b(elem!1, s(s(s(elem!1))))) | (~b(s(z), s(s(elem!1)))) | (~b(s(s(s(elem!1))), s(z))))),
% 2.12/2.39 inference(rewrite,[status(thm)],[])).
% 2.12/2.39 tff(5461,plain,
% 2.12/2.39 (((~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(elem!1, s(s(s(elem!1))))) | (~b(s(z), s(s(elem!1)))) | (~b(s(s(s(elem!1))), s(z))) | (~b(elem!1, s(z))) | (~b(elem!1, s(s(s(elem!1)))))) <=> ((~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(elem!1, s(z))) | (~b(elem!1, s(s(s(elem!1))))) | (~b(s(z), s(s(elem!1)))) | (~b(s(s(s(elem!1))), s(z))))),
% 2.12/2.39 inference(rewrite,[status(thm)],[])).
% 2.12/2.39 tff(5462,plain,
% 2.12/2.39 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(elem!1, s(s(s(elem!1))))) | (~b(s(z), s(s(elem!1)))) | (~b(s(s(s(elem!1))), s(z))) | (~b(elem!1, s(z))) | (~b(elem!1, s(s(s(elem!1))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(elem!1, s(z))) | (~b(elem!1, s(s(s(elem!1))))) | (~b(s(z), s(s(elem!1)))) | (~b(s(s(s(elem!1))), s(z)))))),
% 2.12/2.39 inference(monotonicity,[status(thm)],[5461])).
% 2.12/2.39 tff(5463,plain,
% 2.12/2.39 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(elem!1, s(s(s(elem!1))))) | (~b(s(z), s(s(elem!1)))) | (~b(s(s(s(elem!1))), s(z))) | (~b(elem!1, s(z))) | (~b(elem!1, s(s(s(elem!1))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(elem!1, s(z))) | (~b(elem!1, s(s(s(elem!1))))) | (~b(s(z), s(s(elem!1)))) | (~b(s(s(s(elem!1))), s(z))))),
% 2.12/2.39 inference(transitivity,[status(thm)],[5462, 5460])).
% 2.12/2.39 tff(5464,plain,
% 2.12/2.39 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(elem!1, s(s(s(elem!1))))) | (~b(s(z), s(s(elem!1)))) | (~b(s(s(s(elem!1))), s(z))) | (~b(elem!1, s(z))) | (~b(elem!1, s(s(s(elem!1))))))),
% 2.12/2.39 inference(quant_inst,[status(thm)],[])).
% 2.12/2.39 tff(5465,plain,
% 2.12/2.39 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(elem!1, s(z))) | (~b(elem!1, s(s(s(elem!1))))) | (~b(s(z), s(s(elem!1)))) | (~b(s(s(s(elem!1))), s(z)))),
% 2.12/2.39 inference(modus_ponens,[status(thm)],[5464, 5463])).
% 2.12/2.39 tff(5466,plain,
% 2.12/2.39 ($false),
% 2.12/2.39 inference(unit_resolution,[status(thm)],[5465, 166, 376, 5459, 5452, 96, 5405])).
% 2.12/2.39 tff(5467,plain,((s(s(elem!1)) = s(s(s(elem!1)))) | (~b(s(z), s(s(elem!1)))) | (~b(s(s(s(elem!1))), s(z))) | (~r(s(s(s(elem!1))), z)) | (~b(z, s(z))) | (~r(z, s(s(z))))), inference(lemma,lemma(discharge,[]))).
% 2.12/2.39 tff(5468,plain,
% 2.12/2.39 (s(s(elem!1)) = s(s(s(elem!1)))),
% 2.12/2.39 inference(unit_resolution,[status(thm)],[5467, 5288, 96, 153, 118, 152])).
% 2.12/2.39 tff(5469,plain,
% 2.12/2.39 (s(s(s(elem!1))) = s(elem!1)),
% 2.12/2.39 inference(unit_resolution,[status(thm)],[2594, 5468])).
% 2.12/2.39 tff(5470,plain,
% 2.12/2.39 (s(elem!1) = s(s(s(elem!1)))),
% 2.12/2.39 inference(symmetry,[status(thm)],[5469])).
% 2.12/2.39 tff(5471,plain,
% 2.12/2.39 (inj_0(s(elem!1)) = inj_0(s(s(s(elem!1))))),
% 2.12/2.39 inference(monotonicity,[status(thm)],[5470])).
% 2.12/2.39 tff(5472,plain,
% 2.12/2.39 (elem!1 = s(s(s(elem!1)))),
% 2.12/2.39 inference(transitivity,[status(thm)],[1170, 5471, 104, 5468])).
% 2.12/2.39 tff(5473,plain,
% 2.12/2.39 (b(elem!1, s(s(s(s(z))))) <=> b(s(s(s(elem!1))), s(s(s(s(z)))))),
% 2.12/2.39 inference(monotonicity,[status(thm)],[5472])).
% 2.12/2.39 tff(5474,plain,
% 2.12/2.39 ((s(s(elem!1)) = s(s(s(s(elem!1))))) <=> (s(s(s(elem!1))) = s(s(s(s(elem!1)))))),
% 2.12/2.39 inference(monotonicity,[status(thm)],[5468])).
% 2.12/2.39 tff(5475,plain,
% 2.12/2.39 ((s(s(s(elem!1))) = s(s(s(s(elem!1))))) <=> (s(s(elem!1)) = s(s(s(s(elem!1)))))),
% 2.12/2.39 inference(symmetry,[status(thm)],[5474])).
% 2.12/2.39 tff(5476,plain,
% 2.12/2.39 (s(s(s(elem!1))) = s(s(elem!1))),
% 2.12/2.39 inference(symmetry,[status(thm)],[5468])).
% 2.12/2.39 tff(5477,plain,
% 2.12/2.39 (s(s(s(s(elem!1)))) = s(s(s(elem!1)))),
% 2.12/2.39 inference(monotonicity,[status(thm)],[5476])).
% 2.12/2.39 tff(5478,plain,
% 2.12/2.39 (s(s(s(elem!1))) = s(s(s(s(elem!1))))),
% 2.12/2.39 inference(symmetry,[status(thm)],[5477])).
% 2.12/2.39 tff(5479,plain,
% 2.12/2.39 (s(s(elem!1)) = s(s(s(s(elem!1))))),
% 2.12/2.39 inference(modus_ponens,[status(thm)],[5478, 5475])).
% 2.12/2.39 tff(5480,assumption,(elem!1 = s(s(s(s(z))))), introduced(assumption)).
% 2.12/2.39 tff(5481,plain,
% 2.12/2.39 (s(s(s(s(z)))) = elem!1),
% 2.12/2.39 inference(symmetry,[status(thm)],[5480])).
% 2.12/2.39 tff(5482,plain,
% 2.12/2.39 (s(s(s(s(z)))) = s(s(s(s(elem!1))))),
% 2.12/2.39 inference(transitivity,[status(thm)],[5481, 1170, 1169, 104, 1153])).
% 2.12/2.39 tff(5483,plain,
% 2.12/2.39 (inj_0(s(s(s(s(z))))) = inj_0(s(s(s(s(elem!1)))))),
% 2.12/2.39 inference(monotonicity,[status(thm)],[5482])).
% 2.12/2.39 tff(5484,plain,
% 2.12/2.39 (s(s(s(z))) = s(elem!1)),
% 2.12/2.39 inference(transitivity,[status(thm)],[3277, 5483, 352, 1167])).
% 2.12/2.39 tff(5485,plain,
% 2.12/2.39 (inj_0(s(s(s(z)))) = inj_0(s(elem!1))),
% 2.12/2.39 inference(monotonicity,[status(thm)],[5484])).
% 2.12/2.39 tff(5486,plain,
% 2.12/2.39 (inj_0(s(elem!1)) = inj_0(s(s(s(z))))),
% 2.12/2.39 inference(symmetry,[status(thm)],[5485])).
% 2.12/2.39 tff(5487,plain,
% 2.12/2.39 (s(s(s(s(elem!1)))) = s(s(z))),
% 2.12/2.39 inference(transitivity,[status(thm)],[1154, 105, 1540, 5486, 134])).
% 2.12/2.39 tff(5488,plain,
% 2.12/2.39 ($false),
% 2.12/2.39 inference(unit_resolution,[status(thm)],[733, 5487])).
% 2.12/2.39 tff(5489,plain,((~(elem!1 = s(s(s(s(z)))))) | (~(s(s(elem!1)) = s(s(s(s(elem!1))))))), inference(lemma,lemma(discharge,[]))).
% 2.12/2.39 tff(5490,plain,
% 2.12/2.39 (~(elem!1 = s(s(s(s(z)))))),
% 2.12/2.39 inference(unit_resolution,[status(thm)],[5489, 5479])).
% 2.12/2.39 tff(5491,plain,
% 2.12/2.39 (b(s(s(elem!1)), s(z))),
% 2.12/2.39 inference(unit_resolution,[status(thm)],[4570, 5468, 96])).
% 2.12/2.39 tff(5492,plain,
% 2.12/2.39 (~(s(s(z)) = s(s(elem!1)))),
% 2.12/2.39 inference(unit_resolution,[status(thm)],[3938, 5491, 293])).
% 2.12/2.39 tff(5493,plain,
% 2.12/2.39 (~(s(s(elem!1)) = s(s(z)))),
% 2.12/2.39 inference(unit_resolution,[status(thm)],[131, 5492])).
% 2.12/2.39 tff(5494,plain,
% 2.12/2.39 (~(s(s(s(elem!1))) = s(s(s(z))))),
% 2.12/2.39 inference(unit_resolution,[status(thm)],[139, 5493])).
% 2.12/2.39 tff(5495,plain,
% 2.12/2.39 (b(s(z), s(s(elem!1))) <=> b(s(z), s(s(s(elem!1))))),
% 2.12/2.39 inference(monotonicity,[status(thm)],[334])).
% 2.12/2.39 tff(5496,plain,
% 2.12/2.39 (b(s(z), s(s(s(elem!1)))) <=> b(s(z), s(s(elem!1)))),
% 2.12/2.39 inference(symmetry,[status(thm)],[5495])).
% 2.12/2.39 tff(5497,plain,
% 2.12/2.39 ((~b(s(z), s(s(s(elem!1))))) <=> (~b(s(z), s(s(elem!1))))),
% 2.12/2.39 inference(monotonicity,[status(thm)],[5496])).
% 2.12/2.39 tff(5498,plain,
% 2.12/2.39 (~b(s(z), s(s(elem!1)))),
% 2.12/2.39 inference(modus_ponens,[status(thm)],[98, 5497])).
% 2.12/2.39 tff(5499,plain,
% 2.12/2.39 ($false),
% 2.12/2.39 inference(unit_resolution,[status(thm)],[376, 5498])).
% 2.12/2.39 tff(5500,plain,((~(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,[]))).
% 2.12/2.39 tff(5501,plain,
% 2.12/2.39 (b(s(z), s(s(s(elem!1))))),
% 2.12/2.39 inference(unit_resolution,[status(thm)],[5500, 5468, 5288])).
% 2.12/2.39 tff(5502,plain,
% 2.12/2.39 (~b(z, s(s(s(elem!1))))),
% 2.12/2.39 inference(unit_resolution,[status(thm)],[249, 5501, 118, 96])).
% 2.12/2.39 tff(5503,plain,
% 2.12/2.39 (r(z, s(s(s(elem!1))))),
% 2.12/2.39 inference(unit_resolution,[status(thm)],[261, 5502])).
% 2.12/2.39 tff(5504,plain,
% 2.12/2.39 (~r(s(s(z)), s(s(s(elem!1))))),
% 2.12/2.39 inference(unit_resolution,[status(thm)],[290, 5503, 152, 153])).
% 2.12/2.39 tff(5505,plain,
% 2.12/2.39 (b(s(s(z)), s(s(s(elem!1))))),
% 2.12/2.39 inference(unit_resolution,[status(thm)],[279, 5504])).
% 2.12/2.39 tff(5506,plain,
% 2.12/2.39 (b(s(s(s(elem!1))), s(s(s(z))))),
% 2.12/2.39 inference(unit_resolution,[status(thm)],[3574, 4580, 3567])).
% 2.12/2.39 tff(5507,plain,
% 2.12/2.39 (r(s(s(s(z))), s(s(elem!1))) <=> r(s(s(s(z))), elem!1)),
% 2.12/2.39 inference(symmetry,[status(thm)],[4026])).
% 2.12/2.39 tff(5508,plain,
% 2.12/2.39 (r(s(s(s(z))), s(s(s(elem!1)))) <=> r(s(s(s(z))), elem!1)),
% 2.12/2.39 inference(transitivity,[status(thm)],[4023, 5507])).
% 2.12/2.39 tff(5509,plain,
% 2.12/2.39 ((~r(s(s(s(z))), s(s(s(elem!1))))) <=> (~r(s(s(s(z))), elem!1))),
% 2.12/2.39 inference(monotonicity,[status(thm)],[5508])).
% 2.12/2.39 tff(5510,plain,
% 2.12/2.39 (~r(s(s(s(z))), s(s(s(elem!1))))),
% 2.12/2.39 inference(unit_resolution,[status(thm)],[4120, 197, 154, 155, 1733])).
% 2.12/2.39 tff(5511,plain,
% 2.12/2.39 (~r(s(s(s(z))), elem!1)),
% 2.12/2.39 inference(modus_ponens,[status(thm)],[5510, 5509])).
% 2.12/2.39 tff(5512,plain,
% 2.12/2.39 (b(s(s(s(z))), elem!1)),
% 2.12/2.39 inference(unit_resolution,[status(thm)],[2826, 5511, 4027])).
% 2.12/2.39 tff(5513,plain,
% 2.12/2.39 (b(s(s(s(z))), s(s(s(elem!1))))),
% 2.12/2.39 inference(unit_resolution,[status(thm)],[4078, 5512, 4031])).
% 2.12/2.39 tff(5514,plain,
% 2.12/2.39 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), s(s(s(elem!1))))) | (~b(s(s(s(z))), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(s(s(z))))) | (~b(s(s(z)), s(s(s(z))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(z)), s(s(s(elem!1))))) | (~b(s(s(s(z))), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(s(s(z))))) | (~b(s(s(z)), s(s(s(z))))))),
% 2.12/2.39 inference(rewrite,[status(thm)],[])).
% 2.12/2.39 tff(5515,plain,
% 2.12/2.39 (((~b(s(s(s(z))), s(s(s(elem!1))))) | (~b(s(s(z)), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(s(s(z))))) | (~b(s(s(s(z))), s(s(s(elem!1))))) | (~b(s(s(z)), s(s(s(elem!1))))) | (~b(s(s(z)), s(s(s(z)))))) <=> ((~b(s(s(z)), s(s(s(elem!1))))) | (~b(s(s(s(z))), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(s(s(z))))) | (~b(s(s(z)), s(s(s(z))))))),
% 2.12/2.39 inference(rewrite,[status(thm)],[])).
% 2.12/2.39 tff(5516,plain,
% 2.12/2.39 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), s(s(s(elem!1))))) | (~b(s(s(z)), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(s(s(z))))) | (~b(s(s(s(z))), s(s(s(elem!1))))) | (~b(s(s(z)), s(s(s(elem!1))))) | (~b(s(s(z)), s(s(s(z))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), s(s(s(elem!1))))) | (~b(s(s(s(z))), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(s(s(z))))) | (~b(s(s(z)), s(s(s(z)))))))),
% 2.12/2.39 inference(monotonicity,[status(thm)],[5515])).
% 2.12/2.39 tff(5517,plain,
% 2.12/2.39 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), s(s(s(elem!1))))) | (~b(s(s(z)), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(s(s(z))))) | (~b(s(s(s(z))), s(s(s(elem!1))))) | (~b(s(s(z)), s(s(s(elem!1))))) | (~b(s(s(z)), s(s(s(z))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(z)), s(s(s(elem!1))))) | (~b(s(s(s(z))), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(s(s(z))))) | (~b(s(s(z)), s(s(s(z))))))),
% 2.12/2.39 inference(transitivity,[status(thm)],[5516, 5514])).
% 2.12/2.39 tff(5518,plain,
% 2.12/2.39 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), s(s(s(elem!1))))) | (~b(s(s(z)), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(s(s(z))))) | (~b(s(s(s(z))), s(s(s(elem!1))))) | (~b(s(s(z)), s(s(s(elem!1))))) | (~b(s(s(z)), s(s(s(z))))))),
% 2.12/2.39 inference(quant_inst,[status(thm)],[])).
% 2.12/2.39 tff(5519,plain,
% 2.12/2.39 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(z)), s(s(s(elem!1))))) | (~b(s(s(s(z))), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(s(s(z))))) | (~b(s(s(z)), s(s(s(z)))))),
% 2.12/2.39 inference(modus_ponens,[status(thm)],[5518, 5517])).
% 2.12/2.39 tff(5520,plain,
% 2.12/2.39 (~b(s(s(z)), s(s(s(z))))),
% 2.12/2.39 inference(unit_resolution,[status(thm)],[5519, 166, 263, 5513, 5506])).
% 2.12/2.39 tff(5521,plain,
% 2.12/2.39 (r(s(s(z)), s(s(s(z))))),
% 2.12/2.39 inference(unit_resolution,[status(thm)],[1730, 5520])).
% 2.12/2.39 tff(5522,plain,
% 2.12/2.39 (r(s(s(elem!1)), s(s(s(z)))) <=> r(s(s(s(elem!1))), s(s(s(z))))),
% 2.22/2.40 inference(monotonicity,[status(thm)],[334])).
% 2.22/2.40 tff(5523,plain,
% 2.22/2.40 (r(s(s(s(elem!1))), s(s(s(z)))) <=> r(s(s(elem!1)), s(s(s(z))))),
% 2.22/2.40 inference(symmetry,[status(thm)],[5522])).
% 2.22/2.40 tff(5524,plain,
% 2.22/2.40 ((~r(s(s(s(elem!1))), s(s(s(z))))) <=> (~r(s(s(elem!1)), s(s(s(z)))))),
% 2.22/2.40 inference(monotonicity,[status(thm)],[5523])).
% 2.22/2.40 tff(5525,plain,
% 2.22/2.40 (~r(s(s(elem!1)), s(s(s(z))))),
% 2.22/2.40 inference(modus_ponens,[status(thm)],[4580, 5524])).
% 2.22/2.40 tff(5526,plain,
% 2.22/2.40 ((s(s(s(elem!1))) = s(s(s(z)))) <=> (s(s(elem!1)) = s(s(s(z))))),
% 2.22/2.40 inference(monotonicity,[status(thm)],[2591])).
% 2.22/2.40 tff(5527,plain,
% 2.22/2.40 ((s(s(s(elem!1))) = s(s(s(z)))) <=> (s(s(s(z))) = s(s(elem!1)))),
% 2.22/2.40 inference(transitivity,[status(thm)],[5526, 4437])).
% 2.22/2.40 tff(5528,plain,
% 2.22/2.40 ((~(s(s(s(elem!1))) = s(s(s(z))))) <=> (~(s(s(s(z))) = s(s(elem!1))))),
% 2.22/2.40 inference(monotonicity,[status(thm)],[5527])).
% 2.22/2.40 tff(5529,plain,
% 2.22/2.40 (~(s(s(s(z))) = s(s(elem!1)))),
% 2.22/2.40 inference(modus_ponens,[status(thm)],[3567, 5528])).
% 2.22/2.40 tff(5530,plain,
% 2.22/2.40 ((~r(s(s(s(z))), s(s(s(elem!1))))) <=> (~r(s(s(s(z))), s(s(elem!1))))),
% 2.22/2.40 inference(monotonicity,[status(thm)],[4023])).
% 2.22/2.40 tff(5531,plain,
% 2.22/2.40 (~r(s(s(s(z))), s(s(elem!1)))),
% 2.22/2.40 inference(modus_ponens,[status(thm)],[5510, 5530])).
% 2.22/2.40 tff(5532,plain,
% 2.22/2.40 ((s(s(s(z))) = s(s(elem!1))) <=> (s(s(elem!1)) = s(s(s(z))))),
% 2.22/2.40 inference(symmetry,[status(thm)],[4437])).
% 2.22/2.40 tff(5533,plain,
% 2.22/2.40 ((~(s(s(s(z))) = s(s(elem!1)))) <=> (~(s(s(elem!1)) = s(s(s(z)))))),
% 2.22/2.40 inference(monotonicity,[status(thm)],[5532])).
% 2.22/2.40 tff(5534,assumption,(~(s(s(s(z))) = s(s(elem!1)))), introduced(assumption)).
% 2.22/2.40 tff(5535,plain,
% 2.22/2.40 (~(s(s(elem!1)) = s(s(s(z))))),
% 2.22/2.40 inference(modus_ponens,[status(thm)],[5534, 5533])).
% 2.22/2.40 tff(5536,assumption,(~r(s(s(s(z))), s(s(elem!1)))), introduced(assumption)).
% 2.22/2.40 tff(5537,plain,
% 2.22/2.40 ((s(s(s(z))) = s(s(elem!1))) | b(s(s(s(z))), s(s(elem!1)))),
% 2.22/2.40 inference(unit_resolution,[status(thm)],[4523, 79, 5536])).
% 2.22/2.40 tff(5538,plain,
% 2.22/2.40 (b(s(s(s(z))), s(s(elem!1)))),
% 2.22/2.40 inference(unit_resolution,[status(thm)],[5537, 5534])).
% 2.22/2.40 tff(5539,assumption,(b(s(s(elem!1)), s(s(s(z))))), introduced(assumption)).
% 2.22/2.40 tff(5540,assumption,(b(s(s(s(z))), s(s(elem!1)))), introduced(assumption)).
% 2.22/2.40 tff(5541,plain,
% 2.22/2.40 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(elem!1)))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(elem!1)), s(s(s(z))))) | (~b(s(s(s(z))), s(s(elem!1)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), s(s(elem!1)))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(elem!1)), s(s(s(z))))) | (~b(s(s(s(z))), s(s(elem!1)))))),
% 2.22/2.40 inference(rewrite,[status(thm)],[])).
% 2.22/2.40 tff(5542,plain,
% 2.22/2.40 (((~b(s(s(elem!1)), s(s(s(z))))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(z))), s(s(elem!1)))) | (~b(s(s(elem!1)), s(s(s(z))))) | (~b(s(z), s(s(s(z))))) | (~b(s(z), s(s(elem!1))))) <=> ((~b(s(z), s(s(elem!1)))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(elem!1)), s(s(s(z))))) | (~b(s(s(s(z))), s(s(elem!1)))))),
% 2.22/2.40 inference(rewrite,[status(thm)],[])).
% 2.22/2.40 tff(5543,plain,
% 2.22/2.40 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), s(s(s(z))))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(z))), s(s(elem!1)))) | (~b(s(s(elem!1)), s(s(s(z))))) | (~b(s(z), s(s(s(z))))) | (~b(s(z), s(s(elem!1)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(elem!1)))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(elem!1)), s(s(s(z))))) | (~b(s(s(s(z))), s(s(elem!1))))))),
% 2.22/2.40 inference(monotonicity,[status(thm)],[5542])).
% 2.22/2.40 tff(5544,plain,
% 2.22/2.40 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), s(s(s(z))))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(z))), s(s(elem!1)))) | (~b(s(s(elem!1)), s(s(s(z))))) | (~b(s(z), s(s(s(z))))) | (~b(s(z), s(s(elem!1)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), s(s(elem!1)))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(elem!1)), s(s(s(z))))) | (~b(s(s(s(z))), s(s(elem!1)))))),
% 2.22/2.40 inference(transitivity,[status(thm)],[5543, 5541])).
% 2.22/2.40 tff(5545,plain,
% 2.22/2.40 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), s(s(s(z))))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(z))), s(s(elem!1)))) | (~b(s(s(elem!1)), s(s(s(z))))) | (~b(s(z), s(s(s(z))))) | (~b(s(z), s(s(elem!1)))))),
% 2.22/2.40 inference(quant_inst,[status(thm)],[])).
% 2.22/2.40 tff(5546,plain,
% 2.22/2.40 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), s(s(elem!1)))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(elem!1)), s(s(s(z))))) | (~b(s(s(s(z))), s(s(elem!1))))),
% 2.22/2.40 inference(modus_ponens,[status(thm)],[5545, 5544])).
% 2.22/2.40 tff(5547,plain,
% 2.22/2.40 ($false),
% 2.22/2.40 inference(unit_resolution,[status(thm)],[5546, 166, 376, 988, 5540, 5539])).
% 2.22/2.40 tff(5548,plain,((~b(s(s(elem!1)), s(s(s(z))))) | (~b(s(z), s(s(elem!1)))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(z))), s(s(elem!1))))), inference(lemma,lemma(discharge,[]))).
% 2.22/2.40 tff(5549,plain,
% 2.22/2.40 (~b(s(s(elem!1)), s(s(s(z))))),
% 2.22/2.40 inference(unit_resolution,[status(thm)],[5548, 5538, 988, 376])).
% 2.22/2.40 tff(5550,plain,
% 2.22/2.40 (s(s(elem!1)) = s(s(s(z)))),
% 2.22/2.40 inference(unit_resolution,[status(thm)],[5092, 5549])).
% 2.22/2.40 tff(5551,plain,
% 2.22/2.40 ($false),
% 2.22/2.40 inference(unit_resolution,[status(thm)],[5550, 5535])).
% 2.22/2.40 tff(5552,plain,((s(s(s(z))) = s(s(elem!1))) | r(s(s(elem!1)), s(s(s(z)))) | (~b(s(z), s(s(s(z))))) | (~b(s(z), s(s(elem!1)))) | r(s(s(s(z))), s(s(elem!1)))), inference(lemma,lemma(discharge,[]))).
% 2.22/2.40 tff(5553,plain,
% 2.22/2.40 (~b(s(z), s(s(s(z))))),
% 2.22/2.40 inference(unit_resolution,[status(thm)],[5552, 5531, 376, 5529, 5525])).
% 2.22/2.40 tff(5554,plain,
% 2.22/2.40 (r(s(z), s(s(s(z))))),
% 2.22/2.40 inference(unit_resolution,[status(thm)],[1674, 5553])).
% 2.22/2.40 tff(5555,plain,
% 2.22/2.40 (b(s(z), s(s(s(elem!1))))),
% 2.22/2.40 inference(unit_resolution,[status(thm)],[5500, 334, 376])).
% 2.22/2.40 tff(5556,plain,
% 2.22/2.40 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(s(elem!1))))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(z))), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(s(s(z))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), s(s(s(elem!1))))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(z))), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(s(s(z))))))),
% 2.22/2.40 inference(rewrite,[status(thm)],[])).
% 2.22/2.40 tff(5557,plain,
% 2.22/2.40 (((~b(s(s(s(z))), s(s(s(elem!1))))) | (~b(s(s(s(z))), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(s(s(z))))) | (~b(s(z), s(s(s(elem!1))))) | (~b(s(s(s(z))), s(s(s(elem!1))))) | (~b(s(s(s(z))), s(z)))) <=> ((~b(s(z), s(s(s(elem!1))))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(z))), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(s(s(z))))))),
% 2.22/2.40 inference(rewrite,[status(thm)],[])).
% 2.22/2.40 tff(5558,plain,
% 2.22/2.40 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), s(s(s(elem!1))))) | (~b(s(s(s(z))), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(s(s(z))))) | (~b(s(z), s(s(s(elem!1))))) | (~b(s(s(s(z))), s(s(s(elem!1))))) | (~b(s(s(s(z))), s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(s(elem!1))))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(z))), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(s(s(z)))))))),
% 2.22/2.40 inference(monotonicity,[status(thm)],[5557])).
% 2.22/2.40 tff(5559,plain,
% 2.22/2.40 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), s(s(s(elem!1))))) | (~b(s(s(s(z))), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(s(s(z))))) | (~b(s(z), s(s(s(elem!1))))) | (~b(s(s(s(z))), s(s(s(elem!1))))) | (~b(s(s(s(z))), s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), s(s(s(elem!1))))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(z))), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(s(s(z))))))),
% 2.22/2.40 inference(transitivity,[status(thm)],[5558, 5556])).
% 2.22/2.40 tff(5560,plain,
% 2.22/2.40 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), s(s(s(elem!1))))) | (~b(s(s(s(z))), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(s(s(z))))) | (~b(s(z), s(s(s(elem!1))))) | (~b(s(s(s(z))), s(s(s(elem!1))))) | (~b(s(s(s(z))), s(z))))),
% 2.22/2.40 inference(quant_inst,[status(thm)],[])).
% 2.22/2.40 tff(5561,plain,
% 2.22/2.40 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), s(s(s(elem!1))))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(z))), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(s(s(z)))))),
% 2.22/2.40 inference(modus_ponens,[status(thm)],[5560, 5559])).
% 2.22/2.40 tff(5562,plain,
% 2.22/2.40 (~b(s(s(s(z))), s(z))),
% 2.22/2.40 inference(unit_resolution,[status(thm)],[5561, 166, 5555, 5513, 5506])).
% 2.22/2.40 tff(5563,plain,
% 2.22/2.40 (r(s(s(s(z))), s(z))),
% 2.22/2.40 inference(unit_resolution,[status(thm)],[1763, 5562])).
% 2.22/2.40 tff(5564,plain,
% 2.22/2.40 (((~r(s(s(s(z))), s(z))) | (~r(s(z), s(s(s(z))))) | (~r(s(s(z)), s(s(s(z))))) | (~r(s(s(z)), s(z)))) <=> ((~r(s(s(z)), s(z))) | (~r(s(s(z)), s(s(s(z))))) | (~r(s(z), s(s(s(z))))) | (~r(s(s(s(z))), s(z))))),
% 2.22/2.40 inference(rewrite,[status(thm)],[])).
% 2.22/2.40 tff(5565,plain,
% 2.22/2.40 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(z))), s(z))) | (~r(s(z), s(s(s(z))))) | (~r(s(s(z)), s(s(s(z))))) | (~r(s(s(z)), s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(z)), s(z))) | (~r(s(s(z)), s(s(s(z))))) | (~r(s(z), s(s(s(z))))) | (~r(s(s(s(z))), s(z)))))),
% 2.22/2.40 inference(monotonicity,[status(thm)],[5564])).
% 2.22/2.40 tff(5566,plain,
% 2.22/2.40 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(z))), s(z))) | (~r(s(z), s(s(s(z))))) | (~r(s(s(z)), s(s(s(z))))) | (~r(s(s(z)), s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(z)), s(z))) | (~r(s(s(z)), s(s(s(z))))) | (~r(s(z), s(s(s(z))))) | (~r(s(s(s(z))), s(z))))),
% 2.22/2.40 inference(transitivity,[status(thm)],[5565, 5047])).
% 2.22/2.40 tff(5567,plain,
% 2.22/2.40 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(z))), s(z))) | (~r(s(z), s(s(s(z))))) | (~r(s(s(z)), s(s(s(z))))) | (~r(s(s(z)), s(z))))),
% 2.22/2.40 inference(quant_inst,[status(thm)],[])).
% 2.22/2.40 tff(5568,plain,
% 2.22/2.40 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(z)), s(z))) | (~r(s(s(z)), s(s(s(z))))) | (~r(s(z), s(s(s(z))))) | (~r(s(s(s(z))), s(z)))),
% 2.22/2.40 inference(modus_ponens,[status(thm)],[5567, 5566])).
% 2.22/2.40 tff(5569,plain,
% 2.22/2.40 ($false),
% 2.22/2.40 inference(unit_resolution,[status(thm)],[5568, 197, 392, 5563, 5554, 5521])).
% 2.22/2.40 tff(5570,plain,((~r(s(s(s(z))), z)) | (~r(s(s(z)), s(z))) | (~b(s(s(z)), s(s(s(elem!1))))) | (~b(s(z), s(s(elem!1)))) | (~(s(s(elem!1)) = s(s(s(elem!1))))) | (s(s(s(elem!1))) = s(s(s(z)))) | (~r(s(s(s(elem!1))), z)) | (~r(z, s(s(z))))), inference(lemma,lemma(discharge,[]))).
% 2.22/2.40 tff(5571,plain,
% 2.22/2.40 (~r(s(s(s(z))), z)),
% 2.22/2.40 inference(unit_resolution,[status(thm)],[5570, 309, 5505, 5288, 5468, 5494, 153, 152])).
% 2.22/2.40 tff(5572,plain,
% 2.22/2.40 (b(s(s(s(z))), z)),
% 2.22/2.40 inference(unit_resolution,[status(thm)],[1713, 5571])).
% 2.22/2.40 tff(5573,plain,
% 2.22/2.40 (~r(s(s(s(elem!1))), s(s(z)))),
% 2.22/2.40 inference(unit_resolution,[status(thm)],[1588, 5503, 152, 309])).
% 2.22/2.40 tff(5574,plain,
% 2.22/2.40 (b(s(s(s(elem!1))), s(s(z)))),
% 2.22/2.40 inference(unit_resolution,[status(thm)],[218, 5573])).
% 2.22/2.40 tff(5575,plain,
% 2.22/2.40 (~r(s(s(z)), s(s(elem!1)))),
% 2.22/2.40 inference(unit_resolution,[status(thm)],[338, 5504, 5468])).
% 2.22/2.40 tff(5576,plain,
% 2.22/2.40 (~b(z, s(s(elem!1)))),
% 2.22/2.40 inference(unit_resolution,[status(thm)],[5343, 5491, 118, 5288])).
% 2.22/2.40 tff(5577,plain,
% 2.22/2.40 (r(z, s(s(elem!1)))),
% 2.22/2.40 inference(unit_resolution,[status(thm)],[1795, 5576])).
% 2.22/2.40 tff(5578,plain,
% 2.22/2.40 (~r(s(s(elem!1)), s(s(z)))),
% 2.22/2.40 inference(unit_resolution,[status(thm)],[401, 5577, 152, 309])).
% 2.22/2.40 tff(5579,plain,
% 2.22/2.40 (~b(s(z), s(s(z)))),
% 2.22/2.40 inference(unit_resolution,[status(thm)],[5300, 5578, 5288, 5492, 5575])).
% 2.22/2.40 tff(5580,plain,
% 2.22/2.40 (r(s(z), s(s(z)))),
% 2.22/2.40 inference(unit_resolution,[status(thm)],[427, 5579])).
% 2.22/2.40 tff(5581,plain,
% 2.22/2.40 (~r(s(z), z)),
% 2.22/2.40 inference(unit_resolution,[status(thm)],[3947, 197, 5580, 152, 309])).
% 2.22/2.40 tff(5582,plain,
% 2.22/2.40 (b(s(z), z)),
% 2.22/2.40 inference(unit_resolution,[status(thm)],[230, 5581])).
% 2.22/2.40 tff(5583,plain,
% 2.22/2.40 (~b(s(s(s(z))), s(z))),
% 2.22/2.40 inference(unit_resolution,[status(thm)],[4045, 166, 5582, 118, 5572])).
% 2.22/2.40 tff(5584,plain,
% 2.22/2.40 (r(s(s(s(z))), s(z))),
% 2.22/2.40 inference(unit_resolution,[status(thm)],[1763, 5583])).
% 2.22/2.40 tff(5585,plain,
% 2.22/2.40 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(z)), s(z))) | (~r(s(z), s(s(z)))) | (~r(s(s(z)), s(s(s(z))))) | (~r(s(s(s(z))), s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(z)), s(z))) | (~r(s(z), s(s(z)))) | (~r(s(s(z)), s(s(s(z))))) | (~r(s(s(s(z))), s(z))))),
% 2.22/2.40 inference(rewrite,[status(thm)],[])).
% 2.22/2.40 tff(5586,plain,
% 2.22/2.40 (((~r(s(z), s(s(z)))) | (~r(s(s(s(z))), s(z))) | (~r(s(s(z)), s(z))) | (~r(s(s(z)), s(s(s(z)))))) <=> ((~r(s(s(z)), s(z))) | (~r(s(z), s(s(z)))) | (~r(s(s(z)), s(s(s(z))))) | (~r(s(s(s(z))), s(z))))),
% 2.22/2.40 inference(rewrite,[status(thm)],[])).
% 2.22/2.40 tff(5587,plain,
% 2.22/2.40 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(s(z)))) | (~r(s(s(s(z))), s(z))) | (~r(s(s(z)), s(z))) | (~r(s(s(z)), s(s(s(z))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(z)), s(z))) | (~r(s(z), s(s(z)))) | (~r(s(s(z)), s(s(s(z))))) | (~r(s(s(s(z))), s(z)))))),
% 2.22/2.40 inference(monotonicity,[status(thm)],[5586])).
% 2.22/2.40 tff(5588,plain,
% 2.22/2.40 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(s(z)))) | (~r(s(s(s(z))), s(z))) | (~r(s(s(z)), s(z))) | (~r(s(s(z)), s(s(s(z))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(z)), s(z))) | (~r(s(z), s(s(z)))) | (~r(s(s(z)), s(s(s(z))))) | (~r(s(s(s(z))), s(z))))),
% 2.22/2.40 inference(transitivity,[status(thm)],[5587, 5585])).
% 2.22/2.40 tff(5589,plain,
% 2.22/2.40 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(s(z)))) | (~r(s(s(s(z))), s(z))) | (~r(s(s(z)), s(z))) | (~r(s(s(z)), s(s(s(z))))))),
% 2.22/2.40 inference(quant_inst,[status(thm)],[])).
% 2.22/2.40 tff(5590,plain,
% 2.22/2.40 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(z)), s(z))) | (~r(s(z), s(s(z)))) | (~r(s(s(z)), s(s(s(z))))) | (~r(s(s(s(z))), s(z)))),
% 2.22/2.40 inference(modus_ponens,[status(thm)],[5589, 5588])).
% 2.22/2.40 tff(5591,plain,
% 2.22/2.40 (~r(s(s(z)), s(s(s(z))))),
% 2.22/2.40 inference(unit_resolution,[status(thm)],[5590, 197, 5580, 309, 5584])).
% 2.22/2.40 tff(5592,plain,
% 2.22/2.40 (b(s(s(z)), s(s(s(z))))),
% 2.22/2.40 inference(unit_resolution,[status(thm)],[1730, 5591])).
% 2.22/2.40 tff(5593,plain,
% 2.22/2.40 (~b(s(s(s(elem!1))), s(s(s(z))))),
% 2.22/2.40 inference(unit_resolution,[status(thm)],[3565, 5592, 118, 5574, 5572, 96])).
% 2.22/2.40 tff(5594,plain,
% 2.22/2.40 (r(s(s(s(elem!1))), s(s(s(z))))),
% 2.22/2.40 inference(unit_resolution,[status(thm)],[3574, 5593, 5494])).
% 2.22/2.40 tff(5595,plain,
% 2.22/2.40 (r(s(s(s(z))), s(s(s(elem!1)))) <=> r(s(s(s(z))), s(s(elem!1)))),
% 2.22/2.40 inference(monotonicity,[status(thm)],[5476])).
% 2.22/2.40 tff(5596,plain,
% 2.22/2.40 (r(s(s(s(z))), s(s(elem!1))) <=> r(s(s(s(z))), s(s(s(elem!1))))),
% 2.22/2.40 inference(symmetry,[status(thm)],[5595])).
% 2.22/2.40 tff(5597,plain,
% 2.22/2.40 (elem!1 = s(s(elem!1))),
% 2.22/2.40 inference(transitivity,[status(thm)],[1170, 5471, 104])).
% 2.22/2.40 tff(5598,plain,
% 2.22/2.40 (r(s(s(s(z))), elem!1) <=> r(s(s(s(z))), s(s(elem!1)))),
% 2.22/2.40 inference(monotonicity,[status(thm)],[5597])).
% 2.22/2.40 tff(5599,plain,
% 2.22/2.40 (~(s(s(s(z))) = elem!1)),
% 2.22/2.40 inference(unit_resolution,[status(thm)],[3122, 5468])).
% 2.22/2.40 tff(5600,plain,
% 2.22/2.40 (s(s(s(elem!1))) = s(s(elem!1))),
% 2.22/2.40 inference(unit_resolution,[status(thm)],[4030, 5468])).
% 2.22/2.40 tff(5601,plain,
% 2.22/2.40 (~r(s(s(s(z))), s(s(z)))),
% 2.22/2.40 inference(unit_resolution,[status(thm)],[5076, 197, 5580, 309, 5584])).
% 2.22/2.40 tff(5602,plain,
% 2.22/2.40 (b(s(s(s(z))), s(s(z)))),
% 2.22/2.40 inference(unit_resolution,[status(thm)],[1010, 5601])).
% 2.22/2.40 tff(5603,plain,
% 2.22/2.40 ((~b(s(s(s(z))), s(s(z)))) | (~b(s(s(s(z))), s(s(s(elem!1)))))),
% 2.22/2.40 inference(unit_resolution,[status(thm)],[4061, 166, 5582, 96, 5505, 5572])).
% 2.22/2.40 tff(5604,plain,
% 2.22/2.40 (~b(s(s(s(z))), s(s(s(elem!1))))),
% 2.22/2.40 inference(unit_resolution,[status(thm)],[5603, 5602])).
% 2.22/2.40 tff(5605,plain,
% 2.22/2.40 (~b(s(s(s(z))), elem!1)),
% 2.22/2.40 inference(unit_resolution,[status(thm)],[4078, 5604, 5600])).
% 2.22/2.40 tff(5606,plain,
% 2.22/2.40 (r(s(s(s(z))), elem!1)),
% 2.22/2.40 inference(unit_resolution,[status(thm)],[2826, 5605, 5599])).
% 2.22/2.40 tff(5607,plain,
% 2.22/2.40 (r(s(s(s(z))), s(s(elem!1)))),
% 2.22/2.40 inference(modus_ponens,[status(thm)],[5606, 5598])).
% 2.22/2.40 tff(5608,plain,
% 2.22/2.40 (r(s(s(s(z))), s(s(s(elem!1))))),
% 2.22/2.40 inference(modus_ponens,[status(thm)],[5607, 5596])).
% 2.22/2.40 tff(5609,plain,
% 2.22/2.40 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(z))), s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), z)) | (~r(z, s(s(s(elem!1))))) | (~r(z, s(s(s(z))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(z))), s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), z)) | (~r(z, s(s(s(elem!1))))) | (~r(z, s(s(s(z))))))),
% 2.22/2.40 inference(rewrite,[status(thm)],[])).
% 2.22/2.40 tff(5610,plain,
% 2.22/2.40 (((~r(s(s(s(elem!1))), z)) | (~r(s(s(s(z))), s(s(s(elem!1))))) | (~r(z, s(s(s(elem!1))))) | (~r(z, s(s(s(z)))))) <=> ((~r(s(s(s(z))), s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), z)) | (~r(z, s(s(s(elem!1))))) | (~r(z, s(s(s(z))))))),
% 2.22/2.40 inference(rewrite,[status(thm)],[])).
% 2.22/2.40 tff(5611,plain,
% 2.22/2.40 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), z)) | (~r(s(s(s(z))), s(s(s(elem!1))))) | (~r(z, s(s(s(elem!1))))) | (~r(z, s(s(s(z))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(z))), s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), z)) | (~r(z, s(s(s(elem!1))))) | (~r(z, s(s(s(z)))))))),
% 2.22/2.40 inference(monotonicity,[status(thm)],[5610])).
% 2.22/2.40 tff(5612,plain,
% 2.22/2.40 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), z)) | (~r(s(s(s(z))), s(s(s(elem!1))))) | (~r(z, s(s(s(elem!1))))) | (~r(z, s(s(s(z))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(z))), s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), z)) | (~r(z, s(s(s(elem!1))))) | (~r(z, s(s(s(z))))))),
% 2.22/2.40 inference(transitivity,[status(thm)],[5611, 5609])).
% 2.22/2.40 tff(5613,plain,
% 2.22/2.40 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), z)) | (~r(s(s(s(z))), s(s(s(elem!1))))) | (~r(z, s(s(s(elem!1))))) | (~r(z, s(s(s(z))))))),
% 2.22/2.40 inference(quant_inst,[status(thm)],[])).
% 2.22/2.40 tff(5614,plain,
% 2.22/2.40 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(z))), s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), z)) | (~r(z, s(s(s(elem!1))))) | (~r(z, s(s(s(z)))))),
% 2.22/2.40 inference(modus_ponens,[status(thm)],[5613, 5612])).
% 2.22/2.40 tff(5615,plain,
% 2.22/2.40 ((~r(s(s(s(z))), s(s(s(elem!1))))) | (~r(z, s(s(s(z)))))),
% 2.22/2.40 inference(unit_resolution,[status(thm)],[5614, 197, 153, 5503])).
% 2.22/2.40 tff(5616,plain,
% 2.22/2.40 (~r(z, s(s(s(z))))),
% 2.22/2.40 inference(unit_resolution,[status(thm)],[5615, 5608])).
% 2.22/2.40 tff(5617,plain,
% 2.22/2.40 (b(z, s(s(s(z))))),
% 2.22/2.40 inference(unit_resolution,[status(thm)],[1697, 5616])).
% 2.22/2.41 tff(5618,plain,
% 2.22/2.41 (((~b(s(s(z)), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(z))))) <=> ((~b(s(s(s(z))), s(s(z)))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(s(s(z)))), s(s(s(z))))))),
% 2.22/2.41 inference(rewrite,[status(thm)],[])).
% 2.22/2.41 tff(5619,plain,
% 2.22/2.41 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(z)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), s(s(z)))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(s(s(z)))), s(s(s(z)))))))),
% 2.22/2.41 inference(monotonicity,[status(thm)],[5618])).
% 2.22/2.41 tff(5620,plain,
% 2.22/2.41 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(z)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(s(s(z)))), s(s(s(z))))))),
% 2.22/2.41 inference(transitivity,[status(thm)],[5619, 4872])).
% 2.22/2.41 tff(5621,plain,
% 2.22/2.41 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(z)))))),
% 2.22/2.41 inference(quant_inst,[status(thm)],[])).
% 2.22/2.41 tff(5622,plain,
% 2.22/2.41 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(s(s(z)))), s(s(s(z)))))),
% 2.22/2.41 inference(modus_ponens,[status(thm)],[5621, 5620])).
% 2.22/2.41 tff(5623,plain,
% 2.22/2.41 (~b(s(s(s(s(z)))), s(s(z)))),
% 2.22/2.41 inference(unit_resolution,[status(thm)],[5622, 166, 986, 987, 4732])).
% 2.22/2.41 tff(5624,plain,
% 2.22/2.41 ((s(s(z)) = s(s(s(s(z))))) <=> (s(s(s(s(z)))) = s(s(z)))),
% 2.22/2.41 inference(commutativity,[status(thm)],[])).
% 2.22/2.41 tff(5625,plain,
% 2.22/2.41 ((~(s(s(z)) = s(s(s(s(z)))))) <=> (~(s(s(s(s(z)))) = s(s(z))))),
% 2.22/2.41 inference(monotonicity,[status(thm)],[5624])).
% 2.22/2.41 tff(5626,plain,
% 2.22/2.41 (~(s(s(s(s(z)))) = s(s(z)))),
% 2.22/2.41 inference(modus_ponens,[status(thm)],[4748, 5625])).
% 2.22/2.41 tff(5627,plain,
% 2.22/2.41 (((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((s(s(s(s(z)))) = s(s(z))) | b(s(s(s(s(z)))), s(s(z))) | r(s(s(s(s(z)))), s(s(z))))) <=> ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (s(s(s(s(z)))) = s(s(z))) | b(s(s(s(s(z)))), s(s(z))) | r(s(s(s(s(z)))), s(s(z))))),
% 2.22/2.41 inference(rewrite,[status(thm)],[])).
% 2.22/2.41 tff(5628,plain,
% 2.22/2.41 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((s(s(s(s(z)))) = s(s(z))) | b(s(s(s(s(z)))), s(s(z))) | r(s(s(s(s(z)))), s(s(z))))),
% 2.22/2.41 inference(quant_inst,[status(thm)],[])).
% 2.22/2.41 tff(5629,plain,
% 2.22/2.41 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (s(s(s(s(z)))) = s(s(z))) | b(s(s(s(s(z)))), s(s(z))) | r(s(s(s(s(z)))), s(s(z)))),
% 2.22/2.41 inference(modus_ponens,[status(thm)],[5628, 5627])).
% 2.22/2.41 tff(5630,plain,
% 2.22/2.41 ((s(s(s(s(z)))) = s(s(z))) | b(s(s(s(s(z)))), s(s(z))) | r(s(s(s(s(z)))), s(s(z)))),
% 2.22/2.41 inference(unit_resolution,[status(thm)],[5629, 79])).
% 2.22/2.41 tff(5631,plain,
% 2.22/2.41 (b(s(s(s(s(z)))), s(s(z))) | r(s(s(s(s(z)))), s(s(z)))),
% 2.22/2.41 inference(unit_resolution,[status(thm)],[5630, 5626])).
% 2.22/2.41 tff(5632,plain,
% 2.22/2.41 (r(s(s(s(s(z)))), s(s(z)))),
% 2.22/2.41 inference(unit_resolution,[status(thm)],[5631, 5623])).
% 2.22/2.41 tff(5633,plain,
% 2.22/2.41 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), s(s(z)))) | (~b(z, s(s(s(z))))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(s(z)))), z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(z))), s(s(z)))) | (~b(z, s(s(s(z))))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(s(z)))), z)))),
% 2.22/2.41 inference(rewrite,[status(thm)],[])).
% 2.22/2.41 tff(5634,plain,
% 2.22/2.41 (((~b(s(s(z)), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(z))), s(s(z)))) | (~b(z, s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(s(z)))), z))) <=> ((~b(s(s(s(z))), s(s(z)))) | (~b(z, s(s(s(z))))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(s(z)))), z)))),
% 2.22/2.41 inference(rewrite,[status(thm)],[])).
% 2.22/2.41 tff(5635,plain,
% 2.22/2.41 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(z))), s(s(z)))) | (~b(z, s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(s(z)))), z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), s(s(z)))) | (~b(z, s(s(s(z))))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(s(z)))), z))))),
% 2.22/2.41 inference(monotonicity,[status(thm)],[5634])).
% 2.22/2.41 tff(5636,plain,
% 2.22/2.41 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(z))), s(s(z)))) | (~b(z, s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(s(z)))), z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(z))), s(s(z)))) | (~b(z, s(s(s(z))))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(s(z)))), z)))),
% 2.22/2.41 inference(transitivity,[status(thm)],[5635, 5633])).
% 2.22/2.41 tff(5637,plain,
% 2.22/2.41 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(z))), s(s(z)))) | (~b(z, s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(s(z)))), z)))),
% 2.22/2.41 inference(quant_inst,[status(thm)],[])).
% 2.22/2.41 tff(5638,plain,
% 2.22/2.41 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(z))), s(s(z)))) | (~b(z, s(s(s(z))))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(s(z)))), z))),
% 2.22/2.41 inference(modus_ponens,[status(thm)],[5637, 5636])).
% 2.22/2.41 tff(5639,plain,
% 2.22/2.41 (~b(s(s(s(s(z)))), z)),
% 2.22/2.41 inference(unit_resolution,[status(thm)],[5638, 166, 986, 987, 1700, 4732])).
% 2.22/2.41 tff(5640,plain,
% 2.22/2.41 (r(s(s(s(s(z)))), z)),
% 2.22/2.41 inference(unit_resolution,[status(thm)],[3266, 5639])).
% 2.22/2.41 tff(5641,plain,
% 2.22/2.41 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(z)), s(z))) | (~r(z, s(s(z)))) | (~r(s(s(s(s(z)))), z)) | (~r(s(s(s(s(z)))), s(s(z)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(z)), s(z))) | (~r(z, s(s(z)))) | (~r(s(s(s(s(z)))), z)) | (~r(s(s(s(s(z)))), s(s(z)))))),
% 2.22/2.41 inference(rewrite,[status(thm)],[])).
% 2.22/2.41 tff(5642,plain,
% 2.22/2.41 (((~r(s(s(z)), s(z))) | (~r(z, s(s(z)))) | (~r(s(s(s(s(z)))), s(s(z)))) | (~r(s(s(s(s(z)))), z))) <=> ((~r(s(s(z)), s(z))) | (~r(z, s(s(z)))) | (~r(s(s(s(s(z)))), z)) | (~r(s(s(s(s(z)))), s(s(z)))))),
% 2.22/2.41 inference(rewrite,[status(thm)],[])).
% 2.22/2.41 tff(5643,plain,
% 2.22/2.41 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(z)), s(z))) | (~r(z, s(s(z)))) | (~r(s(s(s(s(z)))), s(s(z)))) | (~r(s(s(s(s(z)))), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(z)), s(z))) | (~r(z, s(s(z)))) | (~r(s(s(s(s(z)))), z)) | (~r(s(s(s(s(z)))), s(s(z))))))),
% 2.22/2.41 inference(monotonicity,[status(thm)],[5642])).
% 2.22/2.41 tff(5644,plain,
% 2.22/2.41 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(z)), s(z))) | (~r(z, s(s(z)))) | (~r(s(s(s(s(z)))), s(s(z)))) | (~r(s(s(s(s(z)))), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(z)), s(z))) | (~r(z, s(s(z)))) | (~r(s(s(s(s(z)))), z)) | (~r(s(s(s(s(z)))), s(s(z)))))),
% 2.22/2.41 inference(transitivity,[status(thm)],[5643, 5641])).
% 2.22/2.41 tff(5645,plain,
% 2.22/2.41 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(z)), s(z))) | (~r(z, s(s(z)))) | (~r(s(s(s(s(z)))), s(s(z)))) | (~r(s(s(s(s(z)))), z)))),
% 2.22/2.41 inference(quant_inst,[status(thm)],[])).
% 2.22/2.41 tff(5646,plain,
% 2.22/2.41 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(z)), s(z))) | (~r(z, s(s(z)))) | (~r(s(s(s(s(z)))), z)) | (~r(s(s(s(s(z)))), s(s(z))))),
% 2.22/2.41 inference(modus_ponens,[status(thm)],[5645, 5644])).
% 2.22/2.41 tff(5647,plain,
% 2.22/2.41 ($false),
% 2.22/2.41 inference(unit_resolution,[status(thm)],[5646, 197, 155, 392, 5640, 5632])).
% 2.22/2.41 tff(5648,plain,((~b(s(s(s(s(z)))), s(s(s(z))))) | (~r(z, s(s(z)))) | (~r(s(s(z)), s(z))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(s(z))), s(s(z)))) | (~b(z, s(s(s(z)))))), inference(lemma,lemma(discharge,[]))).
% 2.22/2.41 tff(5649,plain,
% 2.22/2.41 (~b(s(s(s(s(z)))), s(s(s(z))))),
% 2.22/2.41 inference(unit_resolution,[status(thm)],[5648, 309, 152, 5592, 5602, 5617])).
% 2.22/2.41 tff(5650,plain,
% 2.22/2.41 (r(s(s(s(s(z)))), s(s(s(z))))),
% 2.22/2.41 inference(unit_resolution,[status(thm)],[4662, 5649])).
% 2.22/2.41 tff(5651,plain,
% 2.22/2.41 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), s(s(s(z))))) | (~r(s(s(s(z))), s(z))) | (~r(s(s(s(s(z)))), s(s(s(z))))) | (~r(s(s(s(elem!1))), s(s(s(s(z)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(elem!1))), s(s(s(z))))) | (~r(s(s(s(z))), s(z))) | (~r(s(s(s(s(z)))), s(s(s(z))))) | (~r(s(s(s(elem!1))), s(s(s(s(z)))))))),
% 2.22/2.41 inference(rewrite,[status(thm)],[])).
% 2.22/2.41 tff(5652,plain,
% 2.22/2.41 (((~r(s(s(s(z))), s(z))) | (~r(s(s(s(s(z)))), s(s(s(z))))) | (~r(s(s(s(elem!1))), s(s(s(z))))) | (~r(s(s(s(elem!1))), s(s(s(s(z))))))) <=> ((~r(s(s(s(elem!1))), s(s(s(z))))) | (~r(s(s(s(z))), s(z))) | (~r(s(s(s(s(z)))), s(s(s(z))))) | (~r(s(s(s(elem!1))), s(s(s(s(z)))))))),
% 2.22/2.41 inference(rewrite,[status(thm)],[])).
% 2.22/2.41 tff(5653,plain,
% 2.22/2.41 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(z))), s(z))) | (~r(s(s(s(s(z)))), s(s(s(z))))) | (~r(s(s(s(elem!1))), s(s(s(z))))) | (~r(s(s(s(elem!1))), s(s(s(s(z)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), s(s(s(z))))) | (~r(s(s(s(z))), s(z))) | (~r(s(s(s(s(z)))), s(s(s(z))))) | (~r(s(s(s(elem!1))), s(s(s(s(z))))))))),
% 2.22/2.41 inference(monotonicity,[status(thm)],[5652])).
% 2.22/2.41 tff(5654,plain,
% 2.22/2.41 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(z))), s(z))) | (~r(s(s(s(s(z)))), s(s(s(z))))) | (~r(s(s(s(elem!1))), s(s(s(z))))) | (~r(s(s(s(elem!1))), s(s(s(s(z)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(elem!1))), s(s(s(z))))) | (~r(s(s(s(z))), s(z))) | (~r(s(s(s(s(z)))), s(s(s(z))))) | (~r(s(s(s(elem!1))), s(s(s(s(z)))))))),
% 2.22/2.41 inference(transitivity,[status(thm)],[5653, 5651])).
% 2.22/2.41 tff(5655,plain,
% 2.22/2.41 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(z))), s(z))) | (~r(s(s(s(s(z)))), s(s(s(z))))) | (~r(s(s(s(elem!1))), s(s(s(z))))) | (~r(s(s(s(elem!1))), s(s(s(s(z)))))))),
% 2.22/2.41 inference(quant_inst,[status(thm)],[])).
% 2.22/2.41 tff(5656,plain,
% 2.22/2.41 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(elem!1))), s(s(s(z))))) | (~r(s(s(s(z))), s(z))) | (~r(s(s(s(s(z)))), s(s(s(z))))) | (~r(s(s(s(elem!1))), s(s(s(s(z))))))),
% 2.22/2.41 inference(modus_ponens,[status(thm)],[5655, 5654])).
% 2.22/2.41 tff(5657,plain,
% 2.22/2.41 (~r(s(s(s(elem!1))), s(s(s(s(z)))))),
% 2.22/2.41 inference(unit_resolution,[status(thm)],[5656, 197, 5650, 5584, 5594])).
% 2.22/2.41 tff(5658,plain,
% 2.22/2.41 (inj_0(s(s(s(elem!1)))) = inj_0(s(elem!1))),
% 2.22/2.41 inference(symmetry,[status(thm)],[3117])).
% 2.22/2.41 tff(5659,plain,
% 2.22/2.41 (s(s(s(elem!1))) = elem!1),
% 2.22/2.41 inference(transitivity,[status(thm)],[2591, 105, 5658, 20])).
% 2.22/2.41 tff(5660,plain,
% 2.22/2.41 (r(s(s(s(elem!1))), s(s(s(s(z))))) <=> r(elem!1, s(s(s(s(z)))))),
% 2.22/2.41 inference(monotonicity,[status(thm)],[5659])).
% 2.22/2.41 tff(5661,plain,
% 2.22/2.41 (r(elem!1, s(s(s(s(z))))) <=> r(s(s(s(elem!1))), s(s(s(s(z)))))),
% 2.22/2.41 inference(symmetry,[status(thm)],[5660])).
% 2.22/2.41 tff(5662,plain,
% 2.22/2.41 (r(s(s(s(elem!1))), s(s(s(s(z)))))),
% 2.22/2.41 inference(modus_ponens,[status(thm)],[1089, 5661])).
% 2.22/2.41 tff(5663,assumption,(~r(s(s(s(elem!1))), s(s(s(s(z)))))), introduced(assumption)).
% 2.22/2.41 tff(5664,plain,
% 2.22/2.41 ($false),
% 2.22/2.41 inference(unit_resolution,[status(thm)],[5663, 5662])).
% 2.22/2.41 tff(5665,plain,(r(s(s(s(elem!1))), s(s(s(s(z))))) | (~r(elem!1, s(s(s(s(z)))))) | (~(s(s(elem!1)) = s(s(s(elem!1)))))), inference(lemma,lemma(discharge,[]))).
% 2.22/2.41 tff(5666,plain,
% 2.22/2.41 (~r(elem!1, s(s(s(s(z)))))),
% 2.22/2.41 inference(unit_resolution,[status(thm)],[5665, 5657, 5468])).
% 2.22/2.41 tff(5667,plain,
% 2.22/2.41 (b(elem!1, s(s(s(s(z)))))),
% 2.22/2.41 inference(unit_resolution,[status(thm)],[1098, 5666, 5490])).
% 2.22/2.41 tff(5668,plain,
% 2.22/2.41 (b(s(s(s(elem!1))), s(s(s(s(z)))))),
% 2.22/2.41 inference(modus_ponens,[status(thm)],[5667, 5473])).
% 2.22/2.41 tff(5669,plain,
% 2.22/2.41 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), z)) | (~b(s(z), s(s(elem!1)))) | (~b(z, s(z))) | (~b(s(s(s(z))), z)) | (~b(s(z), s(s(s(z))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), z)) | (~b(s(z), s(s(elem!1)))) | (~b(z, s(z))) | (~b(s(s(s(z))), z)) | (~b(s(z), s(s(s(z))))))),
% 2.22/2.41 inference(rewrite,[status(thm)],[])).
% 2.22/2.41 tff(5670,plain,
% 2.22/2.41 (((~b(s(z), s(s(elem!1)))) | (~b(s(z), s(s(elem!1)))) | (~b(z, s(z))) | (~b(s(s(s(z))), z)) | (~b(s(z), z)) | (~b(s(z), s(s(s(z)))))) <=> ((~b(s(z), z)) | (~b(s(z), s(s(elem!1)))) | (~b(z, s(z))) | (~b(s(s(s(z))), z)) | (~b(s(z), s(s(s(z))))))),
% 2.22/2.41 inference(rewrite,[status(thm)],[])).
% 2.22/2.41 tff(5671,plain,
% 2.22/2.41 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(elem!1)))) | (~b(s(z), s(s(elem!1)))) | (~b(z, s(z))) | (~b(s(s(s(z))), z)) | (~b(s(z), z)) | (~b(s(z), s(s(s(z))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), z)) | (~b(s(z), s(s(elem!1)))) | (~b(z, s(z))) | (~b(s(s(s(z))), z)) | (~b(s(z), s(s(s(z)))))))),
% 2.22/2.41 inference(monotonicity,[status(thm)],[5670])).
% 2.22/2.41 tff(5672,plain,
% 2.22/2.41 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(elem!1)))) | (~b(s(z), s(s(elem!1)))) | (~b(z, s(z))) | (~b(s(s(s(z))), z)) | (~b(s(z), z)) | (~b(s(z), s(s(s(z))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), z)) | (~b(s(z), s(s(elem!1)))) | (~b(z, s(z))) | (~b(s(s(s(z))), z)) | (~b(s(z), s(s(s(z))))))),
% 2.22/2.41 inference(transitivity,[status(thm)],[5671, 5669])).
% 2.22/2.41 tff(5673,plain,
% 2.22/2.41 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(elem!1)))) | (~b(s(z), s(s(elem!1)))) | (~b(z, s(z))) | (~b(s(s(s(z))), z)) | (~b(s(z), z)) | (~b(s(z), s(s(s(z))))))),
% 2.22/2.42 inference(quant_inst,[status(thm)],[])).
% 2.22/2.42 tff(5674,plain,
% 2.22/2.42 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), z)) | (~b(s(z), s(s(elem!1)))) | (~b(z, s(z))) | (~b(s(s(s(z))), z)) | (~b(s(z), s(s(s(z)))))),
% 2.22/2.42 inference(modus_ponens,[status(thm)],[5673, 5672])).
% 2.22/2.42 tff(5675,plain,
% 2.22/2.42 ($false),
% 2.22/2.42 inference(unit_resolution,[status(thm)],[5674, 166, 376, 53, 118, 988, 1699])).
% 2.22/2.42 tff(5676,plain,((~b(s(s(s(z))), z)) | (~b(s(z), s(s(elem!1)))) | (~b(s(z), z)) | (~b(z, s(z))) | (~b(s(z), s(s(s(z)))))), inference(lemma,lemma(discharge,[]))).
% 2.22/2.42 tff(5677,plain,
% 2.22/2.42 (~b(s(z), s(s(s(z))))),
% 2.22/2.42 inference(unit_resolution,[status(thm)],[5676, 5572, 118, 5288, 5582])).
% 2.22/2.42 tff(5678,plain,
% 2.22/2.42 (r(s(z), s(s(s(z))))),
% 2.22/2.42 inference(unit_resolution,[status(thm)],[1674, 5677])).
% 2.22/2.42 tff(5679,plain,
% 2.22/2.42 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(s(s(z))))) | (~r(s(s(s(z))), s(z))) | (~r(s(s(s(s(z)))), s(s(s(z))))) | (~r(s(s(s(s(z)))), s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(z), s(s(s(z))))) | (~r(s(s(s(z))), s(z))) | (~r(s(s(s(s(z)))), s(s(s(z))))) | (~r(s(s(s(s(z)))), s(z))))),
% 2.22/2.42 inference(rewrite,[status(thm)],[])).
% 2.22/2.42 tff(5680,plain,
% 2.22/2.42 (((~r(s(s(s(z))), s(z))) | (~r(s(z), s(s(s(z))))) | (~r(s(s(s(s(z)))), s(s(s(z))))) | (~r(s(s(s(s(z)))), s(z)))) <=> ((~r(s(z), s(s(s(z))))) | (~r(s(s(s(z))), s(z))) | (~r(s(s(s(s(z)))), s(s(s(z))))) | (~r(s(s(s(s(z)))), s(z))))),
% 2.22/2.42 inference(rewrite,[status(thm)],[])).
% 2.22/2.42 tff(5681,plain,
% 2.22/2.42 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(z))), s(z))) | (~r(s(z), s(s(s(z))))) | (~r(s(s(s(s(z)))), s(s(s(z))))) | (~r(s(s(s(s(z)))), s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(s(s(z))))) | (~r(s(s(s(z))), s(z))) | (~r(s(s(s(s(z)))), s(s(s(z))))) | (~r(s(s(s(s(z)))), s(z)))))),
% 2.22/2.42 inference(monotonicity,[status(thm)],[5680])).
% 2.22/2.42 tff(5682,plain,
% 2.22/2.42 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(z))), s(z))) | (~r(s(z), s(s(s(z))))) | (~r(s(s(s(s(z)))), s(s(s(z))))) | (~r(s(s(s(s(z)))), s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(z), s(s(s(z))))) | (~r(s(s(s(z))), s(z))) | (~r(s(s(s(s(z)))), s(s(s(z))))) | (~r(s(s(s(s(z)))), s(z))))),
% 2.22/2.42 inference(transitivity,[status(thm)],[5681, 5679])).
% 2.22/2.42 tff(5683,plain,
% 2.22/2.42 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(z))), s(z))) | (~r(s(z), s(s(s(z))))) | (~r(s(s(s(s(z)))), s(s(s(z))))) | (~r(s(s(s(s(z)))), s(z))))),
% 2.22/2.42 inference(quant_inst,[status(thm)],[])).
% 2.22/2.42 tff(5684,plain,
% 2.22/2.42 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(z), s(s(s(z))))) | (~r(s(s(s(z))), s(z))) | (~r(s(s(s(s(z)))), s(s(s(z))))) | (~r(s(s(s(s(z)))), s(z)))),
% 2.22/2.42 inference(modus_ponens,[status(thm)],[5683, 5682])).
% 2.22/2.42 tff(5685,plain,
% 2.22/2.42 (~r(s(s(s(s(z)))), s(z))),
% 2.22/2.42 inference(unit_resolution,[status(thm)],[5684, 197, 5650, 5584, 5678])).
% 2.22/2.42 tff(5686,plain,
% 2.22/2.42 (b(s(s(s(s(z)))), s(z))),
% 2.22/2.42 inference(unit_resolution,[status(thm)],[3285, 5685])).
% 2.22/2.42 tff(5687,plain,
% 2.22/2.42 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(elem!1))), s(s(s(s(z)))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(elem!1))), s(s(s(s(z)))))))),
% 2.22/2.42 inference(rewrite,[status(thm)],[])).
% 2.22/2.42 tff(5688,plain,
% 2.22/2.42 (((~b(s(s(s(elem!1))), s(z))) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(z), s(s(s(elem!1))))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(s(s(elem!1))), s(s(s(s(z))))))) <=> ((~b(s(z), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(elem!1))), s(s(s(s(z)))))))),
% 2.22/2.42 inference(rewrite,[status(thm)],[])).
% 2.22/2.42 tff(5689,plain,
% 2.22/2.42 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), s(z))) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(z), s(s(s(elem!1))))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(s(s(elem!1))), s(s(s(s(z)))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(elem!1))), s(s(s(s(z))))))))),
% 2.22/2.42 inference(monotonicity,[status(thm)],[5688])).
% 2.22/2.42 tff(5690,plain,
% 2.22/2.42 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), s(z))) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(z), s(s(s(elem!1))))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(s(s(elem!1))), s(s(s(s(z)))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(elem!1))), s(s(s(s(z)))))))),
% 2.22/2.42 inference(transitivity,[status(thm)],[5689, 5687])).
% 2.22/2.42 tff(5691,plain,
% 2.22/2.42 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), s(z))) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(z), s(s(s(elem!1))))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(s(s(elem!1))), s(s(s(s(z)))))))),
% 2.22/2.42 inference(quant_inst,[status(thm)],[])).
% 2.22/2.42 tff(5692,plain,
% 2.22/2.42 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(elem!1))), s(s(s(s(z))))))),
% 2.22/2.42 inference(modus_ponens,[status(thm)],[5691, 5690])).
% 2.22/2.42 tff(5693,plain,
% 2.22/2.42 ($false),
% 2.22/2.42 inference(unit_resolution,[status(thm)],[5692, 166, 5501, 96, 5686, 5668])).
% 2.22/2.42 tff(5694,plain,((~b(s(s(s(elem!1))), s(z))) | (~b(z, s(z))) | b(z, s(s(z))) | b(s(s(s(elem!1))), z)), inference(lemma,lemma(discharge,[]))).
% 2.22/2.42 tff(5695,plain,
% 2.22/2.42 (~b(s(s(s(elem!1))), s(z))),
% 2.22/2.42 inference(unit_resolution,[status(thm)],[5694, 87, 125, 118])).
% 2.22/2.42 tff(5696,plain,
% 2.22/2.42 (r(s(s(s(elem!1))), s(z))),
% 2.22/2.42 inference(unit_resolution,[status(thm)],[1849, 5695])).
% 2.22/2.42 tff(5697,plain,
% 2.22/2.42 ($false),
% 2.22/2.42 inference(unit_resolution,[status(thm)],[3489, 197, 154, 155, 350, 97])).
% 2.22/2.42 tff(5698,plain,((~r(s(z), z)) | (~r(s(s(s(elem!1))), z)) | (~r(z, s(s(z)))) | (~r(s(s(s(elem!1))), s(z)))), inference(lemma,lemma(discharge,[]))).
% 2.22/2.42 tff(5699,plain,
% 2.22/2.42 (~r(s(z), z)),
% 2.22/2.42 inference(unit_resolution,[status(thm)],[5698, 154, 152, 350])).
% 2.22/2.42 tff(5700,plain,
% 2.22/2.42 (b(s(z), z)),
% 2.22/2.42 inference(unit_resolution,[status(thm)],[230, 5699])).
% 2.22/2.42 tff(5701,plain,
% 2.22/2.42 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(s(elem!1)))) | (~r(s(s(s(elem!1))), s(z))) | (~r(s(s(elem!1)), s(s(s(elem!1))))) | (~r(s(s(elem!1)), s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(z), s(s(elem!1)))) | (~r(s(s(s(elem!1))), s(z))) | (~r(s(s(elem!1)), s(s(s(elem!1))))) | (~r(s(s(elem!1)), s(z))))),
% 2.22/2.42 inference(rewrite,[status(thm)],[])).
% 2.22/2.42 tff(5702,plain,
% 2.22/2.42 (((~r(s(z), s(s(elem!1)))) | (~r(s(s(s(elem!1))), s(z))) | (~r(s(s(elem!1)), s(z))) | (~r(s(s(elem!1)), s(s(s(elem!1)))))) <=> ((~r(s(z), s(s(elem!1)))) | (~r(s(s(s(elem!1))), s(z))) | (~r(s(s(elem!1)), s(s(s(elem!1))))) | (~r(s(s(elem!1)), s(z))))),
% 2.22/2.42 inference(rewrite,[status(thm)],[])).
% 2.22/2.42 tff(5703,plain,
% 2.22/2.42 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(s(elem!1)))) | (~r(s(s(s(elem!1))), s(z))) | (~r(s(s(elem!1)), s(z))) | (~r(s(s(elem!1)), s(s(s(elem!1))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(s(elem!1)))) | (~r(s(s(s(elem!1))), s(z))) | (~r(s(s(elem!1)), s(s(s(elem!1))))) | (~r(s(s(elem!1)), s(z)))))),
% 2.22/2.42 inference(monotonicity,[status(thm)],[5702])).
% 2.22/2.42 tff(5704,plain,
% 2.22/2.42 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(s(elem!1)))) | (~r(s(s(s(elem!1))), s(z))) | (~r(s(s(elem!1)), s(z))) | (~r(s(s(elem!1)), s(s(s(elem!1))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(z), s(s(elem!1)))) | (~r(s(s(s(elem!1))), s(z))) | (~r(s(s(elem!1)), s(s(s(elem!1))))) | (~r(s(s(elem!1)), s(z))))),
% 2.22/2.42 inference(transitivity,[status(thm)],[5703, 5701])).
% 2.22/2.42 tff(5705,plain,
% 2.22/2.42 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(s(elem!1)))) | (~r(s(s(s(elem!1))), s(z))) | (~r(s(s(elem!1)), s(z))) | (~r(s(s(elem!1)), s(s(s(elem!1))))))),
% 2.22/2.42 inference(quant_inst,[status(thm)],[])).
% 2.22/2.42 tff(5706,plain,
% 2.22/2.42 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(z), s(s(elem!1)))) | (~r(s(s(s(elem!1))), s(z))) | (~r(s(s(elem!1)), s(s(s(elem!1))))) | (~r(s(s(elem!1)), s(z)))),
% 2.22/2.42 inference(modus_ponens,[status(thm)],[5705, 5704])).
% 2.22/2.42 tff(5707,plain,
% 2.22/2.42 (~r(s(s(elem!1)), s(s(s(elem!1))))),
% 2.22/2.42 inference(unit_resolution,[status(thm)],[5706, 197, 85, 350, 4558])).
% 2.22/2.42 tff(5708,plain,
% 2.22/2.42 (b(s(s(elem!1)), s(s(s(elem!1))))),
% 2.22/2.42 inference(unit_resolution,[status(thm)],[461, 5707, 45])).
% 2.22/2.42 tff(5709,plain,
% 2.22/2.42 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(s(elem!1)))) | (~r(s(s(elem!1)), s(z))) | (~r(s(s(s(elem!1))), s(z))) | (~r(s(s(s(elem!1))), s(s(elem!1)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(z), s(s(elem!1)))) | (~r(s(s(elem!1)), s(z))) | (~r(s(s(s(elem!1))), s(z))) | (~r(s(s(s(elem!1))), s(s(elem!1)))))),
% 2.22/2.42 inference(rewrite,[status(thm)],[])).
% 2.22/2.42 tff(5710,plain,
% 2.22/2.42 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(s(elem!1)))) | (~r(s(s(elem!1)), s(z))) | (~r(s(s(s(elem!1))), s(z))) | (~r(s(s(s(elem!1))), s(s(elem!1)))))),
% 2.22/2.42 inference(quant_inst,[status(thm)],[])).
% 2.22/2.42 tff(5711,plain,
% 2.22/2.42 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(z), s(s(elem!1)))) | (~r(s(s(elem!1)), s(z))) | (~r(s(s(s(elem!1))), s(z))) | (~r(s(s(s(elem!1))), s(s(elem!1))))),
% 2.22/2.42 inference(modus_ponens,[status(thm)],[5710, 5709])).
% 2.22/2.42 tff(5712,plain,
% 2.22/2.42 (~r(s(s(s(elem!1))), s(s(elem!1)))),
% 2.22/2.42 inference(unit_resolution,[status(thm)],[5711, 197, 85, 350, 4558])).
% 2.22/2.42 tff(5713,plain,
% 2.22/2.42 (b(s(s(s(elem!1))), s(s(elem!1)))),
% 2.22/2.42 inference(unit_resolution,[status(thm)],[889, 5712, 51])).
% 2.22/2.42 tff(5714,plain,
% 2.22/2.42 (~r(s(s(s(elem!1))), s(s(z)))),
% 2.22/2.42 inference(unit_resolution,[status(thm)],[200, 197, 154, 155, 866])).
% 2.22/2.42 tff(5715,plain,
% 2.22/2.42 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), z)) | (~r(s(s(z)), z)) | (~r(s(s(z)), s(s(s(elem!1))))) | (~r(z, s(s(z)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(elem!1))), z)) | (~r(s(s(z)), z)) | (~r(s(s(z)), s(s(s(elem!1))))) | (~r(z, s(s(z)))))),
% 2.22/2.42 inference(rewrite,[status(thm)],[])).
% 2.22/2.42 tff(5716,plain,
% 2.22/2.42 (((~r(z, s(s(z)))) | (~r(s(s(s(elem!1))), z)) | (~r(s(s(z)), z)) | (~r(s(s(z)), s(s(s(elem!1)))))) <=> ((~r(s(s(s(elem!1))), z)) | (~r(s(s(z)), z)) | (~r(s(s(z)), s(s(s(elem!1))))) | (~r(z, s(s(z)))))),
% 2.22/2.42 inference(rewrite,[status(thm)],[])).
% 2.22/2.42 tff(5717,plain,
% 2.22/2.42 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(z)))) | (~r(s(s(s(elem!1))), z)) | (~r(s(s(z)), z)) | (~r(s(s(z)), s(s(s(elem!1))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), z)) | (~r(s(s(z)), z)) | (~r(s(s(z)), s(s(s(elem!1))))) | (~r(z, s(s(z))))))),
% 2.22/2.42 inference(monotonicity,[status(thm)],[5716])).
% 2.22/2.42 tff(5718,plain,
% 2.22/2.42 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(z)))) | (~r(s(s(s(elem!1))), z)) | (~r(s(s(z)), z)) | (~r(s(s(z)), s(s(s(elem!1))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(elem!1))), z)) | (~r(s(s(z)), z)) | (~r(s(s(z)), s(s(s(elem!1))))) | (~r(z, s(s(z)))))),
% 2.22/2.42 inference(transitivity,[status(thm)],[5717, 5715])).
% 2.22/2.42 tff(5719,plain,
% 2.22/2.42 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(z)))) | (~r(s(s(s(elem!1))), z)) | (~r(s(s(z)), z)) | (~r(s(s(z)), s(s(s(elem!1))))))),
% 2.22/2.42 inference(quant_inst,[status(thm)],[])).
% 2.22/2.42 tff(5720,plain,
% 2.22/2.42 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(elem!1))), z)) | (~r(s(s(z)), z)) | (~r(s(s(z)), s(s(s(elem!1))))) | (~r(z, s(s(z))))),
% 2.22/2.42 inference(modus_ponens,[status(thm)],[5719, 5718])).
% 2.22/2.42 tff(5721,plain,
% 2.22/2.42 (~r(s(s(z)), s(s(s(elem!1))))),
% 2.22/2.42 inference(unit_resolution,[status(thm)],[5720, 197, 154, 155, 866])).
% 2.22/2.42 tff(5722,plain,
% 2.22/2.42 (~b(s(s(elem!1)), s(s(z)))),
% 2.22/2.42 inference(unit_resolution,[status(thm)],[501, 5721, 463, 5714])).
% 2.22/2.42 tff(5723,plain,
% 2.22/2.42 (b(s(s(s(elem!1))), s(s(z)))),
% 2.22/2.42 inference(unit_resolution,[status(thm)],[218, 5714])).
% 2.22/2.42 tff(5724,plain,
% 2.22/2.42 (~b(s(s(z)), s(s(elem!1)))),
% 2.22/2.42 inference(unit_resolution,[status(thm)],[2068, 5723, 839, 463])).
% 2.22/2.42 tff(5725,plain,
% 2.22/2.42 (~r(z, s(s(elem!1)))),
% 2.22/2.42 inference(unit_resolution,[status(thm)],[2079, 5724, 155, 52, 5722])).
% 2.22/2.42 tff(5726,plain,
% 2.22/2.42 (r(s(s(z)), s(s(elem!1)))),
% 2.22/2.42 inference(unit_resolution,[status(thm)],[390, 5724, 52])).
% 2.22/2.42 tff(5727,plain,
% 2.22/2.42 (~b(s(s(elem!1)), s(z))),
% 2.22/2.42 inference(unit_resolution,[status(thm)],[3358, 53, 1820, 118])).
% 2.22/2.42 tff(5728,plain,
% 2.22/2.42 (r(s(s(elem!1)), s(z))),
% 2.22/2.42 inference(unit_resolution,[status(thm)],[1912, 5727])).
% 2.22/2.42 tff(5729,plain,
% 2.22/2.42 (~r(s(s(s(elem!1))), s(s(z)))),
% 2.22/2.42 inference(unit_resolution,[status(thm)],[526, 333, 155, 154])).
% 2.22/2.42 tff(5730,plain,
% 2.22/2.42 (~b(s(s(s(elem!1))), s(z))),
% 2.22/2.42 inference(unit_resolution,[status(thm)],[5253, 866, 556, 154, 5729, 53, 118])).
% 2.22/2.42 tff(5731,plain,
% 2.22/2.42 (r(s(s(s(elem!1))), s(z))),
% 2.22/2.42 inference(unit_resolution,[status(thm)],[1849, 5730])).
% 2.22/2.42 tff(5732,plain,
% 2.22/2.42 (~(s(s(elem!1)) = s(s(s(elem!1))))),
% 2.22/2.42 inference(unit_resolution,[status(thm)],[338, 5721, 333])).
% 2.22/2.42 tff(5733,plain,
% 2.22/2.42 ((s(s(s(elem!1))) = s(s(z))) | b(s(s(s(elem!1))), s(s(z)))),
% 2.22/2.42 inference(unit_resolution,[status(thm)],[216, 79, 5729])).
% 2.22/2.42 tff(5734,plain,
% 2.22/2.42 (b(s(s(s(elem!1))), s(s(z)))),
% 2.22/2.42 inference(unit_resolution,[status(thm)],[5733, 490])).
% 2.22/2.42 tff(5735,plain,
% 2.22/2.42 (b(s(s(z)), s(s(s(elem!1))))),
% 2.22/2.42 inference(unit_resolution,[status(thm)],[277, 79, 5721, 209])).
% 2.22/2.42 tff(5736,plain,
% 2.22/2.42 (~b(s(z), s(s(s(elem!1))))),
% 2.22/2.42 inference(unit_resolution,[status(thm)],[4185, 166, 556, 5735, 5734])).
% 2.22/2.42 tff(5737,plain,
% 2.22/2.42 (r(s(z), s(s(s(elem!1))))),
% 2.22/2.42 inference(unit_resolution,[status(thm)],[116, 5736])).
% 2.22/2.42 tff(5738,plain,
% 2.22/2.42 (~r(s(s(elem!1)), s(s(s(elem!1))))),
% 2.22/2.42 inference(unit_resolution,[status(thm)],[764, 5737, 311, 5731])).
% 2.22/2.42 tff(5739,plain,
% 2.22/2.42 (b(s(s(elem!1)), s(s(s(elem!1))))),
% 2.22/2.42 inference(unit_resolution,[status(thm)],[461, 5738, 5732])).
% 2.22/2.42 tff(5740,plain,
% 2.22/2.42 (~b(s(s(elem!1)), s(s(z)))),
% 2.22/2.42 inference(unit_resolution,[status(thm)],[501, 5739, 5721, 5729])).
% 2.22/2.42 tff(5741,plain,
% 2.22/2.42 (r(s(s(elem!1)), s(s(z)))),
% 2.22/2.42 inference(unit_resolution,[status(thm)],[441, 5740, 11])).
% 2.22/2.42 tff(5742,plain,
% 2.22/2.42 (~r(s(s(elem!1)), z)),
% 2.22/2.42 inference(unit_resolution,[status(thm)],[2740, 197, 5741, 155, 333])).
% 2.22/2.42 tff(5743,plain,
% 2.22/2.42 (b(s(s(elem!1)), z)),
% 2.22/2.42 inference(unit_resolution,[status(thm)],[608, 5742])).
% 2.22/2.42 tff(5744,plain,
% 2.22/2.42 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(s(s(elem!1)), z)) | (~b(z, s(z))) | (~b(s(s(elem!1)), s(z))) | (~b(s(z), s(s(z)))) | (~b(s(s(z)), s(s(s(elem!1))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(s(s(elem!1)), z)) | (~b(z, s(z))) | (~b(s(s(elem!1)), s(z))) | (~b(s(z), s(s(z)))) | (~b(s(s(z)), s(s(s(elem!1))))))),
% 2.22/2.42 inference(rewrite,[status(thm)],[])).
% 2.22/2.42 tff(5745,plain,
% 2.22/2.42 (((~b(s(s(z)), s(s(s(elem!1))))) | (~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(s(z), s(s(z)))) | (~b(z, s(z))) | (~b(s(s(elem!1)), s(z))) | (~b(s(s(elem!1)), z))) <=> ((~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(s(s(elem!1)), z)) | (~b(z, s(z))) | (~b(s(s(elem!1)), s(z))) | (~b(s(z), s(s(z)))) | (~b(s(s(z)), s(s(s(elem!1))))))),
% 2.22/2.42 inference(rewrite,[status(thm)],[])).
% 2.22/2.42 tff(5746,plain,
% 2.22/2.42 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), s(s(s(elem!1))))) | (~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(s(z), s(s(z)))) | (~b(z, s(z))) | (~b(s(s(elem!1)), s(z))) | (~b(s(s(elem!1)), z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(s(s(elem!1)), z)) | (~b(z, s(z))) | (~b(s(s(elem!1)), s(z))) | (~b(s(z), s(s(z)))) | (~b(s(s(z)), s(s(s(elem!1)))))))),
% 2.22/2.42 inference(monotonicity,[status(thm)],[5745])).
% 2.22/2.42 tff(5747,plain,
% 2.22/2.42 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), s(s(s(elem!1))))) | (~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(s(z), s(s(z)))) | (~b(z, s(z))) | (~b(s(s(elem!1)), s(z))) | (~b(s(s(elem!1)), z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(s(s(elem!1)), z)) | (~b(z, s(z))) | (~b(s(s(elem!1)), s(z))) | (~b(s(z), s(s(z)))) | (~b(s(s(z)), s(s(s(elem!1))))))),
% 2.22/2.42 inference(transitivity,[status(thm)],[5746, 5744])).
% 2.22/2.42 tff(5748,plain,
% 2.22/2.42 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), s(s(s(elem!1))))) | (~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(s(z), s(s(z)))) | (~b(z, s(z))) | (~b(s(s(elem!1)), s(z))) | (~b(s(s(elem!1)), z)))),
% 2.22/2.42 inference(quant_inst,[status(thm)],[])).
% 2.22/2.42 tff(5749,plain,
% 2.22/2.42 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(s(s(elem!1)), z)) | (~b(z, s(z))) | (~b(s(s(elem!1)), s(z))) | (~b(s(z), s(s(z)))) | (~b(s(s(z)), s(s(s(elem!1)))))),
% 2.22/2.42 inference(modus_ponens,[status(thm)],[5748, 5747])).
% 2.22/2.42 tff(5750,plain,
% 2.22/2.42 ((~b(s(s(elem!1)), z)) | (~b(s(s(elem!1)), s(z)))),
% 2.22/2.42 inference(unit_resolution,[status(thm)],[5749, 166, 5739, 556, 118, 5735])).
% 2.22/2.42 tff(5751,plain,
% 2.22/2.42 (~b(s(s(elem!1)), s(z))),
% 2.22/2.42 inference(unit_resolution,[status(thm)],[5750, 5743])).
% 2.22/2.42 tff(5752,plain,
% 2.22/2.42 (r(s(s(elem!1)), s(z))),
% 2.22/2.42 inference(unit_resolution,[status(thm)],[1912, 5751])).
% 2.22/2.42 tff(5753,plain,
% 2.22/2.42 (~(s(s(s(elem!1))) = s(s(s(s(elem!1)))))),
% 2.22/2.43 inference(unit_resolution,[status(thm)],[357, 5732])).
% 2.22/2.43 tff(5754,plain,
% 2.22/2.43 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(s(elem!1)))) | (~r(s(s(z)), s(s(elem!1)))) | (~r(s(s(z)), s(z))) | (~r(s(s(elem!1)), s(s(z)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(z), s(s(elem!1)))) | (~r(s(s(z)), s(s(elem!1)))) | (~r(s(s(z)), s(z))) | (~r(s(s(elem!1)), s(s(z)))))),
% 2.22/2.43 inference(rewrite,[status(thm)],[])).
% 2.22/2.43 tff(5755,plain,
% 2.22/2.43 (((~r(s(s(elem!1)), s(s(z)))) | (~r(s(z), s(s(elem!1)))) | (~r(s(s(z)), s(s(elem!1)))) | (~r(s(s(z)), s(z)))) <=> ((~r(s(z), s(s(elem!1)))) | (~r(s(s(z)), s(s(elem!1)))) | (~r(s(s(z)), s(z))) | (~r(s(s(elem!1)), s(s(z)))))),
% 2.22/2.43 inference(rewrite,[status(thm)],[])).
% 2.22/2.43 tff(5756,plain,
% 2.22/2.43 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(elem!1)), s(s(z)))) | (~r(s(z), s(s(elem!1)))) | (~r(s(s(z)), s(s(elem!1)))) | (~r(s(s(z)), s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(s(elem!1)))) | (~r(s(s(z)), s(s(elem!1)))) | (~r(s(s(z)), s(z))) | (~r(s(s(elem!1)), s(s(z))))))),
% 2.22/2.43 inference(monotonicity,[status(thm)],[5755])).
% 2.22/2.43 tff(5757,plain,
% 2.22/2.43 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(elem!1)), s(s(z)))) | (~r(s(z), s(s(elem!1)))) | (~r(s(s(z)), s(s(elem!1)))) | (~r(s(s(z)), s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(z), s(s(elem!1)))) | (~r(s(s(z)), s(s(elem!1)))) | (~r(s(s(z)), s(z))) | (~r(s(s(elem!1)), s(s(z)))))),
% 2.22/2.43 inference(transitivity,[status(thm)],[5756, 5754])).
% 2.22/2.43 tff(5758,plain,
% 2.22/2.43 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(elem!1)), s(s(z)))) | (~r(s(z), s(s(elem!1)))) | (~r(s(s(z)), s(s(elem!1)))) | (~r(s(s(z)), s(z))))),
% 2.22/2.43 inference(quant_inst,[status(thm)],[])).
% 2.22/2.43 tff(5759,plain,
% 2.22/2.43 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(z), s(s(elem!1)))) | (~r(s(s(z)), s(s(elem!1)))) | (~r(s(s(z)), s(z))) | (~r(s(s(elem!1)), s(s(z))))),
% 2.22/2.43 inference(modus_ponens,[status(thm)],[5758, 5757])).
% 2.22/2.43 tff(5760,plain,
% 2.22/2.43 (~r(s(s(z)), s(z))),
% 2.22/2.43 inference(unit_resolution,[status(thm)],[5759, 197, 311, 5741, 333])).
% 2.22/2.43 tff(5761,plain,
% 2.22/2.43 (b(s(s(z)), s(z))),
% 2.22/2.43 inference(unit_resolution,[status(thm)],[308, 5760])).
% 2.22/2.43 tff(5762,plain,
% 2.22/2.43 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), z)) | (~b(z, s(z))) | (~b(s(s(s(s(elem!1)))), s(z))) | (~b(s(s(s(s(elem!1)))), z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), z)) | (~b(z, s(z))) | (~b(s(s(s(s(elem!1)))), s(z))) | (~b(s(s(s(s(elem!1)))), z)))),
% 2.22/2.43 inference(rewrite,[status(thm)],[])).
% 2.22/2.43 tff(5763,plain,
% 2.22/2.43 (((~b(z, s(z))) | (~b(s(s(s(s(elem!1)))), s(z))) | (~b(s(z), z)) | (~b(z, s(z))) | (~b(s(s(s(s(elem!1)))), s(z))) | (~b(s(s(s(s(elem!1)))), z))) <=> ((~b(s(z), z)) | (~b(z, s(z))) | (~b(s(s(s(s(elem!1)))), s(z))) | (~b(s(s(s(s(elem!1)))), z)))),
% 2.22/2.43 inference(rewrite,[status(thm)],[])).
% 2.22/2.43 tff(5764,plain,
% 2.22/2.43 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(z))) | (~b(s(s(s(s(elem!1)))), s(z))) | (~b(s(z), z)) | (~b(z, s(z))) | (~b(s(s(s(s(elem!1)))), s(z))) | (~b(s(s(s(s(elem!1)))), z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), z)) | (~b(z, s(z))) | (~b(s(s(s(s(elem!1)))), s(z))) | (~b(s(s(s(s(elem!1)))), z))))),
% 2.22/2.43 inference(monotonicity,[status(thm)],[5763])).
% 2.22/2.43 tff(5765,plain,
% 2.22/2.43 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(z))) | (~b(s(s(s(s(elem!1)))), s(z))) | (~b(s(z), z)) | (~b(z, s(z))) | (~b(s(s(s(s(elem!1)))), s(z))) | (~b(s(s(s(s(elem!1)))), z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), z)) | (~b(z, s(z))) | (~b(s(s(s(s(elem!1)))), s(z))) | (~b(s(s(s(s(elem!1)))), z)))),
% 2.22/2.43 inference(transitivity,[status(thm)],[5764, 5762])).
% 2.22/2.43 tff(5766,plain,
% 2.22/2.43 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(z))) | (~b(s(s(s(s(elem!1)))), s(z))) | (~b(s(z), z)) | (~b(z, s(z))) | (~b(s(s(s(s(elem!1)))), s(z))) | (~b(s(s(s(s(elem!1)))), z)))),
% 2.22/2.43 inference(quant_inst,[status(thm)],[])).
% 2.22/2.43 tff(5767,plain,
% 2.22/2.43 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), z)) | (~b(z, s(z))) | (~b(s(s(s(s(elem!1)))), s(z))) | (~b(s(s(s(s(elem!1)))), z))),
% 2.22/2.43 inference(modus_ponens,[status(thm)],[5766, 5765])).
% 2.22/2.43 tff(5768,plain,
% 2.22/2.43 (~b(s(s(s(s(elem!1)))), z)),
% 2.22/2.43 inference(unit_resolution,[status(thm)],[5767, 166, 53, 118, 1402])).
% 2.22/2.43 tff(5769,plain,
% 2.22/2.43 (r(s(s(s(s(elem!1)))), z)),
% 2.22/2.43 inference(unit_resolution,[status(thm)],[1339, 79, 626, 5768])).
% 2.22/2.43 tff(5770,plain,
% 2.22/2.43 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), z)) | (~b(z, s(z))) | (~b(s(s(z)), s(z))) | (~b(s(s(s(s(elem!1)))), s(z))) | (~b(s(s(s(s(elem!1)))), s(s(z)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), z)) | (~b(z, s(z))) | (~b(s(s(z)), s(z))) | (~b(s(s(s(s(elem!1)))), s(z))) | (~b(s(s(s(s(elem!1)))), s(s(z)))))),
% 2.22/2.43 inference(rewrite,[status(thm)],[])).
% 2.22/2.43 tff(5771,plain,
% 2.22/2.43 (((~b(z, s(z))) | (~b(s(s(s(s(elem!1)))), s(z))) | (~b(s(z), z)) | (~b(s(s(z)), s(z))) | (~b(s(s(s(s(elem!1)))), s(z))) | (~b(s(s(s(s(elem!1)))), s(s(z))))) <=> ((~b(s(z), z)) | (~b(z, s(z))) | (~b(s(s(z)), s(z))) | (~b(s(s(s(s(elem!1)))), s(z))) | (~b(s(s(s(s(elem!1)))), s(s(z)))))),
% 2.22/2.43 inference(rewrite,[status(thm)],[])).
% 2.22/2.43 tff(5772,plain,
% 2.22/2.43 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(z))) | (~b(s(s(s(s(elem!1)))), s(z))) | (~b(s(z), z)) | (~b(s(s(z)), s(z))) | (~b(s(s(s(s(elem!1)))), s(z))) | (~b(s(s(s(s(elem!1)))), s(s(z)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), z)) | (~b(z, s(z))) | (~b(s(s(z)), s(z))) | (~b(s(s(s(s(elem!1)))), s(z))) | (~b(s(s(s(s(elem!1)))), s(s(z))))))),
% 2.22/2.43 inference(monotonicity,[status(thm)],[5771])).
% 2.22/2.43 tff(5773,plain,
% 2.22/2.43 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(z))) | (~b(s(s(s(s(elem!1)))), s(z))) | (~b(s(z), z)) | (~b(s(s(z)), s(z))) | (~b(s(s(s(s(elem!1)))), s(z))) | (~b(s(s(s(s(elem!1)))), s(s(z)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), z)) | (~b(z, s(z))) | (~b(s(s(z)), s(z))) | (~b(s(s(s(s(elem!1)))), s(z))) | (~b(s(s(s(s(elem!1)))), s(s(z)))))),
% 2.22/2.43 inference(transitivity,[status(thm)],[5772, 5770])).
% 2.22/2.43 tff(5774,plain,
% 2.22/2.43 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(z))) | (~b(s(s(s(s(elem!1)))), s(z))) | (~b(s(z), z)) | (~b(s(s(z)), s(z))) | (~b(s(s(s(s(elem!1)))), s(z))) | (~b(s(s(s(s(elem!1)))), s(s(z)))))),
% 2.22/2.43 inference(quant_inst,[status(thm)],[])).
% 2.22/2.43 tff(5775,plain,
% 2.22/2.43 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), z)) | (~b(z, s(z))) | (~b(s(s(z)), s(z))) | (~b(s(s(s(s(elem!1)))), s(z))) | (~b(s(s(s(s(elem!1)))), s(s(z))))),
% 2.22/2.43 inference(modus_ponens,[status(thm)],[5774, 5773])).
% 2.22/2.43 tff(5776,plain,
% 2.22/2.43 (~b(s(s(s(s(elem!1)))), s(s(z)))),
% 2.22/2.43 inference(unit_resolution,[status(thm)],[5775, 166, 53, 118, 156, 1402])).
% 2.22/2.43 tff(5777,plain,
% 2.22/2.43 (r(s(s(s(s(elem!1)))), s(s(z)))),
% 2.22/2.43 inference(unit_resolution,[status(thm)],[1299, 5776])).
% 2.22/2.43 tff(5778,plain,
% 2.22/2.43 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(z)), s(s(elem!1)))) | (~r(s(s(s(s(elem!1)))), s(s(z)))) | (~r(z, s(s(z)))) | (~r(s(s(s(s(elem!1)))), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(z)), s(s(elem!1)))) | (~r(s(s(s(s(elem!1)))), s(s(z)))) | (~r(z, s(s(z)))) | (~r(s(s(s(s(elem!1)))), z)))),
% 2.22/2.43 inference(rewrite,[status(thm)],[])).
% 2.22/2.43 tff(5779,plain,
% 2.22/2.43 (((~r(s(s(z)), s(s(elem!1)))) | (~r(z, s(s(z)))) | (~r(s(s(s(s(elem!1)))), s(s(z)))) | (~r(s(s(s(s(elem!1)))), z))) <=> ((~r(s(s(z)), s(s(elem!1)))) | (~r(s(s(s(s(elem!1)))), s(s(z)))) | (~r(z, s(s(z)))) | (~r(s(s(s(s(elem!1)))), z)))),
% 2.22/2.43 inference(rewrite,[status(thm)],[])).
% 2.22/2.43 tff(5780,plain,
% 2.22/2.43 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(z)), s(s(elem!1)))) | (~r(z, s(s(z)))) | (~r(s(s(s(s(elem!1)))), s(s(z)))) | (~r(s(s(s(s(elem!1)))), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(z)), s(s(elem!1)))) | (~r(s(s(s(s(elem!1)))), s(s(z)))) | (~r(z, s(s(z)))) | (~r(s(s(s(s(elem!1)))), z))))),
% 2.22/2.43 inference(monotonicity,[status(thm)],[5779])).
% 2.22/2.43 tff(5781,plain,
% 2.22/2.43 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(z)), s(s(elem!1)))) | (~r(z, s(s(z)))) | (~r(s(s(s(s(elem!1)))), s(s(z)))) | (~r(s(s(s(s(elem!1)))), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(z)), s(s(elem!1)))) | (~r(s(s(s(s(elem!1)))), s(s(z)))) | (~r(z, s(s(z)))) | (~r(s(s(s(s(elem!1)))), z)))),
% 2.22/2.43 inference(transitivity,[status(thm)],[5780, 5778])).
% 2.22/2.43 tff(5782,plain,
% 2.22/2.43 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(z)), s(s(elem!1)))) | (~r(z, s(s(z)))) | (~r(s(s(s(s(elem!1)))), s(s(z)))) | (~r(s(s(s(s(elem!1)))), z)))),
% 2.22/2.43 inference(quant_inst,[status(thm)],[])).
% 2.22/2.43 tff(5783,plain,
% 2.22/2.43 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(z)), s(s(elem!1)))) | (~r(s(s(s(s(elem!1)))), s(s(z)))) | (~r(z, s(s(z)))) | (~r(s(s(s(s(elem!1)))), z))),
% 2.22/2.43 inference(modus_ponens,[status(thm)],[5782, 5781])).
% 2.22/2.43 tff(5784,plain,
% 2.22/2.43 ($false),
% 2.22/2.43 inference(unit_resolution,[status(thm)],[5783, 197, 5777, 155, 333, 5769])).
% 2.22/2.43 tff(5785,plain,((~b(s(s(s(s(elem!1)))), s(z))) | (~r(z, s(s(z)))) | (~r(s(s(z)), s(s(elem!1)))) | (~b(s(z), z)) | (~b(z, s(z))) | (~b(s(s(z)), s(z)))), inference(lemma,lemma(discharge,[]))).
% 2.22/2.43 tff(5786,plain,
% 2.22/2.43 (~b(s(s(s(s(elem!1)))), s(z))),
% 2.22/2.43 inference(unit_resolution,[status(thm)],[5785, 5761, 333, 53, 118, 155])).
% 2.22/2.43 tff(5787,plain,
% 2.22/2.43 (r(s(s(s(s(elem!1)))), s(z))),
% 2.22/2.43 inference(unit_resolution,[status(thm)],[661, 5786])).
% 2.22/2.43 tff(5788,plain,
% 2.22/2.43 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(s(elem!1)))) | (~r(s(s(s(elem!1))), s(z))) | (~r(s(s(s(s(elem!1)))), s(z))) | (~r(s(s(s(s(elem!1)))), s(s(s(elem!1))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(z), s(s(elem!1)))) | (~r(s(s(s(elem!1))), s(z))) | (~r(s(s(s(s(elem!1)))), s(z))) | (~r(s(s(s(s(elem!1)))), s(s(s(elem!1))))))),
% 2.22/2.43 inference(rewrite,[status(thm)],[])).
% 2.22/2.43 tff(5789,plain,
% 2.22/2.43 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(s(elem!1)))) | (~r(s(s(s(elem!1))), s(z))) | (~r(s(s(s(s(elem!1)))), s(z))) | (~r(s(s(s(s(elem!1)))), s(s(s(elem!1))))))),
% 2.22/2.43 inference(quant_inst,[status(thm)],[])).
% 2.22/2.43 tff(5790,plain,
% 2.22/2.43 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(z), s(s(elem!1)))) | (~r(s(s(s(elem!1))), s(z))) | (~r(s(s(s(s(elem!1)))), s(z))) | (~r(s(s(s(s(elem!1)))), s(s(s(elem!1)))))),
% 2.22/2.43 inference(modus_ponens,[status(thm)],[5789, 5788])).
% 2.22/2.43 tff(5791,plain,
% 2.22/2.43 (~r(s(s(s(s(elem!1)))), s(s(s(elem!1))))),
% 2.22/2.43 inference(unit_resolution,[status(thm)],[5790, 197, 311, 350, 700])).
% 2.22/2.43 tff(5792,plain,
% 2.22/2.43 (~r(s(s(s(elem!1))), s(s(s(s(elem!1)))))),
% 2.22/2.43 inference(unit_resolution,[status(thm)],[3469, 700, 350, 311])).
% 2.22/2.43 tff(5793,plain,
% 2.22/2.43 (b(s(s(s(elem!1))), s(s(s(s(elem!1)))))),
% 2.22/2.43 inference(unit_resolution,[status(thm)],[694, 79, 361, 5792])).
% 2.22/2.43 tff(5794,plain,
% 2.22/2.43 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(s(elem!1)))) | (~r(s(s(elem!1)), s(z))) | (~r(s(s(s(s(elem!1)))), s(z))) | (~r(s(s(s(s(elem!1)))), s(s(elem!1)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(z), s(s(elem!1)))) | (~r(s(s(elem!1)), s(z))) | (~r(s(s(s(s(elem!1)))), s(z))) | (~r(s(s(s(s(elem!1)))), s(s(elem!1)))))),
% 2.22/2.43 inference(rewrite,[status(thm)],[])).
% 2.22/2.43 tff(5795,plain,
% 2.22/2.43 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(s(elem!1)))) | (~r(s(s(elem!1)), s(z))) | (~r(s(s(s(s(elem!1)))), s(z))) | (~r(s(s(s(s(elem!1)))), s(s(elem!1)))))),
% 2.22/2.43 inference(quant_inst,[status(thm)],[])).
% 2.22/2.43 tff(5796,plain,
% 2.22/2.43 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(z), s(s(elem!1)))) | (~r(s(s(elem!1)), s(z))) | (~r(s(s(s(s(elem!1)))), s(z))) | (~r(s(s(s(s(elem!1)))), s(s(elem!1))))),
% 2.22/2.43 inference(modus_ponens,[status(thm)],[5795, 5794])).
% 2.22/2.43 tff(5797,plain,
% 2.22/2.43 (~r(s(s(s(s(elem!1)))), s(s(elem!1)))),
% 2.22/2.43 inference(unit_resolution,[status(thm)],[5796, 197, 311, 4577, 700])).
% 2.22/2.43 tff(5798,plain,
% 2.22/2.43 (b(s(s(s(s(elem!1)))), s(s(elem!1)))),
% 2.22/2.43 inference(unit_resolution,[status(thm)],[813, 5797, 806])).
% 2.22/2.43 tff(5799,plain,
% 2.22/2.43 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(s(s(s(s(elem!1)))), s(s(elem!1)))) | (~b(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(s(s(s(elem!1)))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(s(s(s(s(elem!1)))), s(s(elem!1)))) | (~b(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(s(s(s(elem!1)))))))),
% 2.22/2.43 inference(rewrite,[status(thm)],[])).
% 2.22/2.43 tff(5800,plain,
% 2.22/2.43 (((~b(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~b(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(s(s(s(elem!1)))))) | (~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~b(s(s(s(s(elem!1)))), s(s(elem!1))))) <=> ((~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(s(s(s(s(elem!1)))), s(s(elem!1)))) | (~b(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(s(s(s(elem!1)))))))),
% 2.22/2.43 inference(rewrite,[status(thm)],[])).
% 2.22/2.43 tff(5801,plain,
% 2.22/2.43 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~b(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(s(s(s(elem!1)))))) | (~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~b(s(s(s(s(elem!1)))), s(s(elem!1)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(s(s(s(s(elem!1)))), s(s(elem!1)))) | (~b(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(s(s(s(elem!1))))))))),
% 2.22/2.44 inference(monotonicity,[status(thm)],[5800])).
% 2.22/2.44 tff(5802,plain,
% 2.22/2.44 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~b(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(s(s(s(elem!1)))))) | (~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~b(s(s(s(s(elem!1)))), s(s(elem!1)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(s(s(s(s(elem!1)))), s(s(elem!1)))) | (~b(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(s(s(s(elem!1)))))))),
% 2.22/2.44 inference(transitivity,[status(thm)],[5801, 5799])).
% 2.22/2.44 tff(5803,plain,
% 2.22/2.44 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~b(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(s(s(s(elem!1)))))) | (~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~b(s(s(s(s(elem!1)))), s(s(elem!1)))))),
% 2.22/2.44 inference(quant_inst,[status(thm)],[])).
% 2.22/2.44 tff(5804,plain,
% 2.22/2.44 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(s(s(s(s(elem!1)))), s(s(elem!1)))) | (~b(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(s(s(s(elem!1))))))),
% 2.22/2.44 inference(modus_ponens,[status(thm)],[5803, 5802])).
% 2.22/2.44 tff(5805,plain,
% 2.22/2.44 ($false),
% 2.22/2.44 inference(unit_resolution,[status(thm)],[5804, 166, 463, 3457, 1311, 1107])).
% 2.22/2.44 tff(5806,plain,((~b(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(s(s(s(s(elem!1)))), s(s(elem!1)))) | (~b(s(s(s(elem!1))), s(s(s(s(elem!1))))))), inference(lemma,lemma(discharge,[]))).
% 2.22/2.44 tff(5807,plain,
% 2.22/2.44 (~b(s(s(s(s(elem!1)))), s(s(s(elem!1))))),
% 2.22/2.44 inference(unit_resolution,[status(thm)],[5806, 5798, 463, 5793])).
% 2.22/2.44 tff(5808,plain,
% 2.22/2.44 ($false),
% 2.22/2.44 inference(unit_resolution,[status(thm)],[1063, 79, 5807, 5791, 1038])).
% 2.22/2.44 tff(5809,plain,((~r(s(s(s(s(elem!1)))), s(z))) | (~b(s(s(elem!1)), s(s(s(elem!1))))) | (s(s(s(s(elem!1)))) = s(s(elem!1))) | (s(s(s(elem!1))) = s(s(s(s(elem!1))))) | (~r(s(z), s(s(elem!1)))) | (~r(s(s(elem!1)), s(z))) | (~r(s(s(s(elem!1))), s(z)))), inference(lemma,lemma(discharge,[]))).
% 2.22/2.44 tff(5810,plain,
% 2.22/2.44 (s(s(s(s(elem!1)))) = s(s(elem!1))),
% 2.22/2.44 inference(unit_resolution,[status(thm)],[5809, 5787, 5739, 5753, 311, 5752, 5731])).
% 2.22/2.44 tff(5811,plain,
% 2.22/2.44 (s(s(s(elem!1))) = s(elem!1)),
% 2.22/2.44 inference(unit_resolution,[status(thm)],[1166, 5810])).
% 2.22/2.44 tff(5812,plain,
% 2.22/2.44 (inj_0(s(s(s(elem!1)))) = inj_0(s(elem!1))),
% 2.22/2.44 inference(monotonicity,[status(thm)],[5811])).
% 2.22/2.44 tff(5813,plain,
% 2.22/2.44 (s(s(elem!1)) = elem!1),
% 2.22/2.44 inference(transitivity,[status(thm)],[105, 5812, 20])).
% 2.22/2.44 tff(5814,plain,
% 2.22/2.44 (b(s(s(elem!1)), z) <=> b(elem!1, z)),
% 2.22/2.44 inference(monotonicity,[status(thm)],[5813])).
% 2.22/2.44 tff(5815,plain,
% 2.22/2.44 (b(elem!1, z)),
% 2.22/2.44 inference(modus_ponens,[status(thm)],[5743, 5814])).
% 2.22/2.44 tff(5816,plain,
% 2.22/2.44 (b(z, s(s(elem!1))) <=> b(z, elem!1)),
% 2.22/2.44 inference(monotonicity,[status(thm)],[5813])).
% 2.22/2.44 tff(5817,plain,
% 2.22/2.44 (b(z, elem!1)),
% 2.22/2.44 inference(modus_ponens,[status(thm)],[1820, 5816])).
% 2.22/2.44 tff(5818,plain,
% 2.22/2.44 (~(s(s(s(z))) = elem!1)),
% 2.22/2.44 inference(unit_resolution,[status(thm)],[1556, 5811])).
% 2.22/2.44 tff(5819,plain,
% 2.22/2.44 (r(s(s(elem!1)), s(z)) <=> r(elem!1, s(z))),
% 2.22/2.44 inference(monotonicity,[status(thm)],[5813])).
% 2.22/2.44 tff(5820,plain,
% 2.22/2.44 (r(elem!1, s(z))),
% 2.22/2.44 inference(modus_ponens,[status(thm)],[5752, 5819])).
% 2.22/2.44 tff(5821,assumption,(b(elem!1, z)), introduced(assumption)).
% 2.22/2.44 tff(5822,plain,
% 2.22/2.44 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), z)) | (~b(elem!1, z)) | (~b(z, elem!1)) | (~b(s(s(s(z))), z)) | (~b(s(z), s(s(s(z))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), z)) | (~b(elem!1, z)) | (~b(z, elem!1)) | (~b(s(s(s(z))), z)) | (~b(s(z), s(s(s(z))))))),
% 2.22/2.44 inference(rewrite,[status(thm)],[])).
% 2.22/2.44 tff(5823,plain,
% 2.22/2.44 (((~b(elem!1, z)) | (~b(s(z), z)) | (~b(z, elem!1)) | (~b(s(s(s(z))), z)) | (~b(s(z), z)) | (~b(s(z), s(s(s(z)))))) <=> ((~b(s(z), z)) | (~b(elem!1, z)) | (~b(z, elem!1)) | (~b(s(s(s(z))), z)) | (~b(s(z), s(s(s(z))))))),
% 2.22/2.44 inference(rewrite,[status(thm)],[])).
% 2.22/2.44 tff(5824,plain,
% 2.22/2.44 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, z)) | (~b(s(z), z)) | (~b(z, elem!1)) | (~b(s(s(s(z))), z)) | (~b(s(z), z)) | (~b(s(z), s(s(s(z))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), z)) | (~b(elem!1, z)) | (~b(z, elem!1)) | (~b(s(s(s(z))), z)) | (~b(s(z), s(s(s(z)))))))),
% 2.22/2.44 inference(monotonicity,[status(thm)],[5823])).
% 2.22/2.44 tff(5825,plain,
% 2.22/2.44 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, z)) | (~b(s(z), z)) | (~b(z, elem!1)) | (~b(s(s(s(z))), z)) | (~b(s(z), z)) | (~b(s(z), s(s(s(z))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), z)) | (~b(elem!1, z)) | (~b(z, elem!1)) | (~b(s(s(s(z))), z)) | (~b(s(z), s(s(s(z))))))),
% 2.22/2.44 inference(transitivity,[status(thm)],[5824, 5822])).
% 2.22/2.44 tff(5826,plain,
% 2.22/2.44 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, z)) | (~b(s(z), z)) | (~b(z, elem!1)) | (~b(s(s(s(z))), z)) | (~b(s(z), z)) | (~b(s(z), s(s(s(z))))))),
% 2.22/2.44 inference(quant_inst,[status(thm)],[])).
% 2.22/2.44 tff(5827,plain,
% 2.22/2.44 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), z)) | (~b(elem!1, z)) | (~b(z, elem!1)) | (~b(s(s(s(z))), z)) | (~b(s(z), s(s(s(z)))))),
% 2.22/2.44 inference(modus_ponens,[status(thm)],[5826, 5825])).
% 2.22/2.44 tff(5828,plain,
% 2.22/2.44 (~b(s(z), s(s(s(z))))),
% 2.22/2.44 inference(unit_resolution,[status(thm)],[5827, 166, 2517, 5821, 53, 1699])).
% 2.22/2.44 tff(5829,plain,
% 2.22/2.44 (r(s(z), s(s(s(z))))),
% 2.22/2.44 inference(unit_resolution,[status(thm)],[1673, 5828, 1669])).
% 2.22/2.44 tff(5830,plain,
% 2.22/2.44 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, z)) | (~b(z, elem!1)) | (~b(s(s(s(z))), z)) | (~b(s(s(s(z))), elem!1)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, z)) | (~b(z, elem!1)) | (~b(s(s(s(z))), z)) | (~b(s(s(s(z))), elem!1)))),
% 2.22/2.44 inference(rewrite,[status(thm)],[])).
% 2.22/2.44 tff(5831,plain,
% 2.22/2.44 (((~b(elem!1, z)) | (~b(s(s(s(z))), z)) | (~b(z, elem!1)) | (~b(elem!1, z)) | (~b(s(s(s(z))), z)) | (~b(s(s(s(z))), elem!1))) <=> ((~b(elem!1, z)) | (~b(z, elem!1)) | (~b(s(s(s(z))), z)) | (~b(s(s(s(z))), elem!1)))),
% 2.22/2.44 inference(rewrite,[status(thm)],[])).
% 2.22/2.44 tff(5832,plain,
% 2.22/2.44 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, z)) | (~b(s(s(s(z))), z)) | (~b(z, elem!1)) | (~b(elem!1, z)) | (~b(s(s(s(z))), z)) | (~b(s(s(s(z))), elem!1)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, z)) | (~b(z, elem!1)) | (~b(s(s(s(z))), z)) | (~b(s(s(s(z))), elem!1))))),
% 2.22/2.44 inference(monotonicity,[status(thm)],[5831])).
% 2.22/2.44 tff(5833,plain,
% 2.22/2.44 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, z)) | (~b(s(s(s(z))), z)) | (~b(z, elem!1)) | (~b(elem!1, z)) | (~b(s(s(s(z))), z)) | (~b(s(s(s(z))), elem!1)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, z)) | (~b(z, elem!1)) | (~b(s(s(s(z))), z)) | (~b(s(s(s(z))), elem!1)))),
% 2.22/2.44 inference(transitivity,[status(thm)],[5832, 5830])).
% 2.22/2.44 tff(5834,plain,
% 2.22/2.44 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, z)) | (~b(s(s(s(z))), z)) | (~b(z, elem!1)) | (~b(elem!1, z)) | (~b(s(s(s(z))), z)) | (~b(s(s(s(z))), elem!1)))),
% 2.22/2.44 inference(quant_inst,[status(thm)],[])).
% 2.22/2.44 tff(5835,plain,
% 2.22/2.44 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, z)) | (~b(z, elem!1)) | (~b(s(s(s(z))), z)) | (~b(s(s(s(z))), elem!1))),
% 2.22/2.44 inference(modus_ponens,[status(thm)],[5834, 5833])).
% 2.22/2.44 tff(5836,plain,
% 2.22/2.44 (~b(s(s(s(z))), elem!1)),
% 2.22/2.44 inference(unit_resolution,[status(thm)],[5835, 166, 2517, 5821, 1699])).
% 2.22/2.44 tff(5837,plain,
% 2.22/2.44 (r(s(s(s(z))), elem!1)),
% 2.22/2.44 inference(unit_resolution,[status(thm)],[2826, 5836, 1562])).
% 2.22/2.44 tff(5838,plain,
% 2.22/2.44 ((~(s(s(s(z))) = elem!1)) <=> (~(elem!1 = s(s(s(z)))))),
% 2.22/2.44 inference(monotonicity,[status(thm)],[1558])).
% 2.22/2.44 tff(5839,plain,
% 2.22/2.44 (~(elem!1 = s(s(s(z))))),
% 2.22/2.44 inference(modus_ponens,[status(thm)],[1562, 5838])).
% 2.22/2.44 tff(5840,plain,
% 2.22/2.44 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, z)) | (~b(z, elem!1)) | (~b(s(s(s(z))), z)) | (~b(elem!1, s(s(s(z))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, z)) | (~b(z, elem!1)) | (~b(s(s(s(z))), z)) | (~b(elem!1, s(s(s(z))))))),
% 2.22/2.44 inference(rewrite,[status(thm)],[])).
% 2.22/2.44 tff(5841,plain,
% 2.22/2.44 (((~b(elem!1, z)) | (~b(elem!1, z)) | (~b(z, elem!1)) | (~b(s(s(s(z))), z)) | (~b(elem!1, z)) | (~b(elem!1, s(s(s(z)))))) <=> ((~b(elem!1, z)) | (~b(z, elem!1)) | (~b(s(s(s(z))), z)) | (~b(elem!1, s(s(s(z))))))),
% 2.22/2.44 inference(rewrite,[status(thm)],[])).
% 2.22/2.44 tff(5842,plain,
% 2.22/2.44 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, z)) | (~b(elem!1, z)) | (~b(z, elem!1)) | (~b(s(s(s(z))), z)) | (~b(elem!1, z)) | (~b(elem!1, s(s(s(z))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, z)) | (~b(z, elem!1)) | (~b(s(s(s(z))), z)) | (~b(elem!1, s(s(s(z)))))))),
% 2.22/2.44 inference(monotonicity,[status(thm)],[5841])).
% 2.22/2.44 tff(5843,plain,
% 2.22/2.44 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, z)) | (~b(elem!1, z)) | (~b(z, elem!1)) | (~b(s(s(s(z))), z)) | (~b(elem!1, z)) | (~b(elem!1, s(s(s(z))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, z)) | (~b(z, elem!1)) | (~b(s(s(s(z))), z)) | (~b(elem!1, s(s(s(z))))))),
% 2.22/2.44 inference(transitivity,[status(thm)],[5842, 5840])).
% 2.22/2.44 tff(5844,plain,
% 2.22/2.44 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, z)) | (~b(elem!1, z)) | (~b(z, elem!1)) | (~b(s(s(s(z))), z)) | (~b(elem!1, z)) | (~b(elem!1, s(s(s(z))))))),
% 2.22/2.44 inference(quant_inst,[status(thm)],[])).
% 2.22/2.44 tff(5845,plain,
% 2.22/2.44 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, z)) | (~b(z, elem!1)) | (~b(s(s(s(z))), z)) | (~b(elem!1, s(s(s(z)))))),
% 2.22/2.44 inference(modus_ponens,[status(thm)],[5844, 5843])).
% 2.22/2.44 tff(5846,plain,
% 2.22/2.44 (~b(elem!1, s(s(s(z))))),
% 2.22/2.44 inference(unit_resolution,[status(thm)],[5845, 166, 2517, 5821, 1699])).
% 2.22/2.44 tff(5847,plain,
% 2.22/2.44 (r(elem!1, s(s(s(z))))),
% 2.22/2.44 inference(unit_resolution,[status(thm)],[1619, 5846, 5839])).
% 2.22/2.44 tff(5848,plain,
% 2.22/2.44 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(z))) | (~r(s(z), s(s(s(z))))) | (~r(elem!1, s(s(s(z))))) | (~r(s(s(s(z))), elem!1)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(elem!1, s(z))) | (~r(s(z), s(s(s(z))))) | (~r(elem!1, s(s(s(z))))) | (~r(s(s(s(z))), elem!1)))),
% 2.22/2.44 inference(rewrite,[status(thm)],[])).
% 2.22/2.44 tff(5849,plain,
% 2.22/2.44 (((~r(s(s(s(z))), elem!1)) | (~r(s(z), s(s(s(z))))) | (~r(elem!1, s(s(s(z))))) | (~r(elem!1, s(z)))) <=> ((~r(elem!1, s(z))) | (~r(s(z), s(s(s(z))))) | (~r(elem!1, s(s(s(z))))) | (~r(s(s(s(z))), elem!1)))),
% 2.22/2.44 inference(rewrite,[status(thm)],[])).
% 2.22/2.44 tff(5850,plain,
% 2.22/2.44 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(z))), elem!1)) | (~r(s(z), s(s(s(z))))) | (~r(elem!1, s(s(s(z))))) | (~r(elem!1, s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(z))) | (~r(s(z), s(s(s(z))))) | (~r(elem!1, s(s(s(z))))) | (~r(s(s(s(z))), elem!1))))),
% 2.22/2.44 inference(monotonicity,[status(thm)],[5849])).
% 2.22/2.44 tff(5851,plain,
% 2.22/2.44 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(z))), elem!1)) | (~r(s(z), s(s(s(z))))) | (~r(elem!1, s(s(s(z))))) | (~r(elem!1, s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(elem!1, s(z))) | (~r(s(z), s(s(s(z))))) | (~r(elem!1, s(s(s(z))))) | (~r(s(s(s(z))), elem!1)))),
% 2.22/2.44 inference(transitivity,[status(thm)],[5850, 5848])).
% 2.22/2.44 tff(5852,plain,
% 2.22/2.44 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(z))), elem!1)) | (~r(s(z), s(s(s(z))))) | (~r(elem!1, s(s(s(z))))) | (~r(elem!1, s(z))))),
% 2.22/2.44 inference(quant_inst,[status(thm)],[])).
% 2.22/2.44 tff(5853,plain,
% 2.22/2.44 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(elem!1, s(z))) | (~r(s(z), s(s(s(z))))) | (~r(elem!1, s(s(s(z))))) | (~r(s(s(s(z))), elem!1))),
% 2.22/2.44 inference(modus_ponens,[status(thm)],[5852, 5851])).
% 2.22/2.44 tff(5854,plain,
% 2.22/2.44 ($false),
% 2.22/2.44 inference(unit_resolution,[status(thm)],[5853, 197, 744, 5847, 5837, 5829])).
% 2.22/2.44 tff(5855,plain,((~b(s(s(s(z))), z)) | (~r(elem!1, s(z))) | (s(s(s(z))) = elem!1) | (~b(z, elem!1)) | (~b(elem!1, z)) | (~b(s(z), z))), inference(lemma,lemma(discharge,[]))).
% 2.22/2.44 tff(5856,plain,
% 2.22/2.44 (~b(s(s(s(z))), z)),
% 2.22/2.44 inference(unit_resolution,[status(thm)],[5855, 5820, 5818, 5817, 5815, 53])).
% 2.22/2.44 tff(5857,plain,
% 2.22/2.44 (r(s(s(s(z))), z)),
% 2.22/2.44 inference(unit_resolution,[status(thm)],[1713, 5856])).
% 2.22/2.44 tff(5858,plain,
% 2.22/2.44 (~r(s(s(s(z))), s(s(z)))),
% 2.22/2.44 inference(unit_resolution,[status(thm)],[1717, 197, 155, 866, 5857])).
% 2.22/2.44 tff(5859,plain,
% 2.22/2.44 (b(s(s(s(z))), s(s(z)))),
% 2.22/2.44 inference(unit_resolution,[status(thm)],[1008, 79, 5858, 1003])).
% 2.22/2.44 tff(5860,plain,
% 2.22/2.44 (b(s(s(z)), s(s(s(elem!1)))) <=> b(s(s(z)), s(elem!1))),
% 2.22/2.44 inference(monotonicity,[status(thm)],[5811])).
% 2.22/2.44 tff(5861,plain,
% 2.22/2.44 (b(s(s(z)), s(elem!1))),
% 2.22/2.44 inference(modus_ponens,[status(thm)],[5735, 5860])).
% 2.22/2.44 tff(5862,plain,
% 2.22/2.44 (b(s(s(s(elem!1))), s(s(z))) <=> b(s(elem!1), s(s(z)))),
% 2.22/2.44 inference(monotonicity,[status(thm)],[5811])).
% 2.22/2.44 tff(5863,plain,
% 2.22/2.44 (b(s(elem!1), s(s(z)))),
% 2.22/2.44 inference(modus_ponens,[status(thm)],[5734, 5862])).
% 2.22/2.44 tff(5864,plain,
% 2.22/2.44 (b(s(elem!1), s(s(elem!1))) <=> b(s(elem!1), elem!1)),
% 2.22/2.44 inference(monotonicity,[status(thm)],[5813])).
% 2.22/2.44 tff(5865,plain,
% 2.22/2.44 (b(s(s(s(elem!1))), s(s(elem!1))) <=> b(s(elem!1), s(s(elem!1)))),
% 2.22/2.44 inference(monotonicity,[status(thm)],[5811])).
% 2.22/2.44 tff(5866,plain,
% 2.22/2.44 (~(s(s(s(elem!1))) = s(s(elem!1)))),
% 2.22/2.44 inference(unit_resolution,[status(thm)],[50, 5732])).
% 2.22/2.44 tff(5867,plain,
% 2.22/2.44 (~r(s(s(s(elem!1))), s(s(elem!1)))),
% 2.22/2.44 inference(unit_resolution,[status(thm)],[5711, 197, 311, 5731, 5752])).
% 2.22/2.44 tff(5868,plain,
% 2.22/2.44 (b(s(s(s(elem!1))), s(s(elem!1)))),
% 2.22/2.44 inference(unit_resolution,[status(thm)],[889, 5867, 5866])).
% 2.22/2.44 tff(5869,plain,
% 2.22/2.44 (b(s(elem!1), s(s(elem!1)))),
% 2.22/2.44 inference(modus_ponens,[status(thm)],[5868, 5865])).
% 2.22/2.44 tff(5870,plain,
% 2.22/2.44 (b(s(elem!1), elem!1)),
% 2.22/2.44 inference(modus_ponens,[status(thm)],[5869, 5864])).
% 2.22/2.44 tff(5871,plain,
% 2.22/2.44 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), elem!1)) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(s(z)), s(elem!1))) | (~b(s(elem!1), s(s(z)))) | (~b(s(elem!1), s(s(s(z))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(elem!1), elem!1)) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(s(z)), s(elem!1))) | (~b(s(elem!1), s(s(z)))) | (~b(s(elem!1), s(s(s(z))))))),
% 2.22/2.44 inference(rewrite,[status(thm)],[])).
% 2.22/2.44 tff(5872,plain,
% 2.22/2.44 (((~b(s(elem!1), elem!1)) | (~b(s(elem!1), elem!1)) | (~b(s(s(z)), s(elem!1))) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(elem!1), s(s(z)))) | (~b(s(elem!1), s(s(s(z)))))) <=> ((~b(s(elem!1), elem!1)) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(s(z)), s(elem!1))) | (~b(s(elem!1), s(s(z)))) | (~b(s(elem!1), s(s(s(z))))))),
% 2.22/2.44 inference(rewrite,[status(thm)],[])).
% 2.22/2.44 tff(5873,plain,
% 2.22/2.44 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), elem!1)) | (~b(s(elem!1), elem!1)) | (~b(s(s(z)), s(elem!1))) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(elem!1), s(s(z)))) | (~b(s(elem!1), s(s(s(z))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), elem!1)) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(s(z)), s(elem!1))) | (~b(s(elem!1), s(s(z)))) | (~b(s(elem!1), s(s(s(z)))))))),
% 2.22/2.44 inference(monotonicity,[status(thm)],[5872])).
% 2.22/2.44 tff(5874,plain,
% 2.22/2.44 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), elem!1)) | (~b(s(elem!1), elem!1)) | (~b(s(s(z)), s(elem!1))) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(elem!1), s(s(z)))) | (~b(s(elem!1), s(s(s(z))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(elem!1), elem!1)) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(s(z)), s(elem!1))) | (~b(s(elem!1), s(s(z)))) | (~b(s(elem!1), s(s(s(z))))))),
% 2.22/2.44 inference(transitivity,[status(thm)],[5873, 5871])).
% 2.22/2.44 tff(5875,plain,
% 2.22/2.44 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), elem!1)) | (~b(s(elem!1), elem!1)) | (~b(s(s(z)), s(elem!1))) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(elem!1), s(s(z)))) | (~b(s(elem!1), s(s(s(z))))))),
% 2.22/2.44 inference(quant_inst,[status(thm)],[])).
% 2.22/2.44 tff(5876,plain,
% 2.22/2.44 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(elem!1), elem!1)) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(s(z)), s(elem!1))) | (~b(s(elem!1), s(s(z)))) | (~b(s(elem!1), s(s(s(z)))))),
% 2.22/2.44 inference(modus_ponens,[status(thm)],[5875, 5874])).
% 2.22/2.44 tff(5877,plain,
% 2.22/2.44 (~b(s(elem!1), s(s(s(z))))),
% 2.22/2.44 inference(unit_resolution,[status(thm)],[5876, 166, 5870, 5863, 5861, 5859])).
% 2.22/2.44 tff(5878,plain,
% 2.22/2.44 (r(s(elem!1), z)),
% 2.22/2.44 inference(unit_resolution,[status(thm)],[1184, 5811, 154])).
% 2.22/2.44 tff(5879,plain,
% 2.22/2.44 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(elem!1), z)) | (~r(z, s(s(z)))) | (~r(s(s(s(z))), z)) | (~r(s(elem!1), s(s(s(z))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(elem!1), z)) | (~r(z, s(s(z)))) | (~r(s(s(s(z))), z)) | (~r(s(elem!1), s(s(s(z))))))),
% 2.22/2.45 inference(rewrite,[status(thm)],[])).
% 2.22/2.45 tff(5880,plain,
% 2.22/2.45 (((~r(z, s(s(z)))) | (~r(s(s(s(z))), z)) | (~r(s(elem!1), z)) | (~r(s(elem!1), s(s(s(z)))))) <=> ((~r(s(elem!1), z)) | (~r(z, s(s(z)))) | (~r(s(s(s(z))), z)) | (~r(s(elem!1), s(s(s(z))))))),
% 2.22/2.45 inference(rewrite,[status(thm)],[])).
% 2.22/2.45 tff(5881,plain,
% 2.22/2.45 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(z)))) | (~r(s(s(s(z))), z)) | (~r(s(elem!1), z)) | (~r(s(elem!1), s(s(s(z))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(elem!1), z)) | (~r(z, s(s(z)))) | (~r(s(s(s(z))), z)) | (~r(s(elem!1), s(s(s(z)))))))),
% 2.22/2.45 inference(monotonicity,[status(thm)],[5880])).
% 2.22/2.45 tff(5882,plain,
% 2.22/2.45 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(z)))) | (~r(s(s(s(z))), z)) | (~r(s(elem!1), z)) | (~r(s(elem!1), s(s(s(z))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(elem!1), z)) | (~r(z, s(s(z)))) | (~r(s(s(s(z))), z)) | (~r(s(elem!1), s(s(s(z))))))),
% 2.22/2.45 inference(transitivity,[status(thm)],[5881, 5879])).
% 2.22/2.45 tff(5883,plain,
% 2.22/2.45 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(z)))) | (~r(s(s(s(z))), z)) | (~r(s(elem!1), z)) | (~r(s(elem!1), s(s(s(z))))))),
% 2.22/2.45 inference(quant_inst,[status(thm)],[])).
% 2.22/2.45 tff(5884,plain,
% 2.22/2.45 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(elem!1), z)) | (~r(z, s(s(z)))) | (~r(s(s(s(z))), z)) | (~r(s(elem!1), s(s(s(z)))))),
% 2.22/2.45 inference(modus_ponens,[status(thm)],[5883, 5882])).
% 2.22/2.45 tff(5885,plain,
% 2.22/2.45 (~r(s(elem!1), s(s(s(z))))),
% 2.22/2.45 inference(unit_resolution,[status(thm)],[5884, 197, 5878, 155, 5857])).
% 2.22/2.45 tff(5886,plain,
% 2.22/2.45 (((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((s(elem!1) = s(s(s(z)))) | b(s(elem!1), s(s(s(z)))) | r(s(elem!1), s(s(s(z)))))) <=> ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (s(elem!1) = s(s(s(z)))) | b(s(elem!1), s(s(s(z)))) | r(s(elem!1), s(s(s(z)))))),
% 2.22/2.45 inference(rewrite,[status(thm)],[])).
% 2.22/2.45 tff(5887,plain,
% 2.22/2.45 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((s(elem!1) = s(s(s(z)))) | b(s(elem!1), s(s(s(z)))) | r(s(elem!1), s(s(s(z)))))),
% 2.22/2.45 inference(quant_inst,[status(thm)],[])).
% 2.22/2.45 tff(5888,plain,
% 2.22/2.45 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (s(elem!1) = s(s(s(z)))) | b(s(elem!1), s(s(s(z)))) | r(s(elem!1), s(s(s(z))))),
% 2.22/2.45 inference(modus_ponens,[status(thm)],[5887, 5886])).
% 2.22/2.45 tff(5889,plain,
% 2.22/2.45 ((s(elem!1) = s(s(s(z)))) | b(s(elem!1), s(s(s(z))))),
% 2.22/2.45 inference(unit_resolution,[status(thm)],[5888, 79, 5885])).
% 2.22/2.45 tff(5890,plain,
% 2.22/2.45 (s(elem!1) = s(s(s(z)))),
% 2.22/2.45 inference(unit_resolution,[status(thm)],[5889, 5877])).
% 2.22/2.45 tff(5891,plain,
% 2.22/2.45 (s(s(s(z))) = s(elem!1)),
% 2.22/2.45 inference(symmetry,[status(thm)],[5890])).
% 2.22/2.45 tff(5892,plain,
% 2.22/2.45 (inj_0(s(s(s(z)))) = inj_0(s(elem!1))),
% 2.22/2.45 inference(monotonicity,[status(thm)],[5891])).
% 2.22/2.45 tff(5893,plain,
% 2.22/2.45 (s(s(z)) = elem!1),
% 2.22/2.45 inference(transitivity,[status(thm)],[1666, 5892, 20])).
% 2.22/2.45 tff(5894,plain,
% 2.22/2.45 (inj_0(s(elem!1)) = inj_0(s(s(s(elem!1))))),
% 2.22/2.45 inference(symmetry,[status(thm)],[5812])).
% 2.22/2.45 tff(5895,plain,
% 2.22/2.45 (elem!1 = s(s(elem!1))),
% 2.22/2.45 inference(transitivity,[status(thm)],[1170, 5894, 104])).
% 2.22/2.45 tff(5896,plain,
% 2.22/2.45 ((s(s(z)) = elem!1) <=> (s(s(z)) = s(s(elem!1)))),
% 2.22/2.45 inference(monotonicity,[status(thm)],[5895])).
% 2.22/2.45 tff(5897,plain,
% 2.22/2.45 ((s(s(z)) = elem!1) <=> (s(s(elem!1)) = s(s(z)))),
% 2.22/2.45 inference(transitivity,[status(thm)],[5896, 126])).
% 2.22/2.45 tff(5898,plain,
% 2.22/2.45 ((s(s(elem!1)) = s(s(z))) <=> (s(s(z)) = elem!1)),
% 2.22/2.45 inference(symmetry,[status(thm)],[5897])).
% 2.22/2.45 tff(5899,plain,
% 2.22/2.45 ((~(s(s(elem!1)) = s(s(z)))) <=> (~(s(s(z)) = elem!1))),
% 2.22/2.45 inference(monotonicity,[status(thm)],[5898])).
% 2.22/2.45 tff(5900,plain,
% 2.22/2.45 (~(s(s(z)) = elem!1)),
% 2.22/2.45 inference(modus_ponens,[status(thm)],[11, 5899])).
% 2.22/2.45 tff(5901,plain,
% 2.22/2.45 ($false),
% 2.22/2.45 inference(unit_resolution,[status(thm)],[5900, 5893])).
% 2.22/2.45 tff(5902,plain,((~r(s(s(z)), z)) | (~r(z, s(s(z)))) | (~b(s(z), z)) | (s(s(elem!1)) = s(s(z))) | (~b(z, s(s(elem!1)))) | (~r(s(s(s(elem!1))), z)) | (~r(s(z), s(s(elem!1)))) | (~r(s(s(z)), s(s(elem!1)))) | (~b(z, s(z))) | (~b(s(z), s(s(z))))), inference(lemma,lemma(discharge,[]))).
% 2.22/2.45 tff(5903,plain,
% 2.22/2.45 (~r(s(s(z)), z)),
% 2.22/2.45 inference(unit_resolution,[status(thm)],[5902, 556, 53, 11, 1820, 154, 311, 333, 118, 155])).
% 2.22/2.45 tff(5904,plain,
% 2.22/2.45 (b(s(s(z)), z)),
% 2.22/2.45 inference(unit_resolution,[status(thm)],[186, 5903])).
% 2.22/2.45 tff(5905,plain,
% 2.22/2.45 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), z)) | (~b(z, s(z))) | (~b(s(z), s(s(z)))) | (~b(s(s(z)), z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), z)) | (~b(z, s(z))) | (~b(s(z), s(s(z)))) | (~b(s(s(z)), z)))),
% 2.22/2.45 inference(rewrite,[status(thm)],[])).
% 2.22/2.45 tff(5906,plain,
% 2.22/2.45 (((~b(s(z), z)) | (~b(s(z), z)) | (~b(z, s(z))) | (~b(s(s(z)), z)) | (~b(s(z), z)) | (~b(s(z), s(s(z))))) <=> ((~b(s(z), z)) | (~b(z, s(z))) | (~b(s(z), s(s(z)))) | (~b(s(s(z)), z)))),
% 2.22/2.45 inference(rewrite,[status(thm)],[])).
% 2.22/2.45 tff(5907,plain,
% 2.22/2.45 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), z)) | (~b(s(z), z)) | (~b(z, s(z))) | (~b(s(s(z)), z)) | (~b(s(z), z)) | (~b(s(z), s(s(z)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), z)) | (~b(z, s(z))) | (~b(s(z), s(s(z)))) | (~b(s(s(z)), z))))),
% 2.22/2.45 inference(monotonicity,[status(thm)],[5906])).
% 2.22/2.45 tff(5908,plain,
% 2.22/2.45 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), z)) | (~b(s(z), z)) | (~b(z, s(z))) | (~b(s(s(z)), z)) | (~b(s(z), z)) | (~b(s(z), s(s(z)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), z)) | (~b(z, s(z))) | (~b(s(z), s(s(z)))) | (~b(s(s(z)), z)))),
% 2.22/2.45 inference(transitivity,[status(thm)],[5907, 5905])).
% 2.22/2.45 tff(5909,plain,
% 2.22/2.45 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), z)) | (~b(s(z), z)) | (~b(z, s(z))) | (~b(s(s(z)), z)) | (~b(s(z), z)) | (~b(s(z), s(s(z)))))),
% 2.22/2.45 inference(quant_inst,[status(thm)],[])).
% 2.22/2.45 tff(5910,plain,
% 2.22/2.45 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), z)) | (~b(z, s(z))) | (~b(s(z), s(s(z)))) | (~b(s(s(z)), z))),
% 2.22/2.45 inference(modus_ponens,[status(thm)],[5909, 5908])).
% 2.22/2.45 tff(5911,plain,
% 2.22/2.45 ($false),
% 2.22/2.45 inference(unit_resolution,[status(thm)],[5910, 166, 53, 556, 118, 5904])).
% 2.22/2.45 tff(5912,plain,((~b(s(z), s(s(z)))) | (~b(s(z), z)) | (~b(z, s(z))) | (s(s(elem!1)) = s(s(z))) | (~b(z, s(s(elem!1)))) | (~r(s(s(s(elem!1))), z)) | (~r(s(z), s(s(elem!1)))) | (~r(s(s(z)), s(s(elem!1)))) | (~r(z, s(s(z))))), inference(lemma,lemma(discharge,[]))).
% 2.22/2.45 tff(5913,plain,
% 2.22/2.45 (~b(s(z), s(s(z)))),
% 2.22/2.45 inference(unit_resolution,[status(thm)],[5912, 53, 118, 11, 1820, 154, 311, 333, 155])).
% 2.22/2.45 tff(5914,plain,
% 2.22/2.45 (r(s(z), s(s(z)))),
% 2.22/2.45 inference(unit_resolution,[status(thm)],[427, 5913])).
% 2.22/2.45 tff(5915,plain,
% 2.22/2.45 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(s(elem!1)))) | (~r(s(s(z)), s(s(elem!1)))) | (~r(s(s(elem!1)), s(z))) | (~r(s(z), s(s(z)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(z), s(s(elem!1)))) | (~r(s(s(z)), s(s(elem!1)))) | (~r(s(s(elem!1)), s(z))) | (~r(s(z), s(s(z)))))),
% 2.22/2.45 inference(rewrite,[status(thm)],[])).
% 2.22/2.45 tff(5916,plain,
% 2.22/2.45 (((~r(s(s(elem!1)), s(z))) | (~r(s(s(z)), s(s(elem!1)))) | (~r(s(z), s(s(elem!1)))) | (~r(s(z), s(s(z))))) <=> ((~r(s(z), s(s(elem!1)))) | (~r(s(s(z)), s(s(elem!1)))) | (~r(s(s(elem!1)), s(z))) | (~r(s(z), s(s(z)))))),
% 2.22/2.45 inference(rewrite,[status(thm)],[])).
% 2.22/2.45 tff(5917,plain,
% 2.22/2.45 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(elem!1)), s(z))) | (~r(s(s(z)), s(s(elem!1)))) | (~r(s(z), s(s(elem!1)))) | (~r(s(z), s(s(z)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(s(elem!1)))) | (~r(s(s(z)), s(s(elem!1)))) | (~r(s(s(elem!1)), s(z))) | (~r(s(z), s(s(z))))))),
% 2.22/2.45 inference(monotonicity,[status(thm)],[5916])).
% 2.22/2.45 tff(5918,plain,
% 2.22/2.45 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(elem!1)), s(z))) | (~r(s(s(z)), s(s(elem!1)))) | (~r(s(z), s(s(elem!1)))) | (~r(s(z), s(s(z)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(z), s(s(elem!1)))) | (~r(s(s(z)), s(s(elem!1)))) | (~r(s(s(elem!1)), s(z))) | (~r(s(z), s(s(z)))))),
% 2.22/2.45 inference(transitivity,[status(thm)],[5917, 5915])).
% 2.22/2.45 tff(5919,plain,
% 2.22/2.45 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(elem!1)), s(z))) | (~r(s(s(z)), s(s(elem!1)))) | (~r(s(z), s(s(elem!1)))) | (~r(s(z), s(s(z)))))),
% 2.22/2.45 inference(quant_inst,[status(thm)],[])).
% 2.22/2.45 tff(5920,plain,
% 2.22/2.45 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(z), s(s(elem!1)))) | (~r(s(s(z)), s(s(elem!1)))) | (~r(s(s(elem!1)), s(z))) | (~r(s(z), s(s(z))))),
% 2.22/2.45 inference(modus_ponens,[status(thm)],[5919, 5918])).
% 2.22/2.45 tff(5921,plain,
% 2.22/2.45 ($false),
% 2.22/2.45 inference(unit_resolution,[status(thm)],[5920, 197, 311, 5914, 5728, 333])).
% 2.22/2.45 tff(5922,plain,((~b(s(z), z)) | (~r(s(z), s(s(elem!1)))) | (~r(s(s(z)), s(s(elem!1)))) | (~b(z, s(s(elem!1)))) | (~b(z, s(z))) | (s(s(elem!1)) = s(s(z))) | (~r(s(s(s(elem!1))), z)) | (~r(z, s(s(z))))), inference(lemma,lemma(discharge,[]))).
% 2.22/2.45 tff(5923,plain,
% 2.22/2.45 (~b(z, s(s(elem!1)))),
% 2.22/2.45 inference(unit_resolution,[status(thm)],[5922, 5726, 53, 154, 118, 311, 132, 155])).
% 2.22/2.45 tff(5924,plain,
% 2.22/2.45 ($false),
% 2.22/2.45 inference(unit_resolution,[status(thm)],[1795, 5923, 5725])).
% 2.22/2.45 tff(5925,plain,((~r(s(s(z)), z)) | (~b(s(z), z)) | (~r(s(s(s(elem!1))), z)) | (~b(z, s(z))) | (~r(s(z), s(s(elem!1)))) | (~r(z, s(s(z)))) | (s(s(z)) = s(s(elem!1))) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(s(elem!1)), s(s(s(elem!1)))))), inference(lemma,lemma(discharge,[]))).
% 2.22/2.45 tff(5926,plain,
% 2.22/2.45 (~r(s(s(z)), z)),
% 2.22/2.45 inference(unit_resolution,[status(thm)],[5925, 85, 154, 118, 5700, 152, 52, 5713, 5708])).
% 2.22/2.45 tff(5927,plain,
% 2.22/2.45 (b(s(s(z)), z)),
% 2.22/2.45 inference(unit_resolution,[status(thm)],[186, 5926])).
% 2.22/2.45 tff(5928,plain,
% 2.22/2.45 (~b(s(s(z)), s(z))),
% 2.22/2.45 inference(unit_resolution,[status(thm)],[181, 5927, 118, 5700])).
% 2.22/2.45 tff(5929,plain,
% 2.22/2.45 (r(s(s(z)), s(z))),
% 2.22/2.45 inference(unit_resolution,[status(thm)],[308, 5928])).
% 2.22/2.45 tff(5930,plain,
% 2.22/2.45 (~r(s(s(s(elem!1))), s(s(z)))),
% 2.22/2.45 inference(unit_resolution,[status(thm)],[854, 5929, 350, 85])).
% 2.22/2.45 tff(5931,plain,
% 2.22/2.45 (b(s(s(s(elem!1))), s(s(z)))),
% 2.22/2.45 inference(unit_resolution,[status(thm)],[218, 5930])).
% 2.22/2.45 tff(5932,plain,
% 2.22/2.45 (~b(s(s(z)), s(s(elem!1)))),
% 2.22/2.45 inference(unit_resolution,[status(thm)],[2068, 5931, 5713, 5708])).
% 2.22/2.45 tff(5933,plain,
% 2.22/2.45 (r(s(s(z)), s(s(elem!1)))),
% 2.22/2.45 inference(unit_resolution,[status(thm)],[390, 5932, 52])).
% 2.22/2.45 tff(5934,plain,
% 2.22/2.45 (~r(s(s(z)), s(s(s(elem!1))))),
% 2.22/2.45 inference(unit_resolution,[status(thm)],[3958, 5929, 350, 85])).
% 2.22/2.45 tff(5935,plain,
% 2.22/2.45 (~b(s(s(elem!1)), s(s(z)))),
% 2.22/2.45 inference(unit_resolution,[status(thm)],[501, 5934, 5708, 5930])).
% 2.22/2.45 tff(5936,plain,
% 2.22/2.45 (r(s(s(elem!1)), s(s(z)))),
% 2.22/2.45 inference(unit_resolution,[status(thm)],[441, 5935, 132])).
% 2.22/2.45 tff(5937,plain,
% 2.22/2.45 (~r(z, s(s(elem!1)))),
% 2.22/2.45 inference(unit_resolution,[status(thm)],[401, 5936, 152, 5929])).
% 2.22/2.45 tff(5938,plain,
% 2.22/2.45 (b(z, s(s(elem!1)))),
% 2.22/2.45 inference(unit_resolution,[status(thm)],[1795, 5937])).
% 2.22/2.45 tff(5939,plain,
% 2.22/2.45 ($false),
% 2.22/2.45 inference(unit_resolution,[status(thm)],[5922, 5938, 5933, 5700, 154, 118, 85, 132, 152])).
% 2.22/2.45 tff(5940,plain,(b(s(z), s(s(elem!1))) | (~r(s(s(s(elem!1))), z)) | (~b(z, s(z))) | (s(s(z)) = s(s(elem!1))) | (~r(s(s(s(elem!1))), s(z))) | (s(s(elem!1)) = s(s(s(elem!1)))) | b(z, s(s(z)))), inference(lemma,lemma(discharge,[]))).
% 2.22/2.45 tff(5941,plain,
% 2.22/2.45 (b(s(z), s(s(elem!1)))),
% 2.22/2.45 inference(unit_resolution,[status(thm)],[5940, 52, 118, 154, 350, 45, 125])).
% 2.22/2.45 tff(5942,plain,
% 2.22/2.45 (~r(s(z), z)),
% 2.22/2.45 inference(unit_resolution,[status(thm)],[5698, 154, 155, 350])).
% 2.22/2.45 tff(5943,plain,
% 2.22/2.45 (b(s(z), z)),
% 2.22/2.45 inference(unit_resolution,[status(thm)],[230, 5942])).
% 2.22/2.45 tff(5944,plain,
% 2.22/2.45 (~b(s(s(elem!1)), s(z))),
% 2.22/2.45 inference(unit_resolution,[status(thm)],[3500, 156, 155, 118, 53, 52])).
% 2.22/2.45 tff(5945,plain,
% 2.22/2.45 (r(s(s(elem!1)), s(z))),
% 2.22/2.45 inference(unit_resolution,[status(thm)],[1912, 5944])).
% 2.22/2.45 tff(5946,plain,
% 2.22/2.45 (~b(s(s(z)), z)),
% 2.22/2.45 inference(unit_resolution,[status(thm)],[181, 156, 118, 53])).
% 2.22/2.45 tff(5947,plain,
% 2.22/2.45 (r(s(s(z)), z)),
% 2.22/2.45 inference(unit_resolution,[status(thm)],[186, 5946])).
% 2.22/2.45 tff(5948,plain,
% 2.22/2.45 (~b(s(s(elem!1)), s(s(s(elem!1))))),
% 2.22/2.45 inference(unit_resolution,[status(thm)],[501, 405, 273, 213])).
% 2.22/2.45 tff(5949,plain,
% 2.22/2.45 (r(s(s(elem!1)), s(s(s(elem!1))))),
% 2.22/2.45 inference(unit_resolution,[status(thm)],[461, 5948, 45])).
% 2.22/2.45 tff(5950,plain,
% 2.22/2.45 (~r(s(z), s(s(s(elem!1))))),
% 2.22/2.45 inference(unit_resolution,[status(thm)],[5310, 5949, 154, 4577])).
% 2.22/2.45 tff(5951,plain,
% 2.22/2.45 (b(s(z), s(s(s(elem!1))))),
% 2.22/2.45 inference(unit_resolution,[status(thm)],[116, 5950])).
% 2.22/2.45 tff(5952,plain,
% 2.22/2.45 (~r(s(s(s(elem!1))), s(s(elem!1)))),
% 2.22/2.45 inference(unit_resolution,[status(thm)],[1386, 5949, 154, 365])).
% 2.22/2.45 tff(5953,plain,
% 2.22/2.45 (b(s(s(s(elem!1))), s(s(elem!1)))),
% 2.22/2.45 inference(unit_resolution,[status(thm)],[889, 5952, 51])).
% 2.22/2.45 tff(5954,plain,
% 2.22/2.45 ($false),
% 2.22/2.45 inference(unit_resolution,[status(thm)],[5396, 5953, 5951, 376, 405, 446])).
% 2.22/2.45 tff(5955,plain,((~b(s(s(elem!1)), s(s(z)))) | (~b(s(z), s(s(elem!1)))) | (~b(s(s(z)), s(s(elem!1)))) | (~r(s(s(s(elem!1))), z)) | (~r(z, s(s(elem!1)))) | (~r(s(s(elem!1)), s(z))) | (s(s(elem!1)) = s(s(s(elem!1)))) | r(s(s(z)), s(s(s(elem!1)))) | r(s(s(s(elem!1))), s(s(z)))), inference(lemma,lemma(discharge,[]))).
% 2.22/2.45 tff(5956,plain,
% 2.22/2.45 (~b(s(s(elem!1)), s(s(z)))),
% 2.22/2.45 inference(unit_resolution,[status(thm)],[5955, 365, 446, 154, 376, 4577, 45, 5721, 213])).
% 2.22/2.45 tff(5957,plain,
% 2.22/2.45 (r(s(s(elem!1)), s(s(z)))),
% 2.22/2.45 inference(unit_resolution,[status(thm)],[441, 5956, 11])).
% 2.22/2.45 tff(5958,plain,
% 2.22/2.45 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(elem!1)))) | (~r(s(s(z)), z)) | (~r(s(s(elem!1)), s(s(z)))) | (~r(z, s(s(z)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, s(s(elem!1)))) | (~r(s(s(z)), z)) | (~r(s(s(elem!1)), s(s(z)))) | (~r(z, s(s(z)))))),
% 2.22/2.45 inference(rewrite,[status(thm)],[])).
% 2.22/2.45 tff(5959,plain,
% 2.22/2.45 (((~r(s(s(z)), z)) | (~r(s(s(elem!1)), s(s(z)))) | (~r(z, s(s(z)))) | (~r(z, s(s(elem!1))))) <=> ((~r(z, s(s(elem!1)))) | (~r(s(s(z)), z)) | (~r(s(s(elem!1)), s(s(z)))) | (~r(z, s(s(z)))))),
% 2.22/2.45 inference(rewrite,[status(thm)],[])).
% 2.22/2.45 tff(5960,plain,
% 2.22/2.45 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(z)), z)) | (~r(s(s(elem!1)), s(s(z)))) | (~r(z, s(s(z)))) | (~r(z, s(s(elem!1)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(elem!1)))) | (~r(s(s(z)), z)) | (~r(s(s(elem!1)), s(s(z)))) | (~r(z, s(s(z))))))),
% 2.22/2.45 inference(monotonicity,[status(thm)],[5959])).
% 2.22/2.45 tff(5961,plain,
% 2.22/2.45 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(z)), z)) | (~r(s(s(elem!1)), s(s(z)))) | (~r(z, s(s(z)))) | (~r(z, s(s(elem!1)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, s(s(elem!1)))) | (~r(s(s(z)), z)) | (~r(s(s(elem!1)), s(s(z)))) | (~r(z, s(s(z)))))),
% 2.22/2.45 inference(transitivity,[status(thm)],[5960, 5958])).
% 2.22/2.45 tff(5962,plain,
% 2.22/2.45 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(z)), z)) | (~r(s(s(elem!1)), s(s(z)))) | (~r(z, s(s(z)))) | (~r(z, s(s(elem!1)))))),
% 2.22/2.45 inference(quant_inst,[status(thm)],[])).
% 2.22/2.45 tff(5963,plain,
% 2.22/2.45 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, s(s(elem!1)))) | (~r(s(s(z)), z)) | (~r(s(s(elem!1)), s(s(z)))) | (~r(z, s(s(z))))),
% 2.22/2.45 inference(modus_ponens,[status(thm)],[5962, 5961])).
% 2.22/2.45 tff(5964,plain,
% 2.22/2.45 ($false),
% 2.22/2.45 inference(unit_resolution,[status(thm)],[5963, 197, 5957, 155, 365, 866])).
% 2.22/2.45 tff(5965,plain,((~r(z, s(s(elem!1)))) | (~r(z, s(s(z)))) | (~r(s(s(z)), z)) | (s(s(elem!1)) = s(s(z))) | (~b(s(s(z)), s(s(elem!1)))) | (~r(s(s(s(elem!1))), z)) | (~b(s(z), s(s(elem!1)))) | (~r(s(s(elem!1)), s(z))) | (s(s(elem!1)) = s(s(s(elem!1)))) | r(s(s(s(elem!1))), s(s(z)))), inference(lemma,lemma(discharge,[]))).
% 2.22/2.45 tff(5966,plain,
% 2.22/2.45 (~r(z, s(s(elem!1)))),
% 2.22/2.45 inference(unit_resolution,[status(thm)],[5965, 446, 866, 11, 155, 154, 376, 4577, 45, 213])).
% 2.22/2.45 tff(5967,plain,
% 2.22/2.45 (b(z, s(s(elem!1)))),
% 2.22/2.45 inference(unit_resolution,[status(thm)],[1795, 5966])).
% 2.22/2.45 tff(5968,plain,
% 2.22/2.45 (~b(s(s(elem!1)), z)),
% 2.22/2.45 inference(unit_resolution,[status(thm)],[5377, 5967, 376, 53])).
% 2.22/2.45 tff(5969,plain,
% 2.22/2.45 (r(s(s(elem!1)), z)),
% 2.22/2.45 inference(unit_resolution,[status(thm)],[608, 5968])).
% 2.22/2.45 tff(5970,plain,
% 2.22/2.45 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(elem!1)))) | (~b(s(z), z)) | (~b(s(z), s(s(elem!1)))) | (~b(s(s(elem!1)), s(s(z)))) | (~b(s(s(z)), s(s(elem!1)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(s(elem!1)))) | (~b(s(z), z)) | (~b(s(z), s(s(elem!1)))) | (~b(s(s(elem!1)), s(s(z)))) | (~b(s(s(z)), s(s(elem!1)))))),
% 2.22/2.45 inference(rewrite,[status(thm)],[])).
% 2.22/2.45 tff(5971,plain,
% 2.22/2.45 (((~b(s(s(z)), s(s(elem!1)))) | (~b(s(z), s(s(elem!1)))) | (~b(s(s(elem!1)), s(s(z)))) | (~b(z, s(s(elem!1)))) | (~b(s(z), s(s(elem!1)))) | (~b(s(z), z))) <=> ((~b(z, s(s(elem!1)))) | (~b(s(z), z)) | (~b(s(z), s(s(elem!1)))) | (~b(s(s(elem!1)), s(s(z)))) | (~b(s(s(z)), s(s(elem!1)))))),
% 2.22/2.45 inference(rewrite,[status(thm)],[])).
% 2.22/2.45 tff(5972,plain,
% 2.22/2.45 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), s(s(elem!1)))) | (~b(s(z), s(s(elem!1)))) | (~b(s(s(elem!1)), s(s(z)))) | (~b(z, s(s(elem!1)))) | (~b(s(z), s(s(elem!1)))) | (~b(s(z), z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(elem!1)))) | (~b(s(z), z)) | (~b(s(z), s(s(elem!1)))) | (~b(s(s(elem!1)), s(s(z)))) | (~b(s(s(z)), s(s(elem!1))))))),
% 2.22/2.45 inference(monotonicity,[status(thm)],[5971])).
% 2.22/2.45 tff(5973,plain,
% 2.22/2.45 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), s(s(elem!1)))) | (~b(s(z), s(s(elem!1)))) | (~b(s(s(elem!1)), s(s(z)))) | (~b(z, s(s(elem!1)))) | (~b(s(z), s(s(elem!1)))) | (~b(s(z), z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(s(elem!1)))) | (~b(s(z), z)) | (~b(s(z), s(s(elem!1)))) | (~b(s(s(elem!1)), s(s(z)))) | (~b(s(s(z)), s(s(elem!1)))))),
% 2.22/2.45 inference(transitivity,[status(thm)],[5972, 5970])).
% 2.22/2.45 tff(5974,plain,
% 2.22/2.45 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), s(s(elem!1)))) | (~b(s(z), s(s(elem!1)))) | (~b(s(s(elem!1)), s(s(z)))) | (~b(z, s(s(elem!1)))) | (~b(s(z), s(s(elem!1)))) | (~b(s(z), z)))),
% 2.22/2.46 inference(quant_inst,[status(thm)],[])).
% 2.22/2.46 tff(5975,plain,
% 2.22/2.46 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(s(elem!1)))) | (~b(s(z), z)) | (~b(s(z), s(s(elem!1)))) | (~b(s(s(elem!1)), s(s(z)))) | (~b(s(s(z)), s(s(elem!1))))),
% 2.22/2.46 inference(modus_ponens,[status(thm)],[5974, 5973])).
% 2.22/2.46 tff(5976,plain,
% 2.22/2.46 ($false),
% 2.22/2.46 inference(unit_resolution,[status(thm)],[5975, 166, 376, 1820, 53, 405, 446])).
% 2.22/2.46 tff(5977,plain,((~b(s(s(elem!1)), s(s(z)))) | (~b(s(z), s(s(elem!1)))) | (~b(z, s(s(elem!1)))) | (~b(s(z), z)) | (~b(s(s(z)), s(s(elem!1))))), inference(lemma,lemma(discharge,[]))).
% 2.22/2.46 tff(5978,plain,
% 2.22/2.46 (~b(s(s(elem!1)), s(s(z)))),
% 2.22/2.46 inference(unit_resolution,[status(thm)],[5977, 5967, 376, 53, 446])).
% 2.22/2.46 tff(5979,plain,
% 2.22/2.46 (r(s(s(elem!1)), s(s(z)))),
% 2.22/2.46 inference(unit_resolution,[status(thm)],[441, 5978, 11])).
% 2.22/2.46 tff(5980,plain,
% 2.22/2.46 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(elem!1)), z)) | (~r(s(s(z)), z)) | (~r(s(s(elem!1)), s(s(z)))) | (~r(z, s(s(z)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(elem!1)), z)) | (~r(s(s(z)), z)) | (~r(s(s(elem!1)), s(s(z)))) | (~r(z, s(s(z)))))),
% 2.22/2.46 inference(rewrite,[status(thm)],[])).
% 2.22/2.46 tff(5981,plain,
% 2.22/2.46 (((~r(s(s(z)), z)) | (~r(z, s(s(z)))) | (~r(s(s(elem!1)), s(s(z)))) | (~r(s(s(elem!1)), z))) <=> ((~r(s(s(elem!1)), z)) | (~r(s(s(z)), z)) | (~r(s(s(elem!1)), s(s(z)))) | (~r(z, s(s(z)))))),
% 2.22/2.46 inference(rewrite,[status(thm)],[])).
% 2.22/2.46 tff(5982,plain,
% 2.22/2.46 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(z)), z)) | (~r(z, s(s(z)))) | (~r(s(s(elem!1)), s(s(z)))) | (~r(s(s(elem!1)), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(elem!1)), z)) | (~r(s(s(z)), z)) | (~r(s(s(elem!1)), s(s(z)))) | (~r(z, s(s(z))))))),
% 2.22/2.46 inference(monotonicity,[status(thm)],[5981])).
% 2.22/2.46 tff(5983,plain,
% 2.22/2.46 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(z)), z)) | (~r(z, s(s(z)))) | (~r(s(s(elem!1)), s(s(z)))) | (~r(s(s(elem!1)), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(elem!1)), z)) | (~r(s(s(z)), z)) | (~r(s(s(elem!1)), s(s(z)))) | (~r(z, s(s(z)))))),
% 2.22/2.46 inference(transitivity,[status(thm)],[5982, 5980])).
% 2.22/2.46 tff(5984,plain,
% 2.22/2.46 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(z)), z)) | (~r(z, s(s(z)))) | (~r(s(s(elem!1)), s(s(z)))) | (~r(s(s(elem!1)), z)))),
% 2.22/2.46 inference(quant_inst,[status(thm)],[])).
% 2.22/2.46 tff(5985,plain,
% 2.22/2.46 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(elem!1)), z)) | (~r(s(s(z)), z)) | (~r(s(s(elem!1)), s(s(z)))) | (~r(z, s(s(z))))),
% 2.22/2.46 inference(modus_ponens,[status(thm)],[5984, 5983])).
% 2.22/2.46 tff(5986,plain,
% 2.22/2.46 ($false),
% 2.22/2.46 inference(unit_resolution,[status(thm)],[5985, 197, 5979, 155, 5969, 866])).
% 2.22/2.46 tff(5987,plain,((~b(s(s(z)), s(s(elem!1)))) | (~r(z, s(s(z)))) | (~r(s(s(z)), z)) | (s(s(elem!1)) = s(s(z))) | (~b(s(z), s(s(elem!1)))) | (~b(s(z), z)) | (~r(s(s(s(elem!1))), z)) | (~r(s(s(elem!1)), s(z))) | (s(s(elem!1)) = s(s(s(elem!1)))) | r(s(s(s(elem!1))), s(s(z)))), inference(lemma,lemma(discharge,[]))).
% 2.22/2.46 tff(5988,plain,
% 2.22/2.46 (~b(s(s(z)), s(s(elem!1)))),
% 2.22/2.46 inference(unit_resolution,[status(thm)],[5987, 5947, 155, 132, 376, 53, 154, 5945, 45, 213])).
% 2.22/2.46 tff(5989,plain,
% 2.22/2.46 (r(s(s(z)), s(s(elem!1)))),
% 2.22/2.46 inference(unit_resolution,[status(thm)],[390, 5988, 52])).
% 2.22/2.46 tff(5990,plain,
% 2.22/2.46 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(elem!1)))) | (~r(s(s(z)), s(s(elem!1)))) | (~r(s(s(elem!1)), s(z))) | (~r(z, s(s(z)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, s(s(elem!1)))) | (~r(s(s(z)), s(s(elem!1)))) | (~r(s(s(elem!1)), s(z))) | (~r(z, s(s(z)))))),
% 2.22/2.46 inference(rewrite,[status(thm)],[])).
% 2.22/2.46 tff(5991,plain,
% 2.22/2.46 (((~r(s(s(elem!1)), s(z))) | (~r(s(s(z)), s(s(elem!1)))) | (~r(z, s(s(elem!1)))) | (~r(z, s(s(z))))) <=> ((~r(z, s(s(elem!1)))) | (~r(s(s(z)), s(s(elem!1)))) | (~r(s(s(elem!1)), s(z))) | (~r(z, s(s(z)))))),
% 2.22/2.46 inference(rewrite,[status(thm)],[])).
% 2.22/2.46 tff(5992,plain,
% 2.22/2.46 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(elem!1)), s(z))) | (~r(s(s(z)), s(s(elem!1)))) | (~r(z, s(s(elem!1)))) | (~r(z, s(s(z)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(elem!1)))) | (~r(s(s(z)), s(s(elem!1)))) | (~r(s(s(elem!1)), s(z))) | (~r(z, s(s(z))))))),
% 2.22/2.46 inference(monotonicity,[status(thm)],[5991])).
% 2.22/2.46 tff(5993,plain,
% 2.22/2.46 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(elem!1)), s(z))) | (~r(s(s(z)), s(s(elem!1)))) | (~r(z, s(s(elem!1)))) | (~r(z, s(s(z)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, s(s(elem!1)))) | (~r(s(s(z)), s(s(elem!1)))) | (~r(s(s(elem!1)), s(z))) | (~r(z, s(s(z)))))),
% 2.22/2.46 inference(transitivity,[status(thm)],[5992, 5990])).
% 2.22/2.46 tff(5994,plain,
% 2.22/2.46 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(elem!1)), s(z))) | (~r(s(s(z)), s(s(elem!1)))) | (~r(z, s(s(elem!1)))) | (~r(z, s(s(z)))))),
% 2.22/2.46 inference(quant_inst,[status(thm)],[])).
% 2.22/2.46 tff(5995,plain,
% 2.22/2.46 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, s(s(elem!1)))) | (~r(s(s(z)), s(s(elem!1)))) | (~r(s(s(elem!1)), s(z))) | (~r(z, s(s(z))))),
% 2.22/2.46 inference(modus_ponens,[status(thm)],[5994, 5993])).
% 2.22/2.46 tff(5996,plain,
% 2.22/2.46 ($false),
% 2.22/2.46 inference(unit_resolution,[status(thm)],[5995, 197, 155, 4577, 333, 365])).
% 2.22/2.46 tff(5997,plain,((~r(s(s(z)), s(s(elem!1)))) | (~r(z, s(s(z)))) | (~r(s(s(elem!1)), s(z))) | (~r(z, s(s(elem!1))))), inference(lemma,lemma(discharge,[]))).
% 2.22/2.46 tff(5998,plain,
% 2.22/2.46 (~r(z, s(s(elem!1)))),
% 2.22/2.46 inference(unit_resolution,[status(thm)],[5997, 5989, 155, 5945])).
% 2.22/2.46 tff(5999,plain,
% 2.22/2.46 (b(z, s(s(elem!1)))),
% 2.22/2.46 inference(unit_resolution,[status(thm)],[1795, 5998])).
% 2.22/2.46 tff(6000,plain,
% 2.22/2.46 (~b(s(s(elem!1)), z)),
% 2.22/2.46 inference(unit_resolution,[status(thm)],[5377, 5999, 376, 53])).
% 2.22/2.46 tff(6001,plain,
% 2.22/2.46 (r(s(s(elem!1)), z)),
% 2.22/2.46 inference(unit_resolution,[status(thm)],[608, 6000])).
% 2.22/2.46 tff(6002,plain,
% 2.22/2.46 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(elem!1)))) | (~b(s(z), s(s(elem!1)))) | (~b(s(s(elem!1)), s(s(z)))) | (~b(z, s(z))) | (~b(s(s(z)), s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(s(elem!1)))) | (~b(s(z), s(s(elem!1)))) | (~b(s(s(elem!1)), s(s(z)))) | (~b(z, s(z))) | (~b(s(s(z)), s(z))))),
% 2.22/2.46 inference(rewrite,[status(thm)],[])).
% 2.22/2.46 tff(6003,plain,
% 2.22/2.46 (((~b(s(s(z)), s(z))) | (~b(z, s(z))) | (~b(s(s(elem!1)), s(s(z)))) | (~b(s(z), s(s(elem!1)))) | (~b(z, s(s(elem!1)))) | (~b(z, s(z)))) <=> ((~b(z, s(s(elem!1)))) | (~b(s(z), s(s(elem!1)))) | (~b(s(s(elem!1)), s(s(z)))) | (~b(z, s(z))) | (~b(s(s(z)), s(z))))),
% 2.22/2.46 inference(rewrite,[status(thm)],[])).
% 2.22/2.46 tff(6004,plain,
% 2.22/2.46 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), s(z))) | (~b(z, s(z))) | (~b(s(s(elem!1)), s(s(z)))) | (~b(s(z), s(s(elem!1)))) | (~b(z, s(s(elem!1)))) | (~b(z, s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(elem!1)))) | (~b(s(z), s(s(elem!1)))) | (~b(s(s(elem!1)), s(s(z)))) | (~b(z, s(z))) | (~b(s(s(z)), s(z)))))),
% 2.22/2.46 inference(monotonicity,[status(thm)],[6003])).
% 2.22/2.46 tff(6005,plain,
% 2.22/2.46 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), s(z))) | (~b(z, s(z))) | (~b(s(s(elem!1)), s(s(z)))) | (~b(s(z), s(s(elem!1)))) | (~b(z, s(s(elem!1)))) | (~b(z, s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(s(elem!1)))) | (~b(s(z), s(s(elem!1)))) | (~b(s(s(elem!1)), s(s(z)))) | (~b(z, s(z))) | (~b(s(s(z)), s(z))))),
% 2.22/2.46 inference(transitivity,[status(thm)],[6004, 6002])).
% 2.22/2.46 tff(6006,plain,
% 2.22/2.46 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), s(z))) | (~b(z, s(z))) | (~b(s(s(elem!1)), s(s(z)))) | (~b(s(z), s(s(elem!1)))) | (~b(z, s(s(elem!1)))) | (~b(z, s(z))))),
% 2.22/2.46 inference(quant_inst,[status(thm)],[])).
% 2.22/2.46 tff(6007,plain,
% 2.22/2.46 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(s(elem!1)))) | (~b(s(z), s(s(elem!1)))) | (~b(s(s(elem!1)), s(s(z)))) | (~b(z, s(z))) | (~b(s(s(z)), s(z)))),
% 2.22/2.46 inference(modus_ponens,[status(thm)],[6006, 6005])).
% 2.22/2.46 tff(6008,plain,
% 2.22/2.46 ($false),
% 2.22/2.46 inference(unit_resolution,[status(thm)],[6007, 166, 376, 1820, 405, 118, 156])).
% 2.22/2.46 tff(6009,plain,((~b(s(s(elem!1)), s(s(z)))) | (~b(s(z), s(s(elem!1)))) | (~b(z, s(s(elem!1)))) | (~b(z, s(z))) | (~b(s(s(z)), s(z)))), inference(lemma,lemma(discharge,[]))).
% 2.22/2.46 tff(6010,plain,
% 2.22/2.46 (~b(s(s(elem!1)), s(s(z)))),
% 2.22/2.46 inference(unit_resolution,[status(thm)],[6009, 5999, 376, 118, 156])).
% 2.22/2.46 tff(6011,plain,
% 2.22/2.46 (r(s(s(elem!1)), s(s(z)))),
% 2.22/2.46 inference(unit_resolution,[status(thm)],[441, 6010, 132])).
% 2.22/2.46 tff(6012,plain,
% 2.22/2.46 ($false),
% 2.22/2.46 inference(unit_resolution,[status(thm)],[2740, 197, 6011, 155, 5989, 6001])).
% 2.22/2.46 tff(6013,plain,((~b(s(s(z)), s(z))) | (~r(z, s(s(z)))) | (~b(s(z), s(s(elem!1)))) | (~b(z, s(z))) | (~b(s(z), z)) | (s(s(z)) = s(s(elem!1))) | (~r(s(s(s(elem!1))), z)) | (s(s(elem!1)) = s(s(s(elem!1)))) | r(s(s(s(elem!1))), s(s(z)))), inference(lemma,lemma(discharge,[]))).
% 2.22/2.46 tff(6014,plain,
% 2.22/2.46 (~b(s(s(z)), s(z))),
% 2.22/2.46 inference(unit_resolution,[status(thm)],[6013, 213, 376, 118, 5943, 52, 154, 45, 155])).
% 2.22/2.46 tff(6015,plain,
% 2.22/2.46 (r(s(s(z)), s(z))),
% 2.22/2.46 inference(unit_resolution,[status(thm)],[308, 6014])).
% 2.22/2.46 tff(6016,plain,
% 2.22/2.46 (~r(s(s(elem!1)), s(s(z)))),
% 2.22/2.46 inference(unit_resolution,[status(thm)],[401, 365, 155, 6015])).
% 2.22/2.46 tff(6017,plain,
% 2.22/2.46 (b(s(s(elem!1)), s(s(z)))),
% 2.22/2.46 inference(unit_resolution,[status(thm)],[441, 6016, 132])).
% 2.22/2.46 tff(6018,plain,
% 2.22/2.46 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), z)) | (~r(s(s(elem!1)), z)) | (~r(s(s(elem!1)), s(s(s(elem!1))))) | (~r(z, s(s(z)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(elem!1))), z)) | (~r(s(s(elem!1)), z)) | (~r(s(s(elem!1)), s(s(s(elem!1))))) | (~r(z, s(s(z)))))),
% 2.22/2.46 inference(rewrite,[status(thm)],[])).
% 2.22/2.46 tff(6019,plain,
% 2.22/2.46 (((~r(z, s(s(z)))) | (~r(s(s(s(elem!1))), z)) | (~r(s(s(elem!1)), z)) | (~r(s(s(elem!1)), s(s(s(elem!1)))))) <=> ((~r(s(s(s(elem!1))), z)) | (~r(s(s(elem!1)), z)) | (~r(s(s(elem!1)), s(s(s(elem!1))))) | (~r(z, s(s(z)))))),
% 2.22/2.46 inference(rewrite,[status(thm)],[])).
% 2.22/2.46 tff(6020,plain,
% 2.22/2.46 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(z)))) | (~r(s(s(s(elem!1))), z)) | (~r(s(s(elem!1)), z)) | (~r(s(s(elem!1)), s(s(s(elem!1))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), z)) | (~r(s(s(elem!1)), z)) | (~r(s(s(elem!1)), s(s(s(elem!1))))) | (~r(z, s(s(z))))))),
% 2.22/2.46 inference(monotonicity,[status(thm)],[6019])).
% 2.22/2.46 tff(6021,plain,
% 2.22/2.46 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(z)))) | (~r(s(s(s(elem!1))), z)) | (~r(s(s(elem!1)), z)) | (~r(s(s(elem!1)), s(s(s(elem!1))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(elem!1))), z)) | (~r(s(s(elem!1)), z)) | (~r(s(s(elem!1)), s(s(s(elem!1))))) | (~r(z, s(s(z)))))),
% 2.22/2.46 inference(transitivity,[status(thm)],[6020, 6018])).
% 2.22/2.46 tff(6022,plain,
% 2.22/2.46 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(z)))) | (~r(s(s(s(elem!1))), z)) | (~r(s(s(elem!1)), z)) | (~r(s(s(elem!1)), s(s(s(elem!1))))))),
% 2.22/2.46 inference(quant_inst,[status(thm)],[])).
% 2.22/2.46 tff(6023,plain,
% 2.22/2.46 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(elem!1))), z)) | (~r(s(s(elem!1)), z)) | (~r(s(s(elem!1)), s(s(s(elem!1))))) | (~r(z, s(s(z))))),
% 2.22/2.46 inference(modus_ponens,[status(thm)],[6022, 6021])).
% 2.22/2.46 tff(6024,plain,
% 2.22/2.46 (~r(s(s(elem!1)), s(s(s(elem!1))))),
% 2.22/2.46 inference(unit_resolution,[status(thm)],[6023, 197, 154, 155, 1970])).
% 2.22/2.46 tff(6025,plain,
% 2.22/2.46 (b(s(s(elem!1)), s(s(s(elem!1))))),
% 2.22/2.46 inference(unit_resolution,[status(thm)],[461, 6024, 45])).
% 2.22/2.46 tff(6026,plain,
% 2.22/2.46 (r(s(s(z)), s(s(s(elem!1))))),
% 2.22/2.46 inference(unit_resolution,[status(thm)],[501, 6025, 405, 213])).
% 2.22/2.46 tff(6027,plain,
% 2.22/2.46 (~r(s(s(s(elem!1))), s(s(elem!1)))),
% 2.22/2.46 inference(unit_resolution,[status(thm)],[1884, 197, 154, 155, 1970])).
% 2.22/2.46 tff(6028,plain,
% 2.22/2.46 (b(s(s(s(elem!1))), s(s(elem!1)))),
% 2.22/2.46 inference(unit_resolution,[status(thm)],[889, 1863, 1823])).
% 2.22/2.46 tff(6029,plain,
% 2.22/2.46 (~(s(s(elem!1)) = s(s(s(elem!1))))),
% 2.22/2.46 inference(unit_resolution,[status(thm)],[4030, 1863])).
% 2.22/2.46 tff(6030,plain,
% 2.22/2.46 (b(s(s(elem!1)), s(s(s(elem!1))))),
% 2.22/2.46 inference(unit_resolution,[status(thm)],[461, 6029, 1821])).
% 2.22/2.46 tff(6031,plain,
% 2.22/2.46 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(z), s(s(s(elem!1))))) | (~b(s(z), s(s(elem!1)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(z), s(s(s(elem!1))))) | (~b(s(z), s(s(elem!1)))))),
% 2.22/2.46 inference(rewrite,[status(thm)],[])).
% 2.22/2.46 tff(6032,plain,
% 2.22/2.46 (((~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(z), s(s(elem!1)))) | (~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(z), s(s(elem!1)))) | (~b(s(z), s(s(s(elem!1)))))) <=> ((~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(z), s(s(s(elem!1))))) | (~b(s(z), s(s(elem!1)))))),
% 2.22/2.46 inference(rewrite,[status(thm)],[])).
% 2.22/2.46 tff(6033,plain,
% 2.22/2.46 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(z), s(s(elem!1)))) | (~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(z), s(s(elem!1)))) | (~b(s(z), s(s(s(elem!1))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(z), s(s(s(elem!1))))) | (~b(s(z), s(s(elem!1))))))),
% 2.22/2.46 inference(monotonicity,[status(thm)],[6032])).
% 2.22/2.46 tff(6034,plain,
% 2.22/2.46 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(z), s(s(elem!1)))) | (~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(z), s(s(elem!1)))) | (~b(s(z), s(s(s(elem!1))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(z), s(s(s(elem!1))))) | (~b(s(z), s(s(elem!1)))))),
% 2.22/2.47 inference(transitivity,[status(thm)],[6033, 6031])).
% 2.22/2.47 tff(6035,plain,
% 2.22/2.47 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(z), s(s(elem!1)))) | (~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(z), s(s(elem!1)))) | (~b(s(z), s(s(s(elem!1))))))),
% 2.22/2.47 inference(quant_inst,[status(thm)],[])).
% 2.22/2.47 tff(6036,plain,
% 2.22/2.47 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(z), s(s(s(elem!1))))) | (~b(s(z), s(s(elem!1))))),
% 2.22/2.47 inference(modus_ponens,[status(thm)],[6035, 6034])).
% 2.22/2.47 tff(6037,plain,
% 2.22/2.47 ($false),
% 2.22/2.47 inference(unit_resolution,[status(thm)],[6036, 166, 376, 463, 839, 241])).
% 2.22/2.47 tff(6038,plain,((~b(s(s(s(elem!1))), 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(s(elem!1)))))), inference(lemma,lemma(discharge,[]))).
% 2.22/2.47 tff(6039,plain,
% 2.22/2.47 ($false),
% 2.22/2.47 inference(unit_resolution,[status(thm)],[6038, 6030, 6028, 376, 241])).
% 2.22/2.47 tff(6040,plain,((s(s(s(elem!1))) = s(s(elem!1))) | (~b(s(z), s(s(elem!1)))) | (~b(s(z), s(s(s(elem!1))))) | r(s(s(elem!1)), s(s(s(elem!1)))) | r(s(s(s(elem!1))), s(s(elem!1)))), inference(lemma,lemma(discharge,[]))).
% 2.22/2.47 tff(6041,plain,
% 2.22/2.47 (~b(s(z), s(s(s(elem!1))))),
% 2.22/2.47 inference(unit_resolution,[status(thm)],[6040, 6024, 51, 376, 6027])).
% 2.22/2.47 tff(6042,plain,
% 2.22/2.47 (r(s(z), s(s(s(elem!1))))),
% 2.22/2.47 inference(unit_resolution,[status(thm)],[116, 6041])).
% 2.22/2.47 tff(6043,plain,
% 2.22/2.47 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), s(z))) | (~r(s(z), s(s(s(elem!1))))) | (~r(s(s(z)), s(z))) | (~r(s(s(z)), s(s(s(elem!1))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(elem!1))), s(z))) | (~r(s(z), s(s(s(elem!1))))) | (~r(s(s(z)), s(z))) | (~r(s(s(z)), s(s(s(elem!1))))))),
% 2.22/2.47 inference(rewrite,[status(thm)],[])).
% 2.22/2.47 tff(6044,plain,
% 2.22/2.47 (((~r(s(z), s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), s(z))) | (~r(s(s(z)), s(z))) | (~r(s(s(z)), s(s(s(elem!1)))))) <=> ((~r(s(s(s(elem!1))), s(z))) | (~r(s(z), s(s(s(elem!1))))) | (~r(s(s(z)), s(z))) | (~r(s(s(z)), s(s(s(elem!1))))))),
% 2.22/2.47 inference(rewrite,[status(thm)],[])).
% 2.22/2.47 tff(6045,plain,
% 2.22/2.47 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), s(z))) | (~r(s(s(z)), s(z))) | (~r(s(s(z)), s(s(s(elem!1))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), s(z))) | (~r(s(z), s(s(s(elem!1))))) | (~r(s(s(z)), s(z))) | (~r(s(s(z)), s(s(s(elem!1)))))))),
% 2.22/2.47 inference(monotonicity,[status(thm)],[6044])).
% 2.22/2.47 tff(6046,plain,
% 2.22/2.47 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), s(z))) | (~r(s(s(z)), s(z))) | (~r(s(s(z)), s(s(s(elem!1))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(elem!1))), s(z))) | (~r(s(z), s(s(s(elem!1))))) | (~r(s(s(z)), s(z))) | (~r(s(s(z)), s(s(s(elem!1))))))),
% 2.22/2.47 inference(transitivity,[status(thm)],[6045, 6043])).
% 2.22/2.47 tff(6047,plain,
% 2.22/2.47 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), s(z))) | (~r(s(s(z)), s(z))) | (~r(s(s(z)), s(s(s(elem!1))))))),
% 2.22/2.47 inference(quant_inst,[status(thm)],[])).
% 2.22/2.47 tff(6048,plain,
% 2.22/2.47 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(elem!1))), s(z))) | (~r(s(z), s(s(s(elem!1))))) | (~r(s(s(z)), s(z))) | (~r(s(s(z)), s(s(s(elem!1)))))),
% 2.22/2.47 inference(modus_ponens,[status(thm)],[6047, 6046])).
% 2.22/2.47 tff(6049,plain,
% 2.22/2.47 ($false),
% 2.22/2.47 inference(unit_resolution,[status(thm)],[6048, 197, 350, 392, 6042, 6026])).
% 2.22/2.47 tff(6050,plain,((~r(s(s(elem!1)), z)) | (~r(s(s(s(elem!1))), s(z))) | (~r(s(s(z)), s(z))) | (~b(s(s(elem!1)), s(s(z)))) | r(s(s(s(elem!1))), s(s(z))) | (~b(s(z), s(s(elem!1)))) | (s(s(elem!1)) = s(s(s(elem!1)))) | (~r(s(s(s(elem!1))), z)) | (~r(z, s(s(z))))), inference(lemma,lemma(discharge,[]))).
% 2.22/2.47 tff(6051,plain,
% 2.22/2.47 (~r(s(s(elem!1)), z)),
% 2.22/2.47 inference(unit_resolution,[status(thm)],[6050, 6017, 6015, 350, 213, 376, 45, 154, 155])).
% 2.22/2.47 tff(6052,plain,
% 2.22/2.47 (b(s(s(elem!1)), z)),
% 2.22/2.47 inference(unit_resolution,[status(thm)],[608, 6051])).
% 2.22/2.47 tff(6053,plain,
% 2.22/2.47 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), z)) | (~b(s(z), s(s(elem!1)))) | (~b(s(s(elem!1)), s(s(z)))) | (~b(z, s(z))) | (~b(s(s(elem!1)), s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(elem!1)), z)) | (~b(s(z), s(s(elem!1)))) | (~b(s(s(elem!1)), s(s(z)))) | (~b(z, s(z))) | (~b(s(s(elem!1)), s(z))))),
% 2.22/2.47 inference(rewrite,[status(thm)],[])).
% 2.22/2.47 tff(6054,plain,
% 2.22/2.47 (((~b(s(s(elem!1)), s(s(z)))) | (~b(s(s(elem!1)), s(s(z)))) | (~b(s(z), s(s(elem!1)))) | (~b(z, s(z))) | (~b(s(s(elem!1)), s(z))) | (~b(s(s(elem!1)), z))) <=> ((~b(s(s(elem!1)), z)) | (~b(s(z), s(s(elem!1)))) | (~b(s(s(elem!1)), s(s(z)))) | (~b(z, s(z))) | (~b(s(s(elem!1)), s(z))))),
% 2.22/2.47 inference(rewrite,[status(thm)],[])).
% 2.22/2.47 tff(6055,plain,
% 2.22/2.47 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), s(s(z)))) | (~b(s(s(elem!1)), s(s(z)))) | (~b(s(z), s(s(elem!1)))) | (~b(z, s(z))) | (~b(s(s(elem!1)), s(z))) | (~b(s(s(elem!1)), z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), z)) | (~b(s(z), s(s(elem!1)))) | (~b(s(s(elem!1)), s(s(z)))) | (~b(z, s(z))) | (~b(s(s(elem!1)), s(z)))))),
% 2.22/2.47 inference(monotonicity,[status(thm)],[6054])).
% 2.22/2.47 tff(6056,plain,
% 2.22/2.47 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), s(s(z)))) | (~b(s(s(elem!1)), s(s(z)))) | (~b(s(z), s(s(elem!1)))) | (~b(z, s(z))) | (~b(s(s(elem!1)), s(z))) | (~b(s(s(elem!1)), z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(elem!1)), z)) | (~b(s(z), s(s(elem!1)))) | (~b(s(s(elem!1)), s(s(z)))) | (~b(z, s(z))) | (~b(s(s(elem!1)), s(z))))),
% 2.22/2.47 inference(transitivity,[status(thm)],[6055, 6053])).
% 2.22/2.47 tff(6057,plain,
% 2.22/2.47 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), s(s(z)))) | (~b(s(s(elem!1)), s(s(z)))) | (~b(s(z), s(s(elem!1)))) | (~b(z, s(z))) | (~b(s(s(elem!1)), s(z))) | (~b(s(s(elem!1)), z)))),
% 2.22/2.47 inference(quant_inst,[status(thm)],[])).
% 2.22/2.47 tff(6058,plain,
% 2.22/2.47 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(elem!1)), z)) | (~b(s(z), s(s(elem!1)))) | (~b(s(s(elem!1)), s(s(z)))) | (~b(z, s(z))) | (~b(s(s(elem!1)), s(z)))),
% 2.22/2.47 inference(modus_ponens,[status(thm)],[6057, 6056])).
% 2.22/2.47 tff(6059,plain,
% 2.22/2.47 ((~b(s(s(elem!1)), z)) | (~b(s(s(elem!1)), s(z)))),
% 2.22/2.47 inference(unit_resolution,[status(thm)],[6058, 166, 376, 6017, 118])).
% 2.22/2.47 tff(6060,plain,
% 2.22/2.47 (~b(s(s(elem!1)), s(z))),
% 2.22/2.47 inference(unit_resolution,[status(thm)],[6059, 6052])).
% 2.22/2.47 tff(6061,plain,
% 2.22/2.47 (r(s(s(elem!1)), s(z))),
% 2.22/2.47 inference(unit_resolution,[status(thm)],[1912, 6060])).
% 2.22/2.47 tff(6062,plain,
% 2.22/2.47 (~r(s(s(z)), s(s(elem!1)))),
% 2.22/2.47 inference(unit_resolution,[status(thm)],[5997, 6061, 155, 365])).
% 2.22/2.47 tff(6063,plain,
% 2.22/2.47 (b(s(s(z)), s(s(elem!1)))),
% 2.22/2.47 inference(unit_resolution,[status(thm)],[390, 6062, 52])).
% 2.22/2.47 tff(6064,plain,
% 2.22/2.47 (r(s(s(z)), s(s(s(elem!1))))),
% 2.22/2.47 inference(unit_resolution,[status(thm)],[5955, 6063, 365, 154, 376, 6017, 45, 6061, 213])).
% 2.22/2.47 tff(6065,plain,
% 2.22/2.47 (~b(s(z), s(s(z)))),
% 2.22/2.47 inference(unit_resolution,[status(thm)],[5300, 6062, 376, 52, 6016])).
% 2.22/2.47 tff(6066,plain,
% 2.22/2.47 (r(s(z), s(s(z)))),
% 2.22/2.47 inference(unit_resolution,[status(thm)],[427, 6065])).
% 2.22/2.47 tff(6067,plain,
% 2.22/2.47 (~r(s(z), s(s(s(elem!1))))),
% 2.22/2.47 inference(unit_resolution,[status(thm)],[2304, 6066, 154, 6064])).
% 2.22/2.47 tff(6068,plain,
% 2.22/2.47 (b(s(z), s(s(s(elem!1))))),
% 2.22/2.47 inference(unit_resolution,[status(thm)],[116, 6067])).
% 2.22/2.47 tff(6069,plain,
% 2.22/2.47 (~b(s(s(s(elem!1))), s(s(elem!1)))),
% 2.22/2.47 inference(unit_resolution,[status(thm)],[5396, 6068, 376, 6017, 6063])).
% 2.22/2.47 tff(6070,plain,
% 2.22/2.47 (~r(s(s(elem!1)), s(s(z)))),
% 2.22/2.47 inference(unit_resolution,[status(thm)],[5362, 120, 392, 4577])).
% 2.22/2.47 tff(6071,plain,
% 2.22/2.47 (~r(s(s(s(elem!1))), s(s(z)))),
% 2.22/2.47 inference(unit_resolution,[status(thm)],[483, 120, 350, 392])).
% 2.22/2.47 tff(6072,plain,
% 2.22/2.47 (~b(s(s(elem!1)), s(s(z)))),
% 2.22/2.47 inference(unit_resolution,[status(thm)],[501, 6071, 463, 273])).
% 2.22/2.47 tff(6073,plain,
% 2.22/2.47 ($false),
% 2.22/2.47 inference(unit_resolution,[status(thm)],[441, 6072, 6070, 11])).
% 2.22/2.47 tff(6074,plain,((~r(s(z), s(s(z)))) | (s(s(elem!1)) = s(s(z))) | (~b(s(s(elem!1)), s(s(s(elem!1))))) | r(s(s(z)), s(s(s(elem!1)))) | (~r(s(s(z)), s(z))) | (~r(s(s(elem!1)), s(z))) | (~r(s(s(s(elem!1))), s(z)))), inference(lemma,lemma(discharge,[]))).
% 2.22/2.47 tff(6075,plain,
% 2.22/2.47 (r(s(s(z)), s(s(s(elem!1))))),
% 2.22/2.47 inference(unit_resolution,[status(thm)],[6074, 120, 463, 11, 392, 4577, 350])).
% 2.22/2.47 tff(6076,plain,
% 2.22/2.47 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), s(z))) | (~r(s(s(z)), s(z))) | (~r(s(z), s(s(z)))) | (~r(s(s(z)), s(s(s(elem!1))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(elem!1))), s(z))) | (~r(s(s(z)), s(z))) | (~r(s(z), s(s(z)))) | (~r(s(s(z)), s(s(s(elem!1))))))),
% 2.22/2.47 inference(rewrite,[status(thm)],[])).
% 2.22/2.47 tff(6077,plain,
% 2.22/2.47 (((~r(s(z), s(s(z)))) | (~r(s(s(s(elem!1))), s(z))) | (~r(s(s(z)), s(z))) | (~r(s(s(z)), s(s(s(elem!1)))))) <=> ((~r(s(s(s(elem!1))), s(z))) | (~r(s(s(z)), s(z))) | (~r(s(z), s(s(z)))) | (~r(s(s(z)), s(s(s(elem!1))))))),
% 2.22/2.47 inference(rewrite,[status(thm)],[])).
% 2.22/2.47 tff(6078,plain,
% 2.22/2.47 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(s(z)))) | (~r(s(s(s(elem!1))), s(z))) | (~r(s(s(z)), s(z))) | (~r(s(s(z)), s(s(s(elem!1))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), s(z))) | (~r(s(s(z)), s(z))) | (~r(s(z), s(s(z)))) | (~r(s(s(z)), s(s(s(elem!1)))))))),
% 2.22/2.47 inference(monotonicity,[status(thm)],[6077])).
% 2.22/2.47 tff(6079,plain,
% 2.22/2.47 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(s(z)))) | (~r(s(s(s(elem!1))), s(z))) | (~r(s(s(z)), s(z))) | (~r(s(s(z)), s(s(s(elem!1))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(elem!1))), s(z))) | (~r(s(s(z)), s(z))) | (~r(s(z), s(s(z)))) | (~r(s(s(z)), s(s(s(elem!1))))))),
% 2.22/2.47 inference(transitivity,[status(thm)],[6078, 6076])).
% 2.22/2.47 tff(6080,plain,
% 2.22/2.47 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(s(z)))) | (~r(s(s(s(elem!1))), s(z))) | (~r(s(s(z)), s(z))) | (~r(s(s(z)), s(s(s(elem!1))))))),
% 2.22/2.47 inference(quant_inst,[status(thm)],[])).
% 2.22/2.47 tff(6081,plain,
% 2.22/2.47 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(elem!1))), s(z))) | (~r(s(s(z)), s(z))) | (~r(s(z), s(s(z)))) | (~r(s(s(z)), s(s(s(elem!1)))))),
% 2.22/2.47 inference(modus_ponens,[status(thm)],[6080, 6079])).
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% 2.22/2.47 tff(6084,plain,
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% 2.22/2.47 inference(unit_resolution,[status(thm)],[6083, 6066, 350, 6015, 6061, 132])).
% 2.22/2.47 tff(6085,plain,
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% 2.22/2.47 inference(unit_resolution,[status(thm)],[461, 6084, 45])).
% 2.22/2.47 tff(6086,plain,
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% 2.22/2.47 inference(unit_resolution,[status(thm)],[1386, 6085, 154, 365])).
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% 2.22/2.47 tff(6089,plain,
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% 2.22/2.47 tff(6090,plain,
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% 2.22/2.47 inference(unit_resolution,[status(thm)],[608, 6091])).
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% 2.22/2.47 inference(unit_resolution,[status(thm)],[6050, 6092, 6015, 350, 213, 376, 45, 154, 155])).
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% 2.22/2.47 inference(rewrite,[status(thm)],[])).
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% 2.22/2.47 inference(rewrite,[status(thm)],[])).
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% 2.22/2.47 inference(transitivity,[status(thm)],[6097, 6095])).
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% 2.22/2.47 inference(modus_ponens,[status(thm)],[6099, 6098])).
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% 2.22/2.47 tff(6103,plain,
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% 2.22/2.47 tff(6106,plain,
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% 2.22/2.47 tff(6109,plain,
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% 2.22/2.47 inference(unit_resolution,[status(thm)],[526, 6103, 152, 154])).
% 2.22/2.47 tff(6111,plain,
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% 2.22/2.47 inference(unit_resolution,[status(thm)],[483, 6109, 350, 6103])).
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% 2.22/2.47 tff(6115,plain,
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% 2.22/2.47 inference(unit_resolution,[status(thm)],[1795, 6114])).
% 2.22/2.47 tff(6116,plain,
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% 2.22/2.47 inference(unit_resolution,[status(thm)],[5377, 6115, 5941, 5700])).
% 2.22/2.47 tff(6117,plain,
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% 2.22/2.47 tff(6120,plain,
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% 2.22/2.47 inference(monotonicity,[status(thm)],[6120])).
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% 2.22/2.47 tff(6128,plain,
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% 2.22/2.47 inference(monotonicity,[status(thm)],[6127, 6126])).
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% 2.22/2.47 tff(6132,plain,
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% 2.22/2.47 inference(unit_resolution,[status(thm)],[661, 6161])).
% 2.22/2.47 tff(6163,plain,
% 2.22/2.47 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(z))) | (~b(s(z), elem!1)) | (~b(s(s(s(s(elem!1)))), elem!1)) | (~b(s(s(s(s(elem!1)))), s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(z))) | (~b(s(z), elem!1)) | (~b(s(s(s(s(elem!1)))), elem!1)) | (~b(s(s(s(s(elem!1)))), s(z))))),
% 2.22/2.47 inference(rewrite,[status(thm)],[])).
% 2.22/2.47 tff(6164,plain,
% 2.22/2.47 (((~b(elem!1, s(z))) | (~b(s(s(s(s(elem!1)))), s(z))) | (~b(s(z), elem!1)) | (~b(elem!1, s(z))) | (~b(s(s(s(s(elem!1)))), s(z))) | (~b(s(s(s(s(elem!1)))), elem!1))) <=> ((~b(elem!1, s(z))) | (~b(s(z), elem!1)) | (~b(s(s(s(s(elem!1)))), elem!1)) | (~b(s(s(s(s(elem!1)))), s(z))))),
% 2.22/2.48 inference(rewrite,[status(thm)],[])).
% 2.22/2.48 tff(6165,plain,
% 2.22/2.48 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(z))) | (~b(s(s(s(s(elem!1)))), s(z))) | (~b(s(z), elem!1)) | (~b(elem!1, s(z))) | (~b(s(s(s(s(elem!1)))), s(z))) | (~b(s(s(s(s(elem!1)))), elem!1)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(z))) | (~b(s(z), elem!1)) | (~b(s(s(s(s(elem!1)))), elem!1)) | (~b(s(s(s(s(elem!1)))), s(z)))))),
% 2.22/2.48 inference(monotonicity,[status(thm)],[6164])).
% 2.22/2.48 tff(6166,plain,
% 2.22/2.48 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(z))) | (~b(s(s(s(s(elem!1)))), s(z))) | (~b(s(z), elem!1)) | (~b(elem!1, s(z))) | (~b(s(s(s(s(elem!1)))), s(z))) | (~b(s(s(s(s(elem!1)))), elem!1)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(z))) | (~b(s(z), elem!1)) | (~b(s(s(s(s(elem!1)))), elem!1)) | (~b(s(s(s(s(elem!1)))), s(z))))),
% 2.22/2.48 inference(transitivity,[status(thm)],[6165, 6163])).
% 2.22/2.48 tff(6167,plain,
% 2.22/2.48 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(z))) | (~b(s(s(s(s(elem!1)))), s(z))) | (~b(s(z), elem!1)) | (~b(elem!1, s(z))) | (~b(s(s(s(s(elem!1)))), s(z))) | (~b(s(s(s(s(elem!1)))), elem!1)))),
% 2.22/2.48 inference(quant_inst,[status(thm)],[])).
% 2.22/2.48 tff(6168,plain,
% 2.22/2.48 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(z))) | (~b(s(z), elem!1)) | (~b(s(s(s(s(elem!1)))), elem!1)) | (~b(s(s(s(s(elem!1)))), s(z)))),
% 2.22/2.48 inference(modus_ponens,[status(thm)],[6167, 6166])).
% 2.22/2.48 tff(6169,plain,
% 2.22/2.48 (~b(s(s(s(s(elem!1)))), elem!1)),
% 2.22/2.48 inference(unit_resolution,[status(thm)],[6168, 166, 1212, 642, 6162])).
% 2.22/2.48 tff(6170,plain,
% 2.22/2.48 (~b(s(s(s(s(z)))), z)),
% 2.22/2.48 inference(modus_ponens,[status(thm)],[6169, 4669])).
% 2.22/2.48 tff(6171,plain,
% 2.22/2.48 (r(s(s(s(s(z)))), z)),
% 2.22/2.48 inference(unit_resolution,[status(thm)],[3266, 6170])).
% 2.22/2.48 tff(6172,plain,
% 2.22/2.48 (~r(s(s(s(s(z)))), s(s(s(z))))),
% 2.22/2.48 inference(unit_resolution,[status(thm)],[4685, 6171, 152, 1733])).
% 2.22/2.48 tff(6173,plain,
% 2.22/2.48 (b(s(s(s(s(z)))), s(s(s(z))))),
% 2.22/2.48 inference(unit_resolution,[status(thm)],[4662, 6172])).
% 2.22/2.48 tff(6174,plain,
% 2.22/2.48 (~b(elem!1, s(s(s(s(elem!1)))))),
% 2.22/2.48 inference(unit_resolution,[status(thm)],[3430, 166, 1212, 642, 6162])).
% 2.22/2.48 tff(6175,plain,
% 2.22/2.48 (~b(elem!1, s(s(s(s(z)))))),
% 2.22/2.48 inference(unit_resolution,[status(thm)],[1105, 6174, 34])).
% 2.22/2.48 tff(6176,plain,
% 2.22/2.48 (r(elem!1, s(s(s(s(z)))))),
% 2.22/2.48 inference(unit_resolution,[status(thm)],[1098, 6175, 1045])).
% 2.22/2.48 tff(6177,plain,
% 2.22/2.48 (r(elem!1, s(s(z))) <=> r(elem!1, s(s(elem!1)))),
% 2.22/2.48 inference(monotonicity,[status(thm)],[34])).
% 2.22/2.48 tff(6178,plain,
% 2.22/2.48 (r(elem!1, s(s(elem!1))) <=> r(elem!1, s(s(z)))),
% 2.22/2.48 inference(symmetry,[status(thm)],[6177])).
% 2.22/2.48 tff(6179,plain,
% 2.22/2.48 (r(z, s(s(elem!1))) <=> r(elem!1, s(s(z)))),
% 2.22/2.48 inference(transitivity,[status(thm)],[621, 6178])).
% 2.22/2.48 tff(6180,plain,
% 2.22/2.48 (r(elem!1, s(s(z)))),
% 2.22/2.48 inference(modus_ponens,[status(thm)],[2263, 6179])).
% 2.22/2.48 tff(6181,plain,
% 2.22/2.48 ((elem!1 = s(s(s(s(z))))) <=> (s(s(s(s(z)))) = elem!1)),
% 2.22/2.48 inference(symmetry,[status(thm)],[1039])).
% 2.22/2.48 tff(6182,plain,
% 2.22/2.48 ((s(s(s(s(z)))) = z) <=> (s(s(s(s(z)))) = elem!1)),
% 2.22/2.48 inference(transitivity,[status(thm)],[1041, 6181])).
% 2.22/2.48 tff(6183,plain,
% 2.22/2.48 ((~(s(s(s(s(z)))) = z)) <=> (~(s(s(s(s(z)))) = elem!1))),
% 2.22/2.48 inference(monotonicity,[status(thm)],[6182])).
% 2.22/2.48 tff(6184,plain,
% 2.22/2.48 (~(s(s(s(s(z)))) = elem!1)),
% 2.22/2.48 inference(modus_ponens,[status(thm)],[1044, 6183])).
% 2.22/2.48 tff(6185,plain,
% 2.22/2.48 ((~b(s(s(s(s(elem!1)))), elem!1)) <=> (~b(s(s(s(s(z)))), elem!1))),
% 2.22/2.48 inference(monotonicity,[status(thm)],[4667])).
% 2.22/2.48 tff(6186,plain,
% 2.22/2.48 (~b(s(s(s(s(z)))), elem!1)),
% 2.22/2.48 inference(modus_ponens,[status(thm)],[6169, 6185])).
% 2.22/2.48 tff(6187,plain,
% 2.22/2.48 (((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((s(s(s(s(z)))) = elem!1) | b(s(s(s(s(z)))), elem!1) | r(s(s(s(s(z)))), elem!1))) <=> ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (s(s(s(s(z)))) = elem!1) | b(s(s(s(s(z)))), elem!1) | r(s(s(s(s(z)))), elem!1))),
% 2.22/2.48 inference(rewrite,[status(thm)],[])).
% 2.22/2.48 tff(6188,plain,
% 2.22/2.48 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((s(s(s(s(z)))) = elem!1) | b(s(s(s(s(z)))), elem!1) | r(s(s(s(s(z)))), elem!1))),
% 2.22/2.48 inference(quant_inst,[status(thm)],[])).
% 2.22/2.48 tff(6189,plain,
% 2.22/2.48 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (s(s(s(s(z)))) = elem!1) | b(s(s(s(s(z)))), elem!1) | r(s(s(s(s(z)))), elem!1)),
% 2.22/2.48 inference(modus_ponens,[status(thm)],[6188, 6187])).
% 2.22/2.48 tff(6190,plain,
% 2.22/2.48 ((s(s(s(s(z)))) = elem!1) | b(s(s(s(s(z)))), elem!1) | r(s(s(s(s(z)))), elem!1)),
% 2.22/2.48 inference(unit_resolution,[status(thm)],[6189, 79])).
% 2.22/2.48 tff(6191,plain,
% 2.22/2.48 (r(s(s(s(s(z)))), elem!1)),
% 2.22/2.48 inference(unit_resolution,[status(thm)],[6190, 6186, 6184])).
% 2.22/2.48 tff(6192,assumption,(r(s(s(z)), s(s(s(s(z)))))), introduced(assumption)).
% 2.22/2.48 tff(6193,assumption,(r(s(s(s(s(z)))), elem!1)), introduced(assumption)).
% 2.22/2.48 tff(6194,assumption,(r(elem!1, s(s(z)))), introduced(assumption)).
% 2.22/2.48 tff(6195,plain,
% 2.22/2.48 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(s(z)))) | (~r(s(s(s(s(z)))), elem!1)) | (~r(elem!1, s(s(s(s(z)))))) | (~r(s(s(z)), s(s(s(s(z)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(elem!1, s(s(z)))) | (~r(s(s(s(s(z)))), elem!1)) | (~r(elem!1, s(s(s(s(z)))))) | (~r(s(s(z)), s(s(s(s(z)))))))),
% 2.22/2.48 inference(rewrite,[status(thm)],[])).
% 2.22/2.48 tff(6196,plain,
% 2.22/2.48 (((~r(s(s(s(s(z)))), elem!1)) | (~r(s(s(z)), s(s(s(s(z)))))) | (~r(elem!1, s(s(s(s(z)))))) | (~r(elem!1, s(s(z))))) <=> ((~r(elem!1, s(s(z)))) | (~r(s(s(s(s(z)))), elem!1)) | (~r(elem!1, s(s(s(s(z)))))) | (~r(s(s(z)), s(s(s(s(z)))))))),
% 2.22/2.48 inference(rewrite,[status(thm)],[])).
% 2.22/2.48 tff(6197,plain,
% 2.22/2.48 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(z)))), elem!1)) | (~r(s(s(z)), s(s(s(s(z)))))) | (~r(elem!1, s(s(s(s(z)))))) | (~r(elem!1, s(s(z)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(s(z)))) | (~r(s(s(s(s(z)))), elem!1)) | (~r(elem!1, s(s(s(s(z)))))) | (~r(s(s(z)), s(s(s(s(z))))))))),
% 2.22/2.48 inference(monotonicity,[status(thm)],[6196])).
% 2.22/2.48 tff(6198,plain,
% 2.22/2.48 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(z)))), elem!1)) | (~r(s(s(z)), s(s(s(s(z)))))) | (~r(elem!1, s(s(s(s(z)))))) | (~r(elem!1, s(s(z)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(elem!1, s(s(z)))) | (~r(s(s(s(s(z)))), elem!1)) | (~r(elem!1, s(s(s(s(z)))))) | (~r(s(s(z)), s(s(s(s(z)))))))),
% 2.22/2.48 inference(transitivity,[status(thm)],[6197, 6195])).
% 2.22/2.48 tff(6199,plain,
% 2.22/2.48 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(z)))), elem!1)) | (~r(s(s(z)), s(s(s(s(z)))))) | (~r(elem!1, s(s(s(s(z)))))) | (~r(elem!1, s(s(z)))))),
% 2.22/2.48 inference(quant_inst,[status(thm)],[])).
% 2.22/2.48 tff(6200,plain,
% 2.22/2.48 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(elem!1, s(s(z)))) | (~r(s(s(s(s(z)))), elem!1)) | (~r(elem!1, s(s(s(s(z)))))) | (~r(s(s(z)), s(s(s(s(z))))))),
% 2.22/2.48 inference(modus_ponens,[status(thm)],[6199, 6198])).
% 2.22/2.48 tff(6201,plain,
% 2.22/2.48 ($false),
% 2.22/2.48 inference(unit_resolution,[status(thm)],[6200, 197, 6194, 1089, 6193, 6192])).
% 2.22/2.48 tff(6202,plain,((~r(s(s(z)), s(s(s(s(z)))))) | (~r(elem!1, s(s(z)))) | (~r(elem!1, s(s(s(s(z)))))) | (~r(s(s(s(s(z)))), elem!1))), inference(lemma,lemma(discharge,[]))).
% 2.22/2.48 tff(6203,plain,
% 2.22/2.48 (~r(s(s(z)), s(s(s(s(z)))))),
% 2.22/2.48 inference(unit_resolution,[status(thm)],[6202, 6191, 6180, 6176])).
% 2.22/2.48 tff(6204,plain,
% 2.22/2.48 (b(s(s(z)), s(s(s(s(z)))))),
% 2.22/2.48 inference(unit_resolution,[status(thm)],[4753, 6203])).
% 2.22/2.48 tff(6205,plain,
% 2.22/2.48 ($false),
% 2.22/2.48 inference(unit_resolution,[status(thm)],[4741, 6204, 6173, 6160, 6154])).
% 2.22/2.48 tff(6206,plain,(b(s(z), s(s(elem!1))) | (~r(s(s(s(z))), z)) | (~(s(s(z)) = s(s(elem!1)))) | (~b(elem!1, s(z))) | (~b(s(z), elem!1)) | (~r(s(s(s(elem!1))), s(z))) | (s(s(elem!1)) = s(s(s(elem!1)))) | b(z, s(s(z)))), inference(lemma,lemma(discharge,[]))).
% 2.22/2.48 tff(6207,plain,
% 2.22/2.48 (b(s(z), s(s(elem!1)))),
% 2.22/2.48 inference(unit_resolution,[status(thm)],[6206, 6137, 6120, 6139, 6141, 350, 45, 125])).
% 2.22/2.48 tff(6208,plain,
% 2.22/2.48 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), elem!1)) | (~b(elem!1, s(z))) | (~b(s(z), s(s(elem!1)))) | (~b(s(z), elem!1)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(elem!1)), elem!1)) | (~b(elem!1, s(z))) | (~b(s(z), s(s(elem!1)))) | (~b(s(z), elem!1)))),
% 2.22/2.48 inference(rewrite,[status(thm)],[])).
% 2.22/2.48 tff(6209,plain,
% 2.22/2.48 (((~b(s(z), s(s(elem!1)))) | (~b(s(z), s(s(elem!1)))) | (~b(elem!1, s(z))) | (~b(s(s(elem!1)), elem!1)) | (~b(s(z), elem!1)) | (~b(s(z), s(s(elem!1))))) <=> ((~b(s(s(elem!1)), elem!1)) | (~b(elem!1, s(z))) | (~b(s(z), s(s(elem!1)))) | (~b(s(z), elem!1)))),
% 2.22/2.48 inference(rewrite,[status(thm)],[])).
% 2.22/2.48 tff(6210,plain,
% 2.22/2.48 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(elem!1)))) | (~b(s(z), s(s(elem!1)))) | (~b(elem!1, s(z))) | (~b(s(s(elem!1)), elem!1)) | (~b(s(z), elem!1)) | (~b(s(z), s(s(elem!1)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), elem!1)) | (~b(elem!1, s(z))) | (~b(s(z), s(s(elem!1)))) | (~b(s(z), elem!1))))),
% 2.22/2.48 inference(monotonicity,[status(thm)],[6209])).
% 2.22/2.48 tff(6211,plain,
% 2.22/2.48 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(elem!1)))) | (~b(s(z), s(s(elem!1)))) | (~b(elem!1, s(z))) | (~b(s(s(elem!1)), elem!1)) | (~b(s(z), elem!1)) | (~b(s(z), s(s(elem!1)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(elem!1)), elem!1)) | (~b(elem!1, s(z))) | (~b(s(z), s(s(elem!1)))) | (~b(s(z), elem!1)))),
% 2.22/2.48 inference(transitivity,[status(thm)],[6210, 6208])).
% 2.22/2.48 tff(6212,plain,
% 2.22/2.48 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(elem!1)))) | (~b(s(z), s(s(elem!1)))) | (~b(elem!1, s(z))) | (~b(s(s(elem!1)), elem!1)) | (~b(s(z), elem!1)) | (~b(s(z), s(s(elem!1)))))),
% 2.22/2.48 inference(quant_inst,[status(thm)],[])).
% 2.22/2.48 tff(6213,plain,
% 2.22/2.48 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(elem!1)), elem!1)) | (~b(elem!1, s(z))) | (~b(s(z), s(s(elem!1)))) | (~b(s(z), elem!1))),
% 2.22/2.48 inference(modus_ponens,[status(thm)],[6212, 6211])).
% 2.22/2.48 tff(6214,plain,
% 2.22/2.48 ($false),
% 2.22/2.48 inference(unit_resolution,[status(thm)],[6213, 166, 376, 786, 1212, 642])).
% 2.22/2.48 tff(6215,plain,((~b(s(s(elem!1)), elem!1)) | (~b(s(z), s(s(elem!1)))) | (~b(elem!1, s(z))) | (~b(s(z), elem!1))), inference(lemma,lemma(discharge,[]))).
% 2.22/2.48 tff(6216,plain,
% 2.22/2.48 (~b(s(s(elem!1)), elem!1)),
% 2.22/2.48 inference(unit_resolution,[status(thm)],[6215, 6207, 6139, 6141])).
% 2.22/2.48 tff(6217,plain,
% 2.22/2.48 (~b(s(s(z)), z)),
% 2.22/2.48 inference(modus_ponens,[status(thm)],[6216, 6148])).
% 2.22/2.48 tff(6218,plain,
% 2.22/2.48 (r(s(s(z)), z)),
% 2.22/2.48 inference(unit_resolution,[status(thm)],[186, 6217])).
% 2.22/2.48 tff(6219,plain,
% 2.22/2.48 (~r(s(s(s(elem!1))), s(s(z)))),
% 2.22/2.48 inference(unit_resolution,[status(thm)],[6105, 6218, 152, 154])).
% 2.22/2.48 tff(6220,plain,
% 2.22/2.48 (~r(s(s(s(z))), s(s(z)))),
% 2.22/2.48 inference(unit_resolution,[status(thm)],[4714, 6219, 6120])).
% 2.22/2.48 tff(6221,plain,
% 2.22/2.48 (b(s(s(s(z))), s(s(z)))),
% 2.22/2.48 inference(unit_resolution,[status(thm)],[1010, 6220])).
% 2.22/2.48 tff(6222,plain,
% 2.22/2.48 (b(s(z), s(s(z)))),
% 2.22/2.48 inference(unit_resolution,[status(thm)],[5435, 6207, 6120])).
% 2.22/2.48 tff(6223,plain,
% 2.22/2.48 (~r(s(s(z)), s(s(s(z))))),
% 2.22/2.48 inference(unit_resolution,[status(thm)],[1741, 6218, 152, 6137])).
% 2.22/2.48 tff(6224,plain,
% 2.22/2.48 (b(s(s(z)), s(s(s(z))))),
% 2.22/2.48 inference(unit_resolution,[status(thm)],[1730, 6223])).
% 2.22/2.48 tff(6225,plain,
% 2.22/2.48 (~b(s(z), s(s(s(z))))),
% 2.22/2.48 inference(unit_resolution,[status(thm)],[996, 6224, 6222, 6221])).
% 2.22/2.48 tff(6226,plain,
% 2.22/2.48 (r(s(z), s(s(s(z))))),
% 2.22/2.48 inference(unit_resolution,[status(thm)],[1674, 6225])).
% 2.22/2.48 tff(6227,plain,
% 2.22/2.48 (r(s(z), s(s(s(elem!1))))),
% 2.22/2.48 inference(modus_ponens,[status(thm)],[6226, 6142])).
% 2.22/2.48 tff(6228,plain,
% 2.22/2.48 (r(s(s(s(s(z)))), s(s(s(z)))) <=> r(s(s(s(s(elem!1)))), s(s(s(elem!1))))),
% 2.22/2.48 inference(monotonicity,[status(thm)],[1087, 1086])).
% 2.22/2.48 tff(6229,plain,
% 2.22/2.48 (r(s(s(s(s(elem!1)))), s(s(s(elem!1))))),
% 2.22/2.48 inference(modus_ponens,[status(thm)],[4680, 6228])).
% 2.22/2.48 tff(6230,plain,
% 2.22/2.48 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), s(z))) | (~r(s(z), s(s(s(elem!1))))) | (~r(s(s(s(s(elem!1)))), s(z))) | (~r(s(s(s(s(elem!1)))), s(s(s(elem!1))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(elem!1))), s(z))) | (~r(s(z), s(s(s(elem!1))))) | (~r(s(s(s(s(elem!1)))), s(z))) | (~r(s(s(s(s(elem!1)))), s(s(s(elem!1))))))),
% 2.22/2.48 inference(rewrite,[status(thm)],[])).
% 2.22/2.48 tff(6231,plain,
% 2.22/2.48 (((~r(s(s(s(elem!1))), s(z))) | (~r(s(z), s(s(s(elem!1))))) | (~r(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~r(s(s(s(s(elem!1)))), s(z)))) <=> ((~r(s(s(s(elem!1))), s(z))) | (~r(s(z), s(s(s(elem!1))))) | (~r(s(s(s(s(elem!1)))), s(z))) | (~r(s(s(s(s(elem!1)))), s(s(s(elem!1))))))),
% 2.22/2.48 inference(rewrite,[status(thm)],[])).
% 2.22/2.48 tff(6232,plain,
% 2.22/2.48 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), s(z))) | (~r(s(z), s(s(s(elem!1))))) | (~r(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~r(s(s(s(s(elem!1)))), s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), s(z))) | (~r(s(z), s(s(s(elem!1))))) | (~r(s(s(s(s(elem!1)))), s(z))) | (~r(s(s(s(s(elem!1)))), s(s(s(elem!1)))))))),
% 2.22/2.48 inference(monotonicity,[status(thm)],[6231])).
% 2.22/2.48 tff(6233,plain,
% 2.22/2.48 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), s(z))) | (~r(s(z), s(s(s(elem!1))))) | (~r(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~r(s(s(s(s(elem!1)))), s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(elem!1))), s(z))) | (~r(s(z), s(s(s(elem!1))))) | (~r(s(s(s(s(elem!1)))), s(z))) | (~r(s(s(s(s(elem!1)))), s(s(s(elem!1))))))),
% 2.22/2.48 inference(transitivity,[status(thm)],[6232, 6230])).
% 2.22/2.48 tff(6234,plain,
% 2.22/2.48 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), s(z))) | (~r(s(z), s(s(s(elem!1))))) | (~r(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~r(s(s(s(s(elem!1)))), s(z))))),
% 2.22/2.48 inference(quant_inst,[status(thm)],[])).
% 2.22/2.48 tff(6235,plain,
% 2.22/2.48 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(elem!1))), s(z))) | (~r(s(z), s(s(s(elem!1))))) | (~r(s(s(s(s(elem!1)))), s(z))) | (~r(s(s(s(s(elem!1)))), s(s(s(elem!1)))))),
% 2.22/2.48 inference(modus_ponens,[status(thm)],[6234, 6233])).
% 2.22/2.48 tff(6236,plain,
% 2.22/2.48 (~r(s(s(s(s(elem!1)))), s(z))),
% 2.22/2.48 inference(unit_resolution,[status(thm)],[6235, 197, 350, 119, 6229])).
% 2.22/2.48 tff(6237,plain,
% 2.22/2.48 (~r(s(s(s(s(z)))), z)),
% 2.22/2.48 inference(unit_resolution,[status(thm)],[4685, 4680, 155, 1733])).
% 2.22/2.48 tff(6238,plain,
% 2.22/2.48 (b(s(s(s(s(z)))), z)),
% 2.22/2.48 inference(unit_resolution,[status(thm)],[3266, 6237])).
% 2.22/2.48 tff(6239,plain,
% 2.22/2.48 (b(s(s(s(s(elem!1)))), elem!1)),
% 2.22/2.48 inference(modus_ponens,[status(thm)],[6238, 4731])).
% 2.22/2.48 tff(6240,plain,
% 2.22/2.48 (((~b(s(z), elem!1)) | (~b(s(s(s(s(elem!1)))), elem!1)) | (~b(elem!1, s(z))) | (~b(s(z), elem!1)) | (~b(s(s(s(s(elem!1)))), elem!1)) | (~b(s(s(s(s(elem!1)))), s(z)))) <=> ((~b(elem!1, s(z))) | (~b(s(z), elem!1)) | (~b(s(s(s(s(elem!1)))), elem!1)) | (~b(s(s(s(s(elem!1)))), s(z))))),
% 2.22/2.48 inference(rewrite,[status(thm)],[])).
% 2.22/2.48 tff(6241,plain,
% 2.22/2.48 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), elem!1)) | (~b(s(s(s(s(elem!1)))), elem!1)) | (~b(elem!1, s(z))) | (~b(s(z), elem!1)) | (~b(s(s(s(s(elem!1)))), elem!1)) | (~b(s(s(s(s(elem!1)))), s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(z))) | (~b(s(z), elem!1)) | (~b(s(s(s(s(elem!1)))), elem!1)) | (~b(s(s(s(s(elem!1)))), s(z)))))),
% 2.22/2.48 inference(monotonicity,[status(thm)],[6240])).
% 2.22/2.48 tff(6242,plain,
% 2.22/2.48 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), elem!1)) | (~b(s(s(s(s(elem!1)))), elem!1)) | (~b(elem!1, s(z))) | (~b(s(z), elem!1)) | (~b(s(s(s(s(elem!1)))), elem!1)) | (~b(s(s(s(s(elem!1)))), s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(z))) | (~b(s(z), elem!1)) | (~b(s(s(s(s(elem!1)))), elem!1)) | (~b(s(s(s(s(elem!1)))), s(z))))),
% 2.22/2.48 inference(transitivity,[status(thm)],[6241, 6163])).
% 2.22/2.48 tff(6243,plain,
% 2.22/2.48 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), elem!1)) | (~b(s(s(s(s(elem!1)))), elem!1)) | (~b(elem!1, s(z))) | (~b(s(z), elem!1)) | (~b(s(s(s(s(elem!1)))), elem!1)) | (~b(s(s(s(s(elem!1)))), s(z))))),
% 2.22/2.48 inference(quant_inst,[status(thm)],[])).
% 2.22/2.48 tff(6244,plain,
% 2.22/2.48 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(z))) | (~b(s(z), elem!1)) | (~b(s(s(s(s(elem!1)))), elem!1)) | (~b(s(s(s(s(elem!1)))), s(z)))),
% 2.22/2.48 inference(modus_ponens,[status(thm)],[6243, 6242])).
% 2.22/2.48 tff(6245,plain,
% 2.22/2.48 (~b(s(s(s(s(elem!1)))), s(z))),
% 2.22/2.48 inference(unit_resolution,[status(thm)],[6244, 166, 1212, 642, 6239])).
% 2.22/2.48 tff(6246,plain,
% 2.22/2.48 ($false),
% 2.22/2.48 inference(unit_resolution,[status(thm)],[661, 6245, 6236])).
% 2.22/2.48 tff(6247,plain,((~r(s(s(s(s(z)))), s(s(s(z))))) | (~b(elem!1, s(z))) | (~b(s(z), elem!1)) | (~r(s(s(s(elem!1))), s(z))) | (~r(s(z), s(s(s(elem!1))))) | (~(s(s(z)) = s(s(elem!1)))) | (~r(z, s(s(z)))) | (~r(s(s(s(z))), z))), inference(lemma,lemma(discharge,[]))).
% 2.22/2.48 tff(6248,plain,
% 2.22/2.48 (~r(s(s(s(s(z)))), s(s(s(z))))),
% 2.22/2.48 inference(unit_resolution,[status(thm)],[6247, 6227, 6141, 350, 6139, 6120, 152, 6137])).
% 2.22/2.48 tff(6249,plain,
% 2.22/2.48 (b(s(s(s(s(z)))), s(s(s(z))))),
% 2.22/2.48 inference(unit_resolution,[status(thm)],[4662, 6248])).
% 2.22/2.48 tff(6250,plain,
% 2.22/2.48 (b(s(s(s(s(elem!1)))), s(s(s(elem!1))))),
% 2.22/2.48 inference(modus_ponens,[status(thm)],[6249, 6128])).
% 2.22/2.48 tff(6251,plain,
% 2.22/2.48 (~r(s(s(s(elem!1))), s(s(elem!1)))),
% 2.22/2.48 inference(unit_resolution,[status(thm)],[3454, 6219, 6120])).
% 2.22/2.48 tff(6252,plain,
% 2.22/2.48 (b(s(s(s(elem!1))), s(s(elem!1)))),
% 2.22/2.48 inference(unit_resolution,[status(thm)],[889, 6251, 51])).
% 2.22/2.48 tff(6253,plain,
% 2.22/2.48 (b(s(s(elem!1)), s(s(s(z)))) <=> b(s(s(elem!1)), s(s(s(elem!1))))),
% 2.22/2.48 inference(monotonicity,[status(thm)],[6126])).
% 2.22/2.48 tff(6254,plain,
% 2.22/2.48 (b(s(s(z)), s(s(s(z)))) <=> b(s(s(elem!1)), s(s(s(z))))),
% 2.22/2.48 inference(monotonicity,[status(thm)],[6120])).
% 2.22/2.48 tff(6255,plain,
% 2.22/2.48 (b(s(s(z)), s(s(s(z)))) <=> b(s(s(elem!1)), s(s(s(elem!1))))),
% 2.22/2.48 inference(transitivity,[status(thm)],[6254, 6253])).
% 2.22/2.49 tff(6256,plain,
% 2.22/2.49 (b(s(s(elem!1)), s(s(s(elem!1))))),
% 2.22/2.49 inference(modus_ponens,[status(thm)],[6224, 6255])).
% 2.22/2.49 tff(6257,plain,
% 2.22/2.49 (((~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~b(s(s(s(s(elem!1)))), s(s(elem!1))))) <=> ((~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(s(s(s(elem!1)))), s(s(elem!1)))) | (~b(s(s(s(s(elem!1)))), s(s(s(elem!1))))))),
% 2.22/2.49 inference(rewrite,[status(thm)],[])).
% 2.22/2.49 tff(6258,plain,
% 2.22/2.49 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~b(s(s(s(s(elem!1)))), s(s(elem!1)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(s(s(s(elem!1)))), s(s(elem!1)))) | (~b(s(s(s(s(elem!1)))), s(s(s(elem!1)))))))),
% 2.22/2.49 inference(monotonicity,[status(thm)],[6257])).
% 2.22/2.49 tff(6259,plain,
% 2.22/2.49 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~b(s(s(s(s(elem!1)))), s(s(elem!1)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(s(s(s(elem!1)))), s(s(elem!1)))) | (~b(s(s(s(s(elem!1)))), s(s(s(elem!1))))))),
% 2.22/2.49 inference(transitivity,[status(thm)],[6258, 4695])).
% 2.22/2.49 tff(6260,plain,
% 2.22/2.49 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~b(s(s(s(s(elem!1)))), s(s(elem!1)))))),
% 2.22/2.49 inference(quant_inst,[status(thm)],[])).
% 2.22/2.49 tff(6261,plain,
% 2.22/2.49 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(s(s(s(elem!1)))), s(s(elem!1)))) | (~b(s(s(s(s(elem!1)))), s(s(s(elem!1)))))),
% 2.22/2.49 inference(modus_ponens,[status(thm)],[6260, 6259])).
% 2.22/2.49 tff(6262,plain,
% 2.22/2.49 (~b(s(s(s(s(elem!1)))), s(s(elem!1)))),
% 2.22/2.49 inference(unit_resolution,[status(thm)],[6261, 166, 6256, 6252, 6250])).
% 2.22/2.49 tff(6263,plain,
% 2.22/2.49 (r(s(s(s(s(elem!1)))), s(s(elem!1)))),
% 2.22/2.49 inference(unit_resolution,[status(thm)],[813, 6262, 6125])).
% 2.22/2.49 tff(6264,plain,
% 2.22/2.49 ((s(s(s(s(elem!1)))) = z) <=> (s(s(s(s(elem!1)))) = elem!1)),
% 2.22/2.49 inference(monotonicity,[status(thm)],[6130])).
% 2.22/2.49 tff(6265,plain,
% 2.22/2.49 ((s(s(s(s(elem!1)))) = z) <=> (elem!1 = s(s(s(s(elem!1)))))),
% 2.22/2.49 inference(transitivity,[status(thm)],[6264, 2287])).
% 2.22/2.49 tff(6266,plain,
% 2.22/2.49 ((~(s(s(s(s(elem!1)))) = z)) <=> (~(elem!1 = s(s(s(s(elem!1))))))),
% 2.22/2.49 inference(monotonicity,[status(thm)],[6265])).
% 2.22/2.49 tff(6267,plain,
% 2.22/2.49 (~(elem!1 = s(s(s(s(elem!1)))))),
% 2.22/2.49 inference(modus_ponens,[status(thm)],[626, 6266])).
% 2.22/2.49 tff(6268,plain,
% 2.22/2.49 (r(z, s(s(elem!1))) <=> r(elem!1, s(s(elem!1)))),
% 2.22/2.49 inference(monotonicity,[status(thm)],[6130])).
% 2.22/2.49 tff(6269,plain,
% 2.22/2.49 (~b(z, s(s(elem!1)))),
% 2.22/2.49 inference(unit_resolution,[status(thm)],[2261, 6120, 125])).
% 2.22/2.49 tff(6270,plain,
% 2.22/2.49 (r(z, s(s(elem!1)))),
% 2.22/2.49 inference(unit_resolution,[status(thm)],[1795, 6269])).
% 2.22/2.49 tff(6271,plain,
% 2.22/2.49 (r(elem!1, s(s(elem!1)))),
% 2.22/2.49 inference(modus_ponens,[status(thm)],[6270, 6268])).
% 2.22/2.49 tff(6272,plain,
% 2.22/2.49 ((s(s(s(s(z)))) = s(s(s(s(s(s(s(elem!1)))))))) <=> (s(s(s(s(s(s(s(elem!1))))))) = s(s(s(s(z)))))),
% 2.22/2.49 inference(commutativity,[status(thm)],[])).
% 2.22/2.49 tff(6273,plain,
% 2.22/2.49 ((s(s(s(s(elem!1)))) = s(s(s(s(s(s(s(elem!1)))))))) <=> (s(s(s(s(z)))) = s(s(s(s(s(s(s(elem!1))))))))),
% 2.22/2.49 inference(monotonicity,[status(thm)],[2370])).
% 2.22/2.49 tff(6274,plain,
% 2.22/2.49 ((s(s(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(s(z)))))),
% 2.22/2.49 inference(transitivity,[status(thm)],[6273, 6272])).
% 2.22/2.49 tff(6275,plain,
% 2.22/2.49 ((s(s(s(s(s(s(s(elem!1))))))) = s(s(s(s(z))))) <=> (s(s(s(s(elem!1)))) = s(s(s(s(s(s(s(elem!1))))))))),
% 2.22/2.49 inference(symmetry,[status(thm)],[6274])).
% 2.22/2.49 tff(6276,plain,
% 2.22/2.49 ((~(s(s(s(s(s(s(s(elem!1))))))) = s(s(s(s(z)))))) <=> (~(s(s(s(s(elem!1)))) = s(s(s(s(s(s(s(elem!1)))))))))),
% 2.22/2.49 inference(monotonicity,[status(thm)],[6275])).
% 2.22/2.49 tff(6277,plain,
% 2.22/2.49 (s(s(s(elem!1))) = s(s(s(z)))),
% 2.22/2.49 inference(symmetry,[status(thm)],[1086])).
% 2.22/2.49 tff(6278,plain,
% 2.22/2.49 (~(s(s(s(s(s(s(s(elem!1))))))) = s(s(s(s(z)))))),
% 2.22/2.49 inference(unit_resolution,[status(thm)],[4925, 6277])).
% 2.22/2.49 tff(6279,plain,
% 2.22/2.49 (~(s(s(s(s(elem!1)))) = s(s(s(s(s(s(s(elem!1))))))))),
% 2.22/2.49 inference(modus_ponens,[status(thm)],[6278, 6276])).
% 2.22/2.49 tff(6280,assumption,(s(s(s(s(s(s(s(elem!1))))))) = elem!1), introduced(assumption)).
% 2.22/2.49 tff(6281,plain,
% 2.22/2.49 (s(s(s(s(s(s(s(elem!1))))))) = z),
% 2.22/2.49 inference(transitivity,[status(thm)],[6280, 4891])).
% 2.22/2.49 tff(6282,plain,
% 2.22/2.49 ($false),
% 2.22/2.49 inference(unit_resolution,[status(thm)],[4853, 6281])).
% 2.22/2.49 tff(6283,plain,((~(s(s(s(s(s(s(s(elem!1))))))) = elem!1)) | (~(z = elem!1))), inference(lemma,lemma(discharge,[]))).
% 2.22/2.49 tff(6284,plain,
% 2.22/2.49 (~(s(s(s(s(s(s(s(elem!1))))))) = elem!1)),
% 2.22/2.49 inference(unit_resolution,[status(thm)],[6283, 620])).
% 2.22/2.49 tff(6285,plain,
% 2.22/2.49 (r(s(s(elem!1)), z) <=> r(s(s(elem!1)), elem!1)),
% 2.22/2.49 inference(monotonicity,[status(thm)],[620])).
% 2.22/2.49 tff(6286,plain,
% 2.22/2.49 (r(s(s(z)), z) <=> r(s(s(elem!1)), z)),
% 2.22/2.49 inference(monotonicity,[status(thm)],[34])).
% 2.22/2.49 tff(6287,plain,
% 2.22/2.49 (r(s(s(z)), z) <=> r(s(s(elem!1)), elem!1)),
% 2.22/2.49 inference(transitivity,[status(thm)],[6286, 6285])).
% 2.22/2.49 tff(6288,plain,
% 2.22/2.49 (r(s(s(elem!1)), elem!1)),
% 2.22/2.49 inference(modus_ponens,[status(thm)],[5947, 6287])).
% 2.22/2.49 tff(6289,plain,
% 2.22/2.49 ((s(s(s(elem!1))) = z) <=> (s(s(s(elem!1))) = elem!1)),
% 2.22/2.49 inference(monotonicity,[status(thm)],[620])).
% 2.22/2.49 tff(6290,plain,
% 2.22/2.49 ((s(s(s(elem!1))) = z) <=> (elem!1 = s(s(s(elem!1))))),
% 2.22/2.49 inference(transitivity,[status(thm)],[6289, 5406])).
% 2.22/2.49 tff(6291,plain,
% 2.22/2.49 ((~(s(s(s(elem!1))) = z)) <=> (~(elem!1 = s(s(s(elem!1)))))),
% 2.22/2.49 inference(monotonicity,[status(thm)],[6290])).
% 2.22/2.49 tff(6292,plain,
% 2.22/2.49 (~(elem!1 = s(s(s(elem!1))))),
% 2.22/2.49 inference(modus_ponens,[status(thm)],[89, 6291])).
% 2.22/2.49 tff(6293,plain,
% 2.22/2.49 (r(s(s(s(z))), z) <=> r(s(s(s(z))), elem!1)),
% 2.22/2.49 inference(monotonicity,[status(thm)],[620])).
% 2.22/2.49 tff(6294,plain,
% 2.22/2.49 (r(s(s(s(z))), elem!1) <=> r(s(s(s(z))), z)),
% 2.22/2.49 inference(symmetry,[status(thm)],[6293])).
% 2.22/2.49 tff(6295,plain,
% 2.22/2.49 (r(s(s(s(z))), elem!1) <=> r(s(s(s(elem!1))), elem!1)),
% 2.22/2.49 inference(monotonicity,[status(thm)],[1086])).
% 2.22/2.49 tff(6296,plain,
% 2.22/2.49 (r(s(s(s(elem!1))), elem!1) <=> r(s(s(s(z))), elem!1)),
% 2.22/2.49 inference(symmetry,[status(thm)],[6295])).
% 2.22/2.49 tff(6297,plain,
% 2.22/2.49 (r(s(s(s(elem!1))), elem!1) <=> r(s(s(s(z))), z)),
% 2.22/2.49 inference(transitivity,[status(thm)],[6296, 6294])).
% 2.22/2.49 tff(6298,plain,
% 2.22/2.49 (r(s(s(s(z))), z)),
% 2.22/2.49 inference(modus_ponens,[status(thm)],[1013, 6297])).
% 2.22/2.49 tff(6299,plain,
% 2.22/2.49 (r(s(z), s(s(s(z)))) <=> r(s(z), s(s(s(elem!1))))),
% 2.22/2.49 inference(monotonicity,[status(thm)],[1086])).
% 2.22/2.49 tff(6300,plain,
% 2.22/2.49 (b(s(z), s(s(z)))),
% 2.22/2.49 inference(unit_resolution,[status(thm)],[5435, 376, 34])).
% 2.22/2.49 tff(6301,plain,
% 2.22/2.49 (~r(s(s(z)), s(s(s(z))))),
% 2.22/2.49 inference(unit_resolution,[status(thm)],[1741, 5947, 155, 6298])).
% 2.22/2.49 tff(6302,plain,
% 2.22/2.49 (b(s(s(z)), s(s(s(z))))),
% 2.22/2.49 inference(unit_resolution,[status(thm)],[1730, 6301])).
% 2.22/2.49 tff(6303,plain,
% 2.22/2.49 (~b(s(z), s(s(s(z))))),
% 2.22/2.49 inference(unit_resolution,[status(thm)],[996, 6302, 6300, 987])).
% 2.22/2.49 tff(6304,plain,
% 2.22/2.49 (r(s(z), s(s(s(z))))),
% 2.22/2.49 inference(unit_resolution,[status(thm)],[1674, 6303])).
% 2.22/2.49 tff(6305,plain,
% 2.22/2.49 (r(s(z), s(s(s(elem!1))))),
% 2.22/2.49 inference(modus_ponens,[status(thm)],[6304, 6299])).
% 2.22/2.49 tff(6306,plain,
% 2.22/2.49 (~r(s(s(s(s(z)))), s(s(s(z))))),
% 2.22/2.49 inference(unit_resolution,[status(thm)],[6247, 6305, 637, 350, 5417, 34, 155, 6298])).
% 2.22/2.49 tff(6307,plain,
% 2.22/2.49 (b(s(s(s(s(z)))), s(s(s(z))))),
% 2.22/2.49 inference(unit_resolution,[status(thm)],[4662, 6306])).
% 2.22/2.49 tff(6308,plain,
% 2.22/2.49 (b(s(s(s(s(elem!1)))), s(s(s(elem!1))))),
% 2.22/2.49 inference(modus_ponens,[status(thm)],[6307, 4626])).
% 2.22/2.49 tff(6309,plain,
% 2.22/2.49 (b(s(s(z)), s(s(s(z)))) <=> b(s(s(elem!1)), s(s(s(elem!1))))),
% 2.22/2.49 inference(transitivity,[status(thm)],[6149, 6151])).
% 2.22/2.49 tff(6310,plain,
% 2.22/2.49 (b(s(s(elem!1)), s(s(s(elem!1))))),
% 2.22/2.49 inference(modus_ponens,[status(thm)],[6302, 6309])).
% 2.22/2.49 tff(6311,plain,
% 2.22/2.49 (~b(s(s(s(s(elem!1)))), s(s(elem!1)))),
% 2.22/2.49 inference(unit_resolution,[status(thm)],[6261, 166, 6310, 839, 6308])).
% 2.22/2.49 tff(6312,plain,
% 2.22/2.49 (r(s(s(s(s(elem!1)))), s(s(elem!1)))),
% 2.22/2.49 inference(unit_resolution,[status(thm)],[813, 6311, 734])).
% 2.22/2.49 tff(6313,plain,
% 2.22/2.49 (~r(elem!1, s(s(s(s(elem!1)))))),
% 2.22/2.49 inference(unit_resolution,[status(thm)],[3414, 197, 6288, 6312, 1027])).
% 2.22/2.49 tff(6314,plain,
% 2.22/2.49 (b(elem!1, s(s(s(s(elem!1)))))),
% 2.22/2.49 inference(unit_resolution,[status(thm)],[2427, 6313, 2377])).
% 2.22/2.49 tff(6315,plain,
% 2.22/2.49 (b(s(s(elem!1)), s(z))),
% 2.22/2.49 inference(modus_ponens,[status(thm)],[156, 3933])).
% 2.22/2.49 tff(6316,plain,
% 2.22/2.49 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(elem!1, s(z))) | (~b(elem!1, s(s(s(elem!1))))) | (~b(s(s(elem!1)), s(z))) | (~b(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~b(elem!1, s(s(s(s(elem!1)))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(elem!1, s(z))) | (~b(elem!1, s(s(s(elem!1))))) | (~b(s(s(elem!1)), s(z))) | (~b(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~b(elem!1, s(s(s(s(elem!1)))))))),
% 2.22/2.49 inference(rewrite,[status(thm)],[])).
% 2.22/2.49 tff(6317,plain,
% 2.22/2.49 (((~b(s(s(elem!1)), s(z))) | (~b(elem!1, s(z))) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~b(elem!1, s(s(s(elem!1))))) | (~b(elem!1, s(s(s(s(elem!1))))))) <=> ((~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(elem!1, s(z))) | (~b(elem!1, s(s(s(elem!1))))) | (~b(s(s(elem!1)), s(z))) | (~b(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~b(elem!1, s(s(s(s(elem!1)))))))),
% 2.22/2.49 inference(rewrite,[status(thm)],[])).
% 2.22/2.49 tff(6318,plain,
% 2.22/2.49 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), s(z))) | (~b(elem!1, s(z))) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~b(elem!1, s(s(s(elem!1))))) | (~b(elem!1, s(s(s(s(elem!1)))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(elem!1, s(z))) | (~b(elem!1, s(s(s(elem!1))))) | (~b(s(s(elem!1)), s(z))) | (~b(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~b(elem!1, s(s(s(s(elem!1))))))))),
% 2.22/2.49 inference(monotonicity,[status(thm)],[6317])).
% 2.22/2.49 tff(6319,plain,
% 2.22/2.49 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), s(z))) | (~b(elem!1, s(z))) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~b(elem!1, s(s(s(elem!1))))) | (~b(elem!1, s(s(s(s(elem!1)))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(elem!1, s(z))) | (~b(elem!1, s(s(s(elem!1))))) | (~b(s(s(elem!1)), s(z))) | (~b(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~b(elem!1, s(s(s(s(elem!1)))))))),
% 2.22/2.49 inference(transitivity,[status(thm)],[6318, 6316])).
% 2.22/2.49 tff(6320,plain,
% 2.22/2.49 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), s(z))) | (~b(elem!1, s(z))) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~b(elem!1, s(s(s(elem!1))))) | (~b(elem!1, s(s(s(s(elem!1)))))))),
% 2.22/2.49 inference(quant_inst,[status(thm)],[])).
% 2.22/2.49 tff(6321,plain,
% 2.22/2.49 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(elem!1, s(z))) | (~b(elem!1, s(s(s(elem!1))))) | (~b(s(s(elem!1)), s(z))) | (~b(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~b(elem!1, s(s(s(s(elem!1))))))),
% 2.22/2.49 inference(modus_ponens,[status(thm)],[6320, 6319])).
% 2.22/2.49 tff(6322,plain,
% 2.22/2.49 ((~b(elem!1, s(s(s(elem!1))))) | (~b(elem!1, s(s(s(s(elem!1))))))),
% 2.22/2.49 inference(unit_resolution,[status(thm)],[6321, 166, 839, 5417, 6315, 6308])).
% 2.22/2.49 tff(6323,plain,
% 2.22/2.49 (~b(elem!1, s(s(s(elem!1))))),
% 2.22/2.49 inference(unit_resolution,[status(thm)],[6322, 6314])).
% 2.22/2.49 tff(6324,plain,
% 2.22/2.49 (r(elem!1, s(s(s(elem!1))))),
% 2.22/2.49 inference(unit_resolution,[status(thm)],[5451, 6323, 6292])).
% 2.22/2.49 tff(6325,plain,
% 2.22/2.49 ((s(s(s(elem!1))) = s(s(s(s(s(s(s(elem!1)))))))) <=> (s(s(s(z))) = s(s(s(s(s(s(s(elem!1))))))))),
% 2.22/2.49 inference(monotonicity,[status(thm)],[6277])).
% 2.22/2.49 tff(6326,plain,
% 2.22/2.49 ((s(s(s(z))) = s(s(s(s(s(s(s(elem!1)))))))) <=> (s(s(s(elem!1))) = s(s(s(s(s(s(s(elem!1))))))))),
% 2.22/2.49 inference(symmetry,[status(thm)],[6325])).
% 2.22/2.49 tff(6327,plain,
% 2.22/2.49 ((~(s(s(s(z))) = s(s(s(s(s(s(s(elem!1))))))))) <=> (~(s(s(s(elem!1))) = s(s(s(s(s(s(s(elem!1)))))))))),
% 2.22/2.49 inference(monotonicity,[status(thm)],[6326])).
% 2.22/2.49 tff(6328,plain,
% 2.22/2.49 (~(s(s(s(s(s(s(elem!1)))))) = s(s(elem!1)))),
% 2.22/2.49 inference(unit_resolution,[status(thm)],[4986, 619])).
% 2.22/2.49 tff(6329,plain,
% 2.22/2.49 (~(s(s(s(z))) = s(s(s(s(s(s(s(elem!1))))))))),
% 2.22/2.49 inference(unit_resolution,[status(thm)],[4995, 6328, 2153])).
% 2.22/2.49 tff(6330,plain,
% 2.22/2.49 (~(s(s(s(elem!1))) = s(s(s(s(s(s(s(elem!1))))))))),
% 2.22/2.49 inference(modus_ponens,[status(thm)],[6329, 6327])).
% 2.22/2.49 tff(6331,assumption,(r(s(s(s(s(s(s(s(elem!1))))))), elem!1)), introduced(assumption)).
% 2.22/2.49 tff(6332,plain,
% 2.22/2.49 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), elem!1)) | (~r(s(s(s(s(s(s(s(elem!1))))))), elem!1)) | (~r(s(s(s(elem!1))), s(s(s(s(s(s(s(elem!1))))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(elem!1, s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), elem!1)) | (~r(s(s(s(s(s(s(s(elem!1))))))), elem!1)) | (~r(s(s(s(elem!1))), s(s(s(s(s(s(s(elem!1))))))))))),
% 2.22/2.49 inference(rewrite,[status(thm)],[])).
% 2.22/2.49 tff(6333,plain,
% 2.22/2.49 (((~r(elem!1, s(s(s(elem!1))))) | (~r(s(s(s(s(s(s(s(elem!1))))))), elem!1)) | (~r(s(s(s(elem!1))), elem!1)) | (~r(s(s(s(elem!1))), s(s(s(s(s(s(s(elem!1)))))))))) <=> ((~r(elem!1, s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), elem!1)) | (~r(s(s(s(s(s(s(s(elem!1))))))), elem!1)) | (~r(s(s(s(elem!1))), s(s(s(s(s(s(s(elem!1))))))))))),
% 2.22/2.49 inference(rewrite,[status(thm)],[])).
% 2.22/2.49 tff(6334,plain,
% 2.22/2.49 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(s(s(elem!1))))) | (~r(s(s(s(s(s(s(s(elem!1))))))), elem!1)) | (~r(s(s(s(elem!1))), elem!1)) | (~r(s(s(s(elem!1))), s(s(s(s(s(s(s(elem!1))))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), elem!1)) | (~r(s(s(s(s(s(s(s(elem!1))))))), elem!1)) | (~r(s(s(s(elem!1))), s(s(s(s(s(s(s(elem!1)))))))))))),
% 2.22/2.49 inference(monotonicity,[status(thm)],[6333])).
% 2.22/2.49 tff(6335,plain,
% 2.22/2.49 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(s(s(elem!1))))) | (~r(s(s(s(s(s(s(s(elem!1))))))), elem!1)) | (~r(s(s(s(elem!1))), elem!1)) | (~r(s(s(s(elem!1))), s(s(s(s(s(s(s(elem!1))))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(elem!1, s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), elem!1)) | (~r(s(s(s(s(s(s(s(elem!1))))))), elem!1)) | (~r(s(s(s(elem!1))), s(s(s(s(s(s(s(elem!1))))))))))),
% 2.22/2.49 inference(transitivity,[status(thm)],[6334, 6332])).
% 2.22/2.49 tff(6336,plain,
% 2.22/2.49 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(s(s(elem!1))))) | (~r(s(s(s(s(s(s(s(elem!1))))))), elem!1)) | (~r(s(s(s(elem!1))), elem!1)) | (~r(s(s(s(elem!1))), s(s(s(s(s(s(s(elem!1))))))))))),
% 2.22/2.49 inference(quant_inst,[status(thm)],[])).
% 2.22/2.49 tff(6337,plain,
% 2.22/2.49 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(elem!1, s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), elem!1)) | (~r(s(s(s(s(s(s(s(elem!1))))))), elem!1)) | (~r(s(s(s(elem!1))), s(s(s(s(s(s(s(elem!1)))))))))),
% 2.22/2.49 inference(modus_ponens,[status(thm)],[6336, 6335])).
% 2.22/2.49 tff(6338,plain,
% 2.22/2.49 (~r(s(s(s(elem!1))), s(s(s(s(s(s(s(elem!1))))))))),
% 2.22/2.49 inference(unit_resolution,[status(thm)],[6337, 197, 942, 6331, 1013])).
% 2.22/2.49 tff(6339,plain,
% 2.22/2.49 (((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((s(s(s(elem!1))) = s(s(s(s(s(s(s(elem!1)))))))) | b(s(s(s(elem!1))), s(s(s(s(s(s(s(elem!1)))))))) | r(s(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(s(elem!1))) = s(s(s(s(s(s(s(elem!1)))))))) | b(s(s(s(elem!1))), s(s(s(s(s(s(s(elem!1)))))))) | r(s(s(s(elem!1))), s(s(s(s(s(s(s(elem!1)))))))))),
% 2.22/2.49 inference(rewrite,[status(thm)],[])).
% 2.22/2.49 tff(6340,plain,
% 2.22/2.49 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((s(s(s(elem!1))) = s(s(s(s(s(s(s(elem!1)))))))) | b(s(s(s(elem!1))), s(s(s(s(s(s(s(elem!1)))))))) | r(s(s(s(elem!1))), s(s(s(s(s(s(s(elem!1)))))))))),
% 2.22/2.49 inference(quant_inst,[status(thm)],[])).
% 2.22/2.49 tff(6341,plain,
% 2.22/2.49 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (s(s(s(elem!1))) = s(s(s(s(s(s(s(elem!1)))))))) | b(s(s(s(elem!1))), s(s(s(s(s(s(s(elem!1)))))))) | r(s(s(s(elem!1))), s(s(s(s(s(s(s(elem!1))))))))),
% 2.22/2.49 inference(modus_ponens,[status(thm)],[6340, 6339])).
% 2.22/2.49 tff(6342,plain,
% 2.22/2.49 ((s(s(s(elem!1))) = s(s(s(s(s(s(s(elem!1)))))))) | b(s(s(s(elem!1))), s(s(s(s(s(s(s(elem!1))))))))),
% 2.22/2.49 inference(unit_resolution,[status(thm)],[6341, 79, 6338])).
% 2.22/2.49 tff(6343,plain,
% 2.22/2.49 (b(s(s(s(elem!1))), s(s(s(s(s(s(s(elem!1))))))))),
% 2.22/2.49 inference(unit_resolution,[status(thm)],[6342, 6330])).
% 2.22/2.49 tff(6344,plain,
% 2.22/2.49 (s(s(elem!1)) = s(s(z))),
% 2.22/2.49 inference(symmetry,[status(thm)],[34])).
% 2.22/2.49 tff(6345,plain,
% 2.22/2.49 ((s(s(s(s(s(s(s(elem!1))))))) = s(s(elem!1))) <=> (s(s(s(s(s(s(s(elem!1))))))) = s(s(z)))),
% 2.22/2.49 inference(monotonicity,[status(thm)],[6344])).
% 2.22/2.49 tff(6346,plain,
% 2.22/2.49 ((s(s(s(s(s(s(s(elem!1))))))) = s(s(elem!1))) <=> (s(s(z)) = s(s(s(s(s(s(s(elem!1))))))))),
% 2.22/2.49 inference(transitivity,[status(thm)],[6345, 5001])).
% 2.22/2.49 tff(6347,plain,
% 2.22/2.49 ((s(s(z)) = s(s(s(s(s(s(s(elem!1)))))))) <=> (s(s(s(s(s(s(s(elem!1))))))) = s(s(elem!1)))),
% 2.22/2.49 inference(symmetry,[status(thm)],[6346])).
% 2.22/2.49 tff(6348,plain,
% 2.22/2.49 ((~(s(s(z)) = s(s(s(s(s(s(s(elem!1))))))))) <=> (~(s(s(s(s(s(s(s(elem!1))))))) = s(s(elem!1))))),
% 2.22/2.49 inference(monotonicity,[status(thm)],[6347])).
% 2.22/2.49 tff(6349,plain,
% 2.22/2.49 (~(s(s(s(s(s(s(s(elem!1))))))) = s(s(elem!1)))),
% 2.22/2.49 inference(modus_ponens,[status(thm)],[5016, 6348])).
% 2.22/2.49 tff(6350,plain,
% 2.22/2.49 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(elem!1)), elem!1)) | (~r(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(elem!1)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(elem!1)), elem!1)) | (~r(elem!1, s(s(s(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(elem!1)))))),
% 2.22/2.49 inference(rewrite,[status(thm)],[])).
% 2.22/2.49 tff(6351,plain,
% 2.22/2.49 (((~r(elem!1, 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(s(s(s(s(s(elem!1))))))), s(s(elem!1))))) <=> ((~r(s(s(elem!1)), elem!1)) | (~r(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(elem!1)))))),
% 2.22/2.49 inference(rewrite,[status(thm)],[])).
% 2.22/2.49 tff(6352,plain,
% 2.22/2.49 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(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(s(s(s(s(s(elem!1))))))), s(s(elem!1)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(elem!1)), elem!1)) | (~r(elem!1, s(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(elem!1))))))),
% 2.22/2.49 inference(monotonicity,[status(thm)],[6351])).
% 2.22/2.49 tff(6353,plain,
% 2.22/2.49 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(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(s(s(s(s(s(elem!1))))))), s(s(elem!1)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(elem!1)), elem!1)) | (~r(elem!1, s(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(elem!1)))))),
% 2.22/2.49 inference(transitivity,[status(thm)],[6352, 6350])).
% 2.22/2.49 tff(6354,plain,
% 2.22/2.49 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(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(s(s(s(s(s(elem!1))))))), s(s(elem!1)))))),
% 2.22/2.49 inference(quant_inst,[status(thm)],[])).
% 2.22/2.49 tff(6355,plain,
% 2.22/2.49 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(elem!1)), elem!1)) | (~r(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(elem!1))))),
% 2.22/2.49 inference(modus_ponens,[status(thm)],[6354, 6353])).
% 2.22/2.49 tff(6356,plain,
% 2.22/2.49 (~r(s(s(s(s(s(s(s(elem!1))))))), s(s(elem!1)))),
% 2.22/2.49 inference(unit_resolution,[status(thm)],[6355, 197, 942, 768, 6331])).
% 2.22/2.49 tff(6357,plain,
% 2.22/2.49 (((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((s(s(s(s(s(s(s(elem!1))))))) = s(s(elem!1))) | b(s(s(s(s(s(s(s(elem!1))))))), s(s(elem!1))) | r(s(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(s(elem!1))))))) = s(s(elem!1))) | b(s(s(s(s(s(s(s(elem!1))))))), s(s(elem!1))) | r(s(s(s(s(s(s(s(elem!1))))))), s(s(elem!1))))),
% 2.22/2.49 inference(rewrite,[status(thm)],[])).
% 2.22/2.49 tff(6358,plain,
% 2.22/2.49 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((s(s(s(s(s(s(s(elem!1))))))) = s(s(elem!1))) | b(s(s(s(s(s(s(s(elem!1))))))), s(s(elem!1))) | r(s(s(s(s(s(s(s(elem!1))))))), s(s(elem!1))))),
% 2.22/2.49 inference(quant_inst,[status(thm)],[])).
% 2.22/2.49 tff(6359,plain,
% 2.22/2.49 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (s(s(s(s(s(s(s(elem!1))))))) = s(s(elem!1))) | b(s(s(s(s(s(s(s(elem!1))))))), s(s(elem!1))) | r(s(s(s(s(s(s(s(elem!1))))))), s(s(elem!1)))),
% 2.22/2.49 inference(modus_ponens,[status(thm)],[6358, 6357])).
% 2.22/2.49 tff(6360,plain,
% 2.22/2.49 ((s(s(s(s(s(s(s(elem!1))))))) = s(s(elem!1))) | b(s(s(s(s(s(s(s(elem!1))))))), s(s(elem!1)))),
% 2.22/2.49 inference(unit_resolution,[status(thm)],[6359, 79, 6356])).
% 2.22/2.49 tff(6361,plain,
% 2.22/2.49 (b(s(s(s(s(s(s(s(elem!1))))))), s(s(elem!1)))),
% 2.22/2.49 inference(unit_resolution,[status(thm)],[6360, 6349])).
% 2.22/2.49 tff(6362,plain,
% 2.22/2.49 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(s(s(s(s(s(s(elem!1))))))), s(s(elem!1)))) | (~b(s(s(s(elem!1))), s(s(s(s(s(s(s(elem!1))))))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(s(s(s(s(s(s(elem!1))))))), s(s(elem!1)))) | (~b(s(s(s(elem!1))), s(s(s(s(s(s(s(elem!1))))))))))),
% 2.32/2.50 inference(rewrite,[status(thm)],[])).
% 2.32/2.50 tff(6363,plain,
% 2.32/2.50 (((~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(s(s(s(s(s(s(s(elem!1))))))), s(s(elem!1)))) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(s(s(elem!1))), s(s(s(s(s(s(s(elem!1)))))))))) <=> ((~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(s(s(s(s(s(s(elem!1))))))), s(s(elem!1)))) | (~b(s(s(s(elem!1))), s(s(s(s(s(s(s(elem!1))))))))))),
% 2.32/2.50 inference(rewrite,[status(thm)],[])).
% 2.32/2.50 tff(6364,plain,
% 2.32/2.50 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(s(s(s(s(s(s(s(elem!1))))))), s(s(elem!1)))) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(s(s(elem!1))), s(s(s(s(s(s(s(elem!1))))))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(s(s(s(s(s(s(elem!1))))))), s(s(elem!1)))) | (~b(s(s(s(elem!1))), s(s(s(s(s(s(s(elem!1)))))))))))),
% 2.32/2.50 inference(monotonicity,[status(thm)],[6363])).
% 2.32/2.50 tff(6365,plain,
% 2.32/2.50 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(s(s(s(s(s(s(s(elem!1))))))), s(s(elem!1)))) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(s(s(elem!1))), s(s(s(s(s(s(s(elem!1))))))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(s(s(s(s(s(s(elem!1))))))), s(s(elem!1)))) | (~b(s(s(s(elem!1))), s(s(s(s(s(s(s(elem!1))))))))))),
% 2.32/2.50 inference(transitivity,[status(thm)],[6364, 6362])).
% 2.32/2.50 tff(6366,plain,
% 2.32/2.50 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(s(s(s(s(s(s(s(elem!1))))))), s(s(elem!1)))) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(s(s(elem!1))), s(s(s(s(s(s(s(elem!1))))))))))),
% 2.32/2.50 inference(quant_inst,[status(thm)],[])).
% 2.32/2.50 tff(6367,plain,
% 2.32/2.50 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(s(s(s(s(s(s(elem!1))))))), s(s(elem!1)))) | (~b(s(s(s(elem!1))), s(s(s(s(s(s(s(elem!1)))))))))),
% 2.32/2.50 inference(modus_ponens,[status(thm)],[6366, 6365])).
% 2.32/2.50 tff(6368,plain,
% 2.32/2.50 ($false),
% 2.32/2.50 inference(unit_resolution,[status(thm)],[6367, 166, 463, 839, 6361, 6343])).
% 2.32/2.50 tff(6369,plain,((~r(s(s(s(s(s(s(s(elem!1))))))), elem!1)) | (~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~(s(s(z)) = s(s(elem!1)))) | (~r(elem!1, s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), elem!1)) | (~r(s(s(elem!1)), elem!1))), inference(lemma,lemma(discharge,[]))).
% 2.32/2.50 tff(6370,plain,
% 2.32/2.50 (~r(s(s(s(s(s(s(s(elem!1))))))), elem!1)),
% 2.32/2.50 inference(unit_resolution,[status(thm)],[6369, 6310, 839, 34, 6324, 1013, 6288])).
% 2.32/2.50 tff(6371,assumption,(~(s(s(s(s(s(s(s(elem!1))))))) = elem!1)), introduced(assumption)).
% 2.32/2.50 tff(6372,assumption,(~b(s(s(s(s(s(s(s(elem!1))))))), elem!1)), introduced(assumption)).
% 2.32/2.50 tff(6373,assumption,(~r(s(s(s(s(s(s(s(elem!1))))))), elem!1)), introduced(assumption)).
% 2.32/2.50 tff(6374,plain,
% 2.32/2.50 ($false),
% 2.32/2.50 inference(unit_resolution,[status(thm)],[4969, 79, 6373, 6372, 6371])).
% 2.32/2.50 tff(6375,plain,(r(s(s(s(s(s(s(s(elem!1))))))), elem!1) | b(s(s(s(s(s(s(s(elem!1))))))), elem!1) | (s(s(s(s(s(s(s(elem!1))))))) = elem!1)), inference(lemma,lemma(discharge,[]))).
% 2.32/2.50 tff(6376,plain,
% 2.32/2.50 (b(s(s(s(s(s(s(s(elem!1))))))), elem!1)),
% 2.32/2.50 inference(unit_resolution,[status(thm)],[6375, 6370, 6284])).
% 2.32/2.50 tff(6377,plain,
% 2.32/2.50 (~b(s(s(s(s(s(s(s(elem!1))))))), s(z))),
% 2.32/2.50 inference(unit_resolution,[status(thm)],[4946, 166, 5417, 637, 6376])).
% 2.32/2.50 tff(6378,plain,
% 2.32/2.50 (~(s(s(s(s(s(s(s(elem!1))))))) = s(z))),
% 2.32/2.50 inference(unit_resolution,[status(thm)],[4900, 620])).
% 2.32/2.50 tff(6379,plain,
% 2.32/2.50 (r(s(s(s(s(s(s(s(elem!1))))))), s(z))),
% 2.32/2.50 inference(unit_resolution,[status(thm)],[4951, 79, 6378, 6377])).
% 2.32/2.50 tff(6380,plain,
% 2.32/2.50 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(z), s(s(elem!1)))) | (~b(s(z), elem!1)) | (~b(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~b(elem!1, s(s(s(s(elem!1)))))) | (~b(s(z), s(s(s(s(elem!1)))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(z), s(s(elem!1)))) | (~b(s(z), elem!1)) | (~b(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~b(elem!1, s(s(s(s(elem!1)))))) | (~b(s(z), s(s(s(s(elem!1)))))))),
% 2.32/2.50 inference(rewrite,[status(thm)],[])).
% 2.32/2.50 tff(6381,plain,
% 2.32/2.50 (((~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(z), s(s(elem!1)))) | (~b(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~b(elem!1, s(s(s(s(elem!1)))))) | (~b(s(z), s(s(s(s(elem!1)))))) | (~b(s(z), elem!1))) <=> ((~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(z), s(s(elem!1)))) | (~b(s(z), elem!1)) | (~b(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~b(elem!1, s(s(s(s(elem!1)))))) | (~b(s(z), s(s(s(s(elem!1)))))))),
% 2.32/2.50 inference(rewrite,[status(thm)],[])).
% 2.32/2.50 tff(6382,plain,
% 2.32/2.50 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(z), s(s(elem!1)))) | (~b(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~b(elem!1, s(s(s(s(elem!1)))))) | (~b(s(z), s(s(s(s(elem!1)))))) | (~b(s(z), elem!1)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(z), s(s(elem!1)))) | (~b(s(z), elem!1)) | (~b(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~b(elem!1, s(s(s(s(elem!1)))))) | (~b(s(z), s(s(s(s(elem!1))))))))),
% 2.32/2.50 inference(monotonicity,[status(thm)],[6381])).
% 2.32/2.50 tff(6383,plain,
% 2.32/2.50 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(z), s(s(elem!1)))) | (~b(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~b(elem!1, s(s(s(s(elem!1)))))) | (~b(s(z), s(s(s(s(elem!1)))))) | (~b(s(z), elem!1)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(z), s(s(elem!1)))) | (~b(s(z), elem!1)) | (~b(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~b(elem!1, s(s(s(s(elem!1)))))) | (~b(s(z), s(s(s(s(elem!1)))))))),
% 2.32/2.50 inference(transitivity,[status(thm)],[6382, 6380])).
% 2.32/2.50 tff(6384,plain,
% 2.32/2.50 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(z), s(s(elem!1)))) | (~b(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~b(elem!1, s(s(s(s(elem!1)))))) | (~b(s(z), s(s(s(s(elem!1)))))) | (~b(s(z), elem!1)))),
% 2.32/2.50 inference(quant_inst,[status(thm)],[])).
% 2.32/2.50 tff(6385,plain,
% 2.32/2.50 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(z), s(s(elem!1)))) | (~b(s(z), elem!1)) | (~b(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~b(elem!1, s(s(s(s(elem!1)))))) | (~b(s(z), s(s(s(s(elem!1))))))),
% 2.32/2.50 inference(modus_ponens,[status(thm)],[6384, 6383])).
% 2.32/2.50 tff(6386,plain,
% 2.32/2.50 ($false),
% 2.32/2.50 inference(unit_resolution,[status(thm)],[6385, 166, 376, 839, 642, 1327, 1108, 1107])).
% 2.32/2.50 tff(6387,plain,((~b(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~b(s(z), s(s(elem!1)))) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(z), elem!1)) | (~b(s(z), s(s(s(s(elem!1)))))) | (~b(elem!1, s(s(s(s(elem!1))))))), inference(lemma,lemma(discharge,[]))).
% 2.32/2.50 tff(6388,plain,
% 2.32/2.50 (~b(s(z), s(s(s(s(elem!1)))))),
% 2.32/2.50 inference(unit_resolution,[status(thm)],[6387, 6314, 637, 376, 839, 6308])).
% 2.32/2.50 tff(6389,plain,
% 2.32/2.50 (r(s(z), s(s(s(s(elem!1)))))),
% 2.32/2.50 inference(unit_resolution,[status(thm)],[681, 6388])).
% 2.32/2.50 tff(6390,plain,
% 2.32/2.50 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(s(elem!1)))) | (~r(s(s(elem!1)), elem!1)) | (~r(s(s(s(s(elem!1)))), s(s(elem!1)))) | (~r(s(s(s(s(elem!1)))), elem!1)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(elem!1, s(s(elem!1)))) | (~r(s(s(elem!1)), elem!1)) | (~r(s(s(s(s(elem!1)))), s(s(elem!1)))) | (~r(s(s(s(s(elem!1)))), elem!1)))),
% 2.32/2.50 inference(rewrite,[status(thm)],[])).
% 2.32/2.50 tff(6391,plain,
% 2.32/2.50 (((~r(s(s(elem!1)), elem!1)) | (~r(elem!1, s(s(elem!1)))) | (~r(s(s(s(s(elem!1)))), s(s(elem!1)))) | (~r(s(s(s(s(elem!1)))), elem!1))) <=> ((~r(elem!1, s(s(elem!1)))) | (~r(s(s(elem!1)), elem!1)) | (~r(s(s(s(s(elem!1)))), s(s(elem!1)))) | (~r(s(s(s(s(elem!1)))), elem!1)))),
% 2.32/2.50 inference(rewrite,[status(thm)],[])).
% 2.32/2.50 tff(6392,plain,
% 2.32/2.50 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(elem!1)), elem!1)) | (~r(elem!1, s(s(elem!1)))) | (~r(s(s(s(s(elem!1)))), s(s(elem!1)))) | (~r(s(s(s(s(elem!1)))), elem!1)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(s(elem!1)))) | (~r(s(s(elem!1)), elem!1)) | (~r(s(s(s(s(elem!1)))), s(s(elem!1)))) | (~r(s(s(s(s(elem!1)))), elem!1))))),
% 2.32/2.50 inference(monotonicity,[status(thm)],[6391])).
% 2.32/2.50 tff(6393,plain,
% 2.32/2.50 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(elem!1)), elem!1)) | (~r(elem!1, s(s(elem!1)))) | (~r(s(s(s(s(elem!1)))), s(s(elem!1)))) | (~r(s(s(s(s(elem!1)))), elem!1)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(elem!1, s(s(elem!1)))) | (~r(s(s(elem!1)), elem!1)) | (~r(s(s(s(s(elem!1)))), s(s(elem!1)))) | (~r(s(s(s(s(elem!1)))), elem!1)))),
% 2.32/2.50 inference(transitivity,[status(thm)],[6392, 6390])).
% 2.32/2.50 tff(6394,plain,
% 2.32/2.50 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(elem!1)), elem!1)) | (~r(elem!1, s(s(elem!1)))) | (~r(s(s(s(s(elem!1)))), s(s(elem!1)))) | (~r(s(s(s(s(elem!1)))), elem!1)))),
% 2.32/2.50 inference(quant_inst,[status(thm)],[])).
% 2.32/2.50 tff(6395,plain,
% 2.32/2.50 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(elem!1, s(s(elem!1)))) | (~r(s(s(elem!1)), elem!1)) | (~r(s(s(s(s(elem!1)))), s(s(elem!1)))) | (~r(s(s(s(s(elem!1)))), elem!1))),
% 2.32/2.50 inference(modus_ponens,[status(thm)],[6394, 6393])).
% 2.32/2.50 tff(6396,plain,
% 2.32/2.50 (~r(s(s(s(s(elem!1)))), elem!1)),
% 2.32/2.50 inference(unit_resolution,[status(thm)],[6395, 197, 6288, 6312, 1027])).
% 2.32/2.50 tff(6397,plain,
% 2.32/2.50 (b(s(s(s(s(elem!1)))), elem!1)),
% 2.32/2.50 inference(unit_resolution,[status(thm)],[719, 6396, 627])).
% 2.32/2.50 tff(6398,plain,
% 2.32/2.50 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(elem!1, s(z))) | (~b(s(z), s(s(elem!1)))) | (~b(s(s(s(s(elem!1)))), elem!1)) | (~b(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~b(s(s(s(s(elem!1)))), s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(elem!1, s(z))) | (~b(s(z), s(s(elem!1)))) | (~b(s(s(s(s(elem!1)))), elem!1)) | (~b(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~b(s(s(s(s(elem!1)))), s(z))))),
% 2.32/2.50 inference(rewrite,[status(thm)],[])).
% 2.32/2.50 tff(6399,plain,
% 2.32/2.50 (((~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~b(s(z), s(s(elem!1)))) | (~b(elem!1, s(z))) | (~b(s(s(s(s(elem!1)))), s(z))) | (~b(s(s(s(s(elem!1)))), elem!1))) <=> ((~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(elem!1, s(z))) | (~b(s(z), s(s(elem!1)))) | (~b(s(s(s(s(elem!1)))), elem!1)) | (~b(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~b(s(s(s(s(elem!1)))), s(z))))),
% 2.32/2.50 inference(rewrite,[status(thm)],[])).
% 2.32/2.50 tff(6400,plain,
% 2.32/2.50 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~b(s(z), s(s(elem!1)))) | (~b(elem!1, s(z))) | (~b(s(s(s(s(elem!1)))), s(z))) | (~b(s(s(s(s(elem!1)))), elem!1)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(elem!1, s(z))) | (~b(s(z), s(s(elem!1)))) | (~b(s(s(s(s(elem!1)))), elem!1)) | (~b(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~b(s(s(s(s(elem!1)))), s(z)))))),
% 2.32/2.50 inference(monotonicity,[status(thm)],[6399])).
% 2.32/2.50 tff(6401,plain,
% 2.32/2.50 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~b(s(z), s(s(elem!1)))) | (~b(elem!1, s(z))) | (~b(s(s(s(s(elem!1)))), s(z))) | (~b(s(s(s(s(elem!1)))), elem!1)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(elem!1, s(z))) | (~b(s(z), s(s(elem!1)))) | (~b(s(s(s(s(elem!1)))), elem!1)) | (~b(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~b(s(s(s(s(elem!1)))), s(z))))),
% 2.32/2.50 inference(transitivity,[status(thm)],[6400, 6398])).
% 2.32/2.50 tff(6402,plain,
% 2.32/2.50 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~b(s(z), s(s(elem!1)))) | (~b(elem!1, s(z))) | (~b(s(s(s(s(elem!1)))), s(z))) | (~b(s(s(s(s(elem!1)))), elem!1)))),
% 2.32/2.50 inference(quant_inst,[status(thm)],[])).
% 2.32/2.50 tff(6403,plain,
% 2.32/2.50 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(elem!1, s(z))) | (~b(s(z), s(s(elem!1)))) | (~b(s(s(s(s(elem!1)))), elem!1)) | (~b(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~b(s(s(s(s(elem!1)))), s(z)))),
% 2.32/2.50 inference(modus_ponens,[status(thm)],[6402, 6401])).
% 2.32/2.50 tff(6404,plain,
% 2.32/2.50 ((~b(s(s(s(s(elem!1)))), elem!1)) | (~b(s(s(s(s(elem!1)))), s(z)))),
% 2.32/2.50 inference(unit_resolution,[status(thm)],[6403, 166, 376, 6310, 5417, 6308])).
% 2.32/2.50 tff(6405,plain,
% 2.32/2.50 (~b(s(s(s(s(elem!1)))), s(z))),
% 2.32/2.50 inference(unit_resolution,[status(thm)],[6404, 6397])).
% 2.32/2.50 tff(6406,plain,
% 2.32/2.50 (r(s(s(s(s(elem!1)))), s(z))),
% 2.32/2.50 inference(unit_resolution,[status(thm)],[661, 6405])).
% 2.32/2.50 tff(6407,plain,
% 2.32/2.50 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(s(s(s(elem!1)))))) | (~r(s(s(s(s(elem!1)))), s(z))) | (~r(s(s(s(s(elem!1)))), s(s(s(s(s(s(s(elem!1))))))))) | (~r(s(s(s(s(s(s(s(elem!1))))))), s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(z), s(s(s(s(elem!1)))))) | (~r(s(s(s(s(elem!1)))), s(z))) | (~r(s(s(s(s(elem!1)))), s(s(s(s(s(s(s(elem!1))))))))) | (~r(s(s(s(s(s(s(s(elem!1))))))), s(z))))),
% 2.32/2.50 inference(rewrite,[status(thm)],[])).
% 2.32/2.50 tff(6408,plain,
% 2.32/2.50 (((~r(s(z), s(s(s(s(elem!1)))))) | (~r(s(s(s(s(s(s(s(elem!1))))))), s(z))) | (~r(s(s(s(s(elem!1)))), s(z))) | (~r(s(s(s(s(elem!1)))), s(s(s(s(s(s(s(elem!1)))))))))) <=> ((~r(s(z), s(s(s(s(elem!1)))))) | (~r(s(s(s(s(elem!1)))), s(z))) | (~r(s(s(s(s(elem!1)))), s(s(s(s(s(s(s(elem!1))))))))) | (~r(s(s(s(s(s(s(s(elem!1))))))), s(z))))),
% 2.32/2.51 inference(rewrite,[status(thm)],[])).
% 2.32/2.51 tff(6409,plain,
% 2.32/2.51 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(s(s(s(elem!1)))))) | (~r(s(s(s(s(s(s(s(elem!1))))))), s(z))) | (~r(s(s(s(s(elem!1)))), s(z))) | (~r(s(s(s(s(elem!1)))), s(s(s(s(s(s(s(elem!1))))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(s(s(s(elem!1)))))) | (~r(s(s(s(s(elem!1)))), s(z))) | (~r(s(s(s(s(elem!1)))), s(s(s(s(s(s(s(elem!1))))))))) | (~r(s(s(s(s(s(s(s(elem!1))))))), s(z)))))),
% 2.32/2.51 inference(monotonicity,[status(thm)],[6408])).
% 2.32/2.51 tff(6410,plain,
% 2.32/2.51 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(s(s(s(elem!1)))))) | (~r(s(s(s(s(s(s(s(elem!1))))))), s(z))) | (~r(s(s(s(s(elem!1)))), s(z))) | (~r(s(s(s(s(elem!1)))), s(s(s(s(s(s(s(elem!1))))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(z), s(s(s(s(elem!1)))))) | (~r(s(s(s(s(elem!1)))), s(z))) | (~r(s(s(s(s(elem!1)))), s(s(s(s(s(s(s(elem!1))))))))) | (~r(s(s(s(s(s(s(s(elem!1))))))), s(z))))),
% 2.32/2.51 inference(transitivity,[status(thm)],[6409, 6407])).
% 2.32/2.51 tff(6411,plain,
% 2.32/2.51 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(s(s(s(elem!1)))))) | (~r(s(s(s(s(s(s(s(elem!1))))))), s(z))) | (~r(s(s(s(s(elem!1)))), s(z))) | (~r(s(s(s(s(elem!1)))), s(s(s(s(s(s(s(elem!1))))))))))),
% 2.32/2.51 inference(quant_inst,[status(thm)],[])).
% 2.32/2.51 tff(6412,plain,
% 2.32/2.51 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(z), s(s(s(s(elem!1)))))) | (~r(s(s(s(s(elem!1)))), s(z))) | (~r(s(s(s(s(elem!1)))), s(s(s(s(s(s(s(elem!1))))))))) | (~r(s(s(s(s(s(s(s(elem!1))))))), s(z)))),
% 2.32/2.51 inference(modus_ponens,[status(thm)],[6411, 6410])).
% 2.32/2.51 tff(6413,plain,
% 2.32/2.51 (~r(s(s(s(s(elem!1)))), s(s(s(s(s(s(s(elem!1))))))))),
% 2.32/2.51 inference(unit_resolution,[status(thm)],[6412, 197, 6406, 6389, 6379])).
% 2.32/2.51 tff(6414,plain,
% 2.32/2.51 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(z))) | (~b(s(z), elem!1)) | (~b(s(s(s(s(elem!1)))), elem!1)) | (~b(s(s(s(s(s(s(s(elem!1))))))), elem!1)) | (~b(s(s(s(s(elem!1)))), s(s(s(s(s(s(s(elem!1))))))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(z))) | (~b(s(z), elem!1)) | (~b(s(s(s(s(elem!1)))), elem!1)) | (~b(s(s(s(s(s(s(s(elem!1))))))), elem!1)) | (~b(s(s(s(s(elem!1)))), s(s(s(s(s(s(s(elem!1))))))))))),
% 2.32/2.51 inference(rewrite,[status(thm)],[])).
% 2.32/2.51 tff(6415,plain,
% 2.32/2.51 (((~b(s(z), elem!1)) | (~b(s(s(s(s(elem!1)))), elem!1)) | (~b(elem!1, s(z))) | (~b(s(s(s(s(s(s(s(elem!1))))))), elem!1)) | (~b(s(s(s(s(elem!1)))), elem!1)) | (~b(s(s(s(s(elem!1)))), s(s(s(s(s(s(s(elem!1)))))))))) <=> ((~b(elem!1, s(z))) | (~b(s(z), elem!1)) | (~b(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(elem!1)))), s(s(s(s(s(s(s(elem!1))))))))))),
% 2.32/2.51 inference(rewrite,[status(thm)],[])).
% 2.32/2.51 tff(6416,plain,
% 2.32/2.51 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), elem!1)) | (~b(s(s(s(s(elem!1)))), elem!1)) | (~b(elem!1, s(z))) | (~b(s(s(s(s(s(s(s(elem!1))))))), elem!1)) | (~b(s(s(s(s(elem!1)))), elem!1)) | (~b(s(s(s(s(elem!1)))), s(s(s(s(s(s(s(elem!1))))))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(z))) | (~b(s(z), elem!1)) | (~b(s(s(s(s(elem!1)))), elem!1)) | (~b(s(s(s(s(s(s(s(elem!1))))))), elem!1)) | (~b(s(s(s(s(elem!1)))), s(s(s(s(s(s(s(elem!1)))))))))))),
% 2.32/2.51 inference(monotonicity,[status(thm)],[6415])).
% 2.32/2.51 tff(6417,plain,
% 2.32/2.51 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), elem!1)) | (~b(s(s(s(s(elem!1)))), elem!1)) | (~b(elem!1, s(z))) | (~b(s(s(s(s(s(s(s(elem!1))))))), elem!1)) | (~b(s(s(s(s(elem!1)))), elem!1)) | (~b(s(s(s(s(elem!1)))), s(s(s(s(s(s(s(elem!1))))))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(z))) | (~b(s(z), elem!1)) | (~b(s(s(s(s(elem!1)))), elem!1)) | (~b(s(s(s(s(s(s(s(elem!1))))))), elem!1)) | (~b(s(s(s(s(elem!1)))), s(s(s(s(s(s(s(elem!1))))))))))),
% 2.32/2.51 inference(transitivity,[status(thm)],[6416, 6414])).
% 2.32/2.51 tff(6418,plain,
% 2.32/2.51 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), elem!1)) | (~b(s(s(s(s(elem!1)))), elem!1)) | (~b(elem!1, s(z))) | (~b(s(s(s(s(s(s(s(elem!1))))))), elem!1)) | (~b(s(s(s(s(elem!1)))), elem!1)) | (~b(s(s(s(s(elem!1)))), s(s(s(s(s(s(s(elem!1))))))))))),
% 2.32/2.51 inference(quant_inst,[status(thm)],[])).
% 2.32/2.51 tff(6419,plain,
% 2.32/2.51 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(z))) | (~b(s(z), elem!1)) | (~b(s(s(s(s(elem!1)))), elem!1)) | (~b(s(s(s(s(s(s(s(elem!1))))))), elem!1)) | (~b(s(s(s(s(elem!1)))), s(s(s(s(s(s(s(elem!1)))))))))),
% 2.32/2.51 inference(modus_ponens,[status(thm)],[6418, 6417])).
% 2.32/2.51 tff(6420,plain,
% 2.32/2.51 (~b(s(s(s(s(elem!1)))), s(s(s(s(s(s(s(elem!1))))))))),
% 2.32/2.51 inference(unit_resolution,[status(thm)],[6419, 166, 5417, 637, 6397, 6376])).
% 2.32/2.51 tff(6421,plain,
% 2.32/2.51 (((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((s(s(s(s(elem!1)))) = s(s(s(s(s(s(s(elem!1)))))))) | b(s(s(s(s(elem!1)))), s(s(s(s(s(s(s(elem!1)))))))) | r(s(s(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(s(s(elem!1)))) = s(s(s(s(s(s(s(elem!1)))))))) | b(s(s(s(s(elem!1)))), s(s(s(s(s(s(s(elem!1)))))))) | r(s(s(s(s(elem!1)))), s(s(s(s(s(s(s(elem!1)))))))))),
% 2.32/2.51 inference(rewrite,[status(thm)],[])).
% 2.32/2.51 tff(6422,plain,
% 2.32/2.51 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((s(s(s(s(elem!1)))) = s(s(s(s(s(s(s(elem!1)))))))) | b(s(s(s(s(elem!1)))), s(s(s(s(s(s(s(elem!1)))))))) | r(s(s(s(s(elem!1)))), s(s(s(s(s(s(s(elem!1)))))))))),
% 2.32/2.51 inference(quant_inst,[status(thm)],[])).
% 2.32/2.51 tff(6423,plain,
% 2.32/2.51 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (s(s(s(s(elem!1)))) = s(s(s(s(s(s(s(elem!1)))))))) | b(s(s(s(s(elem!1)))), s(s(s(s(s(s(s(elem!1)))))))) | r(s(s(s(s(elem!1)))), s(s(s(s(s(s(s(elem!1))))))))),
% 2.32/2.51 inference(modus_ponens,[status(thm)],[6422, 6421])).
% 2.32/2.51 tff(6424,plain,
% 2.32/2.51 ((s(s(s(s(elem!1)))) = s(s(s(s(s(s(s(elem!1)))))))) | r(s(s(s(s(elem!1)))), s(s(s(s(s(s(s(elem!1))))))))),
% 2.32/2.51 inference(unit_resolution,[status(thm)],[6423, 79, 6420])).
% 2.32/2.51 tff(6425,plain,
% 2.32/2.51 ($false),
% 2.32/2.51 inference(unit_resolution,[status(thm)],[6424, 6413, 6279])).
% 2.32/2.51 tff(6426,plain,((~b(s(s(z)), s(z))) | (~(s(s(z)) = s(s(elem!1)))) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~r(s(s(s(elem!1))), elem!1)) | (~b(s(z), s(s(elem!1)))) | (~r(elem!1, s(s(elem!1)))) | (~r(s(s(s(elem!1))), s(z))) | (~r(z, s(s(z)))) | (~b(s(s(s(z))), s(s(z)))) | (~b(z, s(z))) | (~b(s(z), z))), inference(lemma,lemma(discharge,[]))).
% 2.32/2.51 tff(6427,plain,
% 2.32/2.51 (~b(s(s(z)), s(z))),
% 2.32/2.51 inference(unit_resolution,[status(thm)],[6426, 6252, 6120, 6136, 6207, 6271, 350, 152, 6221, 118, 5700])).
% 2.32/2.51 tff(6428,plain,
% 2.32/2.51 (~b(s(s(elem!1)), s(z))),
% 2.32/2.51 inference(unit_resolution,[status(thm)],[3938, 6427, 6120])).
% 2.32/2.51 tff(6429,plain,
% 2.32/2.51 (r(s(s(elem!1)), s(z))),
% 2.32/2.51 inference(unit_resolution,[status(thm)],[1912, 6428])).
% 2.32/2.51 tff(6430,plain,
% 2.32/2.51 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(s(s(s(elem!1)))))) | (~r(elem!1, s(s(elem!1)))) | (~r(s(s(elem!1)), s(z))) | (~r(s(s(s(s(elem!1)))), s(s(elem!1)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(elem!1, s(s(s(s(elem!1)))))) | (~r(elem!1, s(s(elem!1)))) | (~r(s(s(elem!1)), s(z))) | (~r(s(s(s(s(elem!1)))), s(s(elem!1)))))),
% 2.32/2.51 inference(rewrite,[status(thm)],[])).
% 2.32/2.51 tff(6431,plain,
% 2.32/2.51 (((~r(s(s(elem!1)), s(z))) | (~r(s(s(s(s(elem!1)))), s(s(elem!1)))) | (~r(elem!1, s(s(elem!1)))) | (~r(elem!1, s(s(s(s(elem!1))))))) <=> ((~r(elem!1, s(s(s(s(elem!1)))))) | (~r(elem!1, s(s(elem!1)))) | (~r(s(s(elem!1)), s(z))) | (~r(s(s(s(s(elem!1)))), s(s(elem!1)))))),
% 2.32/2.51 inference(rewrite,[status(thm)],[])).
% 2.32/2.51 tff(6432,plain,
% 2.32/2.51 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(elem!1)), s(z))) | (~r(s(s(s(s(elem!1)))), s(s(elem!1)))) | (~r(elem!1, s(s(elem!1)))) | (~r(elem!1, s(s(s(s(elem!1)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(s(s(s(elem!1)))))) | (~r(elem!1, s(s(elem!1)))) | (~r(s(s(elem!1)), s(z))) | (~r(s(s(s(s(elem!1)))), s(s(elem!1))))))),
% 2.32/2.51 inference(monotonicity,[status(thm)],[6431])).
% 2.32/2.51 tff(6433,plain,
% 2.32/2.51 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(elem!1)), s(z))) | (~r(s(s(s(s(elem!1)))), s(s(elem!1)))) | (~r(elem!1, s(s(elem!1)))) | (~r(elem!1, s(s(s(s(elem!1)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(elem!1, s(s(s(s(elem!1)))))) | (~r(elem!1, s(s(elem!1)))) | (~r(s(s(elem!1)), s(z))) | (~r(s(s(s(s(elem!1)))), s(s(elem!1)))))),
% 2.32/2.51 inference(transitivity,[status(thm)],[6432, 6430])).
% 2.32/2.51 tff(6434,plain,
% 2.32/2.51 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(elem!1)), s(z))) | (~r(s(s(s(s(elem!1)))), s(s(elem!1)))) | (~r(elem!1, s(s(elem!1)))) | (~r(elem!1, s(s(s(s(elem!1)))))))),
% 2.32/2.51 inference(quant_inst,[status(thm)],[])).
% 2.32/2.51 tff(6435,plain,
% 2.32/2.51 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(elem!1, s(s(s(s(elem!1)))))) | (~r(elem!1, s(s(elem!1)))) | (~r(s(s(elem!1)), s(z))) | (~r(s(s(s(s(elem!1)))), s(s(elem!1))))),
% 2.32/2.51 inference(modus_ponens,[status(thm)],[6434, 6433])).
% 2.32/2.51 tff(6436,plain,
% 2.32/2.51 (~r(elem!1, s(s(s(s(elem!1)))))),
% 2.32/2.51 inference(unit_resolution,[status(thm)],[6435, 197, 6429, 6263, 6271])).
% 2.32/2.51 tff(6437,plain,
% 2.32/2.51 (b(elem!1, s(s(s(s(elem!1)))))),
% 2.32/2.51 inference(unit_resolution,[status(thm)],[2427, 6436, 6267])).
% 2.32/2.51 tff(6438,plain,
% 2.32/2.51 (~b(s(z), s(s(s(s(elem!1)))))),
% 2.32/2.51 inference(unit_resolution,[status(thm)],[6387, 6437, 6141, 6207, 6252, 6250])).
% 2.32/2.51 tff(6439,plain,
% 2.32/2.51 (r(s(z), s(s(s(s(elem!1)))))),
% 2.32/2.51 inference(unit_resolution,[status(thm)],[681, 6438])).
% 2.32/2.51 tff(6440,plain,
% 2.32/2.51 ((~(s(s(s(s(elem!1)))) = z)) <=> (~(s(s(s(s(elem!1)))) = elem!1))),
% 2.32/2.51 inference(monotonicity,[status(thm)],[6264])).
% 2.32/2.51 tff(6441,plain,
% 2.32/2.51 (~(s(s(s(s(elem!1)))) = elem!1)),
% 2.32/2.51 inference(modus_ponens,[status(thm)],[626, 6440])).
% 2.32/2.51 tff(6442,plain,
% 2.32/2.51 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(s(elem!1)))) | (~r(s(s(elem!1)), s(z))) | (~r(s(s(s(s(elem!1)))), s(s(elem!1)))) | (~r(s(s(s(s(elem!1)))), elem!1)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(elem!1, s(s(elem!1)))) | (~r(s(s(elem!1)), s(z))) | (~r(s(s(s(s(elem!1)))), s(s(elem!1)))) | (~r(s(s(s(s(elem!1)))), elem!1)))),
% 2.32/2.51 inference(rewrite,[status(thm)],[])).
% 2.32/2.51 tff(6443,plain,
% 2.32/2.51 (((~r(s(s(elem!1)), s(z))) | (~r(elem!1, s(s(elem!1)))) | (~r(s(s(s(s(elem!1)))), s(s(elem!1)))) | (~r(s(s(s(s(elem!1)))), elem!1))) <=> ((~r(elem!1, s(s(elem!1)))) | (~r(s(s(elem!1)), s(z))) | (~r(s(s(s(s(elem!1)))), s(s(elem!1)))) | (~r(s(s(s(s(elem!1)))), elem!1)))),
% 2.32/2.51 inference(rewrite,[status(thm)],[])).
% 2.32/2.51 tff(6444,plain,
% 2.32/2.51 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(elem!1)), s(z))) | (~r(elem!1, s(s(elem!1)))) | (~r(s(s(s(s(elem!1)))), s(s(elem!1)))) | (~r(s(s(s(s(elem!1)))), elem!1)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(s(elem!1)))) | (~r(s(s(elem!1)), s(z))) | (~r(s(s(s(s(elem!1)))), s(s(elem!1)))) | (~r(s(s(s(s(elem!1)))), elem!1))))),
% 2.32/2.51 inference(monotonicity,[status(thm)],[6443])).
% 2.32/2.51 tff(6445,plain,
% 2.32/2.51 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(elem!1)), s(z))) | (~r(elem!1, s(s(elem!1)))) | (~r(s(s(s(s(elem!1)))), s(s(elem!1)))) | (~r(s(s(s(s(elem!1)))), elem!1)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(elem!1, s(s(elem!1)))) | (~r(s(s(elem!1)), s(z))) | (~r(s(s(s(s(elem!1)))), s(s(elem!1)))) | (~r(s(s(s(s(elem!1)))), elem!1)))),
% 2.32/2.51 inference(transitivity,[status(thm)],[6444, 6442])).
% 2.32/2.51 tff(6446,plain,
% 2.32/2.51 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(elem!1)), s(z))) | (~r(elem!1, s(s(elem!1)))) | (~r(s(s(s(s(elem!1)))), s(s(elem!1)))) | (~r(s(s(s(s(elem!1)))), elem!1)))),
% 2.32/2.51 inference(quant_inst,[status(thm)],[])).
% 2.32/2.51 tff(6447,plain,
% 2.32/2.51 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(elem!1, s(s(elem!1)))) | (~r(s(s(elem!1)), s(z))) | (~r(s(s(s(s(elem!1)))), s(s(elem!1)))) | (~r(s(s(s(s(elem!1)))), elem!1))),
% 2.32/2.51 inference(modus_ponens,[status(thm)],[6446, 6445])).
% 2.32/2.51 tff(6448,plain,
% 2.32/2.51 (~r(s(s(s(s(elem!1)))), elem!1)),
% 2.32/2.51 inference(unit_resolution,[status(thm)],[6447, 197, 6429, 6263, 6271])).
% 2.32/2.51 tff(6449,plain,
% 2.32/2.51 (b(s(s(s(s(elem!1)))), elem!1)),
% 2.32/2.51 inference(unit_resolution,[status(thm)],[719, 6448, 6441])).
% 2.32/2.51 tff(6450,plain,
% 2.32/2.51 ((~b(s(s(s(s(elem!1)))), elem!1)) | (~b(s(s(s(s(elem!1)))), s(z)))),
% 2.32/2.51 inference(unit_resolution,[status(thm)],[6403, 166, 6207, 6256, 6139, 6250])).
% 2.32/2.51 tff(6451,plain,
% 2.32/2.51 (~b(s(s(s(s(elem!1)))), s(z))),
% 2.32/2.51 inference(unit_resolution,[status(thm)],[6450, 6449])).
% 2.32/2.51 tff(6452,plain,
% 2.32/2.51 (r(s(s(s(s(elem!1)))), s(z))),
% 2.32/2.51 inference(unit_resolution,[status(thm)],[661, 6451])).
% 2.32/2.51 tff(6453,plain,
% 2.32/2.51 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(elem!1)), s(z))) | (~r(s(z), s(s(s(s(elem!1)))))) | (~r(s(s(s(s(elem!1)))), s(z))) | (~r(s(s(s(s(elem!1)))), s(s(elem!1)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(elem!1)), s(z))) | (~r(s(z), s(s(s(s(elem!1)))))) | (~r(s(s(s(s(elem!1)))), s(z))) | (~r(s(s(s(s(elem!1)))), s(s(elem!1)))))),
% 2.32/2.51 inference(rewrite,[status(thm)],[])).
% 2.32/2.51 tff(6454,plain,
% 2.32/2.51 (((~r(s(z), s(s(s(s(elem!1)))))) | (~r(s(s(elem!1)), s(z))) | (~r(s(s(s(s(elem!1)))), s(z))) | (~r(s(s(s(s(elem!1)))), s(s(elem!1))))) <=> ((~r(s(s(elem!1)), s(z))) | (~r(s(z), s(s(s(s(elem!1)))))) | (~r(s(s(s(s(elem!1)))), s(z))) | (~r(s(s(s(s(elem!1)))), s(s(elem!1)))))),
% 2.32/2.51 inference(rewrite,[status(thm)],[])).
% 2.32/2.51 tff(6455,plain,
% 2.32/2.51 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(s(s(s(elem!1)))))) | (~r(s(s(elem!1)), s(z))) | (~r(s(s(s(s(elem!1)))), s(z))) | (~r(s(s(s(s(elem!1)))), s(s(elem!1)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(elem!1)), s(z))) | (~r(s(z), s(s(s(s(elem!1)))))) | (~r(s(s(s(s(elem!1)))), s(z))) | (~r(s(s(s(s(elem!1)))), s(s(elem!1))))))),
% 2.32/2.51 inference(monotonicity,[status(thm)],[6454])).
% 2.32/2.51 tff(6456,plain,
% 2.32/2.51 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(s(s(s(elem!1)))))) | (~r(s(s(elem!1)), s(z))) | (~r(s(s(s(s(elem!1)))), s(z))) | (~r(s(s(s(s(elem!1)))), s(s(elem!1)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(elem!1)), s(z))) | (~r(s(z), s(s(s(s(elem!1)))))) | (~r(s(s(s(s(elem!1)))), s(z))) | (~r(s(s(s(s(elem!1)))), s(s(elem!1)))))),
% 2.32/2.51 inference(transitivity,[status(thm)],[6455, 6453])).
% 2.32/2.51 tff(6457,plain,
% 2.32/2.51 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(s(s(s(elem!1)))))) | (~r(s(s(elem!1)), s(z))) | (~r(s(s(s(s(elem!1)))), s(z))) | (~r(s(s(s(s(elem!1)))), s(s(elem!1)))))),
% 2.32/2.51 inference(quant_inst,[status(thm)],[])).
% 2.32/2.51 tff(6458,plain,
% 2.32/2.51 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(elem!1)), s(z))) | (~r(s(z), s(s(s(s(elem!1)))))) | (~r(s(s(s(s(elem!1)))), s(z))) | (~r(s(s(s(s(elem!1)))), s(s(elem!1))))),
% 2.32/2.51 inference(modus_ponens,[status(thm)],[6457, 6456])).
% 2.32/2.51 tff(6459,plain,
% 2.32/2.51 ($false),
% 2.32/2.51 inference(unit_resolution,[status(thm)],[6458, 197, 6429, 6452, 6439, 6263])).
% 2.32/2.51 tff(6460,plain,((s(s(elem!1)) = s(s(s(elem!1)))) | (~r(s(s(s(elem!1))), s(z))) | (~b(z, s(z))) | (~r(s(s(s(elem!1))), z)) | b(z, s(s(z)))), inference(lemma,lemma(discharge,[]))).
% 2.32/2.51 tff(6461,plain,
% 2.32/2.51 (s(s(elem!1)) = s(s(s(elem!1)))),
% 2.32/2.51 inference(unit_resolution,[status(thm)],[6460, 5696, 118, 153, 125])).
% 2.32/2.51 tff(6462,plain,
% 2.32/2.51 (s(s(s(elem!1))) = s(s(elem!1))),
% 2.32/2.51 inference(symmetry,[status(thm)],[6461])).
% 2.32/2.51 tff(6463,plain,
% 2.32/2.51 (s(s(s(s(elem!1)))) = s(s(s(elem!1)))),
% 2.32/2.51 inference(monotonicity,[status(thm)],[6462])).
% 2.32/2.51 tff(6464,plain,
% 2.32/2.51 ((s(s(s(s(elem!1)))) = s(s(s(z)))) <=> (s(s(s(elem!1))) = s(s(s(z))))),
% 2.32/2.51 inference(monotonicity,[status(thm)],[6463])).
% 2.32/2.51 tff(6465,plain,
% 2.32/2.51 ((~(s(s(s(s(elem!1)))) = s(s(s(z))))) <=> (~(s(s(s(elem!1))) = s(s(s(z)))))),
% 2.32/2.51 inference(monotonicity,[status(thm)],[6464])).
% 2.32/2.51 tff(6466,plain,
% 2.32/2.51 (~(s(s(s(elem!1))) = s(s(s(z))))),
% 2.32/2.51 inference(modus_ponens,[status(thm)],[5112, 6465])).
% 2.32/2.51 tff(6467,plain,
% 2.32/2.51 (~b(s(s(elem!1)), s(z))),
% 2.32/2.51 inference(unit_resolution,[status(thm)],[3849, 6461, 5695])).
% 2.32/2.51 tff(6468,plain,
% 2.32/2.51 (r(s(s(elem!1)), s(z))),
% 2.32/2.51 inference(unit_resolution,[status(thm)],[1912, 6467])).
% 2.32/2.51 tff(6469,plain,
% 2.32/2.51 (~r(s(z), z)),
% 2.32/2.51 inference(unit_resolution,[status(thm)],[5698, 153, 152, 5696])).
% 2.32/2.51 tff(6470,plain,
% 2.32/2.51 (b(s(z), z)),
% 2.32/2.51 inference(unit_resolution,[status(thm)],[230, 6469])).
% 2.32/2.51 tff(6471,plain,
% 2.32/2.51 (s(s(s(s(elem!1)))) = s(s(s(elem!1)))),
% 2.32/2.51 inference(monotonicity,[status(thm)],[2591])).
% 2.32/2.51 tff(6472,plain,
% 2.32/2.51 ((s(s(s(s(elem!1)))) = s(s(s(z)))) <=> (s(s(s(elem!1))) = s(s(s(z))))),
% 2.32/2.51 inference(monotonicity,[status(thm)],[6471])).
% 2.32/2.51 tff(6473,plain,
% 2.32/2.51 ((~(s(s(s(s(elem!1)))) = s(s(s(z))))) <=> (~(s(s(s(elem!1))) = s(s(s(z)))))),
% 2.32/2.51 inference(monotonicity,[status(thm)],[6472])).
% 2.32/2.51 tff(6474,plain,
% 2.32/2.51 (~(s(s(s(elem!1))) = s(s(s(z))))),
% 2.32/2.51 inference(modus_ponens,[status(thm)],[5112, 6473])).
% 2.32/2.51 tff(6475,plain,
% 2.32/2.51 (~b(s(s(z)), s(z))),
% 2.32/2.51 inference(unit_resolution,[status(thm)],[181, 122, 118, 5943])).
% 2.32/2.51 tff(6476,plain,
% 2.32/2.51 (r(s(s(z)), s(z))),
% 2.32/2.51 inference(unit_resolution,[status(thm)],[308, 6475])).
% 2.32/2.51 tff(6477,plain,
% 2.32/2.51 (~b(s(z), s(s(z)))),
% 2.32/2.51 inference(unit_resolution,[status(thm)],[5910, 166, 5943, 118, 122])).
% 2.32/2.51 tff(6478,plain,
% 2.32/2.51 (r(s(z), s(s(z)))),
% 2.32/2.51 inference(unit_resolution,[status(thm)],[427, 6477])).
% 2.32/2.51 tff(6479,plain,
% 2.32/2.51 (~b(s(s(s(z))), z)),
% 2.32/2.51 inference(unit_resolution,[status(thm)],[5078, 6478, 122, 118, 5943, 6476])).
% 2.32/2.51 tff(6480,plain,
% 2.32/2.51 (r(s(s(s(z))), z)),
% 2.32/2.51 inference(unit_resolution,[status(thm)],[1713, 6479])).
% 2.32/2.51 tff(6481,plain,
% 2.32/2.51 (~r(s(s(s(elem!1))), s(s(s(z))))),
% 2.32/2.51 inference(unit_resolution,[status(thm)],[4103, 197, 154, 155, 6480])).
% 2.32/2.51 tff(6482,plain,
% 2.32/2.51 (b(s(s(s(elem!1))), s(s(s(z))))),
% 2.32/2.51 inference(unit_resolution,[status(thm)],[3574, 6481, 6474])).
% 2.32/2.51 tff(6483,plain,
% 2.32/2.51 (~r(s(s(s(z))), s(s(s(elem!1))))),
% 2.32/2.51 inference(unit_resolution,[status(thm)],[4120, 197, 154, 155, 6480])).
% 2.32/2.51 tff(6484,plain,
% 2.32/2.51 (~r(s(s(s(z))), elem!1)),
% 2.32/2.51 inference(modus_ponens,[status(thm)],[6483, 5509])).
% 2.32/2.51 tff(6485,plain,
% 2.32/2.51 (b(s(s(s(z))), elem!1)),
% 2.32/2.51 inference(unit_resolution,[status(thm)],[2826, 6484, 4027])).
% 2.32/2.51 tff(6486,plain,
% 2.32/2.51 (b(s(s(s(z))), s(s(s(elem!1))))),
% 2.32/2.51 inference(unit_resolution,[status(thm)],[4078, 6485, 4031])).
% 2.32/2.51 tff(6487,plain,
% 2.32/2.51 (~r(s(s(z)), s(s(s(elem!1))))),
% 2.32/2.51 inference(unit_resolution,[status(thm)],[3958, 6476, 350, 311])).
% 2.32/2.51 tff(6488,plain,
% 2.32/2.51 (b(s(s(z)), s(s(s(elem!1))))),
% 2.32/2.51 inference(unit_resolution,[status(thm)],[279, 6487])).
% 2.32/2.51 tff(6489,plain,
% 2.32/2.51 (~b(s(s(s(z))), s(s(z)))),
% 2.32/2.51 inference(unit_resolution,[status(thm)],[4130, 166, 6488, 6486, 6482])).
% 2.32/2.51 tff(6490,plain,
% 2.32/2.51 (r(s(s(s(z))), s(s(z)))),
% 2.32/2.51 inference(unit_resolution,[status(thm)],[1010, 6489])).
% 2.32/2.51 tff(6491,plain,
% 2.32/2.51 ($false),
% 2.32/2.51 inference(unit_resolution,[status(thm)],[4138, 197, 155, 6476, 6490, 6480])).
% 2.32/2.51 tff(6492,plain,((~b(s(s(z)), z)) | (~r(z, s(s(z)))) | (~(s(s(elem!1)) = s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), z)) | (~b(z, s(z))) | (~r(s(s(s(elem!1))), s(z))) | (~r(s(z), s(s(elem!1))))), inference(lemma,lemma(discharge,[]))).
% 2.32/2.51 tff(6493,plain,
% 2.32/2.51 (~b(s(s(z)), z)),
% 2.32/2.51 inference(unit_resolution,[status(thm)],[6492, 311, 334, 154, 118, 350, 155])).
% 2.32/2.51 tff(6494,plain,
% 2.32/2.51 (r(s(s(z)), z)),
% 2.32/2.51 inference(unit_resolution,[status(thm)],[186, 6493])).
% 2.32/2.51 tff(6495,plain,
% 2.32/2.51 (~r(s(s(s(elem!1))), s(s(z)))),
% 2.32/2.51 inference(unit_resolution,[status(thm)],[6105, 866, 155, 154])).
% 2.32/2.51 tff(6496,plain,
% 2.32/2.51 (b(s(s(s(elem!1))), s(s(z)))),
% 2.32/2.51 inference(unit_resolution,[status(thm)],[218, 6495])).
% 2.32/2.51 tff(6497,plain,
% 2.32/2.51 (~r(s(s(s(z))), s(s(z)))),
% 2.32/2.51 inference(unit_resolution,[status(thm)],[1717, 197, 155, 866, 1733])).
% 2.32/2.51 tff(6498,plain,
% 2.32/2.51 (b(s(s(s(z))), s(s(z)))),
% 2.32/2.51 inference(unit_resolution,[status(thm)],[1010, 6497])).
% 2.32/2.51 tff(6499,plain,
% 2.32/2.51 (b(s(s(z)), s(s(s(elem!1))))),
% 2.32/2.51 inference(unit_resolution,[status(thm)],[279, 5721])).
% 2.32/2.51 tff(6500,plain,
% 2.32/2.51 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), s(s(z)))) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(s(z)), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(s(s(z))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(elem!1))), s(s(z)))) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(s(z)), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(s(s(z))))))),
% 2.32/2.51 inference(rewrite,[status(thm)],[])).
% 2.32/2.51 tff(6501,plain,
% 2.32/2.51 (((~b(s(s(s(elem!1))), s(s(z)))) | (~b(s(s(s(elem!1))), s(s(z)))) | (~b(s(s(z)), s(s(s(elem!1))))) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(s(s(elem!1))), s(s(z)))) | (~b(s(s(s(elem!1))), s(s(s(z)))))) <=> ((~b(s(s(s(elem!1))), s(s(z)))) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(s(z)), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(s(s(z))))))),
% 2.32/2.51 inference(rewrite,[status(thm)],[])).
% 2.32/2.51 tff(6502,plain,
% 2.32/2.51 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), s(s(z)))) | (~b(s(s(s(elem!1))), s(s(z)))) | (~b(s(s(z)), s(s(s(elem!1))))) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(s(s(elem!1))), s(s(z)))) | (~b(s(s(s(elem!1))), s(s(s(z))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), s(s(z)))) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(s(z)), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(s(s(z)))))))),
% 2.32/2.51 inference(monotonicity,[status(thm)],[6501])).
% 2.32/2.51 tff(6503,plain,
% 2.32/2.51 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), s(s(z)))) | (~b(s(s(s(elem!1))), s(s(z)))) | (~b(s(s(z)), s(s(s(elem!1))))) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(s(s(elem!1))), s(s(z)))) | (~b(s(s(s(elem!1))), s(s(s(z))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(elem!1))), s(s(z)))) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(s(z)), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(s(s(z))))))),
% 2.32/2.51 inference(transitivity,[status(thm)],[6502, 6500])).
% 2.32/2.51 tff(6504,plain,
% 2.32/2.51 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), s(s(z)))) | (~b(s(s(s(elem!1))), s(s(z)))) | (~b(s(s(z)), s(s(s(elem!1))))) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(s(s(elem!1))), s(s(z)))) | (~b(s(s(s(elem!1))), s(s(s(z))))))),
% 2.32/2.52 inference(quant_inst,[status(thm)],[])).
% 2.32/2.52 tff(6505,plain,
% 2.32/2.52 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(elem!1))), s(s(z)))) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(s(z)), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(s(s(z)))))),
% 2.32/2.52 inference(modus_ponens,[status(thm)],[6504, 6503])).
% 2.32/2.52 tff(6506,plain,
% 2.32/2.52 ($false),
% 2.32/2.52 inference(unit_resolution,[status(thm)],[6505, 166, 6499, 6498, 6496, 5506])).
% 2.32/2.52 tff(6507,plain,((~r(s(s(s(z))), z)) | (s(s(s(elem!1))) = s(s(s(z)))) | (~r(s(s(s(elem!1))), z)) | (~r(z, s(s(z)))) | (~r(s(s(z)), z))), inference(lemma,lemma(discharge,[]))).
% 2.32/2.52 tff(6508,plain,
% 2.32/2.52 (~r(s(s(s(z))), z)),
% 2.32/2.52 inference(unit_resolution,[status(thm)],[6507, 6494, 154, 155, 6474])).
% 2.32/2.52 tff(6509,plain,
% 2.32/2.52 (b(s(s(s(z))), z)),
% 2.32/2.52 inference(unit_resolution,[status(thm)],[1713, 6508])).
% 2.32/2.52 tff(6510,plain,
% 2.32/2.52 (~b(s(s(s(z))), s(z))),
% 2.32/2.52 inference(unit_resolution,[status(thm)],[4045, 166, 5943, 118, 6509])).
% 2.32/2.52 tff(6511,plain,
% 2.32/2.52 (r(s(s(s(z))), s(z))),
% 2.32/2.52 inference(unit_resolution,[status(thm)],[1763, 6510])).
% 2.32/2.52 tff(6512,plain,
% 2.32/2.52 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), s(s(s(z))))) | (~r(s(z), s(s(elem!1)))) | (~r(s(s(s(elem!1))), s(z))) | (~r(s(s(s(z))), s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(elem!1))), s(s(s(z))))) | (~r(s(z), s(s(elem!1)))) | (~r(s(s(s(elem!1))), s(z))) | (~r(s(s(s(z))), s(z))))),
% 2.32/2.52 inference(rewrite,[status(thm)],[])).
% 2.32/2.52 tff(6513,plain,
% 2.32/2.52 (((~r(s(z), s(s(elem!1)))) | (~r(s(s(s(z))), s(z))) | (~r(s(s(s(elem!1))), s(z))) | (~r(s(s(s(elem!1))), s(s(s(z)))))) <=> ((~r(s(s(s(elem!1))), s(s(s(z))))) | (~r(s(z), s(s(elem!1)))) | (~r(s(s(s(elem!1))), s(z))) | (~r(s(s(s(z))), s(z))))),
% 2.32/2.52 inference(rewrite,[status(thm)],[])).
% 2.32/2.52 tff(6514,plain,
% 2.32/2.52 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(s(elem!1)))) | (~r(s(s(s(z))), s(z))) | (~r(s(s(s(elem!1))), s(z))) | (~r(s(s(s(elem!1))), s(s(s(z))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), s(s(s(z))))) | (~r(s(z), s(s(elem!1)))) | (~r(s(s(s(elem!1))), s(z))) | (~r(s(s(s(z))), s(z)))))),
% 2.32/2.52 inference(monotonicity,[status(thm)],[6513])).
% 2.32/2.52 tff(6515,plain,
% 2.32/2.52 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(s(elem!1)))) | (~r(s(s(s(z))), s(z))) | (~r(s(s(s(elem!1))), s(z))) | (~r(s(s(s(elem!1))), s(s(s(z))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(elem!1))), s(s(s(z))))) | (~r(s(z), s(s(elem!1)))) | (~r(s(s(s(elem!1))), s(z))) | (~r(s(s(s(z))), s(z))))),
% 2.32/2.52 inference(transitivity,[status(thm)],[6514, 6512])).
% 2.32/2.52 tff(6516,plain,
% 2.32/2.52 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(s(elem!1)))) | (~r(s(s(s(z))), s(z))) | (~r(s(s(s(elem!1))), s(z))) | (~r(s(s(s(elem!1))), s(s(s(z))))))),
% 2.32/2.52 inference(quant_inst,[status(thm)],[])).
% 2.32/2.52 tff(6517,plain,
% 2.32/2.52 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(elem!1))), s(s(s(z))))) | (~r(s(z), s(s(elem!1)))) | (~r(s(s(s(elem!1))), s(z))) | (~r(s(s(s(z))), s(z)))),
% 2.32/2.52 inference(modus_ponens,[status(thm)],[6516, 6515])).
% 2.32/2.52 tff(6518,plain,
% 2.32/2.52 ($false),
% 2.32/2.52 inference(unit_resolution,[status(thm)],[6517, 197, 311, 350, 1746, 3183])).
% 2.32/2.52 tff(6519,plain,((~r(s(s(s(z))), s(z))) | (~r(s(z), s(s(elem!1)))) | (~r(s(s(s(elem!1))), s(z))) | (~r(s(s(s(elem!1))), s(s(s(z)))))), inference(lemma,lemma(discharge,[]))).
% 2.32/2.52 tff(6520,plain,
% 2.32/2.52 (~r(s(s(s(elem!1))), s(s(s(z))))),
% 2.32/2.52 inference(unit_resolution,[status(thm)],[6519, 6511, 350, 311])).
% 2.32/2.52 tff(6521,plain,
% 2.32/2.52 (b(s(s(s(elem!1))), s(s(s(z))))),
% 2.32/2.52 inference(unit_resolution,[status(thm)],[3574, 6520, 6474])).
% 2.32/2.52 tff(6522,plain,
% 2.32/2.52 (~b(s(z), s(s(s(z))))),
% 2.32/2.52 inference(unit_resolution,[status(thm)],[4037, 166, 5943, 118, 6509])).
% 2.32/2.52 tff(6523,plain,
% 2.32/2.52 (r(s(z), s(s(s(z))))),
% 2.32/2.52 inference(unit_resolution,[status(thm)],[1674, 6522])).
% 2.32/2.52 tff(6524,plain,
% 2.32/2.52 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(s(s(z))))) | (~r(s(s(s(elem!1))), s(z))) | (~r(s(s(s(z))), s(z))) | (~r(s(s(s(z))), s(s(s(elem!1))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(z), s(s(s(z))))) | (~r(s(s(s(elem!1))), s(z))) | (~r(s(s(s(z))), s(z))) | (~r(s(s(s(z))), s(s(s(elem!1))))))),
% 2.32/2.52 inference(rewrite,[status(thm)],[])).
% 2.32/2.52 tff(6525,plain,
% 2.32/2.52 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(s(s(z))))) | (~r(s(s(s(elem!1))), s(z))) | (~r(s(s(s(z))), s(z))) | (~r(s(s(s(z))), s(s(s(elem!1))))))),
% 2.32/2.52 inference(quant_inst,[status(thm)],[])).
% 2.32/2.52 tff(6526,plain,
% 2.32/2.52 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(z), s(s(s(z))))) | (~r(s(s(s(elem!1))), s(z))) | (~r(s(s(s(z))), s(z))) | (~r(s(s(s(z))), s(s(s(elem!1)))))),
% 2.32/2.52 inference(modus_ponens,[status(thm)],[6525, 6524])).
% 2.32/2.52 tff(6527,plain,
% 2.32/2.52 (~r(s(s(s(z))), s(s(s(elem!1))))),
% 2.32/2.52 inference(unit_resolution,[status(thm)],[6526, 197, 350, 6511, 6523])).
% 2.32/2.52 tff(6528,plain,
% 2.32/2.52 (~r(s(s(s(z))), elem!1)),
% 2.32/2.52 inference(modus_ponens,[status(thm)],[6527, 5509])).
% 2.32/2.52 tff(6529,plain,
% 2.32/2.52 (b(s(s(s(z))), elem!1)),
% 2.32/2.52 inference(unit_resolution,[status(thm)],[2826, 6528, 4027])).
% 2.32/2.52 tff(6530,plain,
% 2.32/2.52 (b(s(s(s(z))), s(s(s(elem!1))))),
% 2.32/2.52 inference(unit_resolution,[status(thm)],[4078, 6529, 4031])).
% 2.32/2.52 tff(6531,plain,
% 2.32/2.52 (~r(s(s(z)), s(s(s(elem!1))))),
% 2.32/2.52 inference(unit_resolution,[status(thm)],[5720, 197, 154, 155, 6494])).
% 2.32/2.52 tff(6532,plain,
% 2.32/2.52 (b(s(s(z)), s(s(s(elem!1))))),
% 2.32/2.52 inference(unit_resolution,[status(thm)],[279, 6531])).
% 2.32/2.52 tff(6533,plain,
% 2.32/2.52 (~b(s(s(z)), s(s(s(z))))),
% 2.32/2.52 inference(unit_resolution,[status(thm)],[5519, 166, 6532, 6530, 6521])).
% 2.32/2.52 tff(6534,plain,
% 2.32/2.52 (r(s(s(z)), s(s(s(z))))),
% 2.32/2.52 inference(unit_resolution,[status(thm)],[1730, 6533])).
% 2.32/2.52 tff(6535,plain,
% 2.32/2.52 (~r(s(s(s(elem!1))), s(s(z)))),
% 2.32/2.52 inference(unit_resolution,[status(thm)],[6105, 6494, 155, 154])).
% 2.32/2.52 tff(6536,plain,
% 2.32/2.52 (b(s(s(s(elem!1))), s(s(z)))),
% 2.32/2.52 inference(unit_resolution,[status(thm)],[218, 6535])).
% 2.32/2.52 tff(6537,plain,
% 2.32/2.52 (~r(z, s(s(s(z))))),
% 2.32/2.52 inference(unit_resolution,[status(thm)],[1754, 6534, 6494, 6511])).
% 2.32/2.52 tff(6538,plain,
% 2.32/2.52 (b(z, s(s(s(z))))),
% 2.32/2.52 inference(unit_resolution,[status(thm)],[1697, 6537])).
% 2.32/2.52 tff(6539,plain,
% 2.32/2.52 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(s(elem!1))))) | (~b(z, s(z))) | (~b(s(s(s(z))), z)) | (~b(z, s(s(s(z))))) | (~b(s(s(s(elem!1))), s(s(s(z))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(s(s(elem!1))))) | (~b(z, s(z))) | (~b(s(s(s(z))), z)) | (~b(z, s(s(s(z))))) | (~b(s(s(s(elem!1))), s(s(s(z))))))),
% 2.32/2.52 inference(rewrite,[status(thm)],[])).
% 2.32/2.52 tff(6540,plain,
% 2.32/2.52 (((~b(z, s(z))) | (~b(z, s(z))) | (~b(s(s(s(z))), z)) | (~b(s(s(s(elem!1))), s(s(s(z))))) | (~b(z, s(s(s(z))))) | (~b(z, s(s(s(elem!1)))))) <=> ((~b(z, s(s(s(elem!1))))) | (~b(z, s(z))) | (~b(s(s(s(z))), z)) | (~b(z, s(s(s(z))))) | (~b(s(s(s(elem!1))), s(s(s(z))))))),
% 2.32/2.52 inference(rewrite,[status(thm)],[])).
% 2.32/2.52 tff(6541,plain,
% 2.32/2.52 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(z))) | (~b(z, s(z))) | (~b(s(s(s(z))), z)) | (~b(s(s(s(elem!1))), s(s(s(z))))) | (~b(z, s(s(s(z))))) | (~b(z, s(s(s(elem!1))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(s(elem!1))))) | (~b(z, s(z))) | (~b(s(s(s(z))), z)) | (~b(z, s(s(s(z))))) | (~b(s(s(s(elem!1))), s(s(s(z)))))))),
% 2.32/2.52 inference(monotonicity,[status(thm)],[6540])).
% 2.32/2.52 tff(6542,plain,
% 2.32/2.52 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(z))) | (~b(z, s(z))) | (~b(s(s(s(z))), z)) | (~b(s(s(s(elem!1))), s(s(s(z))))) | (~b(z, s(s(s(z))))) | (~b(z, s(s(s(elem!1))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(s(s(elem!1))))) | (~b(z, s(z))) | (~b(s(s(s(z))), z)) | (~b(z, s(s(s(z))))) | (~b(s(s(s(elem!1))), s(s(s(z))))))),
% 2.32/2.52 inference(transitivity,[status(thm)],[6541, 6539])).
% 2.32/2.52 tff(6543,plain,
% 2.32/2.52 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(z))) | (~b(z, s(z))) | (~b(s(s(s(z))), z)) | (~b(s(s(s(elem!1))), s(s(s(z))))) | (~b(z, s(s(s(z))))) | (~b(z, s(s(s(elem!1))))))),
% 2.32/2.52 inference(quant_inst,[status(thm)],[])).
% 2.32/2.52 tff(6544,plain,
% 2.32/2.52 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(s(s(elem!1))))) | (~b(z, s(z))) | (~b(s(s(s(z))), z)) | (~b(z, s(s(s(z))))) | (~b(s(s(s(elem!1))), s(s(s(z)))))),
% 2.32/2.52 inference(modus_ponens,[status(thm)],[6543, 6542])).
% 2.32/2.52 tff(6545,plain,
% 2.32/2.52 ((~b(z, s(s(s(elem!1))))) | (~b(z, s(s(s(z)))))),
% 2.32/2.52 inference(unit_resolution,[status(thm)],[6544, 166, 118, 6509, 6521])).
% 2.32/2.52 tff(6546,plain,
% 2.32/2.52 (~b(z, s(s(s(elem!1))))),
% 2.32/2.52 inference(unit_resolution,[status(thm)],[6545, 6538])).
% 2.32/2.52 tff(6547,plain,
% 2.32/2.52 (r(z, s(s(s(elem!1))))),
% 2.32/2.52 inference(unit_resolution,[status(thm)],[261, 6546])).
% 2.32/2.52 tff(6548,plain,
% 2.32/2.52 (elem!1 = s(s(s(elem!1)))),
% 2.32/2.52 inference(transitivity,[status(thm)],[1170, 3117, 104, 334])).
% 2.32/2.52 tff(6549,plain,
% 2.32/2.52 (b(elem!1, s(s(s(s(z))))) <=> b(s(s(s(elem!1))), s(s(s(s(z)))))),
% 2.32/2.52 inference(monotonicity,[status(thm)],[6548])).
% 2.32/2.52 tff(6550,plain,
% 2.32/2.52 (b(s(s(s(elem!1))), s(s(s(s(z))))) <=> b(elem!1, s(s(s(s(z)))))),
% 2.32/2.52 inference(symmetry,[status(thm)],[6549])).
% 2.32/2.52 tff(6551,plain,
% 2.32/2.52 ((~b(s(s(s(elem!1))), s(s(s(s(z)))))) <=> (~b(elem!1, s(s(s(s(z))))))),
% 2.32/2.52 inference(monotonicity,[status(thm)],[6550])).
% 2.32/2.52 tff(6552,assumption,(b(s(s(s(z))), s(s(s(elem!1))))), introduced(assumption)).
% 2.32/2.52 tff(6553,assumption,(b(s(s(s(elem!1))), s(s(s(s(z)))))), introduced(assumption)).
% 2.32/2.52 tff(6554,plain,
% 2.32/2.52 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), s(s(z)))) | (~b(s(s(s(z))), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(elem!1))), s(s(s(s(z)))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(elem!1))), s(s(z)))) | (~b(s(s(s(z))), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(elem!1))), s(s(s(s(z)))))))),
% 2.32/2.52 inference(rewrite,[status(thm)],[])).
% 2.32/2.52 tff(6555,plain,
% 2.32/2.52 (((~b(s(s(s(elem!1))), s(s(z)))) | (~b(s(s(s(elem!1))), s(s(z)))) | (~b(s(s(s(z))), s(s(s(elem!1))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(elem!1))), s(s(s(z))))) | (~b(s(s(s(elem!1))), s(s(s(s(z))))))) <=> ((~b(s(s(s(elem!1))), s(s(z)))) | (~b(s(s(s(z))), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(elem!1))), s(s(s(s(z)))))))),
% 2.32/2.52 inference(rewrite,[status(thm)],[])).
% 2.32/2.52 tff(6556,plain,
% 2.32/2.52 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), s(s(z)))) | (~b(s(s(s(elem!1))), s(s(z)))) | (~b(s(s(s(z))), s(s(s(elem!1))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(elem!1))), s(s(s(z))))) | (~b(s(s(s(elem!1))), s(s(s(s(z)))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), s(s(z)))) | (~b(s(s(s(z))), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(elem!1))), s(s(s(s(z))))))))),
% 2.32/2.52 inference(monotonicity,[status(thm)],[6555])).
% 2.32/2.52 tff(6557,plain,
% 2.32/2.52 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), s(s(z)))) | (~b(s(s(s(elem!1))), s(s(z)))) | (~b(s(s(s(z))), s(s(s(elem!1))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(elem!1))), s(s(s(z))))) | (~b(s(s(s(elem!1))), s(s(s(s(z)))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(elem!1))), s(s(z)))) | (~b(s(s(s(z))), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(elem!1))), s(s(s(s(z)))))))),
% 2.32/2.52 inference(transitivity,[status(thm)],[6556, 6554])).
% 2.32/2.52 tff(6558,plain,
% 2.32/2.52 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), s(s(z)))) | (~b(s(s(s(elem!1))), s(s(z)))) | (~b(s(s(s(z))), s(s(s(elem!1))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(elem!1))), s(s(s(z))))) | (~b(s(s(s(elem!1))), s(s(s(s(z)))))))),
% 2.32/2.52 inference(quant_inst,[status(thm)],[])).
% 2.32/2.52 tff(6559,plain,
% 2.32/2.52 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(elem!1))), s(s(z)))) | (~b(s(s(s(z))), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(elem!1))), s(s(s(s(z))))))),
% 2.32/2.52 inference(modus_ponens,[status(thm)],[6558, 6557])).
% 2.32/2.52 tff(6560,plain,
% 2.32/2.52 ($false),
% 2.32/2.52 inference(unit_resolution,[status(thm)],[6559, 166, 6552, 2060, 4732, 3251, 6553])).
% 2.32/2.52 tff(6561,plain,((~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(z))), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(s(z)))) | (~b(s(s(s(elem!1))), s(s(s(z))))) | (~b(s(s(s(elem!1))), s(s(s(s(z))))))), inference(lemma,lemma(discharge,[]))).
% 2.32/2.52 tff(6562,plain,
% 2.32/2.52 (~b(s(s(s(elem!1))), s(s(s(s(z)))))),
% 2.32/2.52 inference(unit_resolution,[status(thm)],[6561, 4732, 2060, 3251, 6552])).
% 2.32/2.52 tff(6563,plain,
% 2.32/2.52 (~b(elem!1, s(s(s(s(z)))))),
% 2.32/2.52 inference(modus_ponens,[status(thm)],[6562, 6551])).
% 2.32/2.52 tff(6564,plain,
% 2.32/2.52 ((s(s(elem!1)) = s(s(s(s(elem!1))))) <=> (s(s(s(elem!1))) = s(s(s(s(elem!1)))))),
% 2.32/2.52 inference(monotonicity,[status(thm)],[334])).
% 2.32/2.52 tff(6565,plain,
% 2.32/2.52 ((s(s(s(elem!1))) = s(s(s(s(elem!1))))) <=> (s(s(elem!1)) = s(s(s(s(elem!1)))))),
% 2.32/2.52 inference(symmetry,[status(thm)],[6564])).
% 2.32/2.52 tff(6566,plain,
% 2.32/2.52 (s(s(s(elem!1))) = s(s(s(s(elem!1))))),
% 2.32/2.52 inference(symmetry,[status(thm)],[6471])).
% 2.32/2.52 tff(6567,plain,
% 2.32/2.52 (s(s(elem!1)) = s(s(s(s(elem!1))))),
% 2.32/2.52 inference(modus_ponens,[status(thm)],[6566, 6565])).
% 2.32/2.52 tff(6568,plain,
% 2.32/2.52 (~(elem!1 = s(s(s(s(z)))))),
% 2.32/2.52 inference(unit_resolution,[status(thm)],[5489, 6567])).
% 2.32/2.52 tff(6569,plain,
% 2.32/2.52 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), z)) | (~b(z, s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(s(z)))), z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(z))), z)) | (~b(z, s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(s(z)))), z)))),
% 2.32/2.52 inference(rewrite,[status(thm)],[])).
% 2.32/2.52 tff(6570,plain,
% 2.32/2.52 (((~b(z, s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(z))), z)) | (~b(z, s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(s(z)))), z))) <=> ((~b(s(s(s(z))), z)) | (~b(z, s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(s(z)))), z)))),
% 2.32/2.53 inference(rewrite,[status(thm)],[])).
% 2.32/2.53 tff(6571,plain,
% 2.32/2.53 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(z))), z)) | (~b(z, s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(s(z)))), z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), z)) | (~b(z, s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(s(z)))), z))))),
% 2.32/2.53 inference(monotonicity,[status(thm)],[6570])).
% 2.32/2.53 tff(6572,plain,
% 2.32/2.53 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(z))), z)) | (~b(z, s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(s(z)))), z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(z))), z)) | (~b(z, s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(s(z)))), z)))),
% 2.32/2.53 inference(transitivity,[status(thm)],[6571, 6569])).
% 2.32/2.53 tff(6573,plain,
% 2.32/2.53 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(z))), z)) | (~b(z, s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(s(z)))), z)))),
% 2.32/2.53 inference(quant_inst,[status(thm)],[])).
% 2.32/2.53 tff(6574,plain,
% 2.32/2.53 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(z))), z)) | (~b(z, s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(s(z)))), z))),
% 2.32/2.53 inference(modus_ponens,[status(thm)],[6573, 6572])).
% 2.32/2.53 tff(6575,plain,
% 2.32/2.53 (~b(s(s(s(s(z)))), z)),
% 2.32/2.53 inference(unit_resolution,[status(thm)],[6574, 166, 1699, 1700, 4732])).
% 2.32/2.53 tff(6576,plain,
% 2.32/2.53 (r(s(s(s(s(z)))), z)),
% 2.32/2.53 inference(unit_resolution,[status(thm)],[3266, 6575])).
% 2.32/2.53 tff(6577,assumption,(r(s(s(s(elem!1))), s(s(s(s(z)))))), introduced(assumption)).
% 2.32/2.53 tff(6578,plain,
% 2.32/2.53 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), z)) | (~r(z, s(s(s(elem!1))))) | (~r(s(s(s(s(z)))), z)) | (~r(s(s(s(elem!1))), s(s(s(s(z)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(elem!1))), z)) | (~r(z, s(s(s(elem!1))))) | (~r(s(s(s(s(z)))), z)) | (~r(s(s(s(elem!1))), s(s(s(s(z)))))))),
% 2.32/2.53 inference(rewrite,[status(thm)],[])).
% 2.32/2.53 tff(6579,plain,
% 2.32/2.53 (((~r(z, s(s(s(elem!1))))) | (~r(s(s(s(s(z)))), z)) | (~r(s(s(s(elem!1))), z)) | (~r(s(s(s(elem!1))), s(s(s(s(z))))))) <=> ((~r(s(s(s(elem!1))), z)) | (~r(z, s(s(s(elem!1))))) | (~r(s(s(s(s(z)))), z)) | (~r(s(s(s(elem!1))), s(s(s(s(z)))))))),
% 2.32/2.53 inference(rewrite,[status(thm)],[])).
% 2.32/2.53 tff(6580,plain,
% 2.32/2.53 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(s(elem!1))))) | (~r(s(s(s(s(z)))), z)) | (~r(s(s(s(elem!1))), z)) | (~r(s(s(s(elem!1))), s(s(s(s(z)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), z)) | (~r(z, s(s(s(elem!1))))) | (~r(s(s(s(s(z)))), z)) | (~r(s(s(s(elem!1))), s(s(s(s(z))))))))),
% 2.32/2.53 inference(monotonicity,[status(thm)],[6579])).
% 2.32/2.53 tff(6581,plain,
% 2.32/2.53 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(s(elem!1))))) | (~r(s(s(s(s(z)))), z)) | (~r(s(s(s(elem!1))), z)) | (~r(s(s(s(elem!1))), s(s(s(s(z)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(elem!1))), z)) | (~r(z, s(s(s(elem!1))))) | (~r(s(s(s(s(z)))), z)) | (~r(s(s(s(elem!1))), s(s(s(s(z)))))))),
% 2.32/2.53 inference(transitivity,[status(thm)],[6580, 6578])).
% 2.32/2.53 tff(6582,plain,
% 2.32/2.53 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(s(elem!1))))) | (~r(s(s(s(s(z)))), z)) | (~r(s(s(s(elem!1))), z)) | (~r(s(s(s(elem!1))), s(s(s(s(z)))))))),
% 2.32/2.53 inference(quant_inst,[status(thm)],[])).
% 2.32/2.53 tff(6583,plain,
% 2.32/2.53 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(elem!1))), z)) | (~r(z, s(s(s(elem!1))))) | (~r(s(s(s(s(z)))), z)) | (~r(s(s(s(elem!1))), s(s(s(s(z))))))),
% 2.32/2.53 inference(modus_ponens,[status(thm)],[6582, 6581])).
% 2.32/2.53 tff(6584,plain,
% 2.32/2.53 ($false),
% 2.32/2.53 inference(unit_resolution,[status(thm)],[6583, 197, 154, 282, 4679, 6577])).
% 2.32/2.53 tff(6585,plain,((~r(s(s(s(s(z)))), z)) | (~r(s(s(s(elem!1))), z)) | (~r(z, s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), s(s(s(s(z))))))), inference(lemma,lemma(discharge,[]))).
% 2.32/2.53 tff(6586,plain,
% 2.32/2.53 (~r(s(s(s(elem!1))), s(s(s(s(z)))))),
% 2.32/2.53 inference(unit_resolution,[status(thm)],[6585, 6576, 154, 282])).
% 2.32/2.53 tff(6587,plain,
% 2.32/2.53 (~r(elem!1, s(s(s(s(z)))))),
% 2.32/2.53 inference(unit_resolution,[status(thm)],[5665, 6586, 334])).
% 2.32/2.53 tff(6588,plain,
% 2.32/2.53 (b(elem!1, s(s(s(s(z)))))),
% 2.32/2.53 inference(unit_resolution,[status(thm)],[1098, 6587, 6568])).
% 2.32/2.53 tff(6589,plain,
% 2.32/2.53 ($false),
% 2.32/2.53 inference(unit_resolution,[status(thm)],[6588, 6563])).
% 2.32/2.53 tff(6590,plain,((~b(s(s(s(s(z)))), s(s(s(z))))) | (~(s(s(elem!1)) = s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), z)) | (~r(z, s(s(s(elem!1))))) | (~b(s(s(s(z))), z)) | (~b(z, s(s(s(z))))) | (~b(s(s(s(elem!1))), s(s(z)))) | (~b(s(s(s(elem!1))), s(s(s(z))))) | (~b(s(s(s(z))), s(s(s(elem!1)))))), inference(lemma,lemma(discharge,[]))).
% 2.32/2.53 tff(6591,plain,
% 2.32/2.53 (~b(s(s(s(s(z)))), s(s(s(z))))),
% 2.32/2.53 inference(unit_resolution,[status(thm)],[6590, 6547, 154, 334, 6509, 6538, 6536, 6521, 6530])).
% 2.32/2.53 tff(6592,plain,
% 2.32/2.53 (r(s(s(s(s(z)))), s(s(s(z))))),
% 2.32/2.53 inference(unit_resolution,[status(thm)],[4662, 6591])).
% 2.32/2.53 tff(6593,plain,
% 2.32/2.53 (~b(s(s(s(z))), s(s(z)))),
% 2.32/2.53 inference(unit_resolution,[status(thm)],[4130, 166, 6532, 6530, 6521])).
% 2.32/2.53 tff(6594,plain,
% 2.32/2.53 (r(s(s(s(z))), s(s(z)))),
% 2.32/2.53 inference(unit_resolution,[status(thm)],[1010, 6593])).
% 2.32/2.53 tff(6595,plain,
% 2.32/2.53 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(z)), s(s(s(z))))) | (~r(s(s(s(z))), s(s(z)))) | (~r(s(s(s(s(z)))), s(s(s(z))))) | (~r(s(s(z)), s(s(s(s(z)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(z)), s(s(s(z))))) | (~r(s(s(s(z))), s(s(z)))) | (~r(s(s(s(s(z)))), s(s(s(z))))) | (~r(s(s(z)), s(s(s(s(z)))))))),
% 2.32/2.53 inference(rewrite,[status(thm)],[])).
% 2.32/2.53 tff(6596,plain,
% 2.32/2.53 (((~r(s(s(s(z))), s(s(z)))) | (~r(s(s(s(s(z)))), s(s(s(z))))) | (~r(s(s(z)), s(s(s(z))))) | (~r(s(s(z)), s(s(s(s(z))))))) <=> ((~r(s(s(z)), s(s(s(z))))) | (~r(s(s(s(z))), s(s(z)))) | (~r(s(s(s(s(z)))), s(s(s(z))))) | (~r(s(s(z)), s(s(s(s(z)))))))),
% 2.32/2.53 inference(rewrite,[status(thm)],[])).
% 2.32/2.53 tff(6597,plain,
% 2.32/2.53 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(z))), s(s(z)))) | (~r(s(s(s(s(z)))), s(s(s(z))))) | (~r(s(s(z)), s(s(s(z))))) | (~r(s(s(z)), s(s(s(s(z)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(z)), s(s(s(z))))) | (~r(s(s(s(z))), s(s(z)))) | (~r(s(s(s(s(z)))), s(s(s(z))))) | (~r(s(s(z)), s(s(s(s(z))))))))),
% 2.32/2.53 inference(monotonicity,[status(thm)],[6596])).
% 2.32/2.53 tff(6598,plain,
% 2.32/2.53 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(z))), s(s(z)))) | (~r(s(s(s(s(z)))), s(s(s(z))))) | (~r(s(s(z)), s(s(s(z))))) | (~r(s(s(z)), s(s(s(s(z)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(z)), s(s(s(z))))) | (~r(s(s(s(z))), s(s(z)))) | (~r(s(s(s(s(z)))), s(s(s(z))))) | (~r(s(s(z)), s(s(s(s(z)))))))),
% 2.32/2.53 inference(transitivity,[status(thm)],[6597, 6595])).
% 2.32/2.53 tff(6599,plain,
% 2.32/2.53 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(z))), s(s(z)))) | (~r(s(s(s(s(z)))), s(s(s(z))))) | (~r(s(s(z)), s(s(s(z))))) | (~r(s(s(z)), s(s(s(s(z)))))))),
% 2.32/2.53 inference(quant_inst,[status(thm)],[])).
% 2.32/2.53 tff(6600,plain,
% 2.32/2.53 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(z)), s(s(s(z))))) | (~r(s(s(s(z))), s(s(z)))) | (~r(s(s(s(s(z)))), s(s(s(z))))) | (~r(s(s(z)), s(s(s(s(z))))))),
% 2.32/2.53 inference(modus_ponens,[status(thm)],[6599, 6598])).
% 2.32/2.53 tff(6601,plain,
% 2.32/2.53 (~r(s(s(z)), s(s(s(s(z)))))),
% 2.32/2.53 inference(unit_resolution,[status(thm)],[6600, 197, 6594, 6592, 6534])).
% 2.32/2.53 tff(6602,plain,
% 2.32/2.53 (b(s(s(z)), s(s(s(s(z)))))),
% 2.32/2.53 inference(unit_resolution,[status(thm)],[4753, 6601])).
% 2.32/2.53 tff(6603,plain,
% 2.32/2.53 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(s(s(z))))) | (~r(s(s(s(z))), s(s(z)))) | (~r(s(s(s(s(z)))), s(s(s(z))))) | (~r(s(s(s(s(z)))), s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(z), s(s(s(z))))) | (~r(s(s(s(z))), s(s(z)))) | (~r(s(s(s(s(z)))), s(s(s(z))))) | (~r(s(s(s(s(z)))), s(z))))),
% 2.32/2.53 inference(rewrite,[status(thm)],[])).
% 2.32/2.53 tff(6604,plain,
% 2.32/2.53 (((~r(s(s(s(z))), s(s(z)))) | (~r(s(z), s(s(s(z))))) | (~r(s(s(s(s(z)))), s(s(s(z))))) | (~r(s(s(s(s(z)))), s(z)))) <=> ((~r(s(z), s(s(s(z))))) | (~r(s(s(s(z))), s(s(z)))) | (~r(s(s(s(s(z)))), s(s(s(z))))) | (~r(s(s(s(s(z)))), s(z))))),
% 2.32/2.53 inference(rewrite,[status(thm)],[])).
% 2.32/2.53 tff(6605,plain,
% 2.32/2.53 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(z))), s(s(z)))) | (~r(s(z), s(s(s(z))))) | (~r(s(s(s(s(z)))), s(s(s(z))))) | (~r(s(s(s(s(z)))), s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(s(s(z))))) | (~r(s(s(s(z))), s(s(z)))) | (~r(s(s(s(s(z)))), s(s(s(z))))) | (~r(s(s(s(s(z)))), s(z)))))),
% 2.32/2.53 inference(monotonicity,[status(thm)],[6604])).
% 2.32/2.53 tff(6606,plain,
% 2.32/2.53 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(z))), s(s(z)))) | (~r(s(z), s(s(s(z))))) | (~r(s(s(s(s(z)))), s(s(s(z))))) | (~r(s(s(s(s(z)))), s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(z), s(s(s(z))))) | (~r(s(s(s(z))), s(s(z)))) | (~r(s(s(s(s(z)))), s(s(s(z))))) | (~r(s(s(s(s(z)))), s(z))))),
% 2.32/2.53 inference(transitivity,[status(thm)],[6605, 6603])).
% 2.32/2.53 tff(6607,plain,
% 2.32/2.53 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(z))), s(s(z)))) | (~r(s(z), s(s(s(z))))) | (~r(s(s(s(s(z)))), s(s(s(z))))) | (~r(s(s(s(s(z)))), s(z))))),
% 2.32/2.53 inference(quant_inst,[status(thm)],[])).
% 2.32/2.53 tff(6608,plain,
% 2.32/2.53 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(z), s(s(s(z))))) | (~r(s(s(s(z))), s(s(z)))) | (~r(s(s(s(s(z)))), s(s(s(z))))) | (~r(s(s(s(s(z)))), s(z)))),
% 2.32/2.53 inference(modus_ponens,[status(thm)],[6607, 6606])).
% 2.32/2.53 tff(6609,plain,
% 2.32/2.53 (~r(s(s(s(s(z)))), s(z))),
% 2.32/2.53 inference(unit_resolution,[status(thm)],[6608, 197, 6594, 6592, 6523])).
% 2.32/2.53 tff(6610,plain,
% 2.32/2.53 (b(s(s(s(s(z)))), s(z))),
% 2.32/2.53 inference(unit_resolution,[status(thm)],[3285, 6609])).
% 2.32/2.53 tff(6611,plain,
% 2.32/2.53 (~r(s(s(z)), s(z))),
% 2.32/2.53 inference(unit_resolution,[status(thm)],[5568, 197, 6511, 6523, 6534])).
% 2.32/2.53 tff(6612,plain,
% 2.32/2.53 (b(s(s(z)), s(z))),
% 2.32/2.53 inference(unit_resolution,[status(thm)],[308, 6611])).
% 2.32/2.53 tff(6613,plain,
% 2.32/2.53 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), z)) | (~b(z, s(z))) | (~b(s(s(z)), s(z))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(z)), s(s(s(s(z)))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), z)) | (~b(z, s(z))) | (~b(s(s(z)), s(z))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(z)), s(s(s(s(z)))))))),
% 2.32/2.53 inference(rewrite,[status(thm)],[])).
% 2.32/2.53 tff(6614,plain,
% 2.32/2.53 (((~b(z, s(z))) | (~b(s(s(z)), s(z))) | (~b(s(z), z)) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(z)), s(z))) | (~b(s(s(z)), s(s(s(s(z))))))) <=> ((~b(s(z), z)) | (~b(z, s(z))) | (~b(s(s(z)), s(z))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(z)), s(s(s(s(z)))))))),
% 2.32/2.53 inference(rewrite,[status(thm)],[])).
% 2.32/2.53 tff(6615,plain,
% 2.32/2.53 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(z))) | (~b(s(s(z)), s(z))) | (~b(s(z), z)) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(z)), s(z))) | (~b(s(s(z)), s(s(s(s(z)))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), z)) | (~b(z, s(z))) | (~b(s(s(z)), s(z))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(z)), s(s(s(s(z))))))))),
% 2.32/2.53 inference(monotonicity,[status(thm)],[6614])).
% 2.32/2.53 tff(6616,plain,
% 2.32/2.53 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(z))) | (~b(s(s(z)), s(z))) | (~b(s(z), z)) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(z)), s(z))) | (~b(s(s(z)), s(s(s(s(z)))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), z)) | (~b(z, s(z))) | (~b(s(s(z)), s(z))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(z)), s(s(s(s(z)))))))),
% 2.32/2.53 inference(transitivity,[status(thm)],[6615, 6613])).
% 2.32/2.53 tff(6617,plain,
% 2.32/2.53 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(z))) | (~b(s(s(z)), s(z))) | (~b(s(z), z)) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(z)), s(z))) | (~b(s(s(z)), s(s(s(s(z)))))))),
% 2.32/2.53 inference(quant_inst,[status(thm)],[])).
% 2.32/2.53 tff(6618,plain,
% 2.32/2.53 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), z)) | (~b(z, s(z))) | (~b(s(s(z)), s(z))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(z)), s(s(s(s(z))))))),
% 2.32/2.53 inference(modus_ponens,[status(thm)],[6617, 6616])).
% 2.32/2.53 tff(6619,plain,
% 2.32/2.53 ($false),
% 2.32/2.53 inference(unit_resolution,[status(thm)],[6618, 166, 5943, 118, 6612, 6610, 6602])).
% 2.32/2.53 tff(6620,plain,((~r(s(z), s(s(elem!1)))) | (~b(z, s(z))) | (~r(s(s(s(elem!1))), z)) | (~(s(s(elem!1)) = s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), s(z))) | (~r(z, s(s(z))))), inference(lemma,lemma(discharge,[]))).
% 2.32/2.53 tff(6621,plain,
% 2.32/2.53 (~r(s(z), s(s(elem!1)))),
% 2.32/2.53 inference(unit_resolution,[status(thm)],[6620, 153, 118, 6461, 5696, 152])).
% 2.32/2.53 tff(6622,plain,
% 2.32/2.53 (b(s(z), s(s(elem!1)))),
% 2.32/2.53 inference(unit_resolution,[status(thm)],[84, 6621])).
% 2.32/2.53 tff(6623,plain,
% 2.32/2.53 (~b(s(s(z)), s(z))),
% 2.32/2.53 inference(unit_resolution,[status(thm)],[181, 122, 118, 53])).
% 2.32/2.53 tff(6624,plain,
% 2.32/2.53 (r(s(s(z)), s(z))),
% 2.32/2.53 inference(unit_resolution,[status(thm)],[308, 6623])).
% 2.32/2.53 tff(6625,plain,
% 2.32/2.53 (b(s(z), s(s(s(elem!1))))),
% 2.32/2.53 inference(unit_resolution,[status(thm)],[5500, 376, 334])).
% 2.32/2.53 tff(6626,plain,
% 2.32/2.53 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), z)) | (~b(s(z), s(s(s(elem!1))))) | (~b(z, s(z))) | (~b(s(z), s(s(z)))) | (~b(s(s(z)), z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), z)) | (~b(s(z), s(s(s(elem!1))))) | (~b(z, s(z))) | (~b(s(z), s(s(z)))) | (~b(s(s(z)), z)))),
% 2.32/2.53 inference(rewrite,[status(thm)],[])).
% 2.32/2.53 tff(6627,plain,
% 2.32/2.53 (((~b(s(z), s(s(s(elem!1))))) | (~b(s(z), s(s(s(elem!1))))) | (~b(z, s(z))) | (~b(s(s(z)), z)) | (~b(s(z), z)) | (~b(s(z), s(s(z))))) <=> ((~b(s(z), z)) | (~b(s(z), s(s(s(elem!1))))) | (~b(z, s(z))) | (~b(s(z), s(s(z)))) | (~b(s(s(z)), z)))),
% 2.32/2.53 inference(rewrite,[status(thm)],[])).
% 2.32/2.53 tff(6628,plain,
% 2.32/2.53 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(s(elem!1))))) | (~b(s(z), s(s(s(elem!1))))) | (~b(z, s(z))) | (~b(s(s(z)), z)) | (~b(s(z), z)) | (~b(s(z), s(s(z)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), z)) | (~b(s(z), s(s(s(elem!1))))) | (~b(z, s(z))) | (~b(s(z), s(s(z)))) | (~b(s(s(z)), z))))),
% 2.32/2.53 inference(monotonicity,[status(thm)],[6627])).
% 2.32/2.53 tff(6629,plain,
% 2.32/2.53 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(s(elem!1))))) | (~b(s(z), s(s(s(elem!1))))) | (~b(z, s(z))) | (~b(s(s(z)), z)) | (~b(s(z), z)) | (~b(s(z), s(s(z)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), z)) | (~b(s(z), s(s(s(elem!1))))) | (~b(z, s(z))) | (~b(s(z), s(s(z)))) | (~b(s(s(z)), z)))),
% 2.32/2.53 inference(transitivity,[status(thm)],[6628, 6626])).
% 2.32/2.53 tff(6630,plain,
% 2.32/2.53 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(s(elem!1))))) | (~b(s(z), s(s(s(elem!1))))) | (~b(z, s(z))) | (~b(s(s(z)), z)) | (~b(s(z), z)) | (~b(s(z), s(s(z)))))),
% 2.32/2.53 inference(quant_inst,[status(thm)],[])).
% 2.32/2.53 tff(6631,plain,
% 2.32/2.53 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), z)) | (~b(s(z), s(s(s(elem!1))))) | (~b(z, s(z))) | (~b(s(z), s(s(z)))) | (~b(s(s(z)), z))),
% 2.32/2.53 inference(modus_ponens,[status(thm)],[6630, 6629])).
% 2.32/2.53 tff(6632,plain,
% 2.32/2.53 (~b(s(z), s(s(z)))),
% 2.32/2.53 inference(unit_resolution,[status(thm)],[6631, 166, 6625, 53, 118, 122])).
% 2.32/2.53 tff(6633,plain,
% 2.32/2.53 (r(s(z), s(s(z)))),
% 2.32/2.53 inference(unit_resolution,[status(thm)],[427, 6632])).
% 2.32/2.53 tff(6634,plain,
% 2.32/2.53 (~b(s(s(s(z))), z)),
% 2.32/2.53 inference(unit_resolution,[status(thm)],[5078, 6633, 122, 118, 53, 6624])).
% 2.32/2.53 tff(6635,plain,
% 2.32/2.53 (r(s(s(s(z))), z)),
% 2.32/2.53 inference(unit_resolution,[status(thm)],[1713, 6634])).
% 2.32/2.53 tff(6636,plain,
% 2.32/2.53 ((s(s(elem!1)) = s(s(z))) <=> (s(s(s(elem!1))) = s(s(z)))),
% 2.32/2.53 inference(monotonicity,[status(thm)],[334])).
% 2.32/2.53 tff(6637,plain,
% 2.32/2.53 ((s(s(elem!1)) = s(s(z))) <=> (s(s(z)) = s(s(s(elem!1))))),
% 2.32/2.53 inference(transitivity,[status(thm)],[6636, 487])).
% 2.32/2.53 tff(6638,plain,
% 2.32/2.53 ((s(s(z)) = s(s(s(elem!1)))) <=> (s(s(elem!1)) = s(s(z)))),
% 2.32/2.53 inference(symmetry,[status(thm)],[6637])).
% 2.32/2.53 tff(6639,plain,
% 2.32/2.53 ((s(s(z)) = s(s(s(elem!1)))) <=> (s(s(z)) = s(s(elem!1)))),
% 2.32/2.53 inference(transitivity,[status(thm)],[6638, 127])).
% 2.32/2.53 tff(6640,plain,
% 2.32/2.53 ((~(s(s(z)) = s(s(s(elem!1))))) <=> (~(s(s(z)) = s(s(elem!1))))),
% 2.32/2.53 inference(monotonicity,[status(thm)],[6639])).
% 2.32/2.53 tff(6641,plain,
% 2.32/2.53 (~(s(s(z)) = s(s(elem!1)))),
% 2.32/2.53 inference(modus_ponens,[status(thm)],[209, 6640])).
% 2.32/2.53 tff(6642,plain,
% 2.32/2.53 (~r(s(s(z)), s(s(elem!1)))),
% 2.32/2.53 inference(unit_resolution,[status(thm)],[5384, 6633, 6624, 4577])).
% 2.32/2.53 tff(6643,plain,
% 2.32/2.53 (b(s(s(z)), s(s(elem!1)))),
% 2.32/2.53 inference(unit_resolution,[status(thm)],[390, 6642, 6641])).
% 2.32/2.53 tff(6644,plain,
% 2.32/2.53 (b(s(s(z)), s(s(elem!1))) <=> b(s(s(z)), s(s(s(elem!1))))),
% 2.32/2.53 inference(monotonicity,[status(thm)],[334])).
% 2.32/2.53 tff(6645,plain,
% 2.32/2.53 (b(s(s(z)), s(s(s(elem!1))))),
% 2.32/2.53 inference(modus_ponens,[status(thm)],[446, 6644])).
% 2.32/2.53 tff(6646,plain,
% 2.32/2.53 ($false),
% 2.32/2.53 inference(unit_resolution,[status(thm)],[274, 6645])).
% 2.32/2.53 tff(6647,plain,((~b(s(s(z)), s(s(elem!1)))) | b(s(s(z)), s(s(s(elem!1)))) | (~(s(s(elem!1)) = s(s(s(elem!1)))))), inference(lemma,lemma(discharge,[]))).
% 2.32/2.53 tff(6648,plain,
% 2.32/2.53 (b(s(s(z)), s(s(s(elem!1))))),
% 2.32/2.53 inference(unit_resolution,[status(thm)],[6647, 6643, 334])).
% 2.32/2.53 tff(6649,plain,
% 2.32/2.53 ($false),
% 2.32/2.53 inference(unit_resolution,[status(thm)],[5570, 6648, 6635, 334, 376, 6624, 6474, 154, 155])).
% 2.32/2.54 tff(6650,plain,((~b(s(s(z)), z)) | (~(s(s(elem!1)) = s(s(s(elem!1))))) | (~b(s(z), s(s(elem!1)))) | (~r(s(s(s(elem!1))), z)) | (~r(z, s(s(z)))) | (~b(z, s(z))) | (~b(s(z), z)) | (~r(s(s(elem!1)), s(z)))), inference(lemma,lemma(discharge,[]))).
% 2.32/2.54 tff(6651,plain,
% 2.32/2.54 (~b(s(s(z)), z)),
% 2.32/2.54 inference(unit_resolution,[status(thm)],[6650, 6461, 6622, 153, 152, 118, 6470, 6468])).
% 2.32/2.54 tff(6652,plain,
% 2.32/2.54 (r(s(s(z)), z)),
% 2.32/2.54 inference(unit_resolution,[status(thm)],[186, 6651])).
% 2.32/2.54 tff(6653,plain,
% 2.32/2.54 (~r(s(s(s(z))), z)),
% 2.32/2.54 inference(unit_resolution,[status(thm)],[6507, 6652, 153, 152, 6466])).
% 2.32/2.54 tff(6654,plain,
% 2.32/2.54 (b(s(s(s(z))), z)),
% 2.32/2.54 inference(unit_resolution,[status(thm)],[1713, 6653])).
% 2.32/2.54 tff(6655,plain,
% 2.32/2.54 (~b(s(s(s(z))), s(z))),
% 2.32/2.54 inference(unit_resolution,[status(thm)],[4045, 166, 6470, 118, 6654])).
% 2.32/2.54 tff(6656,plain,
% 2.32/2.54 (r(s(s(s(z))), s(z))),
% 2.32/2.54 inference(unit_resolution,[status(thm)],[1763, 6655])).
% 2.32/2.54 tff(6657,plain,
% 2.32/2.54 (b(s(s(elem!1)), s(s(z))) <=> b(s(s(s(elem!1))), s(s(z)))),
% 2.32/2.54 inference(monotonicity,[status(thm)],[6461])).
% 2.32/2.54 tff(6658,plain,
% 2.32/2.54 (b(s(s(s(elem!1))), s(s(z))) <=> b(s(s(elem!1)), s(s(z)))),
% 2.32/2.54 inference(symmetry,[status(thm)],[6657])).
% 2.32/2.54 tff(6659,plain,
% 2.32/2.54 (~r(s(s(s(elem!1))), s(s(z)))),
% 2.32/2.54 inference(unit_resolution,[status(thm)],[6105, 6652, 152, 153])).
% 2.32/2.54 tff(6660,plain,
% 2.32/2.54 (b(s(s(s(elem!1))), s(s(z)))),
% 2.32/2.54 inference(unit_resolution,[status(thm)],[218, 6659])).
% 2.32/2.54 tff(6661,plain,
% 2.32/2.54 (b(s(s(elem!1)), s(s(z)))),
% 2.32/2.54 inference(modus_ponens,[status(thm)],[6660, 6658])).
% 2.32/2.54 tff(6662,plain,
% 2.32/2.54 ((s(s(elem!1)) = s(s(z))) <=> (s(s(s(elem!1))) = s(s(z)))),
% 2.32/2.54 inference(monotonicity,[status(thm)],[6461])).
% 2.32/2.54 tff(6663,plain,
% 2.32/2.54 ((s(s(elem!1)) = s(s(z))) <=> (s(s(z)) = s(s(s(elem!1))))),
% 2.32/2.54 inference(transitivity,[status(thm)],[6662, 487])).
% 2.32/2.54 tff(6664,plain,
% 2.32/2.54 ((s(s(z)) = s(s(s(elem!1)))) <=> (s(s(elem!1)) = s(s(z)))),
% 2.32/2.54 inference(symmetry,[status(thm)],[6663])).
% 2.32/2.54 tff(6665,plain,
% 2.32/2.54 ((s(s(z)) = s(s(s(elem!1)))) <=> (s(s(z)) = s(s(elem!1)))),
% 2.32/2.54 inference(transitivity,[status(thm)],[6664, 127])).
% 2.32/2.54 tff(6666,plain,
% 2.32/2.54 ((~(s(s(z)) = s(s(s(elem!1))))) <=> (~(s(s(z)) = s(s(elem!1))))),
% 2.32/2.54 inference(monotonicity,[status(thm)],[6665])).
% 2.32/2.54 tff(6667,plain,
% 2.32/2.54 (~(s(s(z)) = s(s(elem!1)))),
% 2.32/2.54 inference(modus_ponens,[status(thm)],[209, 6666])).
% 2.32/2.54 tff(6668,plain,
% 2.32/2.54 (~r(s(s(z)), s(s(s(elem!1))))),
% 2.32/2.54 inference(unit_resolution,[status(thm)],[5720, 197, 153, 152, 6652])).
% 2.32/2.54 tff(6669,plain,
% 2.32/2.54 (~r(s(s(z)), s(s(elem!1)))),
% 2.32/2.54 inference(unit_resolution,[status(thm)],[338, 6668, 6461])).
% 2.32/2.54 tff(6670,plain,
% 2.32/2.54 (b(s(s(z)), s(s(elem!1)))),
% 2.32/2.54 inference(unit_resolution,[status(thm)],[390, 6669, 6667])).
% 2.32/2.54 tff(6671,plain,
% 2.32/2.54 (~b(s(z), s(s(z)))),
% 2.32/2.54 inference(unit_resolution,[status(thm)],[558, 6670, 6622, 6661])).
% 2.32/2.54 tff(6672,plain,
% 2.32/2.54 (r(s(z), s(s(z)))),
% 2.32/2.54 inference(unit_resolution,[status(thm)],[427, 6671])).
% 2.32/2.54 tff(6673,plain,
% 2.32/2.54 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), s(s(s(z))))) | (~r(s(s(s(elem!1))), s(z))) | (~r(s(z), s(s(z)))) | (~r(s(s(s(z))), s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(elem!1))), s(s(s(z))))) | (~r(s(s(s(elem!1))), s(z))) | (~r(s(z), s(s(z)))) | (~r(s(s(s(z))), s(z))))),
% 2.32/2.54 inference(rewrite,[status(thm)],[])).
% 2.32/2.54 tff(6674,plain,
% 2.32/2.54 (((~r(s(z), s(s(z)))) | (~r(s(s(s(z))), s(z))) | (~r(s(s(s(elem!1))), s(z))) | (~r(s(s(s(elem!1))), s(s(s(z)))))) <=> ((~r(s(s(s(elem!1))), s(s(s(z))))) | (~r(s(s(s(elem!1))), s(z))) | (~r(s(z), s(s(z)))) | (~r(s(s(s(z))), s(z))))),
% 2.32/2.54 inference(rewrite,[status(thm)],[])).
% 2.32/2.54 tff(6675,plain,
% 2.32/2.54 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(s(z)))) | (~r(s(s(s(z))), s(z))) | (~r(s(s(s(elem!1))), s(z))) | (~r(s(s(s(elem!1))), s(s(s(z))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), s(s(s(z))))) | (~r(s(s(s(elem!1))), s(z))) | (~r(s(z), s(s(z)))) | (~r(s(s(s(z))), s(z)))))),
% 2.32/2.54 inference(monotonicity,[status(thm)],[6674])).
% 2.32/2.54 tff(6676,plain,
% 2.32/2.54 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(s(z)))) | (~r(s(s(s(z))), s(z))) | (~r(s(s(s(elem!1))), s(z))) | (~r(s(s(s(elem!1))), s(s(s(z))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(elem!1))), s(s(s(z))))) | (~r(s(s(s(elem!1))), s(z))) | (~r(s(z), s(s(z)))) | (~r(s(s(s(z))), s(z))))),
% 2.32/2.54 inference(transitivity,[status(thm)],[6675, 6673])).
% 2.32/2.54 tff(6677,plain,
% 2.32/2.54 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(s(z)))) | (~r(s(s(s(z))), s(z))) | (~r(s(s(s(elem!1))), s(z))) | (~r(s(s(s(elem!1))), s(s(s(z))))))),
% 2.32/2.54 inference(quant_inst,[status(thm)],[])).
% 2.32/2.54 tff(6678,plain,
% 2.32/2.54 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(elem!1))), s(s(s(z))))) | (~r(s(s(s(elem!1))), s(z))) | (~r(s(z), s(s(z)))) | (~r(s(s(s(z))), s(z)))),
% 2.32/2.54 inference(modus_ponens,[status(thm)],[6677, 6676])).
% 2.32/2.54 tff(6679,plain,
% 2.32/2.54 (~r(s(s(s(elem!1))), s(s(s(z))))),
% 2.32/2.54 inference(unit_resolution,[status(thm)],[6678, 197, 6672, 5696, 6656])).
% 2.32/2.54 tff(6680,plain,
% 2.32/2.54 (b(s(s(s(elem!1))), s(s(s(z))))),
% 2.32/2.54 inference(unit_resolution,[status(thm)],[3574, 6679, 6466])).
% 2.32/2.54 tff(6681,plain,
% 2.32/2.54 (b(s(s(z)), s(s(s(elem!1))))),
% 2.32/2.54 inference(unit_resolution,[status(thm)],[279, 6668])).
% 2.32/2.54 tff(6682,plain,
% 2.32/2.54 (b(s(z), s(s(s(elem!1))))),
% 2.32/2.54 inference(unit_resolution,[status(thm)],[5500, 6622, 6461])).
% 2.32/2.54 tff(6683,plain,
% 2.32/2.54 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(s(z)))) | (~b(s(s(z)), s(z))) | (~b(s(s(z)), s(s(s(elem!1))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(s(z)))) | (~b(s(s(z)), s(z))) | (~b(s(s(z)), s(s(s(elem!1))))))),
% 2.32/2.54 inference(rewrite,[status(thm)],[])).
% 2.32/2.54 tff(6684,plain,
% 2.32/2.54 (((~b(s(s(z)), s(s(s(elem!1))))) | (~b(s(s(z)), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(s(z)))) | (~b(s(z), s(s(s(elem!1))))) | (~b(s(s(z)), s(s(s(elem!1))))) | (~b(s(s(z)), s(z)))) <=> ((~b(s(z), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(s(z)))) | (~b(s(s(z)), s(z))) | (~b(s(s(z)), s(s(s(elem!1))))))),
% 2.32/2.54 inference(rewrite,[status(thm)],[])).
% 2.32/2.54 tff(6685,plain,
% 2.32/2.54 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), s(s(s(elem!1))))) | (~b(s(s(z)), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(s(z)))) | (~b(s(z), s(s(s(elem!1))))) | (~b(s(s(z)), s(s(s(elem!1))))) | (~b(s(s(z)), s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(s(z)))) | (~b(s(s(z)), s(z))) | (~b(s(s(z)), s(s(s(elem!1)))))))),
% 2.32/2.54 inference(monotonicity,[status(thm)],[6684])).
% 2.32/2.54 tff(6686,plain,
% 2.32/2.54 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), s(s(s(elem!1))))) | (~b(s(s(z)), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(s(z)))) | (~b(s(z), s(s(s(elem!1))))) | (~b(s(s(z)), s(s(s(elem!1))))) | (~b(s(s(z)), s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(s(z)))) | (~b(s(s(z)), s(z))) | (~b(s(s(z)), s(s(s(elem!1))))))),
% 2.32/2.54 inference(transitivity,[status(thm)],[6685, 6683])).
% 2.32/2.54 tff(6687,plain,
% 2.32/2.54 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), s(s(s(elem!1))))) | (~b(s(s(z)), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(s(z)))) | (~b(s(z), s(s(s(elem!1))))) | (~b(s(s(z)), s(s(s(elem!1))))) | (~b(s(s(z)), s(z))))),
% 2.32/2.54 inference(quant_inst,[status(thm)],[])).
% 2.32/2.54 tff(6688,plain,
% 2.32/2.54 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(s(z)))) | (~b(s(s(z)), s(z))) | (~b(s(s(z)), s(s(s(elem!1)))))),
% 2.32/2.54 inference(modus_ponens,[status(thm)],[6687, 6686])).
% 2.32/2.54 tff(6689,plain,
% 2.32/2.54 (~b(s(s(z)), s(z))),
% 2.32/2.54 inference(unit_resolution,[status(thm)],[6688, 166, 6682, 6681, 6660])).
% 2.32/2.54 tff(6690,plain,
% 2.32/2.54 (r(s(s(z)), s(z))),
% 2.32/2.54 inference(unit_resolution,[status(thm)],[308, 6689])).
% 2.32/2.54 tff(6691,plain,
% 2.32/2.54 (~r(s(s(z)), s(s(s(z))))),
% 2.32/2.54 inference(unit_resolution,[status(thm)],[5590, 197, 6672, 6690, 6656])).
% 2.32/2.54 tff(6692,plain,
% 2.32/2.54 (b(s(s(z)), s(s(s(z))))),
% 2.32/2.54 inference(unit_resolution,[status(thm)],[1730, 6691])).
% 2.32/2.54 tff(6693,plain,
% 2.32/2.54 (s(s(s(elem!1))) = s(s(elem!1))),
% 2.32/2.54 inference(unit_resolution,[status(thm)],[4030, 6461])).
% 2.32/2.54 tff(6694,plain,
% 2.32/2.54 (~(s(s(s(z))) = elem!1)),
% 2.32/2.54 inference(unit_resolution,[status(thm)],[3122, 6461])).
% 2.32/2.54 tff(6695,plain,
% 2.32/2.54 (s(s(s(elem!1))) = s(elem!1)),
% 2.32/2.54 inference(unit_resolution,[status(thm)],[2594, 6461])).
% 2.32/2.54 tff(6696,plain,
% 2.32/2.54 (s(elem!1) = s(s(s(elem!1)))),
% 2.32/2.54 inference(symmetry,[status(thm)],[6695])).
% 2.32/2.54 tff(6697,plain,
% 2.32/2.54 (inj_0(s(elem!1)) = inj_0(s(s(s(elem!1))))),
% 2.32/2.54 inference(monotonicity,[status(thm)],[6696])).
% 2.32/2.54 tff(6698,plain,
% 2.32/2.54 (elem!1 = s(s(elem!1))),
% 2.32/2.54 inference(transitivity,[status(thm)],[1170, 6697, 104])).
% 2.32/2.54 tff(6699,plain,
% 2.32/2.54 (r(s(s(s(z))), elem!1) <=> r(s(s(s(z))), s(s(elem!1)))),
% 2.32/2.54 inference(monotonicity,[status(thm)],[6698])).
% 2.32/2.54 tff(6700,plain,
% 2.32/2.54 (r(s(s(s(z))), s(s(elem!1))) <=> r(s(s(s(z))), elem!1)),
% 2.32/2.54 inference(symmetry,[status(thm)],[6699])).
% 2.32/2.54 tff(6701,plain,
% 2.32/2.54 (r(s(s(s(z))), s(s(s(elem!1)))) <=> r(s(s(s(z))), s(s(elem!1)))),
% 2.32/2.54 inference(monotonicity,[status(thm)],[6462])).
% 2.32/2.54 tff(6702,plain,
% 2.32/2.54 (r(s(s(s(z))), s(s(s(elem!1)))) <=> r(s(s(s(z))), elem!1)),
% 2.32/2.54 inference(transitivity,[status(thm)],[6701, 6700])).
% 2.32/2.54 tff(6703,plain,
% 2.32/2.54 ((~r(s(s(s(z))), s(s(s(elem!1))))) <=> (~r(s(s(s(z))), elem!1))),
% 2.32/2.54 inference(monotonicity,[status(thm)],[6702])).
% 2.32/2.54 tff(6704,plain,
% 2.32/2.54 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(s(z)))) | (~r(s(s(s(elem!1))), s(z))) | (~r(s(s(s(z))), s(z))) | (~r(s(s(s(z))), s(s(s(elem!1))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(z), s(s(z)))) | (~r(s(s(s(elem!1))), s(z))) | (~r(s(s(s(z))), s(z))) | (~r(s(s(s(z))), s(s(s(elem!1))))))),
% 2.32/2.54 inference(rewrite,[status(thm)],[])).
% 2.32/2.54 tff(6705,plain,
% 2.32/2.54 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(s(z)))) | (~r(s(s(s(elem!1))), s(z))) | (~r(s(s(s(z))), s(z))) | (~r(s(s(s(z))), s(s(s(elem!1))))))),
% 2.32/2.54 inference(quant_inst,[status(thm)],[])).
% 2.32/2.54 tff(6706,plain,
% 2.32/2.54 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(z), s(s(z)))) | (~r(s(s(s(elem!1))), s(z))) | (~r(s(s(s(z))), s(z))) | (~r(s(s(s(z))), s(s(s(elem!1)))))),
% 2.32/2.54 inference(modus_ponens,[status(thm)],[6705, 6704])).
% 2.32/2.54 tff(6707,plain,
% 2.32/2.54 (~r(s(s(s(z))), s(s(s(elem!1))))),
% 2.32/2.54 inference(unit_resolution,[status(thm)],[6706, 197, 6672, 5696, 6656])).
% 2.32/2.54 tff(6708,plain,
% 2.32/2.54 (~r(s(s(s(z))), elem!1)),
% 2.32/2.54 inference(modus_ponens,[status(thm)],[6707, 6703])).
% 2.32/2.54 tff(6709,plain,
% 2.32/2.54 (b(s(s(s(z))), elem!1)),
% 2.32/2.54 inference(unit_resolution,[status(thm)],[2826, 6708, 6694])).
% 2.32/2.54 tff(6710,plain,
% 2.32/2.54 (b(s(s(s(z))), s(s(s(elem!1))))),
% 2.32/2.54 inference(unit_resolution,[status(thm)],[4078, 6709, 6693])).
% 2.32/2.54 tff(6711,plain,
% 2.32/2.54 (((~b(s(s(s(elem!1))), s(s(s(z))))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(s(z))), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(s(s(z))))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(z)), s(s(s(elem!1)))))) <=> ((~b(s(s(z)), s(s(s(elem!1))))) | (~b(s(s(s(z))), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(s(s(z))))) | (~b(s(s(z)), s(s(s(z))))))),
% 2.32/2.54 inference(rewrite,[status(thm)],[])).
% 2.32/2.54 tff(6712,plain,
% 2.32/2.54 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), s(s(s(z))))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(s(z))), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(s(s(z))))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(z)), s(s(s(elem!1))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), s(s(s(elem!1))))) | (~b(s(s(s(z))), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(s(s(z))))) | (~b(s(s(z)), s(s(s(z)))))))),
% 2.32/2.54 inference(monotonicity,[status(thm)],[6711])).
% 2.32/2.54 tff(6713,plain,
% 2.32/2.54 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), s(s(s(z))))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(s(z))), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(s(s(z))))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(z)), s(s(s(elem!1))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(z)), s(s(s(elem!1))))) | (~b(s(s(s(z))), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(s(s(z))))) | (~b(s(s(z)), s(s(s(z))))))),
% 2.32/2.54 inference(transitivity,[status(thm)],[6712, 5514])).
% 2.32/2.54 tff(6714,plain,
% 2.32/2.54 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), s(s(s(z))))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(s(z))), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(s(s(z))))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(z)), s(s(s(elem!1))))))),
% 2.32/2.54 inference(quant_inst,[status(thm)],[])).
% 2.32/2.54 tff(6715,plain,
% 2.32/2.54 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(z)), s(s(s(elem!1))))) | (~b(s(s(s(z))), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(s(s(z))))) | (~b(s(s(z)), s(s(s(z)))))),
% 2.32/2.54 inference(modus_ponens,[status(thm)],[6714, 6713])).
% 2.32/2.54 tff(6716,plain,
% 2.32/2.54 ($false),
% 2.32/2.54 inference(unit_resolution,[status(thm)],[6715, 166, 6681, 6710, 6692, 6680])).
% 2.32/2.54 tff(6717,plain,(b(s(s(s(elem!1))), z) | (~b(z, s(z))) | b(z, s(s(z)))), inference(lemma,lemma(discharge,[]))).
% 2.32/2.54 tff(6718,plain,
% 2.32/2.54 (b(s(s(s(elem!1))), z)),
% 2.32/2.54 inference(unit_resolution,[status(thm)],[6717, 118, 125])).
% 2.32/2.54 tff(6719,plain,
% 2.32/2.54 (~r(s(s(elem!1)), s(s(s(elem!1))))),
% 2.32/2.54 inference(unit_resolution,[status(thm)],[5706, 197, 311, 350, 4577])).
% 2.32/2.54 tff(6720,plain,
% 2.32/2.54 (b(s(s(elem!1)), s(s(s(elem!1))))),
% 2.32/2.54 inference(unit_resolution,[status(thm)],[461, 6719, 45])).
% 2.32/2.54 tff(6721,plain,
% 2.32/2.54 (~b(z, s(s(elem!1)))),
% 2.32/2.54 inference(unit_resolution,[status(thm)],[3593, 6720, 121, 592])).
% 2.32/2.54 tff(6722,plain,
% 2.32/2.54 (r(z, s(s(elem!1)))),
% 2.32/2.54 inference(unit_resolution,[status(thm)],[1795, 6721])).
% 2.32/2.54 tff(6723,plain,
% 2.32/2.54 (~r(s(s(s(elem!1))), s(s(elem!1)))),
% 2.32/2.54 inference(unit_resolution,[status(thm)],[5711, 197, 311, 350, 4577])).
% 2.32/2.54 tff(6724,plain,
% 2.32/2.54 (b(s(s(s(elem!1))), s(s(elem!1)))),
% 2.32/2.54 inference(unit_resolution,[status(thm)],[889, 6723, 51])).
% 2.32/2.54 tff(6725,plain,
% 2.32/2.54 (~b(s(s(z)), s(s(elem!1)))),
% 2.32/2.54 inference(unit_resolution,[status(thm)],[2068, 6720, 2060, 6724])).
% 2.32/2.54 tff(6726,plain,
% 2.32/2.54 (r(s(s(z)), s(s(elem!1)))),
% 2.32/2.54 inference(unit_resolution,[status(thm)],[390, 6725, 52])).
% 2.32/2.54 tff(6727,plain,
% 2.32/2.54 ($false),
% 2.32/2.54 inference(unit_resolution,[status(thm)],[5997, 6726, 6722, 155, 4577])).
% 2.32/2.54 tff(6728,plain,((~r(s(s(s(elem!1))), s(z))) | (~r(z, s(s(z)))) | (~r(s(s(elem!1)), s(z))) | (s(s(z)) = s(s(elem!1))) | (~b(s(s(s(elem!1))), s(s(z)))) | (~b(s(s(s(elem!1))), z)) | (~b(s(s(elem!1)), z)) | (s(s(elem!1)) = s(s(s(elem!1)))) | (~r(s(z), s(s(elem!1))))), inference(lemma,lemma(discharge,[]))).
% 2.32/2.54 tff(6729,plain,
% 2.32/2.54 (~r(s(s(s(elem!1))), s(z))),
% 2.32/2.54 inference(unit_resolution,[status(thm)],[6728, 2060, 4577, 52, 155, 121, 3532, 45, 311])).
% 2.32/2.54 tff(6730,plain,
% 2.32/2.54 (b(s(s(s(elem!1))), s(z))),
% 2.32/2.54 inference(unit_resolution,[status(thm)],[1849, 6729])).
% 2.32/2.54 tff(6731,plain,
% 2.32/2.54 (~b(s(z), s(s(s(elem!1))))),
% 2.32/2.54 inference(unit_resolution,[status(thm)],[3860, 156, 118, 121, 122])).
% 2.32/2.54 tff(6732,plain,
% 2.32/2.54 (r(s(z), s(s(s(elem!1))))),
% 2.32/2.54 inference(unit_resolution,[status(thm)],[116, 6731])).
% 2.32/2.54 tff(6733,plain,
% 2.32/2.54 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(z))) | (~b(s(z), s(s(z)))) | (~b(s(s(z)), z)) | (~b(s(s(z)), s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(z))) | (~b(s(z), s(s(z)))) | (~b(s(s(z)), z)) | (~b(s(s(z)), s(z))))),
% 2.32/2.54 inference(rewrite,[status(thm)],[])).
% 2.32/2.54 tff(6734,plain,
% 2.32/2.54 (((~b(s(s(z)), s(z))) | (~b(s(s(z)), s(z))) | (~b(s(z), s(s(z)))) | (~b(z, s(z))) | (~b(s(s(z)), s(z))) | (~b(s(s(z)), z))) <=> ((~b(z, s(z))) | (~b(s(z), s(s(z)))) | (~b(s(s(z)), z)) | (~b(s(s(z)), s(z))))),
% 2.32/2.54 inference(rewrite,[status(thm)],[])).
% 2.32/2.54 tff(6735,plain,
% 2.32/2.54 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), s(z))) | (~b(s(s(z)), s(z))) | (~b(s(z), s(s(z)))) | (~b(z, s(z))) | (~b(s(s(z)), s(z))) | (~b(s(s(z)), z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(z))) | (~b(s(z), s(s(z)))) | (~b(s(s(z)), z)) | (~b(s(s(z)), s(z)))))),
% 2.32/2.54 inference(monotonicity,[status(thm)],[6734])).
% 2.32/2.54 tff(6736,plain,
% 2.32/2.54 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), s(z))) | (~b(s(s(z)), s(z))) | (~b(s(z), s(s(z)))) | (~b(z, s(z))) | (~b(s(s(z)), s(z))) | (~b(s(s(z)), z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(z))) | (~b(s(z), s(s(z)))) | (~b(s(s(z)), z)) | (~b(s(s(z)), s(z))))),
% 2.32/2.54 inference(transitivity,[status(thm)],[6735, 6733])).
% 2.32/2.54 tff(6737,plain,
% 2.32/2.54 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), s(z))) | (~b(s(s(z)), s(z))) | (~b(s(z), s(s(z)))) | (~b(z, s(z))) | (~b(s(s(z)), s(z))) | (~b(s(s(z)), z)))),
% 2.32/2.54 inference(quant_inst,[status(thm)],[])).
% 2.32/2.54 tff(6738,plain,
% 2.32/2.54 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(z))) | (~b(s(z), s(s(z)))) | (~b(s(s(z)), z)) | (~b(s(s(z)), s(z)))),
% 2.32/2.54 inference(modus_ponens,[status(thm)],[6737, 6736])).
% 2.32/2.54 tff(6739,plain,
% 2.32/2.54 ($false),
% 2.32/2.54 inference(unit_resolution,[status(thm)],[6738, 166, 556, 118, 156, 122])).
% 2.32/2.54 tff(6740,plain,((~b(s(z), s(s(z)))) | (~b(z, s(z))) | (~b(s(s(z)), s(z))) | (~b(s(s(z)), z))), inference(lemma,lemma(discharge,[]))).
% 2.32/2.54 tff(6741,plain,
% 2.32/2.54 (~b(s(z), s(s(z)))),
% 2.32/2.54 inference(unit_resolution,[status(thm)],[6740, 156, 118, 122])).
% 2.32/2.54 tff(6742,plain,
% 2.32/2.54 (r(s(z), s(s(z)))),
% 2.32/2.54 inference(unit_resolution,[status(thm)],[427, 6741])).
% 2.32/2.54 tff(6743,plain,
% 2.32/2.54 ($false),
% 2.32/2.54 inference(unit_resolution,[status(thm)],[5920, 197, 311, 120, 4577, 333])).
% 2.32/2.54 tff(6744,plain,((~r(s(s(z)), s(s(elem!1)))) | (~r(s(z), s(s(elem!1)))) | (~r(s(z), s(s(z)))) | (~r(s(s(elem!1)), s(z)))), inference(lemma,lemma(discharge,[]))).
% 2.32/2.54 tff(6745,plain,
% 2.32/2.54 (~r(s(s(z)), s(s(elem!1)))),
% 2.32/2.54 inference(unit_resolution,[status(thm)],[6744, 6742, 311, 4577])).
% 2.32/2.54 tff(6746,plain,
% 2.32/2.54 (b(s(s(z)), s(s(elem!1)))),
% 2.32/2.54 inference(unit_resolution,[status(thm)],[390, 6745, 52])).
% 2.32/2.54 tff(6747,plain,
% 2.32/2.54 (~r(s(s(z)), s(s(s(z))))),
% 2.32/2.54 inference(unit_resolution,[status(thm)],[3514, 6742, 155, 97])).
% 2.32/2.54 tff(6748,plain,
% 2.32/2.54 (b(s(s(z)), s(s(s(z))))),
% 2.32/2.54 inference(unit_resolution,[status(thm)],[1730, 6747])).
% 2.32/2.54 tff(6749,plain,
% 2.32/2.54 (~r(s(s(s(z))), z)),
% 2.32/2.54 inference(unit_resolution,[status(thm)],[3528, 6748, 155, 97, 156])).
% 2.32/2.54 tff(6750,plain,
% 2.32/2.54 (b(s(s(s(z))), z)),
% 2.32/2.54 inference(unit_resolution,[status(thm)],[1713, 6749])).
% 2.32/2.54 tff(6751,plain,
% 2.32/2.54 (~b(s(s(s(elem!1))), s(s(s(z))))),
% 2.32/2.54 inference(unit_resolution,[status(thm)],[3565, 6750, 118, 2060, 96, 6748])).
% 2.32/2.54 tff(6752,plain,
% 2.32/2.54 (r(s(s(s(elem!1))), s(s(s(z))))),
% 2.32/2.54 inference(unit_resolution,[status(thm)],[3574, 6751, 140])).
% 2.32/2.54 tff(6753,plain,
% 2.32/2.54 (~r(s(s(elem!1)), s(s(s(elem!1))))),
% 2.32/2.54 inference(unit_resolution,[status(thm)],[3583, 6752, 311, 6732])).
% 2.32/2.54 tff(6754,plain,
% 2.32/2.54 (b(s(s(elem!1)), s(s(s(elem!1))))),
% 2.32/2.54 inference(unit_resolution,[status(thm)],[461, 6753, 45])).
% 2.32/2.54 tff(6755,plain,
% 2.32/2.54 (~b(s(s(s(elem!1))), s(s(elem!1)))),
% 2.32/2.54 inference(unit_resolution,[status(thm)],[2068, 6754, 2060, 6746])).
% 2.32/2.54 tff(6756,plain,
% 2.32/2.54 (r(s(s(s(elem!1))), s(s(elem!1)))),
% 2.32/2.54 inference(unit_resolution,[status(thm)],[889, 6755, 51])).
% 2.32/2.54 tff(6757,plain,
% 2.32/2.54 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), s(s(elem!1)))) | (~r(s(z), s(s(elem!1)))) | (~r(s(z), s(s(s(elem!1))))) | (~r(s(s(elem!1)), s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(elem!1))), s(s(elem!1)))) | (~r(s(z), s(s(elem!1)))) | (~r(s(z), s(s(s(elem!1))))) | (~r(s(s(elem!1)), s(z))))),
% 2.32/2.54 inference(rewrite,[status(thm)],[])).
% 2.32/2.54 tff(6758,plain,
% 2.32/2.54 (((~r(s(s(elem!1)), s(z))) | (~r(s(s(s(elem!1))), s(s(elem!1)))) | (~r(s(z), s(s(elem!1)))) | (~r(s(z), s(s(s(elem!1)))))) <=> ((~r(s(s(s(elem!1))), s(s(elem!1)))) | (~r(s(z), s(s(elem!1)))) | (~r(s(z), s(s(s(elem!1))))) | (~r(s(s(elem!1)), s(z))))),
% 2.32/2.54 inference(rewrite,[status(thm)],[])).
% 2.32/2.54 tff(6759,plain,
% 2.32/2.54 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(elem!1)), s(z))) | (~r(s(s(s(elem!1))), s(s(elem!1)))) | (~r(s(z), s(s(elem!1)))) | (~r(s(z), s(s(s(elem!1))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), s(s(elem!1)))) | (~r(s(z), s(s(elem!1)))) | (~r(s(z), s(s(s(elem!1))))) | (~r(s(s(elem!1)), s(z)))))),
% 2.32/2.54 inference(monotonicity,[status(thm)],[6758])).
% 2.32/2.54 tff(6760,plain,
% 2.32/2.54 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(elem!1)), s(z))) | (~r(s(s(s(elem!1))), s(s(elem!1)))) | (~r(s(z), s(s(elem!1)))) | (~r(s(z), s(s(s(elem!1))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(elem!1))), s(s(elem!1)))) | (~r(s(z), s(s(elem!1)))) | (~r(s(z), s(s(s(elem!1))))) | (~r(s(s(elem!1)), s(z))))),
% 2.32/2.54 inference(transitivity,[status(thm)],[6759, 6757])).
% 2.32/2.54 tff(6761,plain,
% 2.32/2.54 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(elem!1)), s(z))) | (~r(s(s(s(elem!1))), s(s(elem!1)))) | (~r(s(z), s(s(elem!1)))) | (~r(s(z), s(s(s(elem!1))))))),
% 2.32/2.54 inference(quant_inst,[status(thm)],[])).
% 2.32/2.54 tff(6762,plain,
% 2.32/2.54 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(elem!1))), s(s(elem!1)))) | (~r(s(z), s(s(elem!1)))) | (~r(s(z), s(s(s(elem!1))))) | (~r(s(s(elem!1)), s(z)))),
% 2.32/2.54 inference(modus_ponens,[status(thm)],[6761, 6760])).
% 2.32/2.54 tff(6763,plain,
% 2.32/2.54 ($false),
% 2.32/2.54 inference(unit_resolution,[status(thm)],[6762, 197, 311, 4577, 6756, 6732])).
% 2.32/2.54 tff(6764,plain,((~b(s(s(z)), s(z))) | (~r(s(z), s(s(elem!1)))) | (~r(s(s(elem!1)), s(z))) | (~b(s(s(s(elem!1))), s(s(z)))) | (s(s(elem!1)) = s(s(s(elem!1)))) | (~b(z, s(z))) | (~b(s(s(s(elem!1))), s(z))) | (~r(z, s(s(z)))) | (~r(s(z), z)) | (s(s(z)) = s(s(elem!1))) | (~b(s(s(s(elem!1))), z)) | (~b(s(s(z)), z))), inference(lemma,lemma(discharge,[]))).
% 2.32/2.54 tff(6765,plain,
% 2.32/2.54 (~b(s(s(z)), s(z))),
% 2.32/2.54 inference(unit_resolution,[status(thm)],[6764, 96, 4577, 2060, 45, 118, 311, 155, 97, 52, 121, 122])).
% 2.32/2.55 tff(6766,plain,
% 2.32/2.55 (r(s(s(z)), s(z))),
% 2.32/2.55 inference(unit_resolution,[status(thm)],[308, 6765])).
% 2.32/2.55 tff(6767,plain,
% 2.32/2.55 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), z)) | (~r(s(s(elem!1)), s(z))) | (~r(s(s(z)), s(z))) | (~r(s(s(z)), s(s(elem!1)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(z), z)) | (~r(s(s(elem!1)), s(z))) | (~r(s(s(z)), s(z))) | (~r(s(s(z)), s(s(elem!1)))))),
% 2.32/2.55 inference(rewrite,[status(thm)],[])).
% 2.32/2.55 tff(6768,plain,
% 2.32/2.55 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), z)) | (~r(s(s(elem!1)), s(z))) | (~r(s(s(z)), s(z))) | (~r(s(s(z)), s(s(elem!1)))))),
% 2.32/2.55 inference(quant_inst,[status(thm)],[])).
% 2.32/2.55 tff(6769,plain,
% 2.32/2.55 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(z), z)) | (~r(s(s(elem!1)), s(z))) | (~r(s(s(z)), s(z))) | (~r(s(s(z)), s(s(elem!1))))),
% 2.32/2.55 inference(modus_ponens,[status(thm)],[6768, 6767])).
% 2.32/2.55 tff(6770,plain,
% 2.32/2.55 ($false),
% 2.32/2.55 inference(unit_resolution,[status(thm)],[6769, 197, 4577, 97, 333, 392])).
% 2.32/2.55 tff(6771,plain,((~r(s(z), z)) | (~r(s(s(elem!1)), s(z))) | (~r(s(s(z)), s(s(elem!1)))) | (~r(s(s(z)), s(z)))), inference(lemma,lemma(discharge,[]))).
% 2.32/2.55 tff(6772,plain,
% 2.32/2.55 (~r(s(s(z)), s(s(elem!1)))),
% 2.32/2.55 inference(unit_resolution,[status(thm)],[6771, 6766, 97, 4577])).
% 2.32/2.55 tff(6773,plain,
% 2.32/2.55 (b(s(s(z)), s(s(elem!1)))),
% 2.32/2.55 inference(unit_resolution,[status(thm)],[390, 6772, 52])).
% 2.32/2.55 tff(6774,plain,
% 2.32/2.55 (~r(s(s(elem!1)), s(s(z)))),
% 2.32/2.55 inference(unit_resolution,[status(thm)],[5331, 6766, 97, 4577])).
% 2.32/2.55 tff(6775,plain,
% 2.32/2.55 (b(s(s(elem!1)), s(s(z)))),
% 2.32/2.55 inference(unit_resolution,[status(thm)],[441, 6774, 132])).
% 2.32/2.55 tff(6776,plain,
% 2.32/2.55 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(s(s(elem!1))), s(s(z)))) | (~b(s(s(s(elem!1))), z)) | (~b(s(s(elem!1)), s(s(z)))) | (~b(s(s(z)), s(s(elem!1)))) | (~b(s(s(z)), z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(s(s(elem!1))), s(s(z)))) | (~b(s(s(s(elem!1))), z)) | (~b(s(s(elem!1)), s(s(z)))) | (~b(s(s(z)), s(s(elem!1)))) | (~b(s(s(z)), z)))),
% 2.32/2.55 inference(rewrite,[status(thm)],[])).
% 2.32/2.55 tff(6777,plain,
% 2.32/2.55 (((~b(s(s(z)), z)) | (~b(s(s(s(elem!1))), z)) | (~b(s(s(elem!1)), s(s(z)))) | (~b(s(s(z)), s(s(elem!1)))) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(s(s(elem!1))), s(s(z))))) <=> ((~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(s(s(elem!1))), s(s(z)))) | (~b(s(s(s(elem!1))), z)) | (~b(s(s(elem!1)), s(s(z)))) | (~b(s(s(z)), s(s(elem!1)))) | (~b(s(s(z)), z)))),
% 2.32/2.55 inference(rewrite,[status(thm)],[])).
% 2.32/2.55 tff(6778,plain,
% 2.32/2.55 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), z)) | (~b(s(s(s(elem!1))), z)) | (~b(s(s(elem!1)), s(s(z)))) | (~b(s(s(z)), s(s(elem!1)))) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(s(s(elem!1))), s(s(z)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(s(s(elem!1))), s(s(z)))) | (~b(s(s(s(elem!1))), z)) | (~b(s(s(elem!1)), s(s(z)))) | (~b(s(s(z)), s(s(elem!1)))) | (~b(s(s(z)), z))))),
% 2.32/2.55 inference(monotonicity,[status(thm)],[6777])).
% 2.32/2.55 tff(6779,plain,
% 2.32/2.55 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), z)) | (~b(s(s(s(elem!1))), z)) | (~b(s(s(elem!1)), s(s(z)))) | (~b(s(s(z)), s(s(elem!1)))) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(s(s(elem!1))), s(s(z)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(s(s(elem!1))), s(s(z)))) | (~b(s(s(s(elem!1))), z)) | (~b(s(s(elem!1)), s(s(z)))) | (~b(s(s(z)), s(s(elem!1)))) | (~b(s(s(z)), z)))),
% 2.32/2.55 inference(transitivity,[status(thm)],[6778, 6776])).
% 2.32/2.55 tff(6780,plain,
% 2.32/2.55 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), z)) | (~b(s(s(s(elem!1))), z)) | (~b(s(s(elem!1)), s(s(z)))) | (~b(s(s(z)), s(s(elem!1)))) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(s(s(elem!1))), s(s(z)))))),
% 2.32/2.55 inference(quant_inst,[status(thm)],[])).
% 2.32/2.55 tff(6781,plain,
% 2.32/2.55 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(s(s(elem!1))), s(s(z)))) | (~b(s(s(s(elem!1))), z)) | (~b(s(s(elem!1)), s(s(z)))) | (~b(s(s(z)), s(s(elem!1)))) | (~b(s(s(z)), z))),
% 2.32/2.55 inference(modus_ponens,[status(thm)],[6780, 6779])).
% 2.32/2.55 tff(6782,plain,
% 2.32/2.55 (~b(s(s(s(elem!1))), s(s(elem!1)))),
% 2.32/2.55 inference(unit_resolution,[status(thm)],[6781, 166, 6775, 121, 6773, 122, 2060])).
% 2.32/2.55 tff(6783,plain,
% 2.32/2.55 (r(s(s(s(elem!1))), s(s(elem!1)))),
% 2.32/2.55 inference(unit_resolution,[status(thm)],[889, 6782, 51])).
% 2.32/2.55 tff(6784,plain,
% 2.32/2.55 (~r(s(z), s(s(s(elem!1))))),
% 2.32/2.55 inference(unit_resolution,[status(thm)],[6762, 197, 311, 4577, 6783])).
% 2.32/2.55 tff(6785,plain,
% 2.32/2.55 (b(s(z), s(s(s(elem!1))))),
% 2.32/2.55 inference(unit_resolution,[status(thm)],[116, 6784])).
% 2.32/2.55 tff(6786,plain,
% 2.32/2.55 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), z)) | (~b(s(s(s(elem!1))), s(z))) | (~b(z, s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), z)) | (~b(s(s(s(elem!1))), s(z))) | (~b(z, s(z))))),
% 2.32/2.55 inference(rewrite,[status(thm)],[])).
% 2.32/2.55 tff(6787,plain,
% 2.32/2.55 (((~b(s(s(s(elem!1))), s(z))) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(z), s(s(s(elem!1))))) | (~b(z, s(z))) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(s(s(elem!1))), z))) <=> ((~b(s(z), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), z)) | (~b(s(s(s(elem!1))), s(z))) | (~b(z, s(z))))),
% 2.32/2.55 inference(rewrite,[status(thm)],[])).
% 2.32/2.55 tff(6788,plain,
% 2.32/2.55 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), s(z))) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(z), s(s(s(elem!1))))) | (~b(z, s(z))) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(s(s(elem!1))), z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), z)) | (~b(s(s(s(elem!1))), s(z))) | (~b(z, s(z)))))),
% 2.32/2.55 inference(monotonicity,[status(thm)],[6787])).
% 2.32/2.55 tff(6789,plain,
% 2.32/2.55 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), s(z))) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(z), s(s(s(elem!1))))) | (~b(z, s(z))) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(s(s(elem!1))), z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), z)) | (~b(s(s(s(elem!1))), s(z))) | (~b(z, s(z))))),
% 2.32/2.55 inference(transitivity,[status(thm)],[6788, 6786])).
% 2.32/2.55 tff(6790,plain,
% 2.32/2.55 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), s(z))) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(z), s(s(s(elem!1))))) | (~b(z, s(z))) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(s(s(elem!1))), z)))),
% 2.32/2.55 inference(quant_inst,[status(thm)],[])).
% 2.32/2.55 tff(6791,plain,
% 2.32/2.55 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), z)) | (~b(s(s(s(elem!1))), s(z))) | (~b(z, s(z)))),
% 2.32/2.55 inference(modus_ponens,[status(thm)],[6790, 6789])).
% 2.32/2.55 tff(6792,plain,
% 2.32/2.55 ($false),
% 2.32/2.55 inference(unit_resolution,[status(thm)],[6791, 166, 6785, 96, 118, 121])).
% 2.32/2.55 tff(6793,plain,((~b(s(s(s(elem!1))), s(z))) | (~b(z, s(z))) | (~b(s(s(s(elem!1))), z)) | (~r(s(z), s(s(elem!1)))) | (~r(s(s(elem!1)), s(z))) | (~b(s(s(z)), z)) | (~b(s(s(s(elem!1))), s(s(z)))) | (s(s(z)) = s(s(elem!1))) | (~r(s(z), z)) | (s(s(elem!1)) = s(s(s(elem!1)))) | (~r(z, s(s(z))))), inference(lemma,lemma(discharge,[]))).
% 2.32/2.55 tff(6794,plain,
% 2.32/2.55 (~b(s(s(z)), z)),
% 2.32/2.55 inference(unit_resolution,[status(thm)],[6793, 6730, 121, 311, 4577, 118, 2060, 52, 97, 45, 155])).
% 2.32/2.55 tff(6795,plain,
% 2.32/2.55 (r(s(s(z)), z)),
% 2.32/2.55 inference(unit_resolution,[status(thm)],[186, 6794])).
% 2.32/2.55 tff(6796,plain,
% 2.32/2.55 (~r(s(s(z)), s(z))),
% 2.32/2.55 inference(unit_resolution,[status(thm)],[4287, 6795, 155, 97])).
% 2.32/2.55 tff(6797,plain,
% 2.32/2.55 (b(s(s(z)), s(z))),
% 2.32/2.55 inference(unit_resolution,[status(thm)],[308, 6796])).
% 2.32/2.55 tff(6798,plain,
% 2.32/2.55 (~r(s(z), s(s(z)))),
% 2.32/2.55 inference(unit_resolution,[status(thm)],[2498, 6795, 155, 97])).
% 2.32/2.55 tff(6799,plain,
% 2.32/2.55 (b(s(z), s(s(z)))),
% 2.32/2.55 inference(unit_resolution,[status(thm)],[427, 6798])).
% 2.32/2.55 tff(6800,plain,
% 2.32/2.55 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), z)) | (~b(s(s(s(elem!1))), s(z))) | (~b(z, s(z))) | (~b(s(z), s(s(z)))) | (~b(s(s(z)), s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(elem!1))), z)) | (~b(s(s(s(elem!1))), s(z))) | (~b(z, s(z))) | (~b(s(z), s(s(z)))) | (~b(s(s(z)), s(z))))),
% 2.32/2.55 inference(rewrite,[status(thm)],[])).
% 2.32/2.55 tff(6801,plain,
% 2.32/2.55 (((~b(s(s(z)), s(z))) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(z), s(s(z)))) | (~b(z, s(z))) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(s(s(elem!1))), z))) <=> ((~b(s(s(s(elem!1))), z)) | (~b(s(s(s(elem!1))), s(z))) | (~b(z, s(z))) | (~b(s(z), s(s(z)))) | (~b(s(s(z)), s(z))))),
% 2.32/2.55 inference(rewrite,[status(thm)],[])).
% 2.32/2.55 tff(6802,plain,
% 2.32/2.55 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), s(z))) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(z), s(s(z)))) | (~b(z, s(z))) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(s(s(elem!1))), z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), z)) | (~b(s(s(s(elem!1))), s(z))) | (~b(z, s(z))) | (~b(s(z), s(s(z)))) | (~b(s(s(z)), s(z)))))),
% 2.32/2.55 inference(monotonicity,[status(thm)],[6801])).
% 2.32/2.55 tff(6803,plain,
% 2.32/2.55 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), s(z))) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(z), s(s(z)))) | (~b(z, s(z))) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(s(s(elem!1))), z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(elem!1))), z)) | (~b(s(s(s(elem!1))), s(z))) | (~b(z, s(z))) | (~b(s(z), s(s(z)))) | (~b(s(s(z)), s(z))))),
% 2.32/2.55 inference(transitivity,[status(thm)],[6802, 6800])).
% 2.32/2.55 tff(6804,plain,
% 2.32/2.55 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), s(z))) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(z), s(s(z)))) | (~b(z, s(z))) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(s(s(elem!1))), z)))),
% 2.32/2.55 inference(quant_inst,[status(thm)],[])).
% 2.32/2.55 tff(6805,plain,
% 2.32/2.55 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(elem!1))), z)) | (~b(s(s(s(elem!1))), s(z))) | (~b(z, s(z))) | (~b(s(z), s(s(z)))) | (~b(s(s(z)), s(z)))),
% 2.32/2.55 inference(modus_ponens,[status(thm)],[6804, 6803])).
% 2.32/2.55 tff(6806,plain,
% 2.32/2.55 ($false),
% 2.32/2.55 inference(unit_resolution,[status(thm)],[6805, 166, 556, 96, 118, 121, 156])).
% 2.32/2.55 tff(6807,plain,((~b(s(s(s(elem!1))), s(z))) | (~b(s(z), s(s(z)))) | (~b(z, s(z))) | (~b(s(s(s(elem!1))), z)) | (~b(s(s(z)), s(z)))), inference(lemma,lemma(discharge,[]))).
% 2.32/2.55 tff(6808,plain,
% 2.32/2.55 ($false),
% 2.32/2.55 inference(unit_resolution,[status(thm)],[6807, 6799, 6797, 6730, 118, 121])).
% 2.32/2.55 tff(6809,plain,((~b(s(s(s(elem!1))), s(s(z)))) | (~b(z, s(z))) | (~b(s(s(s(elem!1))), z)) | (~r(z, s(s(z)))) | (~r(s(z), z)) | (~r(s(z), s(s(elem!1)))) | (~r(s(s(elem!1)), s(z))) | (s(s(z)) = s(s(elem!1))) | (s(s(elem!1)) = s(s(s(elem!1))))), inference(lemma,lemma(discharge,[]))).
% 2.32/2.55 tff(6810,plain,
% 2.32/2.55 (~b(s(s(s(elem!1))), s(s(z)))),
% 2.32/2.55 inference(unit_resolution,[status(thm)],[6809, 52, 121, 155, 97, 311, 4577, 118, 45])).
% 2.32/2.55 tff(6811,plain,
% 2.32/2.55 (r(s(s(s(elem!1))), s(s(z)))),
% 2.32/2.55 inference(unit_resolution,[status(thm)],[218, 6810])).
% 2.32/2.55 tff(6812,plain,
% 2.32/2.55 (~r(z, s(s(s(elem!1))))),
% 2.32/2.55 inference(unit_resolution,[status(thm)],[1588, 392, 155, 464])).
% 2.32/2.55 tff(6813,plain,
% 2.32/2.55 (b(z, s(s(s(elem!1))))),
% 2.32/2.55 inference(unit_resolution,[status(thm)],[261, 6812])).
% 2.32/2.55 tff(6814,plain,
% 2.32/2.55 (~b(s(s(elem!1)), s(s(s(elem!1))))),
% 2.32/2.55 inference(unit_resolution,[status(thm)],[600, 6813, 121, 592])).
% 2.32/2.55 tff(6815,plain,
% 2.32/2.55 (r(s(s(elem!1)), s(s(s(elem!1))))),
% 2.32/2.55 inference(unit_resolution,[status(thm)],[461, 6814, 45])).
% 2.32/2.55 tff(6816,plain,
% 2.32/2.55 (~r(s(s(s(elem!1))), s(z))),
% 2.32/2.55 inference(unit_resolution,[status(thm)],[854, 392, 464, 311])).
% 2.32/2.55 tff(6817,plain,
% 2.32/2.55 (b(s(s(s(elem!1))), s(z))),
% 2.32/2.55 inference(unit_resolution,[status(thm)],[1849, 6816])).
% 2.32/2.55 tff(6818,plain,
% 2.32/2.55 (~b(s(z), s(s(s(elem!1))))),
% 2.32/2.55 inference(unit_resolution,[status(thm)],[249, 6813, 118, 6817])).
% 2.32/2.55 tff(6819,plain,
% 2.32/2.55 (r(s(z), s(s(s(elem!1))))),
% 2.32/2.55 inference(unit_resolution,[status(thm)],[116, 6818])).
% 2.32/2.55 tff(6820,plain,
% 2.32/2.55 ($false),
% 2.32/2.55 inference(unit_resolution,[status(thm)],[2939, 6819, 6815, 311, 464])).
% 2.32/2.55 tff(6821,plain,((~r(s(s(z)), s(z))) | (~r(s(z), s(s(elem!1)))) | (~r(s(s(s(elem!1))), s(s(z)))) | (s(s(elem!1)) = s(s(s(elem!1)))) | (~b(z, s(z))) | (~b(s(s(s(elem!1))), z)) | (~b(s(s(elem!1)), z)) | (~r(z, s(s(z))))), inference(lemma,lemma(discharge,[]))).
% 2.32/2.55 tff(6822,plain,
% 2.32/2.55 (~r(s(s(z)), s(z))),
% 2.32/2.55 inference(unit_resolution,[status(thm)],[6821, 6811, 311, 45, 118, 121, 3532, 155])).
% 2.32/2.55 tff(6823,plain,
% 2.32/2.55 (~b(z, s(s(s(elem!1))))),
% 2.32/2.55 inference(unit_resolution,[status(thm)],[600, 6720, 121, 592])).
% 2.32/2.55 tff(6824,plain,
% 2.32/2.55 (r(z, s(s(s(elem!1))))),
% 2.32/2.55 inference(unit_resolution,[status(thm)],[261, 6823])).
% 2.32/2.55 tff(6825,plain,
% 2.32/2.55 (~r(s(z), s(s(s(elem!1))))),
% 2.32/2.55 inference(unit_resolution,[status(thm)],[3872, 6824, 97, 350])).
% 2.32/2.55 tff(6826,plain,
% 2.32/2.55 (b(s(z), s(s(s(elem!1))))),
% 2.32/2.55 inference(unit_resolution,[status(thm)],[116, 6825])).
% 2.32/2.55 tff(6827,plain,
% 2.32/2.55 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(s(z), s(s(s(elem!1))))) | (~b(s(s(elem!1)), z)) | (~b(s(s(s(elem!1))), z)) | (~b(z, s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(s(z), s(s(s(elem!1))))) | (~b(s(s(elem!1)), z)) | (~b(s(s(s(elem!1))), z)) | (~b(z, s(z))))),
% 2.32/2.55 inference(rewrite,[status(thm)],[])).
% 2.32/2.55 tff(6828,plain,
% 2.32/2.55 (((~b(s(z), s(s(s(elem!1))))) | (~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(z, s(z))) | (~b(s(s(s(elem!1))), z)) | (~b(s(s(elem!1)), z)) | (~b(s(s(elem!1)), s(s(s(elem!1)))))) <=> ((~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(s(z), s(s(s(elem!1))))) | (~b(s(s(elem!1)), z)) | (~b(s(s(s(elem!1))), z)) | (~b(z, s(z))))),
% 2.32/2.55 inference(rewrite,[status(thm)],[])).
% 2.32/2.55 tff(6829,plain,
% 2.32/2.55 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(s(elem!1))))) | (~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(z, s(z))) | (~b(s(s(s(elem!1))), z)) | (~b(s(s(elem!1)), z)) | (~b(s(s(elem!1)), s(s(s(elem!1))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(s(z), s(s(s(elem!1))))) | (~b(s(s(elem!1)), z)) | (~b(s(s(s(elem!1))), z)) | (~b(z, s(z)))))),
% 2.32/2.55 inference(monotonicity,[status(thm)],[6828])).
% 2.32/2.55 tff(6830,plain,
% 2.32/2.55 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(s(elem!1))))) | (~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(z, s(z))) | (~b(s(s(s(elem!1))), z)) | (~b(s(s(elem!1)), z)) | (~b(s(s(elem!1)), s(s(s(elem!1))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(s(z), s(s(s(elem!1))))) | (~b(s(s(elem!1)), z)) | (~b(s(s(s(elem!1))), z)) | (~b(z, s(z))))),
% 2.32/2.55 inference(transitivity,[status(thm)],[6829, 6827])).
% 2.32/2.55 tff(6831,plain,
% 2.32/2.55 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(s(elem!1))))) | (~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(z, s(z))) | (~b(s(s(s(elem!1))), z)) | (~b(s(s(elem!1)), z)) | (~b(s(s(elem!1)), s(s(s(elem!1))))))),
% 2.32/2.55 inference(quant_inst,[status(thm)],[])).
% 2.32/2.55 tff(6832,plain,
% 2.32/2.55 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(s(z), s(s(s(elem!1))))) | (~b(s(s(elem!1)), z)) | (~b(s(s(s(elem!1))), z)) | (~b(z, s(z)))),
% 2.32/2.55 inference(modus_ponens,[status(thm)],[6831, 6830])).
% 2.32/2.55 tff(6833,plain,
% 2.32/2.55 ($false),
% 2.32/2.55 inference(unit_resolution,[status(thm)],[6832, 166, 6720, 6826, 118, 121, 592])).
% 2.32/2.55 tff(6834,plain,((~r(s(s(s(elem!1))), s(z))) | (~b(z, s(z))) | (~b(s(s(s(elem!1))), z)) | (~b(s(s(elem!1)), z)) | (~r(s(z), z)) | (s(s(elem!1)) = s(s(s(elem!1)))) | (~r(s(z), s(s(elem!1)))) | (~r(s(s(elem!1)), s(z)))), inference(lemma,lemma(discharge,[]))).
% 2.32/2.55 tff(6835,plain,
% 2.32/2.55 (~r(s(s(s(elem!1))), s(z))),
% 2.32/2.55 inference(unit_resolution,[status(thm)],[6834, 3532, 121, 118, 97, 45, 311, 4577])).
% 2.32/2.55 tff(6836,plain,
% 2.32/2.55 (b(s(s(s(elem!1))), s(z))),
% 2.32/2.55 inference(unit_resolution,[status(thm)],[1849, 6835])).
% 2.32/2.55 tff(6837,plain,
% 2.32/2.55 (b(s(s(z)), s(z))),
% 2.32/2.55 inference(unit_resolution,[status(thm)],[308, 6822])).
% 2.32/2.55 tff(6838,plain,
% 2.32/2.55 (~r(s(s(z)), s(s(elem!1)))),
% 2.32/2.55 inference(unit_resolution,[status(thm)],[6744, 120, 311, 4577])).
% 2.32/2.55 tff(6839,plain,
% 2.32/2.55 (b(s(s(z)), s(s(elem!1)))),
% 2.32/2.55 inference(unit_resolution,[status(thm)],[390, 6838, 52])).
% 2.32/2.55 tff(6840,plain,
% 2.32/2.55 (~r(s(z), s(s(s(elem!1))))),
% 2.32/2.55 inference(unit_resolution,[status(thm)],[3555, 6839, 121, 45, 6811, 6837, 118, 120, 311])).
% 2.32/2.55 tff(6841,plain,
% 2.32/2.55 (~r(s(s(z)), z)),
% 2.32/2.55 inference(unit_resolution,[status(thm)],[2498, 120, 155, 97])).
% 2.32/2.55 tff(6842,plain,
% 2.32/2.55 (b(s(s(z)), z)),
% 2.32/2.55 inference(unit_resolution,[status(thm)],[186, 6841])).
% 2.32/2.55 tff(6843,plain,
% 2.32/2.55 (~b(s(z), s(s(s(elem!1))))),
% 2.32/2.55 inference(unit_resolution,[status(thm)],[3860, 6842, 118, 121, 6837])).
% 2.32/2.55 tff(6844,plain,
% 2.32/2.55 ($false),
% 2.32/2.55 inference(unit_resolution,[status(thm)],[116, 6843, 6840])).
% 2.32/2.55 tff(6845,plain,((~r(s(z), s(s(z)))) | (~b(z, s(z))) | (~b(s(s(s(elem!1))), z)) | (s(s(elem!1)) = s(s(s(elem!1)))) | (~r(s(z), s(s(elem!1)))) | (s(s(z)) = s(s(elem!1))) | (~r(z, s(s(z)))) | (~r(s(z), z)) | (~r(s(s(elem!1)), s(z)))), inference(lemma,lemma(discharge,[]))).
% 2.32/2.55 tff(6846,plain,
% 2.32/2.55 (~r(s(z), s(s(z)))),
% 2.32/2.55 inference(unit_resolution,[status(thm)],[6845, 52, 121, 45, 311, 118, 155, 97, 4577])).
% 2.32/2.55 tff(6847,plain,
% 2.32/2.55 (b(s(z), s(s(z)))),
% 2.32/2.55 inference(unit_resolution,[status(thm)],[427, 6846])).
% 2.32/2.55 tff(6848,plain,
% 2.32/2.55 (~b(s(s(z)), s(z))),
% 2.32/2.55 inference(unit_resolution,[status(thm)],[6807, 6847, 6836, 118, 121])).
% 2.32/2.55 tff(6849,plain,
% 2.32/2.55 ($false),
% 2.32/2.55 inference(unit_resolution,[status(thm)],[308, 6848, 6822])).
% 2.32/2.56 tff(6850,plain,((s(s(z)) = s(s(elem!1))) | (~b(z, s(z))) | (~b(s(s(s(elem!1))), z)) | (~r(s(z), s(s(elem!1)))) | (s(s(elem!1)) = s(s(s(elem!1)))) | (~r(z, s(s(z)))) | (~r(s(z), z)) | (~r(s(s(elem!1)), s(z)))), inference(lemma,lemma(discharge,[]))).
% 2.32/2.56 tff(6851,plain,
% 2.32/2.56 (s(s(z)) = s(s(elem!1))),
% 2.32/2.56 inference(unit_resolution,[status(thm)],[6850, 97, 6718, 311, 45, 152, 118, 4577])).
% 2.32/2.56 tff(6852,plain,
% 2.32/2.56 (s(elem!1) = s(z)),
% 2.32/2.56 inference(unit_resolution,[status(thm)],[43, 6851])).
% 2.32/2.56 tff(6853,plain,
% 2.32/2.56 (z = elem!1),
% 2.32/2.56 inference(unit_resolution,[status(thm)],[30, 6852])).
% 2.32/2.56 tff(6854,plain,
% 2.32/2.56 (r(z, s(s(elem!1))) <=> r(elem!1, s(s(elem!1)))),
% 2.32/2.56 inference(monotonicity,[status(thm)],[6853])).
% 2.32/2.56 tff(6855,plain,
% 2.32/2.56 (~b(z, s(s(elem!1)))),
% 2.32/2.56 inference(unit_resolution,[status(thm)],[2261, 6851, 125])).
% 2.32/2.56 tff(6856,plain,
% 2.32/2.56 (r(z, s(s(elem!1)))),
% 2.32/2.56 inference(unit_resolution,[status(thm)],[1795, 6855])).
% 2.32/2.56 tff(6857,plain,
% 2.32/2.56 (r(elem!1, s(s(elem!1)))),
% 2.32/2.56 inference(modus_ponens,[status(thm)],[6856, 6854])).
% 2.32/2.56 tff(6858,plain,
% 2.32/2.56 (r(s(z), z) <=> r(s(z), elem!1)),
% 2.32/2.56 inference(monotonicity,[status(thm)],[6853])).
% 2.32/2.56 tff(6859,plain,
% 2.32/2.56 (r(s(z), elem!1)),
% 2.32/2.56 inference(modus_ponens,[status(thm)],[97, 6858])).
% 2.32/2.56 tff(6860,plain,
% 2.32/2.56 ($false),
% 2.32/2.56 inference(unit_resolution,[status(thm)],[5285, 197, 311, 4577, 6859, 6857])).
% 2.32/2.56 tff(6861,plain,((~r(s(z), z)) | (~r(s(z), s(s(elem!1)))) | (~r(s(s(elem!1)), s(z))) | b(z, s(s(z))) | (s(s(elem!1)) = s(s(s(elem!1)))) | (~b(z, s(z)))), inference(lemma,lemma(discharge,[]))).
% 2.32/2.56 tff(6862,plain,
% 2.32/2.56 (~r(s(z), z)),
% 2.32/2.56 inference(unit_resolution,[status(thm)],[6861, 85, 4558, 125, 45, 118])).
% 2.32/2.56 tff(6863,plain,
% 2.32/2.56 (b(s(z), z)),
% 2.32/2.56 inference(unit_resolution,[status(thm)],[230, 6862])).
% 2.32/2.56 tff(6864,plain,
% 2.32/2.56 (((~b(s(z), z)) | (~b(s(s(s(elem!1))), z)) | (~b(z, s(z))) | (~b(s(z), z)) | (~b(s(s(s(elem!1))), z)) | (~b(s(s(s(elem!1))), s(z)))) <=> ((~b(s(z), z)) | (~b(s(s(s(elem!1))), z)) | (~b(s(s(s(elem!1))), s(z))) | (~b(z, s(z))))),
% 2.32/2.56 inference(rewrite,[status(thm)],[])).
% 2.32/2.56 tff(6865,plain,
% 2.32/2.56 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), z)) | (~b(s(s(s(elem!1))), z)) | (~b(z, s(z))) | (~b(s(z), z)) | (~b(s(s(s(elem!1))), z)) | (~b(s(s(s(elem!1))), s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), z)) | (~b(s(s(s(elem!1))), z)) | (~b(s(s(s(elem!1))), s(z))) | (~b(z, s(z)))))),
% 2.32/2.56 inference(monotonicity,[status(thm)],[6864])).
% 2.32/2.56 tff(6866,plain,
% 2.32/2.56 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), z)) | (~b(s(s(s(elem!1))), z)) | (~b(z, s(z))) | (~b(s(z), z)) | (~b(s(s(s(elem!1))), z)) | (~b(s(s(s(elem!1))), s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), z)) | (~b(s(s(s(elem!1))), z)) | (~b(s(s(s(elem!1))), s(z))) | (~b(z, s(z))))),
% 2.32/2.56 inference(transitivity,[status(thm)],[6865, 3992])).
% 2.32/2.56 tff(6867,plain,
% 2.32/2.56 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), z)) | (~b(s(s(s(elem!1))), z)) | (~b(z, s(z))) | (~b(s(z), z)) | (~b(s(s(s(elem!1))), z)) | (~b(s(s(s(elem!1))), s(z))))),
% 2.32/2.56 inference(quant_inst,[status(thm)],[])).
% 2.32/2.56 tff(6868,plain,
% 2.32/2.56 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), z)) | (~b(s(s(s(elem!1))), z)) | (~b(s(s(s(elem!1))), s(z))) | (~b(z, s(z)))),
% 2.32/2.56 inference(modus_ponens,[status(thm)],[6867, 6866])).
% 2.32/2.56 tff(6869,plain,
% 2.32/2.56 (~b(s(s(s(elem!1))), s(z))),
% 2.32/2.56 inference(unit_resolution,[status(thm)],[6868, 166, 53, 118, 121])).
% 2.32/2.56 tff(6870,plain,
% 2.32/2.56 (r(s(s(s(elem!1))), s(z))),
% 2.32/2.56 inference(unit_resolution,[status(thm)],[1849, 6869])).
% 2.32/2.56 tff(6871,plain,
% 2.32/2.56 (~r(s(s(s(elem!1))), s(s(elem!1)))),
% 2.32/2.56 inference(unit_resolution,[status(thm)],[5711, 197, 311, 6870, 4577])).
% 2.32/2.56 tff(6872,plain,
% 2.32/2.56 (b(s(s(s(elem!1))), s(s(elem!1)))),
% 2.32/2.56 inference(unit_resolution,[status(thm)],[889, 6871, 51])).
% 2.32/2.56 tff(6873,plain,
% 2.32/2.56 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), z)) | (~b(s(z), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), z)) | (~b(z, s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), z)) | (~b(s(z), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), z)) | (~b(z, s(z))))),
% 2.32/2.56 inference(rewrite,[status(thm)],[])).
% 2.32/2.56 tff(6874,plain,
% 2.32/2.56 (((~b(s(z), z)) | (~b(s(z), z)) | (~b(z, s(z))) | (~b(s(s(s(elem!1))), z)) | (~b(s(z), z)) | (~b(s(z), s(s(s(elem!1)))))) <=> ((~b(s(z), z)) | (~b(s(z), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), z)) | (~b(z, s(z))))),
% 2.32/2.56 inference(rewrite,[status(thm)],[])).
% 2.32/2.56 tff(6875,plain,
% 2.32/2.56 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), z)) | (~b(s(z), z)) | (~b(z, s(z))) | (~b(s(s(s(elem!1))), z)) | (~b(s(z), z)) | (~b(s(z), s(s(s(elem!1))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), z)) | (~b(s(z), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), z)) | (~b(z, s(z)))))),
% 2.32/2.56 inference(monotonicity,[status(thm)],[6874])).
% 2.32/2.56 tff(6876,plain,
% 2.32/2.56 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), z)) | (~b(s(z), z)) | (~b(z, s(z))) | (~b(s(s(s(elem!1))), z)) | (~b(s(z), z)) | (~b(s(z), s(s(s(elem!1))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), z)) | (~b(s(z), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), z)) | (~b(z, s(z))))),
% 2.32/2.56 inference(transitivity,[status(thm)],[6875, 6873])).
% 2.32/2.56 tff(6877,plain,
% 2.32/2.56 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), z)) | (~b(s(z), z)) | (~b(z, s(z))) | (~b(s(s(s(elem!1))), z)) | (~b(s(z), z)) | (~b(s(z), s(s(s(elem!1))))))),
% 2.32/2.56 inference(quant_inst,[status(thm)],[])).
% 2.32/2.56 tff(6878,plain,
% 2.32/2.56 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), z)) | (~b(s(z), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), z)) | (~b(z, s(z)))),
% 2.32/2.56 inference(modus_ponens,[status(thm)],[6877, 6876])).
% 2.32/2.56 tff(6879,plain,
% 2.32/2.56 (~b(s(z), s(s(s(elem!1))))),
% 2.32/2.56 inference(unit_resolution,[status(thm)],[6878, 166, 53, 118, 121])).
% 2.32/2.56 tff(6880,plain,
% 2.32/2.56 (r(s(z), s(s(s(elem!1))))),
% 2.32/2.56 inference(unit_resolution,[status(thm)],[116, 6879])).
% 2.32/2.56 tff(6881,plain,
% 2.32/2.56 (~r(s(s(elem!1)), s(s(s(elem!1))))),
% 2.32/2.56 inference(unit_resolution,[status(thm)],[764, 6880, 6870, 311])).
% 2.32/2.56 tff(6882,plain,
% 2.32/2.56 (b(s(s(elem!1)), s(s(s(elem!1))))),
% 2.32/2.56 inference(unit_resolution,[status(thm)],[461, 6881, 45])).
% 2.32/2.56 tff(6883,plain,
% 2.32/2.56 (~r(s(s(s(elem!1))), s(s(z)))),
% 2.32/2.56 inference(unit_resolution,[status(thm)],[854, 392, 350, 311])).
% 2.32/2.56 tff(6884,plain,
% 2.32/2.56 (b(s(s(s(elem!1))), s(s(z)))),
% 2.32/2.56 inference(unit_resolution,[status(thm)],[218, 6883])).
% 2.32/2.56 tff(6885,plain,
% 2.32/2.56 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(s(s(elem!1))))) | (~r(s(s(z)), s(s(elem!1)))) | (~r(s(s(z)), s(z))) | (~r(s(s(elem!1)), s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(z), s(s(s(elem!1))))) | (~r(s(s(z)), s(s(elem!1)))) | (~r(s(s(z)), s(z))) | (~r(s(s(elem!1)), s(z))))),
% 2.32/2.56 inference(rewrite,[status(thm)],[])).
% 2.32/2.56 tff(6886,plain,
% 2.32/2.56 (((~r(s(z), s(s(s(elem!1))))) | (~r(s(s(elem!1)), s(z))) | (~r(s(s(z)), s(z))) | (~r(s(s(z)), s(s(elem!1))))) <=> ((~r(s(z), s(s(s(elem!1))))) | (~r(s(s(z)), s(s(elem!1)))) | (~r(s(s(z)), s(z))) | (~r(s(s(elem!1)), s(z))))),
% 2.32/2.56 inference(rewrite,[status(thm)],[])).
% 2.32/2.56 tff(6887,plain,
% 2.32/2.56 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(s(s(elem!1))))) | (~r(s(s(elem!1)), s(z))) | (~r(s(s(z)), s(z))) | (~r(s(s(z)), s(s(elem!1)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(s(s(elem!1))))) | (~r(s(s(z)), s(s(elem!1)))) | (~r(s(s(z)), s(z))) | (~r(s(s(elem!1)), s(z)))))),
% 2.32/2.56 inference(monotonicity,[status(thm)],[6886])).
% 2.32/2.56 tff(6888,plain,
% 2.32/2.56 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(s(s(elem!1))))) | (~r(s(s(elem!1)), s(z))) | (~r(s(s(z)), s(z))) | (~r(s(s(z)), s(s(elem!1)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(z), s(s(s(elem!1))))) | (~r(s(s(z)), s(s(elem!1)))) | (~r(s(s(z)), s(z))) | (~r(s(s(elem!1)), s(z))))),
% 2.32/2.56 inference(transitivity,[status(thm)],[6887, 6885])).
% 2.32/2.56 tff(6889,plain,
% 2.32/2.56 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(s(s(elem!1))))) | (~r(s(s(elem!1)), s(z))) | (~r(s(s(z)), s(z))) | (~r(s(s(z)), s(s(elem!1)))))),
% 2.32/2.56 inference(quant_inst,[status(thm)],[])).
% 2.32/2.56 tff(6890,plain,
% 2.32/2.56 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(z), s(s(s(elem!1))))) | (~r(s(s(z)), s(s(elem!1)))) | (~r(s(s(z)), s(z))) | (~r(s(s(elem!1)), s(z)))),
% 2.32/2.56 inference(modus_ponens,[status(thm)],[6889, 6888])).
% 2.32/2.56 tff(6891,plain,
% 2.32/2.56 ($false),
% 2.32/2.56 inference(unit_resolution,[status(thm)],[6890, 197, 4577, 333, 392, 119])).
% 2.32/2.56 tff(6892,plain,((~r(s(z), s(s(s(elem!1))))) | (~r(s(s(elem!1)), s(z))) | (~r(s(s(z)), s(s(elem!1)))) | (~r(s(s(z)), s(z)))), inference(lemma,lemma(discharge,[]))).
% 2.32/2.56 tff(6893,plain,
% 2.32/2.56 (~r(s(s(z)), s(s(elem!1)))),
% 2.32/2.56 inference(unit_resolution,[status(thm)],[6892, 392, 119, 4577])).
% 2.32/2.56 tff(6894,plain,
% 2.32/2.56 (b(s(s(z)), s(s(elem!1)))),
% 2.32/2.56 inference(unit_resolution,[status(thm)],[390, 6893, 52])).
% 2.32/2.56 tff(6895,plain,
% 2.32/2.56 ($false),
% 2.32/2.56 inference(unit_resolution,[status(thm)],[2068, 6894, 6884, 463, 839])).
% 2.32/2.56 tff(6896,plain,((~r(s(s(z)), s(z))) | (~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (s(s(z)) = s(s(elem!1))) | (~r(s(z), s(s(s(elem!1))))) | (~r(s(s(elem!1)), s(z))) | (~r(s(s(s(elem!1))), s(z))) | (~r(s(z), s(s(elem!1))))), inference(lemma,lemma(discharge,[]))).
% 2.32/2.56 tff(6897,plain,
% 2.32/2.56 (~r(s(s(z)), s(z))),
% 2.32/2.56 inference(unit_resolution,[status(thm)],[6896, 52, 6872, 6882, 6880, 4577, 6870, 311])).
% 2.32/2.56 tff(6898,plain,
% 2.32/2.56 (b(s(s(z)), s(z))),
% 2.32/2.56 inference(unit_resolution,[status(thm)],[308, 6897])).
% 2.32/2.56 tff(6899,plain,
% 2.32/2.56 (~b(s(s(s(s(elem!1)))), s(z))),
% 2.32/2.56 inference(unit_resolution,[status(thm)],[5785, 333, 118, 53, 156, 155])).
% 2.32/2.56 tff(6900,plain,
% 2.32/2.56 (r(s(s(s(s(elem!1)))), s(z))),
% 2.32/2.56 inference(unit_resolution,[status(thm)],[661, 6899])).
% 2.32/2.56 tff(6901,plain,
% 2.32/2.56 (s(s(s(s(elem!1)))) = s(s(elem!1))),
% 2.32/2.56 inference(unit_resolution,[status(thm)],[5809, 6900, 311, 6870, 463, 4577, 361])).
% 2.32/2.56 tff(6902,plain,
% 2.32/2.56 (s(s(s(elem!1))) = s(elem!1)),
% 2.32/2.56 inference(unit_resolution,[status(thm)],[1166, 6901])).
% 2.32/2.56 tff(6903,plain,
% 2.32/2.56 (b(s(s(elem!1)), s(s(s(elem!1)))) <=> b(s(s(elem!1)), s(elem!1))),
% 2.32/2.56 inference(monotonicity,[status(thm)],[6902])).
% 2.32/2.56 tff(6904,plain,
% 2.32/2.56 (b(s(s(elem!1)), s(elem!1))),
% 2.32/2.56 inference(modus_ponens,[status(thm)],[463, 6903])).
% 2.32/2.56 tff(6905,plain,
% 2.32/2.56 (~r(z, s(s(elem!1)))),
% 2.32/2.56 inference(unit_resolution,[status(thm)],[5997, 333, 155, 4577])).
% 2.32/2.56 tff(6906,plain,
% 2.32/2.56 (b(z, s(s(elem!1)))),
% 2.32/2.56 inference(unit_resolution,[status(thm)],[1795, 6905])).
% 2.32/2.56 tff(6907,plain,
% 2.32/2.56 (b(s(s(s(elem!1))), s(s(elem!1))) <=> b(s(elem!1), s(s(elem!1)))),
% 2.32/2.56 inference(monotonicity,[status(thm)],[6902])).
% 2.32/2.56 tff(6908,plain,
% 2.32/2.56 (b(s(elem!1), s(s(elem!1)))),
% 2.32/2.56 inference(modus_ponens,[status(thm)],[839, 6907])).
% 2.32/2.56 tff(6909,plain,
% 2.32/2.56 (b(s(s(s(elem!1))), z) <=> b(s(elem!1), z)),
% 2.32/2.56 inference(monotonicity,[status(thm)],[6902])).
% 2.32/2.56 tff(6910,plain,
% 2.32/2.56 (b(s(elem!1), z)),
% 2.32/2.56 inference(modus_ponens,[status(thm)],[121, 6909])).
% 2.32/2.56 tff(6911,plain,
% 2.32/2.56 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), z)) | (~b(z, s(s(elem!1)))) | (~b(s(elem!1), s(s(elem!1)))) | (~b(s(s(elem!1)), s(elem!1))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(elem!1), z)) | (~b(z, s(s(elem!1)))) | (~b(s(elem!1), s(s(elem!1)))) | (~b(s(s(elem!1)), s(elem!1))))),
% 2.32/2.56 inference(rewrite,[status(thm)],[])).
% 2.32/2.56 tff(6912,plain,
% 2.32/2.56 (((~b(s(elem!1), s(s(elem!1)))) | (~b(s(elem!1), s(s(elem!1)))) | (~b(s(s(elem!1)), s(elem!1))) | (~b(z, s(s(elem!1)))) | (~b(s(elem!1), s(s(elem!1)))) | (~b(s(elem!1), z))) <=> ((~b(s(elem!1), z)) | (~b(z, s(s(elem!1)))) | (~b(s(elem!1), s(s(elem!1)))) | (~b(s(s(elem!1)), s(elem!1))))),
% 2.32/2.56 inference(rewrite,[status(thm)],[])).
% 2.32/2.56 tff(6913,plain,
% 2.32/2.56 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), s(s(elem!1)))) | (~b(s(elem!1), s(s(elem!1)))) | (~b(s(s(elem!1)), s(elem!1))) | (~b(z, s(s(elem!1)))) | (~b(s(elem!1), s(s(elem!1)))) | (~b(s(elem!1), z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), z)) | (~b(z, s(s(elem!1)))) | (~b(s(elem!1), s(s(elem!1)))) | (~b(s(s(elem!1)), s(elem!1)))))),
% 2.32/2.56 inference(monotonicity,[status(thm)],[6912])).
% 2.32/2.56 tff(6914,plain,
% 2.32/2.56 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), s(s(elem!1)))) | (~b(s(elem!1), s(s(elem!1)))) | (~b(s(s(elem!1)), s(elem!1))) | (~b(z, s(s(elem!1)))) | (~b(s(elem!1), s(s(elem!1)))) | (~b(s(elem!1), z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(elem!1), z)) | (~b(z, s(s(elem!1)))) | (~b(s(elem!1), s(s(elem!1)))) | (~b(s(s(elem!1)), s(elem!1))))),
% 2.32/2.56 inference(transitivity,[status(thm)],[6913, 6911])).
% 2.32/2.56 tff(6915,plain,
% 2.32/2.56 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), s(s(elem!1)))) | (~b(s(elem!1), s(s(elem!1)))) | (~b(s(s(elem!1)), s(elem!1))) | (~b(z, s(s(elem!1)))) | (~b(s(elem!1), s(s(elem!1)))) | (~b(s(elem!1), z)))),
% 2.32/2.56 inference(quant_inst,[status(thm)],[])).
% 2.32/2.56 tff(6916,plain,
% 2.32/2.56 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(elem!1), z)) | (~b(z, s(s(elem!1)))) | (~b(s(elem!1), s(s(elem!1)))) | (~b(s(s(elem!1)), s(elem!1)))),
% 2.32/2.56 inference(modus_ponens,[status(thm)],[6915, 6914])).
% 2.32/2.56 tff(6917,plain,
% 2.32/2.56 ($false),
% 2.32/2.56 inference(unit_resolution,[status(thm)],[6916, 166, 2748, 2747, 1820, 1631])).
% 2.32/2.56 tff(6918,plain,((~b(s(s(elem!1)), s(elem!1))) | (~b(s(elem!1), s(s(elem!1)))) | (~b(s(elem!1), z)) | (~b(z, s(s(elem!1))))), inference(lemma,lemma(discharge,[]))).
% 2.32/2.56 tff(6919,plain,
% 2.32/2.56 ($false),
% 2.32/2.56 inference(unit_resolution,[status(thm)],[6918, 6910, 6908, 6906, 6904])).
% 2.32/2.56 tff(6920,plain,((~r(s(s(z)), s(s(elem!1)))) | (~b(s(s(s(elem!1))), z)) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(s(elem!1)), s(s(s(elem!1))))) | (~r(s(z), s(s(elem!1)))) | (~r(s(s(elem!1)), s(z))) | (s(s(s(elem!1))) = s(s(s(s(elem!1))))) | (~b(z, s(z))) | (~b(s(z), z)) | (~b(s(s(z)), s(z))) | (~r(z, s(s(z))))), inference(lemma,lemma(discharge,[]))).
% 2.32/2.56 tff(6921,plain,
% 2.32/2.56 (~r(s(s(z)), s(s(elem!1)))),
% 2.32/2.56 inference(unit_resolution,[status(thm)],[6920, 6898, 6872, 6882, 311, 4577, 358, 118, 53, 121, 155])).
% 2.32/2.56 tff(6922,plain,
% 2.32/2.56 (b(s(s(z)), s(s(elem!1)))),
% 2.32/2.56 inference(unit_resolution,[status(thm)],[390, 6921, 52])).
% 2.32/2.56 tff(6923,plain,
% 2.32/2.56 (~b(s(s(s(elem!1))), s(s(z)))),
% 2.32/2.56 inference(unit_resolution,[status(thm)],[2068, 6922, 6882, 6872])).
% 2.32/2.56 tff(6924,plain,
% 2.32/2.56 (r(s(s(s(elem!1))), s(s(z)))),
% 2.32/2.56 inference(unit_resolution,[status(thm)],[218, 6923])).
% 2.32/2.56 tff(6925,plain,
% 2.32/2.56 ((~b(s(s(z)), s(s(elem!1)))) | (~b(s(s(z)), s(s(s(elem!1)))))),
% 2.32/2.56 inference(unit_resolution,[status(thm)],[3545, 166, 6882, 118, 121, 6898])).
% 2.32/2.56 tff(6926,plain,
% 2.32/2.56 (~b(s(s(z)), s(s(s(elem!1))))),
% 2.32/2.56 inference(unit_resolution,[status(thm)],[6925, 6922])).
% 2.32/2.56 tff(6927,plain,
% 2.32/2.56 (r(s(s(z)), s(s(s(elem!1))))),
% 2.32/2.56 inference(unit_resolution,[status(thm)],[279, 6926])).
% 2.32/2.56 tff(6928,plain,
% 2.32/2.56 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(s(elem!1))))) | (~r(s(s(z)), s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), s(s(z)))) | (~r(z, s(s(z)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, s(s(s(elem!1))))) | (~r(s(s(z)), s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), s(s(z)))) | (~r(z, s(s(z)))))),
% 2.32/2.56 inference(rewrite,[status(thm)],[])).
% 2.32/2.56 tff(6929,plain,
% 2.32/2.56 (((~r(s(s(z)), s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), s(s(z)))) | (~r(z, s(s(z)))) | (~r(z, s(s(s(elem!1)))))) <=> ((~r(z, s(s(s(elem!1))))) | (~r(s(s(z)), s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), s(s(z)))) | (~r(z, s(s(z)))))),
% 2.32/2.56 inference(rewrite,[status(thm)],[])).
% 2.32/2.56 tff(6930,plain,
% 2.32/2.56 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(z)), s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), s(s(z)))) | (~r(z, s(s(z)))) | (~r(z, s(s(s(elem!1))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(s(elem!1))))) | (~r(s(s(z)), s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), s(s(z)))) | (~r(z, s(s(z))))))),
% 2.32/2.56 inference(monotonicity,[status(thm)],[6929])).
% 2.32/2.56 tff(6931,plain,
% 2.32/2.56 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(z)), s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), s(s(z)))) | (~r(z, s(s(z)))) | (~r(z, s(s(s(elem!1))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, s(s(s(elem!1))))) | (~r(s(s(z)), s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), s(s(z)))) | (~r(z, s(s(z)))))),
% 2.32/2.56 inference(transitivity,[status(thm)],[6930, 6928])).
% 2.32/2.56 tff(6932,plain,
% 2.32/2.56 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(z)), s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), s(s(z)))) | (~r(z, s(s(z)))) | (~r(z, s(s(s(elem!1))))))),
% 2.32/2.56 inference(quant_inst,[status(thm)],[])).
% 2.32/2.56 tff(6933,plain,
% 2.32/2.56 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, s(s(s(elem!1))))) | (~r(s(s(z)), s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), s(s(z)))) | (~r(z, s(s(z))))),
% 2.32/2.56 inference(modus_ponens,[status(thm)],[6932, 6931])).
% 2.32/2.56 tff(6934,plain,
% 2.32/2.56 (~r(z, s(s(s(elem!1))))),
% 2.32/2.56 inference(unit_resolution,[status(thm)],[6933, 197, 155, 6927, 6924])).
% 2.32/2.56 tff(6935,plain,
% 2.32/2.56 (b(z, s(s(s(elem!1))))),
% 2.32/2.56 inference(unit_resolution,[status(thm)],[261, 6934])).
% 2.32/2.56 tff(6936,plain,
% 2.32/2.56 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(z, s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), z)) | (~b(s(s(s(z))), z)) | (~b(s(s(s(elem!1))), s(s(s(z))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(z, s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), z)) | (~b(s(s(s(z))), z)) | (~b(s(s(s(elem!1))), s(s(s(z))))))),
% 2.32/2.56 inference(rewrite,[status(thm)],[])).
% 2.32/2.56 tff(6937,plain,
% 2.32/2.56 (((~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(z, s(s(s(elem!1))))) | (~b(s(s(s(z))), z)) | (~b(s(s(s(elem!1))), z)) | (~b(s(s(s(elem!1))), s(s(s(z)))))) <=> ((~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(z, s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), z)) | (~b(s(s(s(z))), z)) | (~b(s(s(s(elem!1))), s(s(s(z))))))),
% 2.32/2.57 inference(rewrite,[status(thm)],[])).
% 2.32/2.57 tff(6938,plain,
% 2.32/2.57 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(z, s(s(s(elem!1))))) | (~b(s(s(s(z))), z)) | (~b(s(s(s(elem!1))), z)) | (~b(s(s(s(elem!1))), s(s(s(z))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(z, s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), z)) | (~b(s(s(s(z))), z)) | (~b(s(s(s(elem!1))), s(s(s(z)))))))),
% 2.32/2.57 inference(monotonicity,[status(thm)],[6937])).
% 2.32/2.57 tff(6939,plain,
% 2.32/2.57 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(z, s(s(s(elem!1))))) | (~b(s(s(s(z))), z)) | (~b(s(s(s(elem!1))), z)) | (~b(s(s(s(elem!1))), s(s(s(z))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(z, s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), z)) | (~b(s(s(s(z))), z)) | (~b(s(s(s(elem!1))), s(s(s(z))))))),
% 2.32/2.57 inference(transitivity,[status(thm)],[6938, 6936])).
% 2.32/2.57 tff(6940,plain,
% 2.32/2.57 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(z, s(s(s(elem!1))))) | (~b(s(s(s(z))), z)) | (~b(s(s(s(elem!1))), z)) | (~b(s(s(s(elem!1))), s(s(s(z))))))),
% 2.32/2.57 inference(quant_inst,[status(thm)],[])).
% 2.32/2.57 tff(6941,plain,
% 2.32/2.57 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(z, s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), z)) | (~b(s(s(s(z))), z)) | (~b(s(s(s(elem!1))), s(s(s(z)))))),
% 2.32/2.57 inference(modus_ponens,[status(thm)],[6940, 6939])).
% 2.32/2.57 tff(6942,plain,
% 2.32/2.57 (~b(s(s(s(elem!1))), s(s(s(z))))),
% 2.32/2.57 inference(unit_resolution,[status(thm)],[6941, 166, 839, 240, 121, 1699])).
% 2.32/2.57 tff(6943,plain,
% 2.32/2.57 (r(s(s(s(elem!1))), s(s(s(z))))),
% 2.32/2.57 inference(unit_resolution,[status(thm)],[3574, 6942, 3567])).
% 2.32/2.57 tff(6944,plain,
% 2.32/2.57 ($false),
% 2.32/2.57 inference(unit_resolution,[status(thm)],[6519, 4047, 6943, 311, 6870])).
% 2.32/2.57 tff(6945,plain,((~b(s(s(s(z))), z)) | (~r(s(z), s(s(elem!1)))) | (s(s(s(elem!1))) = s(s(s(z)))) | (~b(s(z), z)) | (~b(z, s(z))) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(z, s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), z))), inference(lemma,lemma(discharge,[]))).
% 2.32/2.57 tff(6946,plain,
% 2.32/2.57 (~b(s(s(s(z))), z)),
% 2.32/2.57 inference(unit_resolution,[status(thm)],[6945, 140, 311, 53, 118, 6872, 6935, 121])).
% 2.32/2.57 tff(6947,plain,
% 2.32/2.57 (r(s(s(s(z))), z)),
% 2.32/2.57 inference(unit_resolution,[status(thm)],[1713, 6946])).
% 2.32/2.57 tff(6948,plain,
% 2.32/2.57 (~b(s(s(z)), z)),
% 2.32/2.57 inference(unit_resolution,[status(thm)],[181, 6898, 118, 53])).
% 2.32/2.57 tff(6949,plain,
% 2.32/2.57 (r(s(s(z)), z)),
% 2.32/2.57 inference(unit_resolution,[status(thm)],[186, 6948])).
% 2.32/2.57 tff(6950,plain,
% 2.32/2.57 (~r(s(s(s(z))), s(s(z)))),
% 2.32/2.57 inference(unit_resolution,[status(thm)],[1717, 197, 155, 6949, 6947])).
% 2.32/2.57 tff(6951,plain,
% 2.32/2.57 (b(s(s(s(z))), s(s(z)))),
% 2.32/2.57 inference(unit_resolution,[status(thm)],[1010, 6950])).
% 2.32/2.57 tff(6952,plain,
% 2.32/2.57 (((~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(z, s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(z, s(s(s(elem!1))))) | (~b(z, s(s(elem!1))))) <=> ((~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(z, s(s(s(elem!1))))) | (~b(z, s(s(elem!1)))))),
% 2.32/2.57 inference(rewrite,[status(thm)],[])).
% 2.32/2.57 tff(6953,plain,
% 2.32/2.57 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(z, s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(z, s(s(s(elem!1))))) | (~b(z, s(s(elem!1)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(z, s(s(s(elem!1))))) | (~b(z, s(s(elem!1))))))),
% 2.32/2.57 inference(monotonicity,[status(thm)],[6952])).
% 2.32/2.57 tff(6954,plain,
% 2.32/2.57 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(z, s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(z, s(s(s(elem!1))))) | (~b(z, s(s(elem!1)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(z, s(s(s(elem!1))))) | (~b(z, s(s(elem!1)))))),
% 2.32/2.57 inference(transitivity,[status(thm)],[6953, 1825])).
% 2.32/2.57 tff(6955,plain,
% 2.32/2.57 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(z, s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(z, s(s(s(elem!1))))) | (~b(z, s(s(elem!1)))))),
% 2.32/2.57 inference(quant_inst,[status(thm)],[])).
% 2.32/2.57 tff(6956,plain,
% 2.32/2.57 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(z, s(s(s(elem!1))))) | (~b(z, s(s(elem!1))))),
% 2.32/2.57 inference(modus_ponens,[status(thm)],[6955, 6954])).
% 2.32/2.57 tff(6957,plain,
% 2.32/2.57 ($false),
% 2.32/2.57 inference(unit_resolution,[status(thm)],[6956, 166, 6720, 6724, 240, 1820])).
% 2.32/2.57 tff(6958,plain,((~r(s(s(elem!1)), s(z))) | (~b(z, s(s(s(elem!1))))) | (~b(z, s(s(elem!1)))) | (s(s(elem!1)) = s(s(s(elem!1)))) | (~r(s(z), s(s(elem!1)))) | (~r(s(s(s(elem!1))), s(z)))), inference(lemma,lemma(discharge,[]))).
% 2.32/2.57 tff(6959,plain,
% 2.32/2.57 (~b(z, s(s(elem!1)))),
% 2.32/2.57 inference(unit_resolution,[status(thm)],[6958, 6935, 45, 311, 6870, 4577])).
% 2.32/2.57 tff(6960,plain,
% 2.32/2.57 (r(z, s(s(elem!1)))),
% 2.32/2.57 inference(unit_resolution,[status(thm)],[1795, 6959])).
% 2.32/2.57 tff(6961,plain,
% 2.32/2.57 (~r(s(s(elem!1)), s(s(z)))),
% 2.32/2.57 inference(unit_resolution,[status(thm)],[539, 6960, 155, 6927])).
% 2.32/2.57 tff(6962,plain,
% 2.32/2.57 (b(s(s(elem!1)), s(s(z)))),
% 2.32/2.57 inference(unit_resolution,[status(thm)],[441, 6961, 132])).
% 2.32/2.57 tff(6963,plain,
% 2.32/2.57 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(s(s(elem!1)), s(s(z)))) | (~b(s(s(z)), s(s(elem!1)))) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(s(elem!1)), s(s(s(z))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(s(s(elem!1)), s(s(z)))) | (~b(s(s(z)), s(s(elem!1)))) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(s(elem!1)), s(s(s(z))))))),
% 2.32/2.57 inference(rewrite,[status(thm)],[])).
% 2.32/2.57 tff(6964,plain,
% 2.32/2.57 (((~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(s(s(z)), s(s(elem!1)))) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(s(elem!1)), s(s(z)))) | (~b(s(s(elem!1)), s(s(s(z)))))) <=> ((~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(s(s(elem!1)), s(s(z)))) | (~b(s(s(z)), s(s(elem!1)))) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(s(elem!1)), s(s(s(z))))))),
% 2.32/2.57 inference(rewrite,[status(thm)],[])).
% 2.32/2.57 tff(6965,plain,
% 2.32/2.57 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(s(s(z)), s(s(elem!1)))) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(s(elem!1)), s(s(z)))) | (~b(s(s(elem!1)), s(s(s(z))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(s(s(elem!1)), s(s(z)))) | (~b(s(s(z)), s(s(elem!1)))) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(s(elem!1)), s(s(s(z)))))))),
% 2.32/2.57 inference(monotonicity,[status(thm)],[6964])).
% 2.32/2.57 tff(6966,plain,
% 2.32/2.57 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(s(s(z)), s(s(elem!1)))) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(s(elem!1)), s(s(z)))) | (~b(s(s(elem!1)), s(s(s(z))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(s(s(elem!1)), s(s(z)))) | (~b(s(s(z)), s(s(elem!1)))) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(s(elem!1)), s(s(s(z))))))),
% 2.32/2.57 inference(transitivity,[status(thm)],[6965, 6963])).
% 2.32/2.57 tff(6967,plain,
% 2.32/2.57 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(s(s(z)), s(s(elem!1)))) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(s(elem!1)), s(s(z)))) | (~b(s(s(elem!1)), s(s(s(z))))))),
% 2.32/2.57 inference(quant_inst,[status(thm)],[])).
% 2.32/2.57 tff(6968,plain,
% 2.32/2.57 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(s(s(elem!1)), s(s(z)))) | (~b(s(s(z)), s(s(elem!1)))) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(s(elem!1)), s(s(s(z)))))),
% 2.32/2.57 inference(modus_ponens,[status(thm)],[6967, 6966])).
% 2.32/2.57 tff(6969,plain,
% 2.32/2.57 (~b(s(s(elem!1)), s(s(s(z))))),
% 2.32/2.57 inference(unit_resolution,[status(thm)],[6968, 166, 6882, 6962, 6922, 6951])).
% 2.32/2.57 tff(6970,plain,
% 2.32/2.57 (~b(s(s(elem!1)), z)),
% 2.32/2.57 inference(unit_resolution,[status(thm)],[600, 6935, 121, 6882])).
% 2.32/2.57 tff(6971,plain,
% 2.32/2.57 (r(s(s(elem!1)), z)),
% 2.32/2.57 inference(unit_resolution,[status(thm)],[608, 6970])).
% 2.32/2.57 tff(6972,plain,
% 2.32/2.57 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(elem!1)), z)) | (~r(z, s(s(z)))) | (~r(s(s(s(z))), z)) | (~r(s(s(elem!1)), s(s(s(z))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(elem!1)), z)) | (~r(z, s(s(z)))) | (~r(s(s(s(z))), z)) | (~r(s(s(elem!1)), s(s(s(z))))))),
% 2.32/2.57 inference(rewrite,[status(thm)],[])).
% 2.32/2.57 tff(6973,plain,
% 2.32/2.57 (((~r(z, s(s(z)))) | (~r(s(s(s(z))), z)) | (~r(s(s(elem!1)), z)) | (~r(s(s(elem!1)), s(s(s(z)))))) <=> ((~r(s(s(elem!1)), z)) | (~r(z, s(s(z)))) | (~r(s(s(s(z))), z)) | (~r(s(s(elem!1)), s(s(s(z))))))),
% 2.32/2.57 inference(rewrite,[status(thm)],[])).
% 2.32/2.57 tff(6974,plain,
% 2.32/2.57 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(z)))) | (~r(s(s(s(z))), z)) | (~r(s(s(elem!1)), z)) | (~r(s(s(elem!1)), s(s(s(z))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(elem!1)), z)) | (~r(z, s(s(z)))) | (~r(s(s(s(z))), z)) | (~r(s(s(elem!1)), s(s(s(z)))))))),
% 2.32/2.57 inference(monotonicity,[status(thm)],[6973])).
% 2.32/2.57 tff(6975,plain,
% 2.32/2.57 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(z)))) | (~r(s(s(s(z))), z)) | (~r(s(s(elem!1)), z)) | (~r(s(s(elem!1)), s(s(s(z))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(elem!1)), z)) | (~r(z, s(s(z)))) | (~r(s(s(s(z))), z)) | (~r(s(s(elem!1)), s(s(s(z))))))),
% 2.32/2.57 inference(transitivity,[status(thm)],[6974, 6972])).
% 2.32/2.57 tff(6976,plain,
% 2.32/2.57 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(z)))) | (~r(s(s(s(z))), z)) | (~r(s(s(elem!1)), z)) | (~r(s(s(elem!1)), s(s(s(z))))))),
% 2.32/2.57 inference(quant_inst,[status(thm)],[])).
% 2.32/2.57 tff(6977,plain,
% 2.32/2.57 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(elem!1)), z)) | (~r(z, s(s(z)))) | (~r(s(s(s(z))), z)) | (~r(s(s(elem!1)), s(s(s(z)))))),
% 2.32/2.57 inference(modus_ponens,[status(thm)],[6976, 6975])).
% 2.32/2.57 tff(6978,plain,
% 2.32/2.57 (~r(s(s(elem!1)), s(s(s(z))))),
% 2.32/2.57 inference(unit_resolution,[status(thm)],[6977, 197, 155, 6971, 6947])).
% 2.32/2.57 tff(6979,plain,
% 2.32/2.57 ((s(s(elem!1)) = s(s(s(z)))) | b(s(s(elem!1)), s(s(s(z))))),
% 2.32/2.57 inference(unit_resolution,[status(thm)],[5091, 79, 6978])).
% 2.32/2.57 tff(6980,plain,
% 2.32/2.57 (s(s(elem!1)) = s(s(s(z)))),
% 2.32/2.57 inference(unit_resolution,[status(thm)],[6979, 6969])).
% 2.32/2.57 tff(6981,plain,
% 2.32/2.57 (s(s(s(elem!1))) = s(s(s(s(z))))),
% 2.32/2.57 inference(monotonicity,[status(thm)],[6980])).
% 2.32/2.57 tff(6982,plain,
% 2.32/2.57 (s(s(s(s(elem!1)))) = s(s(s(s(s(z)))))),
% 2.32/2.57 inference(monotonicity,[status(thm)],[6981])).
% 2.32/2.57 tff(6983,plain,
% 2.32/2.57 (s(s(s(s(s(z))))) = s(s(s(s(elem!1))))),
% 2.32/2.57 inference(symmetry,[status(thm)],[6982])).
% 2.32/2.57 tff(6984,plain,
% 2.32/2.57 ((s(s(z)) = s(s(s(s(s(z)))))) <=> (s(s(z)) = s(s(s(s(elem!1)))))),
% 2.32/2.57 inference(monotonicity,[status(thm)],[6983])).
% 2.32/2.57 tff(6985,plain,
% 2.32/2.57 ((s(s(z)) = s(s(s(s(s(z)))))) <=> (s(s(s(s(elem!1)))) = s(s(z)))),
% 2.32/2.57 inference(transitivity,[status(thm)],[6984, 1275])).
% 2.32/2.57 tff(6986,plain,
% 2.32/2.57 ((s(s(s(s(elem!1)))) = s(s(z))) <=> (s(s(z)) = s(s(s(s(s(z))))))),
% 2.32/2.57 inference(symmetry,[status(thm)],[6985])).
% 2.32/2.57 tff(6987,plain,
% 2.32/2.57 ((~(s(s(s(s(elem!1)))) = s(s(z)))) <=> (~(s(s(z)) = s(s(s(s(s(z)))))))),
% 2.32/2.57 inference(monotonicity,[status(thm)],[6986])).
% 2.32/2.57 tff(6988,plain,
% 2.32/2.57 (~(s(s(z)) = s(s(s(s(s(z))))))),
% 2.32/2.57 inference(modus_ponens,[status(thm)],[733, 6987])).
% 2.32/2.57 tff(6989,plain,
% 2.32/2.57 (b(s(s(s(s(s(z))))), s(z)) <=> b(s(s(s(s(elem!1)))), s(z))),
% 2.32/2.57 inference(monotonicity,[status(thm)],[6983])).
% 2.32/2.57 tff(6990,plain,
% 2.32/2.57 (b(s(s(s(s(elem!1)))), s(z)) <=> b(s(s(s(s(s(z))))), s(z))),
% 2.32/2.57 inference(symmetry,[status(thm)],[6989])).
% 2.32/2.57 tff(6991,plain,
% 2.32/2.57 (s(s(s(z))) = s(s(elem!1))),
% 2.32/2.57 inference(symmetry,[status(thm)],[6980])).
% 2.32/2.57 tff(6992,plain,
% 2.32/2.57 ((s(s(s(s(elem!1)))) = s(s(s(z)))) <=> (s(s(s(s(elem!1)))) = s(s(elem!1)))),
% 2.32/2.57 inference(monotonicity,[status(thm)],[6991])).
% 2.32/2.57 tff(6993,plain,
% 2.32/2.57 ((s(s(s(s(elem!1)))) = s(s(s(z)))) <=> (s(s(elem!1)) = s(s(s(s(elem!1)))))),
% 2.32/2.57 inference(transitivity,[status(thm)],[6992, 123])).
% 2.32/2.57 tff(6994,plain,
% 2.32/2.57 ((s(s(s(s(elem!1)))) = s(s(s(z)))) <=> (s(s(s(s(elem!1)))) = s(s(elem!1)))),
% 2.32/2.57 inference(transitivity,[status(thm)],[6993, 124])).
% 2.32/2.57 tff(6995,plain,
% 2.32/2.57 ((~(s(s(s(s(elem!1)))) = s(s(s(z))))) <=> (~(s(s(s(s(elem!1)))) = s(s(elem!1))))),
% 2.32/2.57 inference(monotonicity,[status(thm)],[6994])).
% 2.32/2.57 tff(6996,plain,
% 2.32/2.57 (~(s(s(s(s(elem!1)))) = s(s(elem!1)))),
% 2.32/2.57 inference(modus_ponens,[status(thm)],[5112, 6995])).
% 2.32/2.57 tff(6997,plain,
% 2.32/2.57 (~r(s(s(s(s(elem!1)))), s(z))),
% 2.32/2.57 inference(unit_resolution,[status(thm)],[5809, 6996, 311, 6870, 6882, 4577, 358])).
% 2.32/2.57 tff(6998,plain,
% 2.32/2.57 (b(s(s(s(s(elem!1)))), s(z))),
% 2.32/2.57 inference(unit_resolution,[status(thm)],[661, 6997])).
% 2.32/2.57 tff(6999,plain,
% 2.32/2.57 (b(s(s(s(s(s(z))))), s(z))),
% 2.32/2.57 inference(modus_ponens,[status(thm)],[6998, 6990])).
% 2.32/2.57 tff(7000,plain,
% 2.32/2.57 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), z)) | (~b(z, s(z))) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(s(s(s(s(s(z))))), z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), z)) | (~b(z, s(z))) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(s(s(s(s(s(z))))), z)))),
% 2.32/2.57 inference(rewrite,[status(thm)],[])).
% 2.32/2.57 tff(7001,plain,
% 2.32/2.57 (((~b(z, s(z))) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(s(z), z)) | (~b(z, s(z))) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(s(s(s(s(s(z))))), z))) <=> ((~b(s(z), z)) | (~b(z, s(z))) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(s(s(s(s(s(z))))), z)))),
% 2.32/2.58 inference(rewrite,[status(thm)],[])).
% 2.32/2.58 tff(7002,plain,
% 2.32/2.58 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(z))) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(s(z), z)) | (~b(z, s(z))) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(s(s(s(s(s(z))))), z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), z)) | (~b(z, s(z))) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(s(s(s(s(s(z))))), z))))),
% 2.32/2.58 inference(monotonicity,[status(thm)],[7001])).
% 2.32/2.58 tff(7003,plain,
% 2.32/2.58 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(z))) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(s(z), z)) | (~b(z, s(z))) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(s(s(s(s(s(z))))), z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), z)) | (~b(z, s(z))) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(s(s(s(s(s(z))))), z)))),
% 2.32/2.58 inference(transitivity,[status(thm)],[7002, 7000])).
% 2.32/2.58 tff(7004,plain,
% 2.32/2.58 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(z))) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(s(z), z)) | (~b(z, s(z))) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(s(s(s(s(s(z))))), z)))),
% 2.32/2.58 inference(quant_inst,[status(thm)],[])).
% 2.32/2.58 tff(7005,plain,
% 2.32/2.58 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), z)) | (~b(z, s(z))) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(s(s(s(s(s(z))))), z))),
% 2.32/2.58 inference(modus_ponens,[status(thm)],[7004, 7003])).
% 2.32/2.58 tff(7006,plain,
% 2.32/2.58 ((~b(s(s(s(s(s(z))))), s(z))) | (~b(s(s(s(s(s(z))))), z))),
% 2.32/2.58 inference(unit_resolution,[status(thm)],[7005, 166, 53, 118])).
% 2.32/2.58 tff(7007,plain,
% 2.32/2.58 (~b(s(s(s(s(s(z))))), z)),
% 2.32/2.58 inference(unit_resolution,[status(thm)],[7006, 6999])).
% 2.32/2.58 tff(7008,plain,
% 2.32/2.58 (r(s(s(s(s(s(z))))), z)),
% 2.32/2.58 inference(unit_resolution,[status(thm)],[5198, 79, 5195, 7007])).
% 2.32/2.58 tff(7009,plain,
% 2.32/2.58 (~r(s(s(z)), s(s(s(s(s(z))))))),
% 2.32/2.58 inference(unit_resolution,[status(thm)],[5205, 197, 155, 6949, 7008])).
% 2.32/2.58 tff(7010,plain,
% 2.32/2.58 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), z)) | (~b(z, s(z))) | (~b(s(s(z)), s(z))) | (~b(s(s(z)), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), z)) | (~b(z, s(z))) | (~b(s(s(z)), s(z))) | (~b(s(s(z)), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), s(z))))),
% 2.32/2.58 inference(rewrite,[status(thm)],[])).
% 2.32/2.58 tff(7011,plain,
% 2.32/2.58 (((~b(z, s(z))) | (~b(s(s(z)), s(z))) | (~b(s(z), z)) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(s(s(z)), s(z))) | (~b(s(s(z)), s(s(s(s(s(z)))))))) <=> ((~b(s(z), z)) | (~b(z, s(z))) | (~b(s(s(z)), s(z))) | (~b(s(s(z)), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), s(z))))),
% 2.32/2.58 inference(rewrite,[status(thm)],[])).
% 2.32/2.58 tff(7012,plain,
% 2.32/2.58 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(z))) | (~b(s(s(z)), s(z))) | (~b(s(z), z)) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(s(s(z)), s(z))) | (~b(s(s(z)), s(s(s(s(s(z))))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), z)) | (~b(z, s(z))) | (~b(s(s(z)), s(z))) | (~b(s(s(z)), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), s(z)))))),
% 2.32/2.58 inference(monotonicity,[status(thm)],[7011])).
% 2.32/2.58 tff(7013,plain,
% 2.32/2.58 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(z))) | (~b(s(s(z)), s(z))) | (~b(s(z), z)) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(s(s(z)), s(z))) | (~b(s(s(z)), s(s(s(s(s(z))))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), z)) | (~b(z, s(z))) | (~b(s(s(z)), s(z))) | (~b(s(s(z)), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), s(z))))),
% 2.32/2.58 inference(transitivity,[status(thm)],[7012, 7010])).
% 2.32/2.58 tff(7014,plain,
% 2.32/2.58 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(z))) | (~b(s(s(z)), s(z))) | (~b(s(z), z)) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(s(s(z)), s(z))) | (~b(s(s(z)), s(s(s(s(s(z))))))))),
% 2.32/2.58 inference(quant_inst,[status(thm)],[])).
% 2.32/2.58 tff(7015,plain,
% 2.32/2.58 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), z)) | (~b(z, s(z))) | (~b(s(s(z)), s(z))) | (~b(s(s(z)), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), s(z)))),
% 2.32/2.58 inference(modus_ponens,[status(thm)],[7014, 7013])).
% 2.32/2.58 tff(7016,plain,
% 2.32/2.58 ((~b(s(s(z)), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), s(z)))),
% 2.32/2.58 inference(unit_resolution,[status(thm)],[7015, 166, 53, 118, 6898])).
% 2.32/2.58 tff(7017,plain,
% 2.32/2.58 (~b(s(s(z)), s(s(s(s(s(z))))))),
% 2.32/2.58 inference(unit_resolution,[status(thm)],[7016, 6999])).
% 2.32/2.58 tff(7018,plain,
% 2.32/2.58 ((s(s(z)) = s(s(s(s(s(z)))))) | r(s(s(z)), s(s(s(s(s(z))))))),
% 2.32/2.58 inference(unit_resolution,[status(thm)],[5216, 79, 7017])).
% 2.32/2.58 tff(7019,plain,
% 2.32/2.58 ($false),
% 2.32/2.58 inference(unit_resolution,[status(thm)],[7018, 7009, 6988])).
% 2.32/2.58 tff(7020,plain,((s(s(z)) = s(s(elem!1))) | (~r(z, s(s(z)))) | (~b(s(z), z)) | (~b(z, s(z))) | (~r(s(z), s(s(elem!1)))) | (~r(s(s(elem!1)), s(z))) | (~b(s(s(s(elem!1))), z)) | (s(s(elem!1)) = s(s(s(elem!1))))), inference(lemma,lemma(discharge,[]))).
% 2.32/2.58 tff(7021,plain,
% 2.32/2.58 (s(s(z)) = s(s(elem!1))),
% 2.32/2.58 inference(unit_resolution,[status(thm)],[7020, 6863, 152, 118, 85, 4558, 6718, 45])).
% 2.32/2.58 tff(7022,plain,
% 2.32/2.58 (s(s(s(z))) = s(s(s(elem!1)))),
% 2.32/2.58 inference(monotonicity,[status(thm)],[7021])).
% 2.32/2.58 tff(7023,plain,
% 2.32/2.58 (s(s(s(s(z)))) = s(s(s(s(elem!1))))),
% 2.32/2.58 inference(monotonicity,[status(thm)],[7022])).
% 2.32/2.58 tff(7024,plain,
% 2.32/2.58 (s(s(s(s(elem!1)))) = s(s(s(s(z))))),
% 2.32/2.58 inference(symmetry,[status(thm)],[7023])).
% 2.32/2.58 tff(7025,plain,
% 2.32/2.58 (s(elem!1) = s(z)),
% 2.32/2.58 inference(unit_resolution,[status(thm)],[43, 7021])).
% 2.32/2.58 tff(7026,plain,
% 2.32/2.58 (z = elem!1),
% 2.32/2.58 inference(unit_resolution,[status(thm)],[30, 7025])).
% 2.32/2.58 tff(7027,plain,
% 2.32/2.58 ((s(s(s(s(elem!1)))) = z) <=> (s(s(s(s(elem!1)))) = elem!1)),
% 2.32/2.58 inference(monotonicity,[status(thm)],[7026])).
% 2.32/2.58 tff(7028,plain,
% 2.32/2.58 ((s(s(s(s(elem!1)))) = z) <=> (elem!1 = s(s(s(s(elem!1)))))),
% 2.32/2.58 inference(transitivity,[status(thm)],[7027, 2287])).
% 2.32/2.58 tff(7029,plain,
% 2.32/2.58 ((~(s(s(s(s(elem!1)))) = z)) <=> (~(elem!1 = s(s(s(s(elem!1))))))),
% 2.32/2.58 inference(monotonicity,[status(thm)],[7028])).
% 2.32/2.58 tff(7030,plain,
% 2.32/2.58 (~(elem!1 = s(s(s(s(elem!1)))))),
% 2.32/2.58 inference(modus_ponens,[status(thm)],[626, 7029])).
% 2.32/2.58 tff(7031,plain,
% 2.32/2.58 (~b(s(s(s(elem!1))), s(z))),
% 2.32/2.58 inference(unit_resolution,[status(thm)],[6868, 166, 6863, 118, 6718])).
% 2.32/2.58 tff(7032,plain,
% 2.32/2.58 (r(s(s(s(elem!1))), s(z))),
% 2.32/2.58 inference(unit_resolution,[status(thm)],[1849, 7031])).
% 2.32/2.58 tff(7033,plain,
% 2.32/2.58 (~b(s(z), s(s(s(elem!1))))),
% 2.32/2.58 inference(unit_resolution,[status(thm)],[6878, 166, 6863, 118, 6718])).
% 2.32/2.58 tff(7034,plain,
% 2.32/2.58 (r(s(z), s(s(s(elem!1))))),
% 2.32/2.58 inference(unit_resolution,[status(thm)],[116, 7033])).
% 2.32/2.58 tff(7035,plain,
% 2.32/2.58 (~r(s(s(elem!1)), s(s(s(elem!1))))),
% 2.32/2.58 inference(unit_resolution,[status(thm)],[764, 7034, 7032, 85])).
% 2.32/2.58 tff(7036,plain,
% 2.32/2.58 (b(s(s(elem!1)), s(s(s(elem!1))))),
% 2.32/2.58 inference(unit_resolution,[status(thm)],[461, 7035, 45])).
% 2.32/2.58 tff(7037,plain,
% 2.32/2.58 ((s(s(s(s(elem!1)))) = s(s(z))) <=> (s(s(s(s(elem!1)))) = s(s(elem!1)))),
% 2.32/2.58 inference(monotonicity,[status(thm)],[7021])).
% 2.32/2.58 tff(7038,plain,
% 2.32/2.58 ((s(s(s(s(elem!1)))) = s(s(z))) <=> (s(s(elem!1)) = s(s(s(s(elem!1)))))),
% 2.32/2.58 inference(transitivity,[status(thm)],[7037, 123])).
% 2.32/2.58 tff(7039,plain,
% 2.32/2.58 ((s(s(s(s(elem!1)))) = s(s(z))) <=> (s(s(s(s(elem!1)))) = s(s(elem!1)))),
% 2.32/2.58 inference(transitivity,[status(thm)],[7038, 124])).
% 2.32/2.58 tff(7040,plain,
% 2.32/2.58 ((~(s(s(s(s(elem!1)))) = s(s(z)))) <=> (~(s(s(s(s(elem!1)))) = s(s(elem!1))))),
% 2.32/2.58 inference(monotonicity,[status(thm)],[7039])).
% 2.32/2.58 tff(7041,plain,
% 2.32/2.58 (~(s(s(s(s(elem!1)))) = s(s(elem!1)))),
% 2.32/2.58 inference(modus_ponens,[status(thm)],[733, 7040])).
% 2.32/2.58 tff(7042,plain,
% 2.32/2.58 (~r(s(s(s(s(elem!1)))), s(z))),
% 2.32/2.58 inference(unit_resolution,[status(thm)],[5809, 7041, 85, 7032, 7036, 4558, 358])).
% 2.32/2.58 tff(7043,plain,
% 2.32/2.58 (b(s(s(s(s(elem!1)))), s(z))),
% 2.32/2.58 inference(unit_resolution,[status(thm)],[661, 7042])).
% 2.32/2.58 tff(7044,plain,
% 2.32/2.58 (b(s(z), z) <=> b(s(z), elem!1)),
% 2.32/2.58 inference(monotonicity,[status(thm)],[7026])).
% 2.32/2.58 tff(7045,plain,
% 2.32/2.58 (b(s(z), elem!1)),
% 2.32/2.58 inference(modus_ponens,[status(thm)],[6863, 7044])).
% 2.32/2.58 tff(7046,plain,
% 2.32/2.58 (b(z, s(z)) <=> b(elem!1, s(z))),
% 2.32/2.58 inference(monotonicity,[status(thm)],[7026])).
% 2.32/2.58 tff(7047,plain,
% 2.32/2.58 (b(elem!1, s(z))),
% 2.32/2.58 inference(modus_ponens,[status(thm)],[118, 7046])).
% 2.32/2.58 tff(7048,plain,
% 2.32/2.58 (~b(elem!1, s(s(s(s(elem!1)))))),
% 2.32/2.58 inference(unit_resolution,[status(thm)],[3430, 166, 7047, 7045, 7043])).
% 2.32/2.58 tff(7049,plain,
% 2.32/2.58 (r(elem!1, s(s(s(s(elem!1)))))),
% 2.32/2.58 inference(unit_resolution,[status(thm)],[2427, 7048, 7030])).
% 2.32/2.58 tff(7050,plain,
% 2.32/2.58 ((~(s(s(s(s(elem!1)))) = z)) <=> (~(s(s(s(s(elem!1)))) = elem!1))),
% 2.32/2.58 inference(monotonicity,[status(thm)],[7027])).
% 2.32/2.58 tff(7051,plain,
% 2.32/2.58 (~(s(s(s(s(elem!1)))) = elem!1)),
% 2.32/2.58 inference(modus_ponens,[status(thm)],[626, 7050])).
% 2.32/2.58 tff(7052,plain,
% 2.32/2.58 (~b(s(s(s(s(elem!1)))), elem!1)),
% 2.32/2.58 inference(unit_resolution,[status(thm)],[6168, 166, 7047, 7045, 7043])).
% 2.32/2.58 tff(7053,plain,
% 2.32/2.58 (r(s(s(s(s(elem!1)))), elem!1)),
% 2.32/2.58 inference(unit_resolution,[status(thm)],[719, 7052, 7051])).
% 2.32/2.58 tff(7054,plain,
% 2.32/2.58 (~(s(s(s(s(s(s(s(elem!1))))))) = elem!1)),
% 2.32/2.58 inference(unit_resolution,[status(thm)],[6283, 7026])).
% 2.32/2.58 tff(7055,plain,
% 2.32/2.58 (~b(s(z), s(s(z)))),
% 2.32/2.58 inference(unit_resolution,[status(thm)],[4398, 7021, 54])).
% 2.32/2.58 tff(7056,plain,
% 2.32/2.58 (r(s(z), s(s(z)))),
% 2.32/2.58 inference(unit_resolution,[status(thm)],[427, 7055])).
% 2.32/2.58 tff(7057,plain,
% 2.32/2.58 (r(s(s(s(z))), s(z)) <=> r(s(s(s(elem!1))), s(z))),
% 2.32/2.58 inference(monotonicity,[status(thm)],[7022])).
% 2.32/2.58 tff(7058,plain,
% 2.32/2.58 (r(s(s(s(elem!1))), s(z)) <=> r(s(s(s(z))), s(z))),
% 2.32/2.58 inference(symmetry,[status(thm)],[7057])).
% 2.32/2.58 tff(7059,plain,
% 2.32/2.58 (r(s(s(s(z))), s(z))),
% 2.32/2.58 inference(modus_ponens,[status(thm)],[7032, 7058])).
% 2.32/2.58 tff(7060,plain,
% 2.32/2.58 (s(s(elem!1)) = s(s(z))),
% 2.32/2.58 inference(unit_resolution,[status(thm)],[17, 7026])).
% 2.32/2.58 tff(7061,plain,
% 2.32/2.58 (~(s(s(s(s(s(s(elem!1)))))) = s(s(elem!1)))),
% 2.32/2.58 inference(unit_resolution,[status(thm)],[4986, 7025])).
% 2.32/2.58 tff(7062,plain,
% 2.32/2.58 (~(s(s(s(z))) = s(s(s(s(s(s(s(elem!1))))))))),
% 2.32/2.58 inference(unit_resolution,[status(thm)],[4995, 7061, 7060])).
% 2.32/2.58 tff(7063,plain,
% 2.32/2.58 (~(s(s(s(s(s(s(s(elem!1))))))) = s(z))),
% 2.32/2.58 inference(unit_resolution,[status(thm)],[4900, 7026])).
% 2.32/2.58 tff(7064,plain,
% 2.32/2.58 (b(s(s(s(z))), elem!1) <=> b(s(s(s(elem!1))), elem!1)),
% 2.32/2.58 inference(monotonicity,[status(thm)],[7022])).
% 2.32/2.58 tff(7065,plain,
% 2.32/2.58 (b(s(s(s(elem!1))), elem!1) <=> b(s(s(s(z))), elem!1)),
% 2.32/2.58 inference(symmetry,[status(thm)],[7064])).
% 2.32/2.58 tff(7066,plain,
% 2.32/2.58 (b(s(s(s(elem!1))), elem!1)),
% 2.32/2.58 inference(unit_resolution,[status(thm)],[634, 7026, 6718])).
% 2.32/2.58 tff(7067,plain,
% 2.32/2.58 (b(s(s(s(z))), elem!1)),
% 2.32/2.58 inference(modus_ponens,[status(thm)],[7066, 7065])).
% 2.32/2.58 tff(7068,plain,
% 2.32/2.58 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(z))) | (~b(s(z), elem!1)) | (~b(s(s(s(z))), elem!1)) | (~b(s(s(s(s(s(s(s(elem!1))))))), elem!1)) | (~b(s(s(s(z))), s(s(s(s(s(s(s(elem!1))))))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(z))) | (~b(s(z), elem!1)) | (~b(s(s(s(z))), elem!1)) | (~b(s(s(s(s(s(s(s(elem!1))))))), elem!1)) | (~b(s(s(s(z))), s(s(s(s(s(s(s(elem!1))))))))))),
% 2.32/2.58 inference(rewrite,[status(thm)],[])).
% 2.32/2.58 tff(7069,plain,
% 2.32/2.58 (((~b(s(z), elem!1)) | (~b(s(s(s(z))), elem!1)) | (~b(elem!1, s(z))) | (~b(s(s(s(s(s(s(s(elem!1))))))), elem!1)) | (~b(s(s(s(z))), elem!1)) | (~b(s(s(s(z))), s(s(s(s(s(s(s(elem!1)))))))))) <=> ((~b(elem!1, s(z))) | (~b(s(z), elem!1)) | (~b(s(s(s(z))), elem!1)) | (~b(s(s(s(s(s(s(s(elem!1))))))), elem!1)) | (~b(s(s(s(z))), s(s(s(s(s(s(s(elem!1))))))))))),
% 2.32/2.58 inference(rewrite,[status(thm)],[])).
% 2.32/2.58 tff(7070,plain,
% 2.32/2.58 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), elem!1)) | (~b(s(s(s(z))), elem!1)) | (~b(elem!1, s(z))) | (~b(s(s(s(s(s(s(s(elem!1))))))), elem!1)) | (~b(s(s(s(z))), elem!1)) | (~b(s(s(s(z))), s(s(s(s(s(s(s(elem!1))))))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(z))) | (~b(s(z), elem!1)) | (~b(s(s(s(z))), elem!1)) | (~b(s(s(s(s(s(s(s(elem!1))))))), elem!1)) | (~b(s(s(s(z))), s(s(s(s(s(s(s(elem!1)))))))))))),
% 2.32/2.58 inference(monotonicity,[status(thm)],[7069])).
% 2.32/2.58 tff(7071,plain,
% 2.32/2.58 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), elem!1)) | (~b(s(s(s(z))), elem!1)) | (~b(elem!1, s(z))) | (~b(s(s(s(s(s(s(s(elem!1))))))), elem!1)) | (~b(s(s(s(z))), elem!1)) | (~b(s(s(s(z))), s(s(s(s(s(s(s(elem!1))))))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(z))) | (~b(s(z), elem!1)) | (~b(s(s(s(z))), elem!1)) | (~b(s(s(s(s(s(s(s(elem!1))))))), elem!1)) | (~b(s(s(s(z))), s(s(s(s(s(s(s(elem!1))))))))))),
% 2.32/2.58 inference(transitivity,[status(thm)],[7070, 7068])).
% 2.32/2.58 tff(7072,plain,
% 2.32/2.58 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), elem!1)) | (~b(s(s(s(z))), elem!1)) | (~b(elem!1, s(z))) | (~b(s(s(s(s(s(s(s(elem!1))))))), elem!1)) | (~b(s(s(s(z))), elem!1)) | (~b(s(s(s(z))), s(s(s(s(s(s(s(elem!1))))))))))),
% 2.32/2.58 inference(quant_inst,[status(thm)],[])).
% 2.32/2.58 tff(7073,plain,
% 2.32/2.58 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(z))) | (~b(s(z), elem!1)) | (~b(s(s(s(z))), elem!1)) | (~b(s(s(s(s(s(s(s(elem!1))))))), elem!1)) | (~b(s(s(s(z))), s(s(s(s(s(s(s(elem!1)))))))))),
% 2.32/2.58 inference(modus_ponens,[status(thm)],[7072, 7071])).
% 2.32/2.58 tff(7074,plain,
% 2.32/2.58 (~b(s(s(s(z))), s(s(s(s(s(s(s(elem!1))))))))),
% 2.32/2.58 inference(unit_resolution,[status(thm)],[7073, 166, 1212, 642, 4074, 4927])).
% 2.32/2.58 tff(7075,assumption,(~(s(s(s(z))) = s(s(s(s(s(s(s(elem!1))))))))), introduced(assumption)).
% 2.32/2.58 tff(7076,plain,
% 2.32/2.58 (r(s(s(s(z))), s(s(s(s(s(s(s(elem!1))))))))),
% 2.32/2.58 inference(unit_resolution,[status(thm)],[4999, 79, 7075, 7074])).
% 2.32/2.58 tff(7077,plain,
% 2.32/2.58 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(s(z)))) | (~r(s(s(s(z))), s(z))) | (~r(s(s(s(s(s(s(s(elem!1))))))), s(z))) | (~r(s(s(s(z))), s(s(s(s(s(s(s(elem!1))))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(z), s(s(z)))) | (~r(s(s(s(z))), s(z))) | (~r(s(s(s(s(s(s(s(elem!1))))))), s(z))) | (~r(s(s(s(z))), s(s(s(s(s(s(s(elem!1))))))))))),
% 2.32/2.58 inference(rewrite,[status(thm)],[])).
% 2.32/2.58 tff(7078,plain,
% 2.32/2.58 (((~r(s(z), s(s(z)))) | (~r(s(s(s(s(s(s(s(elem!1))))))), s(z))) | (~r(s(s(s(z))), s(z))) | (~r(s(s(s(z))), s(s(s(s(s(s(s(elem!1)))))))))) <=> ((~r(s(z), s(s(z)))) | (~r(s(s(s(z))), s(z))) | (~r(s(s(s(s(s(s(s(elem!1))))))), s(z))) | (~r(s(s(s(z))), s(s(s(s(s(s(s(elem!1))))))))))),
% 2.32/2.58 inference(rewrite,[status(thm)],[])).
% 2.32/2.58 tff(7079,plain,
% 2.32/2.58 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(s(z)))) | (~r(s(s(s(s(s(s(s(elem!1))))))), s(z))) | (~r(s(s(s(z))), s(z))) | (~r(s(s(s(z))), s(s(s(s(s(s(s(elem!1))))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(s(z)))) | (~r(s(s(s(z))), s(z))) | (~r(s(s(s(s(s(s(s(elem!1))))))), s(z))) | (~r(s(s(s(z))), s(s(s(s(s(s(s(elem!1)))))))))))),
% 2.32/2.58 inference(monotonicity,[status(thm)],[7078])).
% 2.32/2.58 tff(7080,plain,
% 2.32/2.58 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(s(z)))) | (~r(s(s(s(s(s(s(s(elem!1))))))), s(z))) | (~r(s(s(s(z))), s(z))) | (~r(s(s(s(z))), s(s(s(s(s(s(s(elem!1))))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(z), s(s(z)))) | (~r(s(s(s(z))), s(z))) | (~r(s(s(s(s(s(s(s(elem!1))))))), s(z))) | (~r(s(s(s(z))), s(s(s(s(s(s(s(elem!1))))))))))),
% 2.32/2.58 inference(transitivity,[status(thm)],[7079, 7077])).
% 2.32/2.58 tff(7081,plain,
% 2.32/2.58 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(s(z)))) | (~r(s(s(s(s(s(s(s(elem!1))))))), s(z))) | (~r(s(s(s(z))), s(z))) | (~r(s(s(s(z))), s(s(s(s(s(s(s(elem!1))))))))))),
% 2.32/2.58 inference(quant_inst,[status(thm)],[])).
% 2.32/2.58 tff(7082,plain,
% 2.32/2.58 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(z), s(s(z)))) | (~r(s(s(s(z))), s(z))) | (~r(s(s(s(s(s(s(s(elem!1))))))), s(z))) | (~r(s(s(s(z))), s(s(s(s(s(s(s(elem!1)))))))))),
% 2.32/2.58 inference(modus_ponens,[status(thm)],[7081, 7080])).
% 2.32/2.58 tff(7083,plain,
% 2.32/2.58 ($false),
% 2.32/2.58 inference(unit_resolution,[status(thm)],[7082, 197, 120, 1746, 7076, 4952])).
% 2.32/2.58 tff(7084,plain,((~b(s(s(s(s(s(s(s(elem!1))))))), elem!1)) | (~r(s(z), s(s(z)))) | (~r(s(s(s(z))), s(z))) | (s(s(s(s(s(s(s(elem!1))))))) = s(z)) | (s(s(s(z))) = s(s(s(s(s(s(s(elem!1)))))))) | (~b(elem!1, s(z))) | (~b(s(z), elem!1)) | (~b(s(s(s(z))), elem!1))), inference(lemma,lemma(discharge,[]))).
% 2.32/2.58 tff(7085,plain,
% 2.32/2.58 (~b(s(s(s(s(s(s(s(elem!1))))))), elem!1)),
% 2.32/2.58 inference(unit_resolution,[status(thm)],[7084, 7067, 7047, 7063, 7062, 7059, 7045, 7056])).
% 2.32/2.58 tff(7086,plain,
% 2.32/2.58 (r(s(s(s(s(s(s(s(elem!1))))))), elem!1)),
% 2.32/2.58 inference(unit_resolution,[status(thm)],[6375, 7085, 7054])).
% 2.32/2.58 tff(7087,plain,
% 2.32/2.58 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(s(s(s(elem!1)))))) | (~r(s(s(s(s(s(s(s(elem!1))))))), elem!1)) | (~r(s(s(s(s(elem!1)))), elem!1)) | (~r(s(s(s(s(elem!1)))), s(s(s(s(s(s(s(elem!1))))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(elem!1, s(s(s(s(elem!1)))))) | (~r(s(s(s(s(s(s(s(elem!1))))))), elem!1)) | (~r(s(s(s(s(elem!1)))), elem!1)) | (~r(s(s(s(s(elem!1)))), s(s(s(s(s(s(s(elem!1))))))))))),
% 2.32/2.58 inference(rewrite,[status(thm)],[])).
% 2.32/2.58 tff(7088,plain,
% 2.32/2.58 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(s(s(s(elem!1)))))) | (~r(s(s(s(s(s(s(s(elem!1))))))), elem!1)) | (~r(s(s(s(s(elem!1)))), elem!1)) | (~r(s(s(s(s(elem!1)))), s(s(s(s(s(s(s(elem!1))))))))))),
% 2.32/2.58 inference(quant_inst,[status(thm)],[])).
% 2.32/2.58 tff(7089,plain,
% 2.32/2.58 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(elem!1, s(s(s(s(elem!1)))))) | (~r(s(s(s(s(s(s(s(elem!1))))))), elem!1)) | (~r(s(s(s(s(elem!1)))), elem!1)) | (~r(s(s(s(s(elem!1)))), s(s(s(s(s(s(s(elem!1)))))))))),
% 2.32/2.58 inference(modus_ponens,[status(thm)],[7088, 7087])).
% 2.32/2.58 tff(7090,plain,
% 2.32/2.58 (~r(s(s(s(s(elem!1)))), s(s(s(s(s(s(s(elem!1))))))))),
% 2.32/2.58 inference(unit_resolution,[status(thm)],[7089, 197, 7086, 7053, 7049])).
% 2.32/2.58 tff(7091,plain,
% 2.32/2.58 (r(s(s(elem!1)), z) <=> r(s(s(elem!1)), elem!1)),
% 2.32/2.58 inference(monotonicity,[status(thm)],[7026])).
% 2.32/2.58 tff(7092,plain,
% 2.32/2.58 (r(s(s(z)), z) <=> r(s(s(elem!1)), z)),
% 2.32/2.58 inference(monotonicity,[status(thm)],[7021])).
% 2.32/2.58 tff(7093,plain,
% 2.32/2.58 (r(s(s(z)), z) <=> r(s(s(elem!1)), elem!1)),
% 2.32/2.58 inference(transitivity,[status(thm)],[7092, 7091])).
% 2.32/2.58 tff(7094,plain,
% 2.32/2.58 (r(s(s(z)), s(z)) <=> r(s(s(elem!1)), s(z))),
% 2.32/2.58 inference(monotonicity,[status(thm)],[7021])).
% 2.32/2.58 tff(7095,plain,
% 2.32/2.58 (r(s(s(elem!1)), s(z)) <=> r(s(s(z)), s(z))),
% 2.32/2.58 inference(symmetry,[status(thm)],[7094])).
% 2.32/2.58 tff(7096,plain,
% 2.32/2.58 (r(s(s(z)), s(z))),
% 2.32/2.58 inference(modus_ponens,[status(thm)],[4558, 7095])).
% 2.32/2.58 tff(7097,plain,
% 2.32/2.58 (b(s(s(s(z))), z) <=> b(s(s(s(z))), elem!1)),
% 2.32/2.58 inference(monotonicity,[status(thm)],[7026])).
% 2.32/2.58 tff(7098,plain,
% 2.32/2.58 (b(s(s(s(z))), elem!1) <=> b(s(s(s(z))), z)),
% 2.32/2.58 inference(symmetry,[status(thm)],[7097])).
% 2.32/2.58 tff(7099,plain,
% 2.32/2.58 (b(s(s(s(elem!1))), elem!1) <=> b(s(s(s(z))), z)),
% 2.32/2.58 inference(transitivity,[status(thm)],[7065, 7098])).
% 2.32/2.58 tff(7100,plain,
% 2.32/2.58 (b(s(s(s(z))), z)),
% 2.32/2.58 inference(modus_ponens,[status(thm)],[7066, 7099])).
% 2.32/2.58 tff(7101,plain,
% 2.32/2.58 (~b(s(s(z)), z)),
% 2.32/2.58 inference(unit_resolution,[status(thm)],[5078, 7100, 6863, 118, 7056, 7096])).
% 2.32/2.58 tff(7102,plain,
% 2.32/2.58 (r(s(s(z)), z)),
% 2.32/2.58 inference(unit_resolution,[status(thm)],[186, 7101])).
% 2.32/2.58 tff(7103,plain,
% 2.32/2.58 (r(s(s(elem!1)), elem!1)),
% 2.32/2.58 inference(modus_ponens,[status(thm)],[7102, 7093])).
% 2.32/2.58 tff(7104,plain,
% 2.32/2.58 (r(z, s(s(elem!1))) <=> r(elem!1, s(s(elem!1)))),
% 2.32/2.58 inference(monotonicity,[status(thm)],[7026])).
% 2.32/2.58 tff(7105,plain,
% 2.32/2.58 (~b(z, s(s(elem!1)))),
% 2.32/2.58 inference(unit_resolution,[status(thm)],[2261, 7021, 125])).
% 2.32/2.58 tff(7106,plain,
% 2.32/2.58 (r(z, s(s(elem!1)))),
% 2.32/2.58 inference(unit_resolution,[status(thm)],[1795, 7105])).
% 2.32/2.58 tff(7107,plain,
% 2.32/2.58 (r(elem!1, s(s(elem!1)))),
% 2.32/2.58 inference(modus_ponens,[status(thm)],[7106, 7104])).
% 2.32/2.58 tff(7108,plain,
% 2.32/2.58 (~r(s(s(s(s(elem!1)))), s(s(elem!1)))),
% 2.32/2.58 inference(unit_resolution,[status(thm)],[3432, 7103, 85, 7030, 7047, 7107, 7045])).
% 2.32/2.58 tff(7109,plain,
% 2.32/2.58 (b(s(s(s(s(elem!1)))), s(s(elem!1)))),
% 2.32/2.58 inference(unit_resolution,[status(thm)],[813, 7108, 7041])).
% 2.32/2.58 tff(7110,plain,
% 2.32/2.58 (~r(s(s(s(elem!1))), s(s(elem!1)))),
% 2.32/2.58 inference(unit_resolution,[status(thm)],[5711, 197, 85, 7032, 4558])).
% 2.32/2.58 tff(7111,plain,
% 2.32/2.58 (b(s(s(s(elem!1))), s(s(elem!1)))),
% 2.32/2.58 inference(unit_resolution,[status(thm)],[889, 7110, 51])).
% 2.32/2.58 tff(7112,plain,
% 2.32/2.58 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(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(s(s(s(s(s(elem!1))))))), s(s(elem!1)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(elem!1, s(s(s(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(s(s(s(s(s(elem!1))))))), s(s(elem!1)))))),
% 2.32/2.58 inference(rewrite,[status(thm)],[])).
% 2.32/2.58 tff(7113,plain,
% 2.32/2.58 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(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(s(s(s(s(s(elem!1))))))), s(s(elem!1)))))),
% 2.32/2.58 inference(quant_inst,[status(thm)],[])).
% 2.32/2.58 tff(7114,plain,
% 2.32/2.58 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(elem!1, s(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(s(s(s(s(s(elem!1))))))), s(s(elem!1))))),
% 2.32/2.58 inference(modus_ponens,[status(thm)],[7113, 7112])).
% 2.32/2.58 tff(7115,plain,
% 2.32/2.58 (~r(s(s(s(s(s(s(s(elem!1))))))), s(s(elem!1)))),
% 2.32/2.58 inference(unit_resolution,[status(thm)],[7114, 197, 768, 6331, 1047])).
% 2.32/2.58 tff(7116,plain,
% 2.32/2.58 ((s(s(s(s(s(s(s(elem!1))))))) = s(s(elem!1))) | b(s(s(s(s(s(s(s(elem!1))))))), s(s(elem!1)))),
% 2.32/2.58 inference(unit_resolution,[status(thm)],[6359, 79, 7115])).
% 2.32/2.58 tff(7117,plain,
% 2.32/2.58 (b(s(s(s(s(s(s(s(elem!1))))))), s(s(elem!1)))),
% 2.32/2.58 inference(unit_resolution,[status(thm)],[7116, 6349])).
% 2.32/2.58 tff(7118,assumption,(b(s(s(s(s(elem!1)))), s(s(s(s(s(s(s(elem!1))))))))), introduced(assumption)).
% 2.32/2.58 tff(7119,plain,
% 2.32/2.58 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(s(s(s(elem!1)))), s(s(elem!1)))) | (~b(s(s(s(s(s(s(s(elem!1))))))), s(s(elem!1)))) | (~b(s(s(s(s(elem!1)))), s(s(s(s(s(s(s(elem!1))))))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(s(s(s(elem!1)))), s(s(elem!1)))) | (~b(s(s(s(s(s(s(s(elem!1))))))), s(s(elem!1)))) | (~b(s(s(s(s(elem!1)))), s(s(s(s(s(s(s(elem!1))))))))))),
% 2.32/2.59 inference(rewrite,[status(thm)],[])).
% 2.32/2.59 tff(7120,plain,
% 2.32/2.59 (((~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(s(s(s(elem!1)))), s(s(elem!1)))) | (~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(s(s(s(s(s(s(s(elem!1))))))), s(s(elem!1)))) | (~b(s(s(s(s(elem!1)))), s(s(elem!1)))) | (~b(s(s(s(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(elem!1))), s(s(elem!1)))) | (~b(s(s(s(s(elem!1)))), s(s(elem!1)))) | (~b(s(s(s(s(s(s(s(elem!1))))))), s(s(elem!1)))) | (~b(s(s(s(s(elem!1)))), s(s(s(s(s(s(s(elem!1))))))))))),
% 2.32/2.59 inference(rewrite,[status(thm)],[])).
% 2.32/2.59 tff(7121,plain,
% 2.32/2.59 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(s(s(s(elem!1)))), s(s(elem!1)))) | (~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(s(s(s(s(s(s(s(elem!1))))))), s(s(elem!1)))) | (~b(s(s(s(s(elem!1)))), s(s(elem!1)))) | (~b(s(s(s(s(elem!1)))), s(s(s(s(s(s(s(elem!1))))))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(s(s(s(elem!1)))), s(s(elem!1)))) | (~b(s(s(s(s(s(s(s(elem!1))))))), s(s(elem!1)))) | (~b(s(s(s(s(elem!1)))), s(s(s(s(s(s(s(elem!1)))))))))))),
% 2.32/2.59 inference(monotonicity,[status(thm)],[7120])).
% 2.32/2.59 tff(7122,plain,
% 2.32/2.59 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(s(s(s(elem!1)))), s(s(elem!1)))) | (~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(s(s(s(s(s(s(s(elem!1))))))), s(s(elem!1)))) | (~b(s(s(s(s(elem!1)))), s(s(elem!1)))) | (~b(s(s(s(s(elem!1)))), s(s(s(s(s(s(s(elem!1))))))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(s(s(s(elem!1)))), s(s(elem!1)))) | (~b(s(s(s(s(s(s(s(elem!1))))))), s(s(elem!1)))) | (~b(s(s(s(s(elem!1)))), s(s(s(s(s(s(s(elem!1))))))))))),
% 2.32/2.59 inference(transitivity,[status(thm)],[7121, 7119])).
% 2.32/2.59 tff(7123,plain,
% 2.32/2.59 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(s(s(s(elem!1)))), s(s(elem!1)))) | (~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(s(s(s(s(s(s(s(elem!1))))))), s(s(elem!1)))) | (~b(s(s(s(s(elem!1)))), s(s(elem!1)))) | (~b(s(s(s(s(elem!1)))), s(s(s(s(s(s(s(elem!1))))))))))),
% 2.32/2.59 inference(quant_inst,[status(thm)],[])).
% 2.32/2.59 tff(7124,plain,
% 2.32/2.59 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(s(s(s(elem!1)))), s(s(elem!1)))) | (~b(s(s(s(s(s(s(s(elem!1))))))), s(s(elem!1)))) | (~b(s(s(s(s(elem!1)))), s(s(s(s(s(s(s(elem!1)))))))))),
% 2.32/2.59 inference(modus_ponens,[status(thm)],[7123, 7122])).
% 2.32/2.59 tff(7125,plain,
% 2.32/2.59 ($false),
% 2.32/2.59 inference(unit_resolution,[status(thm)],[7124, 166, 463, 839, 3457, 7118, 7117])).
% 2.32/2.59 tff(7126,plain,((~b(s(s(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(elem!1))), s(s(elem!1)))) | (~b(s(s(s(s(elem!1)))), s(s(elem!1)))) | (~(s(s(z)) = s(s(elem!1)))) | (~r(s(s(elem!1)), elem!1)) | (~r(s(s(s(s(s(s(s(elem!1))))))), elem!1)) | (~r(elem!1, s(s(s(s(elem!1))))))), inference(lemma,lemma(discharge,[]))).
% 2.32/2.59 tff(7127,plain,
% 2.32/2.59 (~b(s(s(s(s(elem!1)))), s(s(s(s(s(s(s(elem!1))))))))),
% 2.32/2.59 inference(unit_resolution,[status(thm)],[7126, 7036, 7111, 7109, 7021, 7103, 7086, 7049])).
% 2.32/2.59 tff(7128,plain,
% 2.32/2.59 ((s(s(s(s(elem!1)))) = s(s(s(s(s(s(s(elem!1)))))))) | r(s(s(s(s(elem!1)))), s(s(s(s(s(s(s(elem!1))))))))),
% 2.32/2.59 inference(unit_resolution,[status(thm)],[6423, 79, 7127])).
% 2.32/2.59 tff(7129,plain,
% 2.32/2.59 (s(s(s(s(elem!1)))) = s(s(s(s(s(s(s(elem!1)))))))),
% 2.32/2.59 inference(unit_resolution,[status(thm)],[7128, 7090])).
% 2.32/2.59 tff(7130,plain,
% 2.32/2.59 (s(s(s(s(s(s(s(elem!1))))))) = s(s(s(s(elem!1))))),
% 2.32/2.59 inference(symmetry,[status(thm)],[7129])).
% 2.32/2.59 tff(7131,plain,
% 2.32/2.59 (s(s(s(s(s(s(s(elem!1))))))) = s(s(s(s(z))))),
% 2.32/2.59 inference(transitivity,[status(thm)],[7130, 7024])).
% 2.32/2.59 tff(7132,plain,
% 2.32/2.59 (s(s(s(elem!1))) = s(s(s(z)))),
% 2.32/2.59 inference(symmetry,[status(thm)],[7022])).
% 2.32/2.59 tff(7133,plain,
% 2.32/2.59 (~(s(s(s(s(s(s(s(elem!1))))))) = s(s(s(s(z)))))),
% 2.32/2.59 inference(unit_resolution,[status(thm)],[4925, 7132])).
% 2.32/2.59 tff(7134,plain,
% 2.32/2.59 ($false),
% 2.32/2.59 inference(unit_resolution,[status(thm)],[7133, 7131])).
% 2.32/2.59 tff(7135,plain,(b(s(z), s(s(elem!1))) | (~b(z, s(z))) | b(z, s(s(z))) | (s(s(elem!1)) = s(s(s(elem!1))))), inference(lemma,lemma(discharge,[]))).
% 2.32/2.59 tff(7136,plain,
% 2.32/2.59 (b(s(z), s(s(elem!1)))),
% 2.32/2.59 inference(unit_resolution,[status(thm)],[7135, 45, 125, 118])).
% 2.32/2.59 tff(7137,plain,
% 2.32/2.59 (~b(z, s(s(elem!1)))),
% 2.32/2.59 inference(unit_resolution,[status(thm)],[5343, 310, 118, 376])).
% 2.32/2.59 tff(7138,plain,
% 2.32/2.59 (r(z, s(s(elem!1)))),
% 2.32/2.59 inference(unit_resolution,[status(thm)],[1795, 7137])).
% 2.32/2.59 tff(7139,plain,
% 2.32/2.59 (~r(s(s(z)), s(s(elem!1)))),
% 2.32/2.59 inference(unit_resolution,[status(thm)],[385, 377, 155, 7138])).
% 2.32/2.59 tff(7140,plain,
% 2.32/2.59 (b(s(s(z)), s(s(elem!1)))),
% 2.32/2.59 inference(unit_resolution,[status(thm)],[390, 7139, 52])).
% 2.32/2.59 tff(7141,plain,
% 2.32/2.59 (~b(s(s(z)), s(z))),
% 2.32/2.59 inference(unit_resolution,[status(thm)],[454, 7140, 376, 310])).
% 2.32/2.59 tff(7142,plain,
% 2.32/2.59 (r(s(s(z)), s(z))),
% 2.32/2.59 inference(unit_resolution,[status(thm)],[308, 7141])).
% 2.32/2.59 tff(7143,plain,
% 2.32/2.59 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(elem!1)))) | (~b(s(s(s(elem!1))), z)) | (~b(s(s(s(elem!1))), s(z))) | (~b(z, s(z))) | (~b(s(s(elem!1)), s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), s(s(elem!1)))) | (~b(s(s(s(elem!1))), z)) | (~b(s(s(s(elem!1))), s(z))) | (~b(z, s(z))) | (~b(s(s(elem!1)), s(z))))),
% 2.32/2.59 inference(rewrite,[status(thm)],[])).
% 2.32/2.59 tff(7144,plain,
% 2.32/2.59 (((~b(s(s(elem!1)), s(z))) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(z), s(s(elem!1)))) | (~b(z, s(z))) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(s(s(elem!1))), z))) <=> ((~b(s(z), s(s(elem!1)))) | (~b(s(s(s(elem!1))), z)) | (~b(s(s(s(elem!1))), s(z))) | (~b(z, s(z))) | (~b(s(s(elem!1)), s(z))))),
% 2.32/2.59 inference(rewrite,[status(thm)],[])).
% 2.32/2.59 tff(7145,plain,
% 2.32/2.59 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), s(z))) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(z), s(s(elem!1)))) | (~b(z, s(z))) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(s(s(elem!1))), z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(elem!1)))) | (~b(s(s(s(elem!1))), z)) | (~b(s(s(s(elem!1))), s(z))) | (~b(z, s(z))) | (~b(s(s(elem!1)), s(z)))))),
% 2.32/2.59 inference(monotonicity,[status(thm)],[7144])).
% 2.32/2.59 tff(7146,plain,
% 2.32/2.59 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), s(z))) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(z), s(s(elem!1)))) | (~b(z, s(z))) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(s(s(elem!1))), z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), s(s(elem!1)))) | (~b(s(s(s(elem!1))), z)) | (~b(s(s(s(elem!1))), s(z))) | (~b(z, s(z))) | (~b(s(s(elem!1)), s(z))))),
% 2.32/2.59 inference(transitivity,[status(thm)],[7145, 7143])).
% 2.32/2.59 tff(7147,plain,
% 2.32/2.59 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), s(z))) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(z), s(s(elem!1)))) | (~b(z, s(z))) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(s(s(elem!1))), z)))),
% 2.32/2.59 inference(quant_inst,[status(thm)],[])).
% 2.32/2.59 tff(7148,plain,
% 2.32/2.59 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), s(s(elem!1)))) | (~b(s(s(s(elem!1))), z)) | (~b(s(s(s(elem!1))), s(z))) | (~b(z, s(z))) | (~b(s(s(elem!1)), s(z)))),
% 2.32/2.59 inference(modus_ponens,[status(thm)],[7147, 7146])).
% 2.32/2.59 tff(7149,plain,
% 2.32/2.59 ($false),
% 2.32/2.59 inference(unit_resolution,[status(thm)],[7148, 166, 376, 96, 118, 310, 121])).
% 2.32/2.59 tff(7150,plain,((~b(s(s(s(elem!1))), s(z))) | (~b(s(z), s(s(elem!1)))) | (~b(z, s(z))) | (~b(s(s(elem!1)), s(z))) | (~b(s(s(s(elem!1))), z))), inference(lemma,lemma(discharge,[]))).
% 2.32/2.59 tff(7151,plain,
% 2.32/2.59 (~b(s(s(s(elem!1))), s(z))),
% 2.32/2.59 inference(unit_resolution,[status(thm)],[7150, 310, 121, 118, 376])).
% 2.32/2.59 tff(7152,plain,
% 2.32/2.59 (r(s(s(s(elem!1))), s(z))),
% 2.32/2.59 inference(unit_resolution,[status(thm)],[1849, 7151])).
% 2.32/2.59 tff(7153,plain,
% 2.32/2.59 (~r(s(s(elem!1)), s(s(z)))),
% 2.32/2.59 inference(unit_resolution,[status(thm)],[401, 7142, 155, 7138])).
% 2.32/2.59 tff(7154,plain,
% 2.32/2.59 (~b(s(z), s(s(z)))),
% 2.32/2.59 inference(unit_resolution,[status(thm)],[5300, 7153, 376, 52, 7139])).
% 2.32/2.59 tff(7155,plain,
% 2.32/2.59 (r(s(z), s(s(z)))),
% 2.32/2.59 inference(unit_resolution,[status(thm)],[427, 7154])).
% 2.32/2.59 tff(7156,plain,
% 2.32/2.59 (~r(s(s(z)), s(s(s(elem!1))))),
% 2.32/2.59 inference(unit_resolution,[status(thm)],[6081, 197, 7155, 7152, 7142])).
% 2.32/2.59 tff(7157,plain,
% 2.32/2.59 (b(s(s(z)), s(s(s(elem!1))))),
% 2.32/2.59 inference(unit_resolution,[status(thm)],[279, 7156])).
% 2.32/2.59 tff(7158,plain,
% 2.32/2.59 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(elem!1)))) | (~b(s(s(s(elem!1))), z)) | (~b(z, s(z))) | (~b(s(s(z)), s(s(elem!1)))) | (~b(s(s(z)), z)) | (~b(s(s(z)), s(s(s(elem!1))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), s(s(elem!1)))) | (~b(s(s(s(elem!1))), z)) | (~b(z, s(z))) | (~b(s(s(z)), s(s(elem!1)))) | (~b(s(s(z)), z)) | (~b(s(s(z)), s(s(s(elem!1))))))),
% 2.32/2.59 inference(rewrite,[status(thm)],[])).
% 2.32/2.59 tff(7159,plain,
% 2.32/2.59 (((~b(s(z), s(s(elem!1)))) | (~b(s(s(z)), s(s(elem!1)))) | (~b(z, s(z))) | (~b(s(s(s(elem!1))), z)) | (~b(s(s(z)), z)) | (~b(s(s(z)), s(s(s(elem!1)))))) <=> ((~b(s(z), s(s(elem!1)))) | (~b(s(s(s(elem!1))), z)) | (~b(z, s(z))) | (~b(s(s(z)), s(s(elem!1)))) | (~b(s(s(z)), z)) | (~b(s(s(z)), s(s(s(elem!1))))))),
% 2.32/2.59 inference(rewrite,[status(thm)],[])).
% 2.32/2.59 tff(7160,plain,
% 2.32/2.59 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(elem!1)))) | (~b(s(s(z)), s(s(elem!1)))) | (~b(z, s(z))) | (~b(s(s(s(elem!1))), z)) | (~b(s(s(z)), z)) | (~b(s(s(z)), s(s(s(elem!1))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(elem!1)))) | (~b(s(s(s(elem!1))), z)) | (~b(z, s(z))) | (~b(s(s(z)), s(s(elem!1)))) | (~b(s(s(z)), z)) | (~b(s(s(z)), s(s(s(elem!1)))))))),
% 2.32/2.59 inference(monotonicity,[status(thm)],[7159])).
% 2.32/2.59 tff(7161,plain,
% 2.32/2.59 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(elem!1)))) | (~b(s(s(z)), s(s(elem!1)))) | (~b(z, s(z))) | (~b(s(s(s(elem!1))), z)) | (~b(s(s(z)), z)) | (~b(s(s(z)), s(s(s(elem!1))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), s(s(elem!1)))) | (~b(s(s(s(elem!1))), z)) | (~b(z, s(z))) | (~b(s(s(z)), s(s(elem!1)))) | (~b(s(s(z)), z)) | (~b(s(s(z)), s(s(s(elem!1))))))),
% 2.32/2.59 inference(transitivity,[status(thm)],[7160, 7158])).
% 2.32/2.59 tff(7162,plain,
% 2.32/2.59 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(elem!1)))) | (~b(s(s(z)), s(s(elem!1)))) | (~b(z, s(z))) | (~b(s(s(s(elem!1))), z)) | (~b(s(s(z)), z)) | (~b(s(s(z)), s(s(s(elem!1))))))),
% 2.32/2.59 inference(quant_inst,[status(thm)],[])).
% 2.32/2.59 tff(7163,plain,
% 2.32/2.59 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), s(s(elem!1)))) | (~b(s(s(s(elem!1))), z)) | (~b(z, s(z))) | (~b(s(s(z)), s(s(elem!1)))) | (~b(s(s(z)), z)) | (~b(s(s(z)), s(s(s(elem!1)))))),
% 2.32/2.59 inference(modus_ponens,[status(thm)],[7162, 7161])).
% 2.32/2.59 tff(7164,plain,
% 2.32/2.59 ((~b(s(s(z)), z)) | (~b(s(s(z)), s(s(s(elem!1)))))),
% 2.32/2.59 inference(unit_resolution,[status(thm)],[7163, 166, 376, 118, 121, 7140])).
% 2.32/2.59 tff(7165,plain,
% 2.32/2.59 (~b(s(s(z)), z)),
% 2.32/2.59 inference(unit_resolution,[status(thm)],[7164, 7157])).
% 2.32/2.59 tff(7166,plain,
% 2.32/2.59 (r(s(s(z)), z)),
% 2.32/2.59 inference(unit_resolution,[status(thm)],[186, 7165])).
% 2.32/2.59 tff(7167,plain,
% 2.32/2.59 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), z)) | (~b(s(z), s(s(elem!1)))) | (~b(z, s(z))) | (~b(s(s(elem!1)), s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(elem!1)), z)) | (~b(s(z), s(s(elem!1)))) | (~b(z, s(z))) | (~b(s(s(elem!1)), s(z))))),
% 2.32/2.59 inference(rewrite,[status(thm)],[])).
% 2.32/2.59 tff(7168,plain,
% 2.32/2.59 (((~b(s(s(elem!1)), s(z))) | (~b(s(s(elem!1)), s(z))) | (~b(s(z), s(s(elem!1)))) | (~b(z, s(z))) | (~b(s(s(elem!1)), s(z))) | (~b(s(s(elem!1)), z))) <=> ((~b(s(s(elem!1)), z)) | (~b(s(z), s(s(elem!1)))) | (~b(z, s(z))) | (~b(s(s(elem!1)), s(z))))),
% 2.32/2.59 inference(rewrite,[status(thm)],[])).
% 2.32/2.59 tff(7169,plain,
% 2.32/2.59 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), s(z))) | (~b(s(s(elem!1)), s(z))) | (~b(s(z), s(s(elem!1)))) | (~b(z, s(z))) | (~b(s(s(elem!1)), s(z))) | (~b(s(s(elem!1)), z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), z)) | (~b(s(z), s(s(elem!1)))) | (~b(z, s(z))) | (~b(s(s(elem!1)), s(z)))))),
% 2.32/2.59 inference(monotonicity,[status(thm)],[7168])).
% 2.32/2.59 tff(7170,plain,
% 2.32/2.59 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), s(z))) | (~b(s(s(elem!1)), s(z))) | (~b(s(z), s(s(elem!1)))) | (~b(z, s(z))) | (~b(s(s(elem!1)), s(z))) | (~b(s(s(elem!1)), z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(elem!1)), z)) | (~b(s(z), s(s(elem!1)))) | (~b(z, s(z))) | (~b(s(s(elem!1)), s(z))))),
% 2.32/2.59 inference(transitivity,[status(thm)],[7169, 7167])).
% 2.32/2.59 tff(7171,plain,
% 2.32/2.59 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), s(z))) | (~b(s(s(elem!1)), s(z))) | (~b(s(z), s(s(elem!1)))) | (~b(z, s(z))) | (~b(s(s(elem!1)), s(z))) | (~b(s(s(elem!1)), z)))),
% 2.32/2.59 inference(quant_inst,[status(thm)],[])).
% 2.32/2.59 tff(7172,plain,
% 2.32/2.59 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(elem!1)), z)) | (~b(s(z), s(s(elem!1)))) | (~b(z, s(z))) | (~b(s(s(elem!1)), s(z)))),
% 2.32/2.59 inference(modus_ponens,[status(thm)],[7171, 7170])).
% 2.32/2.59 tff(7173,plain,
% 2.32/2.59 (~b(s(s(elem!1)), z)),
% 2.32/2.59 inference(unit_resolution,[status(thm)],[7172, 166, 376, 118, 310])).
% 2.32/2.59 tff(7174,plain,
% 2.32/2.59 (r(s(s(elem!1)), z)),
% 2.32/2.59 inference(unit_resolution,[status(thm)],[608, 7173])).
% 2.32/2.59 tff(7175,plain,
% 2.32/2.59 (b(s(s(elem!1)), s(s(z)))),
% 2.32/2.59 inference(unit_resolution,[status(thm)],[441, 7153, 132])).
% 2.32/2.59 tff(7176,plain,
% 2.32/2.59 (~b(s(s(elem!1)), s(s(s(z))))),
% 2.32/2.59 inference(unit_resolution,[status(thm)],[5086, 166, 405, 446, 6498])).
% 2.32/2.59 tff(7177,plain,
% 2.32/2.59 (~r(s(s(elem!1)), s(s(s(z))))),
% 2.32/2.59 inference(unit_resolution,[status(thm)],[6977, 197, 155, 1970, 1733])).
% 2.32/2.59 tff(7178,plain,
% 2.32/2.59 ((s(s(elem!1)) = s(s(s(z)))) | b(s(s(elem!1)), s(s(s(z))))),
% 2.32/2.59 inference(unit_resolution,[status(thm)],[5091, 79, 7177])).
% 2.32/2.59 tff(7179,plain,
% 2.32/2.59 (s(s(elem!1)) = s(s(s(z)))),
% 2.32/2.59 inference(unit_resolution,[status(thm)],[7178, 7176])).
% 2.32/2.59 tff(7180,plain,
% 2.32/2.59 (s(s(s(z))) = s(s(elem!1))),
% 2.32/2.59 inference(symmetry,[status(thm)],[7179])).
% 2.32/2.59 tff(7181,plain,
% 2.32/2.59 (s(s(s(elem!1))) = s(s(s(s(z))))),
% 2.32/2.59 inference(monotonicity,[status(thm)],[7179])).
% 2.32/2.59 tff(7182,plain,
% 2.32/2.59 (s(s(s(s(elem!1)))) = s(s(s(s(s(z)))))),
% 2.32/2.59 inference(monotonicity,[status(thm)],[7181])).
% 2.32/2.59 tff(7183,plain,
% 2.32/2.59 (s(s(s(s(s(z))))) = s(s(s(s(elem!1))))),
% 2.32/2.59 inference(symmetry,[status(thm)],[7182])).
% 2.32/2.59 tff(7184,plain,
% 2.32/2.59 (r(s(s(s(s(s(z))))), s(s(s(z)))) <=> r(s(s(s(s(elem!1)))), s(s(elem!1)))),
% 2.32/2.59 inference(monotonicity,[status(thm)],[7183, 7180])).
% 2.32/2.59 tff(7185,plain,
% 2.32/2.59 (r(s(s(s(s(elem!1)))), s(s(elem!1))) <=> r(s(s(s(s(s(z))))), s(s(s(z))))),
% 2.32/2.59 inference(symmetry,[status(thm)],[7184])).
% 2.32/2.59 tff(7186,plain,
% 2.32/2.59 ((s(s(s(s(elem!1)))) = s(s(s(z)))) <=> (s(s(s(s(elem!1)))) = s(s(elem!1)))),
% 2.32/2.59 inference(monotonicity,[status(thm)],[7180])).
% 2.32/2.59 tff(7187,plain,
% 2.32/2.59 ((s(s(s(s(elem!1)))) = s(s(s(z)))) <=> (s(s(elem!1)) = s(s(s(s(elem!1)))))),
% 2.32/2.59 inference(transitivity,[status(thm)],[7186, 123])).
% 2.32/2.59 tff(7188,plain,
% 2.32/2.59 ((s(s(s(s(elem!1)))) = s(s(s(z)))) <=> (s(s(s(s(elem!1)))) = s(s(elem!1)))),
% 2.32/2.59 inference(transitivity,[status(thm)],[7187, 124])).
% 2.32/2.59 tff(7189,plain,
% 2.32/2.59 ((~(s(s(s(s(elem!1)))) = s(s(s(z))))) <=> (~(s(s(s(s(elem!1)))) = s(s(elem!1))))),
% 2.32/2.59 inference(monotonicity,[status(thm)],[7188])).
% 2.32/2.59 tff(7190,plain,
% 2.32/2.59 (~(s(s(s(s(elem!1)))) = s(s(elem!1)))),
% 2.32/2.59 inference(modus_ponens,[status(thm)],[5112, 7189])).
% 2.32/2.59 tff(7191,plain,
% 2.32/2.59 (b(s(s(s(s(s(z))))), s(z)) <=> b(s(s(s(s(elem!1)))), s(z))),
% 2.32/2.59 inference(monotonicity,[status(thm)],[7183])).
% 2.32/2.59 tff(7192,plain,
% 2.32/2.59 (b(s(s(s(s(elem!1)))), s(z)) <=> b(s(s(s(s(s(z))))), s(z))),
% 2.32/2.59 inference(symmetry,[status(thm)],[7191])).
% 2.32/2.59 tff(7193,plain,
% 2.32/2.59 (r(s(s(s(s(s(z))))), s(z)) <=> r(s(s(s(s(elem!1)))), s(z))),
% 2.32/2.59 inference(monotonicity,[status(thm)],[7183])).
% 2.32/2.59 tff(7194,plain,
% 2.32/2.59 ((~r(s(s(s(s(s(z))))), s(z))) <=> (~r(s(s(s(s(elem!1)))), s(z)))),
% 2.32/2.59 inference(monotonicity,[status(thm)],[7193])).
% 2.32/2.59 tff(7195,plain,
% 2.32/2.59 (r(s(s(s(elem!1))), s(z)) <=> r(s(s(s(s(z)))), s(z))),
% 2.32/2.59 inference(monotonicity,[status(thm)],[7181])).
% 2.32/2.59 tff(7196,plain,
% 2.32/2.59 (r(s(s(s(s(z)))), s(z))),
% 2.32/2.59 inference(modus_ponens,[status(thm)],[350, 7195])).
% 2.32/2.59 tff(7197,plain,
% 2.32/2.59 (s(s(s(s(z)))) = s(s(s(elem!1)))),
% 2.32/2.59 inference(symmetry,[status(thm)],[7181])).
% 2.32/2.59 tff(7198,plain,
% 2.32/2.59 (b(s(s(s(s(z)))), s(s(z))) <=> b(s(s(s(elem!1))), s(s(z)))),
% 2.32/2.59 inference(monotonicity,[status(thm)],[7197])).
% 2.32/2.59 tff(7199,plain,
% 2.32/2.59 (b(s(s(s(elem!1))), s(s(z))) <=> b(s(s(s(s(z)))), s(s(z)))),
% 2.32/2.59 inference(symmetry,[status(thm)],[7198])).
% 2.32/2.59 tff(7200,plain,
% 2.32/2.59 (b(s(s(s(elem!1))), s(s(z)))),
% 2.32/2.59 inference(unit_resolution,[status(thm)],[218, 6071])).
% 2.32/2.59 tff(7201,plain,
% 2.32/2.59 (b(s(s(s(s(z)))), s(s(z)))),
% 2.32/2.59 inference(modus_ponens,[status(thm)],[7200, 7199])).
% 2.32/2.59 tff(7202,plain,
% 2.32/2.59 (~r(s(s(z)), s(s(s(z))))),
% 2.32/2.59 inference(unit_resolution,[status(thm)],[1741, 1733, 155, 866])).
% 2.32/2.59 tff(7203,plain,
% 2.32/2.59 (b(s(s(z)), s(s(s(z))))),
% 2.32/2.59 inference(unit_resolution,[status(thm)],[1730, 7202])).
% 2.32/2.59 tff(7204,plain,
% 2.32/2.59 (b(s(s(s(s(s(z))))), s(s(z))) <=> b(s(s(s(s(elem!1)))), s(s(z)))),
% 2.32/2.59 inference(monotonicity,[status(thm)],[5168])).
% 2.32/2.59 tff(7205,plain,
% 2.32/2.59 (b(s(s(s(s(elem!1)))), s(s(z))) <=> b(s(s(s(s(s(z))))), s(s(z)))),
% 2.32/2.59 inference(symmetry,[status(thm)],[7204])).
% 2.32/2.60 tff(7206,plain,
% 2.32/2.60 (r(s(s(s(s(s(z))))), s(s(z))) <=> r(s(s(s(s(elem!1)))), s(s(z)))),
% 2.32/2.60 inference(monotonicity,[status(thm)],[5168])).
% 2.32/2.60 tff(7207,plain,
% 2.32/2.60 ((~r(s(s(s(s(s(z))))), s(s(z)))) <=> (~r(s(s(s(s(elem!1)))), s(s(z))))),
% 2.32/2.60 inference(monotonicity,[status(thm)],[7206])).
% 2.32/2.60 tff(7208,assumption,(r(s(s(s(s(s(z))))), s(z))), introduced(assumption)).
% 2.32/2.60 tff(7209,plain,
% 2.32/2.60 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(s(z)))) | (~r(s(s(z)), s(z))) | (~r(s(s(s(s(s(z))))), s(z))) | (~r(s(s(s(s(s(z))))), s(s(z)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(z), s(s(z)))) | (~r(s(s(z)), s(z))) | (~r(s(s(s(s(s(z))))), s(z))) | (~r(s(s(s(s(s(z))))), s(s(z)))))),
% 2.32/2.60 inference(rewrite,[status(thm)],[])).
% 2.32/2.60 tff(7210,plain,
% 2.32/2.60 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(s(z)))) | (~r(s(s(z)), s(z))) | (~r(s(s(s(s(s(z))))), s(z))) | (~r(s(s(s(s(s(z))))), s(s(z)))))),
% 2.32/2.60 inference(quant_inst,[status(thm)],[])).
% 2.32/2.60 tff(7211,plain,
% 2.32/2.60 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(z), s(s(z)))) | (~r(s(s(z)), s(z))) | (~r(s(s(s(s(s(z))))), s(z))) | (~r(s(s(s(s(s(z))))), s(s(z))))),
% 2.32/2.60 inference(modus_ponens,[status(thm)],[7210, 7209])).
% 2.32/2.60 tff(7212,plain,
% 2.32/2.60 ((~r(s(s(s(s(s(z))))), s(z))) | (~r(s(s(s(s(s(z))))), s(s(z))))),
% 2.32/2.60 inference(unit_resolution,[status(thm)],[7211, 197, 120, 392])).
% 2.32/2.60 tff(7213,plain,
% 2.32/2.60 (~r(s(s(s(s(s(z))))), s(s(z)))),
% 2.32/2.60 inference(unit_resolution,[status(thm)],[7212, 7208])).
% 2.32/2.60 tff(7214,plain,
% 2.32/2.60 (~r(s(s(s(s(elem!1)))), s(s(z)))),
% 2.32/2.60 inference(modus_ponens,[status(thm)],[7213, 7207])).
% 2.32/2.60 tff(7215,plain,
% 2.32/2.60 (b(s(s(s(s(elem!1)))), s(s(z)))),
% 2.32/2.60 inference(unit_resolution,[status(thm)],[1299, 7214])).
% 2.32/2.60 tff(7216,plain,
% 2.32/2.60 (b(s(s(s(s(s(z))))), s(s(z)))),
% 2.32/2.60 inference(modus_ponens,[status(thm)],[7215, 7205])).
% 2.42/2.60 tff(7217,plain,
% 2.42/2.60 (s(s(s(s(z)))) = s(s(s(elem!1)))),
% 2.42/2.60 inference(symmetry,[status(thm)],[5166])).
% 2.42/2.60 tff(7218,plain,
% 2.42/2.60 (b(s(s(s(s(z)))), s(s(s(s(s(z)))))) <=> b(s(s(s(elem!1))), s(s(s(s(elem!1)))))),
% 2.42/2.60 inference(monotonicity,[status(thm)],[7217, 5168])).
% 2.42/2.60 tff(7219,plain,
% 2.42/2.60 (b(s(s(s(elem!1))), s(s(s(s(elem!1))))) <=> b(s(s(s(s(z)))), s(s(s(s(s(z))))))),
% 2.42/2.60 inference(symmetry,[status(thm)],[7218])).
% 2.42/2.60 tff(7220,plain,
% 2.42/2.60 (r(s(s(s(s(z)))), s(s(s(s(s(z)))))) <=> r(s(s(s(elem!1))), s(s(s(s(elem!1)))))),
% 2.42/2.60 inference(monotonicity,[status(thm)],[7217, 5168])).
% 2.42/2.60 tff(7221,plain,
% 2.42/2.60 ((~r(s(s(s(s(z)))), s(s(s(s(s(z))))))) <=> (~r(s(s(s(elem!1))), s(s(s(s(elem!1))))))),
% 2.42/2.60 inference(monotonicity,[status(thm)],[7220])).
% 2.42/2.60 tff(7222,assumption,(r(s(s(s(s(z)))), s(z))), introduced(assumption)).
% 2.42/2.60 tff(7223,plain,
% 2.42/2.60 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(s(z)))) | (~r(s(s(s(s(z)))), s(z))) | (~r(s(s(s(s(s(z))))), s(z))) | (~r(s(s(s(s(z)))), s(s(s(s(s(z))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(z), s(s(z)))) | (~r(s(s(s(s(z)))), s(z))) | (~r(s(s(s(s(s(z))))), s(z))) | (~r(s(s(s(s(z)))), s(s(s(s(s(z))))))))),
% 2.42/2.60 inference(rewrite,[status(thm)],[])).
% 2.42/2.60 tff(7224,plain,
% 2.42/2.60 (((~r(s(z), s(s(z)))) | (~r(s(s(s(s(s(z))))), s(z))) | (~r(s(s(s(s(z)))), s(z))) | (~r(s(s(s(s(z)))), s(s(s(s(s(z)))))))) <=> ((~r(s(z), s(s(z)))) | (~r(s(s(s(s(z)))), s(z))) | (~r(s(s(s(s(s(z))))), s(z))) | (~r(s(s(s(s(z)))), s(s(s(s(s(z))))))))),
% 2.42/2.60 inference(rewrite,[status(thm)],[])).
% 2.42/2.60 tff(7225,plain,
% 2.42/2.60 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(s(z)))) | (~r(s(s(s(s(s(z))))), s(z))) | (~r(s(s(s(s(z)))), s(z))) | (~r(s(s(s(s(z)))), s(s(s(s(s(z))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(s(z)))) | (~r(s(s(s(s(z)))), s(z))) | (~r(s(s(s(s(s(z))))), s(z))) | (~r(s(s(s(s(z)))), s(s(s(s(s(z)))))))))),
% 2.42/2.60 inference(monotonicity,[status(thm)],[7224])).
% 2.42/2.60 tff(7226,plain,
% 2.42/2.60 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(s(z)))) | (~r(s(s(s(s(s(z))))), s(z))) | (~r(s(s(s(s(z)))), s(z))) | (~r(s(s(s(s(z)))), s(s(s(s(s(z))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(z), s(s(z)))) | (~r(s(s(s(s(z)))), s(z))) | (~r(s(s(s(s(s(z))))), s(z))) | (~r(s(s(s(s(z)))), s(s(s(s(s(z))))))))),
% 2.42/2.60 inference(transitivity,[status(thm)],[7225, 7223])).
% 2.42/2.60 tff(7227,plain,
% 2.42/2.60 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(s(z)))) | (~r(s(s(s(s(s(z))))), s(z))) | (~r(s(s(s(s(z)))), s(z))) | (~r(s(s(s(s(z)))), s(s(s(s(s(z))))))))),
% 2.42/2.60 inference(quant_inst,[status(thm)],[])).
% 2.42/2.60 tff(7228,plain,
% 2.42/2.60 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(z), s(s(z)))) | (~r(s(s(s(s(z)))), s(z))) | (~r(s(s(s(s(s(z))))), s(z))) | (~r(s(s(s(s(z)))), s(s(s(s(s(z)))))))),
% 2.42/2.60 inference(modus_ponens,[status(thm)],[7227, 7226])).
% 2.42/2.60 tff(7229,plain,
% 2.42/2.60 ((~r(s(s(s(s(s(z))))), s(z))) | (~r(s(s(s(s(z)))), s(s(s(s(s(z)))))))),
% 2.42/2.60 inference(unit_resolution,[status(thm)],[7228, 197, 120, 7222])).
% 2.42/2.60 tff(7230,plain,
% 2.42/2.60 (~r(s(s(s(s(z)))), s(s(s(s(s(z))))))),
% 2.42/2.60 inference(unit_resolution,[status(thm)],[7229, 7208])).
% 2.42/2.60 tff(7231,plain,
% 2.42/2.60 (~r(s(s(s(elem!1))), s(s(s(s(elem!1)))))),
% 2.42/2.60 inference(modus_ponens,[status(thm)],[7230, 7221])).
% 2.42/2.60 tff(7232,plain,
% 2.42/2.60 (b(s(s(s(elem!1))), s(s(s(s(elem!1)))))),
% 2.42/2.60 inference(unit_resolution,[status(thm)],[696, 7231, 361])).
% 2.42/2.60 tff(7233,plain,
% 2.42/2.60 (b(s(s(s(s(z)))), s(s(s(s(s(z))))))),
% 2.42/2.60 inference(modus_ponens,[status(thm)],[7232, 7219])).
% 2.42/2.60 tff(7234,assumption,(b(s(s(s(s(z)))), s(s(z)))), introduced(assumption)).
% 2.42/2.60 tff(7235,plain,
% 2.42/2.60 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), s(s(z)))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(s(s(s(z))))), s(s(z)))) | (~b(s(s(s(s(z)))), s(s(s(s(s(z))))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(s(s(s(z))))), s(s(z)))) | (~b(s(s(s(s(z)))), s(s(s(s(s(z))))))))),
% 2.42/2.60 inference(rewrite,[status(thm)],[])).
% 2.42/2.60 tff(7236,plain,
% 2.42/2.60 (((~b(s(s(s(z))), s(s(z)))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(s(s(s(z))))), s(s(z)))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(s(s(z)))), s(s(s(s(s(z)))))))) <=> ((~b(s(s(s(z))), s(s(z)))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(s(s(s(z))))), s(s(z)))) | (~b(s(s(s(s(z)))), s(s(s(s(s(z))))))))),
% 2.42/2.60 inference(rewrite,[status(thm)],[])).
% 2.42/2.60 tff(7237,plain,
% 2.42/2.60 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), s(s(z)))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(s(s(s(z))))), s(s(z)))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(s(s(z)))), s(s(s(s(s(z))))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), s(s(z)))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(s(s(s(z))))), s(s(z)))) | (~b(s(s(s(s(z)))), s(s(s(s(s(z)))))))))),
% 2.42/2.60 inference(monotonicity,[status(thm)],[7236])).
% 2.42/2.60 tff(7238,plain,
% 2.42/2.60 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), s(s(z)))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(s(s(s(z))))), s(s(z)))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(s(s(z)))), s(s(s(s(s(z))))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(s(s(s(z))))), s(s(z)))) | (~b(s(s(s(s(z)))), s(s(s(s(s(z))))))))),
% 2.42/2.60 inference(transitivity,[status(thm)],[7237, 7235])).
% 2.42/2.60 tff(7239,plain,
% 2.42/2.60 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), s(s(z)))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(s(s(s(z))))), s(s(z)))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(s(s(z)))), s(s(s(s(s(z))))))))),
% 2.42/2.60 inference(quant_inst,[status(thm)],[])).
% 2.42/2.60 tff(7240,plain,
% 2.42/2.60 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(s(s(s(z))))), s(s(z)))) | (~b(s(s(s(s(z)))), s(s(s(s(s(z)))))))),
% 2.42/2.60 inference(modus_ponens,[status(thm)],[7239, 7238])).
% 2.42/2.60 tff(7241,plain,
% 2.42/2.60 (~b(s(s(s(s(s(z))))), s(s(z)))),
% 2.42/2.60 inference(unit_resolution,[status(thm)],[7240, 166, 986, 987, 7234, 7233])).
% 2.42/2.60 tff(7242,plain,
% 2.42/2.60 ($false),
% 2.42/2.60 inference(unit_resolution,[status(thm)],[7241, 7216])).
% 2.42/2.60 tff(7243,plain,((~r(s(s(s(s(s(z))))), s(z))) | (~(s(s(elem!1)) = s(s(s(z))))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(s(s(s(z)))), s(s(z)))) | (s(s(s(elem!1))) = s(s(s(s(elem!1))))) | (~r(s(z), s(s(z)))) | (~r(s(s(s(s(z)))), s(z))) | (~r(s(s(z)), s(z)))), inference(lemma,lemma(discharge,[]))).
% 2.42/2.60 tff(7244,plain,
% 2.42/2.60 (~r(s(s(s(s(s(z))))), s(z))),
% 2.42/2.60 inference(unit_resolution,[status(thm)],[7243, 7179, 7203, 6498, 7201, 361, 120, 7196, 392])).
% 2.42/2.60 tff(7245,plain,
% 2.42/2.60 (~r(s(s(s(s(elem!1)))), s(z))),
% 2.42/2.60 inference(modus_ponens,[status(thm)],[7244, 7194])).
% 2.42/2.60 tff(7246,plain,
% 2.42/2.60 (b(s(s(s(s(elem!1)))), s(z))),
% 2.42/2.60 inference(unit_resolution,[status(thm)],[661, 7245])).
% 2.42/2.60 tff(7247,plain,
% 2.42/2.60 (b(s(s(s(s(s(z))))), s(z))),
% 2.42/2.60 inference(modus_ponens,[status(thm)],[7246, 7192])).
% 2.42/2.60 tff(7248,plain,
% 2.42/2.60 (b(s(s(elem!1)), s(z)) <=> b(s(s(s(z))), s(z))),
% 2.42/2.60 inference(monotonicity,[status(thm)],[7179])).
% 2.42/2.60 tff(7249,plain,
% 2.42/2.60 (b(s(s(s(z))), s(z))),
% 2.42/2.60 inference(modus_ponens,[status(thm)],[310, 7248])).
% 2.42/2.60 tff(7250,plain,
% 2.42/2.60 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), z)) | (~b(z, s(z))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(s(s(s(s(s(z))))), s(s(s(z))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), z)) | (~b(z, s(z))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(s(s(s(s(s(z))))), s(s(s(z))))))),
% 2.42/2.60 inference(rewrite,[status(thm)],[])).
% 2.42/2.60 tff(7251,plain,
% 2.42/2.60 (((~b(z, s(z))) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(s(z), z)) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(s(s(s(s(s(z))))), s(s(s(z)))))) <=> ((~b(s(z), z)) | (~b(z, s(z))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(s(s(s(s(s(z))))), s(s(s(z))))))),
% 2.42/2.60 inference(rewrite,[status(thm)],[])).
% 2.42/2.60 tff(7252,plain,
% 2.42/2.60 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(z))) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(s(z), z)) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(s(s(s(s(s(z))))), s(s(s(z))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), z)) | (~b(z, s(z))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(s(s(s(s(s(z))))), s(s(s(z)))))))),
% 2.42/2.60 inference(monotonicity,[status(thm)],[7251])).
% 2.42/2.60 tff(7253,plain,
% 2.42/2.60 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(z))) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(s(z), z)) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(s(s(s(s(s(z))))), s(s(s(z))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), z)) | (~b(z, s(z))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(s(s(s(s(s(z))))), s(s(s(z))))))),
% 2.42/2.60 inference(transitivity,[status(thm)],[7252, 7250])).
% 2.42/2.60 tff(7254,plain,
% 2.42/2.60 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(z))) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(s(z), z)) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(s(s(s(s(s(z))))), s(s(s(z))))))),
% 2.42/2.60 inference(quant_inst,[status(thm)],[])).
% 2.42/2.60 tff(7255,plain,
% 2.42/2.60 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), z)) | (~b(z, s(z))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(s(s(s(s(s(z))))), s(s(s(z)))))),
% 2.42/2.60 inference(modus_ponens,[status(thm)],[7254, 7253])).
% 2.42/2.60 tff(7256,plain,
% 2.42/2.60 ((~b(s(s(s(s(s(z))))), s(z))) | (~b(s(s(s(s(s(z))))), s(s(s(z)))))),
% 2.42/2.60 inference(unit_resolution,[status(thm)],[7255, 166, 3949, 118, 7249])).
% 2.42/2.60 tff(7257,plain,
% 2.42/2.60 (~b(s(s(s(s(s(z))))), s(s(s(z))))),
% 2.42/2.60 inference(unit_resolution,[status(thm)],[7256, 7247])).
% 2.42/2.60 tff(7258,plain,
% 2.42/2.60 (~b(s(s(s(s(elem!1)))), s(s(elem!1)))),
% 2.42/2.60 inference(unit_resolution,[status(thm)],[5175, 7257, 7179])).
% 2.42/2.60 tff(7259,plain,
% 2.42/2.60 (r(s(s(s(s(elem!1)))), s(s(elem!1)))),
% 2.42/2.60 inference(unit_resolution,[status(thm)],[813, 7258, 7190])).
% 2.42/2.60 tff(7260,plain,
% 2.42/2.60 (r(s(s(s(s(s(z))))), s(s(s(z))))),
% 2.42/2.60 inference(modus_ponens,[status(thm)],[7259, 7185])).
% 2.42/2.60 tff(7261,plain,
% 2.42/2.60 ((~b(s(s(s(s(s(z))))), s(z))) | (~b(s(s(s(s(s(z))))), z))),
% 2.42/2.60 inference(unit_resolution,[status(thm)],[7005, 166, 3949, 118])).
% 2.42/2.60 tff(7262,plain,
% 2.42/2.60 (~b(s(s(s(s(s(z))))), z)),
% 2.42/2.60 inference(unit_resolution,[status(thm)],[7261, 7247])).
% 2.42/2.60 tff(7263,plain,
% 2.42/2.60 (r(s(s(s(s(s(z))))), z)),
% 2.42/2.60 inference(unit_resolution,[status(thm)],[5198, 79, 5195, 7262])).
% 2.42/2.60 tff(7264,plain,
% 2.42/2.60 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(z)))) | (~r(s(s(s(z))), z)) | (~r(s(s(s(s(s(z))))), z)) | (~r(s(s(s(s(s(z))))), s(s(s(z))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, s(s(z)))) | (~r(s(s(s(z))), z)) | (~r(s(s(s(s(s(z))))), z)) | (~r(s(s(s(s(s(z))))), s(s(s(z))))))),
% 2.42/2.60 inference(rewrite,[status(thm)],[])).
% 2.42/2.60 tff(7265,plain,
% 2.42/2.60 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(z)))) | (~r(s(s(s(z))), z)) | (~r(s(s(s(s(s(z))))), z)) | (~r(s(s(s(s(s(z))))), s(s(s(z))))))),
% 2.42/2.60 inference(quant_inst,[status(thm)],[])).
% 2.42/2.60 tff(7266,plain,
% 2.42/2.60 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, s(s(z)))) | (~r(s(s(s(z))), z)) | (~r(s(s(s(s(s(z))))), z)) | (~r(s(s(s(s(s(z))))), s(s(s(z)))))),
% 2.42/2.60 inference(modus_ponens,[status(thm)],[7265, 7264])).
% 2.42/2.60 tff(7267,plain,
% 2.42/2.60 ($false),
% 2.42/2.60 inference(unit_resolution,[status(thm)],[7266, 197, 155, 1733, 7263, 7260])).
% 2.42/2.60 tff(7268,plain,((~r(s(s(s(z))), z)) | (~r(z, s(s(z)))) | (~b(z, s(z))) | (s(s(s(elem!1))) = s(s(s(s(elem!1))))) | (~r(s(z), s(s(z)))) | (~r(s(s(z)), s(z))) | (~r(s(s(s(elem!1))), s(z))) | (~b(s(s(elem!1)), s(z))) | (~b(s(s(elem!1)), s(s(z)))) | (~b(s(s(z)), s(s(elem!1)))) | (~r(s(s(elem!1)), z)) | (~r(s(s(z)), z))), inference(lemma,lemma(discharge,[]))).
% 2.42/2.60 tff(7269,plain,
% 2.42/2.60 (~r(s(s(s(z))), z)),
% 2.42/2.60 inference(unit_resolution,[status(thm)],[7268, 7155, 118, 361, 155, 7142, 7152, 310, 7175, 7140, 7174, 7166])).
% 2.42/2.60 tff(7270,plain,
% 2.42/2.60 (b(s(s(s(z))), z)),
% 2.42/2.60 inference(unit_resolution,[status(thm)],[1713, 7269])).
% 2.42/2.60 tff(7271,plain,
% 2.42/2.60 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), s(z))) | (~r(s(s(elem!1)), z)) | (~r(s(s(elem!1)), s(s(s(elem!1))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), s(z))) | (~r(s(s(elem!1)), z)) | (~r(s(s(elem!1)), s(s(s(elem!1))))))),
% 2.42/2.60 inference(rewrite,[status(thm)],[])).
% 2.42/2.60 tff(7272,plain,
% 2.42/2.60 (((~r(s(s(s(elem!1))), s(z))) | (~r(z, s(s(s(elem!1))))) | (~r(s(s(elem!1)), s(s(s(elem!1))))) | (~r(s(s(elem!1)), z))) <=> ((~r(z, s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), s(z))) | (~r(s(s(elem!1)), z)) | (~r(s(s(elem!1)), s(s(s(elem!1))))))),
% 2.42/2.60 inference(rewrite,[status(thm)],[])).
% 2.42/2.60 tff(7273,plain,
% 2.42/2.60 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), s(z))) | (~r(z, s(s(s(elem!1))))) | (~r(s(s(elem!1)), s(s(s(elem!1))))) | (~r(s(s(elem!1)), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), s(z))) | (~r(s(s(elem!1)), z)) | (~r(s(s(elem!1)), s(s(s(elem!1)))))))),
% 2.42/2.60 inference(monotonicity,[status(thm)],[7272])).
% 2.42/2.60 tff(7274,plain,
% 2.42/2.60 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), s(z))) | (~r(z, s(s(s(elem!1))))) | (~r(s(s(elem!1)), s(s(s(elem!1))))) | (~r(s(s(elem!1)), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), s(z))) | (~r(s(s(elem!1)), z)) | (~r(s(s(elem!1)), s(s(s(elem!1))))))),
% 2.42/2.60 inference(transitivity,[status(thm)],[7273, 7271])).
% 2.42/2.60 tff(7275,plain,
% 2.42/2.60 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), s(z))) | (~r(z, s(s(s(elem!1))))) | (~r(s(s(elem!1)), s(s(s(elem!1))))) | (~r(s(s(elem!1)), z)))),
% 2.42/2.60 inference(quant_inst,[status(thm)],[])).
% 2.42/2.60 tff(7276,plain,
% 2.42/2.60 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), s(z))) | (~r(s(s(elem!1)), z)) | (~r(s(s(elem!1)), s(s(s(elem!1)))))),
% 2.42/2.60 inference(modus_ponens,[status(thm)],[7275, 7274])).
% 2.42/2.60 tff(7277,plain,
% 2.42/2.60 ($false),
% 2.42/2.60 inference(unit_resolution,[status(thm)],[7276, 197, 350, 377, 282, 1970])).
% 2.42/2.60 tff(7278,plain,((~r(z, s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), s(z))) | (~r(s(s(elem!1)), s(s(s(elem!1))))) | (~r(s(s(elem!1)), z))), inference(lemma,lemma(discharge,[]))).
% 2.42/2.60 tff(7279,plain,
% 2.42/2.60 (~r(z, s(s(s(elem!1))))),
% 2.42/2.60 inference(unit_resolution,[status(thm)],[7278, 377, 7152, 7174])).
% 2.42/2.60 tff(7280,plain,
% 2.42/2.60 (b(z, s(s(s(elem!1))))),
% 2.42/2.60 inference(unit_resolution,[status(thm)],[261, 7279])).
% 2.42/2.60 tff(7281,plain,
% 2.42/2.60 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), z)) | (~b(s(s(s(z))), z)) | (~b(s(s(s(elem!1))), s(s(s(z))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), z)) | (~b(s(s(s(z))), z)) | (~b(s(s(s(elem!1))), s(s(s(z))))))),
% 2.42/2.60 inference(rewrite,[status(thm)],[])).
% 2.42/2.60 tff(7282,plain,
% 2.42/2.60 (((~b(s(s(s(elem!1))), z)) | (~b(s(s(s(elem!1))), z)) | (~b(z, s(s(s(elem!1))))) | (~b(s(s(s(z))), z)) | (~b(s(s(s(elem!1))), z)) | (~b(s(s(s(elem!1))), s(s(s(z)))))) <=> ((~b(z, s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), z)) | (~b(s(s(s(z))), z)) | (~b(s(s(s(elem!1))), s(s(s(z))))))),
% 2.42/2.60 inference(rewrite,[status(thm)],[])).
% 2.42/2.60 tff(7283,plain,
% 2.42/2.60 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), z)) | (~b(s(s(s(elem!1))), z)) | (~b(z, s(s(s(elem!1))))) | (~b(s(s(s(z))), z)) | (~b(s(s(s(elem!1))), z)) | (~b(s(s(s(elem!1))), s(s(s(z))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), z)) | (~b(s(s(s(z))), z)) | (~b(s(s(s(elem!1))), s(s(s(z)))))))),
% 2.42/2.61 inference(monotonicity,[status(thm)],[7282])).
% 2.42/2.61 tff(7284,plain,
% 2.42/2.61 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), z)) | (~b(s(s(s(elem!1))), z)) | (~b(z, s(s(s(elem!1))))) | (~b(s(s(s(z))), z)) | (~b(s(s(s(elem!1))), z)) | (~b(s(s(s(elem!1))), s(s(s(z))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), z)) | (~b(s(s(s(z))), z)) | (~b(s(s(s(elem!1))), s(s(s(z))))))),
% 2.42/2.61 inference(transitivity,[status(thm)],[7283, 7281])).
% 2.42/2.61 tff(7285,plain,
% 2.42/2.61 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), z)) | (~b(s(s(s(elem!1))), z)) | (~b(z, s(s(s(elem!1))))) | (~b(s(s(s(z))), z)) | (~b(s(s(s(elem!1))), z)) | (~b(s(s(s(elem!1))), s(s(s(z))))))),
% 2.42/2.61 inference(quant_inst,[status(thm)],[])).
% 2.42/2.61 tff(7286,plain,
% 2.42/2.61 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), z)) | (~b(s(s(s(z))), z)) | (~b(s(s(s(elem!1))), s(s(s(z)))))),
% 2.42/2.61 inference(modus_ponens,[status(thm)],[7285, 7284])).
% 2.42/2.61 tff(7287,plain,
% 2.42/2.61 (~b(s(s(s(elem!1))), s(s(s(z))))),
% 2.42/2.61 inference(unit_resolution,[status(thm)],[7286, 166, 7280, 121, 7270])).
% 2.42/2.61 tff(7288,plain,
% 2.42/2.61 (r(s(s(s(elem!1))), s(s(s(z))))),
% 2.42/2.61 inference(unit_resolution,[status(thm)],[3574, 7287, 140])).
% 2.42/2.61 tff(7289,plain,
% 2.42/2.61 (~r(s(z), z)),
% 2.42/2.61 inference(unit_resolution,[status(thm)],[3947, 197, 7155, 155, 7142])).
% 2.42/2.61 tff(7290,plain,
% 2.42/2.61 (b(s(z), z)),
% 2.42/2.61 inference(unit_resolution,[status(thm)],[230, 7289])).
% 2.42/2.61 tff(7291,plain,
% 2.42/2.61 (~b(s(s(s(z))), s(z))),
% 2.42/2.61 inference(unit_resolution,[status(thm)],[4045, 166, 7290, 118, 7270])).
% 2.42/2.61 tff(7292,plain,
% 2.42/2.61 (r(s(s(s(z))), s(z))),
% 2.42/2.61 inference(unit_resolution,[status(thm)],[1763, 7291])).
% 2.42/2.61 tff(7293,plain,
% 2.42/2.61 ($false),
% 2.42/2.61 inference(unit_resolution,[status(thm)],[6678, 197, 7155, 7152, 7292, 7288])).
% 2.42/2.61 tff(7294,plain,((~r(s(s(elem!1)), s(s(s(elem!1))))) | (~b(z, s(z))) | (~b(s(s(s(elem!1))), z)) | (s(s(s(elem!1))) = s(s(s(s(elem!1))))) | (~r(z, s(s(z)))) | (~b(s(s(elem!1)), s(z))) | (~b(s(z), s(s(elem!1)))) | (s(s(z)) = s(s(elem!1)))), inference(lemma,lemma(discharge,[]))).
% 2.42/2.61 tff(7295,plain,
% 2.42/2.61 (~r(s(s(elem!1)), s(s(s(elem!1))))),
% 2.42/2.61 inference(unit_resolution,[status(thm)],[7294, 310, 121, 358, 155, 118, 376, 52])).
% 2.42/2.61 tff(7296,plain,
% 2.42/2.61 (b(s(s(elem!1)), s(s(s(elem!1))))),
% 2.42/2.61 inference(unit_resolution,[status(thm)],[461, 7295, 45])).
% 2.42/2.61 tff(7297,plain,
% 2.42/2.61 (~b(s(s(z)), s(s(elem!1)))),
% 2.42/2.61 inference(unit_resolution,[status(thm)],[454, 156, 376, 310])).
% 2.42/2.61 tff(7298,plain,
% 2.42/2.61 (~b(s(s(elem!1)), s(s(z)))),
% 2.42/2.61 inference(unit_resolution,[status(thm)],[549, 156, 376, 463, 310])).
% 2.42/2.61 tff(7299,plain,
% 2.42/2.61 ($false),
% 2.42/2.61 inference(unit_resolution,[status(thm)],[2079, 7298, 7297, 155, 52, 365])).
% 2.42/2.61 tff(7300,plain,((~b(s(s(z)), s(z))) | (~r(z, s(s(z)))) | (s(s(z)) = s(s(elem!1))) | (~r(z, s(s(elem!1)))) | (~b(s(z), s(s(elem!1)))) | (~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(s(s(elem!1)), s(z)))), inference(lemma,lemma(discharge,[]))).
% 2.42/2.61 tff(7301,plain,
% 2.42/2.61 (~b(s(s(z)), s(z))),
% 2.42/2.61 inference(unit_resolution,[status(thm)],[7300, 7138, 52, 155, 376, 7296, 310])).
% 2.42/2.61 tff(7302,plain,
% 2.42/2.61 (r(s(s(z)), s(z))),
% 2.42/2.61 inference(unit_resolution,[status(thm)],[308, 7301])).
% 2.42/2.61 tff(7303,plain,
% 2.42/2.61 (~r(s(s(elem!1)), s(s(z)))),
% 2.42/2.61 inference(unit_resolution,[status(thm)],[401, 7302, 155, 7138])).
% 2.42/2.61 tff(7304,plain,
% 2.42/2.61 (b(s(s(elem!1)), s(s(z)))),
% 2.42/2.61 inference(unit_resolution,[status(thm)],[441, 7303, 132])).
% 2.42/2.61 tff(7305,plain,
% 2.42/2.61 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), s(z))) | (~r(s(z), z)) | (~r(s(s(z)), s(z))) | (~r(s(s(z)), s(s(s(elem!1))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(elem!1))), s(z))) | (~r(s(z), z)) | (~r(s(s(z)), s(z))) | (~r(s(s(z)), s(s(s(elem!1))))))),
% 2.42/2.61 inference(rewrite,[status(thm)],[])).
% 2.42/2.61 tff(7306,plain,
% 2.42/2.61 (((~r(s(z), z)) | (~r(s(s(s(elem!1))), s(z))) | (~r(s(s(z)), s(z))) | (~r(s(s(z)), s(s(s(elem!1)))))) <=> ((~r(s(s(s(elem!1))), s(z))) | (~r(s(z), z)) | (~r(s(s(z)), s(z))) | (~r(s(s(z)), s(s(s(elem!1))))))),
% 2.42/2.61 inference(rewrite,[status(thm)],[])).
% 2.42/2.61 tff(7307,plain,
% 2.42/2.61 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), z)) | (~r(s(s(s(elem!1))), s(z))) | (~r(s(s(z)), s(z))) | (~r(s(s(z)), s(s(s(elem!1))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), s(z))) | (~r(s(z), z)) | (~r(s(s(z)), s(z))) | (~r(s(s(z)), s(s(s(elem!1)))))))),
% 2.42/2.61 inference(monotonicity,[status(thm)],[7306])).
% 2.42/2.61 tff(7308,plain,
% 2.42/2.61 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), z)) | (~r(s(s(s(elem!1))), s(z))) | (~r(s(s(z)), s(z))) | (~r(s(s(z)), s(s(s(elem!1))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(elem!1))), s(z))) | (~r(s(z), z)) | (~r(s(s(z)), s(z))) | (~r(s(s(z)), s(s(s(elem!1))))))),
% 2.42/2.61 inference(transitivity,[status(thm)],[7307, 7305])).
% 2.42/2.61 tff(7309,plain,
% 2.42/2.61 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), z)) | (~r(s(s(s(elem!1))), s(z))) | (~r(s(s(z)), s(z))) | (~r(s(s(z)), s(s(s(elem!1))))))),
% 2.42/2.61 inference(quant_inst,[status(thm)],[])).
% 2.42/2.61 tff(7310,plain,
% 2.42/2.61 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(elem!1))), s(z))) | (~r(s(z), z)) | (~r(s(s(z)), s(z))) | (~r(s(s(z)), s(s(s(elem!1)))))),
% 2.42/2.61 inference(modus_ponens,[status(thm)],[7309, 7308])).
% 2.42/2.61 tff(7311,plain,
% 2.42/2.61 ($false),
% 2.42/2.61 inference(unit_resolution,[status(thm)],[7310, 197, 350, 97, 392, 281])).
% 2.42/2.61 tff(7312,plain,((~r(s(z), z)) | (~r(s(s(s(elem!1))), s(z))) | (~r(s(s(z)), s(z))) | (~r(s(s(z)), s(s(s(elem!1)))))), inference(lemma,lemma(discharge,[]))).
% 2.42/2.61 tff(7313,plain,
% 2.42/2.61 (~r(s(z), z)),
% 2.42/2.61 inference(unit_resolution,[status(thm)],[7312, 281, 392, 350])).
% 2.42/2.61 tff(7314,plain,
% 2.42/2.61 (b(s(z), z)),
% 2.42/2.61 inference(unit_resolution,[status(thm)],[230, 7313])).
% 2.42/2.61 tff(7315,plain,
% 2.42/2.61 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), z)) | (~b(s(z), s(s(s(elem!1))))) | (~b(s(z), s(s(elem!1)))) | (~b(s(s(s(elem!1))), z)) | (~b(z, s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), z)) | (~b(s(z), s(s(s(elem!1))))) | (~b(s(z), s(s(elem!1)))) | (~b(s(s(s(elem!1))), z)) | (~b(z, s(z))))),
% 2.42/2.61 inference(rewrite,[status(thm)],[])).
% 2.42/2.61 tff(7316,plain,
% 2.42/2.61 (((~b(s(z), s(s(elem!1)))) | (~b(s(z), s(s(elem!1)))) | (~b(z, s(z))) | (~b(s(s(s(elem!1))), z)) | (~b(s(z), z)) | (~b(s(z), s(s(s(elem!1)))))) <=> ((~b(s(z), z)) | (~b(s(z), s(s(s(elem!1))))) | (~b(s(z), s(s(elem!1)))) | (~b(s(s(s(elem!1))), z)) | (~b(z, s(z))))),
% 2.42/2.61 inference(rewrite,[status(thm)],[])).
% 2.42/2.61 tff(7317,plain,
% 2.42/2.61 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(elem!1)))) | (~b(s(z), s(s(elem!1)))) | (~b(z, s(z))) | (~b(s(s(s(elem!1))), z)) | (~b(s(z), z)) | (~b(s(z), s(s(s(elem!1))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), z)) | (~b(s(z), s(s(s(elem!1))))) | (~b(s(z), s(s(elem!1)))) | (~b(s(s(s(elem!1))), z)) | (~b(z, s(z)))))),
% 2.42/2.61 inference(monotonicity,[status(thm)],[7316])).
% 2.42/2.61 tff(7318,plain,
% 2.42/2.61 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(elem!1)))) | (~b(s(z), s(s(elem!1)))) | (~b(z, s(z))) | (~b(s(s(s(elem!1))), z)) | (~b(s(z), z)) | (~b(s(z), s(s(s(elem!1))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), z)) | (~b(s(z), s(s(s(elem!1))))) | (~b(s(z), s(s(elem!1)))) | (~b(s(s(s(elem!1))), z)) | (~b(z, s(z))))),
% 2.42/2.61 inference(transitivity,[status(thm)],[7317, 7315])).
% 2.42/2.61 tff(7319,plain,
% 2.42/2.61 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(elem!1)))) | (~b(s(z), s(s(elem!1)))) | (~b(z, s(z))) | (~b(s(s(s(elem!1))), z)) | (~b(s(z), z)) | (~b(s(z), s(s(s(elem!1))))))),
% 2.42/2.61 inference(quant_inst,[status(thm)],[])).
% 2.42/2.61 tff(7320,plain,
% 2.42/2.61 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), z)) | (~b(s(z), s(s(s(elem!1))))) | (~b(s(z), s(s(elem!1)))) | (~b(s(s(s(elem!1))), z)) | (~b(z, s(z)))),
% 2.42/2.61 inference(modus_ponens,[status(thm)],[7319, 7318])).
% 2.42/2.61 tff(7321,plain,
% 2.42/2.61 ($false),
% 2.42/2.61 inference(unit_resolution,[status(thm)],[7320, 166, 376, 241, 53, 118, 121])).
% 2.42/2.61 tff(7322,plain,((~b(s(s(s(elem!1))), z)) | (~b(s(z), s(s(elem!1)))) | (~b(s(z), s(s(s(elem!1))))) | (~b(s(z), z)) | (~b(z, s(z)))), inference(lemma,lemma(discharge,[]))).
% 2.42/2.61 tff(7323,plain,
% 2.42/2.61 (~b(s(z), s(s(s(elem!1))))),
% 2.42/2.61 inference(unit_resolution,[status(thm)],[7322, 7314, 118, 121, 376])).
% 2.42/2.61 tff(7324,plain,
% 2.42/2.61 (r(s(z), s(s(s(elem!1))))),
% 2.42/2.61 inference(unit_resolution,[status(thm)],[116, 7323])).
% 2.42/2.61 tff(7325,plain,
% 2.42/2.61 ($false),
% 2.42/2.61 inference(unit_resolution,[status(thm)],[6048, 197, 350, 392, 7324, 281])).
% 2.42/2.61 tff(7326,plain,((~r(s(s(z)), s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), s(z))) | (~r(s(s(z)), s(z))) | (~b(z, s(z))) | (~b(s(s(s(elem!1))), z)) | (~b(s(z), s(s(elem!1))))), inference(lemma,lemma(discharge,[]))).
% 2.42/2.61 tff(7327,plain,
% 2.42/2.61 (~r(s(s(z)), s(s(s(elem!1))))),
% 2.42/2.61 inference(unit_resolution,[status(thm)],[7326, 7152, 7302, 118, 121, 376])).
% 2.42/2.61 tff(7328,plain,
% 2.42/2.61 (r(s(s(s(elem!1))), s(s(z)))),
% 2.42/2.61 inference(unit_resolution,[status(thm)],[501, 7327, 7296, 7304])).
% 2.42/2.61 tff(7329,plain,
% 2.42/2.61 (~r(z, s(s(s(elem!1))))),
% 2.42/2.61 inference(unit_resolution,[status(thm)],[1588, 7328, 155, 7302])).
% 2.42/2.61 tff(7330,plain,
% 2.42/2.61 (b(z, s(s(s(elem!1))))),
% 2.42/2.61 inference(unit_resolution,[status(thm)],[261, 7329])).
% 2.42/2.61 tff(7331,plain,
% 2.42/2.61 (~r(s(z), s(s(z)))),
% 2.42/2.61 inference(unit_resolution,[status(thm)],[483, 7328, 7152, 7302])).
% 2.42/2.61 tff(7332,plain,
% 2.42/2.61 (b(s(z), s(s(z)))),
% 2.42/2.61 inference(unit_resolution,[status(thm)],[427, 7331])).
% 2.42/2.61 tff(7333,plain,
% 2.42/2.61 (r(s(s(z)), s(s(elem!1)))),
% 2.42/2.61 inference(unit_resolution,[status(thm)],[5300, 7332, 376, 52, 7303])).
% 2.42/2.61 tff(7334,plain,
% 2.42/2.61 ($false),
% 2.42/2.61 inference(unit_resolution,[status(thm)],[617, 7333, 7330, 155, 121, 7138, 45])).
% 2.42/2.61 tff(7335,plain,((~b(s(s(elem!1)), s(z))) | (~r(z, s(s(z)))) | (~b(s(s(s(elem!1))), z)) | (s(s(elem!1)) = s(s(s(elem!1)))) | (~b(s(z), s(s(elem!1)))) | (s(s(z)) = s(s(elem!1))) | (~b(z, s(z)))), inference(lemma,lemma(discharge,[]))).
% 2.42/2.61 tff(7336,plain,
% 2.42/2.61 (~b(s(s(elem!1)), s(z))),
% 2.42/2.61 inference(unit_resolution,[status(thm)],[7335, 52, 121, 45, 376, 155, 118])).
% 2.42/2.61 tff(7337,plain,
% 2.42/2.61 (r(s(s(elem!1)), s(z))),
% 2.42/2.61 inference(unit_resolution,[status(thm)],[1912, 7336])).
% 2.42/2.61 tff(7338,plain,
% 2.42/2.61 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(z), s(s(elem!1)))) | (~b(s(s(s(elem!1))), s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(z), s(s(elem!1)))) | (~b(s(s(s(elem!1))), s(z))))),
% 2.42/2.61 inference(rewrite,[status(thm)],[])).
% 2.42/2.61 tff(7339,plain,
% 2.42/2.61 (((~b(s(s(s(elem!1))), s(z))) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(s(z), s(s(elem!1)))) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(s(s(elem!1))), s(z)))) <=> ((~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(z), s(s(elem!1)))) | (~b(s(s(s(elem!1))), s(z))))),
% 2.42/2.61 inference(rewrite,[status(thm)],[])).
% 2.42/2.61 tff(7340,plain,
% 2.42/2.61 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), s(z))) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(s(z), s(s(elem!1)))) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(s(s(elem!1))), s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(z), s(s(elem!1)))) | (~b(s(s(s(elem!1))), s(z)))))),
% 2.42/2.61 inference(monotonicity,[status(thm)],[7339])).
% 2.42/2.61 tff(7341,plain,
% 2.42/2.61 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), s(z))) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(s(z), s(s(elem!1)))) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(s(s(elem!1))), s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(z), s(s(elem!1)))) | (~b(s(s(s(elem!1))), s(z))))),
% 2.42/2.61 inference(transitivity,[status(thm)],[7340, 7338])).
% 2.42/2.61 tff(7342,plain,
% 2.42/2.61 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), s(z))) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(s(z), s(s(elem!1)))) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(s(s(elem!1))), s(z))))),
% 2.42/2.61 inference(quant_inst,[status(thm)],[])).
% 2.42/2.61 tff(7343,plain,
% 2.42/2.61 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(z), s(s(elem!1)))) | (~b(s(s(s(elem!1))), s(z)))),
% 2.42/2.61 inference(modus_ponens,[status(thm)],[7342, 7341])).
% 2.42/2.61 tff(7344,plain,
% 2.42/2.61 (~b(s(s(s(elem!1))), s(s(elem!1)))),
% 2.42/2.61 inference(unit_resolution,[status(thm)],[7343, 166, 376, 463, 96])).
% 2.42/2.61 tff(7345,plain,
% 2.42/2.61 (r(s(s(s(elem!1))), s(s(elem!1)))),
% 2.42/2.61 inference(unit_resolution,[status(thm)],[889, 7344, 1863])).
% 2.42/2.61 tff(7346,plain,
% 2.42/2.61 (~r(z, s(s(elem!1)))),
% 2.42/2.61 inference(unit_resolution,[status(thm)],[1937, 463, 376, 96, 7345])).
% 2.42/2.61 tff(7347,plain,
% 2.42/2.61 (b(z, s(s(elem!1)))),
% 2.42/2.61 inference(unit_resolution,[status(thm)],[1795, 7346])).
% 2.42/2.61 tff(7348,plain,
% 2.42/2.61 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(z, s(s(s(elem!1))))) | (~b(z, s(s(elem!1)))) | (~b(s(z), s(s(elem!1)))) | (~b(s(s(s(elem!1))), s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(z, s(s(s(elem!1))))) | (~b(z, s(s(elem!1)))) | (~b(s(z), s(s(elem!1)))) | (~b(s(s(s(elem!1))), s(z))))),
% 2.42/2.61 inference(rewrite,[status(thm)],[])).
% 2.42/2.61 tff(7349,plain,
% 2.42/2.61 (((~b(s(z), s(s(elem!1)))) | (~b(z, s(s(elem!1)))) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(z, s(s(s(elem!1))))) | (~b(z, s(s(elem!1))))) <=> ((~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(z, s(s(s(elem!1))))) | (~b(z, s(s(elem!1)))) | (~b(s(z), s(s(elem!1)))) | (~b(s(s(s(elem!1))), s(z))))),
% 2.42/2.61 inference(rewrite,[status(thm)],[])).
% 2.42/2.61 tff(7350,plain,
% 2.42/2.61 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(elem!1)))) | (~b(z, s(s(elem!1)))) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(z, s(s(s(elem!1))))) | (~b(z, s(s(elem!1)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(z, s(s(s(elem!1))))) | (~b(z, s(s(elem!1)))) | (~b(s(z), s(s(elem!1)))) | (~b(s(s(s(elem!1))), s(z)))))),
% 2.42/2.61 inference(monotonicity,[status(thm)],[7349])).
% 2.42/2.61 tff(7351,plain,
% 2.42/2.61 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(elem!1)))) | (~b(z, s(s(elem!1)))) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(z, s(s(s(elem!1))))) | (~b(z, s(s(elem!1)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(z, s(s(s(elem!1))))) | (~b(z, s(s(elem!1)))) | (~b(s(z), s(s(elem!1)))) | (~b(s(s(s(elem!1))), s(z))))),
% 2.42/2.61 inference(transitivity,[status(thm)],[7350, 7348])).
% 2.42/2.61 tff(7352,plain,
% 2.42/2.61 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(elem!1)))) | (~b(z, s(s(elem!1)))) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(z, s(s(s(elem!1))))) | (~b(z, s(s(elem!1)))))),
% 2.42/2.61 inference(quant_inst,[status(thm)],[])).
% 2.42/2.61 tff(7353,plain,
% 2.42/2.61 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(z, s(s(s(elem!1))))) | (~b(z, s(s(elem!1)))) | (~b(s(z), s(s(elem!1)))) | (~b(s(s(s(elem!1))), s(z)))),
% 2.42/2.61 inference(modus_ponens,[status(thm)],[7352, 7351])).
% 2.42/2.61 tff(7354,plain,
% 2.42/2.61 (~b(z, s(s(s(elem!1))))),
% 2.42/2.61 inference(unit_resolution,[status(thm)],[7353, 166, 376, 463, 7347, 96])).
% 2.42/2.61 tff(7355,plain,
% 2.42/2.61 (r(z, s(s(s(elem!1))))),
% 2.42/2.61 inference(unit_resolution,[status(thm)],[261, 7354])).
% 2.42/2.61 tff(7356,plain,
% 2.42/2.61 (~r(z, s(z))),
% 2.42/2.61 inference(unit_resolution,[status(thm)],[2002, 197, 7345, 1896, 7355])).
% 2.42/2.61 tff(7357,plain,
% 2.42/2.61 (b(z, s(z))),
% 2.42/2.61 inference(unit_resolution,[status(thm)],[321, 7356])).
% 2.42/2.61 tff(7358,plain,
% 2.42/2.61 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), s(s(elem!1)))) | (~r(s(z), z)) | (~r(s(z), s(s(s(elem!1))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), s(s(elem!1)))) | (~r(s(z), z)) | (~r(s(z), s(s(s(elem!1))))))),
% 2.42/2.61 inference(rewrite,[status(thm)],[])).
% 2.42/2.61 tff(7359,plain,
% 2.42/2.61 (((~r(s(s(s(elem!1))), s(s(elem!1)))) | (~r(z, s(s(s(elem!1))))) | (~r(s(z), s(s(s(elem!1))))) | (~r(s(z), z))) <=> ((~r(z, s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), s(s(elem!1)))) | (~r(s(z), z)) | (~r(s(z), s(s(s(elem!1))))))),
% 2.42/2.61 inference(rewrite,[status(thm)],[])).
% 2.42/2.61 tff(7360,plain,
% 2.42/2.61 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), s(s(elem!1)))) | (~r(z, s(s(s(elem!1))))) | (~r(s(z), s(s(s(elem!1))))) | (~r(s(z), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), s(s(elem!1)))) | (~r(s(z), z)) | (~r(s(z), s(s(s(elem!1)))))))),
% 2.42/2.61 inference(monotonicity,[status(thm)],[7359])).
% 2.42/2.61 tff(7361,plain,
% 2.42/2.61 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), s(s(elem!1)))) | (~r(z, s(s(s(elem!1))))) | (~r(s(z), s(s(s(elem!1))))) | (~r(s(z), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), s(s(elem!1)))) | (~r(s(z), z)) | (~r(s(z), s(s(s(elem!1))))))),
% 2.42/2.62 inference(transitivity,[status(thm)],[7360, 7358])).
% 2.42/2.62 tff(7362,plain,
% 2.42/2.62 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), s(s(elem!1)))) | (~r(z, s(s(s(elem!1))))) | (~r(s(z), s(s(s(elem!1))))) | (~r(s(z), z)))),
% 2.42/2.62 inference(quant_inst,[status(thm)],[])).
% 2.42/2.62 tff(7363,plain,
% 2.42/2.62 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), s(s(elem!1)))) | (~r(s(z), z)) | (~r(s(z), s(s(s(elem!1)))))),
% 2.42/2.62 inference(modus_ponens,[status(thm)],[7362, 7361])).
% 2.42/2.62 tff(7364,plain,
% 2.42/2.62 (~r(s(z), z)),
% 2.42/2.62 inference(unit_resolution,[status(thm)],[7363, 197, 7345, 1896, 7355])).
% 2.42/2.62 tff(7365,plain,
% 2.42/2.62 (b(s(z), z)),
% 2.42/2.62 inference(unit_resolution,[status(thm)],[230, 7364])).
% 2.42/2.62 tff(7366,plain,
% 2.42/2.62 ($false),
% 2.42/2.62 inference(unit_resolution,[status(thm)],[3997, 166, 7365, 96, 7357, 121])).
% 2.42/2.62 tff(7367,plain,((~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(s(s(elem!1))), z)) | (~b(s(z), s(s(elem!1)))) | (s(s(s(elem!1))) = s(s(elem!1)))), inference(lemma,lemma(discharge,[]))).
% 2.42/2.62 tff(7368,plain,
% 2.42/2.62 (~b(s(s(elem!1)), s(s(s(elem!1))))),
% 2.42/2.62 inference(unit_resolution,[status(thm)],[7367, 96, 121, 376, 51])).
% 2.42/2.62 tff(7369,plain,
% 2.42/2.62 (r(s(s(elem!1)), s(s(s(elem!1))))),
% 2.42/2.62 inference(unit_resolution,[status(thm)],[461, 7368, 45])).
% 2.42/2.62 tff(7370,plain,
% 2.42/2.62 (~b(s(z), s(s(s(elem!1))))),
% 2.42/2.62 inference(unit_resolution,[status(thm)],[7322, 53, 118, 121, 376])).
% 2.42/2.62 tff(7371,plain,
% 2.42/2.62 (r(s(z), s(s(s(elem!1))))),
% 2.42/2.62 inference(unit_resolution,[status(thm)],[116, 7370])).
% 2.42/2.62 tff(7372,plain,
% 2.42/2.62 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), s(s(elem!1)))) | (~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, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(elem!1))), s(s(elem!1)))) | (~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))))),
% 2.42/2.62 inference(rewrite,[status(thm)],[])).
% 2.42/2.62 tff(7373,plain,
% 2.42/2.62 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), s(s(elem!1)))) | (~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))))),
% 2.42/2.62 inference(quant_inst,[status(thm)],[])).
% 2.42/2.62 tff(7374,plain,
% 2.42/2.62 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(elem!1))), s(s(elem!1)))) | (~r(s(z), s(s(s(elem!1))))) | (~r(s(s(elem!1)), s(s(s(elem!1))))) | (~r(s(s(elem!1)), s(z)))),
% 2.42/2.62 inference(modus_ponens,[status(thm)],[7373, 7372])).
% 2.42/2.62 tff(7375,plain,
% 2.42/2.62 ($false),
% 2.42/2.62 inference(unit_resolution,[status(thm)],[7374, 197, 4577, 377, 905, 119])).
% 2.42/2.62 tff(7376,plain,((~r(s(s(s(elem!1))), s(s(elem!1)))) | (~r(s(s(elem!1)), s(z))) | (~r(s(s(elem!1)), s(s(s(elem!1))))) | (~r(s(z), s(s(s(elem!1)))))), inference(lemma,lemma(discharge,[]))).
% 2.42/2.62 tff(7377,plain,
% 2.42/2.62 (~r(s(s(s(elem!1))), s(s(elem!1)))),
% 2.42/2.62 inference(unit_resolution,[status(thm)],[7376, 7371, 4577, 377])).
% 2.42/2.62 tff(7378,plain,
% 2.42/2.62 (b(s(s(s(elem!1))), s(s(elem!1)))),
% 2.42/2.62 inference(unit_resolution,[status(thm)],[889, 7377, 1863])).
% 2.42/2.62 tff(7379,plain,
% 2.42/2.62 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(z), z)) | (~b(s(z), s(s(elem!1)))) | (~b(s(s(s(elem!1))), z)) | (~b(s(s(s(elem!1))), s(z))) | (~b(z, s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(z), z)) | (~b(s(z), s(s(elem!1)))) | (~b(s(s(s(elem!1))), z)) | (~b(s(s(s(elem!1))), s(z))) | (~b(z, s(z))))),
% 2.42/2.62 inference(rewrite,[status(thm)],[])).
% 2.42/2.62 tff(7380,plain,
% 2.42/2.62 (((~b(s(z), s(s(elem!1)))) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(z, s(z))) | (~b(s(z), z)) | (~b(s(s(s(elem!1))), z)) | (~b(s(s(s(elem!1))), s(z)))) <=> ((~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(z), z)) | (~b(s(z), s(s(elem!1)))) | (~b(s(s(s(elem!1))), z)) | (~b(s(s(s(elem!1))), s(z))) | (~b(z, s(z))))),
% 2.42/2.62 inference(rewrite,[status(thm)],[])).
% 2.42/2.62 tff(7381,plain,
% 2.42/2.62 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(elem!1)))) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(z, s(z))) | (~b(s(z), z)) | (~b(s(s(s(elem!1))), z)) | (~b(s(s(s(elem!1))), s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(z), z)) | (~b(s(z), s(s(elem!1)))) | (~b(s(s(s(elem!1))), z)) | (~b(s(s(s(elem!1))), s(z))) | (~b(z, s(z)))))),
% 2.42/2.62 inference(monotonicity,[status(thm)],[7380])).
% 2.42/2.62 tff(7382,plain,
% 2.42/2.62 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(elem!1)))) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(z, s(z))) | (~b(s(z), z)) | (~b(s(s(s(elem!1))), z)) | (~b(s(s(s(elem!1))), s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(z), z)) | (~b(s(z), s(s(elem!1)))) | (~b(s(s(s(elem!1))), z)) | (~b(s(s(s(elem!1))), s(z))) | (~b(z, s(z))))),
% 2.42/2.62 inference(transitivity,[status(thm)],[7381, 7379])).
% 2.42/2.62 tff(7383,plain,
% 2.42/2.62 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(elem!1)))) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(z, s(z))) | (~b(s(z), z)) | (~b(s(s(s(elem!1))), z)) | (~b(s(s(s(elem!1))), s(z))))),
% 2.42/2.62 inference(quant_inst,[status(thm)],[])).
% 2.42/2.62 tff(7384,plain,
% 2.42/2.62 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(z), z)) | (~b(s(z), s(s(elem!1)))) | (~b(s(s(s(elem!1))), z)) | (~b(s(s(s(elem!1))), s(z))) | (~b(z, s(z)))),
% 2.42/2.62 inference(modus_ponens,[status(thm)],[7383, 7382])).
% 2.42/2.62 tff(7385,plain,
% 2.42/2.62 ($false),
% 2.42/2.62 inference(unit_resolution,[status(thm)],[7384, 166, 376, 7378, 53, 96, 118, 121])).
% 2.42/2.62 tff(7386,plain,((~b(s(z), z)) | (~b(s(z), s(s(elem!1)))) | (~b(s(s(s(elem!1))), s(z))) | (~b(z, s(z))) | (~b(s(s(s(elem!1))), z)) | (s(s(s(elem!1))) = s(s(elem!1))) | (~r(s(s(elem!1)), s(z))) | (~r(s(s(elem!1)), s(s(s(elem!1)))))), inference(lemma,lemma(discharge,[]))).
% 2.42/2.62 tff(7387,plain,
% 2.42/2.62 (~b(s(z), z)),
% 2.42/2.62 inference(unit_resolution,[status(thm)],[7386, 96, 376, 118, 121, 51, 7337, 7369])).
% 2.42/2.62 tff(7388,plain,
% 2.42/2.62 (r(s(z), z)),
% 2.42/2.62 inference(unit_resolution,[status(thm)],[230, 7387])).
% 2.42/2.62 tff(7389,plain,
% 2.42/2.62 (~b(s(z), s(s(z)))),
% 2.42/2.62 inference(unit_resolution,[status(thm)],[6807, 156, 96, 118, 121])).
% 2.42/2.62 tff(7390,plain,
% 2.42/2.62 (~r(s(s(s(z))), z)),
% 2.42/2.62 inference(unit_resolution,[status(thm)],[3528, 3516, 155, 156, 97])).
% 2.42/2.62 tff(7391,plain,
% 2.42/2.62 (b(s(s(s(z))), z)),
% 2.42/2.62 inference(unit_resolution,[status(thm)],[1713, 7390])).
% 2.42/2.62 tff(7392,plain,
% 2.42/2.62 (b(s(s(z)), s(s(elem!1)))),
% 2.42/2.62 inference(unit_resolution,[status(thm)],[390, 3533, 52])).
% 2.42/2.62 tff(7393,plain,
% 2.42/2.62 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(elem!1)))) | (~b(z, s(z))) | (~b(s(s(z)), s(s(elem!1)))) | (~b(s(s(z)), z)) | (~b(s(s(s(z))), z)) | (~b(s(s(z)), s(s(s(z))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), s(s(elem!1)))) | (~b(z, s(z))) | (~b(s(s(z)), s(s(elem!1)))) | (~b(s(s(z)), z)) | (~b(s(s(s(z))), z)) | (~b(s(s(z)), s(s(s(z))))))),
% 2.42/2.62 inference(rewrite,[status(thm)],[])).
% 2.42/2.62 tff(7394,plain,
% 2.42/2.62 (((~b(s(z), s(s(elem!1)))) | (~b(s(s(z)), s(s(elem!1)))) | (~b(z, s(z))) | (~b(s(s(s(z))), z)) | (~b(s(s(z)), z)) | (~b(s(s(z)), s(s(s(z)))))) <=> ((~b(s(z), s(s(elem!1)))) | (~b(z, s(z))) | (~b(s(s(z)), s(s(elem!1)))) | (~b(s(s(z)), z)) | (~b(s(s(s(z))), z)) | (~b(s(s(z)), s(s(s(z))))))),
% 2.42/2.62 inference(rewrite,[status(thm)],[])).
% 2.42/2.62 tff(7395,plain,
% 2.42/2.62 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(elem!1)))) | (~b(s(s(z)), s(s(elem!1)))) | (~b(z, s(z))) | (~b(s(s(s(z))), z)) | (~b(s(s(z)), z)) | (~b(s(s(z)), s(s(s(z))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(elem!1)))) | (~b(z, s(z))) | (~b(s(s(z)), s(s(elem!1)))) | (~b(s(s(z)), z)) | (~b(s(s(s(z))), z)) | (~b(s(s(z)), s(s(s(z)))))))),
% 2.42/2.62 inference(monotonicity,[status(thm)],[7394])).
% 2.42/2.62 tff(7396,plain,
% 2.42/2.62 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(elem!1)))) | (~b(s(s(z)), s(s(elem!1)))) | (~b(z, s(z))) | (~b(s(s(s(z))), z)) | (~b(s(s(z)), z)) | (~b(s(s(z)), s(s(s(z))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), s(s(elem!1)))) | (~b(z, s(z))) | (~b(s(s(z)), s(s(elem!1)))) | (~b(s(s(z)), z)) | (~b(s(s(s(z))), z)) | (~b(s(s(z)), s(s(s(z))))))),
% 2.42/2.62 inference(transitivity,[status(thm)],[7395, 7393])).
% 2.42/2.62 tff(7397,plain,
% 2.42/2.62 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(elem!1)))) | (~b(s(s(z)), s(s(elem!1)))) | (~b(z, s(z))) | (~b(s(s(s(z))), z)) | (~b(s(s(z)), z)) | (~b(s(s(z)), s(s(s(z))))))),
% 2.42/2.62 inference(quant_inst,[status(thm)],[])).
% 2.42/2.62 tff(7398,plain,
% 2.42/2.62 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), s(s(elem!1)))) | (~b(z, s(z))) | (~b(s(s(z)), s(s(elem!1)))) | (~b(s(s(z)), z)) | (~b(s(s(s(z))), z)) | (~b(s(s(z)), s(s(s(z)))))),
% 2.42/2.62 inference(modus_ponens,[status(thm)],[7397, 7396])).
% 2.42/2.62 tff(7399,plain,
% 2.42/2.62 ($false),
% 2.42/2.62 inference(unit_resolution,[status(thm)],[7398, 166, 376, 118, 7392, 3635, 3516, 7391])).
% 2.42/2.62 tff(7400,plain,((~r(s(z), z)) | (~b(s(z), s(s(elem!1)))) | (~b(z, s(z))) | (~r(z, s(s(z)))) | (~b(s(s(z)), s(z))) | (s(s(z)) = s(s(elem!1))) | (~r(s(z), s(s(z))))), inference(lemma,lemma(discharge,[]))).
% 2.42/2.62 tff(7401,plain,
% 2.42/2.62 (~r(s(z), s(s(z)))),
% 2.42/2.62 inference(unit_resolution,[status(thm)],[7400, 156, 118, 155, 376, 52, 97])).
% 2.42/2.62 tff(7402,plain,
% 2.42/2.62 ($false),
% 2.42/2.62 inference(unit_resolution,[status(thm)],[427, 7401, 7389])).
% 2.42/2.62 tff(7403,plain,((~b(s(s(z)), s(z))) | (~b(z, s(z))) | (~r(z, s(s(z)))) | (~b(s(z), s(s(elem!1)))) | (s(s(z)) = s(s(elem!1))) | (~r(s(z), z)) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(s(s(elem!1))), z))), inference(lemma,lemma(discharge,[]))).
% 2.42/2.62 tff(7404,plain,
% 2.42/2.62 (~b(s(s(z)), s(z))),
% 2.42/2.62 inference(unit_resolution,[status(thm)],[7403, 7388, 155, 376, 52, 118, 96, 121])).
% 2.42/2.62 tff(7405,plain,
% 2.42/2.62 (r(s(s(z)), s(z))),
% 2.42/2.62 inference(unit_resolution,[status(thm)],[308, 7404])).
% 2.42/2.62 tff(7406,plain,
% 2.42/2.62 (~r(s(s(elem!1)), s(s(z)))),
% 2.42/2.62 inference(unit_resolution,[status(thm)],[5331, 7405, 7388, 7337])).
% 2.42/2.62 tff(7407,plain,
% 2.42/2.62 (~r(s(s(z)), s(s(elem!1)))),
% 2.42/2.62 inference(unit_resolution,[status(thm)],[6771, 7405, 7337, 7388])).
% 2.42/2.62 tff(7408,plain,
% 2.42/2.62 (~b(s(z), s(s(z)))),
% 2.42/2.62 inference(unit_resolution,[status(thm)],[5300, 7407, 376, 52, 7406])).
% 2.42/2.62 tff(7409,plain,
% 2.42/2.62 (r(s(z), s(s(z)))),
% 2.42/2.62 inference(unit_resolution,[status(thm)],[427, 7408])).
% 2.42/2.62 tff(7410,plain,
% 2.42/2.62 ($false),
% 2.42/2.62 inference(unit_resolution,[status(thm)],[3947, 197, 7409, 155, 7388, 7405])).
% 2.42/2.62 tff(7411,plain,((~b(s(s(s(elem!1))), s(z))) | (~r(z, s(s(z)))) | (~b(s(z), s(s(elem!1)))) | (s(s(z)) = s(s(elem!1))) | (~b(z, s(z))) | (~b(s(s(s(elem!1))), z)) | (s(s(elem!1)) = s(s(s(elem!1))))), inference(lemma,lemma(discharge,[]))).
% 2.42/2.62 tff(7412,plain,
% 2.42/2.62 (~b(s(s(s(elem!1))), s(z))),
% 2.42/2.62 inference(unit_resolution,[status(thm)],[7411, 52, 376, 155, 118, 121, 45])).
% 2.42/2.62 tff(7413,plain,
% 2.42/2.62 (r(s(s(s(elem!1))), s(z))),
% 2.42/2.62 inference(unit_resolution,[status(thm)],[1849, 7412])).
% 2.42/2.62 tff(7414,plain,
% 2.42/2.62 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), s(z))) | (~r(s(z), z)) | (~r(s(s(elem!1)), s(s(s(elem!1))))) | (~r(s(s(elem!1)), s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(elem!1))), s(z))) | (~r(s(z), z)) | (~r(s(s(elem!1)), s(s(s(elem!1))))) | (~r(s(s(elem!1)), s(z))))),
% 2.42/2.62 inference(rewrite,[status(thm)],[])).
% 2.42/2.62 tff(7415,plain,
% 2.42/2.62 (((~r(s(z), z)) | (~r(s(s(s(elem!1))), s(z))) | (~r(s(s(elem!1)), s(z))) | (~r(s(s(elem!1)), s(s(s(elem!1)))))) <=> ((~r(s(s(s(elem!1))), s(z))) | (~r(s(z), z)) | (~r(s(s(elem!1)), s(s(s(elem!1))))) | (~r(s(s(elem!1)), s(z))))),
% 2.42/2.62 inference(rewrite,[status(thm)],[])).
% 2.42/2.62 tff(7416,plain,
% 2.42/2.62 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), z)) | (~r(s(s(s(elem!1))), s(z))) | (~r(s(s(elem!1)), s(z))) | (~r(s(s(elem!1)), s(s(s(elem!1))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), s(z))) | (~r(s(z), z)) | (~r(s(s(elem!1)), s(s(s(elem!1))))) | (~r(s(s(elem!1)), s(z)))))),
% 2.42/2.62 inference(monotonicity,[status(thm)],[7415])).
% 2.42/2.62 tff(7417,plain,
% 2.42/2.62 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), z)) | (~r(s(s(s(elem!1))), s(z))) | (~r(s(s(elem!1)), s(z))) | (~r(s(s(elem!1)), s(s(s(elem!1))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(elem!1))), s(z))) | (~r(s(z), z)) | (~r(s(s(elem!1)), s(s(s(elem!1))))) | (~r(s(s(elem!1)), s(z))))),
% 2.42/2.62 inference(transitivity,[status(thm)],[7416, 7414])).
% 2.42/2.62 tff(7418,plain,
% 2.42/2.62 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), z)) | (~r(s(s(s(elem!1))), s(z))) | (~r(s(s(elem!1)), s(z))) | (~r(s(s(elem!1)), s(s(s(elem!1))))))),
% 2.42/2.62 inference(quant_inst,[status(thm)],[])).
% 2.42/2.62 tff(7419,plain,
% 2.42/2.62 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(elem!1))), s(z))) | (~r(s(z), z)) | (~r(s(s(elem!1)), s(s(s(elem!1))))) | (~r(s(s(elem!1)), s(z)))),
% 2.42/2.62 inference(modus_ponens,[status(thm)],[7418, 7417])).
% 2.42/2.62 tff(7420,plain,
% 2.42/2.62 (~r(s(s(elem!1)), s(s(s(elem!1))))),
% 2.42/2.62 inference(unit_resolution,[status(thm)],[7419, 197, 350, 4577, 97])).
% 2.42/2.62 tff(7421,plain,
% 2.42/2.62 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), z)) | (~r(s(s(elem!1)), s(z))) | (~r(s(s(s(elem!1))), s(z))) | (~r(s(s(s(elem!1))), s(s(elem!1)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(z), z)) | (~r(s(s(elem!1)), s(z))) | (~r(s(s(s(elem!1))), s(z))) | (~r(s(s(s(elem!1))), s(s(elem!1)))))),
% 2.42/2.62 inference(rewrite,[status(thm)],[])).
% 2.42/2.62 tff(7422,plain,
% 2.42/2.62 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), z)) | (~r(s(s(elem!1)), s(z))) | (~r(s(s(s(elem!1))), s(z))) | (~r(s(s(s(elem!1))), s(s(elem!1)))))),
% 2.42/2.62 inference(quant_inst,[status(thm)],[])).
% 2.42/2.62 tff(7423,plain,
% 2.42/2.62 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(z), z)) | (~r(s(s(elem!1)), s(z))) | (~r(s(s(s(elem!1))), s(z))) | (~r(s(s(s(elem!1))), s(s(elem!1))))),
% 2.42/2.62 inference(modus_ponens,[status(thm)],[7422, 7421])).
% 2.42/2.62 tff(7424,plain,
% 2.42/2.62 (~r(s(s(s(elem!1))), s(s(elem!1)))),
% 2.42/2.62 inference(unit_resolution,[status(thm)],[7423, 197, 350, 4577, 97])).
% 2.42/2.62 tff(7425,plain,
% 2.42/2.62 (~b(s(z), s(s(s(elem!1))))),
% 2.42/2.62 inference(unit_resolution,[status(thm)],[6040, 7424, 1863, 376, 7420])).
% 2.42/2.62 tff(7426,plain,
% 2.42/2.62 (~(s(s(elem!1)) = s(s(s(elem!1))))),
% 2.42/2.62 inference(unit_resolution,[status(thm)],[5500, 376, 98])).
% 2.42/2.62 tff(7427,plain,
% 2.42/2.62 (~(s(s(s(elem!1))) = s(s(elem!1)))),
% 2.42/2.62 inference(unit_resolution,[status(thm)],[50, 7426])).
% 2.42/2.62 tff(7428,plain,
% 2.42/2.62 (b(s(s(s(elem!1))), s(s(elem!1)))),
% 2.42/2.62 inference(unit_resolution,[status(thm)],[889, 7427, 1823])).
% 2.42/2.62 tff(7429,plain,
% 2.42/2.62 (b(s(s(elem!1)), s(s(s(elem!1))))),
% 2.42/2.62 inference(unit_resolution,[status(thm)],[461, 7426, 1821])).
% 2.42/2.62 tff(7430,plain,
% 2.42/2.62 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(z, s(s(s(elem!1))))) | (~b(s(s(elem!1)), z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(z, s(s(s(elem!1))))) | (~b(s(s(elem!1)), z)))),
% 2.42/2.62 inference(rewrite,[status(thm)],[])).
% 2.42/2.62 tff(7431,plain,
% 2.42/2.62 (((~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(z, s(s(s(elem!1))))) | (~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(s(s(elem!1)), z))) <=> ((~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(z, s(s(s(elem!1))))) | (~b(s(s(elem!1)), z)))),
% 2.42/2.62 inference(rewrite,[status(thm)],[])).
% 2.42/2.62 tff(7432,plain,
% 2.42/2.62 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(z, s(s(s(elem!1))))) | (~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(s(s(elem!1)), z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(z, s(s(s(elem!1))))) | (~b(s(s(elem!1)), z))))),
% 2.42/2.62 inference(monotonicity,[status(thm)],[7431])).
% 2.42/2.62 tff(7433,plain,
% 2.42/2.62 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(z, s(s(s(elem!1))))) | (~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(s(s(elem!1)), z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(z, s(s(s(elem!1))))) | (~b(s(s(elem!1)), z)))),
% 2.42/2.62 inference(transitivity,[status(thm)],[7432, 7430])).
% 2.42/2.62 tff(7434,plain,
% 2.42/2.62 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(z, s(s(s(elem!1))))) | (~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(s(s(elem!1)), z)))),
% 2.42/2.62 inference(quant_inst,[status(thm)],[])).
% 2.42/2.62 tff(7435,plain,
% 2.42/2.62 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(z, s(s(s(elem!1))))) | (~b(s(s(elem!1)), z))),
% 2.42/2.62 inference(modus_ponens,[status(thm)],[7434, 7433])).
% 2.42/2.62 tff(7436,plain,
% 2.42/2.62 (~b(s(s(elem!1)), z)),
% 2.42/2.62 inference(unit_resolution,[status(thm)],[7435, 166, 7429, 7428, 240])).
% 2.42/2.62 tff(7437,plain,
% 2.42/2.62 (r(s(s(elem!1)), z)),
% 2.42/2.62 inference(unit_resolution,[status(thm)],[608, 7436])).
% 2.42/2.62 tff(7438,plain,
% 2.42/2.62 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(z, s(s(z)))) | (~b(z, s(s(s(elem!1))))) | (~b(s(z), s(s(elem!1)))) | (~b(z, s(z))) | (~b(s(s(z)), s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(z, s(s(z)))) | (~b(z, s(s(s(elem!1))))) | (~b(s(z), s(s(elem!1)))) | (~b(z, s(z))) | (~b(s(s(z)), s(z))))),
% 2.42/2.63 inference(rewrite,[status(thm)],[])).
% 2.42/2.63 tff(7439,plain,
% 2.42/2.63 (((~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(z, s(s(s(elem!1))))) | (~b(s(z), s(s(elem!1)))) | (~b(s(s(z)), s(z))) | (~b(z, s(z))) | (~b(z, s(s(z))))) <=> ((~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(z, s(s(z)))) | (~b(z, s(s(s(elem!1))))) | (~b(s(z), s(s(elem!1)))) | (~b(z, s(z))) | (~b(s(s(z)), s(z))))),
% 2.42/2.63 inference(rewrite,[status(thm)],[])).
% 2.42/2.63 tff(7440,plain,
% 2.42/2.63 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(z, s(s(s(elem!1))))) | (~b(s(z), s(s(elem!1)))) | (~b(s(s(z)), s(z))) | (~b(z, s(z))) | (~b(z, s(s(z)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(z, s(s(z)))) | (~b(z, s(s(s(elem!1))))) | (~b(s(z), s(s(elem!1)))) | (~b(z, s(z))) | (~b(s(s(z)), s(z)))))),
% 2.42/2.63 inference(monotonicity,[status(thm)],[7439])).
% 2.42/2.63 tff(7441,plain,
% 2.42/2.63 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(z, s(s(s(elem!1))))) | (~b(s(z), s(s(elem!1)))) | (~b(s(s(z)), s(z))) | (~b(z, s(z))) | (~b(z, s(s(z)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(z, s(s(z)))) | (~b(z, s(s(s(elem!1))))) | (~b(s(z), s(s(elem!1)))) | (~b(z, s(z))) | (~b(s(s(z)), s(z))))),
% 2.42/2.63 inference(transitivity,[status(thm)],[7440, 7438])).
% 2.42/2.63 tff(7442,plain,
% 2.42/2.63 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(z, s(s(s(elem!1))))) | (~b(s(z), s(s(elem!1)))) | (~b(s(s(z)), s(z))) | (~b(z, s(z))) | (~b(z, s(s(z)))))),
% 2.42/2.63 inference(quant_inst,[status(thm)],[])).
% 2.42/2.63 tff(7443,plain,
% 2.42/2.63 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(z, s(s(z)))) | (~b(z, s(s(s(elem!1))))) | (~b(s(z), s(s(elem!1)))) | (~b(z, s(z))) | (~b(s(s(z)), s(z)))),
% 2.42/2.63 inference(modus_ponens,[status(thm)],[7442, 7441])).
% 2.42/2.63 tff(7444,plain,
% 2.42/2.63 (~b(z, s(s(z)))),
% 2.42/2.63 inference(unit_resolution,[status(thm)],[7443, 166, 376, 7429, 240, 118, 156])).
% 2.42/2.63 tff(7445,plain,
% 2.42/2.63 (r(z, s(s(z)))),
% 2.42/2.63 inference(unit_resolution,[status(thm)],[151, 7444])).
% 2.42/2.63 tff(7446,plain,
% 2.42/2.63 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(elem!1)), z)) | (~r(s(z), z)) | (~r(s(s(elem!1)), s(z))) | (~r(z, s(s(z)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(elem!1)), z)) | (~r(s(z), z)) | (~r(s(s(elem!1)), s(z))) | (~r(z, s(s(z)))))),
% 2.42/2.63 inference(rewrite,[status(thm)],[])).
% 2.42/2.63 tff(7447,plain,
% 2.42/2.63 (((~r(z, s(s(z)))) | (~r(s(z), z)) | (~r(s(s(elem!1)), z)) | (~r(s(s(elem!1)), s(z)))) <=> ((~r(s(s(elem!1)), z)) | (~r(s(z), z)) | (~r(s(s(elem!1)), s(z))) | (~r(z, s(s(z)))))),
% 2.42/2.63 inference(rewrite,[status(thm)],[])).
% 2.42/2.63 tff(7448,plain,
% 2.42/2.63 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(z)))) | (~r(s(z), z)) | (~r(s(s(elem!1)), z)) | (~r(s(s(elem!1)), s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(elem!1)), z)) | (~r(s(z), z)) | (~r(s(s(elem!1)), s(z))) | (~r(z, s(s(z))))))),
% 2.42/2.63 inference(monotonicity,[status(thm)],[7447])).
% 2.42/2.63 tff(7449,plain,
% 2.42/2.63 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(z)))) | (~r(s(z), z)) | (~r(s(s(elem!1)), z)) | (~r(s(s(elem!1)), s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(elem!1)), z)) | (~r(s(z), z)) | (~r(s(s(elem!1)), s(z))) | (~r(z, s(s(z)))))),
% 2.42/2.63 inference(transitivity,[status(thm)],[7448, 7446])).
% 2.42/2.63 tff(7450,plain,
% 2.42/2.63 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(z)))) | (~r(s(z), z)) | (~r(s(s(elem!1)), z)) | (~r(s(s(elem!1)), s(z))))),
% 2.42/2.63 inference(quant_inst,[status(thm)],[])).
% 2.42/2.63 tff(7451,plain,
% 2.42/2.63 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(elem!1)), z)) | (~r(s(z), z)) | (~r(s(s(elem!1)), s(z))) | (~r(z, s(s(z))))),
% 2.42/2.63 inference(modus_ponens,[status(thm)],[7450, 7449])).
% 2.42/2.63 tff(7452,plain,
% 2.42/2.63 ($false),
% 2.42/2.63 inference(unit_resolution,[status(thm)],[7451, 197, 7445, 4577, 97, 7437])).
% 2.42/2.63 tff(7453,plain,((~b(s(z), s(s(elem!1)))) | (~r(s(s(elem!1)), s(z))) | (~r(s(z), z)) | (~b(z, s(s(s(elem!1))))) | (~b(z, s(z))) | (~b(s(s(z)), s(z))) | r(s(s(s(elem!1))), s(s(elem!1))) | r(s(s(elem!1)), s(s(s(elem!1)))) | b(s(z), s(s(s(elem!1))))), inference(lemma,lemma(discharge,[]))).
% 2.42/2.63 tff(7454,plain,
% 2.42/2.63 (~b(z, s(s(s(elem!1))))),
% 2.42/2.63 inference(unit_resolution,[status(thm)],[7453, 7425, 376, 97, 156, 7424, 7420, 4577, 118])).
% 2.42/2.63 tff(7455,plain,
% 2.42/2.63 (r(s(z), s(s(s(elem!1))))),
% 2.42/2.63 inference(unit_resolution,[status(thm)],[116, 7425])).
% 2.42/2.63 tff(7456,plain,
% 2.42/2.63 (~r(z, s(s(s(elem!1))))),
% 2.42/2.63 inference(unit_resolution,[status(thm)],[3872, 7455, 350, 97])).
% 2.42/2.63 tff(7457,plain,
% 2.42/2.63 ($false),
% 2.42/2.63 inference(unit_resolution,[status(thm)],[261, 7456, 7454])).
% 2.42/2.63 tff(7458,plain,((~r(s(z), z)) | (~r(s(s(s(elem!1))), s(z))) | (~b(s(z), s(s(elem!1)))) | (~b(s(s(z)), s(z))) | (~r(s(s(elem!1)), s(z))) | (~b(z, s(z))) | (s(s(s(elem!1))) = s(s(elem!1)))), inference(lemma,lemma(discharge,[]))).
% 2.42/2.63 tff(7459,plain,
% 2.42/2.63 (~r(s(z), z)),
% 2.42/2.63 inference(unit_resolution,[status(thm)],[7458, 156, 376, 7413, 7337, 118, 51])).
% 2.42/2.63 tff(7460,plain,
% 2.42/2.63 (b(s(z), z)),
% 2.42/2.63 inference(unit_resolution,[status(thm)],[230, 7459])).
% 2.42/2.63 tff(7461,plain,
% 2.42/2.63 (~b(s(z), s(s(s(elem!1))))),
% 2.42/2.63 inference(unit_resolution,[status(thm)],[7322, 7460, 118, 121, 376])).
% 2.42/2.63 tff(7462,plain,
% 2.42/2.63 (r(s(z), s(s(s(elem!1))))),
% 2.42/2.63 inference(unit_resolution,[status(thm)],[116, 7461])).
% 2.42/2.63 tff(7463,plain,
% 2.42/2.63 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), s(s(elem!1)))) | (~r(s(s(s(elem!1))), s(z))) | (~r(s(z), s(s(s(elem!1))))) | (~r(s(s(elem!1)), s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(elem!1))), s(s(elem!1)))) | (~r(s(s(s(elem!1))), s(z))) | (~r(s(z), s(s(s(elem!1))))) | (~r(s(s(elem!1)), s(z))))),
% 2.42/2.63 inference(rewrite,[status(thm)],[])).
% 2.42/2.63 tff(7464,plain,
% 2.42/2.63 (((~r(s(z), s(s(s(elem!1))))) | (~r(s(s(elem!1)), s(z))) | (~r(s(s(s(elem!1))), s(z))) | (~r(s(s(s(elem!1))), s(s(elem!1))))) <=> ((~r(s(s(s(elem!1))), s(s(elem!1)))) | (~r(s(s(s(elem!1))), s(z))) | (~r(s(z), s(s(s(elem!1))))) | (~r(s(s(elem!1)), s(z))))),
% 2.42/2.63 inference(rewrite,[status(thm)],[])).
% 2.42/2.63 tff(7465,plain,
% 2.42/2.63 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(s(s(elem!1))))) | (~r(s(s(elem!1)), s(z))) | (~r(s(s(s(elem!1))), s(z))) | (~r(s(s(s(elem!1))), s(s(elem!1)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), s(s(elem!1)))) | (~r(s(s(s(elem!1))), s(z))) | (~r(s(z), s(s(s(elem!1))))) | (~r(s(s(elem!1)), s(z)))))),
% 2.42/2.63 inference(monotonicity,[status(thm)],[7464])).
% 2.42/2.63 tff(7466,plain,
% 2.42/2.63 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(s(s(elem!1))))) | (~r(s(s(elem!1)), s(z))) | (~r(s(s(s(elem!1))), s(z))) | (~r(s(s(s(elem!1))), s(s(elem!1)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(elem!1))), s(s(elem!1)))) | (~r(s(s(s(elem!1))), s(z))) | (~r(s(z), s(s(s(elem!1))))) | (~r(s(s(elem!1)), s(z))))),
% 2.42/2.63 inference(transitivity,[status(thm)],[7465, 7463])).
% 2.42/2.63 tff(7467,plain,
% 2.42/2.63 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(s(s(elem!1))))) | (~r(s(s(elem!1)), s(z))) | (~r(s(s(s(elem!1))), s(z))) | (~r(s(s(s(elem!1))), s(s(elem!1)))))),
% 2.42/2.63 inference(quant_inst,[status(thm)],[])).
% 2.42/2.63 tff(7468,plain,
% 2.42/2.63 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(elem!1))), s(s(elem!1)))) | (~r(s(s(s(elem!1))), s(z))) | (~r(s(z), s(s(s(elem!1))))) | (~r(s(s(elem!1)), s(z)))),
% 2.42/2.63 inference(modus_ponens,[status(thm)],[7467, 7466])).
% 2.42/2.63 tff(7469,plain,
% 2.42/2.63 (~r(s(s(s(elem!1))), s(s(elem!1)))),
% 2.42/2.63 inference(unit_resolution,[status(thm)],[7468, 197, 7413, 7337, 7462])).
% 2.42/2.63 tff(7470,plain,
% 2.42/2.63 (b(s(s(s(elem!1))), s(s(elem!1)))),
% 2.42/2.63 inference(unit_resolution,[status(thm)],[889, 7469, 51])).
% 2.42/2.63 tff(7471,plain,
% 2.42/2.63 (~b(s(s(z)), z)),
% 2.42/2.63 inference(unit_resolution,[status(thm)],[181, 7460, 118, 156])).
% 2.42/2.63 tff(7472,plain,
% 2.42/2.63 (r(s(s(z)), z)),
% 2.42/2.63 inference(unit_resolution,[status(thm)],[186, 7471])).
% 2.42/2.63 tff(7473,plain,
% 2.42/2.63 (~r(s(s(s(elem!1))), s(s(elem!1)))),
% 2.42/2.63 inference(unit_resolution,[status(thm)],[7468, 197, 7413, 7337, 7371])).
% 2.42/2.63 tff(7474,plain,
% 2.42/2.63 (b(s(s(s(elem!1))), s(s(elem!1)))),
% 2.42/2.63 inference(unit_resolution,[status(thm)],[889, 7473, 51])).
% 2.42/2.63 tff(7475,plain,
% 2.42/2.63 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), s(z))) | (~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, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(elem!1))), s(z))) | (~r(s(z), s(s(s(elem!1))))) | (~r(s(s(elem!1)), s(s(s(elem!1))))) | (~r(s(s(elem!1)), s(z))))),
% 2.42/2.63 inference(rewrite,[status(thm)],[])).
% 2.42/2.63 tff(7476,plain,
% 2.42/2.63 (((~r(s(z), s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), s(z))) | (~r(s(s(elem!1)), s(z))) | (~r(s(s(elem!1)), s(s(s(elem!1)))))) <=> ((~r(s(s(s(elem!1))), s(z))) | (~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))))),
% 2.42/2.63 inference(rewrite,[status(thm)],[])).
% 2.42/2.63 tff(7477,plain,
% 2.42/2.63 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), s(z))) | (~r(s(s(elem!1)), s(z))) | (~r(s(s(elem!1)), s(s(s(elem!1))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), s(z))) | (~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)))))),
% 2.42/2.63 inference(monotonicity,[status(thm)],[7476])).
% 2.42/2.63 tff(7478,plain,
% 2.42/2.63 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), s(z))) | (~r(s(s(elem!1)), s(z))) | (~r(s(s(elem!1)), s(s(s(elem!1))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(elem!1))), s(z))) | (~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))))),
% 2.42/2.63 inference(transitivity,[status(thm)],[7477, 7475])).
% 2.42/2.63 tff(7479,plain,
% 2.42/2.63 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), s(z))) | (~r(s(s(elem!1)), s(z))) | (~r(s(s(elem!1)), s(s(s(elem!1))))))),
% 2.42/2.63 inference(quant_inst,[status(thm)],[])).
% 2.42/2.63 tff(7480,plain,
% 2.42/2.63 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(elem!1))), s(z))) | (~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)))),
% 2.42/2.63 inference(modus_ponens,[status(thm)],[7479, 7478])).
% 2.42/2.63 tff(7481,plain,
% 2.42/2.63 (~r(s(s(elem!1)), s(s(s(elem!1))))),
% 2.42/2.63 inference(unit_resolution,[status(thm)],[7480, 197, 7413, 7337, 7371])).
% 2.42/2.63 tff(7482,plain,
% 2.42/2.63 (b(s(s(elem!1)), s(s(s(elem!1))))),
% 2.42/2.63 inference(unit_resolution,[status(thm)],[461, 7481, 45])).
% 2.42/2.63 tff(7483,plain,
% 2.42/2.63 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(z), s(s(elem!1)))) | (~b(s(z), s(s(z)))) | (~b(s(s(z)), s(s(elem!1)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(z), s(s(elem!1)))) | (~b(s(z), s(s(z)))) | (~b(s(s(z)), s(s(elem!1)))))),
% 2.42/2.63 inference(rewrite,[status(thm)],[])).
% 2.42/2.63 tff(7484,plain,
% 2.42/2.63 (((~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(z), s(s(elem!1)))) | (~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(s(s(z)), s(s(elem!1)))) | (~b(s(z), s(s(elem!1)))) | (~b(s(z), s(s(z))))) <=> ((~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(z), s(s(elem!1)))) | (~b(s(z), s(s(z)))) | (~b(s(s(z)), s(s(elem!1)))))),
% 2.42/2.63 inference(rewrite,[status(thm)],[])).
% 2.42/2.63 tff(7485,plain,
% 2.42/2.63 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(z), s(s(elem!1)))) | (~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(s(s(z)), s(s(elem!1)))) | (~b(s(z), s(s(elem!1)))) | (~b(s(z), s(s(z)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(z), s(s(elem!1)))) | (~b(s(z), s(s(z)))) | (~b(s(s(z)), s(s(elem!1))))))),
% 2.42/2.63 inference(monotonicity,[status(thm)],[7484])).
% 2.42/2.63 tff(7486,plain,
% 2.42/2.63 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(z), s(s(elem!1)))) | (~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(s(s(z)), s(s(elem!1)))) | (~b(s(z), s(s(elem!1)))) | (~b(s(z), s(s(z)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(z), s(s(elem!1)))) | (~b(s(z), s(s(z)))) | (~b(s(s(z)), s(s(elem!1)))))),
% 2.42/2.63 inference(transitivity,[status(thm)],[7485, 7483])).
% 2.42/2.63 tff(7487,plain,
% 2.42/2.63 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(z), s(s(elem!1)))) | (~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(s(s(z)), s(s(elem!1)))) | (~b(s(z), s(s(elem!1)))) | (~b(s(z), s(s(z)))))),
% 2.42/2.63 inference(quant_inst,[status(thm)],[])).
% 2.42/2.63 tff(7488,plain,
% 2.42/2.63 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(z), s(s(elem!1)))) | (~b(s(z), s(s(z)))) | (~b(s(s(z)), s(s(elem!1))))),
% 2.42/2.63 inference(modus_ponens,[status(thm)],[7487, 7486])).
% 2.42/2.63 tff(7489,plain,
% 2.42/2.63 ($false),
% 2.42/2.63 inference(unit_resolution,[status(thm)],[7488, 166, 376, 463, 839, 556, 446])).
% 2.42/2.63 tff(7490,plain,((~b(s(s(z)), s(s(elem!1)))) | (~b(s(z), s(s(elem!1)))) | (~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(z), s(s(z))))), inference(lemma,lemma(discharge,[]))).
% 2.42/2.63 tff(7491,plain,
% 2.42/2.63 (~b(s(s(z)), s(s(elem!1)))),
% 2.42/2.63 inference(unit_resolution,[status(thm)],[7490, 7482, 376, 7474, 556])).
% 2.42/2.63 tff(7492,plain,
% 2.42/2.63 (r(s(s(z)), s(s(elem!1)))),
% 2.42/2.63 inference(unit_resolution,[status(thm)],[390, 7491, 52])).
% 2.42/2.63 tff(7493,plain,
% 2.42/2.63 (~r(z, s(s(elem!1)))),
% 2.42/2.63 inference(unit_resolution,[status(thm)],[5997, 7492, 155, 7337])).
% 2.42/2.63 tff(7494,plain,
% 2.42/2.63 (b(z, s(s(elem!1)))),
% 2.42/2.63 inference(unit_resolution,[status(thm)],[1795, 7493])).
% 2.42/2.63 tff(7495,plain,
% 2.42/2.63 (~b(s(s(elem!1)), z)),
% 2.42/2.63 inference(unit_resolution,[status(thm)],[5377, 7494, 376, 53])).
% 2.42/2.63 tff(7496,plain,
% 2.42/2.63 (r(s(s(elem!1)), z)),
% 2.42/2.63 inference(unit_resolution,[status(thm)],[608, 7495])).
% 2.42/2.63 tff(7497,plain,
% 2.42/2.63 (~b(s(s(elem!1)), s(s(z)))),
% 2.42/2.63 inference(unit_resolution,[status(thm)],[6009, 7494, 376, 118, 156])).
% 2.42/2.63 tff(7498,plain,
% 2.42/2.63 (r(s(s(elem!1)), s(s(z)))),
% 2.42/2.63 inference(unit_resolution,[status(thm)],[441, 7497, 132])).
% 2.42/2.63 tff(7499,plain,
% 2.42/2.63 ($false),
% 2.42/2.63 inference(unit_resolution,[status(thm)],[2740, 197, 7498, 155, 7492, 7496])).
% 2.42/2.63 tff(7500,plain,((~b(s(z), z)) | (~r(z, s(s(z)))) | (~b(s(z), s(s(elem!1)))) | (~b(z, s(z))) | (~b(s(s(z)), s(z))) | (s(s(z)) = s(s(elem!1))) | (~b(s(z), s(s(z)))) | (s(s(elem!1)) = s(s(s(elem!1)))) | (~b(s(s(s(elem!1))), z))), inference(lemma,lemma(discharge,[]))).
% 2.42/2.63 tff(7501,plain,
% 2.42/2.63 (~b(s(z), s(s(z)))),
% 2.42/2.63 inference(unit_resolution,[status(thm)],[7500, 7460, 376, 118, 156, 52, 155, 45, 121])).
% 2.42/2.63 tff(7502,plain,
% 2.42/2.63 (r(s(z), s(s(z)))),
% 2.42/2.63 inference(unit_resolution,[status(thm)],[427, 7501])).
% 2.42/2.63 tff(7503,plain,
% 2.42/2.63 (~r(s(s(s(elem!1))), s(s(z)))),
% 2.42/2.63 inference(unit_resolution,[status(thm)],[874, 7502, 7413, 7472])).
% 2.42/2.63 tff(7504,plain,
% 2.42/2.63 (b(s(s(s(elem!1))), s(s(z)))),
% 2.42/2.63 inference(unit_resolution,[status(thm)],[218, 7503])).
% 2.42/2.63 tff(7505,plain,
% 2.42/2.63 (~r(s(s(elem!1)), s(s(s(elem!1))))),
% 2.42/2.63 inference(unit_resolution,[status(thm)],[7480, 197, 7413, 7337, 7462])).
% 2.42/2.63 tff(7506,plain,
% 2.42/2.63 (b(s(s(elem!1)), s(s(s(elem!1))))),
% 2.42/2.63 inference(unit_resolution,[status(thm)],[461, 7505, 45])).
% 2.42/2.63 tff(7507,plain,
% 2.42/2.63 (~b(s(s(z)), s(s(elem!1)))),
% 2.42/2.63 inference(unit_resolution,[status(thm)],[2068, 7506, 7504, 7470])).
% 2.42/2.63 tff(7508,plain,
% 2.42/2.63 (r(s(s(z)), s(s(elem!1)))),
% 2.42/2.63 inference(unit_resolution,[status(thm)],[390, 7507, 52])).
% 2.42/2.63 tff(7509,plain,
% 2.42/2.63 (~r(z, s(s(elem!1)))),
% 2.42/2.63 inference(unit_resolution,[status(thm)],[5997, 7508, 155, 7337])).
% 2.42/2.63 tff(7510,plain,
% 2.42/2.63 (b(z, s(s(elem!1)))),
% 2.42/2.63 inference(unit_resolution,[status(thm)],[1795, 7509])).
% 2.42/2.63 tff(7511,plain,
% 2.42/2.63 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(z)), s(s(elem!1)))) | (~r(s(s(elem!1)), s(z))) | (~r(s(z), s(s(z)))) | (~r(s(s(elem!1)), s(s(z)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(z)), s(s(elem!1)))) | (~r(s(s(elem!1)), s(z))) | (~r(s(z), s(s(z)))) | (~r(s(s(elem!1)), s(s(z)))))),
% 2.42/2.63 inference(rewrite,[status(thm)],[])).
% 2.42/2.63 tff(7512,plain,
% 2.42/2.63 (((~r(s(s(z)), s(s(elem!1)))) | (~r(s(z), s(s(z)))) | (~r(s(s(elem!1)), s(s(z)))) | (~r(s(s(elem!1)), s(z)))) <=> ((~r(s(s(z)), s(s(elem!1)))) | (~r(s(s(elem!1)), s(z))) | (~r(s(z), s(s(z)))) | (~r(s(s(elem!1)), s(s(z)))))),
% 2.42/2.63 inference(rewrite,[status(thm)],[])).
% 2.42/2.63 tff(7513,plain,
% 2.42/2.63 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(z)), s(s(elem!1)))) | (~r(s(z), s(s(z)))) | (~r(s(s(elem!1)), s(s(z)))) | (~r(s(s(elem!1)), s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(z)), s(s(elem!1)))) | (~r(s(s(elem!1)), s(z))) | (~r(s(z), s(s(z)))) | (~r(s(s(elem!1)), s(s(z))))))),
% 2.42/2.63 inference(monotonicity,[status(thm)],[7512])).
% 2.42/2.63 tff(7514,plain,
% 2.42/2.63 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(z)), s(s(elem!1)))) | (~r(s(z), s(s(z)))) | (~r(s(s(elem!1)), s(s(z)))) | (~r(s(s(elem!1)), s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(z)), s(s(elem!1)))) | (~r(s(s(elem!1)), s(z))) | (~r(s(z), s(s(z)))) | (~r(s(s(elem!1)), s(s(z)))))),
% 2.42/2.64 inference(transitivity,[status(thm)],[7513, 7511])).
% 2.42/2.64 tff(7515,plain,
% 2.42/2.64 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(z)), s(s(elem!1)))) | (~r(s(z), s(s(z)))) | (~r(s(s(elem!1)), s(s(z)))) | (~r(s(s(elem!1)), s(z))))),
% 2.42/2.64 inference(quant_inst,[status(thm)],[])).
% 2.42/2.64 tff(7516,plain,
% 2.42/2.64 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(z)), s(s(elem!1)))) | (~r(s(s(elem!1)), s(z))) | (~r(s(z), s(s(z)))) | (~r(s(s(elem!1)), s(s(z))))),
% 2.42/2.64 inference(modus_ponens,[status(thm)],[7515, 7514])).
% 2.42/2.64 tff(7517,plain,
% 2.42/2.64 ($false),
% 2.42/2.64 inference(unit_resolution,[status(thm)],[7516, 197, 393, 120, 4577, 333])).
% 2.42/2.64 tff(7518,plain,((~r(s(s(elem!1)), s(s(z)))) | (~r(s(z), s(s(z)))) | (~r(s(s(elem!1)), s(z))) | (~r(s(s(z)), s(s(elem!1))))), inference(lemma,lemma(discharge,[]))).
% 2.42/2.64 tff(7519,plain,
% 2.42/2.64 (~r(s(s(elem!1)), s(s(z)))),
% 2.42/2.64 inference(unit_resolution,[status(thm)],[7518, 7508, 7337, 7502])).
% 2.42/2.64 tff(7520,plain,
% 2.42/2.64 (b(s(s(elem!1)), s(s(z)))),
% 2.42/2.64 inference(unit_resolution,[status(thm)],[441, 7519, 132])).
% 2.42/2.64 tff(7521,plain,
% 2.42/2.64 ($false),
% 2.42/2.64 inference(unit_resolution,[status(thm)],[6009, 7520, 7510, 376, 118, 156])).
% 2.42/2.64 tff(7522,plain,((~b(s(s(z)), s(z))) | (~b(s(z), s(s(elem!1)))) | (~b(z, s(z))) | (~r(z, s(s(z)))) | (s(s(z)) = s(s(elem!1))) | (s(s(elem!1)) = s(s(s(elem!1)))) | (~b(s(s(s(elem!1))), z))), inference(lemma,lemma(discharge,[]))).
% 2.42/2.64 tff(7523,plain,
% 2.42/2.64 (~b(s(s(z)), s(z))),
% 2.42/2.64 inference(unit_resolution,[status(thm)],[7522, 52, 118, 155, 376, 45, 121])).
% 2.42/2.64 tff(7524,plain,
% 2.42/2.64 (r(s(s(z)), s(z))),
% 2.42/2.64 inference(unit_resolution,[status(thm)],[308, 7523])).
% 2.42/2.64 tff(7525,plain,
% 2.42/2.64 (~r(s(s(z)), s(s(elem!1)))),
% 2.42/2.64 inference(unit_resolution,[status(thm)],[6892, 119, 4577, 392])).
% 2.42/2.64 tff(7526,plain,
% 2.42/2.64 (b(s(s(z)), s(s(elem!1)))),
% 2.42/2.64 inference(unit_resolution,[status(thm)],[390, 7525, 52])).
% 2.42/2.64 tff(7527,plain,
% 2.42/2.64 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), s(z))) | (~r(s(z), s(s(s(elem!1))))) | (~r(s(s(z)), s(z))) | (~r(s(s(s(elem!1))), s(s(z)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(elem!1))), s(z))) | (~r(s(z), s(s(s(elem!1))))) | (~r(s(s(z)), s(z))) | (~r(s(s(s(elem!1))), s(s(z)))))),
% 2.42/2.64 inference(rewrite,[status(thm)],[])).
% 2.42/2.64 tff(7528,plain,
% 2.42/2.64 (((~r(s(z), s(s(s(elem!1))))) | (~r(s(s(z)), s(z))) | (~r(s(s(s(elem!1))), s(z))) | (~r(s(s(s(elem!1))), s(s(z))))) <=> ((~r(s(s(s(elem!1))), s(z))) | (~r(s(z), s(s(s(elem!1))))) | (~r(s(s(z)), s(z))) | (~r(s(s(s(elem!1))), s(s(z)))))),
% 2.42/2.64 inference(rewrite,[status(thm)],[])).
% 2.42/2.64 tff(7529,plain,
% 2.42/2.64 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(s(s(elem!1))))) | (~r(s(s(z)), s(z))) | (~r(s(s(s(elem!1))), s(z))) | (~r(s(s(s(elem!1))), s(s(z)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), s(z))) | (~r(s(z), s(s(s(elem!1))))) | (~r(s(s(z)), s(z))) | (~r(s(s(s(elem!1))), s(s(z))))))),
% 2.42/2.64 inference(monotonicity,[status(thm)],[7528])).
% 2.42/2.64 tff(7530,plain,
% 2.42/2.64 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(s(s(elem!1))))) | (~r(s(s(z)), s(z))) | (~r(s(s(s(elem!1))), s(z))) | (~r(s(s(s(elem!1))), s(s(z)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(elem!1))), s(z))) | (~r(s(z), s(s(s(elem!1))))) | (~r(s(s(z)), s(z))) | (~r(s(s(s(elem!1))), s(s(z)))))),
% 2.42/2.64 inference(transitivity,[status(thm)],[7529, 7527])).
% 2.42/2.64 tff(7531,plain,
% 2.42/2.64 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(s(s(elem!1))))) | (~r(s(s(z)), s(z))) | (~r(s(s(s(elem!1))), s(z))) | (~r(s(s(s(elem!1))), s(s(z)))))),
% 2.42/2.64 inference(quant_inst,[status(thm)],[])).
% 2.42/2.64 tff(7532,plain,
% 2.42/2.64 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(elem!1))), s(z))) | (~r(s(z), s(s(s(elem!1))))) | (~r(s(s(z)), s(z))) | (~r(s(s(s(elem!1))), s(s(z))))),
% 2.42/2.64 inference(modus_ponens,[status(thm)],[7531, 7530])).
% 2.42/2.64 tff(7533,plain,
% 2.42/2.64 ($false),
% 2.42/2.64 inference(unit_resolution,[status(thm)],[7532, 197, 350, 392, 119, 464])).
% 2.42/2.64 tff(7534,plain,((~r(s(z), s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), s(z))) | (~r(s(s(z)), s(z))) | (~r(s(s(s(elem!1))), s(s(z))))), inference(lemma,lemma(discharge,[]))).
% 2.42/2.64 tff(7535,plain,
% 2.42/2.64 (~r(s(s(s(elem!1))), s(s(z)))),
% 2.42/2.64 inference(unit_resolution,[status(thm)],[7534, 119, 350, 392])).
% 2.42/2.64 tff(7536,plain,
% 2.42/2.64 (b(s(s(s(elem!1))), s(s(z)))),
% 2.42/2.64 inference(unit_resolution,[status(thm)],[218, 7535])).
% 2.42/2.64 tff(7537,plain,
% 2.42/2.64 (~r(s(s(elem!1)), s(s(s(elem!1))))),
% 2.42/2.64 inference(unit_resolution,[status(thm)],[7480, 197, 350, 4577, 119])).
% 2.42/2.64 tff(7538,plain,
% 2.42/2.64 (b(s(s(elem!1)), s(s(s(elem!1))))),
% 2.42/2.64 inference(unit_resolution,[status(thm)],[461, 7537, 45])).
% 2.42/2.64 tff(7539,plain,
% 2.42/2.64 (~r(s(s(s(elem!1))), s(s(elem!1)))),
% 2.42/2.64 inference(unit_resolution,[status(thm)],[7468, 197, 350, 4577, 119])).
% 2.42/2.64 tff(7540,plain,
% 2.42/2.64 (b(s(s(s(elem!1))), s(s(elem!1)))),
% 2.42/2.64 inference(unit_resolution,[status(thm)],[889, 7539, 51])).
% 2.42/2.64 tff(7541,plain,
% 2.42/2.64 ($false),
% 2.42/2.64 inference(unit_resolution,[status(thm)],[2068, 7540, 7538, 7536, 7526])).
% 2.42/2.64 tff(7542,plain,((~r(s(z), s(s(s(elem!1))))) | (s(s(elem!1)) = s(s(s(elem!1)))) | (~r(s(s(s(elem!1))), s(z))) | (~r(s(s(elem!1)), s(z))) | (s(s(z)) = s(s(elem!1))) | (~r(s(s(z)), s(z)))), inference(lemma,lemma(discharge,[]))).
% 2.42/2.64 tff(7543,plain,
% 2.42/2.64 (~r(s(z), s(s(s(elem!1))))),
% 2.42/2.64 inference(unit_resolution,[status(thm)],[7542, 7413, 45, 7337, 52, 7524])).
% 2.42/2.64 tff(7544,plain,
% 2.42/2.64 (b(s(z), s(s(s(elem!1))))),
% 2.42/2.64 inference(unit_resolution,[status(thm)],[116, 7543])).
% 2.42/2.64 tff(7545,plain,
% 2.42/2.64 (~b(s(z), z)),
% 2.42/2.64 inference(unit_resolution,[status(thm)],[7322, 7544, 118, 121, 376])).
% 2.42/2.64 tff(7546,plain,
% 2.42/2.64 (r(s(z), z)),
% 2.42/2.64 inference(unit_resolution,[status(thm)],[230, 7545])).
% 2.42/2.64 tff(7547,plain,
% 2.42/2.64 (~r(s(s(z)), s(s(elem!1)))),
% 2.42/2.64 inference(unit_resolution,[status(thm)],[6771, 7546, 7337, 7524])).
% 2.42/2.64 tff(7548,plain,
% 2.42/2.64 (~r(s(s(elem!1)), s(s(z)))),
% 2.42/2.64 inference(unit_resolution,[status(thm)],[5331, 7546, 7524, 7337])).
% 2.42/2.64 tff(7549,plain,
% 2.42/2.64 (~b(s(z), s(s(z)))),
% 2.42/2.64 inference(unit_resolution,[status(thm)],[5300, 7548, 376, 52, 7547])).
% 2.42/2.64 tff(7550,plain,
% 2.42/2.64 (r(s(z), s(s(z)))),
% 2.42/2.64 inference(unit_resolution,[status(thm)],[427, 7549])).
% 2.42/2.64 tff(7551,plain,
% 2.42/2.64 (~b(s(s(elem!1)), s(s(s(elem!1))))),
% 2.42/2.64 inference(unit_resolution,[status(thm)],[6083, 7550, 132, 7337, 7413, 7524])).
% 2.42/2.64 tff(7552,plain,
% 2.42/2.64 (r(s(s(elem!1)), s(s(s(elem!1))))),
% 2.42/2.64 inference(unit_resolution,[status(thm)],[461, 7551, 45])).
% 2.42/2.64 tff(7553,plain,
% 2.42/2.64 ($false),
% 2.42/2.64 inference(unit_resolution,[status(thm)],[7419, 197, 7413, 7337, 7546, 7552])).
% 2.42/2.64 tff(7554,plain,((s(s(z)) = s(s(elem!1))) | (s(s(elem!1)) = s(s(s(elem!1)))) | (~b(s(z), s(s(elem!1)))) | (~b(z, s(z))) | (~b(s(s(s(elem!1))), z)) | (~r(z, s(s(z))))), inference(lemma,lemma(discharge,[]))).
% 2.42/2.64 tff(7555,plain,
% 2.42/2.64 (s(s(z)) = s(s(elem!1))),
% 2.42/2.64 inference(unit_resolution,[status(thm)],[7554, 45, 7136, 118, 6718, 152])).
% 2.42/2.64 tff(7556,plain,
% 2.42/2.64 (r(elem!1, s(s(z))) <=> r(elem!1, s(s(elem!1)))),
% 2.42/2.64 inference(monotonicity,[status(thm)],[7555])).
% 2.42/2.64 tff(7557,plain,
% 2.42/2.64 (r(elem!1, s(s(elem!1))) <=> r(elem!1, s(s(z)))),
% 2.42/2.64 inference(symmetry,[status(thm)],[7556])).
% 2.42/2.64 tff(7558,plain,
% 2.42/2.64 (s(elem!1) = s(z)),
% 2.42/2.64 inference(unit_resolution,[status(thm)],[43, 7555])).
% 2.42/2.64 tff(7559,plain,
% 2.42/2.64 (z = elem!1),
% 2.42/2.64 inference(unit_resolution,[status(thm)],[30, 7558])).
% 2.42/2.64 tff(7560,plain,
% 2.42/2.64 (r(z, s(s(elem!1))) <=> r(elem!1, s(s(elem!1)))),
% 2.42/2.64 inference(monotonicity,[status(thm)],[7559])).
% 2.42/2.64 tff(7561,plain,
% 2.42/2.64 (r(z, s(s(elem!1))) <=> r(elem!1, s(s(z)))),
% 2.42/2.64 inference(transitivity,[status(thm)],[7560, 7557])).
% 2.42/2.64 tff(7562,plain,
% 2.42/2.64 (~b(z, s(s(elem!1)))),
% 2.42/2.64 inference(unit_resolution,[status(thm)],[2261, 7555, 125])).
% 2.42/2.64 tff(7563,plain,
% 2.42/2.64 (r(z, s(s(elem!1)))),
% 2.42/2.64 inference(unit_resolution,[status(thm)],[1795, 7562])).
% 2.42/2.64 tff(7564,plain,
% 2.42/2.64 (r(elem!1, s(s(z)))),
% 2.42/2.64 inference(modus_ponens,[status(thm)],[7563, 7561])).
% 2.42/2.64 tff(7565,plain,
% 2.42/2.64 (r(elem!1, s(s(elem!1)))),
% 2.42/2.64 inference(modus_ponens,[status(thm)],[7563, 7560])).
% 2.42/2.64 tff(7566,plain,
% 2.42/2.64 (s(s(z)) = s(s(elem!1))),
% 2.42/2.64 inference(unit_resolution,[status(thm)],[7554, 45, 376, 118, 121, 155])).
% 2.42/2.64 tff(7567,plain,
% 2.42/2.64 (s(elem!1) = s(z)),
% 2.42/2.64 inference(unit_resolution,[status(thm)],[43, 7566])).
% 2.42/2.64 tff(7568,plain,
% 2.42/2.64 (z = elem!1),
% 2.42/2.64 inference(unit_resolution,[status(thm)],[30, 7567])).
% 2.42/2.64 tff(7569,plain,
% 2.42/2.64 ((s(s(s(s(elem!1)))) = z) <=> (s(s(s(s(elem!1)))) = elem!1)),
% 2.42/2.64 inference(monotonicity,[status(thm)],[7568])).
% 2.42/2.64 tff(7570,plain,
% 2.42/2.64 ((~(s(s(s(s(elem!1)))) = z)) <=> (~(s(s(s(s(elem!1)))) = elem!1))),
% 2.42/2.64 inference(monotonicity,[status(thm)],[7569])).
% 2.42/2.64 tff(7571,plain,
% 2.42/2.64 (~(s(s(s(s(elem!1)))) = elem!1)),
% 2.42/2.64 inference(modus_ponens,[status(thm)],[626, 7570])).
% 2.42/2.64 tff(7572,plain,
% 2.42/2.64 (b(s(z), s(s(z)))),
% 2.42/2.64 inference(unit_resolution,[status(thm)],[5435, 7566, 376])).
% 2.42/2.64 tff(7573,plain,
% 2.42/2.64 (b(s(s(z)), s(z))),
% 2.42/2.64 inference(unit_resolution,[status(thm)],[3938, 310, 7566])).
% 2.42/2.64 tff(7574,plain,
% 2.42/2.64 (~b(s(s(elem!1)), z)),
% 2.42/2.64 inference(unit_resolution,[status(thm)],[4447, 7573, 118, 310, 7572])).
% 2.42/2.64 tff(7575,plain,
% 2.42/2.64 (r(s(s(elem!1)), z)),
% 2.42/2.64 inference(unit_resolution,[status(thm)],[608, 7574])).
% 2.42/2.64 tff(7576,plain,
% 2.42/2.64 (r(s(s(elem!1)), elem!1)),
% 2.42/2.64 inference(unit_resolution,[status(thm)],[3398, 7575, 7568])).
% 2.42/2.64 tff(7577,plain,
% 2.42/2.64 ((s(s(s(s(elem!1)))) = s(s(z))) <=> (s(s(s(s(elem!1)))) = s(s(elem!1)))),
% 2.42/2.64 inference(monotonicity,[status(thm)],[7566])).
% 2.42/2.64 tff(7578,plain,
% 2.42/2.64 ((s(s(s(s(elem!1)))) = s(s(z))) <=> (s(s(elem!1)) = s(s(s(s(elem!1)))))),
% 2.42/2.64 inference(transitivity,[status(thm)],[7577, 123])).
% 2.42/2.64 tff(7579,plain,
% 2.42/2.64 ((s(s(s(s(elem!1)))) = s(s(z))) <=> (s(s(s(s(elem!1)))) = s(s(elem!1)))),
% 2.42/2.64 inference(transitivity,[status(thm)],[7578, 124])).
% 2.42/2.64 tff(7580,plain,
% 2.42/2.64 ((~(s(s(s(s(elem!1)))) = s(s(z)))) <=> (~(s(s(s(s(elem!1)))) = s(s(elem!1))))),
% 2.42/2.64 inference(monotonicity,[status(thm)],[7579])).
% 2.42/2.64 tff(7581,plain,
% 2.42/2.64 (~(s(s(s(s(elem!1)))) = s(s(elem!1)))),
% 2.42/2.64 inference(modus_ponens,[status(thm)],[733, 7580])).
% 2.42/2.64 tff(7582,plain,
% 2.42/2.64 (b(s(s(s(elem!1))), elem!1)),
% 2.42/2.64 inference(unit_resolution,[status(thm)],[634, 7568, 121])).
% 2.42/2.64 tff(7583,plain,
% 2.42/2.64 (b(z, s(z)) <=> b(elem!1, s(z))),
% 2.42/2.64 inference(monotonicity,[status(thm)],[7568])).
% 2.42/2.64 tff(7584,plain,
% 2.42/2.64 (b(elem!1, s(z))),
% 2.42/2.64 inference(modus_ponens,[status(thm)],[118, 7583])).
% 2.42/2.64 tff(7585,plain,
% 2.42/2.64 (b(s(s(elem!1)), z) <=> b(s(s(elem!1)), elem!1)),
% 2.42/2.64 inference(monotonicity,[status(thm)],[7568])).
% 2.42/2.64 tff(7586,plain,
% 2.42/2.64 (b(s(s(z)), z) <=> b(s(s(elem!1)), z)),
% 2.42/2.64 inference(monotonicity,[status(thm)],[7566])).
% 2.42/2.64 tff(7587,plain,
% 2.42/2.64 (b(s(s(z)), z) <=> b(s(s(elem!1)), elem!1)),
% 2.42/2.64 inference(transitivity,[status(thm)],[7586, 7585])).
% 2.42/2.64 tff(7588,plain,
% 2.42/2.64 (~b(s(s(z)), s(z))),
% 2.42/2.64 inference(unit_resolution,[status(thm)],[6807, 96, 7572, 118, 121])).
% 2.42/2.64 tff(7589,plain,
% 2.42/2.64 (r(s(s(z)), s(z))),
% 2.42/2.64 inference(unit_resolution,[status(thm)],[308, 7588])).
% 2.42/2.64 tff(7590,plain,
% 2.42/2.64 (~b(s(s(elem!1)), s(z))),
% 2.42/2.64 inference(unit_resolution,[status(thm)],[7150, 96, 121, 118, 376])).
% 2.42/2.64 tff(7591,plain,
% 2.42/2.64 (r(s(s(elem!1)), s(z))),
% 2.42/2.64 inference(unit_resolution,[status(thm)],[1912, 7590])).
% 2.42/2.64 tff(7592,plain,
% 2.42/2.64 (~b(s(z), z)),
% 2.42/2.64 inference(unit_resolution,[status(thm)],[7386, 7591, 376, 118, 121, 51, 96, 7369])).
% 2.42/2.64 tff(7593,plain,
% 2.42/2.64 (r(s(z), z)),
% 2.42/2.64 inference(unit_resolution,[status(thm)],[230, 7592])).
% 2.42/2.64 tff(7594,plain,
% 2.42/2.64 (~r(s(s(z)), z)),
% 2.42/2.64 inference(unit_resolution,[status(thm)],[4287, 7593, 155, 7589])).
% 2.42/2.64 tff(7595,plain,
% 2.42/2.64 (b(s(s(z)), z)),
% 2.42/2.64 inference(unit_resolution,[status(thm)],[186, 7594])).
% 2.42/2.64 tff(7596,plain,
% 2.42/2.64 (b(s(s(elem!1)), elem!1)),
% 2.42/2.64 inference(modus_ponens,[status(thm)],[7595, 7587])).
% 2.42/2.64 tff(7597,plain,
% 2.42/2.64 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), elem!1)) | (~b(elem!1, s(z))) | (~b(s(z), s(s(elem!1)))) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(s(s(elem!1))), elem!1)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(elem!1)), elem!1)) | (~b(elem!1, s(z))) | (~b(s(z), s(s(elem!1)))) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(s(s(elem!1))), elem!1)))),
% 2.42/2.64 inference(rewrite,[status(thm)],[])).
% 2.42/2.64 tff(7598,plain,
% 2.42/2.64 (((~b(s(s(elem!1)), elem!1)) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(z), s(s(elem!1)))) | (~b(elem!1, s(z))) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(s(s(elem!1))), elem!1))) <=> ((~b(s(s(elem!1)), elem!1)) | (~b(elem!1, s(z))) | (~b(s(z), s(s(elem!1)))) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(s(s(elem!1))), elem!1)))),
% 2.42/2.64 inference(rewrite,[status(thm)],[])).
% 2.42/2.64 tff(7599,plain,
% 2.42/2.64 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), elem!1)) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(z), s(s(elem!1)))) | (~b(elem!1, s(z))) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(s(s(elem!1))), elem!1)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), elem!1)) | (~b(elem!1, s(z))) | (~b(s(z), s(s(elem!1)))) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(s(s(elem!1))), elem!1))))),
% 2.42/2.64 inference(monotonicity,[status(thm)],[7598])).
% 2.42/2.64 tff(7600,plain,
% 2.42/2.64 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), elem!1)) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(z), s(s(elem!1)))) | (~b(elem!1, s(z))) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(s(s(elem!1))), elem!1)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(elem!1)), elem!1)) | (~b(elem!1, s(z))) | (~b(s(z), s(s(elem!1)))) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(s(s(elem!1))), elem!1)))),
% 2.42/2.64 inference(transitivity,[status(thm)],[7599, 7597])).
% 2.42/2.64 tff(7601,plain,
% 2.42/2.64 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), elem!1)) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(z), s(s(elem!1)))) | (~b(elem!1, s(z))) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(s(s(elem!1))), elem!1)))),
% 2.42/2.64 inference(quant_inst,[status(thm)],[])).
% 2.42/2.64 tff(7602,plain,
% 2.42/2.64 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(elem!1)), elem!1)) | (~b(elem!1, s(z))) | (~b(s(z), s(s(elem!1)))) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(s(s(elem!1))), elem!1))),
% 2.42/2.64 inference(modus_ponens,[status(thm)],[7601, 7600])).
% 2.42/2.64 tff(7603,plain,
% 2.42/2.64 ($false),
% 2.42/2.64 inference(unit_resolution,[status(thm)],[7602, 166, 376, 7596, 96, 7584, 7582])).
% 2.42/2.64 tff(7604,plain,((~b(s(s(s(elem!1))), s(z))) | (~b(s(z), s(s(elem!1)))) | (~r(z, s(s(z)))) | (~b(z, s(z))) | (~b(s(s(s(elem!1))), z)) | (s(s(elem!1)) = s(s(s(elem!1))))), inference(lemma,lemma(discharge,[]))).
% 2.42/2.64 tff(7605,plain,
% 2.42/2.64 (~b(s(s(s(elem!1))), s(z))),
% 2.42/2.64 inference(unit_resolution,[status(thm)],[7604, 376, 155, 118, 121, 45])).
% 2.42/2.64 tff(7606,plain,
% 2.42/2.64 (r(s(s(s(elem!1))), s(z))),
% 2.42/2.64 inference(unit_resolution,[status(thm)],[1849, 7605])).
% 2.42/2.64 tff(7607,plain,
% 2.42/2.64 (b(s(s(z)), s(z))),
% 2.42/2.64 inference(unit_resolution,[status(thm)],[3938, 310, 34])).
% 2.42/2.64 tff(7608,plain,
% 2.42/2.64 (~b(s(s(z)), z)),
% 2.42/2.64 inference(unit_resolution,[status(thm)],[6740, 7607, 118, 5436])).
% 2.42/2.64 tff(7609,plain,
% 2.42/2.64 (r(s(s(z)), z)),
% 2.42/2.64 inference(unit_resolution,[status(thm)],[186, 7608])).
% 2.42/2.64 tff(7610,plain,
% 2.42/2.64 (~b(s(s(elem!1)), z)),
% 2.42/2.64 inference(unit_resolution,[status(thm)],[4447, 7607, 118, 310, 5436])).
% 2.42/2.64 tff(7611,plain,
% 2.42/2.64 (r(s(s(elem!1)), z)),
% 2.42/2.64 inference(unit_resolution,[status(thm)],[608, 7610])).
% 2.42/2.64 tff(7612,plain,
% 2.42/2.64 (r(s(s(elem!1)), elem!1)),
% 2.42/2.64 inference(unit_resolution,[status(thm)],[3398, 7611, 620])).
% 2.42/2.64 tff(7613,plain,
% 2.42/2.64 (r(s(s(s(elem!1))), s(elem!1)) <=> r(s(s(s(elem!1))), s(z))),
% 2.42/2.64 inference(monotonicity,[status(thm)],[619])).
% 2.42/2.64 tff(7614,plain,
% 2.42/2.64 (r(s(s(s(elem!1))), s(z)) <=> r(s(s(s(elem!1))), s(elem!1))),
% 2.42/2.64 inference(symmetry,[status(thm)],[7613])).
% 2.42/2.64 tff(7615,plain,
% 2.42/2.64 (r(s(s(s(elem!1))), s(elem!1))),
% 2.42/2.64 inference(modus_ponens,[status(thm)],[350, 7614])).
% 2.42/2.64 tff(7616,assumption,(r(s(s(s(elem!1))), s(elem!1))), introduced(assumption)).
% 2.42/2.64 tff(7617,plain,
% 2.42/2.64 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(elem!1)), elem!1)) | (~r(s(s(s(elem!1))), s(elem!1))) | (~r(elem!1, s(s(s(elem!1))))) | (~r(s(s(elem!1)), s(s(s(elem!1))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(elem!1)), elem!1)) | (~r(s(s(s(elem!1))), s(elem!1))) | (~r(elem!1, s(s(s(elem!1))))) | (~r(s(s(elem!1)), s(s(s(elem!1))))))),
% 2.42/2.64 inference(rewrite,[status(thm)],[])).
% 2.42/2.64 tff(7618,plain,
% 2.42/2.64 (((~r(s(s(s(elem!1))), s(elem!1))) | (~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(s(elem!1))), s(elem!1))) | (~r(elem!1, s(s(s(elem!1))))) | (~r(s(s(elem!1)), s(s(s(elem!1))))))),
% 2.42/2.64 inference(rewrite,[status(thm)],[])).
% 2.42/2.64 tff(7619,plain,
% 2.42/2.64 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), s(elem!1))) | (~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, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(elem!1)), elem!1)) | (~r(s(s(s(elem!1))), s(elem!1))) | (~r(elem!1, s(s(s(elem!1))))) | (~r(s(s(elem!1)), s(s(s(elem!1)))))))),
% 2.42/2.64 inference(monotonicity,[status(thm)],[7618])).
% 2.42/2.64 tff(7620,plain,
% 2.42/2.64 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), s(elem!1))) | (~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, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(elem!1)), elem!1)) | (~r(s(s(s(elem!1))), s(elem!1))) | (~r(elem!1, s(s(s(elem!1))))) | (~r(s(s(elem!1)), s(s(s(elem!1))))))),
% 2.42/2.64 inference(transitivity,[status(thm)],[7619, 7617])).
% 2.42/2.64 tff(7621,plain,
% 2.42/2.64 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), s(elem!1))) | (~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)))),
% 2.42/2.64 inference(quant_inst,[status(thm)],[])).
% 2.42/2.64 tff(7622,plain,
% 2.42/2.64 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(elem!1)), elem!1)) | (~r(s(s(s(elem!1))), s(elem!1))) | (~r(elem!1, s(s(s(elem!1))))) | (~r(s(s(elem!1)), s(s(s(elem!1)))))),
% 2.42/2.64 inference(modus_ponens,[status(thm)],[7621, 7620])).
% 2.42/2.64 tff(7623,plain,
% 2.42/2.64 ($false),
% 2.42/2.64 inference(unit_resolution,[status(thm)],[7622, 197, 7616, 768, 377, 942])).
% 2.42/2.64 tff(7624,plain,((~r(elem!1, s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), s(elem!1))) | (~r(s(s(elem!1)), elem!1)) | (~r(s(s(elem!1)), s(s(s(elem!1)))))), inference(lemma,lemma(discharge,[]))).
% 2.42/2.64 tff(7625,plain,
% 2.42/2.64 (~r(elem!1, s(s(s(elem!1))))),
% 2.42/2.64 inference(unit_resolution,[status(thm)],[7624, 377, 7615, 7612])).
% 2.42/2.64 tff(7626,plain,
% 2.42/2.64 (b(elem!1, s(s(s(elem!1))))),
% 2.42/2.64 inference(unit_resolution,[status(thm)],[5451, 7625, 6292])).
% 2.42/2.64 tff(7627,plain,
% 2.42/2.64 (~b(s(s(s(s(elem!1)))), elem!1)),
% 2.42/2.64 inference(unit_resolution,[status(thm)],[710, 637, 361, 2157, 7626, 7371])).
% 2.42/2.64 tff(7628,plain,
% 2.42/2.64 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(z))) | (~b(elem!1, s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~b(elem!1, s(s(s(s(elem!1)))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(z))) | (~b(elem!1, s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~b(elem!1, s(s(s(s(elem!1)))))))),
% 2.42/2.64 inference(rewrite,[status(thm)],[])).
% 2.42/2.64 tff(7629,plain,
% 2.42/2.64 (((~b(elem!1, s(z))) | (~b(elem!1, s(z))) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~b(elem!1, s(s(s(elem!1))))) | (~b(elem!1, s(s(s(s(elem!1))))))) <=> ((~b(elem!1, s(z))) | (~b(elem!1, s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~b(elem!1, s(s(s(s(elem!1)))))))),
% 2.42/2.64 inference(rewrite,[status(thm)],[])).
% 2.42/2.64 tff(7630,plain,
% 2.42/2.64 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(z))) | (~b(elem!1, s(z))) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~b(elem!1, s(s(s(elem!1))))) | (~b(elem!1, s(s(s(s(elem!1)))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(z))) | (~b(elem!1, s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~b(elem!1, s(s(s(s(elem!1))))))))),
% 2.42/2.64 inference(monotonicity,[status(thm)],[7629])).
% 2.42/2.64 tff(7631,plain,
% 2.42/2.64 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(z))) | (~b(elem!1, s(z))) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~b(elem!1, s(s(s(elem!1))))) | (~b(elem!1, s(s(s(s(elem!1)))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(z))) | (~b(elem!1, s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~b(elem!1, s(s(s(s(elem!1)))))))),
% 2.42/2.64 inference(transitivity,[status(thm)],[7630, 7628])).
% 2.42/2.64 tff(7632,plain,
% 2.42/2.64 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(z))) | (~b(elem!1, s(z))) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~b(elem!1, s(s(s(elem!1))))) | (~b(elem!1, s(s(s(s(elem!1)))))))),
% 2.42/2.64 inference(quant_inst,[status(thm)],[])).
% 2.42/2.64 tff(7633,plain,
% 2.42/2.64 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(z))) | (~b(elem!1, s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~b(elem!1, s(s(s(s(elem!1))))))),
% 2.42/2.64 inference(modus_ponens,[status(thm)],[7632, 7631])).
% 2.42/2.64 tff(7634,plain,
% 2.42/2.64 (~b(elem!1, s(s(s(s(elem!1)))))),
% 2.42/2.64 inference(unit_resolution,[status(thm)],[7633, 166, 643, 1212, 641, 1107])).
% 2.42/2.64 tff(7635,plain,
% 2.42/2.64 (r(elem!1, s(s(s(s(elem!1)))))),
% 2.42/2.64 inference(unit_resolution,[status(thm)],[2427, 7634, 2377])).
% 2.42/2.64 tff(7636,plain,
% 2.42/2.64 (b(s(s(z)), s(s(s(s(z))))) <=> b(s(s(elem!1)), s(s(s(s(elem!1)))))),
% 2.42/2.64 inference(monotonicity,[status(thm)],[34, 1087])).
% 2.42/2.64 tff(7637,plain,
% 2.42/2.64 (~b(elem!1, s(s(s(s(z)))))),
% 2.42/2.64 inference(unit_resolution,[status(thm)],[1105, 7634, 34])).
% 2.42/2.64 tff(7638,plain,
% 2.42/2.64 (r(elem!1, s(s(s(s(z)))))),
% 2.42/2.64 inference(unit_resolution,[status(thm)],[1098, 7637, 1045])).
% 2.42/2.64 tff(7639,plain,
% 2.42/2.64 (~b(s(s(s(s(z)))), elem!1)),
% 2.42/2.64 inference(modus_ponens,[status(thm)],[714, 6185])).
% 2.42/2.64 tff(7640,plain,
% 2.42/2.64 (r(s(s(s(s(z)))), elem!1)),
% 2.42/2.64 inference(unit_resolution,[status(thm)],[6190, 7639, 6184])).
% 2.42/2.64 tff(7641,plain,
% 2.42/2.64 (~r(s(s(z)), s(s(s(s(z)))))),
% 2.42/2.64 inference(unit_resolution,[status(thm)],[6202, 7640, 6194, 7638])).
% 2.42/2.64 tff(7642,plain,
% 2.42/2.64 (b(s(s(z)), s(s(s(s(z)))))),
% 2.42/2.64 inference(unit_resolution,[status(thm)],[4753, 7641])).
% 2.42/2.64 tff(7643,plain,
% 2.42/2.64 (b(s(s(elem!1)), s(s(s(s(elem!1)))))),
% 2.42/2.64 inference(modus_ponens,[status(thm)],[7642, 7636])).
% 2.42/2.64 tff(7644,plain,
% 2.42/2.65 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(elem!1)))) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(z), elem!1)) | (~b(s(s(elem!1)), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~b(s(z), s(s(s(s(elem!1)))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), s(s(elem!1)))) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(z), elem!1)) | (~b(s(s(elem!1)), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~b(s(z), s(s(s(s(elem!1)))))))),
% 2.42/2.65 inference(rewrite,[status(thm)],[])).
% 2.42/2.65 tff(7645,plain,
% 2.42/2.65 (((~b(s(s(s(elem!1))), elem!1)) | (~b(s(z), elem!1)) | (~b(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~b(s(s(elem!1)), s(s(s(s(elem!1)))))) | (~b(s(z), s(s(s(s(elem!1)))))) | (~b(s(z), s(s(elem!1))))) <=> ((~b(s(z), s(s(elem!1)))) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(z), elem!1)) | (~b(s(s(elem!1)), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~b(s(z), s(s(s(s(elem!1)))))))),
% 2.42/2.65 inference(rewrite,[status(thm)],[])).
% 2.42/2.65 tff(7646,plain,
% 2.42/2.65 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), elem!1)) | (~b(s(z), elem!1)) | (~b(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~b(s(s(elem!1)), s(s(s(s(elem!1)))))) | (~b(s(z), s(s(s(s(elem!1)))))) | (~b(s(z), s(s(elem!1)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(elem!1)))) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(z), elem!1)) | (~b(s(s(elem!1)), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~b(s(z), s(s(s(s(elem!1))))))))),
% 2.42/2.65 inference(monotonicity,[status(thm)],[7645])).
% 2.42/2.65 tff(7647,plain,
% 2.42/2.65 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), elem!1)) | (~b(s(z), elem!1)) | (~b(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~b(s(s(elem!1)), s(s(s(s(elem!1)))))) | (~b(s(z), s(s(s(s(elem!1)))))) | (~b(s(z), s(s(elem!1)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), s(s(elem!1)))) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(z), elem!1)) | (~b(s(s(elem!1)), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~b(s(z), s(s(s(s(elem!1)))))))),
% 2.42/2.65 inference(transitivity,[status(thm)],[7646, 7644])).
% 2.42/2.65 tff(7648,plain,
% 2.42/2.65 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), elem!1)) | (~b(s(z), elem!1)) | (~b(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~b(s(s(elem!1)), s(s(s(s(elem!1)))))) | (~b(s(z), s(s(s(s(elem!1)))))) | (~b(s(z), s(s(elem!1)))))),
% 2.42/2.65 inference(quant_inst,[status(thm)],[])).
% 2.42/2.65 tff(7649,plain,
% 2.42/2.65 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), s(s(elem!1)))) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(z), elem!1)) | (~b(s(s(elem!1)), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~b(s(z), s(s(s(s(elem!1))))))),
% 2.42/2.65 inference(modus_ponens,[status(thm)],[7648, 7647])).
% 2.42/2.65 tff(7650,plain,
% 2.42/2.65 (~b(s(z), s(s(s(s(elem!1)))))),
% 2.42/2.65 inference(unit_resolution,[status(thm)],[7649, 166, 376, 642, 7643, 641, 1107])).
% 2.42/2.65 tff(7651,plain,
% 2.42/2.65 (r(s(z), s(s(s(s(elem!1)))))),
% 2.42/2.65 inference(unit_resolution,[status(thm)],[681, 7650])).
% 2.42/2.65 tff(7652,plain,
% 2.42/2.65 (r(s(s(s(s(s(s(s(elem!1))))))), s(z))),
% 2.42/2.65 inference(unit_resolution,[status(thm)],[4951, 79, 6378, 4947])).
% 2.42/2.65 tff(7653,plain,
% 2.42/2.65 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), s(z))) | (~r(s(z), s(s(s(s(elem!1)))))) | (~r(s(s(s(elem!1))), s(s(s(s(s(s(s(elem!1))))))))) | (~r(s(s(s(s(s(s(s(elem!1))))))), s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(elem!1))), s(z))) | (~r(s(z), s(s(s(s(elem!1)))))) | (~r(s(s(s(elem!1))), s(s(s(s(s(s(s(elem!1))))))))) | (~r(s(s(s(s(s(s(s(elem!1))))))), s(z))))),
% 2.42/2.65 inference(rewrite,[status(thm)],[])).
% 2.42/2.65 tff(7654,plain,
% 2.42/2.65 (((~r(s(z), s(s(s(s(elem!1)))))) | (~r(s(s(s(s(s(s(s(elem!1))))))), s(z))) | (~r(s(s(s(elem!1))), s(z))) | (~r(s(s(s(elem!1))), s(s(s(s(s(s(s(elem!1)))))))))) <=> ((~r(s(s(s(elem!1))), s(z))) | (~r(s(z), s(s(s(s(elem!1)))))) | (~r(s(s(s(elem!1))), s(s(s(s(s(s(s(elem!1))))))))) | (~r(s(s(s(s(s(s(s(elem!1))))))), s(z))))),
% 2.42/2.65 inference(rewrite,[status(thm)],[])).
% 2.42/2.65 tff(7655,plain,
% 2.42/2.65 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(s(s(s(elem!1)))))) | (~r(s(s(s(s(s(s(s(elem!1))))))), s(z))) | (~r(s(s(s(elem!1))), s(z))) | (~r(s(s(s(elem!1))), s(s(s(s(s(s(s(elem!1))))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), s(z))) | (~r(s(z), s(s(s(s(elem!1)))))) | (~r(s(s(s(elem!1))), s(s(s(s(s(s(s(elem!1))))))))) | (~r(s(s(s(s(s(s(s(elem!1))))))), s(z)))))),
% 2.42/2.65 inference(monotonicity,[status(thm)],[7654])).
% 2.42/2.65 tff(7656,plain,
% 2.42/2.65 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(s(s(s(elem!1)))))) | (~r(s(s(s(s(s(s(s(elem!1))))))), s(z))) | (~r(s(s(s(elem!1))), s(z))) | (~r(s(s(s(elem!1))), s(s(s(s(s(s(s(elem!1))))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(elem!1))), s(z))) | (~r(s(z), s(s(s(s(elem!1)))))) | (~r(s(s(s(elem!1))), s(s(s(s(s(s(s(elem!1))))))))) | (~r(s(s(s(s(s(s(s(elem!1))))))), s(z))))),
% 2.42/2.65 inference(transitivity,[status(thm)],[7655, 7653])).
% 2.42/2.65 tff(7657,plain,
% 2.42/2.65 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(s(s(s(elem!1)))))) | (~r(s(s(s(s(s(s(s(elem!1))))))), s(z))) | (~r(s(s(s(elem!1))), s(z))) | (~r(s(s(s(elem!1))), s(s(s(s(s(s(s(elem!1))))))))))),
% 2.42/2.65 inference(quant_inst,[status(thm)],[])).
% 2.42/2.65 tff(7658,plain,
% 2.42/2.65 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(elem!1))), s(z))) | (~r(s(z), s(s(s(s(elem!1)))))) | (~r(s(s(s(elem!1))), s(s(s(s(s(s(s(elem!1))))))))) | (~r(s(s(s(s(s(s(s(elem!1))))))), s(z)))),
% 2.42/2.65 inference(modus_ponens,[status(thm)],[7657, 7656])).
% 2.42/2.65 tff(7659,plain,
% 2.42/2.65 (~r(s(s(s(elem!1))), s(s(s(s(s(s(s(elem!1))))))))),
% 2.42/2.65 inference(unit_resolution,[status(thm)],[7658, 197, 350, 699, 7652])).
% 2.42/2.65 tff(7660,plain,
% 2.42/2.65 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(s(s(s(s(s(s(elem!1))))))), elem!1)) | (~b(s(s(s(elem!1))), s(s(s(s(s(s(s(elem!1))))))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(s(s(s(s(s(s(elem!1))))))), elem!1)) | (~b(s(s(s(elem!1))), s(s(s(s(s(s(s(elem!1))))))))))),
% 2.42/2.65 inference(rewrite,[status(thm)],[])).
% 2.42/2.65 tff(7661,plain,
% 2.42/2.65 (((~b(s(s(s(elem!1))), elem!1)) | (~b(s(s(s(elem!1))), elem!1)) | (~b(elem!1, s(s(s(elem!1))))) | (~b(s(s(s(s(s(s(s(elem!1))))))), elem!1)) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(s(s(elem!1))), s(s(s(s(s(s(s(elem!1)))))))))) <=> ((~b(elem!1, s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(s(s(s(s(s(s(elem!1))))))), elem!1)) | (~b(s(s(s(elem!1))), s(s(s(s(s(s(s(elem!1))))))))))),
% 2.42/2.65 inference(rewrite,[status(thm)],[])).
% 2.42/2.65 tff(7662,plain,
% 2.42/2.65 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), elem!1)) | (~b(s(s(s(elem!1))), elem!1)) | (~b(elem!1, s(s(s(elem!1))))) | (~b(s(s(s(s(s(s(s(elem!1))))))), elem!1)) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(s(s(elem!1))), s(s(s(s(s(s(s(elem!1))))))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(s(s(s(s(s(s(elem!1))))))), elem!1)) | (~b(s(s(s(elem!1))), s(s(s(s(s(s(s(elem!1)))))))))))),
% 2.42/2.65 inference(monotonicity,[status(thm)],[7661])).
% 2.42/2.65 tff(7663,plain,
% 2.42/2.65 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), elem!1)) | (~b(s(s(s(elem!1))), elem!1)) | (~b(elem!1, s(s(s(elem!1))))) | (~b(s(s(s(s(s(s(s(elem!1))))))), elem!1)) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(s(s(elem!1))), s(s(s(s(s(s(s(elem!1))))))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(s(s(s(s(s(s(elem!1))))))), elem!1)) | (~b(s(s(s(elem!1))), s(s(s(s(s(s(s(elem!1))))))))))),
% 2.42/2.65 inference(transitivity,[status(thm)],[7662, 7660])).
% 2.42/2.65 tff(7664,plain,
% 2.42/2.65 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), elem!1)) | (~b(s(s(s(elem!1))), elem!1)) | (~b(elem!1, s(s(s(elem!1))))) | (~b(s(s(s(s(s(s(s(elem!1))))))), elem!1)) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(s(s(elem!1))), s(s(s(s(s(s(s(elem!1))))))))))),
% 2.42/2.65 inference(quant_inst,[status(thm)],[])).
% 2.42/2.65 tff(7665,plain,
% 2.42/2.65 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(s(s(s(s(s(s(elem!1))))))), elem!1)) | (~b(s(s(s(elem!1))), s(s(s(s(s(s(s(elem!1)))))))))),
% 2.42/2.65 inference(modus_ponens,[status(thm)],[7664, 7663])).
% 2.42/2.65 tff(7666,plain,
% 2.42/2.65 (~b(s(s(s(elem!1))), s(s(s(s(s(s(s(elem!1))))))))),
% 2.42/2.65 inference(unit_resolution,[status(thm)],[7665, 166, 643, 641, 4927])).
% 2.42/2.65 tff(7667,plain,
% 2.42/2.65 ((s(s(s(elem!1))) = s(s(s(s(s(s(s(elem!1)))))))) | r(s(s(s(elem!1))), s(s(s(s(s(s(s(elem!1))))))))),
% 2.42/2.65 inference(unit_resolution,[status(thm)],[6341, 79, 7666])).
% 2.42/2.65 tff(7668,plain,
% 2.42/2.65 ($false),
% 2.42/2.65 inference(unit_resolution,[status(thm)],[7667, 7659, 6330])).
% 2.42/2.65 tff(7669,plain,((~b(s(s(s(s(s(s(s(elem!1))))))), elem!1)) | (~r(s(s(s(elem!1))), s(z))) | (~r(s(z), s(s(s(s(elem!1)))))) | (~(s(s(z)) = s(s(elem!1)))) | (~b(elem!1, s(z))) | (~b(s(z), elem!1)) | (~b(elem!1, s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), elem!1))), inference(lemma,lemma(discharge,[]))).
% 2.42/2.65 tff(7670,plain,
% 2.42/2.65 (~b(s(s(s(s(s(s(s(elem!1))))))), elem!1)),
% 2.42/2.65 inference(unit_resolution,[status(thm)],[7669, 7651, 350, 34, 1212, 642, 643, 641])).
% 2.42/2.65 tff(7671,plain,
% 2.42/2.65 (r(s(s(s(s(s(s(s(elem!1))))))), elem!1)),
% 2.42/2.65 inference(unit_resolution,[status(thm)],[6375, 7670, 6284])).
% 2.42/2.65 tff(7672,plain,
% 2.42/2.65 (~r(s(s(s(s(s(s(s(elem!1))))))), s(s(elem!1)))),
% 2.42/2.65 inference(unit_resolution,[status(thm)],[7114, 197, 768, 7671, 7635])).
% 2.42/2.65 tff(7673,plain,
% 2.42/2.65 ((s(s(s(s(s(s(s(elem!1))))))) = s(s(elem!1))) | b(s(s(s(s(s(s(s(elem!1))))))), s(s(elem!1)))),
% 2.42/2.65 inference(unit_resolution,[status(thm)],[6359, 79, 7672])).
% 2.42/2.65 tff(7674,plain,
% 2.42/2.65 (b(s(s(s(s(s(s(s(elem!1))))))), s(s(elem!1)))),
% 2.42/2.65 inference(unit_resolution,[status(thm)],[7673, 6349])).
% 2.42/2.65 tff(7675,plain,
% 2.42/2.65 (r(s(s(s(s(elem!1)))), elem!1)),
% 2.42/2.65 inference(unit_resolution,[status(thm)],[719, 714, 627])).
% 2.42/2.65 tff(7676,plain,
% 2.42/2.65 (~r(s(s(s(s(elem!1)))), s(s(s(s(s(s(s(elem!1))))))))),
% 2.42/2.65 inference(unit_resolution,[status(thm)],[7089, 197, 7671, 7675, 7635])).
% 2.42/2.65 tff(7677,plain,
% 2.42/2.65 ((s(s(s(s(elem!1)))) = s(s(s(s(s(s(s(elem!1)))))))) | b(s(s(s(s(elem!1)))), s(s(s(s(s(s(s(elem!1))))))))),
% 2.42/2.65 inference(unit_resolution,[status(thm)],[6423, 79, 7676])).
% 2.42/2.65 tff(7678,plain,
% 2.42/2.65 (b(s(s(s(s(elem!1)))), s(s(s(s(s(s(s(elem!1))))))))),
% 2.42/2.65 inference(unit_resolution,[status(thm)],[7677, 6279])).
% 2.42/2.65 tff(7679,plain,
% 2.42/2.65 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(s(s(s(elem!1)))))) | (~r(s(s(elem!1)), elem!1)) | (~r(s(s(s(s(elem!1)))), s(s(elem!1)))) | (~r(s(s(s(s(elem!1)))), elem!1)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(elem!1, s(s(s(s(elem!1)))))) | (~r(s(s(elem!1)), elem!1)) | (~r(s(s(s(s(elem!1)))), s(s(elem!1)))) | (~r(s(s(s(s(elem!1)))), elem!1)))),
% 2.42/2.65 inference(rewrite,[status(thm)],[])).
% 2.42/2.65 tff(7680,plain,
% 2.42/2.65 (((~r(elem!1, s(s(s(s(elem!1)))))) | (~r(s(s(elem!1)), elem!1)) | (~r(s(s(s(s(elem!1)))), elem!1)) | (~r(s(s(s(s(elem!1)))), s(s(elem!1))))) <=> ((~r(elem!1, s(s(s(s(elem!1)))))) | (~r(s(s(elem!1)), elem!1)) | (~r(s(s(s(s(elem!1)))), s(s(elem!1)))) | (~r(s(s(s(s(elem!1)))), elem!1)))),
% 2.42/2.65 inference(rewrite,[status(thm)],[])).
% 2.42/2.65 tff(7681,plain,
% 2.42/2.65 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(s(s(s(elem!1)))))) | (~r(s(s(elem!1)), elem!1)) | (~r(s(s(s(s(elem!1)))), elem!1)) | (~r(s(s(s(s(elem!1)))), s(s(elem!1)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(s(s(s(elem!1)))))) | (~r(s(s(elem!1)), elem!1)) | (~r(s(s(s(s(elem!1)))), s(s(elem!1)))) | (~r(s(s(s(s(elem!1)))), elem!1))))),
% 2.42/2.65 inference(monotonicity,[status(thm)],[7680])).
% 2.42/2.65 tff(7682,plain,
% 2.42/2.65 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(s(s(s(elem!1)))))) | (~r(s(s(elem!1)), elem!1)) | (~r(s(s(s(s(elem!1)))), elem!1)) | (~r(s(s(s(s(elem!1)))), s(s(elem!1)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(elem!1, s(s(s(s(elem!1)))))) | (~r(s(s(elem!1)), elem!1)) | (~r(s(s(s(s(elem!1)))), s(s(elem!1)))) | (~r(s(s(s(s(elem!1)))), elem!1)))),
% 2.42/2.65 inference(transitivity,[status(thm)],[7681, 7679])).
% 2.42/2.65 tff(7683,plain,
% 2.42/2.65 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(s(s(s(elem!1)))))) | (~r(s(s(elem!1)), elem!1)) | (~r(s(s(s(s(elem!1)))), elem!1)) | (~r(s(s(s(s(elem!1)))), s(s(elem!1)))))),
% 2.42/2.65 inference(quant_inst,[status(thm)],[])).
% 2.42/2.65 tff(7684,plain,
% 2.42/2.65 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(elem!1, s(s(s(s(elem!1)))))) | (~r(s(s(elem!1)), elem!1)) | (~r(s(s(s(s(elem!1)))), s(s(elem!1)))) | (~r(s(s(s(s(elem!1)))), elem!1))),
% 2.42/2.65 inference(modus_ponens,[status(thm)],[7683, 7682])).
% 2.42/2.65 tff(7685,plain,
% 2.42/2.65 (~r(s(s(s(s(elem!1)))), s(s(elem!1)))),
% 2.42/2.65 inference(unit_resolution,[status(thm)],[7684, 197, 768, 7675, 7635])).
% 2.42/2.65 tff(7686,plain,
% 2.42/2.65 (b(s(s(s(s(elem!1)))), s(s(elem!1)))),
% 2.42/2.65 inference(unit_resolution,[status(thm)],[813, 7685, 734])).
% 2.42/2.65 tff(7687,plain,
% 2.42/2.65 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(elem!1)))), s(s(elem!1)))) | (~b(s(z), s(s(elem!1)))) | (~b(s(s(elem!1)), s(z))) | (~b(s(s(s(s(s(s(s(elem!1))))))), s(s(elem!1)))) | (~b(s(s(s(s(elem!1)))), s(s(s(s(s(s(s(elem!1))))))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(elem!1)))), s(s(elem!1)))) | (~b(s(z), s(s(elem!1)))) | (~b(s(s(elem!1)), s(z))) | (~b(s(s(s(s(s(s(s(elem!1))))))), s(s(elem!1)))) | (~b(s(s(s(s(elem!1)))), s(s(s(s(s(s(s(elem!1))))))))))),
% 2.42/2.65 inference(rewrite,[status(thm)],[])).
% 2.42/2.65 tff(7688,plain,
% 2.42/2.65 (((~b(s(z), s(s(elem!1)))) | (~b(s(s(s(s(elem!1)))), s(s(elem!1)))) | (~b(s(s(elem!1)), s(z))) | (~b(s(s(s(s(s(s(s(elem!1))))))), s(s(elem!1)))) | (~b(s(s(s(s(elem!1)))), s(s(elem!1)))) | (~b(s(s(s(s(elem!1)))), s(s(s(s(s(s(s(elem!1)))))))))) <=> ((~b(s(s(s(s(elem!1)))), s(s(elem!1)))) | (~b(s(z), s(s(elem!1)))) | (~b(s(s(elem!1)), s(z))) | (~b(s(s(s(s(s(s(s(elem!1))))))), s(s(elem!1)))) | (~b(s(s(s(s(elem!1)))), s(s(s(s(s(s(s(elem!1))))))))))),
% 2.42/2.65 inference(rewrite,[status(thm)],[])).
% 2.42/2.65 tff(7689,plain,
% 2.42/2.65 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(elem!1)))) | (~b(s(s(s(s(elem!1)))), s(s(elem!1)))) | (~b(s(s(elem!1)), s(z))) | (~b(s(s(s(s(s(s(s(elem!1))))))), s(s(elem!1)))) | (~b(s(s(s(s(elem!1)))), s(s(elem!1)))) | (~b(s(s(s(s(elem!1)))), s(s(s(s(s(s(s(elem!1))))))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(elem!1)))), s(s(elem!1)))) | (~b(s(z), s(s(elem!1)))) | (~b(s(s(elem!1)), s(z))) | (~b(s(s(s(s(s(s(s(elem!1))))))), s(s(elem!1)))) | (~b(s(s(s(s(elem!1)))), s(s(s(s(s(s(s(elem!1)))))))))))),
% 2.42/2.65 inference(monotonicity,[status(thm)],[7688])).
% 2.42/2.65 tff(7690,plain,
% 2.42/2.65 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(elem!1)))) | (~b(s(s(s(s(elem!1)))), s(s(elem!1)))) | (~b(s(s(elem!1)), s(z))) | (~b(s(s(s(s(s(s(s(elem!1))))))), s(s(elem!1)))) | (~b(s(s(s(s(elem!1)))), s(s(elem!1)))) | (~b(s(s(s(s(elem!1)))), s(s(s(s(s(s(s(elem!1))))))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(elem!1)))), s(s(elem!1)))) | (~b(s(z), s(s(elem!1)))) | (~b(s(s(elem!1)), s(z))) | (~b(s(s(s(s(s(s(s(elem!1))))))), s(s(elem!1)))) | (~b(s(s(s(s(elem!1)))), s(s(s(s(s(s(s(elem!1))))))))))),
% 2.42/2.65 inference(transitivity,[status(thm)],[7689, 7687])).
% 2.42/2.65 tff(7691,plain,
% 2.42/2.65 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(elem!1)))) | (~b(s(s(s(s(elem!1)))), s(s(elem!1)))) | (~b(s(s(elem!1)), s(z))) | (~b(s(s(s(s(s(s(s(elem!1))))))), s(s(elem!1)))) | (~b(s(s(s(s(elem!1)))), s(s(elem!1)))) | (~b(s(s(s(s(elem!1)))), s(s(s(s(s(s(s(elem!1))))))))))),
% 2.42/2.65 inference(quant_inst,[status(thm)],[])).
% 2.42/2.65 tff(7692,plain,
% 2.42/2.65 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(elem!1)))), s(s(elem!1)))) | (~b(s(z), s(s(elem!1)))) | (~b(s(s(elem!1)), s(z))) | (~b(s(s(s(s(s(s(s(elem!1))))))), s(s(elem!1)))) | (~b(s(s(s(s(elem!1)))), s(s(s(s(s(s(s(elem!1)))))))))),
% 2.42/2.65 inference(modus_ponens,[status(thm)],[7691, 7690])).
% 2.42/2.65 tff(7693,plain,
% 2.42/2.65 ($false),
% 2.42/2.65 inference(unit_resolution,[status(thm)],[7692, 166, 376, 310, 7686, 7678, 7674])).
% 2.42/2.65 tff(7694,plain,((~b(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~b(s(z), s(s(elem!1)))) | (~b(s(s(elem!1)), s(z))) | (~(s(s(z)) = s(s(elem!1)))) | (~r(s(s(elem!1)), elem!1)) | (~r(s(s(s(elem!1))), s(z))) | (~b(elem!1, s(z))) | (~b(s(z), elem!1)) | (~b(elem!1, s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), elem!1)) | (~r(elem!1, s(s(z)))) | b(s(s(s(s(elem!1)))), elem!1)), inference(lemma,lemma(discharge,[]))).
% 2.42/2.65 tff(7695,plain,
% 2.42/2.65 (~b(s(s(s(s(elem!1)))), s(s(s(elem!1))))),
% 2.42/2.65 inference(unit_resolution,[status(thm)],[7694, 637, 310, 34, 7612, 350, 5417, 376, 7626, 2157, 6194, 7627])).
% 2.42/2.65 tff(7696,plain,
% 2.42/2.65 (r(s(s(s(s(elem!1)))), s(s(s(elem!1))))),
% 2.42/2.65 inference(unit_resolution,[status(thm)],[1065, 7695, 1038])).
% 2.42/2.65 tff(7697,plain,
% 2.42/2.65 (~r(s(s(s(s(elem!1)))), s(z))),
% 2.42/2.65 inference(unit_resolution,[status(thm)],[6235, 197, 350, 7371, 7696])).
% 2.42/2.65 tff(7698,plain,
% 2.42/2.65 (b(s(s(s(s(elem!1)))), s(z))),
% 2.42/2.65 inference(unit_resolution,[status(thm)],[661, 7697])).
% 2.42/2.65 tff(7699,plain,
% 2.42/2.65 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), s(z))) | (~r(s(s(elem!1)), s(s(s(elem!1))))) | (~r(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~r(s(s(elem!1)), s(s(s(s(elem!1)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(elem!1))), s(z))) | (~r(s(s(elem!1)), s(s(s(elem!1))))) | (~r(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~r(s(s(elem!1)), s(s(s(s(elem!1)))))))),
% 2.42/2.66 inference(rewrite,[status(thm)],[])).
% 2.42/2.66 tff(7700,plain,
% 2.42/2.66 (((~r(s(s(s(elem!1))), s(z))) | (~r(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(elem!1))))))) <=> ((~r(s(s(s(elem!1))), s(z))) | (~r(s(s(elem!1)), s(s(s(elem!1))))) | (~r(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~r(s(s(elem!1)), s(s(s(s(elem!1)))))))),
% 2.42/2.66 inference(rewrite,[status(thm)],[])).
% 2.42/2.66 tff(7701,plain,
% 2.42/2.66 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), s(z))) | (~r(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(elem!1)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), s(z))) | (~r(s(s(elem!1)), s(s(s(elem!1))))) | (~r(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~r(s(s(elem!1)), s(s(s(s(elem!1))))))))),
% 2.42/2.66 inference(monotonicity,[status(thm)],[7700])).
% 2.42/2.66 tff(7702,plain,
% 2.42/2.66 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), s(z))) | (~r(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(elem!1)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(elem!1))), s(z))) | (~r(s(s(elem!1)), s(s(s(elem!1))))) | (~r(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~r(s(s(elem!1)), s(s(s(s(elem!1)))))))),
% 2.42/2.66 inference(transitivity,[status(thm)],[7701, 7699])).
% 2.42/2.66 tff(7703,plain,
% 2.42/2.66 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), s(z))) | (~r(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(elem!1)))))))),
% 2.42/2.66 inference(quant_inst,[status(thm)],[])).
% 2.42/2.66 tff(7704,plain,
% 2.42/2.66 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(elem!1))), s(z))) | (~r(s(s(elem!1)), s(s(s(elem!1))))) | (~r(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~r(s(s(elem!1)), s(s(s(s(elem!1))))))),
% 2.42/2.66 inference(modus_ponens,[status(thm)],[7703, 7702])).
% 2.42/2.66 tff(7705,plain,
% 2.42/2.66 (~r(s(s(elem!1)), s(s(s(s(elem!1)))))),
% 2.42/2.66 inference(unit_resolution,[status(thm)],[7704, 197, 350, 377, 7696])).
% 2.42/2.66 tff(7706,plain,
% 2.42/2.66 (b(s(s(elem!1)), s(s(s(s(elem!1)))))),
% 2.42/2.66 inference(unit_resolution,[status(thm)],[827, 7705, 816])).
% 2.42/2.66 tff(7707,plain,
% 2.42/2.66 ($false),
% 2.42/2.66 inference(unit_resolution,[status(thm)],[822, 166, 376, 310, 7706, 7698])).
% 2.42/2.66 tff(7708,plain,((~b(s(z), z)) | (~b(s(z), s(s(elem!1)))) | (~b(s(s(elem!1)), s(z))) | (~r(s(s(s(elem!1))), s(z))) | (~r(s(s(elem!1)), s(s(s(elem!1))))) | (~(s(s(z)) = s(s(elem!1)))) | (~r(elem!1, s(s(z)))) | (s(s(s(elem!1))) = s(s(s(s(elem!1))))) | (~b(z, s(z))) | (~b(s(s(s(elem!1))), z))), inference(lemma,lemma(discharge,[]))).
% 2.42/2.66 tff(7709,plain,
% 2.42/2.66 (~b(s(z), z)),
% 2.42/2.66 inference(unit_resolution,[status(thm)],[7708, 377, 310, 350, 376, 34, 6194, 361, 118, 121])).
% 2.42/2.66 tff(7710,plain,
% 2.42/2.66 (r(s(z), z)),
% 2.42/2.66 inference(unit_resolution,[status(thm)],[230, 7709])).
% 2.42/2.66 tff(7711,plain,
% 2.42/2.66 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(z)), z)) | (~r(z, s(s(z)))) | (~r(s(s(s(s(z)))), z)) | (~r(s(s(z)), s(s(s(s(z)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(z)), z)) | (~r(z, s(s(z)))) | (~r(s(s(s(s(z)))), z)) | (~r(s(s(z)), s(s(s(s(z)))))))),
% 2.42/2.66 inference(rewrite,[status(thm)],[])).
% 2.42/2.66 tff(7712,plain,
% 2.42/2.66 (((~r(z, s(s(z)))) | (~r(s(s(s(s(z)))), z)) | (~r(s(s(z)), z)) | (~r(s(s(z)), s(s(s(s(z))))))) <=> ((~r(s(s(z)), z)) | (~r(z, s(s(z)))) | (~r(s(s(s(s(z)))), z)) | (~r(s(s(z)), s(s(s(s(z)))))))),
% 2.42/2.66 inference(rewrite,[status(thm)],[])).
% 2.42/2.66 tff(7713,plain,
% 2.42/2.66 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(z)))) | (~r(s(s(s(s(z)))), z)) | (~r(s(s(z)), z)) | (~r(s(s(z)), s(s(s(s(z)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(z)), z)) | (~r(z, s(s(z)))) | (~r(s(s(s(s(z)))), z)) | (~r(s(s(z)), s(s(s(s(z))))))))),
% 2.42/2.66 inference(monotonicity,[status(thm)],[7712])).
% 2.42/2.66 tff(7714,plain,
% 2.42/2.66 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(z)))) | (~r(s(s(s(s(z)))), z)) | (~r(s(s(z)), z)) | (~r(s(s(z)), s(s(s(s(z)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(z)), z)) | (~r(z, s(s(z)))) | (~r(s(s(s(s(z)))), z)) | (~r(s(s(z)), s(s(s(s(z)))))))),
% 2.42/2.66 inference(transitivity,[status(thm)],[7713, 7711])).
% 2.42/2.66 tff(7715,plain,
% 2.42/2.66 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(z)))) | (~r(s(s(s(s(z)))), z)) | (~r(s(s(z)), z)) | (~r(s(s(z)), s(s(s(s(z)))))))),
% 2.42/2.66 inference(quant_inst,[status(thm)],[])).
% 2.42/2.66 tff(7716,plain,
% 2.42/2.66 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(z)), z)) | (~r(z, s(s(z)))) | (~r(s(s(s(s(z)))), z)) | (~r(s(s(z)), s(s(s(s(z))))))),
% 2.42/2.66 inference(modus_ponens,[status(thm)],[7715, 7714])).
% 2.42/2.66 tff(7717,plain,
% 2.42/2.66 (~r(s(s(z)), s(s(s(s(z)))))),
% 2.42/2.66 inference(unit_resolution,[status(thm)],[7716, 197, 155, 866, 4679])).
% 2.42/2.66 tff(7718,plain,
% 2.42/2.66 (b(s(s(z)), s(s(s(s(z)))))),
% 2.42/2.66 inference(unit_resolution,[status(thm)],[4752, 7717, 4748])).
% 2.42/2.66 tff(7719,plain,
% 2.42/2.66 (~r(s(s(s(s(z)))), s(z))),
% 2.42/2.66 inference(unit_resolution,[status(thm)],[3273, 197, 155, 97, 4679])).
% 2.42/2.66 tff(7720,plain,
% 2.42/2.66 (b(s(s(s(s(z)))), s(z))),
% 2.42/2.66 inference(unit_resolution,[status(thm)],[3285, 7719])).
% 2.42/2.66 tff(7721,plain,
% 2.42/2.66 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(z)))) | (~b(s(s(z)), s(z))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(z)), s(s(s(s(z)))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), s(s(z)))) | (~b(s(s(z)), s(z))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(z)), s(s(s(s(z)))))))),
% 2.42/2.66 inference(rewrite,[status(thm)],[])).
% 2.42/2.66 tff(7722,plain,
% 2.42/2.66 (((~b(s(s(z)), s(z))) | (~b(s(s(z)), s(z))) | (~b(s(z), s(s(z)))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(z)), s(z))) | (~b(s(s(z)), s(s(s(s(z))))))) <=> ((~b(s(z), s(s(z)))) | (~b(s(s(z)), s(z))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(z)), s(s(s(s(z)))))))),
% 2.42/2.66 inference(rewrite,[status(thm)],[])).
% 2.42/2.66 tff(7723,plain,
% 2.42/2.66 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), s(z))) | (~b(s(s(z)), s(z))) | (~b(s(z), s(s(z)))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(z)), s(z))) | (~b(s(s(z)), s(s(s(s(z)))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(z)))) | (~b(s(s(z)), s(z))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(z)), s(s(s(s(z))))))))),
% 2.42/2.66 inference(monotonicity,[status(thm)],[7722])).
% 2.42/2.66 tff(7724,plain,
% 2.42/2.66 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), s(z))) | (~b(s(s(z)), s(z))) | (~b(s(z), s(s(z)))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(z)), s(z))) | (~b(s(s(z)), s(s(s(s(z)))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), s(s(z)))) | (~b(s(s(z)), s(z))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(z)), s(s(s(s(z)))))))),
% 2.42/2.66 inference(transitivity,[status(thm)],[7723, 7721])).
% 2.42/2.66 tff(7725,plain,
% 2.42/2.66 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), s(z))) | (~b(s(s(z)), s(z))) | (~b(s(z), s(s(z)))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(z)), s(z))) | (~b(s(s(z)), s(s(s(s(z)))))))),
% 2.42/2.66 inference(quant_inst,[status(thm)],[])).
% 2.42/2.66 tff(7726,plain,
% 2.42/2.66 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), s(s(z)))) | (~b(s(s(z)), s(z))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(z)), s(s(s(s(z))))))),
% 2.42/2.66 inference(modus_ponens,[status(thm)],[7725, 7724])).
% 2.42/2.66 tff(7727,plain,
% 2.42/2.66 ($false),
% 2.42/2.66 inference(unit_resolution,[status(thm)],[7726, 166, 556, 156, 7720, 7718])).
% 2.42/2.66 tff(7728,plain,((~r(s(s(s(s(z)))), z)) | (~b(s(z), s(s(z)))) | (~b(s(s(z)), s(z))) | (~r(z, s(s(z)))) | (~r(s(s(z)), z)) | (~r(s(z), z))), inference(lemma,lemma(discharge,[]))).
% 2.42/2.66 tff(7729,plain,
% 2.42/2.66 (~r(s(s(s(s(z)))), z)),
% 2.42/2.66 inference(unit_resolution,[status(thm)],[7728, 7710, 155, 7609, 7607, 5436])).
% 2.42/2.66 tff(7730,plain,
% 2.42/2.66 (b(s(s(s(s(z)))), z)),
% 2.42/2.66 inference(unit_resolution,[status(thm)],[3266, 7729])).
% 2.42/2.66 tff(7731,plain,
% 2.42/2.66 (b(s(s(s(s(elem!1)))), elem!1)),
% 2.42/2.66 inference(modus_ponens,[status(thm)],[7730, 4731])).
% 2.42/2.66 tff(7732,plain,
% 2.42/2.66 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(s(s(s(elem!1)))), elem!1)) | (~b(s(s(s(s(elem!1)))), s(s(s(elem!1))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(s(s(s(elem!1)))), elem!1)) | (~b(s(s(s(s(elem!1)))), s(s(s(elem!1))))))),
% 2.42/2.66 inference(rewrite,[status(thm)],[])).
% 2.42/2.66 tff(7733,plain,
% 2.42/2.66 (((~b(s(s(s(elem!1))), elem!1)) | (~b(s(s(s(s(elem!1)))), elem!1)) | (~b(elem!1, s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(s(s(s(elem!1)))), elem!1)) | (~b(s(s(s(s(elem!1)))), s(s(s(elem!1)))))) <=> ((~b(elem!1, s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(s(s(s(elem!1)))), elem!1)) | (~b(s(s(s(s(elem!1)))), s(s(s(elem!1))))))),
% 2.42/2.66 inference(rewrite,[status(thm)],[])).
% 2.42/2.66 tff(7734,plain,
% 2.42/2.66 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), elem!1)) | (~b(s(s(s(s(elem!1)))), elem!1)) | (~b(elem!1, s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(s(s(s(elem!1)))), elem!1)) | (~b(s(s(s(s(elem!1)))), s(s(s(elem!1))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(s(s(s(elem!1)))), elem!1)) | (~b(s(s(s(s(elem!1)))), s(s(s(elem!1)))))))),
% 2.42/2.66 inference(monotonicity,[status(thm)],[7733])).
% 2.42/2.66 tff(7735,plain,
% 2.42/2.66 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), elem!1)) | (~b(s(s(s(s(elem!1)))), elem!1)) | (~b(elem!1, s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(s(s(s(elem!1)))), elem!1)) | (~b(s(s(s(s(elem!1)))), s(s(s(elem!1))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(s(s(s(elem!1)))), elem!1)) | (~b(s(s(s(s(elem!1)))), s(s(s(elem!1))))))),
% 2.42/2.66 inference(transitivity,[status(thm)],[7734, 7732])).
% 2.42/2.66 tff(7736,plain,
% 2.42/2.66 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), elem!1)) | (~b(s(s(s(s(elem!1)))), elem!1)) | (~b(elem!1, s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(s(s(s(elem!1)))), elem!1)) | (~b(s(s(s(s(elem!1)))), s(s(s(elem!1))))))),
% 2.42/2.66 inference(quant_inst,[status(thm)],[])).
% 2.42/2.66 tff(7737,plain,
% 2.42/2.66 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(s(s(s(elem!1)))), elem!1)) | (~b(s(s(s(s(elem!1)))), s(s(s(elem!1)))))),
% 2.42/2.66 inference(modus_ponens,[status(thm)],[7736, 7735])).
% 2.42/2.66 tff(7738,plain,
% 2.42/2.66 (~b(s(s(s(s(elem!1)))), s(s(s(elem!1))))),
% 2.42/2.66 inference(unit_resolution,[status(thm)],[7737, 166, 7626, 2157, 7731])).
% 2.42/2.66 tff(7739,plain,
% 2.42/2.66 (r(s(s(s(s(elem!1)))), s(s(s(elem!1))))),
% 2.42/2.66 inference(unit_resolution,[status(thm)],[1065, 7738, 1038])).
% 2.42/2.66 tff(7740,plain,
% 2.42/2.66 (r(s(s(s(elem!1))), s(s(s(s(elem!1))))) <=> r(s(s(s(elem!1))), s(s(s(s(z)))))),
% 2.42/2.66 inference(monotonicity,[status(thm)],[2370])).
% 2.42/2.66 tff(7741,plain,
% 2.42/2.66 (r(s(s(s(elem!1))), s(s(s(s(z))))) <=> r(s(s(s(elem!1))), s(s(s(s(elem!1)))))),
% 2.42/2.66 inference(symmetry,[status(thm)],[7740])).
% 2.42/2.66 tff(7742,plain,
% 2.42/2.66 (r(s(s(s(z))), s(s(s(s(z))))) <=> r(s(s(s(elem!1))), s(s(s(s(z)))))),
% 2.42/2.66 inference(monotonicity,[status(thm)],[1086])).
% 2.42/2.66 tff(7743,plain,
% 2.42/2.66 (r(s(s(s(z))), s(s(s(s(z))))) <=> r(s(s(s(elem!1))), s(s(s(s(elem!1)))))),
% 2.42/2.66 inference(transitivity,[status(thm)],[7742, 7741])).
% 2.42/2.66 tff(7744,plain,
% 2.42/2.66 (r(s(s(s(elem!1))), s(z)) <=> r(s(s(s(elem!1))), s(elem!1))),
% 2.42/2.66 inference(monotonicity,[status(thm)],[13])).
% 2.42/2.66 tff(7745,plain,
% 2.42/2.66 (r(s(s(s(elem!1))), s(elem!1))),
% 2.42/2.66 inference(modus_ponens,[status(thm)],[350, 7744])).
% 2.42/2.66 tff(7746,plain,
% 2.42/2.66 ((z = s(s(s(elem!1)))) <=> (s(s(s(elem!1))) = z)),
% 2.42/2.66 inference(commutativity,[status(thm)],[])).
% 2.42/2.66 tff(7747,plain,
% 2.42/2.66 ((elem!1 = s(s(s(elem!1)))) <=> (z = s(s(s(elem!1))))),
% 2.42/2.66 inference(monotonicity,[status(thm)],[4891])).
% 2.42/2.66 tff(7748,plain,
% 2.42/2.66 ((elem!1 = s(s(s(elem!1)))) <=> (s(s(s(elem!1))) = z)),
% 2.42/2.66 inference(transitivity,[status(thm)],[7747, 7746])).
% 2.42/2.66 tff(7749,plain,
% 2.42/2.66 ((s(s(s(elem!1))) = z) <=> (elem!1 = s(s(s(elem!1))))),
% 2.42/2.66 inference(symmetry,[status(thm)],[7748])).
% 2.42/2.66 tff(7750,plain,
% 2.42/2.66 ((~(s(s(s(elem!1))) = z)) <=> (~(elem!1 = s(s(s(elem!1)))))),
% 2.42/2.66 inference(monotonicity,[status(thm)],[7749])).
% 2.42/2.66 tff(7751,plain,
% 2.42/2.66 (~(elem!1 = s(s(s(elem!1))))),
% 2.42/2.66 inference(modus_ponens,[status(thm)],[89, 7750])).
% 2.42/2.66 tff(7752,plain,
% 2.42/2.66 (b(z, s(s(s(elem!1)))) <=> b(elem!1, s(s(s(elem!1))))),
% 2.42/2.66 inference(monotonicity,[status(thm)],[12])).
% 2.42/2.66 tff(7753,plain,
% 2.42/2.66 ((~b(z, s(s(s(elem!1))))) <=> (~b(elem!1, s(s(s(elem!1)))))),
% 2.42/2.66 inference(monotonicity,[status(thm)],[7752])).
% 2.42/2.66 tff(7754,plain,
% 2.42/2.66 (~b(elem!1, s(s(s(elem!1))))),
% 2.42/2.66 inference(modus_ponens,[status(thm)],[256, 7753])).
% 2.42/2.66 tff(7755,plain,
% 2.42/2.66 (r(elem!1, s(s(s(elem!1))))),
% 2.42/2.66 inference(unit_resolution,[status(thm)],[5451, 7754, 7751])).
% 2.42/2.66 tff(7756,plain,
% 2.42/2.66 ($false),
% 2.42/2.66 inference(unit_resolution,[status(thm)],[7624, 7755, 7745, 768, 377])).
% 2.42/2.66 tff(7757,plain,((~(z = elem!1)) | (~r(s(s(elem!1)), elem!1)) | (~r(s(s(elem!1)), s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), s(z))) | b(z, s(s(s(elem!1))))), inference(lemma,lemma(discharge,[]))).
% 2.42/2.66 tff(7758,plain,
% 2.42/2.66 (b(z, s(s(s(elem!1))))),
% 2.42/2.66 inference(unit_resolution,[status(thm)],[7757, 377, 620, 350, 7612])).
% 2.42/2.66 tff(7759,plain,
% 2.42/2.66 (b(s(s(s(z))), z) <=> b(s(s(s(z))), elem!1)),
% 2.42/2.66 inference(monotonicity,[status(thm)],[620])).
% 2.42/2.66 tff(7760,plain,
% 2.42/2.66 (b(s(s(s(z))), elem!1) <=> b(s(s(s(z))), z)),
% 2.42/2.66 inference(symmetry,[status(thm)],[7759])).
% 2.42/2.66 tff(7761,plain,
% 2.42/2.66 (b(s(s(s(z))), elem!1) <=> b(s(s(s(elem!1))), elem!1)),
% 2.42/2.66 inference(monotonicity,[status(thm)],[1086])).
% 2.42/2.66 tff(7762,plain,
% 2.42/2.66 (b(s(s(s(elem!1))), elem!1) <=> b(s(s(s(z))), elem!1)),
% 2.42/2.66 inference(symmetry,[status(thm)],[7761])).
% 2.42/2.66 tff(7763,plain,
% 2.42/2.66 (b(s(s(s(elem!1))), elem!1) <=> b(s(s(s(z))), z)),
% 2.42/2.66 inference(transitivity,[status(thm)],[7762, 7760])).
% 2.42/2.66 tff(7764,plain,
% 2.42/2.66 (b(s(s(s(z))), z)),
% 2.42/2.66 inference(modus_ponens,[status(thm)],[2157, 7763])).
% 2.42/2.66 tff(7765,plain,
% 2.42/2.66 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), z)) | (~b(s(s(s(z))), z)) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), z)) | (~b(s(s(s(z))), z)) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), z)))),
% 2.42/2.66 inference(rewrite,[status(thm)],[])).
% 2.42/2.66 tff(7766,plain,
% 2.42/2.66 (((~b(s(s(s(elem!1))), z)) | (~b(s(s(s(z))), z)) | (~b(z, s(s(s(elem!1))))) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(z))), z)) | (~b(s(s(s(z))), s(s(s(s(z))))))) <=> ((~b(z, s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), z)) | (~b(s(s(s(z))), z)) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), z)))),
% 2.42/2.66 inference(rewrite,[status(thm)],[])).
% 2.42/2.66 tff(7767,plain,
% 2.42/2.66 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), z)) | (~b(s(s(s(z))), z)) | (~b(z, s(s(s(elem!1))))) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(z))), z)) | (~b(s(s(s(z))), s(s(s(s(z)))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), z)) | (~b(s(s(s(z))), z)) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), z))))),
% 2.42/2.66 inference(monotonicity,[status(thm)],[7766])).
% 2.42/2.66 tff(7768,plain,
% 2.42/2.66 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), z)) | (~b(s(s(s(z))), z)) | (~b(z, s(s(s(elem!1))))) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(z))), z)) | (~b(s(s(s(z))), s(s(s(s(z)))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), z)) | (~b(s(s(s(z))), z)) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), z)))),
% 2.42/2.66 inference(transitivity,[status(thm)],[7767, 7765])).
% 2.42/2.66 tff(7769,plain,
% 2.42/2.66 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), z)) | (~b(s(s(s(z))), z)) | (~b(z, s(s(s(elem!1))))) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(z))), z)) | (~b(s(s(s(z))), s(s(s(s(z)))))))),
% 2.42/2.66 inference(quant_inst,[status(thm)],[])).
% 2.42/2.66 tff(7770,plain,
% 2.42/2.66 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), z)) | (~b(s(s(s(z))), z)) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), z))),
% 2.42/2.66 inference(modus_ponens,[status(thm)],[7769, 7768])).
% 2.42/2.66 tff(7771,plain,
% 2.42/2.66 ($false),
% 2.42/2.66 inference(unit_resolution,[status(thm)],[7770, 166, 240, 121, 1699, 3252, 3253])).
% 2.42/2.66 tff(7772,plain,((~b(s(s(s(s(z)))), z)) | (~b(z, s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), z)) | (~b(s(s(s(z))), z)) | (~b(s(s(s(z))), s(s(s(s(z))))))), inference(lemma,lemma(discharge,[]))).
% 2.42/2.66 tff(7773,plain,
% 2.42/2.66 (~b(s(s(s(z))), s(s(s(s(z)))))),
% 2.42/2.66 inference(unit_resolution,[status(thm)],[7772, 7730, 121, 7764, 7758])).
% 2.42/2.66 tff(7774,plain,
% 2.42/2.66 (r(s(s(s(z))), s(s(s(s(z)))))),
% 2.42/2.66 inference(unit_resolution,[status(thm)],[2233, 7773])).
% 2.42/2.66 tff(7775,plain,
% 2.42/2.66 (r(s(s(s(elem!1))), s(s(s(s(elem!1)))))),
% 2.42/2.66 inference(modus_ponens,[status(thm)],[7774, 7743])).
% 2.42/2.66 tff(7776,plain,
% 2.42/2.66 (~r(s(s(s(s(elem!1)))), s(s(elem!1)))),
% 2.42/2.66 inference(unit_resolution,[status(thm)],[2917, 197, 350, 377, 7739])).
% 2.42/2.66 tff(7777,plain,
% 2.42/2.66 (b(s(s(s(s(elem!1)))), s(s(elem!1)))),
% 2.42/2.66 inference(unit_resolution,[status(thm)],[813, 7776, 734])).
% 2.42/2.66 tff(7778,plain,
% 2.42/2.66 (~r(s(s(elem!1)), s(s(s(s(elem!1)))))),
% 2.42/2.66 inference(unit_resolution,[status(thm)],[7704, 197, 350, 377, 7739])).
% 2.42/2.66 tff(7779,plain,
% 2.42/2.66 (b(s(s(elem!1)), s(s(s(s(elem!1)))))),
% 2.42/2.66 inference(unit_resolution,[status(thm)],[827, 7778, 816])).
% 2.42/2.66 tff(7780,plain,
% 2.42/2.66 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(elem!1)))), s(s(elem!1)))) | (~b(s(z), s(s(elem!1)))) | (~b(s(s(elem!1)), s(s(s(s(elem!1)))))) | (~b(s(z), s(s(s(s(elem!1)))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(elem!1)))), s(s(elem!1)))) | (~b(s(z), s(s(elem!1)))) | (~b(s(s(elem!1)), s(s(s(s(elem!1)))))) | (~b(s(z), s(s(s(s(elem!1)))))))),
% 2.42/2.67 inference(rewrite,[status(thm)],[])).
% 2.42/2.67 tff(7781,plain,
% 2.42/2.67 (((~b(s(s(s(s(elem!1)))), s(s(elem!1)))) | (~b(s(z), s(s(elem!1)))) | (~b(s(s(elem!1)), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), s(s(elem!1)))) | (~b(s(z), s(s(elem!1)))) | (~b(s(z), s(s(s(s(elem!1))))))) <=> ((~b(s(s(s(s(elem!1)))), s(s(elem!1)))) | (~b(s(z), s(s(elem!1)))) | (~b(s(s(elem!1)), s(s(s(s(elem!1)))))) | (~b(s(z), s(s(s(s(elem!1)))))))),
% 2.42/2.67 inference(rewrite,[status(thm)],[])).
% 2.42/2.67 tff(7782,plain,
% 2.42/2.67 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(elem!1)))), s(s(elem!1)))) | (~b(s(z), s(s(elem!1)))) | (~b(s(s(elem!1)), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), s(s(elem!1)))) | (~b(s(z), s(s(elem!1)))) | (~b(s(z), s(s(s(s(elem!1)))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(elem!1)))), s(s(elem!1)))) | (~b(s(z), s(s(elem!1)))) | (~b(s(s(elem!1)), s(s(s(s(elem!1)))))) | (~b(s(z), s(s(s(s(elem!1))))))))),
% 2.42/2.67 inference(monotonicity,[status(thm)],[7781])).
% 2.42/2.67 tff(7783,plain,
% 2.42/2.67 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(elem!1)))), s(s(elem!1)))) | (~b(s(z), s(s(elem!1)))) | (~b(s(s(elem!1)), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), s(s(elem!1)))) | (~b(s(z), s(s(elem!1)))) | (~b(s(z), s(s(s(s(elem!1)))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(elem!1)))), s(s(elem!1)))) | (~b(s(z), s(s(elem!1)))) | (~b(s(s(elem!1)), s(s(s(s(elem!1)))))) | (~b(s(z), s(s(s(s(elem!1)))))))),
% 2.42/2.67 inference(transitivity,[status(thm)],[7782, 7780])).
% 2.42/2.67 tff(7784,plain,
% 2.42/2.67 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(elem!1)))), s(s(elem!1)))) | (~b(s(z), s(s(elem!1)))) | (~b(s(s(elem!1)), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), s(s(elem!1)))) | (~b(s(z), s(s(elem!1)))) | (~b(s(z), s(s(s(s(elem!1)))))))),
% 2.42/2.67 inference(quant_inst,[status(thm)],[])).
% 2.42/2.67 tff(7785,plain,
% 2.42/2.67 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(elem!1)))), s(s(elem!1)))) | (~b(s(z), s(s(elem!1)))) | (~b(s(s(elem!1)), s(s(s(s(elem!1)))))) | (~b(s(z), s(s(s(s(elem!1))))))),
% 2.42/2.67 inference(modus_ponens,[status(thm)],[7784, 7783])).
% 2.42/2.67 tff(7786,plain,
% 2.42/2.67 (~b(s(z), s(s(s(s(elem!1)))))),
% 2.42/2.67 inference(unit_resolution,[status(thm)],[7785, 166, 376, 7779, 7777])).
% 2.42/2.67 tff(7787,plain,
% 2.42/2.67 (r(s(z), s(s(s(s(elem!1)))))),
% 2.42/2.67 inference(unit_resolution,[status(thm)],[681, 7786])).
% 2.42/2.67 tff(7788,plain,
% 2.42/2.67 (~r(s(z), s(s(s(elem!1))))),
% 2.42/2.67 inference(unit_resolution,[status(thm)],[2125, 7787, 7775, 7739])).
% 2.42/2.67 tff(7789,plain,
% 2.42/2.67 (b(s(z), s(s(s(elem!1))))),
% 2.42/2.67 inference(unit_resolution,[status(thm)],[116, 7788])).
% 2.42/2.67 tff(7790,plain,
% 2.42/2.67 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(z))) | (~b(s(z), s(s(s(elem!1))))) | (~b(elem!1, s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), elem!1)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(z))) | (~b(s(z), s(s(s(elem!1))))) | (~b(elem!1, s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), elem!1)))),
% 2.42/2.67 inference(rewrite,[status(thm)],[])).
% 2.42/2.67 tff(7791,plain,
% 2.42/2.67 (((~b(elem!1, s(s(s(elem!1))))) | (~b(elem!1, s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(z), s(s(s(elem!1))))) | (~b(elem!1, s(s(s(elem!1))))) | (~b(elem!1, s(z)))) <=> ((~b(elem!1, s(z))) | (~b(s(z), s(s(s(elem!1))))) | (~b(elem!1, s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), elem!1)))),
% 2.42/2.67 inference(rewrite,[status(thm)],[])).
% 2.42/2.67 tff(7792,plain,
% 2.42/2.67 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(s(s(elem!1))))) | (~b(elem!1, s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(z), s(s(s(elem!1))))) | (~b(elem!1, s(s(s(elem!1))))) | (~b(elem!1, s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(z))) | (~b(s(z), s(s(s(elem!1))))) | (~b(elem!1, s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), elem!1))))),
% 2.42/2.67 inference(monotonicity,[status(thm)],[7791])).
% 2.42/2.67 tff(7793,plain,
% 2.42/2.67 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(s(s(elem!1))))) | (~b(elem!1, s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(z), s(s(s(elem!1))))) | (~b(elem!1, s(s(s(elem!1))))) | (~b(elem!1, s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(z))) | (~b(s(z), s(s(s(elem!1))))) | (~b(elem!1, s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), elem!1)))),
% 2.42/2.67 inference(transitivity,[status(thm)],[7792, 7790])).
% 2.42/2.67 tff(7794,plain,
% 2.42/2.67 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(s(s(elem!1))))) | (~b(elem!1, s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(z), s(s(s(elem!1))))) | (~b(elem!1, s(s(s(elem!1))))) | (~b(elem!1, s(z))))),
% 2.42/2.67 inference(quant_inst,[status(thm)],[])).
% 2.42/2.67 tff(7795,plain,
% 2.42/2.67 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(z))) | (~b(s(z), s(s(s(elem!1))))) | (~b(elem!1, s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), elem!1))),
% 2.42/2.67 inference(modus_ponens,[status(thm)],[7794, 7793])).
% 2.42/2.67 tff(7796,plain,
% 2.42/2.67 ($false),
% 2.42/2.67 inference(unit_resolution,[status(thm)],[7795, 166, 7626, 7789, 5417, 2157])).
% 2.42/2.67 tff(7797,plain,((~r(s(s(elem!1)), s(s(s(elem!1))))) | (~b(s(z), s(s(elem!1)))) | (~r(s(s(s(elem!1))), s(z))) | (~(s(s(z)) = s(s(elem!1)))) | (~b(s(s(s(elem!1))), z)) | (~r(z, s(s(z)))) | (~b(s(s(elem!1)), s(z))) | (~r(elem!1, s(s(z)))) | (s(s(s(elem!1))) = s(s(s(s(elem!1))))) | (~b(z, s(z)))), inference(lemma,lemma(discharge,[]))).
% 2.42/2.67 tff(7798,plain,
% 2.42/2.67 (~r(s(s(elem!1)), s(s(s(elem!1))))),
% 2.42/2.67 inference(unit_resolution,[status(thm)],[7797, 310, 7606, 7566, 121, 155, 376, 6194, 358, 118])).
% 2.42/2.67 tff(7799,plain,
% 2.42/2.67 (b(s(s(elem!1)), s(s(s(elem!1))))),
% 2.42/2.67 inference(unit_resolution,[status(thm)],[461, 7798, 45])).
% 2.42/2.67 tff(7800,plain,
% 2.42/2.67 (b(s(z), z) <=> b(s(z), elem!1)),
% 2.42/2.67 inference(monotonicity,[status(thm)],[7568])).
% 2.42/2.67 tff(7801,plain,
% 2.42/2.67 (~b(s(s(z)), z)),
% 2.42/2.67 inference(unit_resolution,[status(thm)],[6740, 7573, 118, 7572])).
% 2.42/2.67 tff(7802,plain,
% 2.42/2.67 (r(s(s(z)), z)),
% 2.42/2.67 inference(unit_resolution,[status(thm)],[186, 7801])).
% 2.42/2.67 tff(7803,plain,
% 2.42/2.67 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(elem!1, s(z))) | (~b(s(z), s(s(s(elem!1))))) | (~b(s(s(elem!1)), s(z))) | (~b(s(s(s(elem!1))), elem!1)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(elem!1, s(z))) | (~b(s(z), s(s(s(elem!1))))) | (~b(s(s(elem!1)), s(z))) | (~b(s(s(s(elem!1))), elem!1)))),
% 2.42/2.67 inference(rewrite,[status(thm)],[])).
% 2.42/2.67 tff(7804,plain,
% 2.42/2.67 (((~b(elem!1, s(z))) | (~b(s(s(elem!1)), s(z))) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(z), s(s(s(elem!1))))) | (~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(s(s(elem!1)), s(z)))) <=> ((~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(elem!1, s(z))) | (~b(s(z), s(s(s(elem!1))))) | (~b(s(s(elem!1)), s(z))) | (~b(s(s(s(elem!1))), elem!1)))),
% 2.42/2.67 inference(rewrite,[status(thm)],[])).
% 2.42/2.67 tff(7805,plain,
% 2.42/2.67 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(z))) | (~b(s(s(elem!1)), s(z))) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(z), s(s(s(elem!1))))) | (~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(s(s(elem!1)), s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(elem!1, s(z))) | (~b(s(z), s(s(s(elem!1))))) | (~b(s(s(elem!1)), s(z))) | (~b(s(s(s(elem!1))), elem!1))))),
% 2.42/2.67 inference(monotonicity,[status(thm)],[7804])).
% 2.42/2.67 tff(7806,plain,
% 2.42/2.67 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(z))) | (~b(s(s(elem!1)), s(z))) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(z), s(s(s(elem!1))))) | (~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(s(s(elem!1)), s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(elem!1, s(z))) | (~b(s(z), s(s(s(elem!1))))) | (~b(s(s(elem!1)), s(z))) | (~b(s(s(s(elem!1))), elem!1)))),
% 2.42/2.67 inference(transitivity,[status(thm)],[7805, 7803])).
% 2.42/2.67 tff(7807,plain,
% 2.42/2.67 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(z))) | (~b(s(s(elem!1)), s(z))) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(z), s(s(s(elem!1))))) | (~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(s(s(elem!1)), s(z))))),
% 2.42/2.67 inference(quant_inst,[status(thm)],[])).
% 2.42/2.67 tff(7808,plain,
% 2.42/2.67 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(elem!1, s(z))) | (~b(s(z), s(s(s(elem!1))))) | (~b(s(s(elem!1)), s(z))) | (~b(s(s(s(elem!1))), elem!1))),
% 2.42/2.67 inference(modus_ponens,[status(thm)],[7807, 7806])).
% 2.42/2.67 tff(7809,plain,
% 2.42/2.67 ($false),
% 2.42/2.67 inference(unit_resolution,[status(thm)],[7808, 166, 463, 241, 1212, 310, 641])).
% 2.42/2.67 tff(7810,plain,((~b(s(z), s(s(s(elem!1))))) | (~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(elem!1, s(z))) | (~b(s(s(elem!1)), s(z))) | (~b(s(s(s(elem!1))), elem!1))), inference(lemma,lemma(discharge,[]))).
% 2.42/2.67 tff(7811,plain,
% 2.42/2.67 (~b(s(z), s(s(s(elem!1))))),
% 2.42/2.67 inference(unit_resolution,[status(thm)],[7810, 7799, 7584, 310, 7582])).
% 2.42/2.67 tff(7812,plain,
% 2.42/2.67 (r(s(z), s(s(s(elem!1))))),
% 2.42/2.67 inference(unit_resolution,[status(thm)],[116, 7811])).
% 2.42/2.67 tff(7813,plain,
% 2.42/2.67 (~r(s(s(s(s(z)))), z)),
% 2.42/2.67 inference(unit_resolution,[status(thm)],[7728, 97, 155, 866, 156, 556])).
% 2.42/2.67 tff(7814,plain,
% 2.42/2.67 (b(s(s(s(s(z)))), z)),
% 2.42/2.67 inference(unit_resolution,[status(thm)],[3266, 7813])).
% 2.42/2.67 tff(7815,plain,
% 2.42/2.67 (b(s(s(s(s(elem!1)))), elem!1)),
% 2.42/2.67 inference(modus_ponens,[status(thm)],[7814, 4731])).
% 2.42/2.67 tff(7816,plain,
% 2.42/2.67 (~r(z, s(s(s(elem!1))))),
% 2.42/2.67 inference(unit_resolution,[status(thm)],[3872, 97, 350, 119])).
% 2.42/2.67 tff(7817,plain,
% 2.42/2.67 (~r(elem!1, s(s(s(elem!1))))),
% 2.42/2.67 inference(unit_resolution,[status(thm)],[5446, 7816, 620])).
% 2.42/2.67 tff(7818,plain,
% 2.42/2.67 (b(elem!1, s(s(s(elem!1))))),
% 2.42/2.67 inference(unit_resolution,[status(thm)],[5451, 7817, 6292])).
% 2.42/2.67 tff(7819,plain,
% 2.42/2.67 (~b(s(s(s(s(elem!1)))), s(s(s(elem!1))))),
% 2.42/2.67 inference(unit_resolution,[status(thm)],[7737, 166, 7818, 2157, 7815])).
% 2.42/2.67 tff(7820,plain,
% 2.42/2.67 (r(s(s(s(s(elem!1)))), s(s(s(elem!1))))),
% 2.42/2.67 inference(unit_resolution,[status(thm)],[1065, 7819, 1058])).
% 2.42/2.67 tff(7821,plain,
% 2.42/2.67 (b(z, s(s(s(elem!1))))),
% 2.42/2.67 inference(unit_resolution,[status(thm)],[261, 7816])).
% 2.42/2.67 tff(7822,plain,
% 2.42/2.67 (~b(s(s(s(z))), s(s(s(s(z)))))),
% 2.42/2.67 inference(unit_resolution,[status(thm)],[7772, 7821, 121, 7764, 7814])).
% 2.42/2.67 tff(7823,plain,
% 2.42/2.67 (r(s(s(s(z))), s(s(s(s(z)))))),
% 2.42/2.67 inference(unit_resolution,[status(thm)],[2233, 7822])).
% 2.42/2.67 tff(7824,plain,
% 2.42/2.67 (r(s(s(s(elem!1))), s(s(s(s(elem!1)))))),
% 2.42/2.67 inference(modus_ponens,[status(thm)],[7823, 7743])).
% 2.42/2.67 tff(7825,plain,
% 2.42/2.67 (~r(s(z), s(s(s(s(elem!1)))))),
% 2.42/2.67 inference(unit_resolution,[status(thm)],[2125, 7820, 119, 7824])).
% 2.42/2.67 tff(7826,plain,
% 2.42/2.67 (b(s(z), s(s(s(s(elem!1)))))),
% 2.42/2.67 inference(unit_resolution,[status(thm)],[681, 7825])).
% 2.42/2.67 tff(7827,plain,
% 2.42/2.67 (((~b(s(s(s(s(elem!1)))), elem!1)) | (~b(s(s(s(s(elem!1)))), elem!1)) | (~b(s(z), s(s(s(s(elem!1)))))) | (~b(elem!1, s(z))) | (~b(s(s(s(s(elem!1)))), s(z))) | (~b(s(s(s(s(elem!1)))), elem!1))) <=> ((~b(elem!1, s(z))) | (~b(s(s(s(s(elem!1)))), elem!1)) | (~b(s(s(s(s(elem!1)))), s(z))) | (~b(s(z), s(s(s(s(elem!1)))))))),
% 2.42/2.67 inference(rewrite,[status(thm)],[])).
% 2.42/2.67 tff(7828,plain,
% 2.42/2.67 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(elem!1)))), elem!1)) | (~b(s(s(s(s(elem!1)))), elem!1)) | (~b(s(z), s(s(s(s(elem!1)))))) | (~b(elem!1, s(z))) | (~b(s(s(s(s(elem!1)))), s(z))) | (~b(s(s(s(s(elem!1)))), elem!1)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(z))) | (~b(s(s(s(s(elem!1)))), elem!1)) | (~b(s(s(s(s(elem!1)))), s(z))) | (~b(s(z), s(s(s(s(elem!1))))))))),
% 2.42/2.67 inference(monotonicity,[status(thm)],[7827])).
% 2.42/2.67 tff(7829,plain,
% 2.42/2.67 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(elem!1)))), elem!1)) | (~b(s(s(s(s(elem!1)))), elem!1)) | (~b(s(z), s(s(s(s(elem!1)))))) | (~b(elem!1, s(z))) | (~b(s(s(s(s(elem!1)))), s(z))) | (~b(s(s(s(s(elem!1)))), elem!1)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(z))) | (~b(s(s(s(s(elem!1)))), elem!1)) | (~b(s(s(s(s(elem!1)))), s(z))) | (~b(s(z), s(s(s(s(elem!1)))))))),
% 2.42/2.67 inference(transitivity,[status(thm)],[7828, 4670])).
% 2.42/2.67 tff(7830,plain,
% 2.42/2.67 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(elem!1)))), elem!1)) | (~b(s(s(s(s(elem!1)))), elem!1)) | (~b(s(z), s(s(s(s(elem!1)))))) | (~b(elem!1, s(z))) | (~b(s(s(s(s(elem!1)))), s(z))) | (~b(s(s(s(s(elem!1)))), elem!1)))),
% 2.42/2.67 inference(quant_inst,[status(thm)],[])).
% 2.42/2.67 tff(7831,plain,
% 2.42/2.67 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(z))) | (~b(s(s(s(s(elem!1)))), elem!1)) | (~b(s(s(s(s(elem!1)))), s(z))) | (~b(s(z), s(s(s(s(elem!1))))))),
% 2.42/2.67 inference(modus_ponens,[status(thm)],[7830, 7829])).
% 2.42/2.67 tff(7832,plain,
% 2.42/2.67 (~b(s(s(s(s(elem!1)))), s(z))),
% 2.42/2.67 inference(unit_resolution,[status(thm)],[7831, 166, 1212, 7826, 7815])).
% 2.42/2.67 tff(7833,plain,
% 2.42/2.67 (r(s(s(s(s(elem!1)))), s(z))),
% 2.42/2.67 inference(unit_resolution,[status(thm)],[661, 7832])).
% 2.42/2.67 tff(7834,plain,
% 2.42/2.67 ($false),
% 2.42/2.67 inference(unit_resolution,[status(thm)],[6235, 197, 350, 7833, 119, 7820])).
% 2.42/2.67 tff(7835,plain,((~r(s(z), z)) | (~r(s(s(s(elem!1))), s(z))) | (~r(s(z), s(s(s(elem!1))))) | (~b(elem!1, s(z))) | (s(s(s(s(elem!1)))) = s(s(s(elem!1)))) | (~(s(s(z)) = s(s(elem!1)))) | (~b(s(s(s(elem!1))), z)) | (~r(z, s(s(z)))) | (~r(s(s(z)), z)) | (~b(s(s(z)), s(z))) | (~b(s(z), s(s(z))))), inference(lemma,lemma(discharge,[]))).
% 2.42/2.67 tff(7836,plain,
% 2.42/2.67 (~r(s(z), z)),
% 2.42/2.67 inference(unit_resolution,[status(thm)],[7835, 7812, 7606, 7584, 364, 7566, 121, 155, 7802, 7573, 7572])).
% 2.42/2.67 tff(7837,plain,
% 2.42/2.67 (b(s(z), z)),
% 2.42/2.67 inference(unit_resolution,[status(thm)],[230, 7836])).
% 2.42/2.67 tff(7838,plain,
% 2.42/2.67 (b(s(z), elem!1)),
% 2.42/2.67 inference(modus_ponens,[status(thm)],[7837, 7800])).
% 2.42/2.67 tff(7839,plain,
% 2.42/2.67 (~b(s(z), s(s(s(elem!1))))),
% 2.42/2.67 inference(unit_resolution,[status(thm)],[7810, 463, 1212, 310, 641])).
% 2.42/2.67 tff(7840,plain,
% 2.42/2.67 (r(s(z), s(s(s(elem!1))))),
% 2.42/2.67 inference(unit_resolution,[status(thm)],[116, 7839])).
% 2.42/2.67 tff(7841,plain,
% 2.42/2.67 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(s(elem!1)))) | (~r(s(s(s(elem!1))), s(s(elem!1)))) | (~r(s(s(elem!1)), elem!1)) | (~r(elem!1, s(s(s(elem!1))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(elem!1, s(s(elem!1)))) | (~r(s(s(s(elem!1))), s(s(elem!1)))) | (~r(s(s(elem!1)), elem!1)) | (~r(elem!1, s(s(s(elem!1))))))),
% 2.42/2.67 inference(rewrite,[status(thm)],[])).
% 2.42/2.67 tff(7842,plain,
% 2.42/2.67 (((~r(s(s(elem!1)), elem!1)) | (~r(s(s(s(elem!1))), s(s(elem!1)))) | (~r(elem!1, s(s(elem!1)))) | (~r(elem!1, s(s(s(elem!1)))))) <=> ((~r(elem!1, s(s(elem!1)))) | (~r(s(s(s(elem!1))), s(s(elem!1)))) | (~r(s(s(elem!1)), elem!1)) | (~r(elem!1, s(s(s(elem!1))))))),
% 2.42/2.67 inference(rewrite,[status(thm)],[])).
% 2.42/2.67 tff(7843,plain,
% 2.42/2.67 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(elem!1)), elem!1)) | (~r(s(s(s(elem!1))), s(s(elem!1)))) | (~r(elem!1, s(s(elem!1)))) | (~r(elem!1, s(s(s(elem!1))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(s(elem!1)))) | (~r(s(s(s(elem!1))), s(s(elem!1)))) | (~r(s(s(elem!1)), elem!1)) | (~r(elem!1, s(s(s(elem!1)))))))),
% 2.42/2.67 inference(monotonicity,[status(thm)],[7842])).
% 2.42/2.67 tff(7844,plain,
% 2.42/2.67 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(elem!1)), elem!1)) | (~r(s(s(s(elem!1))), s(s(elem!1)))) | (~r(elem!1, s(s(elem!1)))) | (~r(elem!1, s(s(s(elem!1))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(elem!1, s(s(elem!1)))) | (~r(s(s(s(elem!1))), s(s(elem!1)))) | (~r(s(s(elem!1)), elem!1)) | (~r(elem!1, s(s(s(elem!1))))))),
% 2.42/2.67 inference(transitivity,[status(thm)],[7843, 7841])).
% 2.42/2.67 tff(7845,plain,
% 2.42/2.67 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(elem!1)), elem!1)) | (~r(s(s(s(elem!1))), s(s(elem!1)))) | (~r(elem!1, s(s(elem!1)))) | (~r(elem!1, s(s(s(elem!1))))))),
% 2.42/2.67 inference(quant_inst,[status(thm)],[])).
% 2.42/2.67 tff(7846,plain,
% 2.42/2.67 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(elem!1, s(s(elem!1)))) | (~r(s(s(s(elem!1))), s(s(elem!1)))) | (~r(s(s(elem!1)), elem!1)) | (~r(elem!1, s(s(s(elem!1)))))),
% 2.42/2.67 inference(modus_ponens,[status(thm)],[7845, 7844])).
% 2.42/2.67 tff(7847,plain,
% 2.42/2.67 (~r(elem!1, s(s(s(elem!1))))),
% 2.42/2.67 inference(unit_resolution,[status(thm)],[7846, 197, 768, 905, 1027])).
% 2.42/2.67 tff(7848,plain,
% 2.42/2.67 (b(elem!1, s(s(s(elem!1))))),
% 2.42/2.67 inference(unit_resolution,[status(thm)],[5451, 7847, 6292])).
% 2.42/2.67 tff(7849,plain,
% 2.42/2.67 (~b(s(s(s(s(elem!1)))), elem!1)),
% 2.42/2.67 inference(unit_resolution,[status(thm)],[710, 7848, 361, 641, 642, 7840])).
% 2.42/2.67 tff(7850,plain,
% 2.42/2.67 (~b(s(s(s(s(z)))), elem!1)),
% 2.42/2.67 inference(modus_ponens,[status(thm)],[7849, 6185])).
% 2.42/2.67 tff(7851,plain,
% 2.42/2.67 (r(s(s(z)), s(s(s(s(z))))) <=> r(s(s(elem!1)), s(s(s(s(elem!1)))))),
% 2.42/2.67 inference(monotonicity,[status(thm)],[34, 1087])).
% 2.42/2.67 tff(7852,plain,
% 2.42/2.67 (r(s(s(elem!1)), s(s(s(s(elem!1))))) <=> r(s(s(z)), s(s(s(s(z)))))),
% 2.42/2.67 inference(symmetry,[status(thm)],[7851])).
% 2.42/2.67 tff(7853,plain,
% 2.42/2.67 (r(s(s(s(z))), s(s(z))) <=> r(s(s(s(z))), s(s(elem!1)))),
% 2.42/2.67 inference(monotonicity,[status(thm)],[34])).
% 2.42/2.67 tff(7854,plain,
% 2.42/2.67 (r(s(s(s(z))), s(s(elem!1))) <=> r(s(s(s(z))), s(s(z)))),
% 2.42/2.67 inference(symmetry,[status(thm)],[7853])).
% 2.42/2.67 tff(7855,plain,
% 2.42/2.67 (r(s(s(s(z))), s(s(elem!1))) <=> r(s(s(s(elem!1))), s(s(elem!1)))),
% 2.42/2.67 inference(monotonicity,[status(thm)],[1086])).
% 2.42/2.67 tff(7856,plain,
% 2.42/2.67 (r(s(s(s(elem!1))), s(s(elem!1))) <=> r(s(s(s(z))), s(s(elem!1)))),
% 2.42/2.67 inference(symmetry,[status(thm)],[7855])).
% 2.42/2.67 tff(7857,plain,
% 2.42/2.68 (r(s(s(s(elem!1))), s(s(elem!1))) <=> r(s(s(s(z))), s(s(z)))),
% 2.42/2.68 inference(transitivity,[status(thm)],[7856, 7854])).
% 2.42/2.68 tff(7858,plain,
% 2.42/2.68 (r(s(s(s(z))), s(s(z)))),
% 2.42/2.68 inference(modus_ponens,[status(thm)],[905, 7857])).
% 2.42/2.68 tff(7859,plain,
% 2.42/2.68 (~b(s(s(s(s(elem!1)))), s(s(s(elem!1))))),
% 2.42/2.68 inference(unit_resolution,[status(thm)],[7694, 7848, 310, 34, 768, 350, 1212, 376, 642, 641, 6194, 7849])).
% 2.42/2.68 tff(7860,plain,
% 2.42/2.68 (~b(s(s(s(s(z)))), s(s(s(z))))),
% 2.42/2.68 inference(modus_ponens,[status(thm)],[7859, 4628])).
% 2.42/2.68 tff(7861,plain,
% 2.42/2.68 (r(s(s(s(s(z)))), s(s(s(z))))),
% 2.42/2.68 inference(unit_resolution,[status(thm)],[4662, 7860])).
% 2.42/2.68 tff(7862,plain,
% 2.42/2.68 (r(s(s(s(s(z)))), s(z)) <=> r(s(s(s(s(elem!1)))), s(z))),
% 2.42/2.68 inference(monotonicity,[status(thm)],[2197])).
% 2.42/2.68 tff(7863,plain,
% 2.42/2.68 (r(s(s(s(s(elem!1)))), s(z)) <=> r(s(s(s(s(z)))), s(z))),
% 2.42/2.68 inference(symmetry,[status(thm)],[7862])).
% 2.42/2.68 tff(7864,plain,
% 2.42/2.68 (r(s(s(s(s(z)))), s(z))),
% 2.42/2.68 inference(modus_ponens,[status(thm)],[700, 7863])).
% 2.42/2.68 tff(7865,plain,
% 2.42/2.68 ((~r(s(z), s(s(s(z))))) | (~r(s(s(s(s(z)))), s(z)))),
% 2.42/2.68 inference(unit_resolution,[status(thm)],[6608, 197, 1676, 4680])).
% 2.42/2.68 tff(7866,plain,
% 2.42/2.68 ($false),
% 2.42/2.68 inference(unit_resolution,[status(thm)],[7865, 7864, 2204])).
% 2.42/2.68 tff(7867,plain,((~r(s(s(s(s(z)))), s(s(s(z))))) | (~r(s(s(s(z))), s(s(z)))) | (~r(s(s(s(s(elem!1)))), s(z))) | (~(s(s(elem!1)) = s(s(z)))) | (~r(s(z), s(s(s(elem!1)))))), inference(lemma,lemma(discharge,[]))).
% 2.42/2.68 tff(7868,plain,
% 2.42/2.68 (~r(s(s(s(s(elem!1)))), s(z))),
% 2.42/2.68 inference(unit_resolution,[status(thm)],[7867, 7861, 2153, 7840, 7858])).
% 2.42/2.68 tff(7869,plain,
% 2.42/2.68 (b(s(s(s(s(elem!1)))), s(z))),
% 2.42/2.68 inference(unit_resolution,[status(thm)],[661, 7868])).
% 2.42/2.68 tff(7870,plain,
% 2.42/2.68 (~b(s(s(elem!1)), s(s(s(s(elem!1)))))),
% 2.42/2.68 inference(unit_resolution,[status(thm)],[1410, 7869, 376, 310, 463])).
% 2.42/2.68 tff(7871,plain,
% 2.42/2.68 (r(s(s(elem!1)), s(s(s(s(elem!1)))))),
% 2.42/2.68 inference(unit_resolution,[status(thm)],[827, 7870, 816])).
% 2.42/2.68 tff(7872,plain,
% 2.42/2.68 (r(s(s(z)), s(s(s(s(z)))))),
% 2.42/2.68 inference(modus_ponens,[status(thm)],[7871, 7852])).
% 2.42/2.68 tff(7873,plain,
% 2.42/2.68 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(elem!1, s(z))) | (~b(elem!1, s(s(s(elem!1))))) | (~b(s(z), s(s(elem!1)))) | (~b(elem!1, s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(elem!1, s(z))) | (~b(elem!1, s(s(s(elem!1))))) | (~b(s(z), s(s(elem!1)))) | (~b(elem!1, s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), s(z))))),
% 2.42/2.68 inference(rewrite,[status(thm)],[])).
% 2.42/2.68 tff(7874,plain,
% 2.42/2.68 (((~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(elem!1, s(s(s(elem!1))))) | (~b(s(z), s(s(elem!1)))) | (~b(s(s(s(s(elem!1)))), s(z))) | (~b(elem!1, s(z))) | (~b(elem!1, s(s(s(s(elem!1))))))) <=> ((~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(elem!1, s(z))) | (~b(elem!1, s(s(s(elem!1))))) | (~b(s(z), s(s(elem!1)))) | (~b(elem!1, s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), s(z))))),
% 2.42/2.68 inference(rewrite,[status(thm)],[])).
% 2.42/2.68 tff(7875,plain,
% 2.42/2.68 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(elem!1, s(s(s(elem!1))))) | (~b(s(z), s(s(elem!1)))) | (~b(s(s(s(s(elem!1)))), s(z))) | (~b(elem!1, s(z))) | (~b(elem!1, s(s(s(s(elem!1)))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(elem!1, s(z))) | (~b(elem!1, s(s(s(elem!1))))) | (~b(s(z), s(s(elem!1)))) | (~b(elem!1, s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), s(z)))))),
% 2.42/2.68 inference(monotonicity,[status(thm)],[7874])).
% 2.42/2.68 tff(7876,plain,
% 2.42/2.68 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(elem!1, s(s(s(elem!1))))) | (~b(s(z), s(s(elem!1)))) | (~b(s(s(s(s(elem!1)))), s(z))) | (~b(elem!1, s(z))) | (~b(elem!1, s(s(s(s(elem!1)))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(elem!1, s(z))) | (~b(elem!1, s(s(s(elem!1))))) | (~b(s(z), s(s(elem!1)))) | (~b(elem!1, s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), s(z))))),
% 2.42/2.68 inference(transitivity,[status(thm)],[7875, 7873])).
% 2.42/2.68 tff(7877,plain,
% 2.42/2.68 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(elem!1, s(s(s(elem!1))))) | (~b(s(z), s(s(elem!1)))) | (~b(s(s(s(s(elem!1)))), s(z))) | (~b(elem!1, s(z))) | (~b(elem!1, s(s(s(s(elem!1)))))))),
% 2.42/2.68 inference(quant_inst,[status(thm)],[])).
% 2.42/2.68 tff(7878,plain,
% 2.42/2.68 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(elem!1, s(z))) | (~b(elem!1, s(s(s(elem!1))))) | (~b(s(z), s(s(elem!1)))) | (~b(elem!1, s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), s(z)))),
% 2.42/2.68 inference(modus_ponens,[status(thm)],[7877, 7876])).
% 2.42/2.68 tff(7879,plain,
% 2.42/2.68 (~b(elem!1, s(s(s(s(elem!1)))))),
% 2.42/2.68 inference(unit_resolution,[status(thm)],[7878, 166, 376, 463, 7848, 1212, 7869])).
% 2.42/2.68 tff(7880,plain,
% 2.42/2.68 (~b(elem!1, s(s(s(s(z)))))),
% 2.42/2.68 inference(unit_resolution,[status(thm)],[1105, 7879, 34])).
% 2.42/2.68 tff(7881,plain,
% 2.42/2.68 (r(elem!1, s(s(s(s(z)))))),
% 2.42/2.68 inference(unit_resolution,[status(thm)],[1098, 7880, 1045])).
% 2.42/2.68 tff(7882,plain,
% 2.42/2.68 (~r(s(s(s(s(z)))), elem!1)),
% 2.42/2.68 inference(unit_resolution,[status(thm)],[6202, 7881, 6194, 7872])).
% 2.42/2.68 tff(7883,plain,
% 2.42/2.68 (b(s(s(s(s(z)))), elem!1)),
% 2.42/2.68 inference(unit_resolution,[status(thm)],[6190, 7882, 6184])).
% 2.42/2.68 tff(7884,plain,
% 2.42/2.68 ($false),
% 2.42/2.68 inference(unit_resolution,[status(thm)],[7883, 7850])).
% 2.42/2.68 tff(7885,plain,((~r(s(s(s(elem!1))), s(s(elem!1)))) | (~(s(s(z)) = s(s(elem!1)))) | (~r(elem!1, s(s(z)))) | (~b(s(z), s(s(elem!1)))) | (~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(elem!1, s(z))) | (~b(s(s(elem!1)), s(z))) | (~r(s(s(elem!1)), elem!1)) | (~r(s(s(s(elem!1))), s(z))) | (~b(s(z), elem!1)) | (~b(s(s(s(elem!1))), elem!1)) | (s(s(s(elem!1))) = s(s(s(s(elem!1))))) | (~r(elem!1, s(s(elem!1))))), inference(lemma,lemma(discharge,[]))).
% 2.42/2.68 tff(7886,plain,
% 2.42/2.68 (~r(s(s(s(elem!1))), s(s(elem!1)))),
% 2.42/2.68 inference(unit_resolution,[status(thm)],[7885, 7799, 6194, 376, 7566, 7584, 310, 7576, 7606, 7838, 7582, 358, 1027])).
% 2.42/2.68 tff(7887,plain,
% 2.42/2.68 (b(s(s(s(elem!1))), s(s(elem!1)))),
% 2.42/2.68 inference(unit_resolution,[status(thm)],[889, 7886, 51])).
% 2.42/2.68 tff(7888,plain,
% 2.42/2.68 (~b(s(s(s(elem!1))), s(s(s(s(elem!1)))))),
% 2.42/2.68 inference(unit_resolution,[status(thm)],[3459, 3457, 463, 839])).
% 2.42/2.68 tff(7889,plain,
% 2.42/2.68 (r(s(s(s(elem!1))), s(s(s(s(elem!1)))))),
% 2.42/2.68 inference(unit_resolution,[status(thm)],[696, 7888, 361])).
% 2.42/2.68 tff(7890,plain,
% 2.42/2.68 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(s(s(s(elem!1)))), s(s(elem!1)))) | (~b(s(z), s(s(elem!1)))) | (~b(s(z), s(s(s(s(elem!1)))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(s(s(s(elem!1)))), s(s(elem!1)))) | (~b(s(z), s(s(elem!1)))) | (~b(s(z), s(s(s(s(elem!1)))))))),
% 2.42/2.68 inference(rewrite,[status(thm)],[])).
% 2.42/2.68 tff(7891,plain,
% 2.42/2.68 (((~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(z), s(s(elem!1)))) | (~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(s(s(s(s(elem!1)))), s(s(elem!1)))) | (~b(s(z), s(s(elem!1)))) | (~b(s(z), s(s(s(s(elem!1))))))) <=> ((~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(s(s(s(elem!1)))), s(s(elem!1)))) | (~b(s(z), s(s(elem!1)))) | (~b(s(z), s(s(s(s(elem!1)))))))),
% 2.42/2.68 inference(rewrite,[status(thm)],[])).
% 2.42/2.68 tff(7892,plain,
% 2.42/2.68 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(z), s(s(elem!1)))) | (~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(s(s(s(s(elem!1)))), s(s(elem!1)))) | (~b(s(z), s(s(elem!1)))) | (~b(s(z), s(s(s(s(elem!1)))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(s(s(s(elem!1)))), s(s(elem!1)))) | (~b(s(z), s(s(elem!1)))) | (~b(s(z), s(s(s(s(elem!1))))))))),
% 2.42/2.68 inference(monotonicity,[status(thm)],[7891])).
% 2.42/2.68 tff(7893,plain,
% 2.42/2.68 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(z), s(s(elem!1)))) | (~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(s(s(s(s(elem!1)))), s(s(elem!1)))) | (~b(s(z), s(s(elem!1)))) | (~b(s(z), s(s(s(s(elem!1)))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(s(s(s(elem!1)))), s(s(elem!1)))) | (~b(s(z), s(s(elem!1)))) | (~b(s(z), s(s(s(s(elem!1)))))))),
% 2.42/2.68 inference(transitivity,[status(thm)],[7892, 7890])).
% 2.42/2.68 tff(7894,plain,
% 2.42/2.68 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(z), s(s(elem!1)))) | (~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(s(s(s(s(elem!1)))), s(s(elem!1)))) | (~b(s(z), s(s(elem!1)))) | (~b(s(z), s(s(s(s(elem!1)))))))),
% 2.42/2.68 inference(quant_inst,[status(thm)],[])).
% 2.42/2.68 tff(7895,plain,
% 2.42/2.68 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(s(s(s(elem!1)))), s(s(elem!1)))) | (~b(s(z), s(s(elem!1)))) | (~b(s(z), s(s(s(s(elem!1))))))),
% 2.42/2.68 inference(modus_ponens,[status(thm)],[7894, 7893])).
% 2.42/2.68 tff(7896,plain,
% 2.42/2.68 (~b(s(z), s(s(s(s(elem!1)))))),
% 2.42/2.68 inference(unit_resolution,[status(thm)],[7895, 166, 376, 463, 839, 3457])).
% 2.42/2.68 tff(7897,plain,
% 2.42/2.68 (r(s(z), s(s(s(s(elem!1)))))),
% 2.42/2.68 inference(unit_resolution,[status(thm)],[681, 7896])).
% 2.42/2.68 tff(7898,plain,
% 2.42/2.68 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(s(s(s(elem!1)))), s(s(elem!1)))) | (~b(s(z), s(s(elem!1)))) | (~b(s(s(elem!1)), s(z))) | (~b(s(s(s(s(elem!1)))), s(s(s(elem!1))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(s(s(s(elem!1)))), s(s(elem!1)))) | (~b(s(z), s(s(elem!1)))) | (~b(s(s(elem!1)), s(z))) | (~b(s(s(s(s(elem!1)))), s(s(s(elem!1))))))),
% 2.42/2.68 inference(rewrite,[status(thm)],[])).
% 2.42/2.68 tff(7899,plain,
% 2.42/2.68 (((~b(s(z), s(s(elem!1)))) | (~b(s(s(s(s(elem!1)))), s(s(elem!1)))) | (~b(s(s(elem!1)), s(z))) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(s(s(s(elem!1)))), s(s(elem!1)))) | (~b(s(s(s(s(elem!1)))), s(s(s(elem!1)))))) <=> ((~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(s(s(s(elem!1)))), s(s(elem!1)))) | (~b(s(z), s(s(elem!1)))) | (~b(s(s(elem!1)), s(z))) | (~b(s(s(s(s(elem!1)))), s(s(s(elem!1))))))),
% 2.42/2.68 inference(rewrite,[status(thm)],[])).
% 2.42/2.68 tff(7900,plain,
% 2.42/2.68 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(elem!1)))) | (~b(s(s(s(s(elem!1)))), s(s(elem!1)))) | (~b(s(s(elem!1)), s(z))) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(s(s(s(elem!1)))), s(s(elem!1)))) | (~b(s(s(s(s(elem!1)))), s(s(s(elem!1))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(s(s(s(elem!1)))), s(s(elem!1)))) | (~b(s(z), s(s(elem!1)))) | (~b(s(s(elem!1)), s(z))) | (~b(s(s(s(s(elem!1)))), s(s(s(elem!1)))))))),
% 2.42/2.68 inference(monotonicity,[status(thm)],[7899])).
% 2.42/2.68 tff(7901,plain,
% 2.42/2.68 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(elem!1)))) | (~b(s(s(s(s(elem!1)))), s(s(elem!1)))) | (~b(s(s(elem!1)), s(z))) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(s(s(s(elem!1)))), s(s(elem!1)))) | (~b(s(s(s(s(elem!1)))), s(s(s(elem!1))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(s(s(s(elem!1)))), s(s(elem!1)))) | (~b(s(z), s(s(elem!1)))) | (~b(s(s(elem!1)), s(z))) | (~b(s(s(s(s(elem!1)))), s(s(s(elem!1))))))),
% 2.42/2.68 inference(transitivity,[status(thm)],[7900, 7898])).
% 2.42/2.68 tff(7902,plain,
% 2.42/2.68 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(elem!1)))) | (~b(s(s(s(s(elem!1)))), s(s(elem!1)))) | (~b(s(s(elem!1)), s(z))) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(s(s(s(elem!1)))), s(s(elem!1)))) | (~b(s(s(s(s(elem!1)))), s(s(s(elem!1))))))),
% 2.42/2.68 inference(quant_inst,[status(thm)],[])).
% 2.42/2.68 tff(7903,plain,
% 2.42/2.68 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(s(s(s(elem!1)))), s(s(elem!1)))) | (~b(s(z), s(s(elem!1)))) | (~b(s(s(elem!1)), s(z))) | (~b(s(s(s(s(elem!1)))), s(s(s(elem!1)))))),
% 2.42/2.68 inference(modus_ponens,[status(thm)],[7902, 7901])).
% 2.42/2.68 tff(7904,plain,
% 2.42/2.68 (~b(s(s(s(s(elem!1)))), s(s(s(elem!1))))),
% 2.42/2.68 inference(unit_resolution,[status(thm)],[7903, 166, 376, 839, 310, 3457])).
% 2.42/2.68 tff(7905,plain,
% 2.42/2.68 (r(s(s(s(s(elem!1)))), s(s(s(elem!1))))),
% 2.42/2.68 inference(unit_resolution,[status(thm)],[1065, 7904, 1038])).
% 2.42/2.68 tff(7906,plain,
% 2.42/2.68 ($false),
% 2.42/2.68 inference(unit_resolution,[status(thm)],[2125, 7905, 7897, 119, 7889])).
% 2.42/2.68 tff(7907,plain,((~b(s(s(s(s(elem!1)))), s(s(elem!1)))) | (~r(s(z), s(s(s(elem!1))))) | (~b(s(z), s(s(elem!1)))) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(s(elem!1)), s(z))) | (~b(s(s(elem!1)), s(s(s(elem!1))))) | (s(s(s(elem!1))) = s(s(s(s(elem!1)))))), inference(lemma,lemma(discharge,[]))).
% 2.42/2.68 tff(7908,plain,
% 2.42/2.68 (~b(s(s(s(s(elem!1)))), s(s(elem!1)))),
% 2.42/2.68 inference(unit_resolution,[status(thm)],[7907, 7812, 376, 7887, 310, 7799, 358])).
% 2.42/2.68 tff(7909,plain,
% 2.42/2.68 (r(s(s(s(s(elem!1)))), s(s(elem!1)))),
% 2.42/2.68 inference(unit_resolution,[status(thm)],[813, 7908, 7581])).
% 2.42/2.68 tff(7910,plain,
% 2.42/2.68 ($false),
% 2.42/2.68 inference(unit_resolution,[status(thm)],[6395, 197, 768, 3408, 743, 1027])).
% 2.42/2.68 tff(7911,plain,((~r(s(s(s(s(elem!1)))), s(s(elem!1)))) | (~r(s(s(elem!1)), elem!1)) | (~r(s(s(s(s(elem!1)))), elem!1)) | (~r(elem!1, s(s(elem!1))))), inference(lemma,lemma(discharge,[]))).
% 2.42/2.68 tff(7912,plain,
% 2.42/2.68 (~r(s(s(s(s(elem!1)))), elem!1)),
% 2.42/2.68 inference(unit_resolution,[status(thm)],[7911, 7909, 7576, 1027])).
% 2.42/2.68 tff(7913,plain,
% 2.42/2.68 (b(s(s(s(s(elem!1)))), elem!1)),
% 2.42/2.68 inference(unit_resolution,[status(thm)],[719, 7912, 7571])).
% 2.42/2.68 tff(7914,plain,
% 2.42/2.68 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(elem!1, s(z))) | (~b(s(z), s(s(elem!1)))) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(s(s(s(elem!1)))), elem!1)) | (~b(s(s(s(elem!1))), s(s(s(s(elem!1)))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(elem!1, s(z))) | (~b(s(z), s(s(elem!1)))) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(s(s(s(elem!1)))), elem!1)) | (~b(s(s(s(elem!1))), s(s(s(s(elem!1)))))))),
% 2.42/2.68 inference(rewrite,[status(thm)],[])).
% 2.42/2.68 tff(7915,plain,
% 2.42/2.68 (((~b(s(z), s(s(elem!1)))) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(elem!1, s(z))) | (~b(s(s(s(s(elem!1)))), elem!1)) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(s(s(elem!1))), s(s(s(s(elem!1))))))) <=> ((~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(elem!1, s(z))) | (~b(s(z), s(s(elem!1)))) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(s(s(s(elem!1)))), elem!1)) | (~b(s(s(s(elem!1))), s(s(s(s(elem!1)))))))),
% 2.42/2.68 inference(rewrite,[status(thm)],[])).
% 2.42/2.68 tff(7916,plain,
% 2.42/2.68 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(elem!1)))) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(elem!1, s(z))) | (~b(s(s(s(s(elem!1)))), elem!1)) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(s(s(elem!1))), s(s(s(s(elem!1)))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(elem!1, s(z))) | (~b(s(z), s(s(elem!1)))) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(s(s(s(elem!1)))), elem!1)) | (~b(s(s(s(elem!1))), s(s(s(s(elem!1))))))))),
% 2.42/2.68 inference(monotonicity,[status(thm)],[7915])).
% 2.42/2.68 tff(7917,plain,
% 2.42/2.68 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(elem!1)))) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(elem!1, s(z))) | (~b(s(s(s(s(elem!1)))), elem!1)) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(s(s(elem!1))), s(s(s(s(elem!1)))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(elem!1, s(z))) | (~b(s(z), s(s(elem!1)))) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(s(s(s(elem!1)))), elem!1)) | (~b(s(s(s(elem!1))), s(s(s(s(elem!1)))))))),
% 2.42/2.68 inference(transitivity,[status(thm)],[7916, 7914])).
% 2.42/2.68 tff(7918,plain,
% 2.42/2.68 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(elem!1)))) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(elem!1, s(z))) | (~b(s(s(s(s(elem!1)))), elem!1)) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(s(s(elem!1))), s(s(s(s(elem!1)))))))),
% 2.42/2.68 inference(quant_inst,[status(thm)],[])).
% 2.42/2.68 tff(7919,plain,
% 2.42/2.68 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(elem!1, s(z))) | (~b(s(z), s(s(elem!1)))) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(s(s(s(elem!1)))), elem!1)) | (~b(s(s(s(elem!1))), s(s(s(s(elem!1))))))),
% 2.42/2.68 inference(modus_ponens,[status(thm)],[7918, 7917])).
% 2.42/2.68 tff(7920,plain,
% 2.42/2.68 (~b(s(s(s(elem!1))), s(s(s(s(elem!1)))))),
% 2.42/2.68 inference(unit_resolution,[status(thm)],[7919, 166, 376, 7887, 7584, 7582, 7913])).
% 2.42/2.68 tff(7921,plain,
% 2.42/2.68 (r(s(s(s(elem!1))), s(s(s(s(elem!1)))))),
% 2.42/2.68 inference(unit_resolution,[status(thm)],[696, 7920, 358])).
% 2.42/2.68 tff(7922,plain,
% 2.42/2.68 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(z))) | (~b(s(z), s(s(elem!1)))) | (~b(s(z), elem!1)) | (~b(s(s(s(s(elem!1)))), elem!1)) | (~b(s(z), s(s(s(s(elem!1)))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(z))) | (~b(s(z), s(s(elem!1)))) | (~b(s(z), elem!1)) | (~b(s(s(s(s(elem!1)))), elem!1)) | (~b(s(z), s(s(s(s(elem!1)))))))),
% 2.42/2.68 inference(rewrite,[status(thm)],[])).
% 2.42/2.68 tff(7923,plain,
% 2.42/2.68 (((~b(s(z), s(s(elem!1)))) | (~b(s(z), s(s(elem!1)))) | (~b(elem!1, s(z))) | (~b(s(s(s(s(elem!1)))), elem!1)) | (~b(s(z), elem!1)) | (~b(s(z), s(s(s(s(elem!1))))))) <=> ((~b(elem!1, s(z))) | (~b(s(z), s(s(elem!1)))) | (~b(s(z), elem!1)) | (~b(s(s(s(s(elem!1)))), elem!1)) | (~b(s(z), s(s(s(s(elem!1)))))))),
% 2.42/2.69 inference(rewrite,[status(thm)],[])).
% 2.42/2.69 tff(7924,plain,
% 2.42/2.69 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(elem!1)))) | (~b(s(z), s(s(elem!1)))) | (~b(elem!1, s(z))) | (~b(s(s(s(s(elem!1)))), elem!1)) | (~b(s(z), elem!1)) | (~b(s(z), s(s(s(s(elem!1)))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(z))) | (~b(s(z), s(s(elem!1)))) | (~b(s(z), elem!1)) | (~b(s(s(s(s(elem!1)))), elem!1)) | (~b(s(z), s(s(s(s(elem!1))))))))),
% 2.42/2.69 inference(monotonicity,[status(thm)],[7923])).
% 2.42/2.69 tff(7925,plain,
% 2.42/2.69 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(elem!1)))) | (~b(s(z), s(s(elem!1)))) | (~b(elem!1, s(z))) | (~b(s(s(s(s(elem!1)))), elem!1)) | (~b(s(z), elem!1)) | (~b(s(z), s(s(s(s(elem!1)))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(z))) | (~b(s(z), s(s(elem!1)))) | (~b(s(z), elem!1)) | (~b(s(s(s(s(elem!1)))), elem!1)) | (~b(s(z), s(s(s(s(elem!1)))))))),
% 2.42/2.69 inference(transitivity,[status(thm)],[7924, 7922])).
% 2.42/2.69 tff(7926,plain,
% 2.42/2.69 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(elem!1)))) | (~b(s(z), s(s(elem!1)))) | (~b(elem!1, s(z))) | (~b(s(s(s(s(elem!1)))), elem!1)) | (~b(s(z), elem!1)) | (~b(s(z), s(s(s(s(elem!1)))))))),
% 2.42/2.69 inference(quant_inst,[status(thm)],[])).
% 2.42/2.69 tff(7927,plain,
% 2.42/2.69 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(z))) | (~b(s(z), s(s(elem!1)))) | (~b(s(z), elem!1)) | (~b(s(s(s(s(elem!1)))), elem!1)) | (~b(s(z), s(s(s(s(elem!1))))))),
% 2.42/2.69 inference(modus_ponens,[status(thm)],[7926, 7925])).
% 2.42/2.69 tff(7928,plain,
% 2.42/2.69 (~b(s(z), s(s(s(s(elem!1)))))),
% 2.42/2.69 inference(unit_resolution,[status(thm)],[7927, 166, 376, 7584, 7838, 7913])).
% 2.42/2.69 tff(7929,plain,
% 2.42/2.69 (r(s(z), s(s(s(s(elem!1)))))),
% 2.42/2.69 inference(unit_resolution,[status(thm)],[681, 7928])).
% 2.42/2.69 tff(7930,plain,
% 2.42/2.69 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(z))) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(z), elem!1)) | (~b(s(s(s(s(elem!1)))), elem!1)) | (~b(s(s(s(s(elem!1)))), s(s(s(elem!1))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(z))) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(z), elem!1)) | (~b(s(s(s(s(elem!1)))), elem!1)) | (~b(s(s(s(s(elem!1)))), s(s(s(elem!1))))))),
% 2.42/2.69 inference(rewrite,[status(thm)],[])).
% 2.42/2.69 tff(7931,plain,
% 2.42/2.69 (((~b(s(z), elem!1)) | (~b(s(s(s(s(elem!1)))), elem!1)) | (~b(elem!1, s(z))) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(s(s(s(elem!1)))), elem!1)) | (~b(s(s(s(s(elem!1)))), s(s(s(elem!1)))))) <=> ((~b(elem!1, s(z))) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(z), elem!1)) | (~b(s(s(s(s(elem!1)))), elem!1)) | (~b(s(s(s(s(elem!1)))), s(s(s(elem!1))))))),
% 2.42/2.69 inference(rewrite,[status(thm)],[])).
% 2.42/2.69 tff(7932,plain,
% 2.42/2.69 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), elem!1)) | (~b(s(s(s(s(elem!1)))), elem!1)) | (~b(elem!1, s(z))) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(s(s(s(elem!1)))), elem!1)) | (~b(s(s(s(s(elem!1)))), s(s(s(elem!1))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(z))) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(z), elem!1)) | (~b(s(s(s(s(elem!1)))), elem!1)) | (~b(s(s(s(s(elem!1)))), s(s(s(elem!1)))))))),
% 2.42/2.69 inference(monotonicity,[status(thm)],[7931])).
% 2.42/2.69 tff(7933,plain,
% 2.42/2.69 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), elem!1)) | (~b(s(s(s(s(elem!1)))), elem!1)) | (~b(elem!1, s(z))) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(s(s(s(elem!1)))), elem!1)) | (~b(s(s(s(s(elem!1)))), s(s(s(elem!1))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(z))) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(z), elem!1)) | (~b(s(s(s(s(elem!1)))), elem!1)) | (~b(s(s(s(s(elem!1)))), s(s(s(elem!1))))))),
% 2.42/2.69 inference(transitivity,[status(thm)],[7932, 7930])).
% 2.42/2.69 tff(7934,plain,
% 2.42/2.69 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), elem!1)) | (~b(s(s(s(s(elem!1)))), elem!1)) | (~b(elem!1, s(z))) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(s(s(s(elem!1)))), elem!1)) | (~b(s(s(s(s(elem!1)))), s(s(s(elem!1))))))),
% 2.42/2.69 inference(quant_inst,[status(thm)],[])).
% 2.42/2.69 tff(7935,plain,
% 2.42/2.69 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(z))) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(z), elem!1)) | (~b(s(s(s(s(elem!1)))), elem!1)) | (~b(s(s(s(s(elem!1)))), s(s(s(elem!1)))))),
% 2.42/2.69 inference(modus_ponens,[status(thm)],[7934, 7933])).
% 2.42/2.69 tff(7936,plain,
% 2.42/2.69 (~b(s(s(s(s(elem!1)))), s(s(s(elem!1))))),
% 2.42/2.69 inference(unit_resolution,[status(thm)],[7935, 166, 7584, 7838, 7582, 7913])).
% 2.42/2.69 tff(7937,plain,
% 2.42/2.69 (r(s(s(s(s(elem!1)))), s(s(s(elem!1))))),
% 2.42/2.69 inference(unit_resolution,[status(thm)],[1065, 7936, 364])).
% 2.42/2.69 tff(7938,plain,
% 2.42/2.69 ($false),
% 2.42/2.69 inference(unit_resolution,[status(thm)],[2125, 7937, 7929, 7812, 7921])).
% 2.42/2.69 tff(7939,plain,((~b(s(s(elem!1)), s(z))) | (~b(s(z), s(s(elem!1)))) | (~r(elem!1, s(s(elem!1)))) | (~r(elem!1, s(s(z)))) | (~b(s(s(s(elem!1))), z)) | (~r(z, s(s(z)))) | (s(s(elem!1)) = s(s(s(elem!1)))) | (~b(z, s(z)))), inference(lemma,lemma(discharge,[]))).
% 2.42/2.69 tff(7940,plain,
% 2.42/2.69 (~b(s(s(elem!1)), s(z))),
% 2.42/2.69 inference(unit_resolution,[status(thm)],[7939, 7136, 7565, 7564, 6718, 152, 45, 118])).
% 2.42/2.69 tff(7941,plain,
% 2.42/2.69 (r(s(s(elem!1)), s(z))),
% 2.42/2.69 inference(unit_resolution,[status(thm)],[1912, 7940])).
% 2.42/2.69 tff(7942,plain,
% 2.42/2.69 (~b(s(s(s(elem!1))), s(z))),
% 2.42/2.69 inference(unit_resolution,[status(thm)],[7604, 7136, 152, 118, 6718, 45])).
% 2.42/2.69 tff(7943,plain,
% 2.42/2.69 (r(s(s(s(elem!1))), s(z))),
% 2.42/2.69 inference(unit_resolution,[status(thm)],[1849, 7942])).
% 2.42/2.69 tff(7944,plain,
% 2.42/2.69 (b(s(s(s(elem!1))), elem!1)),
% 2.42/2.69 inference(unit_resolution,[status(thm)],[634, 7559, 6718])).
% 2.42/2.69 tff(7945,plain,
% 2.42/2.69 (r(s(s(z)), s(z)) <=> r(s(s(elem!1)), s(z))),
% 2.42/2.69 inference(monotonicity,[status(thm)],[7555])).
% 2.42/2.69 tff(7946,plain,
% 2.42/2.69 (r(s(s(elem!1)), s(z)) <=> r(s(s(z)), s(z))),
% 2.42/2.69 inference(symmetry,[status(thm)],[7945])).
% 2.42/2.69 tff(7947,plain,
% 2.42/2.69 (r(s(s(z)), s(z))),
% 2.42/2.69 inference(modus_ponens,[status(thm)],[7941, 7946])).
% 2.42/2.69 tff(7948,plain,
% 2.42/2.69 (r(s(s(z)), s(z))),
% 2.42/2.69 inference(modus_ponens,[status(thm)],[4577, 6156])).
% 2.42/2.69 tff(7949,plain,
% 2.42/2.69 (~b(s(z), z)),
% 2.42/2.69 inference(unit_resolution,[status(thm)],[7322, 241, 118, 121, 376])).
% 2.42/2.69 tff(7950,plain,
% 2.42/2.69 (r(s(z), z)),
% 2.42/2.69 inference(unit_resolution,[status(thm)],[230, 7949])).
% 2.42/2.69 tff(7951,plain,
% 2.42/2.69 (~r(s(s(s(elem!1))), z)),
% 2.42/2.69 inference(unit_resolution,[status(thm)],[4466, 4458, 350, 97])).
% 2.42/2.69 tff(7952,plain,
% 2.42/2.69 (b(s(s(s(elem!1))), z)),
% 2.42/2.69 inference(unit_resolution,[status(thm)],[94, 7951])).
% 2.42/2.69 tff(7953,plain,
% 2.42/2.69 (b(s(s(elem!1)), s(s(s(elem!1))))),
% 2.42/2.69 inference(unit_resolution,[status(thm)],[461, 4469, 7420])).
% 2.42/2.69 tff(7954,plain,
% 2.42/2.69 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(elem!1)))) | (~r(s(s(elem!1)), z)) | (~r(s(z), z)) | (~r(s(s(elem!1)), s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, s(s(elem!1)))) | (~r(s(s(elem!1)), z)) | (~r(s(z), z)) | (~r(s(s(elem!1)), s(z))))),
% 2.42/2.69 inference(rewrite,[status(thm)],[])).
% 2.42/2.69 tff(7955,plain,
% 2.42/2.69 (((~r(z, s(s(elem!1)))) | (~r(s(z), z)) | (~r(s(s(elem!1)), z)) | (~r(s(s(elem!1)), s(z)))) <=> ((~r(z, s(s(elem!1)))) | (~r(s(s(elem!1)), z)) | (~r(s(z), z)) | (~r(s(s(elem!1)), s(z))))),
% 2.42/2.69 inference(rewrite,[status(thm)],[])).
% 2.42/2.69 tff(7956,plain,
% 2.42/2.69 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(elem!1)))) | (~r(s(z), z)) | (~r(s(s(elem!1)), z)) | (~r(s(s(elem!1)), s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(elem!1)))) | (~r(s(s(elem!1)), z)) | (~r(s(z), z)) | (~r(s(s(elem!1)), s(z)))))),
% 2.42/2.69 inference(monotonicity,[status(thm)],[7955])).
% 2.42/2.69 tff(7957,plain,
% 2.42/2.69 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(elem!1)))) | (~r(s(z), z)) | (~r(s(s(elem!1)), z)) | (~r(s(s(elem!1)), s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, s(s(elem!1)))) | (~r(s(s(elem!1)), z)) | (~r(s(z), z)) | (~r(s(s(elem!1)), s(z))))),
% 2.42/2.69 inference(transitivity,[status(thm)],[7956, 7954])).
% 2.42/2.69 tff(7958,plain,
% 2.42/2.69 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(elem!1)))) | (~r(s(z), z)) | (~r(s(s(elem!1)), z)) | (~r(s(s(elem!1)), s(z))))),
% 2.42/2.69 inference(quant_inst,[status(thm)],[])).
% 2.42/2.69 tff(7959,plain,
% 2.42/2.69 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, s(s(elem!1)))) | (~r(s(s(elem!1)), z)) | (~r(s(z), z)) | (~r(s(s(elem!1)), s(z)))),
% 2.42/2.69 inference(modus_ponens,[status(thm)],[7958, 7957])).
% 2.42/2.69 tff(7960,plain,
% 2.42/2.69 ($false),
% 2.42/2.69 inference(unit_resolution,[status(thm)],[7959, 197, 4577, 97, 365, 1970])).
% 2.42/2.69 tff(7961,plain,((~r(s(s(elem!1)), z)) | (~r(s(s(elem!1)), s(z))) | (~r(s(z), z)) | (~r(z, s(s(elem!1))))), inference(lemma,lemma(discharge,[]))).
% 2.42/2.69 tff(7962,plain,
% 2.42/2.69 (~r(s(s(elem!1)), z)),
% 2.42/2.69 inference(unit_resolution,[status(thm)],[7961, 4458, 97, 4577])).
% 2.42/2.69 tff(7963,plain,
% 2.42/2.69 (b(s(s(elem!1)), z)),
% 2.42/2.69 inference(unit_resolution,[status(thm)],[608, 7962])).
% 2.42/2.69 tff(7964,plain,
% 2.42/2.69 ($false),
% 2.42/2.69 inference(unit_resolution,[status(thm)],[600, 7963, 7953, 240, 7952])).
% 2.42/2.69 tff(7965,plain,(b(z, s(s(elem!1))) | (~b(z, s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), s(z))) | (~r(s(z), z)) | (~r(s(s(elem!1)), s(z)))), inference(lemma,lemma(discharge,[]))).
% 2.42/2.69 tff(7966,plain,
% 2.42/2.69 (~b(z, s(s(s(elem!1))))),
% 2.42/2.69 inference(unit_resolution,[status(thm)],[7965, 7950, 1790, 350, 4577])).
% 2.42/2.69 tff(7967,plain,
% 2.42/2.69 (r(z, s(s(s(elem!1))))),
% 2.42/2.69 inference(unit_resolution,[status(thm)],[261, 7966])).
% 2.42/2.69 tff(7968,plain,
% 2.42/2.69 (~r(s(s(s(elem!1))), s(s(z)))),
% 2.42/2.69 inference(unit_resolution,[status(thm)],[1588, 7967, 155, 7948])).
% 2.42/2.69 tff(7969,plain,
% 2.42/2.69 (~r(s(s(elem!1)), s(s(s(elem!1))))),
% 2.42/2.69 inference(unit_resolution,[status(thm)],[933, 7967, 4458, 350])).
% 2.42/2.69 tff(7970,plain,
% 2.42/2.69 (r(s(s(s(elem!1))), s(s(elem!1)))),
% 2.42/2.69 inference(unit_resolution,[status(thm)],[6040, 7969, 1863, 376, 241])).
% 2.42/2.69 tff(7971,plain,
% 2.42/2.69 ($false),
% 2.42/2.69 inference(unit_resolution,[status(thm)],[3454, 7970, 7968, 34])).
% 2.42/2.69 tff(7972,plain,((~b(s(z), s(s(s(elem!1))))) | (~(s(s(z)) = s(s(elem!1)))) | (s(s(s(elem!1))) = s(s(elem!1))) | (~b(s(z), s(s(elem!1)))) | (~r(z, s(s(z)))) | (~r(s(s(s(elem!1))), s(z))) | b(z, s(s(elem!1))) | (~r(s(s(elem!1)), s(z))) | (~b(z, s(z))) | (~b(s(s(s(elem!1))), z))), inference(lemma,lemma(discharge,[]))).
% 2.42/2.69 tff(7973,plain,
% 2.42/2.69 (~b(s(z), s(s(s(elem!1))))),
% 2.42/2.69 inference(unit_resolution,[status(thm)],[7972, 7555, 51, 7136, 152, 7943, 7562, 7941, 118, 6718])).
% 2.42/2.69 tff(7974,plain,
% 2.42/2.69 (r(s(z), s(s(s(elem!1))))),
% 2.42/2.69 inference(unit_resolution,[status(thm)],[116, 7973])).
% 2.42/2.69 tff(7975,plain,
% 2.42/2.69 (~r(s(s(s(elem!1))), s(s(z)))),
% 2.42/2.69 inference(unit_resolution,[status(thm)],[7534, 7974, 7943, 7947])).
% 2.42/2.69 tff(7976,plain,
% 2.42/2.69 (~r(s(s(s(elem!1))), s(s(elem!1)))),
% 2.42/2.69 inference(unit_resolution,[status(thm)],[3454, 7975, 7555])).
% 2.42/2.69 tff(7977,plain,
% 2.42/2.69 (b(s(s(s(elem!1))), s(s(elem!1)))),
% 2.42/2.69 inference(unit_resolution,[status(thm)],[889, 7976, 51])).
% 2.42/2.69 tff(7978,plain,
% 2.42/2.69 ((s(s(s(s(elem!1)))) = s(s(z))) <=> (s(s(s(s(elem!1)))) = s(s(elem!1)))),
% 2.42/2.69 inference(monotonicity,[status(thm)],[7555])).
% 2.42/2.69 tff(7979,plain,
% 2.42/2.69 ((s(s(s(s(elem!1)))) = s(s(z))) <=> (s(s(elem!1)) = s(s(s(s(elem!1)))))),
% 2.42/2.69 inference(transitivity,[status(thm)],[7978, 123])).
% 2.42/2.69 tff(7980,plain,
% 2.42/2.69 ((s(s(s(s(elem!1)))) = s(s(z))) <=> (s(s(s(s(elem!1)))) = s(s(elem!1)))),
% 2.42/2.69 inference(transitivity,[status(thm)],[7979, 124])).
% 2.42/2.69 tff(7981,plain,
% 2.42/2.69 ((~(s(s(s(s(elem!1)))) = s(s(z)))) <=> (~(s(s(s(s(elem!1)))) = s(s(elem!1))))),
% 2.42/2.69 inference(monotonicity,[status(thm)],[7980])).
% 2.42/2.69 tff(7982,plain,
% 2.42/2.69 (~(s(s(s(s(elem!1)))) = s(s(elem!1)))),
% 2.42/2.69 inference(modus_ponens,[status(thm)],[733, 7981])).
% 2.42/2.69 tff(7983,plain,
% 2.42/2.69 (b(z, s(z)) <=> b(elem!1, s(z))),
% 2.42/2.69 inference(monotonicity,[status(thm)],[7559])).
% 2.42/2.69 tff(7984,plain,
% 2.42/2.69 (b(elem!1, s(z))),
% 2.42/2.69 inference(modus_ponens,[status(thm)],[118, 7983])).
% 2.42/2.69 tff(7985,plain,
% 2.42/2.69 (~r(s(s(elem!1)), s(s(s(elem!1))))),
% 2.42/2.69 inference(unit_resolution,[status(thm)],[7480, 197, 7943, 7941, 7974])).
% 2.42/2.69 tff(7986,plain,
% 2.42/2.69 (b(s(s(elem!1)), s(s(s(elem!1))))),
% 2.42/2.69 inference(unit_resolution,[status(thm)],[461, 7985, 45])).
% 2.42/2.69 tff(7987,plain,
% 2.42/2.69 ((s(s(elem!1)) = elem!1) <=> (s(s(elem!1)) = z)),
% 2.42/2.69 inference(monotonicity,[status(thm)],[4891])).
% 2.42/2.69 tff(7988,plain,
% 2.42/2.69 ((s(s(elem!1)) = z) <=> (s(s(elem!1)) = elem!1)),
% 2.42/2.69 inference(symmetry,[status(thm)],[7987])).
% 2.42/2.69 tff(7989,plain,
% 2.42/2.69 ((~(s(s(elem!1)) = z)) <=> (~(s(s(elem!1)) = elem!1))),
% 2.42/2.69 inference(monotonicity,[status(thm)],[7988])).
% 2.42/2.69 tff(7990,plain,
% 2.42/2.69 (~(s(s(elem!1)) = elem!1)),
% 2.42/2.69 inference(modus_ponens,[status(thm)],[108, 7989])).
% 2.42/2.69 tff(7991,plain,
% 2.42/2.69 (b(s(z), z) <=> b(s(z), elem!1)),
% 2.42/2.69 inference(monotonicity,[status(thm)],[12])).
% 2.42/2.69 tff(7992,plain,
% 2.42/2.69 (b(s(z), elem!1)),
% 2.42/2.69 inference(modus_ponens,[status(thm)],[53, 7991])).
% 2.42/2.69 tff(7993,plain,
% 2.42/2.69 (~b(s(s(elem!1)), elem!1)),
% 2.42/2.69 inference(unit_resolution,[status(thm)],[6215, 7992, 376, 1212])).
% 2.42/2.69 tff(7994,plain,
% 2.42/2.69 (r(s(s(elem!1)), elem!1)),
% 2.42/2.69 inference(unit_resolution,[status(thm)],[784, 7993, 7990])).
% 2.42/2.69 tff(7995,plain,
% 2.42/2.69 ((s(s(s(s(elem!1)))) = z) <=> (s(s(s(s(elem!1)))) = elem!1)),
% 2.42/2.69 inference(monotonicity,[status(thm)],[12])).
% 2.42/2.69 tff(7996,plain,
% 2.42/2.69 ((~(s(s(s(s(elem!1)))) = z)) <=> (~(s(s(s(s(elem!1)))) = elem!1))),
% 2.42/2.69 inference(monotonicity,[status(thm)],[7995])).
% 2.42/2.69 tff(7997,plain,
% 2.42/2.69 (~(s(s(s(s(elem!1)))) = elem!1)),
% 2.42/2.69 inference(modus_ponens,[status(thm)],[626, 7996])).
% 2.42/2.69 tff(7998,plain,
% 2.42/2.69 ((s(s(s(elem!1))) = z) <=> (s(s(s(elem!1))) = elem!1)),
% 2.42/2.69 inference(monotonicity,[status(thm)],[12])).
% 2.42/2.69 tff(7999,plain,
% 2.42/2.69 ((s(s(s(elem!1))) = z) <=> (elem!1 = s(s(s(elem!1))))),
% 2.42/2.69 inference(transitivity,[status(thm)],[7998, 5406])).
% 2.42/2.69 tff(8000,plain,
% 2.42/2.69 ((~(s(s(s(elem!1))) = z)) <=> (~(elem!1 = s(s(s(elem!1)))))),
% 2.42/2.69 inference(monotonicity,[status(thm)],[7999])).
% 2.42/2.69 tff(8001,plain,
% 2.42/2.69 (~(elem!1 = s(s(s(elem!1))))),
% 2.42/2.69 inference(modus_ponens,[status(thm)],[89, 8000])).
% 2.42/2.69 tff(8002,plain,
% 2.42/2.69 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), s(z))) | (~r(s(z), s(s(s(elem!1))))) | (~r(s(z), s(s(s(s(elem!1)))))) | (~r(s(s(s(s(elem!1)))), s(s(s(elem!1))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(elem!1))), s(z))) | (~r(s(z), s(s(s(elem!1))))) | (~r(s(z), s(s(s(s(elem!1)))))) | (~r(s(s(s(s(elem!1)))), s(s(s(elem!1))))))),
% 2.42/2.69 inference(rewrite,[status(thm)],[])).
% 2.42/2.69 tff(8003,plain,
% 2.42/2.69 (((~r(s(s(s(elem!1))), s(z))) | (~r(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~r(s(z), s(s(s(elem!1))))) | (~r(s(z), s(s(s(s(elem!1))))))) <=> ((~r(s(s(s(elem!1))), s(z))) | (~r(s(z), s(s(s(elem!1))))) | (~r(s(z), s(s(s(s(elem!1)))))) | (~r(s(s(s(s(elem!1)))), s(s(s(elem!1))))))),
% 2.42/2.69 inference(rewrite,[status(thm)],[])).
% 2.42/2.69 tff(8004,plain,
% 2.42/2.69 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), s(z))) | (~r(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~r(s(z), s(s(s(elem!1))))) | (~r(s(z), s(s(s(s(elem!1)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), s(z))) | (~r(s(z), s(s(s(elem!1))))) | (~r(s(z), s(s(s(s(elem!1)))))) | (~r(s(s(s(s(elem!1)))), s(s(s(elem!1)))))))),
% 2.42/2.69 inference(monotonicity,[status(thm)],[8003])).
% 2.42/2.69 tff(8005,plain,
% 2.42/2.69 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), s(z))) | (~r(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~r(s(z), s(s(s(elem!1))))) | (~r(s(z), s(s(s(s(elem!1)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(elem!1))), s(z))) | (~r(s(z), s(s(s(elem!1))))) | (~r(s(z), s(s(s(s(elem!1)))))) | (~r(s(s(s(s(elem!1)))), s(s(s(elem!1))))))),
% 2.42/2.69 inference(transitivity,[status(thm)],[8004, 8002])).
% 2.42/2.69 tff(8006,plain,
% 2.42/2.69 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), s(z))) | (~r(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~r(s(z), s(s(s(elem!1))))) | (~r(s(z), s(s(s(s(elem!1)))))))),
% 2.42/2.69 inference(quant_inst,[status(thm)],[])).
% 2.42/2.69 tff(8007,plain,
% 2.42/2.69 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(elem!1))), s(z))) | (~r(s(z), s(s(s(elem!1))))) | (~r(s(z), s(s(s(s(elem!1)))))) | (~r(s(s(s(s(elem!1)))), s(s(s(elem!1)))))),
% 2.42/2.69 inference(modus_ponens,[status(thm)],[8006, 8005])).
% 2.42/2.69 tff(8008,plain,
% 2.42/2.69 (~r(s(z), s(s(s(s(elem!1)))))),
% 2.42/2.69 inference(unit_resolution,[status(thm)],[8007, 197, 350, 119, 1048])).
% 2.42/2.69 tff(8009,plain,
% 2.42/2.69 (b(s(z), s(s(s(s(elem!1)))))),
% 2.42/2.69 inference(unit_resolution,[status(thm)],[681, 8008])).
% 2.42/2.69 tff(8010,plain,
% 2.42/2.69 (~r(z, s(s(s(elem!1))))),
% 2.42/2.69 inference(unit_resolution,[status(thm)],[1514, 8009, 350, 1048, 53])).
% 2.42/2.69 tff(8011,plain,
% 2.42/2.69 (~r(elem!1, s(s(s(elem!1))))),
% 2.42/2.69 inference(unit_resolution,[status(thm)],[5446, 8010, 12])).
% 2.42/2.69 tff(8012,plain,
% 2.42/2.69 (b(elem!1, s(s(s(elem!1))))),
% 2.42/2.69 inference(unit_resolution,[status(thm)],[5451, 8011, 8001])).
% 2.42/2.69 tff(8013,plain,
% 2.42/2.69 (~b(s(s(s(s(elem!1)))), elem!1)),
% 2.42/2.69 inference(unit_resolution,[status(thm)],[710, 8012, 361, 641, 7992, 119])).
% 2.42/2.69 tff(8014,plain,
% 2.42/2.69 (r(s(s(s(s(elem!1)))), elem!1)),
% 2.42/2.69 inference(unit_resolution,[status(thm)],[719, 8013, 7997])).
% 2.42/2.69 tff(8015,plain,
% 2.42/2.69 (~r(s(s(s(s(elem!1)))), s(s(elem!1)))),
% 2.42/2.69 inference(unit_resolution,[status(thm)],[7911, 8014, 768, 1027])).
% 2.42/2.69 tff(8016,plain,
% 2.42/2.69 (b(s(s(s(s(elem!1)))), s(s(elem!1)))),
% 2.42/2.69 inference(unit_resolution,[status(thm)],[813, 8015, 806])).
% 2.42/2.69 tff(8017,plain,
% 2.42/2.69 ($false),
% 2.42/2.69 inference(unit_resolution,[status(thm)],[7895, 166, 376, 463, 839, 8009, 8016])).
% 2.42/2.69 tff(8018,plain,((~r(s(s(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(s(s(elem!1))), s(s(elem!1)))) | (s(s(s(s(elem!1)))) = s(s(elem!1))) | (~r(s(s(elem!1)), elem!1)) | (~r(elem!1, s(s(elem!1)))) | (s(s(s(elem!1))) = s(s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), elem!1)) | (~r(s(z), s(s(s(elem!1))))) | (~(z = elem!1)) | (~r(s(s(s(elem!1))), s(z))) | (~b(s(z), z))), inference(lemma,lemma(discharge,[]))).
% 2.42/2.69 tff(8019,plain,
% 2.42/2.69 (~r(s(s(s(s(elem!1)))), s(s(s(elem!1))))),
% 2.42/2.69 inference(unit_resolution,[status(thm)],[8018, 7994, 463, 839, 806, 376, 1027, 361, 641, 119, 12, 350, 53])).
% 2.42/2.69 tff(8020,plain,
% 2.42/2.69 (b(s(s(s(s(elem!1)))), s(s(s(elem!1))))),
% 2.42/2.69 inference(unit_resolution,[status(thm)],[1065, 8019, 1038])).
% 2.42/2.69 tff(8021,plain,
% 2.42/2.69 (~b(s(s(s(s(elem!1)))), s(s(elem!1)))),
% 2.42/2.69 inference(unit_resolution,[status(thm)],[6261, 166, 463, 839, 8020])).
% 2.42/2.69 tff(8022,plain,
% 2.42/2.69 (r(s(s(s(s(elem!1)))), s(s(elem!1)))),
% 2.42/2.69 inference(unit_resolution,[status(thm)],[813, 8021, 806])).
% 2.42/2.69 tff(8023,plain,
% 2.42/2.69 (~r(s(s(s(s(elem!1)))), elem!1)),
% 2.42/2.69 inference(unit_resolution,[status(thm)],[7911, 8022, 7994, 1027])).
% 2.42/2.69 tff(8024,plain,
% 2.42/2.69 (b(s(s(s(s(elem!1)))), elem!1)),
% 2.42/2.69 inference(unit_resolution,[status(thm)],[719, 8023, 7997])).
% 2.42/2.69 tff(8025,plain,
% 2.42/2.69 ((~b(s(s(s(s(elem!1)))), elem!1)) | (~b(s(s(s(s(elem!1)))), s(z)))),
% 2.42/2.69 inference(unit_resolution,[status(thm)],[6403, 166, 376, 463, 1212, 8020])).
% 2.42/2.69 tff(8026,plain,
% 2.42/2.69 (~b(s(s(s(s(elem!1)))), s(z))),
% 2.42/2.69 inference(unit_resolution,[status(thm)],[8025, 8024])).
% 2.42/2.69 tff(8027,plain,
% 2.42/2.69 (r(s(s(s(s(elem!1)))), s(z))),
% 2.42/2.69 inference(unit_resolution,[status(thm)],[661, 8026])).
% 2.42/2.69 tff(8028,plain,
% 2.42/2.69 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(s(s(elem!1))))) | (~r(s(s(elem!1)), s(z))) | (~r(s(s(s(s(elem!1)))), s(z))) | (~r(s(s(s(s(elem!1)))), s(s(elem!1)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(z), s(s(s(elem!1))))) | (~r(s(s(elem!1)), s(z))) | (~r(s(s(s(s(elem!1)))), s(z))) | (~r(s(s(s(s(elem!1)))), s(s(elem!1)))))),
% 2.42/2.69 inference(rewrite,[status(thm)],[])).
% 2.42/2.69 tff(8029,plain,
% 2.42/2.69 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(s(s(elem!1))))) | (~r(s(s(elem!1)), s(z))) | (~r(s(s(s(s(elem!1)))), s(z))) | (~r(s(s(s(s(elem!1)))), s(s(elem!1)))))),
% 2.42/2.69 inference(quant_inst,[status(thm)],[])).
% 2.42/2.69 tff(8030,plain,
% 2.42/2.69 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(z), s(s(s(elem!1))))) | (~r(s(s(elem!1)), s(z))) | (~r(s(s(s(s(elem!1)))), s(z))) | (~r(s(s(s(s(elem!1)))), s(s(elem!1))))),
% 2.42/2.69 inference(modus_ponens,[status(thm)],[8029, 8028])).
% 2.42/2.69 tff(8031,plain,
% 2.42/2.69 ($false),
% 2.42/2.69 inference(unit_resolution,[status(thm)],[8030, 197, 4577, 8027, 119, 8022])).
% 2.42/2.69 tff(8032,plain,((~b(s(z), z)) | (~r(s(s(elem!1)), s(z))) | (~r(s(z), s(s(s(elem!1))))) | (~b(s(z), s(s(elem!1)))) | (~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(elem!1, s(z))) | (~r(elem!1, s(s(elem!1)))) | (s(s(s(s(elem!1)))) = s(s(elem!1))) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (s(s(s(elem!1))) = s(s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), elem!1)) | (~(z = elem!1)) | (~r(s(s(s(elem!1))), s(z)))), inference(lemma,lemma(discharge,[]))).
% 2.42/2.69 tff(8033,plain,
% 2.42/2.69 (~b(s(z), z)),
% 2.42/2.69 inference(unit_resolution,[status(thm)],[8032, 7941, 7974, 7136, 7986, 7984, 7565, 7982, 7977, 358, 7944, 7559, 7943])).
% 2.42/2.69 tff(8034,plain,
% 2.42/2.69 (r(s(z), z)),
% 2.42/2.69 inference(unit_resolution,[status(thm)],[230, 8033])).
% 2.42/2.69 tff(8035,plain,
% 2.42/2.69 (~b(z, s(s(s(elem!1))))),
% 2.42/2.69 inference(unit_resolution,[status(thm)],[7965, 8034, 7562, 7943, 7941])).
% 2.42/2.69 tff(8036,plain,
% 2.42/2.69 (~r(z, s(s(s(elem!1))))),
% 2.42/2.69 inference(unit_resolution,[status(thm)],[3872, 8034, 7943, 7974])).
% 2.42/2.69 tff(8037,plain,
% 2.42/2.69 ($false),
% 2.42/2.69 inference(unit_resolution,[status(thm)],[261, 8036, 8035])).
% 2.42/2.69 tff(8038,plain,((s(s(elem!1)) = s(s(s(elem!1)))) | (~b(z, s(z))) | b(z, s(s(z)))), inference(lemma,lemma(discharge,[]))).
% 2.42/2.69 tff(8039,plain,
% 2.42/2.69 (s(s(elem!1)) = s(s(s(elem!1)))),
% 2.42/2.69 inference(unit_resolution,[status(thm)],[8038, 118, 125])).
% 2.42/2.69 tff(8040,plain,
% 2.42/2.69 ((s(s(elem!1)) = s(s(z))) <=> (s(s(s(elem!1))) = s(s(z)))),
% 2.42/2.69 inference(monotonicity,[status(thm)],[8039])).
% 2.42/2.69 tff(8041,plain,
% 2.42/2.69 ((s(s(elem!1)) = s(s(z))) <=> (s(s(z)) = s(s(s(elem!1))))),
% 2.42/2.69 inference(transitivity,[status(thm)],[8040, 487])).
% 2.42/2.69 tff(8042,plain,
% 2.42/2.69 ((s(s(z)) = s(s(s(elem!1)))) <=> (s(s(elem!1)) = s(s(z)))),
% 2.42/2.69 inference(symmetry,[status(thm)],[8041])).
% 2.42/2.69 tff(8043,plain,
% 2.42/2.69 ((s(s(z)) = s(s(s(elem!1)))) <=> (s(s(z)) = s(s(elem!1)))),
% 2.42/2.69 inference(transitivity,[status(thm)],[8042, 127])).
% 2.42/2.69 tff(8044,plain,
% 2.42/2.69 ((~(s(s(z)) = s(s(s(elem!1))))) <=> (~(s(s(z)) = s(s(elem!1))))),
% 2.42/2.69 inference(monotonicity,[status(thm)],[8043])).
% 2.42/2.69 tff(8045,plain,
% 2.42/2.69 (~(s(s(z)) = s(s(elem!1)))),
% 2.42/2.69 inference(modus_ponens,[status(thm)],[209, 8044])).
% 2.42/2.69 tff(8046,plain,
% 2.42/2.69 (~b(s(s(s(elem!1))), s(z))),
% 2.42/2.69 inference(unit_resolution,[status(thm)],[4570, 4557, 8039])).
% 2.42/2.69 tff(8047,plain,
% 2.42/2.69 (r(s(s(s(elem!1))), s(z))),
% 2.42/2.69 inference(unit_resolution,[status(thm)],[1849, 8046])).
% 2.42/2.69 tff(8048,plain,
% 2.42/2.69 (r(s(z), s(s(elem!1))) <=> r(s(z), s(s(s(elem!1))))),
% 2.42/2.69 inference(monotonicity,[status(thm)],[334])).
% 2.42/2.69 tff(8049,plain,
% 2.52/2.70 (r(s(z), s(s(s(elem!1))))),
% 2.52/2.70 inference(modus_ponens,[status(thm)],[311, 8048])).
% 2.52/2.70 tff(8050,plain,
% 2.52/2.70 (~r(z, s(s(s(elem!1))))),
% 2.52/2.70 inference(unit_resolution,[status(thm)],[3872, 97, 350, 8049])).
% 2.52/2.70 tff(8051,plain,
% 2.52/2.70 (b(z, s(s(s(elem!1))))),
% 2.52/2.70 inference(unit_resolution,[status(thm)],[261, 8050])).
% 2.52/2.70 tff(8052,plain,
% 2.52/2.70 (r(s(z), s(s(s(s(elem!1))))) <=> r(s(z), s(s(s(elem!1))))),
% 2.52/2.70 inference(monotonicity,[status(thm)],[6471])).
% 2.52/2.70 tff(8053,plain,
% 2.52/2.70 (r(s(z), s(s(s(elem!1)))) <=> r(s(z), s(s(s(s(elem!1)))))),
% 2.52/2.70 inference(symmetry,[status(thm)],[8052])).
% 2.52/2.70 tff(8054,plain,
% 2.52/2.70 (r(s(z), s(s(elem!1))) <=> r(s(z), s(s(s(s(elem!1)))))),
% 2.52/2.70 inference(transitivity,[status(thm)],[8048, 8053])).
% 2.52/2.70 tff(8055,plain,
% 2.52/2.70 (r(s(z), s(s(s(s(elem!1)))))),
% 2.52/2.70 inference(modus_ponens,[status(thm)],[311, 8054])).
% 2.52/2.70 tff(8056,plain,
% 2.52/2.70 (~r(s(s(z)), z)),
% 2.52/2.70 inference(unit_resolution,[status(thm)],[4287, 392, 155, 97])).
% 2.52/2.70 tff(8057,plain,
% 2.52/2.70 (b(s(s(z)), z)),
% 2.52/2.70 inference(unit_resolution,[status(thm)],[186, 8056])).
% 2.52/2.70 tff(8058,plain,
% 2.52/2.70 (~r(s(s(z)), s(s(s(elem!1))))),
% 2.52/2.70 inference(unit_resolution,[status(thm)],[1323, 392, 350, 699])).
% 2.52/2.70 tff(8059,plain,
% 2.52/2.70 (b(s(s(z)), s(s(s(elem!1))))),
% 2.52/2.70 inference(unit_resolution,[status(thm)],[279, 8058])).
% 2.52/2.70 tff(8060,plain,
% 2.52/2.70 (((~b(z, s(s(s(elem!1))))) | (~b(s(s(z)), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), z)) | (~b(z, s(s(s(elem!1))))) | (~b(s(s(z)), s(s(s(elem!1))))) | (~b(s(s(z)), z))) <=> ((~b(z, s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), z)) | (~b(s(s(z)), z)) | (~b(s(s(z)), s(s(s(elem!1))))))),
% 2.52/2.70 inference(rewrite,[status(thm)],[])).
% 2.52/2.70 tff(8061,plain,
% 2.52/2.70 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(s(elem!1))))) | (~b(s(s(z)), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), z)) | (~b(z, s(s(s(elem!1))))) | (~b(s(s(z)), s(s(s(elem!1))))) | (~b(s(s(z)), z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), z)) | (~b(s(s(z)), z)) | (~b(s(s(z)), s(s(s(elem!1)))))))),
% 2.52/2.70 inference(monotonicity,[status(thm)],[8060])).
% 2.52/2.70 tff(8062,plain,
% 2.52/2.70 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(s(elem!1))))) | (~b(s(s(z)), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), z)) | (~b(z, s(s(s(elem!1))))) | (~b(s(s(z)), s(s(s(elem!1))))) | (~b(s(s(z)), z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), z)) | (~b(s(s(z)), z)) | (~b(s(s(z)), s(s(s(elem!1))))))),
% 2.52/2.70 inference(transitivity,[status(thm)],[8061, 3161])).
% 2.52/2.70 tff(8063,plain,
% 2.52/2.70 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(s(elem!1))))) | (~b(s(s(z)), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), z)) | (~b(z, s(s(s(elem!1))))) | (~b(s(s(z)), s(s(s(elem!1))))) | (~b(s(s(z)), z)))),
% 2.52/2.70 inference(quant_inst,[status(thm)],[])).
% 2.52/2.70 tff(8064,plain,
% 2.52/2.70 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), z)) | (~b(s(s(z)), z)) | (~b(s(s(z)), s(s(s(elem!1)))))),
% 2.52/2.70 inference(modus_ponens,[status(thm)],[8063, 8062])).
% 2.52/2.70 tff(8065,plain,
% 2.52/2.70 ($false),
% 2.52/2.70 inference(unit_resolution,[status(thm)],[8064, 166, 240, 121, 8059, 8057])).
% 2.52/2.70 tff(8066,plain,((~r(s(s(z)), s(z))) | (~b(z, s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), z)) | (~r(z, s(s(z)))) | (~r(s(z), z)) | (~r(s(s(s(elem!1))), s(z))) | (~r(s(z), s(s(s(s(elem!1))))))), inference(lemma,lemma(discharge,[]))).
% 2.52/2.70 tff(8067,plain,
% 2.52/2.70 (~r(s(s(z)), s(z))),
% 2.52/2.70 inference(unit_resolution,[status(thm)],[8066, 8051, 121, 155, 97, 350, 8055])).
% 2.52/2.70 tff(8068,plain,
% 2.52/2.70 (b(s(s(z)), s(z))),
% 2.52/2.70 inference(unit_resolution,[status(thm)],[308, 8067])).
% 2.52/2.70 tff(8069,plain,
% 2.52/2.70 (~b(s(s(z)), s(s(s(elem!1))))),
% 2.52/2.70 inference(unit_resolution,[status(thm)],[3166, 166, 240, 121, 122])).
% 2.52/2.70 tff(8070,plain,
% 2.52/2.70 (r(s(s(z)), s(s(s(elem!1))))),
% 2.52/2.70 inference(unit_resolution,[status(thm)],[279, 8069])).
% 2.52/2.70 tff(8071,plain,
% 2.52/2.70 (b(s(s(s(z))), elem!1) <=> b(s(s(s(z))), s(s(s(elem!1))))),
% 2.52/2.70 inference(monotonicity,[status(thm)],[6548])).
% 2.52/2.70 tff(8072,plain,
% 2.52/2.70 (r(s(s(s(z))), s(s(s(elem!1)))) <=> r(s(s(s(z))), elem!1)),
% 2.52/2.70 inference(monotonicity,[status(thm)],[5659])).
% 2.52/2.70 tff(8073,plain,
% 2.52/2.70 (r(s(s(s(z))), elem!1) <=> r(s(s(s(z))), s(s(s(elem!1))))),
% 2.52/2.70 inference(symmetry,[status(thm)],[8072])).
% 2.52/2.70 tff(8074,assumption,(r(s(s(s(z))), elem!1)), introduced(assumption)).
% 2.52/2.70 tff(8075,plain,
% 2.52/2.70 (r(s(s(s(z))), s(s(s(elem!1))))),
% 2.52/2.70 inference(modus_ponens,[status(thm)],[8074, 8073])).
% 2.52/2.70 tff(8076,plain,
% 2.52/2.70 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(z))), s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), s(z))) | (~r(s(s(z)), s(s(s(elem!1))))) | (~r(s(s(z)), s(s(s(z))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(z))), s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), s(z))) | (~r(s(s(z)), s(s(s(elem!1))))) | (~r(s(s(z)), s(s(s(z))))))),
% 2.52/2.70 inference(rewrite,[status(thm)],[])).
% 2.52/2.70 tff(8077,plain,
% 2.52/2.70 (((~r(s(s(s(elem!1))), s(z))) | (~r(s(s(s(z))), s(s(s(elem!1))))) | (~r(s(s(z)), s(s(s(elem!1))))) | (~r(s(s(z)), s(s(s(z)))))) <=> ((~r(s(s(s(z))), s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), s(z))) | (~r(s(s(z)), s(s(s(elem!1))))) | (~r(s(s(z)), s(s(s(z))))))),
% 2.52/2.70 inference(rewrite,[status(thm)],[])).
% 2.52/2.70 tff(8078,plain,
% 2.52/2.70 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), s(z))) | (~r(s(s(s(z))), s(s(s(elem!1))))) | (~r(s(s(z)), s(s(s(elem!1))))) | (~r(s(s(z)), s(s(s(z))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(z))), s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), s(z))) | (~r(s(s(z)), s(s(s(elem!1))))) | (~r(s(s(z)), s(s(s(z)))))))),
% 2.52/2.70 inference(monotonicity,[status(thm)],[8077])).
% 2.52/2.70 tff(8079,plain,
% 2.52/2.70 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), s(z))) | (~r(s(s(s(z))), s(s(s(elem!1))))) | (~r(s(s(z)), s(s(s(elem!1))))) | (~r(s(s(z)), s(s(s(z))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(z))), s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), s(z))) | (~r(s(s(z)), s(s(s(elem!1))))) | (~r(s(s(z)), s(s(s(z))))))),
% 2.52/2.70 inference(transitivity,[status(thm)],[8078, 8076])).
% 2.52/2.70 tff(8080,plain,
% 2.52/2.70 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), s(z))) | (~r(s(s(s(z))), s(s(s(elem!1))))) | (~r(s(s(z)), s(s(s(elem!1))))) | (~r(s(s(z)), s(s(s(z))))))),
% 2.52/2.70 inference(quant_inst,[status(thm)],[])).
% 2.52/2.70 tff(8081,plain,
% 2.52/2.70 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(z))), s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), s(z))) | (~r(s(s(z)), s(s(s(elem!1))))) | (~r(s(s(z)), s(s(s(z)))))),
% 2.52/2.70 inference(modus_ponens,[status(thm)],[8080, 8079])).
% 2.52/2.70 tff(8082,plain,
% 2.52/2.70 (~r(s(s(s(z))), s(s(s(elem!1))))),
% 2.52/2.70 inference(unit_resolution,[status(thm)],[8081, 197, 350, 281, 1732])).
% 2.52/2.70 tff(8083,plain,
% 2.52/2.70 ($false),
% 2.52/2.70 inference(unit_resolution,[status(thm)],[8082, 8075])).
% 2.52/2.70 tff(8084,plain,((~r(s(s(s(z))), elem!1)) | (~(s(s(elem!1)) = s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), s(z))) | (~r(s(s(z)), s(s(s(elem!1))))) | (~r(s(s(z)), s(s(s(z)))))), inference(lemma,lemma(discharge,[]))).
% 2.52/2.70 tff(8085,plain,
% 2.52/2.70 (~r(s(s(s(z))), elem!1)),
% 2.52/2.70 inference(unit_resolution,[status(thm)],[8084, 1732, 350, 281, 334])).
% 2.52/2.70 tff(8086,plain,
% 2.52/2.70 (b(s(s(s(z))), elem!1)),
% 2.52/2.70 inference(unit_resolution,[status(thm)],[2826, 8085, 4027])).
% 2.52/2.70 tff(8087,plain,
% 2.52/2.70 (b(s(s(s(z))), s(s(s(elem!1))))),
% 2.52/2.70 inference(modus_ponens,[status(thm)],[8086, 8071])).
% 2.52/2.70 tff(8088,plain,
% 2.52/2.70 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), z)) | (~b(s(s(s(z))), z)) | (~b(s(s(s(z))), s(s(s(elem!1))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), z)) | (~b(s(s(s(z))), z)) | (~b(s(s(s(z))), s(s(s(elem!1))))))),
% 2.52/2.70 inference(rewrite,[status(thm)],[])).
% 2.52/2.70 tff(8089,plain,
% 2.52/2.70 (((~b(z, s(s(s(elem!1))))) | (~b(s(s(s(z))), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), z)) | (~b(z, s(s(s(elem!1))))) | (~b(s(s(s(z))), s(s(s(elem!1))))) | (~b(s(s(s(z))), z))) <=> ((~b(z, s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), z)) | (~b(s(s(s(z))), z)) | (~b(s(s(s(z))), s(s(s(elem!1))))))),
% 2.52/2.70 inference(rewrite,[status(thm)],[])).
% 2.52/2.70 tff(8090,plain,
% 2.52/2.70 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(s(elem!1))))) | (~b(s(s(s(z))), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), z)) | (~b(z, s(s(s(elem!1))))) | (~b(s(s(s(z))), s(s(s(elem!1))))) | (~b(s(s(s(z))), z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), z)) | (~b(s(s(s(z))), z)) | (~b(s(s(s(z))), s(s(s(elem!1)))))))),
% 2.52/2.70 inference(monotonicity,[status(thm)],[8089])).
% 2.52/2.70 tff(8091,plain,
% 2.52/2.70 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(s(elem!1))))) | (~b(s(s(s(z))), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), z)) | (~b(z, s(s(s(elem!1))))) | (~b(s(s(s(z))), s(s(s(elem!1))))) | (~b(s(s(s(z))), z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), z)) | (~b(s(s(s(z))), z)) | (~b(s(s(s(z))), s(s(s(elem!1))))))),
% 2.52/2.70 inference(transitivity,[status(thm)],[8090, 8088])).
% 2.52/2.70 tff(8092,plain,
% 2.52/2.70 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(s(elem!1))))) | (~b(s(s(s(z))), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), z)) | (~b(z, s(s(s(elem!1))))) | (~b(s(s(s(z))), s(s(s(elem!1))))) | (~b(s(s(s(z))), z)))),
% 2.52/2.70 inference(quant_inst,[status(thm)],[])).
% 2.52/2.70 tff(8093,plain,
% 2.52/2.70 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), z)) | (~b(s(s(s(z))), z)) | (~b(s(s(s(z))), s(s(s(elem!1)))))),
% 2.52/2.70 inference(modus_ponens,[status(thm)],[8092, 8091])).
% 2.52/2.70 tff(8094,plain,
% 2.52/2.70 (~b(s(s(s(z))), z)),
% 2.52/2.70 inference(unit_resolution,[status(thm)],[8093, 166, 240, 121, 8087])).
% 2.52/2.70 tff(8095,plain,
% 2.52/2.70 (r(s(s(s(z))), z)),
% 2.52/2.70 inference(unit_resolution,[status(thm)],[1713, 8094])).
% 2.52/2.70 tff(8096,plain,
% 2.52/2.70 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), z)) | (~b(s(s(s(z))), s(s(s(elem!1))))) | (~b(z, s(s(s(z))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), z)) | (~b(s(s(s(z))), s(s(s(elem!1))))) | (~b(z, s(s(s(z))))))),
% 2.52/2.70 inference(rewrite,[status(thm)],[])).
% 2.52/2.70 tff(8097,plain,
% 2.52/2.70 (((~b(z, s(s(s(elem!1))))) | (~b(z, s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), z)) | (~b(s(s(s(z))), s(s(s(elem!1))))) | (~b(z, s(s(s(elem!1))))) | (~b(z, s(s(s(z)))))) <=> ((~b(z, s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), z)) | (~b(s(s(s(z))), s(s(s(elem!1))))) | (~b(z, s(s(s(z))))))),
% 2.52/2.70 inference(rewrite,[status(thm)],[])).
% 2.52/2.70 tff(8098,plain,
% 2.52/2.70 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(s(elem!1))))) | (~b(z, s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), z)) | (~b(s(s(s(z))), s(s(s(elem!1))))) | (~b(z, s(s(s(elem!1))))) | (~b(z, s(s(s(z))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), z)) | (~b(s(s(s(z))), s(s(s(elem!1))))) | (~b(z, s(s(s(z)))))))),
% 2.52/2.70 inference(monotonicity,[status(thm)],[8097])).
% 2.52/2.70 tff(8099,plain,
% 2.52/2.70 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(s(elem!1))))) | (~b(z, s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), z)) | (~b(s(s(s(z))), s(s(s(elem!1))))) | (~b(z, s(s(s(elem!1))))) | (~b(z, s(s(s(z))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), z)) | (~b(s(s(s(z))), s(s(s(elem!1))))) | (~b(z, s(s(s(z))))))),
% 2.52/2.70 inference(transitivity,[status(thm)],[8098, 8096])).
% 2.52/2.70 tff(8100,plain,
% 2.52/2.70 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(s(elem!1))))) | (~b(z, s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), z)) | (~b(s(s(s(z))), s(s(s(elem!1))))) | (~b(z, s(s(s(elem!1))))) | (~b(z, s(s(s(z))))))),
% 2.52/2.70 inference(quant_inst,[status(thm)],[])).
% 2.52/2.70 tff(8101,plain,
% 2.52/2.70 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), z)) | (~b(s(s(s(z))), s(s(s(elem!1))))) | (~b(z, s(s(s(z)))))),
% 2.52/2.70 inference(modus_ponens,[status(thm)],[8100, 8099])).
% 2.52/2.70 tff(8102,plain,
% 2.52/2.70 (~b(z, s(s(s(z))))),
% 2.52/2.70 inference(unit_resolution,[status(thm)],[8101, 166, 240, 121, 8087])).
% 2.52/2.70 tff(8103,plain,
% 2.52/2.70 (r(z, s(s(s(z))))),
% 2.52/2.70 inference(unit_resolution,[status(thm)],[1696, 8102, 1692])).
% 2.52/2.70 tff(8104,plain,
% 2.52/2.70 ($false),
% 2.52/2.70 inference(unit_resolution,[status(thm)],[4554, 197, 155, 8103, 8095, 1732])).
% 2.52/2.70 tff(8105,plain,((~r(s(s(z)), s(s(s(z))))) | (~r(z, s(s(z)))) | (~b(z, s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), z)) | (~(s(s(elem!1)) = s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), s(z))) | (~r(s(s(z)), s(s(s(elem!1)))))), inference(lemma,lemma(discharge,[]))).
% 2.52/2.70 tff(8106,plain,
% 2.52/2.70 (~r(s(s(z)), s(s(s(z))))),
% 2.52/2.70 inference(unit_resolution,[status(thm)],[8105, 8070, 155, 350, 121, 334, 240])).
% 2.52/2.70 tff(8107,plain,
% 2.52/2.70 (b(s(s(z)), s(s(s(z))))),
% 2.52/2.70 inference(unit_resolution,[status(thm)],[1730, 8106])).
% 2.52/2.70 tff(8108,plain,
% 2.52/2.70 (~r(s(s(s(z))), z)),
% 2.52/2.70 inference(unit_resolution,[status(thm)],[3528, 8107, 156, 155, 97])).
% 2.52/2.70 tff(8109,plain,
% 2.52/2.70 (b(s(s(s(z))), z)),
% 2.52/2.70 inference(unit_resolution,[status(thm)],[1713, 8108])).
% 2.52/2.70 tff(8110,plain,
% 2.52/2.70 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), z)) | (~b(s(s(z)), z)) | (~b(s(s(s(z))), z)) | (~b(s(s(z)), s(s(s(z))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), z)) | (~b(s(s(z)), z)) | (~b(s(s(s(z))), z)) | (~b(s(s(z)), s(s(s(z))))))),
% 2.52/2.70 inference(rewrite,[status(thm)],[])).
% 2.52/2.70 tff(8111,plain,
% 2.52/2.70 (((~b(s(s(s(elem!1))), z)) | (~b(s(s(z)), z)) | (~b(z, s(s(s(elem!1))))) | (~b(s(s(s(z))), z)) | (~b(s(s(z)), z)) | (~b(s(s(z)), s(s(s(z)))))) <=> ((~b(z, s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), z)) | (~b(s(s(z)), z)) | (~b(s(s(s(z))), z)) | (~b(s(s(z)), s(s(s(z))))))),
% 2.52/2.70 inference(rewrite,[status(thm)],[])).
% 2.52/2.70 tff(8112,plain,
% 2.52/2.70 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), z)) | (~b(s(s(z)), z)) | (~b(z, s(s(s(elem!1))))) | (~b(s(s(s(z))), z)) | (~b(s(s(z)), z)) | (~b(s(s(z)), s(s(s(z))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), z)) | (~b(s(s(z)), z)) | (~b(s(s(s(z))), z)) | (~b(s(s(z)), s(s(s(z)))))))),
% 2.52/2.70 inference(monotonicity,[status(thm)],[8111])).
% 2.52/2.70 tff(8113,plain,
% 2.52/2.70 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), z)) | (~b(s(s(z)), z)) | (~b(z, s(s(s(elem!1))))) | (~b(s(s(s(z))), z)) | (~b(s(s(z)), z)) | (~b(s(s(z)), s(s(s(z))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), z)) | (~b(s(s(z)), z)) | (~b(s(s(s(z))), z)) | (~b(s(s(z)), s(s(s(z))))))),
% 2.52/2.70 inference(transitivity,[status(thm)],[8112, 8110])).
% 2.52/2.70 tff(8114,plain,
% 2.52/2.70 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), z)) | (~b(s(s(z)), z)) | (~b(z, s(s(s(elem!1))))) | (~b(s(s(s(z))), z)) | (~b(s(s(z)), z)) | (~b(s(s(z)), s(s(s(z))))))),
% 2.52/2.70 inference(quant_inst,[status(thm)],[])).
% 2.52/2.70 tff(8115,plain,
% 2.52/2.70 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), z)) | (~b(s(s(z)), z)) | (~b(s(s(s(z))), z)) | (~b(s(s(z)), s(s(s(z)))))),
% 2.52/2.70 inference(modus_ponens,[status(thm)],[8114, 8113])).
% 2.52/2.70 tff(8116,plain,
% 2.52/2.70 ($false),
% 2.52/2.70 inference(unit_resolution,[status(thm)],[8115, 166, 240, 121, 122, 8107, 8109])).
% 2.52/2.70 tff(8117,plain,((~b(s(s(z)), z)) | (~b(z, s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), z)) | (~b(s(s(z)), s(z))) | (~r(z, s(s(z)))) | (~r(s(z), z)) | (~r(s(s(s(elem!1))), s(z))) | (~(s(s(elem!1)) = s(s(s(elem!1)))))), inference(lemma,lemma(discharge,[]))).
% 2.52/2.70 tff(8118,plain,
% 2.52/2.70 (~b(s(s(z)), z)),
% 2.52/2.70 inference(unit_resolution,[status(thm)],[8117, 97, 121, 156, 155, 240, 350, 334])).
% 2.52/2.70 tff(8119,plain,
% 2.52/2.70 (r(s(s(z)), z)),
% 2.52/2.70 inference(unit_resolution,[status(thm)],[186, 8118])).
% 2.52/2.70 tff(8120,plain,
% 2.52/2.70 (~b(s(s(z)), s(s(s(z))))),
% 2.52/2.70 inference(unit_resolution,[status(thm)],[3528, 1733, 156, 155, 97])).
% 2.52/2.70 tff(8121,plain,
% 2.52/2.70 ($false),
% 2.52/2.70 inference(unit_resolution,[status(thm)],[1730, 8120, 7202])).
% 2.52/2.70 tff(8122,plain,((~r(s(s(s(z))), z)) | (~b(s(s(z)), s(z))) | (~r(z, s(s(z)))) | (~r(s(z), z)) | (~r(s(s(z)), z))), inference(lemma,lemma(discharge,[]))).
% 2.52/2.70 tff(8123,plain,
% 2.52/2.70 (~r(s(s(s(z))), z)),
% 2.52/2.70 inference(unit_resolution,[status(thm)],[8122, 8119, 155, 97, 156])).
% 2.52/2.70 tff(8124,plain,
% 2.52/2.70 (b(s(s(s(z))), z)),
% 2.52/2.70 inference(unit_resolution,[status(thm)],[1713, 8123])).
% 2.52/2.70 tff(8125,plain,
% 2.52/2.70 (~b(s(s(s(elem!1))), s(s(s(z))))),
% 2.52/2.70 inference(unit_resolution,[status(thm)],[7286, 166, 240, 121, 8124])).
% 2.52/2.70 tff(8126,plain,
% 2.52/2.70 (r(s(s(s(elem!1))), s(s(s(z))))),
% 2.52/2.70 inference(unit_resolution,[status(thm)],[3574, 8125, 3567])).
% 2.52/2.70 tff(8127,plain,
% 2.52/2.70 (~r(s(s(s(s(z)))), z)),
% 2.52/2.70 inference(unit_resolution,[status(thm)],[7728, 8119, 156, 155, 556, 97])).
% 2.52/2.70 tff(8128,plain,
% 2.52/2.70 (b(s(s(s(s(z)))), z)),
% 2.52/2.70 inference(unit_resolution,[status(thm)],[3266, 8127])).
% 2.52/2.70 tff(8129,plain,
% 2.52/2.70 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), z)) | (~b(s(s(s(z))), z)) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(s(z)))), z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), z)) | (~b(s(s(s(z))), z)) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(s(z)))), z)))),
% 2.52/2.70 inference(rewrite,[status(thm)],[])).
% 2.52/2.70 tff(8130,plain,
% 2.52/2.71 (((~b(s(s(s(elem!1))), z)) | (~b(s(s(s(s(z)))), z)) | (~b(z, s(s(s(elem!1))))) | (~b(s(s(s(z))), z)) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(s(z)))), s(s(s(z)))))) <=> ((~b(z, s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), z)) | (~b(s(s(s(z))), z)) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(s(z)))), z)))),
% 2.52/2.71 inference(rewrite,[status(thm)],[])).
% 2.52/2.71 tff(8131,plain,
% 2.52/2.71 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), z)) | (~b(s(s(s(s(z)))), z)) | (~b(z, s(s(s(elem!1))))) | (~b(s(s(s(z))), z)) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(s(z)))), s(s(s(z))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), z)) | (~b(s(s(s(z))), z)) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(s(z)))), z))))),
% 2.52/2.71 inference(monotonicity,[status(thm)],[8130])).
% 2.52/2.71 tff(8132,plain,
% 2.52/2.71 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), z)) | (~b(s(s(s(s(z)))), z)) | (~b(z, s(s(s(elem!1))))) | (~b(s(s(s(z))), z)) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(s(z)))), s(s(s(z))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), z)) | (~b(s(s(s(z))), z)) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(s(z)))), z)))),
% 2.52/2.71 inference(transitivity,[status(thm)],[8131, 8129])).
% 2.52/2.71 tff(8133,plain,
% 2.52/2.71 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), z)) | (~b(s(s(s(s(z)))), z)) | (~b(z, s(s(s(elem!1))))) | (~b(s(s(s(z))), z)) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(s(z)))), s(s(s(z))))))),
% 2.52/2.71 inference(quant_inst,[status(thm)],[])).
% 2.52/2.71 tff(8134,plain,
% 2.52/2.71 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), z)) | (~b(s(s(s(z))), z)) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(s(z)))), z))),
% 2.52/2.71 inference(modus_ponens,[status(thm)],[8133, 8132])).
% 2.52/2.71 tff(8135,plain,
% 2.52/2.71 (~b(s(s(s(s(z)))), s(s(s(z))))),
% 2.52/2.71 inference(unit_resolution,[status(thm)],[8134, 166, 240, 121, 8124, 8128])).
% 2.52/2.71 tff(8136,plain,
% 2.52/2.71 (r(s(s(s(s(z)))), s(s(s(z))))),
% 2.52/2.71 inference(unit_resolution,[status(thm)],[4662, 8135])).
% 2.52/2.71 tff(8137,plain,
% 2.52/2.71 (~r(s(s(s(z))), s(z))),
% 2.52/2.71 inference(unit_resolution,[status(thm)],[6519, 8126, 350, 311])).
% 2.52/2.71 tff(8138,plain,
% 2.52/2.71 (b(s(s(s(z))), s(z))),
% 2.52/2.71 inference(unit_resolution,[status(thm)],[1763, 8137])).
% 2.52/2.71 tff(8139,plain,
% 2.52/2.71 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(z)))) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(z)), s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), s(s(z)))) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(z)), s(z))))),
% 2.52/2.71 inference(rewrite,[status(thm)],[])).
% 2.52/2.71 tff(8140,plain,
% 2.52/2.71 (((~b(s(s(z)), s(z))) | (~b(s(s(s(z))), s(z))) | (~b(s(z), s(s(z)))) | (~b(s(s(z)), s(z))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(z))), s(s(z))))) <=> ((~b(s(z), s(s(z)))) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(z)), s(z))))),
% 2.52/2.71 inference(rewrite,[status(thm)],[])).
% 2.52/2.71 tff(8141,plain,
% 2.52/2.71 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), s(z))) | (~b(s(s(s(z))), s(z))) | (~b(s(z), s(s(z)))) | (~b(s(s(z)), s(z))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(z))), s(s(z)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(z)))) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(z)), s(z)))))),
% 2.52/2.71 inference(monotonicity,[status(thm)],[8140])).
% 2.52/2.71 tff(8142,plain,
% 2.52/2.71 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), s(z))) | (~b(s(s(s(z))), s(z))) | (~b(s(z), s(s(z)))) | (~b(s(s(z)), s(z))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(z))), s(s(z)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), s(s(z)))) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(z)), s(z))))),
% 2.52/2.71 inference(transitivity,[status(thm)],[8141, 8139])).
% 2.52/2.71 tff(8143,plain,
% 2.52/2.71 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), s(z))) | (~b(s(s(s(z))), s(z))) | (~b(s(z), s(s(z)))) | (~b(s(s(z)), s(z))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(z))), s(s(z)))))),
% 2.52/2.71 inference(quant_inst,[status(thm)],[])).
% 2.52/2.71 tff(8144,plain,
% 2.52/2.71 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), s(s(z)))) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(z)), s(z)))),
% 2.52/2.71 inference(modus_ponens,[status(thm)],[8143, 8142])).
% 2.52/2.71 tff(8145,plain,
% 2.52/2.71 (~b(s(s(s(z))), s(s(z)))),
% 2.52/2.71 inference(unit_resolution,[status(thm)],[8144, 166, 556, 156, 8138])).
% 2.52/2.71 tff(8146,plain,
% 2.52/2.71 (r(s(s(s(z))), s(s(z)))),
% 2.52/2.71 inference(unit_resolution,[status(thm)],[1010, 8145])).
% 2.52/2.71 tff(8147,plain,
% 2.52/2.71 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), s(s(s(z))))) | (~r(s(s(s(z))), s(s(z)))) | (~r(s(s(s(s(z)))), s(s(s(z))))) | (~r(s(s(s(elem!1))), s(s(s(s(z)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(elem!1))), s(s(s(z))))) | (~r(s(s(s(z))), s(s(z)))) | (~r(s(s(s(s(z)))), s(s(s(z))))) | (~r(s(s(s(elem!1))), s(s(s(s(z)))))))),
% 2.52/2.71 inference(rewrite,[status(thm)],[])).
% 2.52/2.71 tff(8148,plain,
% 2.52/2.71 (((~r(s(s(s(z))), s(s(z)))) | (~r(s(s(s(s(z)))), s(s(s(z))))) | (~r(s(s(s(elem!1))), s(s(s(z))))) | (~r(s(s(s(elem!1))), s(s(s(s(z))))))) <=> ((~r(s(s(s(elem!1))), s(s(s(z))))) | (~r(s(s(s(z))), s(s(z)))) | (~r(s(s(s(s(z)))), s(s(s(z))))) | (~r(s(s(s(elem!1))), s(s(s(s(z)))))))),
% 2.52/2.71 inference(rewrite,[status(thm)],[])).
% 2.52/2.71 tff(8149,plain,
% 2.52/2.71 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(z))), s(s(z)))) | (~r(s(s(s(s(z)))), s(s(s(z))))) | (~r(s(s(s(elem!1))), s(s(s(z))))) | (~r(s(s(s(elem!1))), s(s(s(s(z)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), s(s(s(z))))) | (~r(s(s(s(z))), s(s(z)))) | (~r(s(s(s(s(z)))), s(s(s(z))))) | (~r(s(s(s(elem!1))), s(s(s(s(z))))))))),
% 2.52/2.71 inference(monotonicity,[status(thm)],[8148])).
% 2.52/2.71 tff(8150,plain,
% 2.52/2.71 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(z))), s(s(z)))) | (~r(s(s(s(s(z)))), s(s(s(z))))) | (~r(s(s(s(elem!1))), s(s(s(z))))) | (~r(s(s(s(elem!1))), s(s(s(s(z)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(elem!1))), s(s(s(z))))) | (~r(s(s(s(z))), s(s(z)))) | (~r(s(s(s(s(z)))), s(s(s(z))))) | (~r(s(s(s(elem!1))), s(s(s(s(z)))))))),
% 2.52/2.71 inference(transitivity,[status(thm)],[8149, 8147])).
% 2.52/2.71 tff(8151,plain,
% 2.52/2.71 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(z))), s(s(z)))) | (~r(s(s(s(s(z)))), s(s(s(z))))) | (~r(s(s(s(elem!1))), s(s(s(z))))) | (~r(s(s(s(elem!1))), s(s(s(s(z)))))))),
% 2.52/2.71 inference(quant_inst,[status(thm)],[])).
% 2.52/2.71 tff(8152,plain,
% 2.52/2.71 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(elem!1))), s(s(s(z))))) | (~r(s(s(s(z))), s(s(z)))) | (~r(s(s(s(s(z)))), s(s(s(z))))) | (~r(s(s(s(elem!1))), s(s(s(s(z))))))),
% 2.52/2.71 inference(modus_ponens,[status(thm)],[8151, 8150])).
% 2.52/2.71 tff(8153,plain,
% 2.52/2.71 (~r(s(s(s(elem!1))), s(s(s(s(z)))))),
% 2.52/2.71 inference(unit_resolution,[status(thm)],[8152, 197, 8146, 8136, 8126])).
% 2.52/2.71 tff(8154,plain,
% 2.52/2.71 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), z)) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(elem!1))), s(s(s(s(z)))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), z)) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(elem!1))), s(s(s(s(z)))))))),
% 2.52/2.71 inference(rewrite,[status(thm)],[])).
% 2.52/2.71 tff(8155,plain,
% 2.52/2.71 (((~b(s(s(s(elem!1))), z)) | (~b(s(s(s(elem!1))), z)) | (~b(z, s(s(s(elem!1))))) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(elem!1))), z)) | (~b(s(s(s(elem!1))), s(s(s(s(z))))))) <=> ((~b(z, s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), z)) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(elem!1))), s(s(s(s(z)))))))),
% 2.52/2.71 inference(rewrite,[status(thm)],[])).
% 2.52/2.71 tff(8156,plain,
% 2.52/2.71 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), z)) | (~b(s(s(s(elem!1))), z)) | (~b(z, s(s(s(elem!1))))) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(elem!1))), z)) | (~b(s(s(s(elem!1))), s(s(s(s(z)))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), z)) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(elem!1))), s(s(s(s(z))))))))),
% 2.52/2.71 inference(monotonicity,[status(thm)],[8155])).
% 2.52/2.71 tff(8157,plain,
% 2.52/2.71 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), z)) | (~b(s(s(s(elem!1))), z)) | (~b(z, s(s(s(elem!1))))) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(elem!1))), z)) | (~b(s(s(s(elem!1))), s(s(s(s(z)))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), z)) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(elem!1))), s(s(s(s(z)))))))),
% 2.52/2.71 inference(transitivity,[status(thm)],[8156, 8154])).
% 2.52/2.71 tff(8158,plain,
% 2.52/2.71 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), z)) | (~b(s(s(s(elem!1))), z)) | (~b(z, s(s(s(elem!1))))) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(elem!1))), z)) | (~b(s(s(s(elem!1))), s(s(s(s(z)))))))),
% 2.52/2.71 inference(quant_inst,[status(thm)],[])).
% 2.52/2.71 tff(8159,plain,
% 2.52/2.71 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), z)) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(elem!1))), s(s(s(s(z))))))),
% 2.52/2.71 inference(modus_ponens,[status(thm)],[8158, 8157])).
% 2.52/2.71 tff(8160,plain,
% 2.52/2.71 (~b(s(s(s(elem!1))), s(s(s(s(z)))))),
% 2.52/2.71 inference(unit_resolution,[status(thm)],[8159, 166, 240, 121, 8128])).
% 2.52/2.71 tff(8161,plain,
% 2.52/2.71 (~b(elem!1, s(s(s(s(z)))))),
% 2.52/2.71 inference(modus_ponens,[status(thm)],[8160, 6551])).
% 2.52/2.71 tff(8162,plain,
% 2.52/2.71 (r(elem!1, s(s(s(s(z)))))),
% 2.52/2.71 inference(unit_resolution,[status(thm)],[1098, 8161, 6568])).
% 2.52/2.71 tff(8163,plain,
% 2.52/2.71 ($false),
% 2.52/2.71 inference(unit_resolution,[status(thm)],[5665, 8162, 8153, 334])).
% 2.52/2.71 tff(8164,plain,((~r(s(z), z)) | (~(s(s(elem!1)) = s(s(s(elem!1))))) | (~b(z, s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), z)) | (~b(s(s(z)), s(z))) | (~r(z, s(s(z)))) | (~b(s(z), s(s(z)))) | (~r(s(s(s(elem!1))), s(z))) | (~r(s(z), s(s(elem!1)))) | (s(s(s(elem!1))) = s(s(s(z))))), inference(lemma,lemma(discharge,[]))).
% 2.52/2.71 tff(8165,plain,
% 2.52/2.71 (~b(s(z), s(s(z)))),
% 2.52/2.71 inference(unit_resolution,[status(thm)],[8164, 8068, 155, 121, 334, 6474, 97, 8051, 311, 350])).
% 2.52/2.71 tff(8166,plain,
% 2.52/2.71 (r(s(z), s(s(z)))),
% 2.52/2.71 inference(unit_resolution,[status(thm)],[427, 8165])).
% 2.52/2.71 tff(8167,plain,
% 2.52/2.71 (~b(s(s(z)), z)),
% 2.52/2.71 inference(unit_resolution,[status(thm)],[8117, 8068, 155, 121, 350, 8051, 97, 334])).
% 2.52/2.71 tff(8168,plain,
% 2.52/2.71 (r(s(s(z)), z)),
% 2.52/2.71 inference(unit_resolution,[status(thm)],[186, 8167])).
% 2.52/2.71 tff(8169,plain,
% 2.52/2.71 ($false),
% 2.52/2.71 inference(unit_resolution,[status(thm)],[2498, 8168, 8166, 155, 97])).
% 2.52/2.71 tff(8170,plain,((~r(s(z), z)) | (~r(z, s(s(z)))) | (~b(s(s(s(elem!1))), z)) | (~r(s(s(s(elem!1))), s(z))) | (~(s(s(elem!1)) = s(s(s(elem!1))))) | (~r(s(z), s(s(elem!1))))), inference(lemma,lemma(discharge,[]))).
% 2.52/2.71 tff(8171,plain,
% 2.52/2.71 (~r(s(z), z)),
% 2.52/2.71 inference(unit_resolution,[status(thm)],[8170, 8047, 6718, 152, 8039, 85])).
% 2.52/2.71 tff(8172,plain,
% 2.52/2.71 (b(s(z), z)),
% 2.52/2.71 inference(unit_resolution,[status(thm)],[230, 8171])).
% 2.52/2.71 tff(8173,plain,
% 2.52/2.71 (s(s(s(elem!1))) = s(s(elem!1))),
% 2.52/2.71 inference(symmetry,[status(thm)],[8039])).
% 2.52/2.71 tff(8174,plain,
% 2.52/2.71 (s(s(s(s(elem!1)))) = s(s(s(elem!1)))),
% 2.52/2.71 inference(monotonicity,[status(thm)],[8173])).
% 2.52/2.71 tff(8175,plain,
% 2.52/2.71 ((s(s(s(s(elem!1)))) = s(s(s(z)))) <=> (s(s(s(elem!1))) = s(s(s(z))))),
% 2.52/2.71 inference(monotonicity,[status(thm)],[8174])).
% 2.52/2.71 tff(8176,plain,
% 2.52/2.71 ((~(s(s(s(s(elem!1)))) = s(s(s(z))))) <=> (~(s(s(s(elem!1))) = s(s(s(z)))))),
% 2.52/2.71 inference(monotonicity,[status(thm)],[8175])).
% 2.52/2.71 tff(8177,plain,
% 2.52/2.71 (~(s(s(s(elem!1))) = s(s(s(z))))),
% 2.52/2.71 inference(modus_ponens,[status(thm)],[5112, 8176])).
% 2.52/2.71 tff(8178,plain,
% 2.52/2.71 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), z)) | (~b(s(s(s(elem!1))), z)) | (~b(z, s(z))) | (~b(s(s(s(z))), z)) | (~b(s(s(s(elem!1))), s(s(s(z))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), z)) | (~b(s(s(s(elem!1))), z)) | (~b(z, s(z))) | (~b(s(s(s(z))), z)) | (~b(s(s(s(elem!1))), s(s(s(z))))))),
% 2.52/2.71 inference(rewrite,[status(thm)],[])).
% 2.52/2.71 tff(8179,plain,
% 2.52/2.71 (((~b(s(z), z)) | (~b(s(s(s(elem!1))), z)) | (~b(z, s(z))) | (~b(s(s(s(z))), z)) | (~b(s(s(s(elem!1))), z)) | (~b(s(s(s(elem!1))), s(s(s(z)))))) <=> ((~b(s(z), z)) | (~b(s(s(s(elem!1))), z)) | (~b(z, s(z))) | (~b(s(s(s(z))), z)) | (~b(s(s(s(elem!1))), s(s(s(z))))))),
% 2.52/2.71 inference(rewrite,[status(thm)],[])).
% 2.52/2.71 tff(8180,plain,
% 2.52/2.71 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), z)) | (~b(s(s(s(elem!1))), z)) | (~b(z, s(z))) | (~b(s(s(s(z))), z)) | (~b(s(s(s(elem!1))), z)) | (~b(s(s(s(elem!1))), s(s(s(z))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), z)) | (~b(s(s(s(elem!1))), z)) | (~b(z, s(z))) | (~b(s(s(s(z))), z)) | (~b(s(s(s(elem!1))), s(s(s(z)))))))),
% 2.52/2.71 inference(monotonicity,[status(thm)],[8179])).
% 2.52/2.71 tff(8181,plain,
% 2.52/2.71 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), z)) | (~b(s(s(s(elem!1))), z)) | (~b(z, s(z))) | (~b(s(s(s(z))), z)) | (~b(s(s(s(elem!1))), z)) | (~b(s(s(s(elem!1))), s(s(s(z))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), z)) | (~b(s(s(s(elem!1))), z)) | (~b(z, s(z))) | (~b(s(s(s(z))), z)) | (~b(s(s(s(elem!1))), s(s(s(z))))))),
% 2.52/2.71 inference(transitivity,[status(thm)],[8180, 8178])).
% 2.52/2.71 tff(8182,plain,
% 2.52/2.71 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), z)) | (~b(s(s(s(elem!1))), z)) | (~b(z, s(z))) | (~b(s(s(s(z))), z)) | (~b(s(s(s(elem!1))), z)) | (~b(s(s(s(elem!1))), s(s(s(z))))))),
% 2.52/2.71 inference(quant_inst,[status(thm)],[])).
% 2.52/2.72 tff(8183,plain,
% 2.52/2.72 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), z)) | (~b(s(s(s(elem!1))), z)) | (~b(z, s(z))) | (~b(s(s(s(z))), z)) | (~b(s(s(s(elem!1))), s(s(s(z)))))),
% 2.52/2.72 inference(modus_ponens,[status(thm)],[8182, 8181])).
% 2.52/2.72 tff(8184,plain,
% 2.52/2.72 (~b(s(s(s(elem!1))), s(s(s(z))))),
% 2.52/2.72 inference(unit_resolution,[status(thm)],[8183, 166, 53, 118, 121, 1699])).
% 2.52/2.72 tff(8185,plain,
% 2.52/2.72 (r(s(s(s(elem!1))), s(s(s(z))))),
% 2.52/2.72 inference(unit_resolution,[status(thm)],[3574, 8184, 3567])).
% 2.52/2.72 tff(8186,plain,
% 2.52/2.72 ($false),
% 2.52/2.72 inference(unit_resolution,[status(thm)],[6519, 4047, 8185, 311, 350])).
% 2.52/2.72 tff(8187,plain,((~b(s(s(s(z))), z)) | (~r(s(z), s(s(elem!1)))) | (~r(s(s(s(elem!1))), s(z))) | (s(s(s(elem!1))) = s(s(s(z)))) | (~b(s(z), z)) | (~b(z, s(z))) | (~b(s(s(s(elem!1))), z))), inference(lemma,lemma(discharge,[]))).
% 2.52/2.72 tff(8188,plain,
% 2.52/2.72 (~b(s(s(s(z))), z)),
% 2.52/2.72 inference(unit_resolution,[status(thm)],[8187, 85, 8047, 8177, 8172, 118, 6718])).
% 2.52/2.72 tff(8189,plain,
% 2.52/2.72 (r(s(s(s(z))), z)),
% 2.52/2.72 inference(unit_resolution,[status(thm)],[1713, 8188])).
% 2.52/2.72 tff(8190,plain,
% 2.52/2.72 (~r(s(z), z)),
% 2.52/2.72 inference(unit_resolution,[status(thm)],[8170, 350, 121, 155, 334, 311])).
% 2.52/2.72 tff(8191,plain,
% 2.52/2.72 (b(s(z), z)),
% 2.52/2.72 inference(unit_resolution,[status(thm)],[230, 8190])).
% 2.52/2.72 tff(8192,plain,
% 2.52/2.72 (~b(s(s(s(z))), z)),
% 2.52/2.72 inference(unit_resolution,[status(thm)],[8187, 311, 350, 6474, 8191, 118, 121])).
% 2.52/2.72 tff(8193,plain,
% 2.52/2.72 (r(s(s(s(z))), z)),
% 2.52/2.72 inference(unit_resolution,[status(thm)],[1713, 8192])).
% 2.52/2.72 tff(8194,plain,
% 2.52/2.72 (~r(s(s(s(elem!1))), s(s(z)))),
% 2.52/2.72 inference(unit_resolution,[status(thm)],[854, 392, 311, 350])).
% 2.52/2.72 tff(8195,plain,
% 2.52/2.72 (b(s(s(s(elem!1))), s(s(z)))),
% 2.52/2.72 inference(unit_resolution,[status(thm)],[218, 8194])).
% 2.52/2.72 tff(8196,plain,
% 2.52/2.72 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), z)) | (~b(s(s(s(elem!1))), s(s(z)))) | (~b(s(s(s(elem!1))), z)) | (~b(z, s(z))) | (~b(s(s(z)), z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), z)) | (~b(s(s(s(elem!1))), s(s(z)))) | (~b(s(s(s(elem!1))), z)) | (~b(z, s(z))) | (~b(s(s(z)), z)))),
% 2.52/2.72 inference(rewrite,[status(thm)],[])).
% 2.52/2.72 tff(8197,plain,
% 2.52/2.72 (((~b(s(z), z)) | (~b(s(s(s(elem!1))), z)) | (~b(z, s(z))) | (~b(s(s(z)), z)) | (~b(s(s(s(elem!1))), z)) | (~b(s(s(s(elem!1))), s(s(z))))) <=> ((~b(s(z), z)) | (~b(s(s(s(elem!1))), s(s(z)))) | (~b(s(s(s(elem!1))), z)) | (~b(z, s(z))) | (~b(s(s(z)), z)))),
% 2.52/2.72 inference(rewrite,[status(thm)],[])).
% 2.52/2.72 tff(8198,plain,
% 2.52/2.72 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), z)) | (~b(s(s(s(elem!1))), z)) | (~b(z, s(z))) | (~b(s(s(z)), z)) | (~b(s(s(s(elem!1))), z)) | (~b(s(s(s(elem!1))), s(s(z)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), z)) | (~b(s(s(s(elem!1))), s(s(z)))) | (~b(s(s(s(elem!1))), z)) | (~b(z, s(z))) | (~b(s(s(z)), z))))),
% 2.52/2.72 inference(monotonicity,[status(thm)],[8197])).
% 2.52/2.72 tff(8199,plain,
% 2.52/2.72 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), z)) | (~b(s(s(s(elem!1))), z)) | (~b(z, s(z))) | (~b(s(s(z)), z)) | (~b(s(s(s(elem!1))), z)) | (~b(s(s(s(elem!1))), s(s(z)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), z)) | (~b(s(s(s(elem!1))), s(s(z)))) | (~b(s(s(s(elem!1))), z)) | (~b(z, s(z))) | (~b(s(s(z)), z)))),
% 2.52/2.72 inference(transitivity,[status(thm)],[8198, 8196])).
% 2.52/2.72 tff(8200,plain,
% 2.52/2.72 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), z)) | (~b(s(s(s(elem!1))), z)) | (~b(z, s(z))) | (~b(s(s(z)), z)) | (~b(s(s(s(elem!1))), z)) | (~b(s(s(s(elem!1))), s(s(z)))))),
% 2.52/2.72 inference(quant_inst,[status(thm)],[])).
% 2.52/2.72 tff(8201,plain,
% 2.52/2.72 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), z)) | (~b(s(s(s(elem!1))), s(s(z)))) | (~b(s(s(s(elem!1))), z)) | (~b(z, s(z))) | (~b(s(s(z)), z))),
% 2.52/2.72 inference(modus_ponens,[status(thm)],[8200, 8199])).
% 2.52/2.72 tff(8202,plain,
% 2.52/2.72 ($false),
% 2.52/2.72 inference(unit_resolution,[status(thm)],[8201, 166, 53, 118, 121, 122, 2060])).
% 2.52/2.72 tff(8203,plain,((~b(s(s(z)), z)) | (~b(s(z), z)) | (~b(z, s(z))) | (~b(s(s(s(elem!1))), z)) | (~b(s(s(s(elem!1))), s(s(z))))), inference(lemma,lemma(discharge,[]))).
% 2.52/2.72 tff(8204,plain,
% 2.52/2.72 (~b(s(s(z)), z)),
% 2.52/2.72 inference(unit_resolution,[status(thm)],[8203, 8195, 118, 121, 8191])).
% 2.52/2.72 tff(8205,plain,
% 2.52/2.72 (r(s(s(z)), z)),
% 2.52/2.72 inference(unit_resolution,[status(thm)],[186, 8204])).
% 2.52/2.72 tff(8206,plain,
% 2.52/2.72 (~r(s(s(s(z))), s(s(z)))),
% 2.52/2.72 inference(unit_resolution,[status(thm)],[1717, 197, 155, 8205, 8193])).
% 2.52/2.72 tff(8207,plain,
% 2.52/2.72 (b(s(s(s(z))), s(s(z)))),
% 2.52/2.72 inference(unit_resolution,[status(thm)],[1010, 8206])).
% 2.52/2.72 tff(8208,plain,
% 2.52/2.72 (~r(s(s(z)), s(s(s(z))))),
% 2.52/2.72 inference(unit_resolution,[status(thm)],[1741, 8205, 155, 8193])).
% 2.52/2.72 tff(8209,plain,
% 2.52/2.72 (b(s(s(z)), s(s(s(z))))),
% 2.52/2.72 inference(unit_resolution,[status(thm)],[1730, 8208])).
% 2.52/2.72 tff(8210,plain,
% 2.52/2.72 (~r(s(s(z)), s(s(s(elem!1))))),
% 2.52/2.72 inference(unit_resolution,[status(thm)],[1323, 392, 350, 8055])).
% 2.52/2.72 tff(8211,plain,
% 2.52/2.72 (b(s(s(z)), s(s(s(elem!1))))),
% 2.52/2.72 inference(unit_resolution,[status(thm)],[279, 8210])).
% 2.52/2.72 tff(8212,plain,
% 2.52/2.72 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), s(s(z)))) | (~b(s(s(s(elem!1))), z)) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(s(z)), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(s(s(z))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(elem!1))), s(s(z)))) | (~b(s(s(s(elem!1))), z)) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(s(z)), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(s(s(z))))))),
% 2.52/2.72 inference(rewrite,[status(thm)],[])).
% 2.52/2.72 tff(8213,plain,
% 2.52/2.72 (((~b(s(s(s(elem!1))), z)) | (~b(s(s(s(elem!1))), z)) | (~b(s(s(z)), s(s(s(elem!1))))) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(s(s(elem!1))), s(s(z)))) | (~b(s(s(s(elem!1))), s(s(s(z)))))) <=> ((~b(s(s(s(elem!1))), s(s(z)))) | (~b(s(s(s(elem!1))), z)) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(s(z)), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(s(s(z))))))),
% 2.52/2.72 inference(rewrite,[status(thm)],[])).
% 2.52/2.72 tff(8214,plain,
% 2.52/2.72 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), z)) | (~b(s(s(s(elem!1))), z)) | (~b(s(s(z)), s(s(s(elem!1))))) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(s(s(elem!1))), s(s(z)))) | (~b(s(s(s(elem!1))), s(s(s(z))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), s(s(z)))) | (~b(s(s(s(elem!1))), z)) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(s(z)), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(s(s(z)))))))),
% 2.52/2.72 inference(monotonicity,[status(thm)],[8213])).
% 2.52/2.72 tff(8215,plain,
% 2.52/2.72 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), z)) | (~b(s(s(s(elem!1))), z)) | (~b(s(s(z)), s(s(s(elem!1))))) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(s(s(elem!1))), s(s(z)))) | (~b(s(s(s(elem!1))), s(s(s(z))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(elem!1))), s(s(z)))) | (~b(s(s(s(elem!1))), z)) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(s(z)), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(s(s(z))))))),
% 2.52/2.72 inference(transitivity,[status(thm)],[8214, 8212])).
% 2.52/2.72 tff(8216,plain,
% 2.52/2.72 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), z)) | (~b(s(s(s(elem!1))), z)) | (~b(s(s(z)), s(s(s(elem!1))))) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(s(s(elem!1))), s(s(z)))) | (~b(s(s(s(elem!1))), s(s(s(z))))))),
% 2.52/2.72 inference(quant_inst,[status(thm)],[])).
% 2.52/2.72 tff(8217,plain,
% 2.52/2.72 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(elem!1))), s(s(z)))) | (~b(s(s(s(elem!1))), z)) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(s(z)), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(s(s(z)))))),
% 2.52/2.72 inference(modus_ponens,[status(thm)],[8216, 8215])).
% 2.52/2.72 tff(8218,plain,
% 2.52/2.72 (~b(s(s(s(elem!1))), s(s(s(z))))),
% 2.52/2.72 inference(unit_resolution,[status(thm)],[8217, 166, 121, 8211, 8207, 8195])).
% 2.52/2.72 tff(8219,plain,
% 2.52/2.72 (r(s(s(s(elem!1))), s(s(s(z))))),
% 2.52/2.72 inference(unit_resolution,[status(thm)],[3574, 8218, 6474])).
% 2.52/2.72 tff(8220,plain,
% 2.52/2.72 (~r(s(s(s(z))), s(z))),
% 2.52/2.72 inference(unit_resolution,[status(thm)],[6519, 8219, 311, 350])).
% 2.52/2.72 tff(8221,plain,
% 2.52/2.72 (b(s(s(s(z))), s(z))),
% 2.52/2.72 inference(unit_resolution,[status(thm)],[1763, 8220])).
% 2.52/2.72 tff(8222,plain,
% 2.52/2.72 (~(elem!1 = s(s(s(z))))),
% 2.52/2.72 inference(unit_resolution,[status(thm)],[1564, 4027])).
% 2.52/2.72 tff(8223,plain,
% 2.52/2.72 (b(elem!1, s(s(s(z)))) <=> b(s(s(s(elem!1))), s(s(s(z))))),
% 2.52/2.72 inference(monotonicity,[status(thm)],[6548])).
% 2.52/2.72 tff(8224,plain,
% 2.52/2.72 (b(s(s(s(elem!1))), s(s(s(z)))) <=> b(elem!1, s(s(s(z))))),
% 2.52/2.72 inference(symmetry,[status(thm)],[8223])).
% 2.52/2.72 tff(8225,plain,
% 2.52/2.72 ((~b(s(s(s(elem!1))), s(s(s(z))))) <=> (~b(elem!1, s(s(s(z)))))),
% 2.52/2.72 inference(monotonicity,[status(thm)],[8224])).
% 2.52/2.72 tff(8226,plain,
% 2.52/2.72 (~b(elem!1, s(s(s(z))))),
% 2.52/2.72 inference(modus_ponens,[status(thm)],[8218, 8225])).
% 2.52/2.72 tff(8227,plain,
% 2.52/2.72 (r(elem!1, s(s(s(z))))),
% 2.52/2.72 inference(unit_resolution,[status(thm)],[1619, 8226, 8222])).
% 2.52/2.72 tff(8228,plain,
% 2.52/2.72 (inj_0(s(s(elem!1))) = inj_0(s(elem!1))),
% 2.52/2.72 inference(symmetry,[status(thm)],[4070])).
% 2.52/2.72 tff(8229,plain,
% 2.52/2.72 (s(s(elem!1)) = s(s(s(elem!1)))),
% 2.52/2.72 inference(symmetry,[status(thm)],[47])).
% 2.52/2.72 tff(8230,plain,
% 2.52/2.72 (s(s(elem!1)) = elem!1),
% 2.52/2.72 inference(transitivity,[status(thm)],[8229, 4067, 39, 8228, 20])).
% 2.52/2.72 tff(8231,plain,
% 2.52/2.72 (r(s(s(elem!1)), s(s(s(z)))) <=> r(elem!1, s(s(s(z))))),
% 2.52/2.72 inference(monotonicity,[status(thm)],[8230])).
% 2.52/2.72 tff(8232,plain,
% 2.52/2.72 (r(elem!1, s(s(s(z)))) <=> r(s(s(elem!1)), s(s(s(z))))),
% 2.52/2.72 inference(symmetry,[status(thm)],[8231])).
% 2.52/2.72 tff(8233,plain,
% 2.52/2.72 (r(s(s(elem!1)), s(s(s(z))))),
% 2.52/2.72 inference(modus_ponens,[status(thm)],[1604, 8232])).
% 2.52/2.72 tff(8234,plain,
% 2.52/2.72 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(elem!1)), s(z))) | (~r(s(s(s(z))), z)) | (~r(s(z), s(s(s(z))))) | (~r(s(s(elem!1)), s(s(s(z))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(elem!1)), s(z))) | (~r(s(s(s(z))), z)) | (~r(s(z), s(s(s(z))))) | (~r(s(s(elem!1)), s(s(s(z))))))),
% 2.52/2.72 inference(rewrite,[status(thm)],[])).
% 2.52/2.72 tff(8235,plain,
% 2.52/2.72 (((~r(s(s(s(z))), z)) | (~r(s(z), s(s(s(z))))) | (~r(s(s(elem!1)), s(s(s(z))))) | (~r(s(s(elem!1)), s(z)))) <=> ((~r(s(s(elem!1)), s(z))) | (~r(s(s(s(z))), z)) | (~r(s(z), s(s(s(z))))) | (~r(s(s(elem!1)), s(s(s(z))))))),
% 2.52/2.72 inference(rewrite,[status(thm)],[])).
% 2.52/2.72 tff(8236,plain,
% 2.52/2.72 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(z))), z)) | (~r(s(z), s(s(s(z))))) | (~r(s(s(elem!1)), s(s(s(z))))) | (~r(s(s(elem!1)), s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(elem!1)), s(z))) | (~r(s(s(s(z))), z)) | (~r(s(z), s(s(s(z))))) | (~r(s(s(elem!1)), s(s(s(z)))))))),
% 2.52/2.72 inference(monotonicity,[status(thm)],[8235])).
% 2.52/2.72 tff(8237,plain,
% 2.52/2.72 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(z))), z)) | (~r(s(z), s(s(s(z))))) | (~r(s(s(elem!1)), s(s(s(z))))) | (~r(s(s(elem!1)), s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(elem!1)), s(z))) | (~r(s(s(s(z))), z)) | (~r(s(z), s(s(s(z))))) | (~r(s(s(elem!1)), s(s(s(z))))))),
% 2.52/2.72 inference(transitivity,[status(thm)],[8236, 8234])).
% 2.52/2.72 tff(8238,plain,
% 2.52/2.72 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(z))), z)) | (~r(s(z), s(s(s(z))))) | (~r(s(s(elem!1)), s(s(s(z))))) | (~r(s(s(elem!1)), s(z))))),
% 2.52/2.72 inference(quant_inst,[status(thm)],[])).
% 2.52/2.72 tff(8239,plain,
% 2.52/2.72 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(elem!1)), s(z))) | (~r(s(s(s(z))), z)) | (~r(s(z), s(s(s(z))))) | (~r(s(s(elem!1)), s(s(s(z)))))),
% 2.52/2.72 inference(modus_ponens,[status(thm)],[8238, 8237])).
% 2.52/2.72 tff(8240,plain,
% 2.52/2.72 (~r(s(s(elem!1)), s(s(s(z))))),
% 2.52/2.72 inference(unit_resolution,[status(thm)],[8239, 197, 4577, 1733, 1653])).
% 2.52/2.72 tff(8241,plain,
% 2.52/2.72 ($false),
% 2.52/2.72 inference(unit_resolution,[status(thm)],[8240, 8233])).
% 2.52/2.72 tff(8242,plain,((~r(elem!1, s(s(s(z))))) | (~(s(s(s(elem!1))) = s(s(elem!1)))) | (~r(s(s(elem!1)), s(z))) | (~r(s(s(s(z))), z)) | (~r(s(z), s(s(s(z)))))), inference(lemma,lemma(discharge,[]))).
% 2.52/2.72 tff(8243,plain,
% 2.52/2.72 (~r(s(z), s(s(s(z))))),
% 2.52/2.72 inference(unit_resolution,[status(thm)],[8242, 8227, 4031, 4577, 8193])).
% 2.52/2.72 tff(8244,plain,
% 2.52/2.72 (b(s(z), s(s(s(z))))),
% 2.52/2.72 inference(unit_resolution,[status(thm)],[1674, 8243])).
% 2.52/2.72 tff(8245,plain,
% 2.52/2.72 (~b(s(z), s(s(z)))),
% 2.52/2.72 inference(unit_resolution,[status(thm)],[996, 8244, 8209, 8207])).
% 2.52/2.72 tff(8246,plain,
% 2.52/2.72 (r(s(z), s(s(z)))),
% 2.52/2.72 inference(unit_resolution,[status(thm)],[427, 8245])).
% 2.52/2.72 tff(8247,plain,
% 2.52/2.72 (~b(s(s(s(s(z)))), s(s(s(z))))),
% 2.52/2.72 inference(unit_resolution,[status(thm)],[4778, 8246, 8244, 8221, 8209, 8207])).
% 2.52/2.72 tff(8248,plain,
% 2.52/2.72 (r(s(s(s(s(z)))), s(s(s(z))))),
% 2.52/2.72 inference(unit_resolution,[status(thm)],[4662, 8247])).
% 2.52/2.72 tff(8249,plain,
% 2.52/2.72 (~r(s(s(s(s(z)))), z)),
% 2.52/2.72 inference(unit_resolution,[status(thm)],[4685, 8248, 155, 8193])).
% 2.52/2.72 tff(8250,plain,
% 2.52/2.72 (b(s(s(s(s(z)))), z)),
% 2.52/2.72 inference(unit_resolution,[status(thm)],[3266, 8249])).
% 2.52/2.72 tff(8251,plain,
% 2.52/2.72 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), z)) | (~b(s(s(s(elem!1))), z)) | (~b(z, s(z))) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(elem!1))), s(s(s(s(z)))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), z)) | (~b(s(s(s(elem!1))), z)) | (~b(z, s(z))) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(elem!1))), s(s(s(s(z)))))))),
% 2.52/2.72 inference(rewrite,[status(thm)],[])).
% 2.52/2.72 tff(8252,plain,
% 2.52/2.72 (((~b(s(z), z)) | (~b(s(s(s(elem!1))), z)) | (~b(z, s(z))) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(elem!1))), z)) | (~b(s(s(s(elem!1))), s(s(s(s(z))))))) <=> ((~b(s(z), z)) | (~b(s(s(s(elem!1))), z)) | (~b(z, s(z))) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(elem!1))), s(s(s(s(z)))))))),
% 2.52/2.72 inference(rewrite,[status(thm)],[])).
% 2.52/2.72 tff(8253,plain,
% 2.52/2.72 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), z)) | (~b(s(s(s(elem!1))), z)) | (~b(z, s(z))) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(elem!1))), z)) | (~b(s(s(s(elem!1))), s(s(s(s(z)))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), z)) | (~b(s(s(s(elem!1))), z)) | (~b(z, s(z))) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(elem!1))), s(s(s(s(z))))))))),
% 2.52/2.72 inference(monotonicity,[status(thm)],[8252])).
% 2.52/2.72 tff(8254,plain,
% 2.52/2.72 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), z)) | (~b(s(s(s(elem!1))), z)) | (~b(z, s(z))) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(elem!1))), z)) | (~b(s(s(s(elem!1))), s(s(s(s(z)))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), z)) | (~b(s(s(s(elem!1))), z)) | (~b(z, s(z))) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(elem!1))), s(s(s(s(z)))))))),
% 2.52/2.72 inference(transitivity,[status(thm)],[8253, 8251])).
% 2.52/2.72 tff(8255,plain,
% 2.52/2.72 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), z)) | (~b(s(s(s(elem!1))), z)) | (~b(z, s(z))) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(elem!1))), z)) | (~b(s(s(s(elem!1))), s(s(s(s(z)))))))),
% 2.52/2.72 inference(quant_inst,[status(thm)],[])).
% 2.52/2.72 tff(8256,plain,
% 2.52/2.72 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), z)) | (~b(s(s(s(elem!1))), z)) | (~b(z, s(z))) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(elem!1))), s(s(s(s(z))))))),
% 2.52/2.72 inference(modus_ponens,[status(thm)],[8255, 8254])).
% 2.52/2.72 tff(8257,plain,
% 2.52/2.72 (~b(s(s(s(elem!1))), s(s(s(s(z)))))),
% 2.52/2.72 inference(unit_resolution,[status(thm)],[8256, 166, 8191, 118, 121, 8250])).
% 2.52/2.72 tff(8258,plain,
% 2.52/2.72 (~b(elem!1, s(s(s(s(z)))))),
% 2.52/2.72 inference(modus_ponens,[status(thm)],[8257, 6551])).
% 2.52/2.72 tff(8259,plain,
% 2.52/2.72 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), s(s(s(z))))) | (~r(s(s(s(z))), z)) | (~r(s(s(s(s(z)))), s(s(s(z))))) | (~r(s(s(s(elem!1))), s(s(s(s(z)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(elem!1))), s(s(s(z))))) | (~r(s(s(s(z))), z)) | (~r(s(s(s(s(z)))), s(s(s(z))))) | (~r(s(s(s(elem!1))), s(s(s(s(z)))))))),
% 2.52/2.72 inference(rewrite,[status(thm)],[])).
% 2.52/2.72 tff(8260,plain,
% 2.52/2.72 (((~r(s(s(s(z))), z)) | (~r(s(s(s(s(z)))), s(s(s(z))))) | (~r(s(s(s(elem!1))), s(s(s(z))))) | (~r(s(s(s(elem!1))), s(s(s(s(z))))))) <=> ((~r(s(s(s(elem!1))), s(s(s(z))))) | (~r(s(s(s(z))), z)) | (~r(s(s(s(s(z)))), s(s(s(z))))) | (~r(s(s(s(elem!1))), s(s(s(s(z)))))))),
% 2.52/2.72 inference(rewrite,[status(thm)],[])).
% 2.52/2.72 tff(8261,plain,
% 2.52/2.72 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(z))), z)) | (~r(s(s(s(s(z)))), s(s(s(z))))) | (~r(s(s(s(elem!1))), s(s(s(z))))) | (~r(s(s(s(elem!1))), s(s(s(s(z)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), s(s(s(z))))) | (~r(s(s(s(z))), z)) | (~r(s(s(s(s(z)))), s(s(s(z))))) | (~r(s(s(s(elem!1))), s(s(s(s(z))))))))),
% 2.52/2.72 inference(monotonicity,[status(thm)],[8260])).
% 2.52/2.72 tff(8262,plain,
% 2.52/2.72 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(z))), z)) | (~r(s(s(s(s(z)))), s(s(s(z))))) | (~r(s(s(s(elem!1))), s(s(s(z))))) | (~r(s(s(s(elem!1))), s(s(s(s(z)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(elem!1))), s(s(s(z))))) | (~r(s(s(s(z))), z)) | (~r(s(s(s(s(z)))), s(s(s(z))))) | (~r(s(s(s(elem!1))), s(s(s(s(z)))))))),
% 2.52/2.72 inference(transitivity,[status(thm)],[8261, 8259])).
% 2.52/2.72 tff(8263,plain,
% 2.52/2.72 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(z))), z)) | (~r(s(s(s(s(z)))), s(s(s(z))))) | (~r(s(s(s(elem!1))), s(s(s(z))))) | (~r(s(s(s(elem!1))), s(s(s(s(z)))))))),
% 2.52/2.72 inference(quant_inst,[status(thm)],[])).
% 2.52/2.72 tff(8264,plain,
% 2.52/2.72 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(elem!1))), s(s(s(z))))) | (~r(s(s(s(z))), z)) | (~r(s(s(s(s(z)))), s(s(s(z))))) | (~r(s(s(s(elem!1))), s(s(s(s(z))))))),
% 2.52/2.72 inference(modus_ponens,[status(thm)],[8263, 8262])).
% 2.52/2.72 tff(8265,plain,
% 2.52/2.72 (~r(s(s(s(elem!1))), s(s(s(s(z)))))),
% 2.52/2.72 inference(unit_resolution,[status(thm)],[8264, 197, 8248, 8193, 8219])).
% 2.52/2.72 tff(8266,plain,
% 2.52/2.72 (~r(elem!1, s(s(s(s(z)))))),
% 2.52/2.72 inference(unit_resolution,[status(thm)],[5665, 8265, 334])).
% 2.52/2.73 tff(8267,plain,
% 2.52/2.73 (b(elem!1, s(s(s(s(z)))))),
% 2.52/2.73 inference(unit_resolution,[status(thm)],[1098, 8266, 6568])).
% 2.52/2.73 tff(8268,plain,
% 2.52/2.73 ($false),
% 2.52/2.73 inference(unit_resolution,[status(thm)],[8267, 8258])).
% 2.52/2.73 tff(8269,plain,((~r(s(s(z)), s(z))) | (~(s(s(elem!1)) = s(s(s(elem!1))))) | (~b(z, s(z))) | (~b(s(s(s(elem!1))), z)) | (~r(z, s(s(z)))) | (~r(s(s(elem!1)), s(z))) | (~r(s(z), s(s(elem!1)))) | (~r(s(s(s(elem!1))), s(z)))), inference(lemma,lemma(discharge,[]))).
% 2.52/2.73 tff(8270,plain,
% 2.52/2.73 (~r(s(s(z)), s(z))),
% 2.52/2.73 inference(unit_resolution,[status(thm)],[8269, 4558, 118, 6718, 152, 8039, 85, 8047])).
% 2.52/2.73 tff(8271,plain,
% 2.52/2.73 (b(s(s(z)), s(z))),
% 2.52/2.73 inference(unit_resolution,[status(thm)],[308, 8270])).
% 2.52/2.73 tff(8272,plain,
% 2.52/2.73 (~b(s(s(z)), z)),
% 2.52/2.73 inference(unit_resolution,[status(thm)],[181, 8271, 118, 8172])).
% 2.52/2.73 tff(8273,plain,
% 2.52/2.73 (r(s(s(z)), z)),
% 2.52/2.73 inference(unit_resolution,[status(thm)],[186, 8272])).
% 2.52/2.73 tff(8274,plain,
% 2.52/2.73 (~r(s(s(z)), s(s(s(z))))),
% 2.52/2.73 inference(unit_resolution,[status(thm)],[1741, 8273, 152, 8189])).
% 2.52/2.73 tff(8275,plain,
% 2.52/2.73 (b(s(s(z)), s(s(s(z))))),
% 2.52/2.73 inference(unit_resolution,[status(thm)],[1730, 8274])).
% 2.52/2.73 tff(8276,plain,
% 2.52/2.73 (~r(s(s(s(z))), s(s(z)))),
% 2.52/2.73 inference(unit_resolution,[status(thm)],[1717, 197, 152, 8273, 8189])).
% 2.52/2.73 tff(8277,plain,
% 2.52/2.73 (b(s(s(s(z))), s(s(z)))),
% 2.52/2.73 inference(unit_resolution,[status(thm)],[1010, 8276])).
% 2.52/2.73 tff(8278,plain,
% 2.52/2.73 (s(s(s(elem!1))) = s(s(elem!1))),
% 2.52/2.73 inference(unit_resolution,[status(thm)],[4030, 8039])).
% 2.52/2.73 tff(8279,plain,
% 2.52/2.73 (s(s(s(elem!1))) = s(elem!1)),
% 2.52/2.73 inference(unit_resolution,[status(thm)],[2594, 8039])).
% 2.52/2.73 tff(8280,plain,
% 2.52/2.73 (s(elem!1) = s(s(s(elem!1)))),
% 2.52/2.73 inference(symmetry,[status(thm)],[8279])).
% 2.52/2.73 tff(8281,plain,
% 2.52/2.73 (inj_0(s(elem!1)) = inj_0(s(s(s(elem!1))))),
% 2.52/2.73 inference(monotonicity,[status(thm)],[8280])).
% 2.52/2.73 tff(8282,plain,
% 2.52/2.73 (elem!1 = s(s(s(elem!1)))),
% 2.52/2.73 inference(transitivity,[status(thm)],[1170, 8281, 104, 8039])).
% 2.52/2.73 tff(8283,plain,
% 2.52/2.73 (b(elem!1, s(s(s(z)))) <=> b(s(s(s(elem!1))), s(s(s(z))))),
% 2.52/2.73 inference(monotonicity,[status(thm)],[8282])).
% 2.52/2.73 tff(8284,plain,
% 2.52/2.73 (~(s(s(s(z))) = elem!1)),
% 2.52/2.73 inference(unit_resolution,[status(thm)],[3122, 8039])).
% 2.52/2.73 tff(8285,plain,
% 2.52/2.73 (~(elem!1 = s(s(s(z))))),
% 2.52/2.73 inference(unit_resolution,[status(thm)],[1564, 8284])).
% 2.52/2.73 tff(8286,plain,
% 2.52/2.73 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), z)) | (~b(s(s(s(elem!1))), s(s(z)))) | (~b(s(s(s(elem!1))), z)) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(s(z)), s(z))) | (~b(s(s(s(elem!1))), s(s(s(z))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), z)) | (~b(s(s(s(elem!1))), s(s(z)))) | (~b(s(s(s(elem!1))), z)) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(s(z)), s(z))) | (~b(s(s(s(elem!1))), s(s(s(z))))))),
% 2.52/2.73 inference(rewrite,[status(thm)],[])).
% 2.52/2.73 tff(8287,plain,
% 2.52/2.73 (((~b(s(z), z)) | (~b(s(s(s(elem!1))), z)) | (~b(s(s(z)), s(z))) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(s(s(elem!1))), s(s(z)))) | (~b(s(s(s(elem!1))), s(s(s(z)))))) <=> ((~b(s(z), z)) | (~b(s(s(s(elem!1))), s(s(z)))) | (~b(s(s(s(elem!1))), z)) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(s(z)), s(z))) | (~b(s(s(s(elem!1))), s(s(s(z))))))),
% 2.52/2.73 inference(rewrite,[status(thm)],[])).
% 2.52/2.73 tff(8288,plain,
% 2.52/2.73 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), z)) | (~b(s(s(s(elem!1))), z)) | (~b(s(s(z)), s(z))) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(s(s(elem!1))), s(s(z)))) | (~b(s(s(s(elem!1))), s(s(s(z))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), z)) | (~b(s(s(s(elem!1))), s(s(z)))) | (~b(s(s(s(elem!1))), z)) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(s(z)), s(z))) | (~b(s(s(s(elem!1))), s(s(s(z)))))))),
% 2.52/2.73 inference(monotonicity,[status(thm)],[8287])).
% 2.52/2.73 tff(8289,plain,
% 2.52/2.73 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), z)) | (~b(s(s(s(elem!1))), z)) | (~b(s(s(z)), s(z))) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(s(s(elem!1))), s(s(z)))) | (~b(s(s(s(elem!1))), s(s(s(z))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), z)) | (~b(s(s(s(elem!1))), s(s(z)))) | (~b(s(s(s(elem!1))), z)) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(s(z)), s(z))) | (~b(s(s(s(elem!1))), s(s(s(z))))))),
% 2.52/2.73 inference(transitivity,[status(thm)],[8288, 8286])).
% 2.52/2.73 tff(8290,plain,
% 2.52/2.73 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), z)) | (~b(s(s(s(elem!1))), z)) | (~b(s(s(z)), s(z))) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(s(s(elem!1))), s(s(z)))) | (~b(s(s(s(elem!1))), s(s(s(z))))))),
% 2.52/2.73 inference(quant_inst,[status(thm)],[])).
% 2.52/2.73 tff(8291,plain,
% 2.52/2.73 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), z)) | (~b(s(s(s(elem!1))), s(s(z)))) | (~b(s(s(s(elem!1))), z)) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(s(z)), s(z))) | (~b(s(s(s(elem!1))), s(s(s(z)))))),
% 2.52/2.73 inference(modus_ponens,[status(thm)],[8290, 8289])).
% 2.52/2.73 tff(8292,plain,
% 2.52/2.73 (~b(s(s(s(elem!1))), s(s(s(z))))),
% 2.52/2.73 inference(unit_resolution,[status(thm)],[8291, 166, 8191, 121, 156, 6498, 2060])).
% 2.52/2.73 tff(8293,plain,
% 2.52/2.73 (~b(elem!1, s(s(s(z))))),
% 2.52/2.73 inference(modus_ponens,[status(thm)],[8292, 8225])).
% 2.52/2.73 tff(8294,plain,
% 2.52/2.73 (r(s(s(s(elem!1))), s(s(s(z))))),
% 2.52/2.73 inference(unit_resolution,[status(thm)],[3574, 8292, 6474])).
% 2.52/2.73 tff(8295,plain,
% 2.52/2.73 (~r(s(s(s(z))), s(z))),
% 2.52/2.73 inference(unit_resolution,[status(thm)],[6519, 8294, 311, 350])).
% 2.52/2.73 tff(8296,plain,
% 2.52/2.73 (b(s(s(s(z))), s(z))),
% 2.52/2.73 inference(unit_resolution,[status(thm)],[1763, 8295])).
% 2.52/2.73 tff(8297,plain,
% 2.52/2.73 (~b(s(z), s(s(s(z))))),
% 2.52/2.73 inference(unit_resolution,[status(thm)],[3248, 8296, 156, 7203])).
% 2.52/2.73 tff(8298,plain,
% 2.52/2.73 (r(s(z), s(s(s(z))))),
% 2.52/2.73 inference(unit_resolution,[status(thm)],[1674, 8297])).
% 2.52/2.73 tff(8299,plain,
% 2.52/2.73 (~r(elem!1, s(s(s(z))))),
% 2.52/2.73 inference(unit_resolution,[status(thm)],[8242, 8298, 4031, 4577, 1733])).
% 2.52/2.73 tff(8300,plain,
% 2.52/2.73 (b(elem!1, s(s(s(z))))),
% 2.52/2.73 inference(unit_resolution,[status(thm)],[1619, 8299, 8222])).
% 2.52/2.73 tff(8301,plain,
% 2.52/2.73 ($false),
% 2.52/2.73 inference(unit_resolution,[status(thm)],[8300, 8293])).
% 2.52/2.73 tff(8302,plain,((~r(s(s(s(z))), z)) | (~(s(s(elem!1)) = s(s(s(elem!1))))) | (~r(s(s(elem!1)), s(z))) | (~b(s(s(z)), s(z))) | (~r(s(z), s(s(elem!1)))) | (~r(s(s(s(elem!1))), s(z))) | (~b(s(s(s(elem!1))), z)) | (~b(s(s(s(elem!1))), s(s(z)))) | (~r(z, s(s(z)))) | (~r(s(s(z)), z))), inference(lemma,lemma(discharge,[]))).
% 2.52/2.73 tff(8303,plain,
% 2.52/2.73 (~b(s(s(s(elem!1))), s(s(z)))),
% 2.52/2.73 inference(unit_resolution,[status(thm)],[8302, 8273, 4558, 8189, 85, 8047, 6718, 8039, 152, 8271])).
% 2.52/2.73 tff(8304,plain,
% 2.52/2.73 (r(s(s(s(elem!1))), s(s(z)))),
% 2.52/2.73 inference(unit_resolution,[status(thm)],[218, 8303])).
% 2.52/2.73 tff(8305,plain,
% 2.52/2.73 (~r(s(z), s(s(z)))),
% 2.52/2.73 inference(unit_resolution,[status(thm)],[874, 8304, 8047, 8273])).
% 2.52/2.73 tff(8306,plain,
% 2.52/2.73 (b(s(z), s(s(z)))),
% 2.52/2.73 inference(unit_resolution,[status(thm)],[427, 8305])).
% 2.52/2.73 tff(8307,plain,
% 2.52/2.73 (~b(s(z), s(s(s(z))))),
% 2.52/2.73 inference(unit_resolution,[status(thm)],[996, 8277, 8275, 8306])).
% 2.52/2.73 tff(8308,plain,
% 2.52/2.73 (r(s(z), s(s(s(z))))),
% 2.52/2.73 inference(unit_resolution,[status(thm)],[1674, 8307])).
% 2.52/2.73 tff(8309,plain,
% 2.52/2.73 (~r(elem!1, s(s(s(z))))),
% 2.52/2.73 inference(unit_resolution,[status(thm)],[8242, 8308, 8278, 4558, 8189])).
% 2.52/2.73 tff(8310,plain,
% 2.52/2.73 (b(elem!1, s(s(s(z))))),
% 2.52/2.73 inference(unit_resolution,[status(thm)],[1619, 8309, 8285])).
% 2.52/2.73 tff(8311,plain,
% 2.52/2.73 (b(s(s(s(elem!1))), s(s(s(z))))),
% 2.52/2.73 inference(modus_ponens,[status(thm)],[8310, 8283])).
% 2.52/2.73 tff(8312,plain,
% 2.52/2.73 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), s(s(z)))) | (~b(s(s(z)), s(z))) | (~b(s(s(z)), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(s(s(z))))) | (~b(s(s(z)), s(s(s(z))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(s(z)), s(z))) | (~b(s(s(z)), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(s(s(z))))) | (~b(s(s(z)), s(s(s(z))))))),
% 2.52/2.73 inference(rewrite,[status(thm)],[])).
% 2.52/2.73 tff(8313,plain,
% 2.52/2.73 (((~b(s(s(z)), s(z))) | (~b(s(s(z)), s(z))) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(s(s(elem!1))), s(s(s(z))))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(z)), s(s(s(elem!1)))))) <=> ((~b(s(s(s(z))), s(s(z)))) | (~b(s(s(z)), s(z))) | (~b(s(s(z)), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(s(s(z))))) | (~b(s(s(z)), s(s(s(z))))))),
% 2.52/2.73 inference(rewrite,[status(thm)],[])).
% 2.52/2.73 tff(8314,plain,
% 2.52/2.73 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), s(z))) | (~b(s(s(z)), s(z))) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(s(s(elem!1))), s(s(s(z))))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(z)), s(s(s(elem!1))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), s(s(z)))) | (~b(s(s(z)), s(z))) | (~b(s(s(z)), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(s(s(z))))) | (~b(s(s(z)), s(s(s(z)))))))),
% 2.52/2.73 inference(monotonicity,[status(thm)],[8313])).
% 2.52/2.73 tff(8315,plain,
% 2.52/2.73 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), s(z))) | (~b(s(s(z)), s(z))) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(s(s(elem!1))), s(s(s(z))))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(z)), s(s(s(elem!1))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(s(z)), s(z))) | (~b(s(s(z)), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(s(s(z))))) | (~b(s(s(z)), s(s(s(z))))))),
% 2.52/2.73 inference(transitivity,[status(thm)],[8314, 8312])).
% 2.52/2.73 tff(8316,plain,
% 2.52/2.73 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), s(z))) | (~b(s(s(z)), s(z))) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(s(s(elem!1))), s(s(s(z))))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(z)), s(s(s(elem!1))))))),
% 2.52/2.73 inference(quant_inst,[status(thm)],[])).
% 2.52/2.73 tff(8317,plain,
% 2.52/2.73 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(s(z)), s(z))) | (~b(s(s(z)), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(s(s(z))))) | (~b(s(s(z)), s(s(s(z)))))),
% 2.52/2.73 inference(modus_ponens,[status(thm)],[8316, 8315])).
% 2.52/2.73 tff(8318,plain,
% 2.52/2.73 (~b(s(s(z)), s(s(s(elem!1))))),
% 2.52/2.73 inference(unit_resolution,[status(thm)],[8317, 166, 8271, 8275, 8277, 8311])).
% 2.52/2.73 tff(8319,plain,
% 2.52/2.73 (~b(s(s(z)), s(s(elem!1)))),
% 2.52/2.73 inference(unit_resolution,[status(thm)],[6647, 8318, 8039])).
% 2.52/2.73 tff(8320,plain,
% 2.52/2.73 (r(s(s(z)), s(s(elem!1)))),
% 2.52/2.73 inference(unit_resolution,[status(thm)],[390, 8319, 8045])).
% 2.52/2.73 tff(8321,plain,
% 2.52/2.73 (~r(z, s(s(elem!1)))),
% 2.52/2.73 inference(unit_resolution,[status(thm)],[5997, 8320, 152, 4558])).
% 2.52/2.73 tff(8322,plain,
% 2.52/2.73 (b(z, s(s(elem!1)))),
% 2.52/2.73 inference(unit_resolution,[status(thm)],[1795, 8321])).
% 2.52/2.73 tff(8323,plain,
% 2.52/2.73 (b(z, s(s(s(elem!1)))) <=> b(z, s(s(elem!1)))),
% 2.52/2.73 inference(monotonicity,[status(thm)],[47])).
% 2.52/2.73 tff(8324,plain,
% 2.52/2.73 (b(z, s(s(elem!1))) <=> b(z, s(s(s(elem!1))))),
% 2.52/2.73 inference(symmetry,[status(thm)],[8323])).
% 2.52/2.73 tff(8325,plain,
% 2.52/2.73 (b(z, s(s(s(elem!1))))),
% 2.52/2.73 inference(modus_ponens,[status(thm)],[1820, 8324])).
% 2.52/2.73 tff(8326,plain,
% 2.52/2.73 ($false),
% 2.52/2.73 inference(unit_resolution,[status(thm)],[256, 8325])).
% 2.52/2.73 tff(8327,plain,((~(s(s(s(elem!1))) = s(s(elem!1)))) | b(z, s(s(s(elem!1)))) | (~b(z, s(s(elem!1))))), inference(lemma,lemma(discharge,[]))).
% 2.52/2.73 tff(8328,plain,
% 2.52/2.73 (b(z, s(s(s(elem!1))))),
% 2.52/2.73 inference(unit_resolution,[status(thm)],[8327, 8322, 8278])).
% 2.52/2.73 tff(8329,plain,
% 2.52/2.73 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(s(elem!1))))) | (~b(s(z), z)) | (~b(s(s(s(elem!1))), z)) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(s(s(elem!1))))) | (~b(s(z), z)) | (~b(s(s(s(elem!1))), z)) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), z)))),
% 2.52/2.73 inference(rewrite,[status(thm)],[])).
% 2.52/2.73 tff(8330,plain,
% 2.52/2.73 (((~b(s(s(s(elem!1))), z)) | (~b(s(z), z)) | (~b(z, s(s(s(elem!1))))) | (~b(s(s(s(s(z)))), z)) | (~b(s(z), z)) | (~b(s(z), s(s(s(s(z))))))) <=> ((~b(z, s(s(s(elem!1))))) | (~b(s(z), z)) | (~b(s(s(s(elem!1))), z)) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), z)))),
% 2.52/2.73 inference(rewrite,[status(thm)],[])).
% 2.52/2.73 tff(8331,plain,
% 2.52/2.73 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), z)) | (~b(s(z), z)) | (~b(z, s(s(s(elem!1))))) | (~b(s(s(s(s(z)))), z)) | (~b(s(z), z)) | (~b(s(z), s(s(s(s(z)))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(s(elem!1))))) | (~b(s(z), z)) | (~b(s(s(s(elem!1))), z)) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), z))))),
% 2.52/2.73 inference(monotonicity,[status(thm)],[8330])).
% 2.52/2.73 tff(8332,plain,
% 2.52/2.73 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), z)) | (~b(s(z), z)) | (~b(z, s(s(s(elem!1))))) | (~b(s(s(s(s(z)))), z)) | (~b(s(z), z)) | (~b(s(z), s(s(s(s(z)))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(s(s(elem!1))))) | (~b(s(z), z)) | (~b(s(s(s(elem!1))), z)) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), z)))),
% 2.52/2.73 inference(transitivity,[status(thm)],[8331, 8329])).
% 2.52/2.73 tff(8333,plain,
% 2.52/2.73 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), z)) | (~b(s(z), z)) | (~b(z, s(s(s(elem!1))))) | (~b(s(s(s(s(z)))), z)) | (~b(s(z), z)) | (~b(s(z), s(s(s(s(z)))))))),
% 2.52/2.73 inference(quant_inst,[status(thm)],[])).
% 2.52/2.73 tff(8334,plain,
% 2.52/2.73 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(s(s(elem!1))))) | (~b(s(z), z)) | (~b(s(s(s(elem!1))), z)) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), z))),
% 2.52/2.73 inference(modus_ponens,[status(thm)],[8333, 8332])).
% 2.52/2.73 tff(8335,plain,
% 2.52/2.73 (~b(s(z), s(s(s(s(z)))))),
% 2.52/2.73 inference(unit_resolution,[status(thm)],[8334, 166, 240, 53, 121, 3253])).
% 2.52/2.73 tff(8336,plain,
% 2.52/2.73 (r(s(z), s(s(s(s(z)))))),
% 2.52/2.73 inference(unit_resolution,[status(thm)],[3302, 8335])).
% 2.52/2.73 tff(8337,plain,
% 2.52/2.73 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), z)) | (~b(z, s(z))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(s(z)))), z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), z)) | (~b(z, s(z))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(s(z)))), z)))),
% 2.52/2.73 inference(rewrite,[status(thm)],[])).
% 2.52/2.73 tff(8338,plain,
% 2.52/2.73 (((~b(s(z), z)) | (~b(s(s(s(s(z)))), z)) | (~b(z, s(z))) | (~b(s(z), z)) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(s(z)))), s(z)))) <=> ((~b(s(z), z)) | (~b(z, s(z))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(s(z)))), z)))),
% 2.52/2.73 inference(rewrite,[status(thm)],[])).
% 2.52/2.73 tff(8339,plain,
% 2.52/2.73 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), z)) | (~b(s(s(s(s(z)))), z)) | (~b(z, s(z))) | (~b(s(z), z)) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(s(z)))), s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), z)) | (~b(z, s(z))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(s(z)))), z))))),
% 2.52/2.73 inference(monotonicity,[status(thm)],[8338])).
% 2.52/2.73 tff(8340,plain,
% 2.52/2.73 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), z)) | (~b(s(s(s(s(z)))), z)) | (~b(z, s(z))) | (~b(s(z), z)) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(s(z)))), s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), z)) | (~b(z, s(z))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(s(z)))), z)))),
% 2.52/2.73 inference(transitivity,[status(thm)],[8339, 8337])).
% 2.52/2.73 tff(8341,plain,
% 2.52/2.73 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), z)) | (~b(s(s(s(s(z)))), z)) | (~b(z, s(z))) | (~b(s(z), z)) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(s(z)))), s(z))))),
% 2.52/2.73 inference(quant_inst,[status(thm)],[])).
% 2.52/2.73 tff(8342,plain,
% 2.52/2.73 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), z)) | (~b(z, s(z))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(s(z)))), z))),
% 2.52/2.73 inference(modus_ponens,[status(thm)],[8341, 8340])).
% 2.52/2.73 tff(8343,plain,
% 2.52/2.73 (~b(s(s(s(s(z)))), s(z))),
% 2.52/2.73 inference(unit_resolution,[status(thm)],[8342, 166, 53, 118, 3253])).
% 2.52/2.73 tff(8344,plain,
% 2.52/2.73 (r(s(s(s(s(z)))), s(z))),
% 2.52/2.73 inference(unit_resolution,[status(thm)],[3285, 8343])).
% 2.52/2.73 tff(8345,plain,
% 2.52/2.73 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), s(z))) | (~r(s(z), s(s(s(s(z)))))) | (~r(s(s(s(s(z)))), s(z))) | (~r(s(s(s(elem!1))), s(s(s(s(z)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(elem!1))), s(z))) | (~r(s(z), s(s(s(s(z)))))) | (~r(s(s(s(s(z)))), s(z))) | (~r(s(s(s(elem!1))), s(s(s(s(z)))))))),
% 2.52/2.73 inference(rewrite,[status(thm)],[])).
% 2.52/2.73 tff(8346,plain,
% 2.52/2.73 (((~r(s(z), s(s(s(s(z)))))) | (~r(s(s(s(s(z)))), s(z))) | (~r(s(s(s(elem!1))), s(z))) | (~r(s(s(s(elem!1))), s(s(s(s(z))))))) <=> ((~r(s(s(s(elem!1))), s(z))) | (~r(s(z), s(s(s(s(z)))))) | (~r(s(s(s(s(z)))), s(z))) | (~r(s(s(s(elem!1))), s(s(s(s(z)))))))),
% 2.52/2.73 inference(rewrite,[status(thm)],[])).
% 2.52/2.73 tff(8347,plain,
% 2.52/2.73 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(s(s(s(z)))))) | (~r(s(s(s(s(z)))), s(z))) | (~r(s(s(s(elem!1))), s(z))) | (~r(s(s(s(elem!1))), s(s(s(s(z)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), s(z))) | (~r(s(z), s(s(s(s(z)))))) | (~r(s(s(s(s(z)))), s(z))) | (~r(s(s(s(elem!1))), s(s(s(s(z))))))))),
% 2.52/2.73 inference(monotonicity,[status(thm)],[8346])).
% 2.52/2.73 tff(8348,plain,
% 2.52/2.73 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(s(s(s(z)))))) | (~r(s(s(s(s(z)))), s(z))) | (~r(s(s(s(elem!1))), s(z))) | (~r(s(s(s(elem!1))), s(s(s(s(z)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(elem!1))), s(z))) | (~r(s(z), s(s(s(s(z)))))) | (~r(s(s(s(s(z)))), s(z))) | (~r(s(s(s(elem!1))), s(s(s(s(z)))))))),
% 2.52/2.73 inference(transitivity,[status(thm)],[8347, 8345])).
% 2.52/2.73 tff(8349,plain,
% 2.52/2.73 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(s(s(s(z)))))) | (~r(s(s(s(s(z)))), s(z))) | (~r(s(s(s(elem!1))), s(z))) | (~r(s(s(s(elem!1))), s(s(s(s(z)))))))),
% 2.52/2.73 inference(quant_inst,[status(thm)],[])).
% 2.52/2.73 tff(8350,plain,
% 2.52/2.74 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(elem!1))), s(z))) | (~r(s(z), s(s(s(s(z)))))) | (~r(s(s(s(s(z)))), s(z))) | (~r(s(s(s(elem!1))), s(s(s(s(z))))))),
% 2.52/2.74 inference(modus_ponens,[status(thm)],[8349, 8348])).
% 2.52/2.74 tff(8351,plain,
% 2.52/2.74 (~r(s(s(s(elem!1))), s(s(s(s(z)))))),
% 2.52/2.74 inference(unit_resolution,[status(thm)],[8350, 197, 350, 8344, 8336])).
% 2.52/2.74 tff(8352,plain,
% 2.52/2.74 (~b(s(s(s(elem!1))), s(s(s(s(z)))))),
% 2.52/2.74 inference(unit_resolution,[status(thm)],[8159, 166, 240, 121, 3253])).
% 2.52/2.74 tff(8353,plain,
% 2.52/2.74 (~b(elem!1, s(s(s(s(z)))))),
% 2.52/2.74 inference(modus_ponens,[status(thm)],[8352, 6551])).
% 2.52/2.74 tff(8354,plain,
% 2.52/2.74 (r(elem!1, s(s(s(s(z)))))),
% 2.52/2.74 inference(unit_resolution,[status(thm)],[1098, 8353, 6568])).
% 2.52/2.74 tff(8355,plain,
% 2.52/2.74 ($false),
% 2.52/2.74 inference(unit_resolution,[status(thm)],[5665, 8354, 8351, 334])).
% 2.52/2.74 tff(8356,plain,((~b(s(s(s(s(z)))), z)) | (~(s(s(elem!1)) = s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), s(z))) | (~b(s(z), z)) | (~b(z, s(z))) | (~b(z, s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), z))), inference(lemma,lemma(discharge,[]))).
% 2.52/2.74 tff(8357,plain,
% 2.52/2.74 (~b(s(s(s(s(z)))), z)),
% 2.52/2.74 inference(unit_resolution,[status(thm)],[8356, 8047, 8039, 8172, 118, 8328, 6718])).
% 2.52/2.74 tff(8358,plain,
% 2.52/2.74 (r(s(s(s(s(z)))), z)),
% 2.52/2.74 inference(unit_resolution,[status(thm)],[3266, 8357])).
% 2.52/2.74 tff(8359,plain,
% 2.52/2.74 (~r(s(s(s(s(z)))), s(s(s(z))))),
% 2.52/2.74 inference(unit_resolution,[status(thm)],[4685, 8358, 152, 8189])).
% 2.52/2.74 tff(8360,plain,
% 2.52/2.74 (b(s(s(s(s(z)))), s(s(s(z))))),
% 2.52/2.74 inference(unit_resolution,[status(thm)],[4662, 8359])).
% 2.52/2.74 tff(8361,plain,
% 2.52/2.74 (~b(s(s(z)), s(s(s(s(z)))))),
% 2.52/2.74 inference(unit_resolution,[status(thm)],[4741, 8360, 8277, 8275])).
% 2.52/2.74 tff(8362,plain,
% 2.52/2.74 (r(s(s(z)), s(s(s(s(z)))))),
% 2.52/2.74 inference(unit_resolution,[status(thm)],[4753, 8361])).
% 2.52/2.74 tff(8363,plain,
% 2.52/2.74 ($false),
% 2.52/2.74 inference(unit_resolution,[status(thm)],[7716, 197, 152, 8273, 8358, 8362])).
% 2.52/2.74 tff(8364,plain,(b(s(z), s(s(elem!1))) | (~b(z, s(z))) | b(z, s(s(z)))), inference(lemma,lemma(discharge,[]))).
% 2.52/2.74 tff(8365,plain,
% 2.52/2.74 (b(s(z), s(s(elem!1)))),
% 2.52/2.74 inference(unit_resolution,[status(thm)],[8364, 118, 125])).
% 2.52/2.74 tff(8366,plain,
% 2.52/2.74 (b(s(z), s(s(s(elem!1))))),
% 2.52/2.74 inference(unit_resolution,[status(thm)],[5500, 8365, 8039])).
% 2.52/2.74 tff(8367,plain,
% 2.52/2.74 (((~b(s(s(s(elem!1))), z)) | (~b(s(s(s(elem!1))), z)) | (~b(s(z), s(s(s(elem!1))))) | (~b(z, s(z))) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(s(s(elem!1))), z))) <=> ((~b(s(z), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), z)) | (~b(s(s(s(elem!1))), s(z))) | (~b(z, s(z))))),
% 2.52/2.74 inference(rewrite,[status(thm)],[])).
% 2.52/2.74 tff(8368,plain,
% 2.52/2.74 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), z)) | (~b(s(s(s(elem!1))), z)) | (~b(s(z), s(s(s(elem!1))))) | (~b(z, s(z))) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(s(s(elem!1))), z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), z)) | (~b(s(s(s(elem!1))), s(z))) | (~b(z, s(z)))))),
% 2.52/2.74 inference(monotonicity,[status(thm)],[8367])).
% 2.52/2.74 tff(8369,plain,
% 2.52/2.74 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), z)) | (~b(s(s(s(elem!1))), z)) | (~b(s(z), s(s(s(elem!1))))) | (~b(z, s(z))) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(s(s(elem!1))), z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), z)) | (~b(s(s(s(elem!1))), s(z))) | (~b(z, s(z))))),
% 2.52/2.74 inference(transitivity,[status(thm)],[8368, 6786])).
% 2.52/2.74 tff(8370,plain,
% 2.52/2.74 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), z)) | (~b(s(s(s(elem!1))), z)) | (~b(s(z), s(s(s(elem!1))))) | (~b(z, s(z))) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(s(s(elem!1))), z)))),
% 2.52/2.74 inference(quant_inst,[status(thm)],[])).
% 2.52/2.74 tff(8371,plain,
% 2.52/2.74 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), z)) | (~b(s(s(s(elem!1))), s(z))) | (~b(z, s(z)))),
% 2.52/2.74 inference(modus_ponens,[status(thm)],[8370, 8369])).
% 2.52/2.74 tff(8372,plain,
% 2.52/2.74 (~b(s(s(s(elem!1))), s(z))),
% 2.52/2.74 inference(unit_resolution,[status(thm)],[8371, 166, 8366, 118, 6718])).
% 2.52/2.74 tff(8373,plain,
% 2.52/2.74 (~b(s(s(elem!1)), s(z))),
% 2.52/2.74 inference(unit_resolution,[status(thm)],[3849, 8372, 8039])).
% 2.52/2.74 tff(8374,plain,
% 2.52/2.74 (r(s(s(elem!1)), s(z))),
% 2.52/2.74 inference(unit_resolution,[status(thm)],[1912, 8373])).
% 2.52/2.74 tff(8375,plain,
% 2.52/2.74 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(s(elem!1))))) | (~b(s(z), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), z)) | (~b(z, s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(s(s(elem!1))))) | (~b(s(z), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), z)) | (~b(z, s(z))))),
% 2.52/2.74 inference(rewrite,[status(thm)],[])).
% 2.52/2.74 tff(8376,plain,
% 2.52/2.74 (((~b(z, s(z))) | (~b(z, s(z))) | (~b(s(s(s(elem!1))), z)) | (~b(s(z), s(s(s(elem!1))))) | (~b(z, s(s(s(elem!1))))) | (~b(z, s(z)))) <=> ((~b(z, s(s(s(elem!1))))) | (~b(s(z), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), z)) | (~b(z, s(z))))),
% 2.52/2.74 inference(rewrite,[status(thm)],[])).
% 2.52/2.74 tff(8377,plain,
% 2.52/2.74 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(z))) | (~b(z, s(z))) | (~b(s(s(s(elem!1))), z)) | (~b(s(z), s(s(s(elem!1))))) | (~b(z, s(s(s(elem!1))))) | (~b(z, s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(s(elem!1))))) | (~b(s(z), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), z)) | (~b(z, s(z)))))),
% 2.52/2.74 inference(monotonicity,[status(thm)],[8376])).
% 2.52/2.74 tff(8378,plain,
% 2.52/2.74 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(z))) | (~b(z, s(z))) | (~b(s(s(s(elem!1))), z)) | (~b(s(z), s(s(s(elem!1))))) | (~b(z, s(s(s(elem!1))))) | (~b(z, s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(s(s(elem!1))))) | (~b(s(z), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), z)) | (~b(z, s(z))))),
% 2.52/2.74 inference(transitivity,[status(thm)],[8377, 8375])).
% 2.52/2.74 tff(8379,plain,
% 2.52/2.74 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(z))) | (~b(z, s(z))) | (~b(s(s(s(elem!1))), z)) | (~b(s(z), s(s(s(elem!1))))) | (~b(z, s(s(s(elem!1))))) | (~b(z, s(z))))),
% 2.52/2.74 inference(quant_inst,[status(thm)],[])).
% 2.52/2.74 tff(8380,plain,
% 2.52/2.74 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(s(s(elem!1))))) | (~b(s(z), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), z)) | (~b(z, s(z)))),
% 2.52/2.74 inference(modus_ponens,[status(thm)],[8379, 8378])).
% 2.52/2.74 tff(8381,plain,
% 2.52/2.74 (~b(z, s(s(s(elem!1))))),
% 2.52/2.74 inference(unit_resolution,[status(thm)],[8380, 166, 8366, 118, 6718])).
% 2.52/2.74 tff(8382,plain,
% 2.52/2.74 (~b(z, s(s(elem!1)))),
% 2.52/2.74 inference(unit_resolution,[status(thm)],[8327, 8381, 8278])).
% 2.52/2.74 tff(8383,plain,
% 2.52/2.74 (r(z, s(s(elem!1)))),
% 2.52/2.74 inference(unit_resolution,[status(thm)],[1795, 8382])).
% 2.52/2.74 tff(8384,plain,
% 2.52/2.74 (~r(s(s(z)), s(s(elem!1)))),
% 2.52/2.74 inference(unit_resolution,[status(thm)],[5997, 8383, 152, 8374])).
% 2.52/2.74 tff(8385,plain,
% 2.52/2.74 (b(s(s(z)), s(s(elem!1)))),
% 2.52/2.74 inference(unit_resolution,[status(thm)],[390, 8384, 8045])).
% 2.52/2.74 tff(8386,plain,
% 2.52/2.74 (b(s(s(z)), s(s(s(elem!1))))),
% 2.52/2.74 inference(unit_resolution,[status(thm)],[6647, 8385, 8039])).
% 2.52/2.74 tff(8387,plain,
% 2.52/2.74 (~b(s(z), z)),
% 2.52/2.74 inference(unit_resolution,[status(thm)],[7322, 8366, 118, 6718, 8365])).
% 2.52/2.74 tff(8388,plain,
% 2.52/2.74 (r(s(z), z)),
% 2.52/2.74 inference(unit_resolution,[status(thm)],[230, 8387])).
% 2.52/2.74 tff(8389,plain,
% 2.52/2.74 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), z)) | (~b(z, s(z))) | (~b(s(s(z)), z)) | (~b(s(s(z)), s(s(s(elem!1))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), z)) | (~b(z, s(z))) | (~b(s(s(z)), z)) | (~b(s(s(z)), s(s(s(elem!1))))))),
% 2.52/2.74 inference(rewrite,[status(thm)],[])).
% 2.52/2.74 tff(8390,plain,
% 2.52/2.74 (((~b(s(z), s(s(s(elem!1))))) | (~b(s(s(z)), s(s(s(elem!1))))) | (~b(z, s(z))) | (~b(s(s(s(elem!1))), z)) | (~b(s(s(z)), z)) | (~b(s(s(z)), s(s(s(elem!1)))))) <=> ((~b(s(z), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), z)) | (~b(z, s(z))) | (~b(s(s(z)), z)) | (~b(s(s(z)), s(s(s(elem!1))))))),
% 2.52/2.74 inference(rewrite,[status(thm)],[])).
% 2.52/2.74 tff(8391,plain,
% 2.52/2.74 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(s(elem!1))))) | (~b(s(s(z)), s(s(s(elem!1))))) | (~b(z, s(z))) | (~b(s(s(s(elem!1))), z)) | (~b(s(s(z)), z)) | (~b(s(s(z)), s(s(s(elem!1))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), z)) | (~b(z, s(z))) | (~b(s(s(z)), z)) | (~b(s(s(z)), s(s(s(elem!1)))))))),
% 2.52/2.74 inference(monotonicity,[status(thm)],[8390])).
% 2.52/2.74 tff(8392,plain,
% 2.52/2.74 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(s(elem!1))))) | (~b(s(s(z)), s(s(s(elem!1))))) | (~b(z, s(z))) | (~b(s(s(s(elem!1))), z)) | (~b(s(s(z)), z)) | (~b(s(s(z)), s(s(s(elem!1))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), z)) | (~b(z, s(z))) | (~b(s(s(z)), z)) | (~b(s(s(z)), s(s(s(elem!1))))))),
% 2.52/2.74 inference(transitivity,[status(thm)],[8391, 8389])).
% 2.52/2.74 tff(8393,plain,
% 2.52/2.74 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(s(elem!1))))) | (~b(s(s(z)), s(s(s(elem!1))))) | (~b(z, s(z))) | (~b(s(s(s(elem!1))), z)) | (~b(s(s(z)), z)) | (~b(s(s(z)), s(s(s(elem!1))))))),
% 2.52/2.74 inference(quant_inst,[status(thm)],[])).
% 2.52/2.74 tff(8394,plain,
% 2.52/2.74 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), z)) | (~b(z, s(z))) | (~b(s(s(z)), z)) | (~b(s(s(z)), s(s(s(elem!1)))))),
% 2.52/2.74 inference(modus_ponens,[status(thm)],[8393, 8392])).
% 2.52/2.74 tff(8395,plain,
% 2.52/2.74 (~b(s(s(z)), z)),
% 2.52/2.74 inference(unit_resolution,[status(thm)],[8394, 166, 8366, 118, 6718, 8386])).
% 2.52/2.74 tff(8396,plain,
% 2.52/2.74 (r(s(s(z)), z)),
% 2.52/2.74 inference(unit_resolution,[status(thm)],[186, 8395])).
% 2.52/2.74 tff(8397,plain,
% 2.52/2.74 (~r(s(s(z)), s(z))),
% 2.52/2.74 inference(unit_resolution,[status(thm)],[4287, 8396, 152, 8388])).
% 2.52/2.74 tff(8398,plain,
% 2.52/2.74 (b(s(s(z)), s(z))),
% 2.52/2.74 inference(unit_resolution,[status(thm)],[308, 8397])).
% 2.52/2.74 tff(8399,plain,
% 2.52/2.74 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), z)) | (~b(z, s(z))) | (~b(s(s(z)), s(z))) | (~b(s(s(z)), s(s(s(elem!1))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), z)) | (~b(z, s(z))) | (~b(s(s(z)), s(z))) | (~b(s(s(z)), s(s(s(elem!1))))))),
% 2.52/2.74 inference(rewrite,[status(thm)],[])).
% 2.52/2.74 tff(8400,plain,
% 2.52/2.74 (((~b(z, s(z))) | (~b(s(s(z)), s(z))) | (~b(s(s(s(elem!1))), z)) | (~b(s(z), s(s(s(elem!1))))) | (~b(s(s(z)), s(s(s(elem!1))))) | (~b(s(s(z)), s(z)))) <=> ((~b(s(z), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), z)) | (~b(z, s(z))) | (~b(s(s(z)), s(z))) | (~b(s(s(z)), s(s(s(elem!1))))))),
% 2.52/2.74 inference(rewrite,[status(thm)],[])).
% 2.52/2.74 tff(8401,plain,
% 2.52/2.74 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(z))) | (~b(s(s(z)), s(z))) | (~b(s(s(s(elem!1))), z)) | (~b(s(z), s(s(s(elem!1))))) | (~b(s(s(z)), s(s(s(elem!1))))) | (~b(s(s(z)), s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), z)) | (~b(z, s(z))) | (~b(s(s(z)), s(z))) | (~b(s(s(z)), s(s(s(elem!1)))))))),
% 2.52/2.74 inference(monotonicity,[status(thm)],[8400])).
% 2.52/2.74 tff(8402,plain,
% 2.52/2.74 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(z))) | (~b(s(s(z)), s(z))) | (~b(s(s(s(elem!1))), z)) | (~b(s(z), s(s(s(elem!1))))) | (~b(s(s(z)), s(s(s(elem!1))))) | (~b(s(s(z)), s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), z)) | (~b(z, s(z))) | (~b(s(s(z)), s(z))) | (~b(s(s(z)), s(s(s(elem!1))))))),
% 2.52/2.74 inference(transitivity,[status(thm)],[8401, 8399])).
% 2.52/2.74 tff(8403,plain,
% 2.52/2.74 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(z))) | (~b(s(s(z)), s(z))) | (~b(s(s(s(elem!1))), z)) | (~b(s(z), s(s(s(elem!1))))) | (~b(s(s(z)), s(s(s(elem!1))))) | (~b(s(s(z)), s(z))))),
% 2.52/2.74 inference(quant_inst,[status(thm)],[])).
% 2.52/2.74 tff(8404,plain,
% 2.52/2.74 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), z)) | (~b(z, s(z))) | (~b(s(s(z)), s(z))) | (~b(s(s(z)), s(s(s(elem!1)))))),
% 2.52/2.74 inference(modus_ponens,[status(thm)],[8403, 8402])).
% 2.52/2.74 tff(8405,plain,
% 2.52/2.74 ($false),
% 2.52/2.74 inference(unit_resolution,[status(thm)],[8404, 166, 8366, 118, 6718, 8398, 8386])).
% 2.52/2.74 tff(8406,plain,((~b(z, s(z))) | b(z, s(s(z)))), inference(lemma,lemma(discharge,[]))).
% 2.52/2.74 tff(8407,plain,
% 2.52/2.74 (~b(z, s(z))),
% 2.52/2.74 inference(unit_resolution,[status(thm)],[8406, 125])).
% 2.52/2.74 tff(8408,plain,
% 2.52/2.74 (r(z, s(z))),
% 2.52/2.74 inference(unit_resolution,[status(thm)],[321, 8407])).
% 2.52/2.74 tff(8409,plain,
% 2.52/2.74 (~r(s(s(z)), s(z))),
% 2.52/2.74 inference(unit_resolution,[status(thm)],[2680, 97, 152, 8408])).
% 2.52/2.74 tff(8410,plain,
% 2.52/2.74 (b(s(s(z)), s(z))),
% 2.52/2.74 inference(unit_resolution,[status(thm)],[308, 8409])).
% 2.52/2.74 tff(8411,plain,
% 2.52/2.74 (~r(s(z), s(s(z)))),
% 2.52/2.74 inference(unit_resolution,[status(thm)],[2959, 866, 155, 323])).
% 2.52/2.74 tff(8412,plain,
% 2.52/2.74 (b(s(z), s(s(z)))),
% 2.52/2.74 inference(unit_resolution,[status(thm)],[427, 8411])).
% 2.52/2.74 tff(8413,plain,
% 2.52/2.74 ($false),
% 2.52/2.74 inference(unit_resolution,[status(thm)],[4251, 166, 8412, 96, 156, 6496])).
% 2.52/2.74 tff(8414,plain,((~r(s(s(z)), z)) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(s(z)), s(z))) | (~r(z, s(s(z)))) | (~r(s(s(s(elem!1))), z)) | (~r(z, s(z)))), inference(lemma,lemma(discharge,[]))).
% 2.52/2.74 tff(8415,plain,
% 2.52/2.74 (~r(s(s(z)), z)),
% 2.52/2.74 inference(unit_resolution,[status(thm)],[8414, 8410, 96, 152, 154, 8408])).
% 2.52/2.74 tff(8416,plain,
% 2.52/2.74 (b(s(s(z)), z)),
% 2.52/2.74 inference(unit_resolution,[status(thm)],[186, 8415])).
% 2.52/2.74 tff(8417,plain,
% 2.52/2.74 (~r(s(s(elem!1)), z)),
% 2.52/2.74 inference(unit_resolution,[status(thm)],[2274, 311, 152, 97])).
% 2.52/2.74 tff(8418,plain,
% 2.52/2.74 (b(s(s(elem!1)), z)),
% 2.52/2.74 inference(unit_resolution,[status(thm)],[608, 8417])).
% 2.52/2.74 tff(8419,plain,
% 2.52/2.74 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(elem!1)))) | (~r(z, s(z))) | (~r(s(z), z)) | (~r(s(s(elem!1)), s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, s(s(elem!1)))) | (~r(z, s(z))) | (~r(s(z), z)) | (~r(s(s(elem!1)), s(z))))),
% 2.52/2.74 inference(rewrite,[status(thm)],[])).
% 2.52/2.74 tff(8420,plain,
% 2.52/2.74 (((~r(s(z), z)) | (~r(s(s(elem!1)), s(z))) | (~r(z, s(z))) | (~r(z, s(s(elem!1))))) <=> ((~r(z, s(s(elem!1)))) | (~r(z, s(z))) | (~r(s(z), z)) | (~r(s(s(elem!1)), s(z))))),
% 2.52/2.74 inference(rewrite,[status(thm)],[])).
% 2.52/2.74 tff(8421,plain,
% 2.52/2.74 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), z)) | (~r(s(s(elem!1)), s(z))) | (~r(z, s(z))) | (~r(z, s(s(elem!1)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(elem!1)))) | (~r(z, s(z))) | (~r(s(z), z)) | (~r(s(s(elem!1)), s(z)))))),
% 2.52/2.74 inference(monotonicity,[status(thm)],[8420])).
% 2.52/2.74 tff(8422,plain,
% 2.52/2.74 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), z)) | (~r(s(s(elem!1)), s(z))) | (~r(z, s(z))) | (~r(z, s(s(elem!1)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, s(s(elem!1)))) | (~r(z, s(z))) | (~r(s(z), z)) | (~r(s(s(elem!1)), s(z))))),
% 2.52/2.74 inference(transitivity,[status(thm)],[8421, 8419])).
% 2.52/2.74 tff(8423,plain,
% 2.52/2.74 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), z)) | (~r(s(s(elem!1)), s(z))) | (~r(z, s(z))) | (~r(z, s(s(elem!1)))))),
% 2.52/2.74 inference(quant_inst,[status(thm)],[])).
% 2.52/2.74 tff(8424,plain,
% 2.52/2.74 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, s(s(elem!1)))) | (~r(z, s(z))) | (~r(s(z), z)) | (~r(s(s(elem!1)), s(z)))),
% 2.52/2.74 inference(modus_ponens,[status(thm)],[8423, 8422])).
% 2.52/2.74 tff(8425,plain,
% 2.52/2.74 ($false),
% 2.52/2.74 inference(unit_resolution,[status(thm)],[8424, 197, 323, 4577, 97, 365])).
% 2.52/2.74 tff(8426,plain,((~r(s(z), z)) | (~r(z, s(z))) | (~r(s(s(elem!1)), s(z))) | (~r(z, s(s(elem!1))))), inference(lemma,lemma(discharge,[]))).
% 2.52/2.74 tff(8427,plain,
% 2.52/2.74 (~r(z, s(s(elem!1)))),
% 2.52/2.74 inference(unit_resolution,[status(thm)],[8426, 4577, 8408, 97])).
% 2.52/2.74 tff(8428,plain,
% 2.52/2.74 (b(z, s(s(elem!1)))),
% 2.52/2.74 inference(unit_resolution,[status(thm)],[1795, 8427])).
% 2.52/2.74 tff(8429,plain,
% 2.52/2.74 (~b(s(s(z)), s(s(elem!1)))),
% 2.52/2.74 inference(unit_resolution,[status(thm)],[4605, 166, 8428, 8418, 122])).
% 2.52/2.74 tff(8430,plain,
% 2.52/2.74 (~r(z, s(s(elem!1)))),
% 2.52/2.74 inference(unit_resolution,[status(thm)],[413, 377, 311, 323])).
% 2.52/2.74 tff(8431,plain,
% 2.52/2.74 (b(z, s(s(elem!1)))),
% 2.52/2.74 inference(unit_resolution,[status(thm)],[1795, 8430])).
% 2.52/2.74 tff(8432,plain,
% 2.52/2.74 (~b(s(s(s(elem!1))), s(s(z)))),
% 2.52/2.74 inference(unit_resolution,[status(thm)],[4253, 333, 377, 96, 311])).
% 2.52/2.74 tff(8433,plain,
% 2.52/2.74 ($false),
% 2.52/2.74 inference(unit_resolution,[status(thm)],[218, 8432, 5729])).
% 2.52/2.74 tff(8434,plain,((~r(s(s(z)), s(s(elem!1)))) | (~r(s(s(elem!1)), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(z))) | (~r(s(z), s(s(elem!1)))) | (~r(z, s(s(z)))) | (~r(s(s(s(elem!1))), z))), inference(lemma,lemma(discharge,[]))).
% 2.52/2.74 tff(8435,plain,
% 2.52/2.74 (~r(s(s(z)), s(s(elem!1)))),
% 2.52/2.74 inference(unit_resolution,[status(thm)],[8434, 377, 311, 96, 152, 154])).
% 2.52/2.74 tff(8436,plain,
% 2.52/2.74 (s(s(z)) = s(s(elem!1))),
% 2.52/2.74 inference(unit_resolution,[status(thm)],[390, 8435, 2072])).
% 2.52/2.74 tff(8437,plain,
% 2.52/2.74 ($false),
% 2.52/2.74 inference(unit_resolution,[status(thm)],[2261, 8436, 8431, 125])).
% 2.52/2.74 tff(8438,plain,((~r(s(s(elem!1)), s(s(s(elem!1))))) | b(z, s(s(z))) | b(s(s(z)), s(s(elem!1))) | (~r(s(z), s(s(elem!1)))) | (~b(s(s(s(elem!1))), s(z))) | (~r(s(s(s(elem!1))), z)) | (~r(z, s(z)))), inference(lemma,lemma(discharge,[]))).
% 2.52/2.74 tff(8439,plain,
% 2.52/2.74 (~r(s(s(elem!1)), s(s(s(elem!1))))),
% 2.52/2.74 inference(unit_resolution,[status(thm)],[8438, 8429, 8408, 154, 96, 125, 311])).
% 2.52/2.74 tff(8440,plain,
% 2.52/2.74 (~(s(s(z)) = s(s(elem!1)))),
% 2.52/2.74 inference(unit_resolution,[status(thm)],[2261, 8428, 125])).
% 2.52/2.74 tff(8441,plain,
% 2.52/2.74 (r(s(s(z)), s(s(elem!1)))),
% 2.52/2.75 inference(unit_resolution,[status(thm)],[390, 8429, 8440])).
% 2.52/2.75 tff(8442,plain,
% 2.52/2.75 (~(s(s(elem!1)) = s(s(z)))),
% 2.52/2.75 inference(unit_resolution,[status(thm)],[131, 8440])).
% 2.52/2.75 tff(8443,plain,
% 2.52/2.75 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(elem!1)))) | (~b(s(s(elem!1)), z)) | (~b(s(s(elem!1)), s(s(z)))) | (~b(s(s(z)), z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(s(elem!1)))) | (~b(s(s(elem!1)), z)) | (~b(s(s(elem!1)), s(s(z)))) | (~b(s(s(z)), z)))),
% 2.52/2.75 inference(rewrite,[status(thm)],[])).
% 2.52/2.75 tff(8444,plain,
% 2.52/2.75 (((~b(s(s(elem!1)), z)) | (~b(s(s(elem!1)), z)) | (~b(z, s(s(elem!1)))) | (~b(s(s(z)), z)) | (~b(s(s(elem!1)), z)) | (~b(s(s(elem!1)), s(s(z))))) <=> ((~b(z, s(s(elem!1)))) | (~b(s(s(elem!1)), z)) | (~b(s(s(elem!1)), s(s(z)))) | (~b(s(s(z)), z)))),
% 2.52/2.75 inference(rewrite,[status(thm)],[])).
% 2.52/2.75 tff(8445,plain,
% 2.52/2.75 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), z)) | (~b(s(s(elem!1)), z)) | (~b(z, s(s(elem!1)))) | (~b(s(s(z)), z)) | (~b(s(s(elem!1)), z)) | (~b(s(s(elem!1)), s(s(z)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(elem!1)))) | (~b(s(s(elem!1)), z)) | (~b(s(s(elem!1)), s(s(z)))) | (~b(s(s(z)), z))))),
% 2.52/2.75 inference(monotonicity,[status(thm)],[8444])).
% 2.52/2.75 tff(8446,plain,
% 2.52/2.75 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), z)) | (~b(s(s(elem!1)), z)) | (~b(z, s(s(elem!1)))) | (~b(s(s(z)), z)) | (~b(s(s(elem!1)), z)) | (~b(s(s(elem!1)), s(s(z)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(s(elem!1)))) | (~b(s(s(elem!1)), z)) | (~b(s(s(elem!1)), s(s(z)))) | (~b(s(s(z)), z)))),
% 2.52/2.75 inference(transitivity,[status(thm)],[8445, 8443])).
% 2.52/2.75 tff(8447,plain,
% 2.52/2.75 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), z)) | (~b(s(s(elem!1)), z)) | (~b(z, s(s(elem!1)))) | (~b(s(s(z)), z)) | (~b(s(s(elem!1)), z)) | (~b(s(s(elem!1)), s(s(z)))))),
% 2.52/2.75 inference(quant_inst,[status(thm)],[])).
% 2.52/2.75 tff(8448,plain,
% 2.52/2.75 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(s(elem!1)))) | (~b(s(s(elem!1)), z)) | (~b(s(s(elem!1)), s(s(z)))) | (~b(s(s(z)), z))),
% 2.52/2.75 inference(modus_ponens,[status(thm)],[8447, 8446])).
% 2.52/2.75 tff(8449,plain,
% 2.52/2.75 (~b(s(s(elem!1)), s(s(z)))),
% 2.52/2.75 inference(unit_resolution,[status(thm)],[8448, 166, 8428, 8418, 122])).
% 2.52/2.75 tff(8450,plain,
% 2.52/2.75 (r(s(s(elem!1)), s(s(z)))),
% 2.52/2.75 inference(unit_resolution,[status(thm)],[441, 8449, 8442])).
% 2.52/2.75 tff(8451,plain,
% 2.52/2.75 (b(s(s(elem!1)), s(s(s(elem!1))))),
% 2.52/2.75 inference(unit_resolution,[status(thm)],[461, 8439, 45])).
% 2.52/2.75 tff(8452,plain,
% 2.52/2.75 (~b(s(s(s(elem!1))), s(s(elem!1)))),
% 2.52/2.75 inference(unit_resolution,[status(thm)],[2349, 119, 97, 1820, 463])).
% 2.52/2.75 tff(8453,plain,
% 2.52/2.75 (r(s(s(s(elem!1))), s(s(elem!1)))),
% 2.52/2.75 inference(unit_resolution,[status(thm)],[889, 8452, 1863])).
% 2.52/2.75 tff(8454,plain,
% 2.52/2.75 ($false),
% 2.52/2.75 inference(unit_resolution,[status(thm)],[6762, 197, 311, 4577, 8453, 119])).
% 2.52/2.75 tff(8455,plain,((~r(s(z), s(s(s(elem!1))))) | (~r(s(z), s(s(elem!1)))) | (~r(s(s(elem!1)), s(z))) | (s(s(s(elem!1))) = s(s(elem!1))) | (~r(s(z), z)) | (~b(z, s(s(elem!1)))) | (~b(s(s(elem!1)), s(s(s(elem!1)))))), inference(lemma,lemma(discharge,[]))).
% 2.52/2.75 tff(8456,plain,
% 2.52/2.75 (~r(s(z), s(s(s(elem!1))))),
% 2.52/2.75 inference(unit_resolution,[status(thm)],[8455, 8451, 311, 4577, 97, 8428, 51])).
% 2.52/2.75 tff(8457,plain,
% 2.52/2.75 (b(s(z), s(s(s(elem!1))))),
% 2.52/2.75 inference(unit_resolution,[status(thm)],[116, 8456])).
% 2.52/2.75 tff(8458,plain,
% 2.52/2.75 (~b(s(s(z)), s(s(s(elem!1))))),
% 2.52/2.75 inference(unit_resolution,[status(thm)],[271, 8457, 96, 8410])).
% 2.52/2.75 tff(8459,plain,
% 2.52/2.75 (r(s(s(z)), s(s(s(elem!1))))),
% 2.52/2.75 inference(unit_resolution,[status(thm)],[279, 8458])).
% 2.52/2.75 tff(8460,plain,
% 2.52/2.75 (~r(s(s(s(elem!1))), s(s(elem!1)))),
% 2.52/2.75 inference(unit_resolution,[status(thm)],[4513, 8459, 8450, 8441])).
% 2.52/2.75 tff(8461,plain,
% 2.52/2.75 (~r(z, s(s(s(elem!1))))),
% 2.52/2.75 inference(unit_resolution,[status(thm)],[290, 8459, 152, 154])).
% 2.52/2.75 tff(8462,plain,
% 2.52/2.75 (b(z, s(s(s(elem!1))))),
% 2.52/2.75 inference(unit_resolution,[status(thm)],[261, 8461])).
% 2.52/2.75 tff(8463,plain,
% 2.52/2.75 ($false),
% 2.52/2.75 inference(unit_resolution,[status(thm)],[1834, 8462, 8460, 45, 8428, 8439])).
% 2.52/2.75 tff(8464,plain,((~b(s(s(z)), z)) | (s(s(elem!1)) = s(s(s(elem!1)))) | (~r(s(s(s(elem!1))), z)) | (~b(s(s(s(elem!1))), s(z))) | (~r(s(z), s(s(elem!1)))) | (~r(s(s(elem!1)), s(z))) | (~r(s(z), z)) | b(z, s(s(z)))), inference(lemma,lemma(discharge,[]))).
% 2.52/2.75 tff(8465,plain,
% 2.52/2.75 (~r(s(s(elem!1)), s(z))),
% 2.52/2.75 inference(unit_resolution,[status(thm)],[8464, 85, 154, 96, 8416, 45, 97, 125])).
% 2.52/2.75 tff(8466,plain,
% 2.52/2.75 ($false),
% 2.52/2.75 inference(unit_resolution,[status(thm)],[1912, 8465, 4557])).
% 2.52/2.75 tff(8467,plain,(b(s(z), s(s(elem!1))) | (~r(s(s(s(elem!1))), z)) | (~b(s(s(s(elem!1))), s(z))) | (s(s(elem!1)) = s(s(s(elem!1)))) | (~r(s(z), z)) | b(z, s(s(z)))), inference(lemma,lemma(discharge,[]))).
% 2.52/2.75 tff(8468,plain,
% 2.52/2.75 (b(s(z), s(s(elem!1)))),
% 2.52/2.75 inference(unit_resolution,[status(thm)],[8467, 45, 96, 154, 97, 125])).
% 2.52/2.75 tff(8469,plain,
% 2.52/2.75 (~b(s(s(z)), s(s(elem!1)))),
% 2.52/2.75 inference(unit_resolution,[status(thm)],[454, 376, 310, 156])).
% 2.52/2.75 tff(8470,plain,
% 2.52/2.75 (r(s(s(z)), s(s(elem!1)))),
% 2.52/2.75 inference(unit_resolution,[status(thm)],[390, 8469, 52])).
% 2.52/2.75 tff(8471,plain,
% 2.52/2.75 (~r(s(s(s(elem!1))), s(s(z)))),
% 2.52/2.75 inference(unit_resolution,[status(thm)],[526, 8470, 155, 154])).
% 2.52/2.75 tff(8472,plain,
% 2.52/2.75 (b(s(s(s(elem!1))), s(s(z)))),
% 2.52/2.75 inference(unit_resolution,[status(thm)],[218, 8471])).
% 2.52/2.75 tff(8473,plain,
% 2.52/2.75 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), s(s(z)))) | (~b(s(z), s(s(elem!1)))) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(s(elem!1)), s(z))) | (~b(s(s(z)), s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(elem!1))), s(s(z)))) | (~b(s(z), s(s(elem!1)))) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(s(elem!1)), s(z))) | (~b(s(s(z)), s(z))))),
% 2.52/2.75 inference(rewrite,[status(thm)],[])).
% 2.52/2.75 tff(8474,plain,
% 2.52/2.75 (((~b(s(s(elem!1)), s(z))) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(z), s(s(elem!1)))) | (~b(s(s(z)), s(z))) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(s(s(elem!1))), s(s(z))))) <=> ((~b(s(s(s(elem!1))), s(s(z)))) | (~b(s(z), s(s(elem!1)))) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(s(elem!1)), s(z))) | (~b(s(s(z)), s(z))))),
% 2.52/2.75 inference(rewrite,[status(thm)],[])).
% 2.52/2.75 tff(8475,plain,
% 2.52/2.75 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), s(z))) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(z), s(s(elem!1)))) | (~b(s(s(z)), s(z))) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(s(s(elem!1))), s(s(z)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), s(s(z)))) | (~b(s(z), s(s(elem!1)))) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(s(elem!1)), s(z))) | (~b(s(s(z)), s(z)))))),
% 2.52/2.75 inference(monotonicity,[status(thm)],[8474])).
% 2.52/2.75 tff(8476,plain,
% 2.52/2.75 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), s(z))) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(z), s(s(elem!1)))) | (~b(s(s(z)), s(z))) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(s(s(elem!1))), s(s(z)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(elem!1))), s(s(z)))) | (~b(s(z), s(s(elem!1)))) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(s(elem!1)), s(z))) | (~b(s(s(z)), s(z))))),
% 2.52/2.75 inference(transitivity,[status(thm)],[8475, 8473])).
% 2.52/2.75 tff(8477,plain,
% 2.52/2.75 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), s(z))) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(z), s(s(elem!1)))) | (~b(s(s(z)), s(z))) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(s(s(elem!1))), s(s(z)))))),
% 2.52/2.75 inference(quant_inst,[status(thm)],[])).
% 2.52/2.75 tff(8478,plain,
% 2.52/2.75 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(elem!1))), s(s(z)))) | (~b(s(z), s(s(elem!1)))) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(s(elem!1)), s(z))) | (~b(s(s(z)), s(z)))),
% 2.52/2.75 inference(modus_ponens,[status(thm)],[8477, 8476])).
% 2.52/2.75 tff(8479,plain,
% 2.52/2.75 ($false),
% 2.52/2.75 inference(unit_resolution,[status(thm)],[8478, 166, 376, 96, 310, 156, 8472])).
% 2.52/2.75 tff(8480,plain,((~b(s(z), s(s(elem!1)))) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(s(elem!1)), s(z))) | (~b(s(s(z)), s(z))) | (~r(z, s(s(z)))) | (~r(s(s(s(elem!1))), z)) | (s(s(z)) = s(s(elem!1)))), inference(lemma,lemma(discharge,[]))).
% 2.52/2.75 tff(8481,plain,
% 2.52/2.75 (~b(s(s(elem!1)), s(z))),
% 2.52/2.75 inference(unit_resolution,[status(thm)],[8480, 8468, 152, 96, 154, 8410, 52])).
% 2.52/2.75 tff(8482,plain,
% 2.52/2.75 (r(s(s(elem!1)), s(z))),
% 2.52/2.75 inference(unit_resolution,[status(thm)],[1912, 8481])).
% 2.52/2.75 tff(8483,plain,
% 2.52/2.75 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(z))) | (~r(s(s(elem!1)), z)) | (~r(s(z), z)) | (~r(s(s(elem!1)), s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, s(z))) | (~r(s(s(elem!1)), z)) | (~r(s(z), z)) | (~r(s(s(elem!1)), s(z))))),
% 2.52/2.75 inference(rewrite,[status(thm)],[])).
% 2.52/2.75 tff(8484,plain,
% 2.52/2.75 (((~r(s(z), z)) | (~r(z, s(z))) | (~r(s(s(elem!1)), s(z))) | (~r(s(s(elem!1)), z))) <=> ((~r(z, s(z))) | (~r(s(s(elem!1)), z)) | (~r(s(z), z)) | (~r(s(s(elem!1)), s(z))))),
% 2.52/2.75 inference(rewrite,[status(thm)],[])).
% 2.52/2.75 tff(8485,plain,
% 2.52/2.75 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), z)) | (~r(z, s(z))) | (~r(s(s(elem!1)), s(z))) | (~r(s(s(elem!1)), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(z))) | (~r(s(s(elem!1)), z)) | (~r(s(z), z)) | (~r(s(s(elem!1)), s(z)))))),
% 2.52/2.75 inference(monotonicity,[status(thm)],[8484])).
% 2.52/2.75 tff(8486,plain,
% 2.52/2.75 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), z)) | (~r(z, s(z))) | (~r(s(s(elem!1)), s(z))) | (~r(s(s(elem!1)), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, s(z))) | (~r(s(s(elem!1)), z)) | (~r(s(z), z)) | (~r(s(s(elem!1)), s(z))))),
% 2.52/2.75 inference(transitivity,[status(thm)],[8485, 8483])).
% 2.52/2.75 tff(8487,plain,
% 2.52/2.75 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), z)) | (~r(z, s(z))) | (~r(s(s(elem!1)), s(z))) | (~r(s(s(elem!1)), z)))),
% 2.52/2.75 inference(quant_inst,[status(thm)],[])).
% 2.52/2.75 tff(8488,plain,
% 2.52/2.75 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, s(z))) | (~r(s(s(elem!1)), z)) | (~r(s(z), z)) | (~r(s(s(elem!1)), s(z)))),
% 2.52/2.75 inference(modus_ponens,[status(thm)],[8487, 8486])).
% 2.52/2.75 tff(8489,plain,
% 2.52/2.75 ($false),
% 2.52/2.75 inference(unit_resolution,[status(thm)],[8488, 197, 323, 4577, 97, 1970])).
% 2.52/2.75 tff(8490,plain,((~r(z, s(z))) | (~r(s(s(elem!1)), s(z))) | (~r(s(z), z)) | (~r(s(s(elem!1)), z))), inference(lemma,lemma(discharge,[]))).
% 2.52/2.75 tff(8491,plain,
% 2.52/2.75 (~r(s(s(elem!1)), z)),
% 2.52/2.75 inference(unit_resolution,[status(thm)],[8490, 8482, 8408, 97])).
% 2.52/2.75 tff(8492,plain,
% 2.52/2.75 (b(s(s(elem!1)), z)),
% 2.52/2.75 inference(unit_resolution,[status(thm)],[608, 8491])).
% 2.52/2.75 tff(8493,plain,
% 2.52/2.75 (~r(z, s(s(elem!1)))),
% 2.52/2.75 inference(unit_resolution,[status(thm)],[8426, 8482, 8408, 97])).
% 2.52/2.75 tff(8494,plain,
% 2.52/2.75 (b(z, s(s(elem!1)))),
% 2.52/2.75 inference(unit_resolution,[status(thm)],[1795, 8493])).
% 2.52/2.75 tff(8495,plain,
% 2.52/2.75 (~b(s(s(z)), s(s(elem!1)))),
% 2.52/2.75 inference(unit_resolution,[status(thm)],[4605, 166, 8494, 8492, 8416])).
% 2.52/2.75 tff(8496,plain,
% 2.52/2.75 (r(s(s(z)), s(s(elem!1)))),
% 2.52/2.75 inference(unit_resolution,[status(thm)],[390, 8495, 52])).
% 2.52/2.75 tff(8497,plain,
% 2.52/2.75 (~r(s(s(s(elem!1))), s(s(z)))),
% 2.52/2.75 inference(unit_resolution,[status(thm)],[526, 8496, 152, 154])).
% 2.52/2.75 tff(8498,plain,
% 2.52/2.75 (b(s(s(s(elem!1))), s(s(z)))),
% 2.52/2.75 inference(unit_resolution,[status(thm)],[218, 8497])).
% 2.52/2.75 tff(8499,plain,
% 2.52/2.75 (~r(s(z), s(s(z)))),
% 2.52/2.75 inference(unit_resolution,[status(thm)],[347, 8496, 152, 97])).
% 2.52/2.75 tff(8500,plain,
% 2.52/2.75 (b(s(z), s(s(z)))),
% 2.52/2.75 inference(unit_resolution,[status(thm)],[427, 8499])).
% 2.52/2.75 tff(8501,plain,
% 2.52/2.75 (~b(s(s(elem!1)), s(s(z)))),
% 2.52/2.75 inference(unit_resolution,[status(thm)],[8448, 166, 8494, 8492, 8416])).
% 2.52/2.75 tff(8502,plain,
% 2.52/2.75 (r(s(s(elem!1)), s(s(z)))),
% 2.52/2.75 inference(unit_resolution,[status(thm)],[441, 8501, 132])).
% 2.52/2.75 tff(8503,plain,
% 2.52/2.75 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), z)) | (~b(s(z), s(s(elem!1)))) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(s(z)), z)) | (~b(s(s(z)), s(z))) | (~b(s(s(z)), s(s(s(elem!1))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(elem!1)), z)) | (~b(s(z), s(s(elem!1)))) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(s(z)), z)) | (~b(s(s(z)), s(z))) | (~b(s(s(z)), s(s(s(elem!1))))))),
% 2.52/2.75 inference(rewrite,[status(thm)],[])).
% 2.52/2.75 tff(8504,plain,
% 2.52/2.75 (((~b(s(s(elem!1)), z)) | (~b(s(s(z)), z)) | (~b(s(z), s(s(elem!1)))) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(s(z)), s(z))) | (~b(s(s(z)), s(s(s(elem!1)))))) <=> ((~b(s(s(elem!1)), z)) | (~b(s(z), s(s(elem!1)))) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(s(z)), z)) | (~b(s(s(z)), s(z))) | (~b(s(s(z)), s(s(s(elem!1))))))),
% 2.52/2.75 inference(rewrite,[status(thm)],[])).
% 2.52/2.75 tff(8505,plain,
% 2.52/2.75 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), z)) | (~b(s(s(z)), z)) | (~b(s(z), s(s(elem!1)))) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(s(z)), s(z))) | (~b(s(s(z)), s(s(s(elem!1))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), z)) | (~b(s(z), s(s(elem!1)))) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(s(z)), z)) | (~b(s(s(z)), s(z))) | (~b(s(s(z)), s(s(s(elem!1)))))))),
% 2.52/2.75 inference(monotonicity,[status(thm)],[8504])).
% 2.52/2.75 tff(8506,plain,
% 2.52/2.75 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), z)) | (~b(s(s(z)), z)) | (~b(s(z), s(s(elem!1)))) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(s(z)), s(z))) | (~b(s(s(z)), s(s(s(elem!1))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(elem!1)), z)) | (~b(s(z), s(s(elem!1)))) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(s(z)), z)) | (~b(s(s(z)), s(z))) | (~b(s(s(z)), s(s(s(elem!1))))))),
% 2.52/2.75 inference(transitivity,[status(thm)],[8505, 8503])).
% 2.52/2.75 tff(8507,plain,
% 2.52/2.75 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), z)) | (~b(s(s(z)), z)) | (~b(s(z), s(s(elem!1)))) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(s(z)), s(z))) | (~b(s(s(z)), s(s(s(elem!1))))))),
% 2.52/2.75 inference(quant_inst,[status(thm)],[])).
% 2.52/2.75 tff(8508,plain,
% 2.52/2.75 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(elem!1)), z)) | (~b(s(z), s(s(elem!1)))) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(s(z)), z)) | (~b(s(s(z)), s(z))) | (~b(s(s(z)), s(s(s(elem!1)))))),
% 2.52/2.75 inference(modus_ponens,[status(thm)],[8507, 8506])).
% 2.52/2.75 tff(8509,plain,
% 2.52/2.75 (~b(s(s(z)), s(s(s(elem!1))))),
% 2.52/2.75 inference(unit_resolution,[status(thm)],[8508, 166, 8468, 96, 8492, 8410, 8416])).
% 2.52/2.75 tff(8510,plain,
% 2.52/2.75 (r(s(s(z)), s(s(s(elem!1))))),
% 2.52/2.75 inference(unit_resolution,[status(thm)],[279, 8509])).
% 2.52/2.75 tff(8511,plain,
% 2.52/2.75 (~r(s(s(s(elem!1))), s(s(elem!1)))),
% 2.52/2.75 inference(unit_resolution,[status(thm)],[4513, 8510, 8502, 8496])).
% 2.52/2.75 tff(8512,plain,
% 2.52/2.75 (b(s(s(s(elem!1))), s(s(elem!1)))),
% 2.52/2.75 inference(unit_resolution,[status(thm)],[889, 8511, 51])).
% 2.52/2.75 tff(8513,plain,
% 2.52/2.75 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(s(s(elem!1))), s(s(z)))) | (~b(s(z), s(s(elem!1)))) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(z), s(s(z)))) | (~b(s(s(z)), s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(s(s(elem!1))), s(s(z)))) | (~b(s(z), s(s(elem!1)))) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(z), s(s(z)))) | (~b(s(s(z)), s(z))))),
% 2.52/2.75 inference(rewrite,[status(thm)],[])).
% 2.52/2.75 tff(8514,plain,
% 2.52/2.75 (((~b(s(z), s(s(elem!1)))) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(s(z)), s(z))) | (~b(s(z), s(s(z)))) | (~b(s(s(s(elem!1))), s(s(z)))) | (~b(s(s(s(elem!1))), s(z)))) <=> ((~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(s(s(elem!1))), s(s(z)))) | (~b(s(z), s(s(elem!1)))) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(z), s(s(z)))) | (~b(s(s(z)), s(z))))),
% 2.52/2.75 inference(rewrite,[status(thm)],[])).
% 2.52/2.75 tff(8515,plain,
% 2.52/2.75 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(elem!1)))) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(s(z)), s(z))) | (~b(s(z), s(s(z)))) | (~b(s(s(s(elem!1))), s(s(z)))) | (~b(s(s(s(elem!1))), s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(s(s(elem!1))), s(s(z)))) | (~b(s(z), s(s(elem!1)))) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(z), s(s(z)))) | (~b(s(s(z)), s(z)))))),
% 2.52/2.75 inference(monotonicity,[status(thm)],[8514])).
% 2.52/2.75 tff(8516,plain,
% 2.52/2.75 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(elem!1)))) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(s(z)), s(z))) | (~b(s(z), s(s(z)))) | (~b(s(s(s(elem!1))), s(s(z)))) | (~b(s(s(s(elem!1))), s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(s(s(elem!1))), s(s(z)))) | (~b(s(z), s(s(elem!1)))) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(z), s(s(z)))) | (~b(s(s(z)), s(z))))),
% 2.52/2.75 inference(transitivity,[status(thm)],[8515, 8513])).
% 2.52/2.75 tff(8517,plain,
% 2.52/2.75 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(elem!1)))) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(s(z)), s(z))) | (~b(s(z), s(s(z)))) | (~b(s(s(s(elem!1))), s(s(z)))) | (~b(s(s(s(elem!1))), s(z))))),
% 2.52/2.75 inference(quant_inst,[status(thm)],[])).
% 2.52/2.75 tff(8518,plain,
% 2.52/2.75 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(s(s(elem!1))), s(s(z)))) | (~b(s(z), s(s(elem!1)))) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(z), s(s(z)))) | (~b(s(s(z)), s(z)))),
% 2.52/2.75 inference(modus_ponens,[status(thm)],[8517, 8516])).
% 2.52/2.75 tff(8519,plain,
% 2.52/2.75 ($false),
% 2.52/2.75 inference(unit_resolution,[status(thm)],[8518, 166, 8468, 8512, 8500, 96, 8410, 8498])).
% 2.52/2.75 tff(8520,plain,((s(s(elem!1)) = s(s(s(elem!1)))) | (~b(s(s(s(elem!1))), s(z))) | (~r(s(z), z)) | (~r(s(s(s(elem!1))), z)) | (s(s(z)) = s(s(elem!1))) | b(z, s(s(z)))), inference(lemma,lemma(discharge,[]))).
% 2.52/2.76 tff(8521,plain,
% 2.52/2.76 (s(s(elem!1)) = s(s(s(elem!1)))),
% 2.52/2.76 inference(unit_resolution,[status(thm)],[8520, 52, 97, 154, 96, 125])).
% 2.52/2.76 tff(8522,plain,
% 2.52/2.76 (b(s(s(elem!1)), s(z))),
% 2.52/2.76 inference(unit_resolution,[status(thm)],[4570, 8521, 96])).
% 2.52/2.76 tff(8523,plain,
% 2.52/2.76 (b(s(z), s(s(elem!1)))),
% 2.52/2.76 inference(unit_resolution,[status(thm)],[4556, 8522, 125])).
% 2.52/2.76 tff(8524,plain,
% 2.52/2.76 ($false),
% 2.52/2.76 inference(unit_resolution,[status(thm)],[8480, 8523, 8522, 152, 96, 154, 8410, 52])).
% 2.52/2.76 tff(8525,plain,((s(s(z)) = s(s(elem!1))) | (~b(s(s(s(elem!1))), s(z))) | (~r(s(s(s(elem!1))), z)) | b(z, s(s(z))) | (~r(s(z), z))), inference(lemma,lemma(discharge,[]))).
% 2.52/2.76 tff(8526,plain,
% 2.52/2.76 (s(s(z)) = s(s(elem!1))),
% 2.52/2.76 inference(unit_resolution,[status(thm)],[8525, 97, 154, 125, 96])).
% 2.52/2.76 tff(8527,plain,
% 2.52/2.76 (~b(z, s(s(elem!1)))),
% 2.52/2.76 inference(unit_resolution,[status(thm)],[2261, 8526, 125])).
% 2.52/2.76 tff(8528,plain,
% 2.52/2.76 (r(z, s(s(elem!1)))),
% 2.52/2.76 inference(unit_resolution,[status(thm)],[1795, 8527])).
% 2.52/2.76 tff(8529,plain,
% 2.52/2.76 (~r(s(s(elem!1)), s(z))),
% 2.52/2.76 inference(unit_resolution,[status(thm)],[8426, 8528, 8408, 97])).
% 2.52/2.76 tff(8530,plain,
% 2.52/2.76 (b(s(s(elem!1)), s(z))),
% 2.52/2.76 inference(unit_resolution,[status(thm)],[1912, 8529])).
% 2.52/2.76 tff(8531,plain,
% 2.52/2.76 (b(s(z), s(s(elem!1)))),
% 2.52/2.76 inference(unit_resolution,[status(thm)],[4556, 8530, 125])).
% 2.52/2.76 tff(8532,plain,
% 2.52/2.76 (~b(s(s(s(elem!1))), s(s(elem!1)))),
% 2.52/2.76 inference(unit_resolution,[status(thm)],[1858, 8530, 96, 8531])).
% 2.52/2.76 tff(8533,plain,
% 2.52/2.76 ((s(s(z)) = s(s(s(elem!1)))) <=> (s(s(elem!1)) = s(s(s(elem!1))))),
% 2.52/2.76 inference(monotonicity,[status(thm)],[8526])).
% 2.52/2.76 tff(8534,plain,
% 2.52/2.76 ((s(s(z)) = s(s(s(elem!1)))) <=> (s(s(s(elem!1))) = s(s(elem!1)))),
% 2.52/2.76 inference(transitivity,[status(thm)],[8533, 3341])).
% 2.52/2.76 tff(8535,plain,
% 2.52/2.76 ((~(s(s(z)) = s(s(s(elem!1))))) <=> (~(s(s(s(elem!1))) = s(s(elem!1))))),
% 2.52/2.76 inference(monotonicity,[status(thm)],[8534])).
% 2.52/2.76 tff(8536,plain,
% 2.52/2.76 (~(s(s(s(elem!1))) = s(s(elem!1)))),
% 2.52/2.76 inference(modus_ponens,[status(thm)],[209, 8535])).
% 2.52/2.76 tff(8537,plain,
% 2.52/2.76 (r(s(s(s(elem!1))), s(s(elem!1)))),
% 2.52/2.76 inference(unit_resolution,[status(thm)],[889, 8536, 8532])).
% 2.52/2.76 tff(8538,plain,
% 2.52/2.76 ((~(s(s(z)) = s(s(s(elem!1))))) <=> (~(s(s(elem!1)) = s(s(s(elem!1)))))),
% 2.52/2.76 inference(monotonicity,[status(thm)],[8533])).
% 2.52/2.76 tff(8539,plain,
% 2.52/2.76 (~(s(s(elem!1)) = s(s(s(elem!1))))),
% 2.52/2.76 inference(modus_ponens,[status(thm)],[209, 8538])).
% 2.52/2.76 tff(8540,plain,
% 2.52/2.76 (((~b(s(s(elem!1)), s(z))) | (~b(s(s(elem!1)), s(z))) | (~b(s(z), s(s(elem!1)))) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(s(elem!1)), s(z))) | (~b(s(s(elem!1)), s(s(s(elem!1)))))) <=> ((~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(s(z), s(s(elem!1)))) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(s(elem!1)), s(z))))),
% 2.52/2.76 inference(rewrite,[status(thm)],[])).
% 2.52/2.76 tff(8541,plain,
% 2.52/2.76 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), s(z))) | (~b(s(s(elem!1)), s(z))) | (~b(s(z), s(s(elem!1)))) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(s(elem!1)), s(z))) | (~b(s(s(elem!1)), s(s(s(elem!1))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(s(z), s(s(elem!1)))) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(s(elem!1)), s(z)))))),
% 2.52/2.76 inference(monotonicity,[status(thm)],[8540])).
% 2.52/2.76 tff(8542,plain,
% 2.52/2.76 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), s(z))) | (~b(s(s(elem!1)), s(z))) | (~b(s(z), s(s(elem!1)))) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(s(elem!1)), s(z))) | (~b(s(s(elem!1)), s(s(s(elem!1))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(s(z), s(s(elem!1)))) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(s(elem!1)), s(z))))),
% 2.52/2.76 inference(transitivity,[status(thm)],[8541, 1897])).
% 2.52/2.76 tff(8543,plain,
% 2.52/2.76 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), s(z))) | (~b(s(s(elem!1)), s(z))) | (~b(s(z), s(s(elem!1)))) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(s(elem!1)), s(z))) | (~b(s(s(elem!1)), s(s(s(elem!1))))))),
% 2.52/2.76 inference(quant_inst,[status(thm)],[])).
% 2.52/2.76 tff(8544,plain,
% 2.52/2.76 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(s(z), s(s(elem!1)))) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(s(elem!1)), s(z)))),
% 2.52/2.76 inference(modus_ponens,[status(thm)],[8543, 8542])).
% 2.52/2.76 tff(8545,plain,
% 2.52/2.76 (~b(s(s(elem!1)), s(s(s(elem!1))))),
% 2.52/2.76 inference(unit_resolution,[status(thm)],[8544, 166, 8531, 96, 8530])).
% 2.52/2.76 tff(8546,plain,
% 2.52/2.76 (r(s(s(elem!1)), s(s(s(elem!1))))),
% 2.52/2.76 inference(unit_resolution,[status(thm)],[461, 8545, 8539])).
% 2.52/2.76 tff(8547,plain,
% 2.52/2.76 ($false),
% 2.52/2.76 inference(unit_resolution,[status(thm)],[1386, 8546, 8537, 154, 8528])).
% 2.52/2.76 tff(8548,plain,((~r(s(z), z)) | (~r(s(s(s(elem!1))), z)) | (~b(s(s(s(elem!1))), s(z))) | b(z, s(s(z)))), inference(lemma,lemma(discharge,[]))).
% 2.52/2.76 tff(8549,plain,
% 2.52/2.76 (~r(s(z), z)),
% 2.52/2.76 inference(unit_resolution,[status(thm)],[8548, 154, 96, 125])).
% 2.52/2.76 tff(8550,plain,
% 2.52/2.76 (b(s(z), z)),
% 2.52/2.76 inference(unit_resolution,[status(thm)],[230, 8549])).
% 2.52/2.76 tff(8551,plain,
% 2.52/2.76 (~b(s(s(elem!1)), s(z))),
% 2.52/2.76 inference(unit_resolution,[status(thm)],[2253, 45, 152, 8408, 8550])).
% 2.52/2.76 tff(8552,plain,
% 2.52/2.76 (r(s(s(elem!1)), s(z))),
% 2.52/2.76 inference(unit_resolution,[status(thm)],[1912, 8551])).
% 2.52/2.76 tff(8553,plain,
% 2.52/2.76 (~b(s(s(s(elem!1))), s(s(z)))),
% 2.52/2.76 inference(unit_resolution,[status(thm)],[4251, 166, 556, 96, 156])).
% 2.52/2.76 tff(8554,plain,
% 2.52/2.76 (r(s(s(s(elem!1))), s(s(z)))),
% 2.52/2.76 inference(unit_resolution,[status(thm)],[218, 8553])).
% 2.52/2.76 tff(8555,plain,
% 2.52/2.76 (~b(s(s(z)), s(s(s(elem!1))))),
% 2.52/2.76 inference(unit_resolution,[status(thm)],[4503, 166, 556, 96, 156])).
% 2.52/2.76 tff(8556,plain,
% 2.52/2.76 (r(s(s(z)), s(s(s(elem!1))))),
% 2.52/2.76 inference(unit_resolution,[status(thm)],[279, 8555])).
% 2.52/2.76 tff(8557,plain,
% 2.52/2.76 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), z)) | (~r(s(s(z)), s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), s(s(z)))) | (~r(z, s(s(z)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(elem!1))), z)) | (~r(s(s(z)), s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), s(s(z)))) | (~r(z, s(s(z)))))),
% 2.52/2.76 inference(rewrite,[status(thm)],[])).
% 2.52/2.76 tff(8558,plain,
% 2.52/2.76 (((~r(s(s(z)), s(s(s(elem!1))))) | (~r(z, s(s(z)))) | (~r(s(s(s(elem!1))), s(s(z)))) | (~r(s(s(s(elem!1))), z))) <=> ((~r(s(s(s(elem!1))), z)) | (~r(s(s(z)), s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), s(s(z)))) | (~r(z, s(s(z)))))),
% 2.52/2.76 inference(rewrite,[status(thm)],[])).
% 2.52/2.76 tff(8559,plain,
% 2.52/2.76 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(z)), s(s(s(elem!1))))) | (~r(z, s(s(z)))) | (~r(s(s(s(elem!1))), s(s(z)))) | (~r(s(s(s(elem!1))), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), z)) | (~r(s(s(z)), s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), s(s(z)))) | (~r(z, s(s(z))))))),
% 2.52/2.76 inference(monotonicity,[status(thm)],[8558])).
% 2.52/2.76 tff(8560,plain,
% 2.52/2.76 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(z)), s(s(s(elem!1))))) | (~r(z, s(s(z)))) | (~r(s(s(s(elem!1))), s(s(z)))) | (~r(s(s(s(elem!1))), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(elem!1))), z)) | (~r(s(s(z)), s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), s(s(z)))) | (~r(z, s(s(z)))))),
% 2.52/2.76 inference(transitivity,[status(thm)],[8559, 8557])).
% 2.52/2.76 tff(8561,plain,
% 2.52/2.76 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(z)), s(s(s(elem!1))))) | (~r(z, s(s(z)))) | (~r(s(s(s(elem!1))), s(s(z)))) | (~r(s(s(s(elem!1))), z)))),
% 2.52/2.76 inference(quant_inst,[status(thm)],[])).
% 2.52/2.76 tff(8562,plain,
% 2.52/2.76 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(elem!1))), z)) | (~r(s(s(z)), s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), s(s(z)))) | (~r(z, s(s(z))))),
% 2.52/2.76 inference(modus_ponens,[status(thm)],[8561, 8560])).
% 2.52/2.76 tff(8563,plain,
% 2.52/2.76 ($false),
% 2.52/2.76 inference(unit_resolution,[status(thm)],[8562, 197, 154, 155, 8556, 8554])).
% 2.52/2.76 tff(8564,plain,((~b(s(z), s(s(z)))) | (~r(s(s(s(elem!1))), z)) | (~r(z, s(s(z)))) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(s(z)), s(z)))), inference(lemma,lemma(discharge,[]))).
% 2.52/2.76 tff(8565,plain,
% 2.52/2.76 (~b(s(z), s(s(z)))),
% 2.52/2.76 inference(unit_resolution,[status(thm)],[8564, 156, 155, 96, 154])).
% 2.52/2.76 tff(8566,plain,
% 2.52/2.76 (r(s(z), s(s(z)))),
% 2.52/2.76 inference(unit_resolution,[status(thm)],[427, 8565])).
% 2.52/2.76 tff(8567,plain,
% 2.52/2.76 (~r(s(s(z)), s(s(s(elem!1))))),
% 2.52/2.76 inference(unit_resolution,[status(thm)],[331, 8566, 155, 323])).
% 2.52/2.76 tff(8568,plain,
% 2.52/2.76 (b(s(s(z)), s(s(s(elem!1))))),
% 2.52/2.76 inference(unit_resolution,[status(thm)],[279, 8567])).
% 2.52/2.76 tff(8569,plain,
% 2.52/2.76 (~b(s(z), s(s(s(elem!1))))),
% 2.52/2.76 inference(unit_resolution,[status(thm)],[271, 8568, 96, 156])).
% 2.52/2.76 tff(8570,plain,
% 2.52/2.76 (r(s(z), s(s(s(elem!1))))),
% 2.52/2.76 inference(unit_resolution,[status(thm)],[116, 8569])).
% 2.52/2.76 tff(8571,plain,
% 2.52/2.76 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(s(elem!1)))) | (~r(z, s(z))) | (~r(s(s(z)), s(z))) | (~r(z, s(s(z)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(z), s(s(elem!1)))) | (~r(z, s(z))) | (~r(s(s(z)), s(z))) | (~r(z, s(s(z)))))),
% 2.52/2.76 inference(rewrite,[status(thm)],[])).
% 2.52/2.76 tff(8572,plain,
% 2.52/2.76 (((~r(s(z), s(s(elem!1)))) | (~r(s(s(z)), s(z))) | (~r(z, s(z))) | (~r(z, s(s(z))))) <=> ((~r(s(z), s(s(elem!1)))) | (~r(z, s(z))) | (~r(s(s(z)), s(z))) | (~r(z, s(s(z)))))),
% 2.52/2.76 inference(rewrite,[status(thm)],[])).
% 2.52/2.76 tff(8573,plain,
% 2.52/2.76 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(s(elem!1)))) | (~r(s(s(z)), s(z))) | (~r(z, s(z))) | (~r(z, s(s(z)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(s(elem!1)))) | (~r(z, s(z))) | (~r(s(s(z)), s(z))) | (~r(z, s(s(z))))))),
% 2.52/2.76 inference(monotonicity,[status(thm)],[8572])).
% 2.52/2.76 tff(8574,plain,
% 2.52/2.76 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(s(elem!1)))) | (~r(s(s(z)), s(z))) | (~r(z, s(z))) | (~r(z, s(s(z)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(z), s(s(elem!1)))) | (~r(z, s(z))) | (~r(s(s(z)), s(z))) | (~r(z, s(s(z)))))),
% 2.52/2.76 inference(transitivity,[status(thm)],[8573, 8571])).
% 2.52/2.76 tff(8575,plain,
% 2.52/2.76 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(s(elem!1)))) | (~r(s(s(z)), s(z))) | (~r(z, s(z))) | (~r(z, s(s(z)))))),
% 2.52/2.76 inference(quant_inst,[status(thm)],[])).
% 2.52/2.76 tff(8576,plain,
% 2.52/2.76 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(z), s(s(elem!1)))) | (~r(z, s(z))) | (~r(s(s(z)), s(z))) | (~r(z, s(s(z))))),
% 2.52/2.76 inference(modus_ponens,[status(thm)],[8575, 8574])).
% 2.52/2.76 tff(8577,plain,
% 2.52/2.76 ($false),
% 2.52/2.76 inference(unit_resolution,[status(thm)],[8576, 197, 311, 155, 323, 392])).
% 2.52/2.76 tff(8578,plain,((~r(s(s(z)), s(z))) | (~r(s(z), s(s(elem!1)))) | (~r(z, s(s(z)))) | (~r(z, s(z)))), inference(lemma,lemma(discharge,[]))).
% 2.52/2.76 tff(8579,plain,
% 2.52/2.76 (~r(s(s(z)), s(z))),
% 2.52/2.76 inference(unit_resolution,[status(thm)],[8578, 311, 155, 323])).
% 2.52/2.76 tff(8580,plain,
% 2.52/2.76 (b(s(s(z)), s(z))),
% 2.52/2.76 inference(unit_resolution,[status(thm)],[308, 8579])).
% 2.52/2.76 tff(8581,plain,
% 2.52/2.76 (~r(s(s(z)), z)),
% 2.52/2.76 inference(unit_resolution,[status(thm)],[8414, 8580, 96, 155, 154, 323])).
% 2.52/2.76 tff(8582,plain,
% 2.52/2.76 (b(s(s(z)), z)),
% 2.52/2.76 inference(unit_resolution,[status(thm)],[186, 8581])).
% 2.52/2.76 tff(8583,plain,
% 2.52/2.76 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(s(elem!1)))) | (~r(z, s(z))) | (~r(s(s(elem!1)), z)) | (~r(s(s(elem!1)), s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(z), s(s(elem!1)))) | (~r(z, s(z))) | (~r(s(s(elem!1)), z)) | (~r(s(s(elem!1)), s(z))))),
% 2.52/2.76 inference(rewrite,[status(thm)],[])).
% 2.52/2.76 tff(8584,plain,
% 2.52/2.76 (((~r(s(z), s(s(elem!1)))) | (~r(z, s(z))) | (~r(s(s(elem!1)), s(z))) | (~r(s(s(elem!1)), z))) <=> ((~r(s(z), s(s(elem!1)))) | (~r(z, s(z))) | (~r(s(s(elem!1)), z)) | (~r(s(s(elem!1)), s(z))))),
% 2.52/2.76 inference(rewrite,[status(thm)],[])).
% 2.52/2.76 tff(8585,plain,
% 2.52/2.76 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(s(elem!1)))) | (~r(z, s(z))) | (~r(s(s(elem!1)), s(z))) | (~r(s(s(elem!1)), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(s(elem!1)))) | (~r(z, s(z))) | (~r(s(s(elem!1)), z)) | (~r(s(s(elem!1)), s(z)))))),
% 2.52/2.76 inference(monotonicity,[status(thm)],[8584])).
% 2.52/2.76 tff(8586,plain,
% 2.52/2.76 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(s(elem!1)))) | (~r(z, s(z))) | (~r(s(s(elem!1)), s(z))) | (~r(s(s(elem!1)), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(z), s(s(elem!1)))) | (~r(z, s(z))) | (~r(s(s(elem!1)), z)) | (~r(s(s(elem!1)), s(z))))),
% 2.52/2.76 inference(transitivity,[status(thm)],[8585, 8583])).
% 2.52/2.76 tff(8587,plain,
% 2.52/2.76 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(s(elem!1)))) | (~r(z, s(z))) | (~r(s(s(elem!1)), s(z))) | (~r(s(s(elem!1)), z)))),
% 2.52/2.76 inference(quant_inst,[status(thm)],[])).
% 2.52/2.76 tff(8588,plain,
% 2.52/2.76 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(z), s(s(elem!1)))) | (~r(z, s(z))) | (~r(s(s(elem!1)), z)) | (~r(s(s(elem!1)), s(z)))),
% 2.52/2.76 inference(modus_ponens,[status(thm)],[8587, 8586])).
% 2.52/2.76 tff(8589,plain,
% 2.52/2.76 ($false),
% 2.52/2.76 inference(unit_resolution,[status(thm)],[8588, 197, 311, 323, 4577, 1970])).
% 2.52/2.76 tff(8590,plain,((~r(s(s(elem!1)), s(z))) | (~r(s(z), s(s(elem!1)))) | (~r(z, s(z))) | (~r(s(s(elem!1)), z))), inference(lemma,lemma(discharge,[]))).
% 2.52/2.76 tff(8591,plain,
% 2.52/2.76 (~r(s(s(elem!1)), z)),
% 2.52/2.76 inference(unit_resolution,[status(thm)],[8590, 311, 323, 4577])).
% 2.52/2.76 tff(8592,plain,
% 2.52/2.76 (b(s(s(elem!1)), z)),
% 2.52/2.76 inference(unit_resolution,[status(thm)],[608, 8591])).
% 2.52/2.76 tff(8593,plain,
% 2.52/2.76 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(s(elem!1)))) | (~r(z, s(s(elem!1)))) | (~r(z, s(z))) | (~r(s(s(elem!1)), s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(z), s(s(elem!1)))) | (~r(z, s(s(elem!1)))) | (~r(z, s(z))) | (~r(s(s(elem!1)), s(z))))),
% 2.52/2.76 inference(rewrite,[status(thm)],[])).
% 2.52/2.76 tff(8594,plain,
% 2.52/2.76 (((~r(s(z), s(s(elem!1)))) | (~r(s(s(elem!1)), s(z))) | (~r(z, s(z))) | (~r(z, s(s(elem!1))))) <=> ((~r(s(z), s(s(elem!1)))) | (~r(z, s(s(elem!1)))) | (~r(z, s(z))) | (~r(s(s(elem!1)), s(z))))),
% 2.52/2.76 inference(rewrite,[status(thm)],[])).
% 2.52/2.76 tff(8595,plain,
% 2.52/2.76 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(s(elem!1)))) | (~r(s(s(elem!1)), s(z))) | (~r(z, s(z))) | (~r(z, s(s(elem!1)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(s(elem!1)))) | (~r(z, s(s(elem!1)))) | (~r(z, s(z))) | (~r(s(s(elem!1)), s(z)))))),
% 2.52/2.76 inference(monotonicity,[status(thm)],[8594])).
% 2.52/2.76 tff(8596,plain,
% 2.52/2.76 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(s(elem!1)))) | (~r(s(s(elem!1)), s(z))) | (~r(z, s(z))) | (~r(z, s(s(elem!1)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(z), s(s(elem!1)))) | (~r(z, s(s(elem!1)))) | (~r(z, s(z))) | (~r(s(s(elem!1)), s(z))))),
% 2.52/2.76 inference(transitivity,[status(thm)],[8595, 8593])).
% 2.52/2.76 tff(8597,plain,
% 2.52/2.76 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(s(elem!1)))) | (~r(s(s(elem!1)), s(z))) | (~r(z, s(z))) | (~r(z, s(s(elem!1)))))),
% 2.52/2.76 inference(quant_inst,[status(thm)],[])).
% 2.52/2.76 tff(8598,plain,
% 2.52/2.76 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(z), s(s(elem!1)))) | (~r(z, s(s(elem!1)))) | (~r(z, s(z))) | (~r(s(s(elem!1)), s(z)))),
% 2.52/2.76 inference(modus_ponens,[status(thm)],[8597, 8596])).
% 2.52/2.76 tff(8599,plain,
% 2.52/2.76 ($false),
% 2.52/2.76 inference(unit_resolution,[status(thm)],[8598, 197, 311, 323, 4577, 365])).
% 2.52/2.76 tff(8600,plain,((~r(s(s(elem!1)), s(z))) | (~r(s(z), s(s(elem!1)))) | (~r(z, s(z))) | (~r(z, s(s(elem!1))))), inference(lemma,lemma(discharge,[]))).
% 2.52/2.76 tff(8601,plain,
% 2.52/2.76 (~r(z, s(s(elem!1)))),
% 2.52/2.76 inference(unit_resolution,[status(thm)],[8600, 311, 323, 4577])).
% 2.52/2.76 tff(8602,plain,
% 2.52/2.76 (b(z, s(s(elem!1)))),
% 2.52/2.76 inference(unit_resolution,[status(thm)],[1795, 8601])).
% 2.52/2.76 tff(8603,plain,
% 2.52/2.76 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(elem!1)))) | (~b(s(z), z)) | (~b(s(s(elem!1)), z)) | (~b(s(s(z)), z)) | (~b(s(s(z)), s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(s(elem!1)))) | (~b(s(z), z)) | (~b(s(s(elem!1)), z)) | (~b(s(s(z)), z)) | (~b(s(s(z)), s(z))))),
% 2.52/2.76 inference(rewrite,[status(thm)],[])).
% 2.52/2.76 tff(8604,plain,
% 2.52/2.76 (((~b(s(s(elem!1)), z)) | (~b(s(s(z)), z)) | (~b(z, s(s(elem!1)))) | (~b(s(z), z)) | (~b(s(s(z)), z)) | (~b(s(s(z)), s(z)))) <=> ((~b(z, s(s(elem!1)))) | (~b(s(z), z)) | (~b(s(s(elem!1)), z)) | (~b(s(s(z)), z)) | (~b(s(s(z)), s(z))))),
% 2.52/2.77 inference(rewrite,[status(thm)],[])).
% 2.52/2.77 tff(8605,plain,
% 2.52/2.77 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), z)) | (~b(s(s(z)), z)) | (~b(z, s(s(elem!1)))) | (~b(s(z), z)) | (~b(s(s(z)), z)) | (~b(s(s(z)), s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(elem!1)))) | (~b(s(z), z)) | (~b(s(s(elem!1)), z)) | (~b(s(s(z)), z)) | (~b(s(s(z)), s(z)))))),
% 2.52/2.77 inference(monotonicity,[status(thm)],[8604])).
% 2.52/2.77 tff(8606,plain,
% 2.52/2.77 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), z)) | (~b(s(s(z)), z)) | (~b(z, s(s(elem!1)))) | (~b(s(z), z)) | (~b(s(s(z)), z)) | (~b(s(s(z)), s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(s(elem!1)))) | (~b(s(z), z)) | (~b(s(s(elem!1)), z)) | (~b(s(s(z)), z)) | (~b(s(s(z)), s(z))))),
% 2.52/2.77 inference(transitivity,[status(thm)],[8605, 8603])).
% 2.52/2.77 tff(8607,plain,
% 2.52/2.77 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), z)) | (~b(s(s(z)), z)) | (~b(z, s(s(elem!1)))) | (~b(s(z), z)) | (~b(s(s(z)), z)) | (~b(s(s(z)), s(z))))),
% 2.52/2.77 inference(quant_inst,[status(thm)],[])).
% 2.52/2.77 tff(8608,plain,
% 2.52/2.77 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(s(elem!1)))) | (~b(s(z), z)) | (~b(s(s(elem!1)), z)) | (~b(s(s(z)), z)) | (~b(s(s(z)), s(z)))),
% 2.52/2.77 inference(modus_ponens,[status(thm)],[8607, 8606])).
% 2.52/2.77 tff(8609,plain,
% 2.52/2.77 ($false),
% 2.52/2.77 inference(unit_resolution,[status(thm)],[8608, 166, 8602, 53, 8592, 8580, 8582])).
% 2.52/2.77 tff(8610,plain,((~r(s(z), s(s(elem!1)))) | (~b(s(z), z)) | (~b(s(s(s(elem!1))), s(z))) | (~r(z, s(s(z)))) | (~r(s(s(s(elem!1))), z)) | (~r(z, s(z))) | (~r(s(s(elem!1)), s(z)))), inference(lemma,lemma(discharge,[]))).
% 2.52/2.77 tff(8611,plain,
% 2.52/2.77 (~r(s(z), s(s(elem!1)))),
% 2.52/2.77 inference(unit_resolution,[status(thm)],[8610, 4577, 96, 155, 154, 323, 53])).
% 2.52/2.77 tff(8612,plain,
% 2.52/2.77 (b(s(z), s(s(elem!1)))),
% 2.52/2.77 inference(unit_resolution,[status(thm)],[84, 8611])).
% 2.52/2.77 tff(8613,plain,
% 2.52/2.77 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(z))) | (~r(s(s(elem!1)), z)) | (~r(s(s(elem!1)), s(z))) | (~r(s(z), s(s(z)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, s(z))) | (~r(s(s(elem!1)), z)) | (~r(s(s(elem!1)), s(z))) | (~r(s(z), s(s(z)))))),
% 2.52/2.77 inference(rewrite,[status(thm)],[])).
% 2.52/2.77 tff(8614,plain,
% 2.52/2.77 (((~r(s(z), s(s(z)))) | (~r(z, s(z))) | (~r(s(s(elem!1)), s(z))) | (~r(s(s(elem!1)), z))) <=> ((~r(z, s(z))) | (~r(s(s(elem!1)), z)) | (~r(s(s(elem!1)), s(z))) | (~r(s(z), s(s(z)))))),
% 2.52/2.77 inference(rewrite,[status(thm)],[])).
% 2.52/2.77 tff(8615,plain,
% 2.52/2.77 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(s(z)))) | (~r(z, s(z))) | (~r(s(s(elem!1)), s(z))) | (~r(s(s(elem!1)), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(z))) | (~r(s(s(elem!1)), z)) | (~r(s(s(elem!1)), s(z))) | (~r(s(z), s(s(z))))))),
% 2.52/2.77 inference(monotonicity,[status(thm)],[8614])).
% 2.52/2.77 tff(8616,plain,
% 2.52/2.77 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(s(z)))) | (~r(z, s(z))) | (~r(s(s(elem!1)), s(z))) | (~r(s(s(elem!1)), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, s(z))) | (~r(s(s(elem!1)), z)) | (~r(s(s(elem!1)), s(z))) | (~r(s(z), s(s(z)))))),
% 2.52/2.77 inference(transitivity,[status(thm)],[8615, 8613])).
% 2.52/2.77 tff(8617,plain,
% 2.52/2.77 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(s(z)))) | (~r(z, s(z))) | (~r(s(s(elem!1)), s(z))) | (~r(s(s(elem!1)), z)))),
% 2.52/2.77 inference(quant_inst,[status(thm)],[])).
% 2.52/2.77 tff(8618,plain,
% 2.52/2.77 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, s(z))) | (~r(s(s(elem!1)), z)) | (~r(s(s(elem!1)), s(z))) | (~r(s(z), s(s(z))))),
% 2.52/2.77 inference(modus_ponens,[status(thm)],[8617, 8616])).
% 2.52/2.77 tff(8619,plain,
% 2.52/2.77 ($false),
% 2.52/2.77 inference(unit_resolution,[status(thm)],[8618, 197, 120, 323, 4577, 1970])).
% 2.52/2.77 tff(8620,plain,((~r(s(z), s(s(z)))) | (~r(z, s(z))) | (~r(s(s(elem!1)), s(z))) | (~r(s(s(elem!1)), z))), inference(lemma,lemma(discharge,[]))).
% 2.52/2.77 tff(8621,plain,
% 2.52/2.77 (~r(s(s(elem!1)), z)),
% 2.52/2.77 inference(unit_resolution,[status(thm)],[8620, 8566, 4577, 323])).
% 2.52/2.77 tff(8622,plain,
% 2.52/2.77 (b(s(s(elem!1)), z)),
% 2.52/2.77 inference(unit_resolution,[status(thm)],[608, 8621])).
% 2.52/2.77 tff(8623,plain,
% 2.52/2.77 (~b(z, s(s(elem!1)))),
% 2.52/2.77 inference(unit_resolution,[status(thm)],[5377, 8622, 53, 8612])).
% 2.52/2.77 tff(8624,plain,
% 2.52/2.77 (r(z, s(s(elem!1)))),
% 2.52/2.77 inference(unit_resolution,[status(thm)],[1795, 8623])).
% 2.52/2.77 tff(8625,plain,
% 2.52/2.77 ($false),
% 2.52/2.77 inference(unit_resolution,[status(thm)],[1935, 197, 323, 4577, 365, 119])).
% 2.52/2.77 tff(8626,plain,((~r(z, s(z))) | (~r(s(s(elem!1)), s(z))) | (~r(z, s(s(elem!1)))) | (~r(s(z), s(s(s(elem!1)))))), inference(lemma,lemma(discharge,[]))).
% 2.52/2.77 tff(8627,plain,
% 2.52/2.77 ($false),
% 2.52/2.77 inference(unit_resolution,[status(thm)],[8626, 8624, 8570, 323, 4577])).
% 2.52/2.77 tff(8628,plain,((~b(s(s(z)), s(z))) | (~r(z, s(z))) | (~r(s(s(elem!1)), s(z))) | (~b(s(z), z)) | (~b(s(s(s(elem!1))), s(z))) | (~r(z, s(s(z)))) | (~r(s(s(s(elem!1))), z))), inference(lemma,lemma(discharge,[]))).
% 2.52/2.77 tff(8629,plain,
% 2.52/2.77 (~b(s(s(z)), s(z))),
% 2.52/2.77 inference(unit_resolution,[status(thm)],[8628, 8552, 8408, 8550, 96, 152, 154])).
% 2.52/2.77 tff(8630,plain,
% 2.52/2.77 (r(s(s(z)), s(z))),
% 2.52/2.77 inference(unit_resolution,[status(thm)],[308, 8629])).
% 2.52/2.77 tff(8631,plain,
% 2.52/2.77 (~r(s(z), s(s(z)))),
% 2.52/2.77 inference(unit_resolution,[status(thm)],[553, 392, 155, 323])).
% 2.52/2.77 tff(8632,plain,
% 2.52/2.77 (b(s(z), s(s(z)))),
% 2.52/2.77 inference(unit_resolution,[status(thm)],[427, 8631])).
% 2.52/2.77 tff(8633,plain,
% 2.52/2.77 (~r(s(s(z)), s(s(elem!1)))),
% 2.52/2.77 inference(unit_resolution,[status(thm)],[5997, 365, 155, 4577])).
% 2.52/2.77 tff(8634,plain,
% 2.52/2.77 (~r(s(s(elem!1)), s(s(z)))),
% 2.52/2.77 inference(unit_resolution,[status(thm)],[401, 365, 155, 392])).
% 2.52/2.77 tff(8635,plain,
% 2.52/2.77 ($false),
% 2.52/2.77 inference(unit_resolution,[status(thm)],[5300, 8634, 8633, 376, 52, 556])).
% 2.52/2.77 tff(8636,plain,((~r(z, s(s(elem!1)))) | (~b(s(z), s(s(elem!1)))) | (s(s(z)) = s(s(elem!1))) | (~b(s(z), s(s(z)))) | (~r(z, s(s(z)))) | (~r(s(s(z)), s(z))) | (~r(s(s(elem!1)), s(z)))), inference(lemma,lemma(discharge,[]))).
% 2.52/2.77 tff(8637,plain,
% 2.52/2.77 (~r(z, s(s(elem!1)))),
% 2.52/2.77 inference(unit_resolution,[status(thm)],[8636, 8632, 52, 8612, 155, 392, 4577])).
% 2.52/2.77 tff(8638,plain,
% 2.52/2.77 (b(z, s(s(elem!1)))),
% 2.52/2.77 inference(unit_resolution,[status(thm)],[1795, 8637])).
% 2.52/2.77 tff(8639,plain,
% 2.52/2.77 (~b(s(s(elem!1)), z)),
% 2.52/2.77 inference(unit_resolution,[status(thm)],[5377, 8638, 53, 8612])).
% 2.52/2.77 tff(8640,plain,
% 2.52/2.77 (r(s(s(elem!1)), z)),
% 2.52/2.77 inference(unit_resolution,[status(thm)],[608, 8639])).
% 2.52/2.77 tff(8641,plain,
% 2.52/2.77 ($false),
% 2.52/2.77 inference(unit_resolution,[status(thm)],[6100, 197, 393, 155, 392, 1970])).
% 2.52/2.77 tff(8642,plain,((~r(s(s(elem!1)), s(s(z)))) | (~r(z, s(s(z)))) | (~r(s(s(z)), s(z))) | (~r(s(s(elem!1)), z))), inference(lemma,lemma(discharge,[]))).
% 2.52/2.77 tff(8643,plain,
% 2.52/2.77 (~r(s(s(elem!1)), s(s(z)))),
% 2.52/2.77 inference(unit_resolution,[status(thm)],[8642, 392, 155, 8640])).
% 2.52/2.77 tff(8644,plain,
% 2.52/2.77 (r(s(s(z)), s(s(elem!1)))),
% 2.52/2.77 inference(unit_resolution,[status(thm)],[5300, 8643, 8612, 52, 8632])).
% 2.52/2.77 tff(8645,plain,
% 2.52/2.77 (~r(s(z), s(s(s(elem!1))))),
% 2.52/2.77 inference(unit_resolution,[status(thm)],[6892, 8644, 4577, 392])).
% 2.52/2.77 tff(8646,plain,
% 2.52/2.77 (b(s(z), s(s(s(elem!1))))),
% 2.52/2.77 inference(unit_resolution,[status(thm)],[116, 8645])).
% 2.52/2.77 tff(8647,plain,
% 2.52/2.77 (b(s(s(elem!1)), s(s(z)))),
% 2.52/2.77 inference(unit_resolution,[status(thm)],[441, 8643, 132])).
% 2.52/2.77 tff(8648,plain,
% 2.52/2.77 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(z)), s(s(elem!1)))) | (~r(s(s(z)), s(z))) | (~r(s(s(elem!1)), s(z))) | (~r(s(z), s(s(s(z))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(z)), s(s(elem!1)))) | (~r(s(s(z)), s(z))) | (~r(s(s(elem!1)), s(z))) | (~r(s(z), s(s(s(z))))))),
% 2.52/2.77 inference(rewrite,[status(thm)],[])).
% 2.52/2.77 tff(8649,plain,
% 2.52/2.77 (((~r(s(z), s(s(s(z))))) | (~r(s(s(elem!1)), s(z))) | (~r(s(s(z)), s(z))) | (~r(s(s(z)), s(s(elem!1))))) <=> ((~r(s(s(z)), s(s(elem!1)))) | (~r(s(s(z)), s(z))) | (~r(s(s(elem!1)), s(z))) | (~r(s(z), s(s(s(z))))))),
% 2.52/2.77 inference(rewrite,[status(thm)],[])).
% 2.52/2.77 tff(8650,plain,
% 2.52/2.77 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(s(s(z))))) | (~r(s(s(elem!1)), s(z))) | (~r(s(s(z)), s(z))) | (~r(s(s(z)), s(s(elem!1)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(z)), s(s(elem!1)))) | (~r(s(s(z)), s(z))) | (~r(s(s(elem!1)), s(z))) | (~r(s(z), s(s(s(z)))))))),
% 2.52/2.77 inference(monotonicity,[status(thm)],[8649])).
% 2.52/2.77 tff(8651,plain,
% 2.52/2.77 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(s(s(z))))) | (~r(s(s(elem!1)), s(z))) | (~r(s(s(z)), s(z))) | (~r(s(s(z)), s(s(elem!1)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(z)), s(s(elem!1)))) | (~r(s(s(z)), s(z))) | (~r(s(s(elem!1)), s(z))) | (~r(s(z), s(s(s(z))))))),
% 2.52/2.77 inference(transitivity,[status(thm)],[8650, 8648])).
% 2.52/2.77 tff(8652,plain,
% 2.52/2.77 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(s(s(z))))) | (~r(s(s(elem!1)), s(z))) | (~r(s(s(z)), s(z))) | (~r(s(s(z)), s(s(elem!1)))))),
% 2.52/2.77 inference(quant_inst,[status(thm)],[])).
% 2.52/2.77 tff(8653,plain,
% 2.52/2.77 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(z)), s(s(elem!1)))) | (~r(s(s(z)), s(z))) | (~r(s(s(elem!1)), s(z))) | (~r(s(z), s(s(s(z)))))),
% 2.52/2.77 inference(modus_ponens,[status(thm)],[8652, 8651])).
% 2.52/2.77 tff(8654,plain,
% 2.52/2.77 ($false),
% 2.52/2.77 inference(unit_resolution,[status(thm)],[8653, 197, 4577, 333, 392, 1653])).
% 2.52/2.77 tff(8655,plain,((~r(s(z), s(s(s(z))))) | (~r(s(s(elem!1)), s(z))) | (~r(s(s(z)), s(s(elem!1)))) | (~r(s(s(z)), s(z)))), inference(lemma,lemma(discharge,[]))).
% 2.52/2.77 tff(8656,plain,
% 2.52/2.77 (~r(s(z), s(s(s(z))))),
% 2.52/2.77 inference(unit_resolution,[status(thm)],[8655, 8644, 4577, 392])).
% 2.52/2.77 tff(8657,plain,
% 2.52/2.77 (b(s(z), s(s(s(z))))),
% 2.52/2.77 inference(unit_resolution,[status(thm)],[1674, 8656])).
% 2.52/2.77 tff(8658,plain,
% 2.52/2.77 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(z), s(s(z)))) | (~b(s(s(z)), s(s(s(elem!1))))) | (~b(s(z), s(s(s(z))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(z), s(s(z)))) | (~b(s(s(z)), s(s(s(elem!1))))) | (~b(s(z), s(s(s(z))))))),
% 2.52/2.77 inference(rewrite,[status(thm)],[])).
% 2.52/2.77 tff(8659,plain,
% 2.52/2.77 (((~b(s(z), s(s(s(z))))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(s(z)), s(s(s(elem!1))))) | (~b(s(z), s(s(s(elem!1))))) | (~b(s(z), s(s(z))))) <=> ((~b(s(z), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(z), s(s(z)))) | (~b(s(s(z)), s(s(s(elem!1))))) | (~b(s(z), s(s(s(z))))))),
% 2.52/2.77 inference(rewrite,[status(thm)],[])).
% 2.52/2.77 tff(8660,plain,
% 2.52/2.77 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(s(z))))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(s(z)), s(s(s(elem!1))))) | (~b(s(z), s(s(s(elem!1))))) | (~b(s(z), s(s(z)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(z), s(s(z)))) | (~b(s(s(z)), s(s(s(elem!1))))) | (~b(s(z), s(s(s(z)))))))),
% 2.52/2.77 inference(monotonicity,[status(thm)],[8659])).
% 2.52/2.77 tff(8661,plain,
% 2.52/2.77 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(s(z))))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(s(z)), s(s(s(elem!1))))) | (~b(s(z), s(s(s(elem!1))))) | (~b(s(z), s(s(z)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(z), s(s(z)))) | (~b(s(s(z)), s(s(s(elem!1))))) | (~b(s(z), s(s(s(z))))))),
% 2.52/2.77 inference(transitivity,[status(thm)],[8660, 8658])).
% 2.52/2.77 tff(8662,plain,
% 2.52/2.77 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(s(z))))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(s(z)), s(s(s(elem!1))))) | (~b(s(z), s(s(s(elem!1))))) | (~b(s(z), s(s(z)))))),
% 2.52/2.77 inference(quant_inst,[status(thm)],[])).
% 2.52/2.77 tff(8663,plain,
% 2.52/2.77 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(z), s(s(z)))) | (~b(s(s(z)), s(s(s(elem!1))))) | (~b(s(z), s(s(s(z)))))),
% 2.52/2.77 inference(modus_ponens,[status(thm)],[8662, 8661])).
% 2.52/2.77 tff(8664,plain,
% 2.52/2.77 ($false),
% 2.52/2.77 inference(unit_resolution,[status(thm)],[8663, 166, 241, 556, 96, 263, 988])).
% 2.52/2.77 tff(8665,plain,((~b(s(s(z)), s(s(s(elem!1))))) | (~b(s(z), s(s(s(elem!1))))) | (~b(s(z), s(s(z)))) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(z), s(s(s(z)))))), inference(lemma,lemma(discharge,[]))).
% 2.52/2.77 tff(8666,plain,
% 2.52/2.77 (~b(s(s(z)), s(s(s(elem!1))))),
% 2.52/2.77 inference(unit_resolution,[status(thm)],[8665, 8657, 96, 8632, 8646])).
% 2.52/2.77 tff(8667,plain,
% 2.52/2.77 (r(s(s(z)), s(s(s(elem!1))))),
% 2.52/2.77 inference(unit_resolution,[status(thm)],[279, 8666])).
% 2.52/2.77 tff(8668,plain,
% 2.52/2.77 (~r(z, s(s(s(elem!1))))),
% 2.52/2.77 inference(unit_resolution,[status(thm)],[290, 8667, 155, 154])).
% 2.52/2.77 tff(8669,plain,
% 2.52/2.77 (b(z, s(s(s(elem!1))))),
% 2.52/2.77 inference(unit_resolution,[status(thm)],[261, 8668])).
% 2.52/2.77 tff(8670,plain,
% 2.52/2.77 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), s(s(elem!1)))) | (~r(s(s(z)), s(s(elem!1)))) | (~r(s(s(elem!1)), s(z))) | (~r(s(s(z)), s(s(s(elem!1))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(elem!1))), s(s(elem!1)))) | (~r(s(s(z)), s(s(elem!1)))) | (~r(s(s(elem!1)), s(z))) | (~r(s(s(z)), s(s(s(elem!1))))))),
% 2.52/2.77 inference(rewrite,[status(thm)],[])).
% 2.52/2.77 tff(8671,plain,
% 2.52/2.77 (((~r(s(s(elem!1)), s(z))) | (~r(s(s(s(elem!1))), s(s(elem!1)))) | (~r(s(s(z)), s(s(elem!1)))) | (~r(s(s(z)), s(s(s(elem!1)))))) <=> ((~r(s(s(s(elem!1))), s(s(elem!1)))) | (~r(s(s(z)), s(s(elem!1)))) | (~r(s(s(elem!1)), s(z))) | (~r(s(s(z)), s(s(s(elem!1))))))),
% 2.52/2.77 inference(rewrite,[status(thm)],[])).
% 2.52/2.77 tff(8672,plain,
% 2.52/2.77 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(elem!1)), s(z))) | (~r(s(s(s(elem!1))), s(s(elem!1)))) | (~r(s(s(z)), s(s(elem!1)))) | (~r(s(s(z)), s(s(s(elem!1))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), s(s(elem!1)))) | (~r(s(s(z)), s(s(elem!1)))) | (~r(s(s(elem!1)), s(z))) | (~r(s(s(z)), s(s(s(elem!1)))))))),
% 2.52/2.77 inference(monotonicity,[status(thm)],[8671])).
% 2.52/2.77 tff(8673,plain,
% 2.52/2.77 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(elem!1)), s(z))) | (~r(s(s(s(elem!1))), s(s(elem!1)))) | (~r(s(s(z)), s(s(elem!1)))) | (~r(s(s(z)), s(s(s(elem!1))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(elem!1))), s(s(elem!1)))) | (~r(s(s(z)), s(s(elem!1)))) | (~r(s(s(elem!1)), s(z))) | (~r(s(s(z)), s(s(s(elem!1))))))),
% 2.52/2.77 inference(transitivity,[status(thm)],[8672, 8670])).
% 2.52/2.77 tff(8674,plain,
% 2.52/2.77 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(elem!1)), s(z))) | (~r(s(s(s(elem!1))), s(s(elem!1)))) | (~r(s(s(z)), s(s(elem!1)))) | (~r(s(s(z)), s(s(s(elem!1))))))),
% 2.52/2.77 inference(quant_inst,[status(thm)],[])).
% 2.52/2.77 tff(8675,plain,
% 2.52/2.77 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(elem!1))), s(s(elem!1)))) | (~r(s(s(z)), s(s(elem!1)))) | (~r(s(s(elem!1)), s(z))) | (~r(s(s(z)), s(s(s(elem!1)))))),
% 2.52/2.77 inference(modus_ponens,[status(thm)],[8674, 8673])).
% 2.52/2.77 tff(8676,plain,
% 2.52/2.77 ($false),
% 2.52/2.77 inference(unit_resolution,[status(thm)],[8675, 197, 4577, 333, 905, 281])).
% 2.52/2.77 tff(8677,plain,((~r(s(s(s(elem!1))), s(s(elem!1)))) | (~r(s(s(elem!1)), s(z))) | (~r(s(s(z)), s(s(elem!1)))) | (~r(s(s(z)), s(s(s(elem!1)))))), inference(lemma,lemma(discharge,[]))).
% 2.52/2.77 tff(8678,plain,
% 2.52/2.77 (~r(s(s(s(elem!1))), s(s(elem!1)))),
% 2.52/2.77 inference(unit_resolution,[status(thm)],[8677, 8667, 4577, 8644])).
% 2.52/2.77 tff(8679,plain,
% 2.52/2.77 (b(s(s(s(elem!1))), s(s(elem!1)))),
% 2.52/2.77 inference(unit_resolution,[status(thm)],[889, 8678, 1863])).
% 2.52/2.77 tff(8680,plain,
% 2.52/2.77 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(z, s(s(s(elem!1))))) | (~b(s(z), z)) | (~b(s(z), s(s(s(elem!1))))) | (~b(s(s(elem!1)), s(s(z)))) | (~b(s(z), s(s(z)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(z, s(s(s(elem!1))))) | (~b(s(z), z)) | (~b(s(z), s(s(s(elem!1))))) | (~b(s(s(elem!1)), s(s(z)))) | (~b(s(z), s(s(z)))))),
% 2.52/2.78 inference(rewrite,[status(thm)],[])).
% 2.52/2.78 tff(8681,plain,
% 2.52/2.78 (((~b(s(s(elem!1)), s(s(z)))) | (~b(s(z), s(s(z)))) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(z, s(s(s(elem!1))))) | (~b(s(z), s(s(s(elem!1))))) | (~b(s(z), z))) <=> ((~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(z, s(s(s(elem!1))))) | (~b(s(z), z)) | (~b(s(z), s(s(s(elem!1))))) | (~b(s(s(elem!1)), s(s(z)))) | (~b(s(z), s(s(z)))))),
% 2.52/2.78 inference(rewrite,[status(thm)],[])).
% 2.52/2.78 tff(8682,plain,
% 2.52/2.78 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), s(s(z)))) | (~b(s(z), s(s(z)))) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(z, s(s(s(elem!1))))) | (~b(s(z), s(s(s(elem!1))))) | (~b(s(z), z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(z, s(s(s(elem!1))))) | (~b(s(z), z)) | (~b(s(z), s(s(s(elem!1))))) | (~b(s(s(elem!1)), s(s(z)))) | (~b(s(z), s(s(z))))))),
% 2.52/2.78 inference(monotonicity,[status(thm)],[8681])).
% 2.52/2.78 tff(8683,plain,
% 2.52/2.78 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), s(s(z)))) | (~b(s(z), s(s(z)))) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(z, s(s(s(elem!1))))) | (~b(s(z), s(s(s(elem!1))))) | (~b(s(z), z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(z, s(s(s(elem!1))))) | (~b(s(z), z)) | (~b(s(z), s(s(s(elem!1))))) | (~b(s(s(elem!1)), s(s(z)))) | (~b(s(z), s(s(z)))))),
% 2.52/2.78 inference(transitivity,[status(thm)],[8682, 8680])).
% 2.52/2.78 tff(8684,plain,
% 2.52/2.78 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), s(s(z)))) | (~b(s(z), s(s(z)))) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(z, s(s(s(elem!1))))) | (~b(s(z), s(s(s(elem!1))))) | (~b(s(z), z)))),
% 2.52/2.78 inference(quant_inst,[status(thm)],[])).
% 2.52/2.78 tff(8685,plain,
% 2.52/2.78 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(z, s(s(s(elem!1))))) | (~b(s(z), z)) | (~b(s(z), s(s(s(elem!1))))) | (~b(s(s(elem!1)), s(s(z)))) | (~b(s(z), s(s(z))))),
% 2.52/2.78 inference(modus_ponens,[status(thm)],[8684, 8683])).
% 2.52/2.78 tff(8686,plain,
% 2.52/2.78 ($false),
% 2.52/2.78 inference(unit_resolution,[status(thm)],[8685, 166, 839, 241, 240, 53, 405, 556])).
% 2.52/2.78 tff(8687,plain,((~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(z), s(s(s(elem!1))))) | (~b(z, s(s(s(elem!1))))) | (~b(s(z), z)) | (~b(s(s(elem!1)), s(s(z)))) | (~b(s(z), s(s(z))))), inference(lemma,lemma(discharge,[]))).
% 2.52/2.78 tff(8688,plain,
% 2.52/2.78 ($false),
% 2.52/2.78 inference(unit_resolution,[status(thm)],[8687, 8679, 8669, 53, 8647, 8632, 8646])).
% 2.52/2.78 tff(8689,plain,((~r(s(s(z)), s(z))) | (~b(s(z), z)) | (s(s(s(elem!1))) = s(s(elem!1))) | (~r(s(s(elem!1)), s(z))) | (~r(z, s(s(z)))) | (~r(s(s(s(elem!1))), z)) | (~b(s(s(s(elem!1))), s(z))) | (s(s(z)) = s(s(elem!1))) | (~r(z, s(z)))), inference(lemma,lemma(discharge,[]))).
% 2.52/2.78 tff(8690,plain,
% 2.52/2.78 (s(s(z)) = s(s(elem!1))),
% 2.52/2.78 inference(unit_resolution,[status(thm)],[8689, 8630, 51, 8552, 152, 154, 96, 8550, 8408])).
% 2.52/2.78 tff(8691,plain,
% 2.52/2.78 (~b(z, s(s(elem!1)))),
% 2.52/2.78 inference(unit_resolution,[status(thm)],[2261, 8690, 125])).
% 2.52/2.78 tff(8692,plain,
% 2.52/2.78 (r(z, s(s(elem!1)))),
% 2.52/2.78 inference(unit_resolution,[status(thm)],[1795, 8691])).
% 2.52/2.78 tff(8693,plain,
% 2.52/2.78 (s(elem!1) = s(z)),
% 2.52/2.78 inference(unit_resolution,[status(thm)],[43, 8690])).
% 2.52/2.78 tff(8694,plain,
% 2.52/2.78 (z = elem!1),
% 2.52/2.78 inference(unit_resolution,[status(thm)],[30, 8693])).
% 2.52/2.78 tff(8695,plain,
% 2.52/2.78 (b(s(elem!1), z) <=> b(s(elem!1), elem!1)),
% 2.52/2.78 inference(monotonicity,[status(thm)],[12])).
% 2.52/2.78 tff(8696,plain,
% 2.52/2.78 (b(s(elem!1), elem!1) <=> b(s(elem!1), z)),
% 2.52/2.78 inference(symmetry,[status(thm)],[8695])).
% 2.52/2.78 tff(8697,plain,
% 2.52/2.78 (b(s(z), elem!1) <=> b(s(elem!1), elem!1)),
% 2.52/2.78 inference(monotonicity,[status(thm)],[13])).
% 2.52/2.78 tff(8698,plain,
% 2.52/2.78 (b(s(z), z) <=> b(s(elem!1), z)),
% 2.52/2.78 inference(transitivity,[status(thm)],[7991, 8697, 8696])).
% 2.52/2.78 tff(8699,plain,
% 2.52/2.78 (b(s(elem!1), z)),
% 2.52/2.78 inference(modus_ponens,[status(thm)],[53, 8698])).
% 2.52/2.78 tff(8700,assumption,(~b(s(elem!1), z)), introduced(assumption)).
% 2.52/2.78 tff(8701,plain,
% 2.52/2.78 ($false),
% 2.52/2.78 inference(unit_resolution,[status(thm)],[8700, 8699])).
% 2.52/2.78 tff(8702,plain,(b(s(elem!1), z) | (~b(s(z), z)) | (~(z = elem!1))), inference(lemma,lemma(discharge,[]))).
% 2.52/2.78 tff(8703,plain,
% 2.52/2.78 (b(s(elem!1), z)),
% 2.52/2.78 inference(unit_resolution,[status(thm)],[8702, 8694, 8550])).
% 2.52/2.78 tff(8704,plain,
% 2.52/2.78 (b(s(elem!1), elem!1) <=> b(s(z), elem!1)),
% 2.52/2.78 inference(monotonicity,[status(thm)],[8693])).
% 2.52/2.78 tff(8705,plain,
% 2.52/2.78 (b(s(z), elem!1) <=> b(s(elem!1), elem!1)),
% 2.52/2.78 inference(symmetry,[status(thm)],[8704])).
% 2.52/2.78 tff(8706,plain,
% 2.52/2.78 (b(s(z), z) <=> b(s(z), elem!1)),
% 2.52/2.78 inference(monotonicity,[status(thm)],[8694])).
% 2.52/2.78 tff(8707,plain,
% 2.52/2.78 (b(s(z), z) <=> b(s(elem!1), elem!1)),
% 2.52/2.78 inference(transitivity,[status(thm)],[8706, 8705])).
% 2.52/2.78 tff(8708,plain,
% 2.52/2.78 (b(s(elem!1), elem!1)),
% 2.52/2.78 inference(modus_ponens,[status(thm)],[8550, 8707])).
% 2.52/2.78 tff(8709,plain,
% 2.52/2.78 (~r(s(z), s(s(s(elem!1))))),
% 2.52/2.78 inference(unit_resolution,[status(thm)],[8626, 8692, 8408, 8552])).
% 2.52/2.78 tff(8710,plain,
% 2.52/2.78 (b(s(z), s(s(s(elem!1))))),
% 2.52/2.78 inference(unit_resolution,[status(thm)],[116, 8709])).
% 2.52/2.78 tff(8711,plain,
% 2.52/2.78 (~r(s(z), s(s(z)))),
% 2.52/2.78 inference(unit_resolution,[status(thm)],[553, 8630, 152, 8408])).
% 2.52/2.78 tff(8712,plain,
% 2.52/2.78 (b(s(z), s(s(z)))),
% 2.52/2.78 inference(unit_resolution,[status(thm)],[427, 8711])).
% 2.52/2.78 tff(8713,plain,
% 2.52/2.78 (s(s(s(z))) = s(s(s(elem!1)))),
% 2.52/2.78 inference(monotonicity,[status(thm)],[8690])).
% 2.52/2.78 tff(8714,plain,
% 2.52/2.78 (b(s(z), s(s(s(z)))) <=> b(s(z), s(s(s(elem!1))))),
% 2.52/2.78 inference(monotonicity,[status(thm)],[8713])).
% 2.52/2.78 tff(8715,plain,
% 2.52/2.78 (b(s(z), s(s(s(elem!1)))) <=> b(s(z), s(s(s(z))))),
% 2.52/2.78 inference(symmetry,[status(thm)],[8714])).
% 2.52/2.78 tff(8716,plain,
% 2.52/2.78 (b(s(z), s(s(s(z))))),
% 2.52/2.78 inference(modus_ponens,[status(thm)],[8710, 8715])).
% 2.52/2.78 tff(8717,plain,
% 2.52/2.78 (~b(s(s(z)), s(s(s(elem!1))))),
% 2.52/2.78 inference(unit_resolution,[status(thm)],[8665, 8716, 96, 8712, 8710])).
% 2.52/2.78 tff(8718,plain,
% 2.52/2.78 (r(s(s(z)), s(s(s(elem!1))))),
% 2.52/2.78 inference(unit_resolution,[status(thm)],[279, 8717])).
% 2.52/2.78 tff(8719,plain,
% 2.52/2.78 (~r(z, s(s(s(elem!1))))),
% 2.52/2.78 inference(unit_resolution,[status(thm)],[290, 8718, 152, 154])).
% 2.52/2.78 tff(8720,plain,
% 2.52/2.78 (b(z, s(s(s(elem!1))))),
% 2.52/2.78 inference(unit_resolution,[status(thm)],[261, 8719])).
% 2.52/2.78 tff(8721,plain,
% 2.52/2.78 (b(s(z), s(s(s(elem!1)))) <=> b(s(elem!1), s(s(s(elem!1))))),
% 2.52/2.78 inference(monotonicity,[status(thm)],[13])).
% 2.52/2.78 tff(8722,plain,
% 2.52/2.78 (b(s(elem!1), s(s(s(elem!1))))),
% 2.52/2.78 inference(modus_ponens,[status(thm)],[241, 8721])).
% 2.52/2.78 tff(8723,assumption,(~b(s(elem!1), s(s(s(elem!1))))), introduced(assumption)).
% 2.52/2.78 tff(8724,plain,
% 2.52/2.78 ($false),
% 2.52/2.78 inference(unit_resolution,[status(thm)],[8723, 8722])).
% 2.52/2.78 tff(8725,plain,((~b(s(z), s(s(s(elem!1))))) | b(s(elem!1), s(s(s(elem!1)))) | (~(z = elem!1))), inference(lemma,lemma(discharge,[]))).
% 2.52/2.78 tff(8726,plain,
% 2.52/2.78 (b(s(elem!1), s(s(s(elem!1))))),
% 2.52/2.78 inference(unit_resolution,[status(thm)],[8725, 8710, 8694])).
% 2.52/2.78 tff(8727,plain,
% 2.52/2.78 (r(s(s(s(z))), z) <=> r(s(s(s(z))), elem!1)),
% 2.52/2.78 inference(monotonicity,[status(thm)],[8694])).
% 2.52/2.78 tff(8728,plain,
% 2.52/2.78 (r(s(s(s(z))), elem!1) <=> r(s(s(s(z))), z)),
% 2.52/2.78 inference(symmetry,[status(thm)],[8727])).
% 2.52/2.78 tff(8729,plain,
% 2.52/2.78 (r(s(s(s(z))), elem!1) <=> r(s(s(s(elem!1))), elem!1)),
% 2.52/2.78 inference(monotonicity,[status(thm)],[8713])).
% 2.52/2.78 tff(8730,plain,
% 2.52/2.78 (r(s(s(s(elem!1))), elem!1) <=> r(s(s(s(z))), elem!1)),
% 2.52/2.78 inference(symmetry,[status(thm)],[8729])).
% 2.52/2.78 tff(8731,plain,
% 2.52/2.78 (r(s(s(s(elem!1))), elem!1) <=> r(s(s(s(z))), z)),
% 2.52/2.78 inference(transitivity,[status(thm)],[8730, 8728])).
% 2.52/2.78 tff(8732,plain,
% 2.52/2.78 (r(s(s(s(elem!1))), elem!1)),
% 2.52/2.78 inference(unit_resolution,[status(thm)],[966, 8694, 154])).
% 2.52/2.78 tff(8733,plain,
% 2.52/2.78 (r(s(s(s(z))), z)),
% 2.52/2.78 inference(modus_ponens,[status(thm)],[8732, 8731])).
% 2.52/2.78 tff(8734,plain,
% 2.52/2.78 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(z))) | (~r(s(s(z)), z)) | (~r(s(s(s(z))), z)) | (~r(s(s(s(z))), s(s(z)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, s(z))) | (~r(s(s(z)), z)) | (~r(s(s(s(z))), z)) | (~r(s(s(s(z))), s(s(z)))))),
% 2.52/2.78 inference(rewrite,[status(thm)],[])).
% 2.52/2.78 tff(8735,plain,
% 2.52/2.78 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(z))) | (~r(s(s(z)), z)) | (~r(s(s(s(z))), z)) | (~r(s(s(s(z))), s(s(z)))))),
% 2.52/2.78 inference(quant_inst,[status(thm)],[])).
% 2.52/2.78 tff(8736,plain,
% 2.52/2.78 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, s(z))) | (~r(s(s(z)), z)) | (~r(s(s(s(z))), z)) | (~r(s(s(s(z))), s(s(z))))),
% 2.52/2.78 inference(modus_ponens,[status(thm)],[8735, 8734])).
% 2.52/2.78 tff(8737,plain,
% 2.52/2.78 (~r(s(s(s(z))), s(s(z)))),
% 2.52/2.78 inference(unit_resolution,[status(thm)],[8736, 197, 323, 866, 1733])).
% 2.52/2.78 tff(8738,plain,
% 2.52/2.78 (b(s(s(s(z))), s(s(z)))),
% 2.52/2.78 inference(unit_resolution,[status(thm)],[1010, 8737])).
% 2.52/2.78 tff(8739,plain,
% 2.52/2.78 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(z))) | (~r(s(s(z)), z)) | (~r(s(s(z)), s(s(s(z))))) | (~r(s(s(s(z))), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, s(z))) | (~r(s(s(z)), z)) | (~r(s(s(z)), s(s(s(z))))) | (~r(s(s(s(z))), z)))),
% 2.52/2.78 inference(rewrite,[status(thm)],[])).
% 2.52/2.78 tff(8740,plain,
% 2.52/2.78 (((~r(z, s(z))) | (~r(s(s(s(z))), z)) | (~r(s(s(z)), z)) | (~r(s(s(z)), s(s(s(z)))))) <=> ((~r(z, s(z))) | (~r(s(s(z)), z)) | (~r(s(s(z)), s(s(s(z))))) | (~r(s(s(s(z))), z)))),
% 2.52/2.78 inference(rewrite,[status(thm)],[])).
% 2.52/2.78 tff(8741,plain,
% 2.52/2.78 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(z))) | (~r(s(s(s(z))), z)) | (~r(s(s(z)), z)) | (~r(s(s(z)), s(s(s(z))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(z))) | (~r(s(s(z)), z)) | (~r(s(s(z)), s(s(s(z))))) | (~r(s(s(s(z))), z))))),
% 2.52/2.78 inference(monotonicity,[status(thm)],[8740])).
% 2.52/2.78 tff(8742,plain,
% 2.52/2.78 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(z))) | (~r(s(s(s(z))), z)) | (~r(s(s(z)), z)) | (~r(s(s(z)), s(s(s(z))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, s(z))) | (~r(s(s(z)), z)) | (~r(s(s(z)), s(s(s(z))))) | (~r(s(s(s(z))), z)))),
% 2.52/2.78 inference(transitivity,[status(thm)],[8741, 8739])).
% 2.52/2.78 tff(8743,plain,
% 2.52/2.78 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(z))) | (~r(s(s(s(z))), z)) | (~r(s(s(z)), z)) | (~r(s(s(z)), s(s(s(z))))))),
% 2.52/2.78 inference(quant_inst,[status(thm)],[])).
% 2.52/2.78 tff(8744,plain,
% 2.52/2.78 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, s(z))) | (~r(s(s(z)), z)) | (~r(s(s(z)), s(s(s(z))))) | (~r(s(s(s(z))), z))),
% 2.52/2.78 inference(modus_ponens,[status(thm)],[8743, 8742])).
% 2.52/2.78 tff(8745,plain,
% 2.52/2.78 (~r(s(s(z)), s(s(s(z))))),
% 2.52/2.78 inference(unit_resolution,[status(thm)],[8744, 197, 323, 866, 1733])).
% 2.52/2.78 tff(8746,plain,
% 2.52/2.78 (b(s(s(z)), s(s(s(z))))),
% 2.52/2.78 inference(unit_resolution,[status(thm)],[1730, 8745])).
% 2.52/2.78 tff(8747,plain,
% 2.52/2.78 ($false),
% 2.52/2.78 inference(unit_resolution,[status(thm)],[996, 8746, 8738, 556, 988])).
% 2.52/2.78 tff(8748,plain,((~r(s(s(s(z))), z)) | (~b(s(z), s(s(z)))) | (~b(s(z), s(s(s(z))))) | (~r(z, s(z))) | (~r(s(s(z)), z))), inference(lemma,lemma(discharge,[]))).
% 2.52/2.78 tff(8749,plain,
% 2.52/2.78 (~r(s(s(z)), z)),
% 2.52/2.78 inference(unit_resolution,[status(thm)],[8748, 8733, 8408, 8716, 8712])).
% 2.52/2.78 tff(8750,plain,
% 2.52/2.78 (b(s(s(z)), z)),
% 2.52/2.78 inference(unit_resolution,[status(thm)],[186, 8749])).
% 2.52/2.78 tff(8751,plain,
% 2.52/2.78 (b(s(s(z)), z) <=> b(s(s(elem!1)), elem!1)),
% 2.52/2.78 inference(transitivity,[status(thm)],[2962, 5412])).
% 2.52/2.78 tff(8752,plain,
% 2.52/2.78 (b(s(s(elem!1)), elem!1)),
% 2.52/2.78 inference(modus_ponens,[status(thm)],[122, 8751])).
% 2.52/2.78 tff(8753,plain,
% 2.52/2.78 ($false),
% 2.52/2.78 inference(unit_resolution,[status(thm)],[779, 8752])).
% 2.52/2.78 tff(8754,plain,((~b(s(s(z)), z)) | b(s(s(elem!1)), elem!1) | (~(s(s(z)) = s(s(elem!1))))), inference(lemma,lemma(discharge,[]))).
% 2.52/2.78 tff(8755,plain,
% 2.52/2.78 (b(s(s(elem!1)), elem!1)),
% 2.52/2.78 inference(unit_resolution,[status(thm)],[8754, 8750, 8690])).
% 2.52/2.78 tff(8756,plain,
% 2.52/2.78 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), elem!1)) | (~b(s(elem!1), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(elem!1), elem!1)) | (~b(z, s(s(s(elem!1))))) | (~b(s(elem!1), z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(elem!1)), elem!1)) | (~b(s(elem!1), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(elem!1), elem!1)) | (~b(z, s(s(s(elem!1))))) | (~b(s(elem!1), z)))),
% 2.52/2.78 inference(rewrite,[status(thm)],[])).
% 2.52/2.78 tff(8757,plain,
% 2.52/2.78 (((~b(s(s(elem!1)), elem!1)) | (~b(s(elem!1), elem!1)) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(z, s(s(s(elem!1))))) | (~b(s(elem!1), s(s(s(elem!1))))) | (~b(s(elem!1), z))) <=> ((~b(s(s(elem!1)), elem!1)) | (~b(s(elem!1), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(elem!1), elem!1)) | (~b(z, s(s(s(elem!1))))) | (~b(s(elem!1), z)))),
% 2.52/2.78 inference(rewrite,[status(thm)],[])).
% 2.52/2.78 tff(8758,plain,
% 2.52/2.78 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), elem!1)) | (~b(s(elem!1), elem!1)) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(z, s(s(s(elem!1))))) | (~b(s(elem!1), s(s(s(elem!1))))) | (~b(s(elem!1), z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), elem!1)) | (~b(s(elem!1), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(elem!1), elem!1)) | (~b(z, s(s(s(elem!1))))) | (~b(s(elem!1), z))))),
% 2.52/2.78 inference(monotonicity,[status(thm)],[8757])).
% 2.52/2.78 tff(8759,plain,
% 2.52/2.78 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), elem!1)) | (~b(s(elem!1), elem!1)) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(z, s(s(s(elem!1))))) | (~b(s(elem!1), s(s(s(elem!1))))) | (~b(s(elem!1), z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(elem!1)), elem!1)) | (~b(s(elem!1), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(elem!1), elem!1)) | (~b(z, s(s(s(elem!1))))) | (~b(s(elem!1), z)))),
% 2.52/2.78 inference(transitivity,[status(thm)],[8758, 8756])).
% 2.52/2.78 tff(8760,plain,
% 2.52/2.78 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), elem!1)) | (~b(s(elem!1), elem!1)) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(z, s(s(s(elem!1))))) | (~b(s(elem!1), s(s(s(elem!1))))) | (~b(s(elem!1), z)))),
% 2.52/2.78 inference(quant_inst,[status(thm)],[])).
% 2.52/2.78 tff(8761,plain,
% 2.52/2.78 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(elem!1)), elem!1)) | (~b(s(elem!1), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(elem!1), elem!1)) | (~b(z, s(s(s(elem!1))))) | (~b(s(elem!1), z))),
% 2.52/2.78 inference(modus_ponens,[status(thm)],[8760, 8759])).
% 2.52/2.78 tff(8762,plain,
% 2.52/2.78 ((~b(s(s(elem!1)), elem!1)) | (~b(s(elem!1), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(elem!1), elem!1)) | (~b(z, s(s(s(elem!1))))) | (~b(s(elem!1), z))),
% 2.52/2.78 inference(unit_resolution,[status(thm)],[8761, 166])).
% 2.52/2.78 tff(8763,plain,
% 2.52/2.78 (~b(s(s(s(elem!1))), s(s(elem!1)))),
% 2.52/2.78 inference(unit_resolution,[status(thm)],[8762, 8755, 8726, 8720, 8708, 8703])).
% 2.52/2.78 tff(8764,plain,
% 2.52/2.78 (r(s(s(s(elem!1))), s(s(elem!1)))),
% 2.52/2.78 inference(unit_resolution,[status(thm)],[889, 8763, 51])).
% 2.52/2.78 tff(8765,plain,
% 2.52/2.78 (b(s(s(elem!1)), z)),
% 2.52/2.78 inference(unit_resolution,[status(thm)],[2965, 8750, 8690])).
% 2.52/2.78 tff(8766,plain,
% 2.52/2.78 (b(elem!1, s(s(s(elem!1))))),
% 2.52/2.78 inference(modus_ponens,[status(thm)],[240, 7752])).
% 2.52/2.78 tff(8767,plain,
% 2.52/2.78 (b(s(s(elem!1)), z) <=> b(s(s(elem!1)), elem!1)),
% 2.52/2.78 inference(monotonicity,[status(thm)],[12])).
% 2.52/2.78 tff(8768,plain,
% 2.52/2.78 (b(s(s(elem!1)), elem!1)),
% 2.52/2.78 inference(modus_ponens,[status(thm)],[592, 8767])).
% 2.52/2.78 tff(8769,plain,
% 2.52/2.78 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(s(s(elem!1)), elem!1)) | (~b(elem!1, s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(z), elem!1)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(s(s(elem!1)), elem!1)) | (~b(elem!1, s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(z), elem!1)))),
% 2.52/2.78 inference(rewrite,[status(thm)],[])).
% 2.52/2.78 tff(8770,plain,
% 2.52/2.78 (((~b(s(z), elem!1)) | (~b(s(s(elem!1)), elem!1)) | (~b(s(s(s(elem!1))), s(z))) | (~b(elem!1, s(s(s(elem!1))))) | (~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(s(s(elem!1)), elem!1))) <=> ((~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(s(s(elem!1)), elem!1)) | (~b(elem!1, s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(z), elem!1)))),
% 2.52/2.78 inference(rewrite,[status(thm)],[])).
% 2.52/2.78 tff(8771,plain,
% 2.52/2.78 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), elem!1)) | (~b(s(s(elem!1)), elem!1)) | (~b(s(s(s(elem!1))), s(z))) | (~b(elem!1, s(s(s(elem!1))))) | (~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(s(s(elem!1)), elem!1)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(s(s(elem!1)), elem!1)) | (~b(elem!1, s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(z), elem!1))))),
% 2.52/2.78 inference(monotonicity,[status(thm)],[8770])).
% 2.52/2.78 tff(8772,plain,
% 2.52/2.78 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), elem!1)) | (~b(s(s(elem!1)), elem!1)) | (~b(s(s(s(elem!1))), s(z))) | (~b(elem!1, s(s(s(elem!1))))) | (~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(s(s(elem!1)), elem!1)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(s(s(elem!1)), elem!1)) | (~b(elem!1, s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(z), elem!1)))),
% 2.52/2.78 inference(transitivity,[status(thm)],[8771, 8769])).
% 2.52/2.78 tff(8773,plain,
% 2.52/2.78 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), elem!1)) | (~b(s(s(elem!1)), elem!1)) | (~b(s(s(s(elem!1))), s(z))) | (~b(elem!1, s(s(s(elem!1))))) | (~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(s(s(elem!1)), elem!1)))),
% 2.52/2.78 inference(quant_inst,[status(thm)],[])).
% 2.52/2.78 tff(8774,plain,
% 2.52/2.78 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(s(s(elem!1)), elem!1)) | (~b(elem!1, s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(z), elem!1))),
% 2.52/2.78 inference(modus_ponens,[status(thm)],[8773, 8772])).
% 2.52/2.78 tff(8775,plain,
% 2.52/2.78 ($false),
% 2.52/2.78 inference(unit_resolution,[status(thm)],[8774, 166, 463, 8768, 8766, 96, 7992])).
% 2.52/2.79 tff(8776,plain,((~(z = elem!1)) | (~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(s(elem!1)), z)) | (~b(s(z), z)) | (~b(z, s(s(s(elem!1)))))), inference(lemma,lemma(discharge,[]))).
% 2.52/2.79 tff(8777,plain,
% 2.52/2.79 (~b(s(s(elem!1)), s(s(s(elem!1))))),
% 2.52/2.79 inference(unit_resolution,[status(thm)],[8776, 8720, 96, 8550, 8694, 8765])).
% 2.52/2.79 tff(8778,plain,
% 2.52/2.79 (r(s(s(elem!1)), s(s(s(elem!1))))),
% 2.52/2.79 inference(unit_resolution,[status(thm)],[461, 8777, 45])).
% 2.52/2.79 tff(8779,plain,
% 2.52/2.79 ($false),
% 2.52/2.79 inference(unit_resolution,[status(thm)],[1386, 8778, 8764, 154, 8692])).
% 2.52/2.79 tff(8780,plain,((s(s(elem!1)) = s(s(s(elem!1)))) | (~r(s(s(s(elem!1))), z)) | (~b(s(s(s(elem!1))), s(z))) | b(z, s(s(z)))), inference(lemma,lemma(discharge,[]))).
% 2.52/2.79 tff(8781,plain,
% 2.52/2.79 (s(s(elem!1)) = s(s(s(elem!1)))),
% 2.52/2.79 inference(unit_resolution,[status(thm)],[8780, 154, 96, 125])).
% 2.52/2.79 tff(8782,plain,
% 2.52/2.79 (b(s(s(elem!1)), s(z))),
% 2.52/2.79 inference(unit_resolution,[status(thm)],[4570, 8781, 96])).
% 2.52/2.79 tff(8783,plain,
% 2.52/2.79 (b(s(z), s(s(elem!1)))),
% 2.52/2.79 inference(unit_resolution,[status(thm)],[4556, 8782, 125])).
% 2.52/2.79 tff(8784,plain,
% 2.52/2.79 (b(s(z), s(s(s(elem!1))))),
% 2.52/2.79 inference(unit_resolution,[status(thm)],[5500, 8783, 8781])).
% 2.52/2.79 tff(8785,plain,
% 2.52/2.79 (((~b(s(z), s(s(elem!1)))) | (~b(s(z), s(s(elem!1)))) | (~b(s(s(elem!1)), s(z))) | (~b(z, s(s(elem!1)))) | (~b(s(z), s(s(elem!1)))) | (~b(s(z), z))) <=> ((~b(z, s(s(elem!1)))) | (~b(s(z), z)) | (~b(s(z), s(s(elem!1)))) | (~b(s(s(elem!1)), s(z))))),
% 2.52/2.79 inference(rewrite,[status(thm)],[])).
% 2.52/2.79 tff(8786,plain,
% 2.52/2.79 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(elem!1)))) | (~b(s(z), s(s(elem!1)))) | (~b(s(s(elem!1)), s(z))) | (~b(z, s(s(elem!1)))) | (~b(s(z), s(s(elem!1)))) | (~b(s(z), z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(elem!1)))) | (~b(s(z), z)) | (~b(s(z), s(s(elem!1)))) | (~b(s(s(elem!1)), s(z)))))),
% 2.52/2.79 inference(monotonicity,[status(thm)],[8785])).
% 2.52/2.79 tff(8787,plain,
% 2.52/2.79 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(elem!1)))) | (~b(s(z), s(s(elem!1)))) | (~b(s(s(elem!1)), s(z))) | (~b(z, s(s(elem!1)))) | (~b(s(z), s(s(elem!1)))) | (~b(s(z), z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(s(elem!1)))) | (~b(s(z), z)) | (~b(s(z), s(s(elem!1)))) | (~b(s(s(elem!1)), s(z))))),
% 2.52/2.79 inference(transitivity,[status(thm)],[8786, 1805])).
% 2.52/2.79 tff(8788,plain,
% 2.52/2.79 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(elem!1)))) | (~b(s(z), s(s(elem!1)))) | (~b(s(s(elem!1)), s(z))) | (~b(z, s(s(elem!1)))) | (~b(s(z), s(s(elem!1)))) | (~b(s(z), z)))),
% 2.52/2.79 inference(quant_inst,[status(thm)],[])).
% 2.52/2.79 tff(8789,plain,
% 2.52/2.79 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(s(elem!1)))) | (~b(s(z), z)) | (~b(s(z), s(s(elem!1)))) | (~b(s(s(elem!1)), s(z)))),
% 2.52/2.79 inference(modus_ponens,[status(thm)],[8788, 8787])).
% 2.52/2.79 tff(8790,plain,
% 2.52/2.79 ($false),
% 2.52/2.79 inference(unit_resolution,[status(thm)],[8789, 166, 376, 1820, 53, 310])).
% 2.52/2.79 tff(8791,plain,((~b(z, s(s(elem!1)))) | (~b(s(z), s(s(elem!1)))) | (~b(s(z), z)) | (~b(s(s(elem!1)), s(z)))), inference(lemma,lemma(discharge,[]))).
% 2.52/2.79 tff(8792,plain,
% 2.52/2.79 (~b(z, s(s(elem!1)))),
% 2.52/2.79 inference(unit_resolution,[status(thm)],[8791, 8782, 8550, 8783])).
% 2.52/2.79 tff(8793,plain,
% 2.52/2.79 (~b(z, s(s(s(elem!1))))),
% 2.52/2.79 inference(unit_resolution,[status(thm)],[4345, 8792, 8781])).
% 2.52/2.79 tff(8794,plain,
% 2.52/2.79 (r(z, s(s(s(elem!1))))),
% 2.52/2.79 inference(unit_resolution,[status(thm)],[261, 8793])).
% 2.52/2.79 tff(8795,plain,
% 2.52/2.79 (~r(s(s(z)), s(s(s(elem!1))))),
% 2.52/2.79 inference(unit_resolution,[status(thm)],[290, 8794, 152, 154])).
% 2.52/2.79 tff(8796,plain,
% 2.52/2.79 (b(s(s(z)), s(s(s(elem!1))))),
% 2.52/2.79 inference(unit_resolution,[status(thm)],[279, 8795])).
% 2.52/2.79 tff(8797,plain,
% 2.52/2.79 (~b(s(s(z)), s(z))),
% 2.52/2.79 inference(unit_resolution,[status(thm)],[271, 8796, 96, 8784])).
% 2.52/2.79 tff(8798,plain,
% 2.52/2.79 (~(s(s(z)) = s(s(elem!1)))),
% 2.52/2.79 inference(unit_resolution,[status(thm)],[3938, 8797, 8782])).
% 2.52/2.79 tff(8799,plain,
% 2.52/2.79 (~r(s(s(z)), s(s(elem!1)))),
% 2.52/2.79 inference(unit_resolution,[status(thm)],[338, 8795, 8781])).
% 2.52/2.79 tff(8800,plain,
% 2.52/2.79 (r(z, s(s(elem!1)))),
% 2.52/2.79 inference(unit_resolution,[status(thm)],[1795, 8792])).
% 2.52/2.79 tff(8801,plain,
% 2.52/2.79 (r(s(s(z)), s(z))),
% 2.52/2.79 inference(unit_resolution,[status(thm)],[308, 8797])).
% 2.52/2.79 tff(8802,plain,
% 2.52/2.79 (~r(s(s(elem!1)), s(s(z)))),
% 2.52/2.79 inference(unit_resolution,[status(thm)],[401, 8801, 152, 8800])).
% 2.52/2.79 tff(8803,plain,
% 2.52/2.79 (~r(s(z), s(s(z)))),
% 2.52/2.79 inference(unit_resolution,[status(thm)],[553, 8801, 152, 8408])).
% 2.52/2.79 tff(8804,plain,
% 2.52/2.79 (b(s(z), s(s(z)))),
% 2.52/2.79 inference(unit_resolution,[status(thm)],[427, 8803])).
% 2.52/2.79 tff(8805,plain,
% 2.52/2.79 ($false),
% 2.52/2.79 inference(unit_resolution,[status(thm)],[5300, 8804, 8802, 8783, 8799, 8798])).
% 2.52/2.79 tff(8806,plain,((~r(s(s(s(elem!1))), z)) | (~b(s(s(s(elem!1))), s(z))) | b(z, s(s(z)))), inference(lemma,lemma(discharge,[]))).
% 2.52/2.79 tff(8807,plain,
% 2.52/2.79 (~r(s(s(s(elem!1))), z)),
% 2.52/2.79 inference(unit_resolution,[status(thm)],[8806, 96, 125])).
% 2.52/2.79 tff(8808,plain,
% 2.52/2.79 (b(s(s(s(elem!1))), z)),
% 2.52/2.79 inference(unit_resolution,[status(thm)],[94, 8807])).
% 2.52/2.79 tff(8809,plain,
% 2.52/2.79 (b(s(z), s(s(elem!1)))),
% 2.52/2.79 inference(unit_resolution,[status(thm)],[4556, 310, 125])).
% 2.52/2.79 tff(8810,plain,
% 2.52/2.79 (~b(s(s(s(elem!1))), s(s(elem!1)))),
% 2.52/2.79 inference(unit_resolution,[status(thm)],[1858, 310, 96, 376])).
% 2.52/2.79 tff(8811,plain,
% 2.52/2.79 (~b(s(s(z)), s(s(elem!1)))),
% 2.52/2.79 inference(unit_resolution,[status(thm)],[454, 2682, 376, 310])).
% 2.52/2.79 tff(8812,plain,
% 2.52/2.79 (r(s(s(z)), s(s(elem!1)))),
% 2.52/2.79 inference(unit_resolution,[status(thm)],[390, 8811, 52])).
% 2.52/2.79 tff(8813,plain,
% 2.52/2.79 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(elem!1)))) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(s(elem!1)), s(z))) | (~b(s(s(z)), s(z))) | (~b(s(s(z)), s(s(s(elem!1))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), s(s(elem!1)))) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(s(elem!1)), s(z))) | (~b(s(s(z)), s(z))) | (~b(s(s(z)), s(s(s(elem!1))))))),
% 2.52/2.79 inference(rewrite,[status(thm)],[])).
% 2.52/2.79 tff(8814,plain,
% 2.52/2.79 (((~b(s(s(elem!1)), s(z))) | (~b(s(s(z)), s(z))) | (~b(s(z), s(s(elem!1)))) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(s(z)), s(z))) | (~b(s(s(z)), s(s(s(elem!1)))))) <=> ((~b(s(z), s(s(elem!1)))) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(s(elem!1)), s(z))) | (~b(s(s(z)), s(z))) | (~b(s(s(z)), s(s(s(elem!1))))))),
% 2.52/2.79 inference(rewrite,[status(thm)],[])).
% 2.52/2.79 tff(8815,plain,
% 2.52/2.79 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), s(z))) | (~b(s(s(z)), s(z))) | (~b(s(z), s(s(elem!1)))) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(s(z)), s(z))) | (~b(s(s(z)), s(s(s(elem!1))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(elem!1)))) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(s(elem!1)), s(z))) | (~b(s(s(z)), s(z))) | (~b(s(s(z)), s(s(s(elem!1)))))))),
% 2.52/2.79 inference(monotonicity,[status(thm)],[8814])).
% 2.52/2.79 tff(8816,plain,
% 2.52/2.79 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), s(z))) | (~b(s(s(z)), s(z))) | (~b(s(z), s(s(elem!1)))) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(s(z)), s(z))) | (~b(s(s(z)), s(s(s(elem!1))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), s(s(elem!1)))) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(s(elem!1)), s(z))) | (~b(s(s(z)), s(z))) | (~b(s(s(z)), s(s(s(elem!1))))))),
% 2.52/2.79 inference(transitivity,[status(thm)],[8815, 8813])).
% 2.52/2.79 tff(8817,plain,
% 2.52/2.79 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), s(z))) | (~b(s(s(z)), s(z))) | (~b(s(z), s(s(elem!1)))) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(s(z)), s(z))) | (~b(s(s(z)), s(s(s(elem!1))))))),
% 2.52/2.79 inference(quant_inst,[status(thm)],[])).
% 2.52/2.79 tff(8818,plain,
% 2.52/2.79 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), s(s(elem!1)))) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(s(elem!1)), s(z))) | (~b(s(s(z)), s(z))) | (~b(s(s(z)), s(s(s(elem!1)))))),
% 2.52/2.79 inference(modus_ponens,[status(thm)],[8817, 8816])).
% 2.52/2.79 tff(8819,plain,
% 2.52/2.79 (~b(s(s(z)), s(s(s(elem!1))))),
% 2.52/2.79 inference(unit_resolution,[status(thm)],[8818, 166, 376, 96, 310, 2682])).
% 2.52/2.79 tff(8820,plain,
% 2.52/2.79 (r(s(s(z)), s(s(s(elem!1))))),
% 2.52/2.79 inference(unit_resolution,[status(thm)],[279, 8819])).
% 2.52/2.79 tff(8821,plain,
% 2.52/2.79 (~r(s(s(s(elem!1))), s(s(elem!1)))),
% 2.52/2.79 inference(unit_resolution,[status(thm)],[4513, 8820, 8812, 2692])).
% 2.52/2.79 tff(8822,plain,
% 2.52/2.79 (s(s(s(elem!1))) = s(s(elem!1))),
% 2.52/2.79 inference(unit_resolution,[status(thm)],[889, 8821, 8810])).
% 2.52/2.79 tff(8823,plain,
% 2.52/2.79 ((s(s(s(elem!1))) = s(s(s(z)))) <=> (s(s(elem!1)) = s(s(s(z))))),
% 2.52/2.79 inference(monotonicity,[status(thm)],[8822])).
% 2.52/2.79 tff(8824,plain,
% 2.52/2.79 ((s(s(s(elem!1))) = s(s(s(z)))) <=> (s(s(s(z))) = s(s(elem!1)))),
% 2.52/2.79 inference(transitivity,[status(thm)],[8823, 4437])).
% 2.52/2.79 tff(8825,plain,
% 2.52/2.79 ((s(s(s(elem!1))) = s(s(s(z)))) <=> (s(s(elem!1)) = s(s(s(z))))),
% 2.52/2.79 inference(transitivity,[status(thm)],[8824, 5532])).
% 2.52/2.79 tff(8826,plain,
% 2.52/2.79 ((~(s(s(s(elem!1))) = s(s(s(z))))) <=> (~(s(s(elem!1)) = s(s(s(z)))))),
% 2.52/2.79 inference(monotonicity,[status(thm)],[8825])).
% 2.52/2.79 tff(8827,plain,
% 2.52/2.79 (~(s(s(elem!1)) = s(s(s(z))))),
% 2.52/2.79 inference(modus_ponens,[status(thm)],[140, 8826])).
% 2.52/2.79 tff(8828,plain,
% 2.52/2.79 (s(s(elem!1)) = s(s(s(elem!1)))),
% 2.52/2.79 inference(unit_resolution,[status(thm)],[50, 8822])).
% 2.52/2.79 tff(8829,plain,
% 2.52/2.79 (b(s(z), s(s(s(elem!1))))),
% 2.52/2.79 inference(unit_resolution,[status(thm)],[5500, 8828, 376])).
% 2.52/2.79 tff(8830,plain,
% 2.52/2.79 (~r(s(z), s(s(z)))),
% 2.52/2.79 inference(unit_resolution,[status(thm)],[347, 8812, 155, 97])).
% 2.52/2.79 tff(8831,plain,
% 2.52/2.79 (b(s(z), s(s(z)))),
% 2.52/2.79 inference(unit_resolution,[status(thm)],[427, 8830])).
% 2.52/2.79 tff(8832,plain,
% 2.52/2.79 (~b(s(s(s(elem!1))), s(s(z)))),
% 2.52/2.79 inference(unit_resolution,[status(thm)],[8478, 166, 376, 96, 310, 2682])).
% 2.52/2.79 tff(8833,plain,
% 2.52/2.79 (r(s(s(s(elem!1))), s(s(z)))),
% 2.52/2.79 inference(unit_resolution,[status(thm)],[218, 8832])).
% 2.52/2.79 tff(8834,plain,
% 2.52/2.79 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(s(s(z))), s(s(s(elem!1))))) | (~b(s(z), s(s(s(z))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(s(s(z))), s(s(s(elem!1))))) | (~b(s(z), s(s(s(z))))))),
% 2.52/2.79 inference(rewrite,[status(thm)],[])).
% 2.52/2.79 tff(8835,plain,
% 2.52/2.79 (((~b(s(z), s(s(s(z))))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(s(s(z))), s(s(s(elem!1))))) | (~b(s(z), s(s(s(elem!1))))) | (~b(s(z), s(s(s(z)))))) <=> ((~b(s(z), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(s(s(z))), s(s(s(elem!1))))) | (~b(s(z), s(s(s(z))))))),
% 2.52/2.79 inference(rewrite,[status(thm)],[])).
% 2.52/2.79 tff(8836,plain,
% 2.52/2.79 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(s(z))))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(s(s(z))), s(s(s(elem!1))))) | (~b(s(z), s(s(s(elem!1))))) | (~b(s(z), s(s(s(z))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(s(s(z))), s(s(s(elem!1))))) | (~b(s(z), s(s(s(z)))))))),
% 2.52/2.79 inference(monotonicity,[status(thm)],[8835])).
% 2.52/2.79 tff(8837,plain,
% 2.52/2.79 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(s(z))))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(s(s(z))), s(s(s(elem!1))))) | (~b(s(z), s(s(s(elem!1))))) | (~b(s(z), s(s(s(z))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(s(s(z))), s(s(s(elem!1))))) | (~b(s(z), s(s(s(z))))))),
% 2.52/2.79 inference(transitivity,[status(thm)],[8836, 8834])).
% 2.52/2.79 tff(8838,plain,
% 2.52/2.79 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(s(z))))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(s(s(z))), s(s(s(elem!1))))) | (~b(s(z), s(s(s(elem!1))))) | (~b(s(z), s(s(s(z))))))),
% 2.52/2.79 inference(quant_inst,[status(thm)],[])).
% 2.52/2.79 tff(8839,plain,
% 2.52/2.79 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(s(s(z))), s(s(s(elem!1))))) | (~b(s(z), s(s(s(z)))))),
% 2.52/2.79 inference(modus_ponens,[status(thm)],[8838, 8837])).
% 2.52/2.79 tff(8840,plain,
% 2.52/2.79 ($false),
% 2.52/2.79 inference(unit_resolution,[status(thm)],[8839, 166, 241, 96, 6552, 988])).
% 2.52/2.79 tff(8841,plain,((~b(s(s(s(elem!1))), s(z))) | (~b(s(z), s(s(s(elem!1))))) | (~b(s(s(s(z))), s(s(s(elem!1))))) | (~b(s(z), s(s(s(z)))))), inference(lemma,lemma(discharge,[]))).
% 2.52/2.79 tff(8842,plain,
% 2.52/2.79 (~b(s(s(s(z))), s(s(s(elem!1))))),
% 2.52/2.79 inference(unit_resolution,[status(thm)],[8841, 988, 96, 241])).
% 2.52/2.79 tff(8843,plain,
% 2.52/2.79 (~b(s(s(s(z))), elem!1)),
% 2.52/2.79 inference(unit_resolution,[status(thm)],[4078, 8842, 4031])).
% 2.52/2.79 tff(8844,plain,
% 2.52/2.79 (r(s(s(s(z))), elem!1)),
% 2.52/2.79 inference(unit_resolution,[status(thm)],[2826, 8843, 4027])).
% 2.52/2.79 tff(8845,plain,
% 2.52/2.79 (r(s(s(s(z))), s(s(elem!1)))),
% 2.52/2.79 inference(modus_ponens,[status(thm)],[8844, 4026])).
% 2.52/2.79 tff(8846,plain,
% 2.52/2.79 (r(s(s(s(z))), s(s(s(elem!1))))),
% 2.52/2.79 inference(modus_ponens,[status(thm)],[8845, 4024])).
% 2.52/2.79 tff(8847,plain,
% 2.52/2.79 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(z))), s(s(s(elem!1))))) | (~r(s(s(z)), s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), s(s(z)))) | (~r(s(s(s(z))), s(s(z)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(z))), s(s(s(elem!1))))) | (~r(s(s(z)), s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), s(s(z)))) | (~r(s(s(s(z))), s(s(z)))))),
% 2.52/2.79 inference(rewrite,[status(thm)],[])).
% 2.52/2.79 tff(8848,plain,
% 2.52/2.79 (((~r(s(s(s(elem!1))), s(s(z)))) | (~r(s(s(z)), s(s(s(elem!1))))) | (~r(s(s(s(z))), s(s(s(elem!1))))) | (~r(s(s(s(z))), s(s(z))))) <=> ((~r(s(s(s(z))), s(s(s(elem!1))))) | (~r(s(s(z)), s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), s(s(z)))) | (~r(s(s(s(z))), s(s(z)))))),
% 2.52/2.79 inference(rewrite,[status(thm)],[])).
% 2.52/2.79 tff(8849,plain,
% 2.52/2.79 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), s(s(z)))) | (~r(s(s(z)), s(s(s(elem!1))))) | (~r(s(s(s(z))), s(s(s(elem!1))))) | (~r(s(s(s(z))), s(s(z)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(z))), s(s(s(elem!1))))) | (~r(s(s(z)), s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), s(s(z)))) | (~r(s(s(s(z))), s(s(z))))))),
% 2.52/2.79 inference(monotonicity,[status(thm)],[8848])).
% 2.52/2.79 tff(8850,plain,
% 2.52/2.79 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), s(s(z)))) | (~r(s(s(z)), s(s(s(elem!1))))) | (~r(s(s(s(z))), s(s(s(elem!1))))) | (~r(s(s(s(z))), s(s(z)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(z))), s(s(s(elem!1))))) | (~r(s(s(z)), s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), s(s(z)))) | (~r(s(s(s(z))), s(s(z)))))),
% 2.52/2.79 inference(transitivity,[status(thm)],[8849, 8847])).
% 2.52/2.79 tff(8851,plain,
% 2.52/2.79 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), s(s(z)))) | (~r(s(s(z)), s(s(s(elem!1))))) | (~r(s(s(s(z))), s(s(s(elem!1))))) | (~r(s(s(s(z))), s(s(z)))))),
% 2.52/2.79 inference(quant_inst,[status(thm)],[])).
% 2.52/2.79 tff(8852,plain,
% 2.52/2.79 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(z))), s(s(s(elem!1))))) | (~r(s(s(z)), s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), s(s(z)))) | (~r(s(s(s(z))), s(s(z))))),
% 2.52/2.79 inference(modus_ponens,[status(thm)],[8851, 8850])).
% 2.52/2.79 tff(8853,plain,
% 2.52/2.79 ((~r(s(s(s(z))), s(s(s(elem!1))))) | (~r(s(s(s(z))), s(s(z))))),
% 2.52/2.79 inference(unit_resolution,[status(thm)],[8852, 197, 281, 464])).
% 2.52/2.79 tff(8854,plain,
% 2.52/2.79 (~r(s(s(s(z))), s(s(z)))),
% 2.52/2.79 inference(unit_resolution,[status(thm)],[8853, 8846])).
% 2.52/2.79 tff(8855,plain,
% 2.52/2.79 (b(s(s(s(z))), s(s(z)))),
% 2.52/2.79 inference(unit_resolution,[status(thm)],[1010, 8854])).
% 2.52/2.79 tff(8856,plain,
% 2.52/2.79 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(z))), s(s(s(elem!1))))) | (~r(s(s(z)), s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), s(s(z)))) | (~r(s(s(z)), s(s(s(z))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(z))), s(s(s(elem!1))))) | (~r(s(s(z)), s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), s(s(z)))) | (~r(s(s(z)), s(s(s(z))))))),
% 2.52/2.79 inference(rewrite,[status(thm)],[])).
% 2.52/2.79 tff(8857,plain,
% 2.52/2.79 (((~r(s(s(s(elem!1))), s(s(z)))) | (~r(s(s(s(z))), s(s(s(elem!1))))) | (~r(s(s(z)), s(s(s(elem!1))))) | (~r(s(s(z)), s(s(s(z)))))) <=> ((~r(s(s(s(z))), s(s(s(elem!1))))) | (~r(s(s(z)), s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), s(s(z)))) | (~r(s(s(z)), s(s(s(z))))))),
% 2.52/2.79 inference(rewrite,[status(thm)],[])).
% 2.52/2.79 tff(8858,plain,
% 2.52/2.79 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), s(s(z)))) | (~r(s(s(s(z))), s(s(s(elem!1))))) | (~r(s(s(z)), s(s(s(elem!1))))) | (~r(s(s(z)), s(s(s(z))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(z))), s(s(s(elem!1))))) | (~r(s(s(z)), s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), s(s(z)))) | (~r(s(s(z)), s(s(s(z)))))))),
% 2.52/2.79 inference(monotonicity,[status(thm)],[8857])).
% 2.52/2.79 tff(8859,plain,
% 2.52/2.79 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), s(s(z)))) | (~r(s(s(s(z))), s(s(s(elem!1))))) | (~r(s(s(z)), s(s(s(elem!1))))) | (~r(s(s(z)), s(s(s(z))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(z))), s(s(s(elem!1))))) | (~r(s(s(z)), s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), s(s(z)))) | (~r(s(s(z)), s(s(s(z))))))),
% 2.52/2.79 inference(transitivity,[status(thm)],[8858, 8856])).
% 2.52/2.79 tff(8860,plain,
% 2.52/2.79 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), s(s(z)))) | (~r(s(s(s(z))), s(s(s(elem!1))))) | (~r(s(s(z)), s(s(s(elem!1))))) | (~r(s(s(z)), s(s(s(z))))))),
% 2.52/2.79 inference(quant_inst,[status(thm)],[])).
% 2.52/2.79 tff(8861,plain,
% 2.52/2.79 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(z))), s(s(s(elem!1))))) | (~r(s(s(z)), s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), s(s(z)))) | (~r(s(s(z)), s(s(s(z)))))),
% 2.52/2.79 inference(modus_ponens,[status(thm)],[8860, 8859])).
% 2.52/2.79 tff(8862,plain,
% 2.52/2.79 ((~r(s(s(s(z))), s(s(s(elem!1))))) | (~r(s(s(z)), s(s(s(z)))))),
% 2.52/2.79 inference(unit_resolution,[status(thm)],[8861, 197, 281, 464])).
% 2.52/2.79 tff(8863,plain,
% 2.52/2.79 (~r(s(s(z)), s(s(s(z))))),
% 2.52/2.79 inference(unit_resolution,[status(thm)],[8862, 8846])).
% 2.52/2.79 tff(8864,plain,
% 2.52/2.79 (b(s(s(z)), s(s(s(z))))),
% 2.52/2.80 inference(unit_resolution,[status(thm)],[1730, 8863])).
% 2.52/2.80 tff(8865,plain,
% 2.52/2.80 ($false),
% 2.52/2.80 inference(unit_resolution,[status(thm)],[996, 8864, 8855, 556, 988])).
% 2.52/2.80 tff(8866,plain,((~b(s(z), s(s(s(z))))) | (~b(s(z), s(s(z)))) | (~r(s(s(z)), s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), s(s(z)))) | (~(s(s(elem!1)) = s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(z), s(s(s(elem!1)))))), inference(lemma,lemma(discharge,[]))).
% 2.52/2.80 tff(8867,plain,
% 2.52/2.80 (~b(s(z), s(s(s(z))))),
% 2.52/2.80 inference(unit_resolution,[status(thm)],[8866, 8828, 8820, 8833, 8831, 96, 8829])).
% 2.52/2.80 tff(8868,plain,
% 2.52/2.80 (r(s(z), s(s(s(z))))),
% 2.52/2.80 inference(unit_resolution,[status(thm)],[1674, 8867])).
% 2.52/2.80 tff(8869,plain,
% 2.52/2.80 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(z))) | (~r(s(z), z)) | (~r(s(s(s(z))), z)) | (~r(s(z), s(s(s(z))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, s(z))) | (~r(s(z), z)) | (~r(s(s(s(z))), z)) | (~r(s(z), s(s(s(z))))))),
% 2.62/2.80 inference(rewrite,[status(thm)],[])).
% 2.62/2.80 tff(8870,plain,
% 2.62/2.80 (((~r(z, s(z))) | (~r(s(s(s(z))), z)) | (~r(s(z), z)) | (~r(s(z), s(s(s(z)))))) <=> ((~r(z, s(z))) | (~r(s(z), z)) | (~r(s(s(s(z))), z)) | (~r(s(z), s(s(s(z))))))),
% 2.62/2.80 inference(rewrite,[status(thm)],[])).
% 2.62/2.80 tff(8871,plain,
% 2.62/2.80 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(z))) | (~r(s(s(s(z))), z)) | (~r(s(z), z)) | (~r(s(z), s(s(s(z))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(z))) | (~r(s(z), z)) | (~r(s(s(s(z))), z)) | (~r(s(z), s(s(s(z)))))))),
% 2.62/2.80 inference(monotonicity,[status(thm)],[8870])).
% 2.62/2.80 tff(8872,plain,
% 2.62/2.80 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(z))) | (~r(s(s(s(z))), z)) | (~r(s(z), z)) | (~r(s(z), s(s(s(z))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, s(z))) | (~r(s(z), z)) | (~r(s(s(s(z))), z)) | (~r(s(z), s(s(s(z))))))),
% 2.62/2.80 inference(transitivity,[status(thm)],[8871, 8869])).
% 2.62/2.80 tff(8873,plain,
% 2.62/2.80 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(z))) | (~r(s(s(s(z))), z)) | (~r(s(z), z)) | (~r(s(z), s(s(s(z))))))),
% 2.62/2.80 inference(quant_inst,[status(thm)],[])).
% 2.62/2.80 tff(8874,plain,
% 2.62/2.80 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, s(z))) | (~r(s(z), z)) | (~r(s(s(s(z))), z)) | (~r(s(z), s(s(s(z)))))),
% 2.62/2.80 inference(modus_ponens,[status(thm)],[8873, 8872])).
% 2.62/2.80 tff(8875,plain,
% 2.62/2.80 ($false),
% 2.62/2.80 inference(unit_resolution,[status(thm)],[8874, 197, 323, 97, 1733, 1653])).
% 2.62/2.80 tff(8876,plain,((~r(s(s(s(z))), z)) | (~r(z, s(z))) | (~r(s(z), z)) | (~r(s(z), s(s(s(z)))))), inference(lemma,lemma(discharge,[]))).
% 2.62/2.80 tff(8877,plain,
% 2.62/2.80 (~r(s(s(s(z))), z)),
% 2.62/2.80 inference(unit_resolution,[status(thm)],[8876, 8868, 323, 97])).
% 2.62/2.80 tff(8878,plain,
% 2.62/2.80 (b(s(s(s(z))), z)),
% 2.62/2.80 inference(unit_resolution,[status(thm)],[1713, 8877])).
% 2.62/2.80 tff(8879,plain,
% 2.62/2.80 (~r(s(s(elem!1)), z)),
% 2.62/2.80 inference(unit_resolution,[status(thm)],[2974, 8828, 86])).
% 2.62/2.80 tff(8880,plain,
% 2.62/2.80 (b(s(s(elem!1)), z)),
% 2.62/2.80 inference(unit_resolution,[status(thm)],[608, 8879])).
% 2.62/2.80 tff(8881,plain,
% 2.62/2.80 (~r(z, s(s(elem!1)))),
% 2.62/2.80 inference(unit_resolution,[status(thm)],[2079, 2691, 155, 52, 8811])).
% 2.62/2.80 tff(8882,plain,
% 2.62/2.80 (b(z, s(s(elem!1)))),
% 2.62/2.80 inference(unit_resolution,[status(thm)],[1795, 8881])).
% 2.62/2.80 tff(8883,plain,
% 2.62/2.80 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(elem!1)))) | (~b(s(s(elem!1)), z)) | (~b(s(s(elem!1)), s(z))) | (~b(s(s(s(z))), z)) | (~b(s(s(elem!1)), s(s(s(z))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(s(elem!1)))) | (~b(s(s(elem!1)), z)) | (~b(s(s(elem!1)), s(z))) | (~b(s(s(s(z))), z)) | (~b(s(s(elem!1)), s(s(s(z))))))),
% 2.62/2.80 inference(rewrite,[status(thm)],[])).
% 2.62/2.80 tff(8884,plain,
% 2.62/2.80 (((~b(s(s(elem!1)), s(z))) | (~b(s(s(elem!1)), s(z))) | (~b(z, s(s(elem!1)))) | (~b(s(s(s(z))), z)) | (~b(s(s(elem!1)), z)) | (~b(s(s(elem!1)), s(s(s(z)))))) <=> ((~b(z, s(s(elem!1)))) | (~b(s(s(elem!1)), z)) | (~b(s(s(elem!1)), s(z))) | (~b(s(s(s(z))), z)) | (~b(s(s(elem!1)), s(s(s(z))))))),
% 2.62/2.80 inference(rewrite,[status(thm)],[])).
% 2.62/2.80 tff(8885,plain,
% 2.62/2.80 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), s(z))) | (~b(s(s(elem!1)), s(z))) | (~b(z, s(s(elem!1)))) | (~b(s(s(s(z))), z)) | (~b(s(s(elem!1)), z)) | (~b(s(s(elem!1)), s(s(s(z))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(elem!1)))) | (~b(s(s(elem!1)), z)) | (~b(s(s(elem!1)), s(z))) | (~b(s(s(s(z))), z)) | (~b(s(s(elem!1)), s(s(s(z)))))))),
% 2.62/2.80 inference(monotonicity,[status(thm)],[8884])).
% 2.62/2.80 tff(8886,plain,
% 2.62/2.80 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), s(z))) | (~b(s(s(elem!1)), s(z))) | (~b(z, s(s(elem!1)))) | (~b(s(s(s(z))), z)) | (~b(s(s(elem!1)), z)) | (~b(s(s(elem!1)), s(s(s(z))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(s(elem!1)))) | (~b(s(s(elem!1)), z)) | (~b(s(s(elem!1)), s(z))) | (~b(s(s(s(z))), z)) | (~b(s(s(elem!1)), s(s(s(z))))))),
% 2.62/2.80 inference(transitivity,[status(thm)],[8885, 8883])).
% 2.62/2.80 tff(8887,plain,
% 2.62/2.80 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), s(z))) | (~b(s(s(elem!1)), s(z))) | (~b(z, s(s(elem!1)))) | (~b(s(s(s(z))), z)) | (~b(s(s(elem!1)), z)) | (~b(s(s(elem!1)), s(s(s(z))))))),
% 2.62/2.80 inference(quant_inst,[status(thm)],[])).
% 2.62/2.80 tff(8888,plain,
% 2.62/2.80 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(s(elem!1)))) | (~b(s(s(elem!1)), z)) | (~b(s(s(elem!1)), s(z))) | (~b(s(s(s(z))), z)) | (~b(s(s(elem!1)), s(s(s(z)))))),
% 2.62/2.80 inference(modus_ponens,[status(thm)],[8887, 8886])).
% 2.62/2.80 tff(8889,plain,
% 2.62/2.80 (~b(s(s(elem!1)), s(s(s(z))))),
% 2.62/2.80 inference(unit_resolution,[status(thm)],[8888, 166, 8882, 310, 8880, 8878])).
% 2.62/2.80 tff(8890,plain,
% 2.62/2.80 (r(s(s(elem!1)), s(s(s(z))))),
% 2.62/2.80 inference(unit_resolution,[status(thm)],[5091, 79, 8889, 8827])).
% 2.62/2.80 tff(8891,plain,
% 2.62/2.80 (s(s(s(elem!1))) = s(elem!1)),
% 2.62/2.80 inference(unit_resolution,[status(thm)],[2594, 8828])).
% 2.62/2.80 tff(8892,plain,
% 2.62/2.80 (s(elem!1) = s(s(s(elem!1)))),
% 2.62/2.80 inference(symmetry,[status(thm)],[8891])).
% 2.62/2.80 tff(8893,plain,
% 2.62/2.80 (s(elem!1) = s(s(elem!1))),
% 2.62/2.80 inference(transitivity,[status(thm)],[8892, 8822])).
% 2.62/2.80 tff(8894,plain,
% 2.62/2.80 (inj_0(s(elem!1)) = inj_0(s(s(elem!1)))),
% 2.62/2.80 inference(monotonicity,[status(thm)],[8893])).
% 2.62/2.80 tff(8895,plain,
% 2.62/2.80 (elem!1 = s(s(elem!1))),
% 2.62/2.80 inference(transitivity,[status(thm)],[1170, 8894, 38, 8892, 8822])).
% 2.62/2.80 tff(8896,plain,
% 2.62/2.80 (r(s(s(s(z))), elem!1) <=> r(s(s(s(z))), s(s(elem!1)))),
% 2.62/2.80 inference(monotonicity,[status(thm)],[8895])).
% 2.62/2.80 tff(8897,plain,
% 2.62/2.80 (~(s(s(s(z))) = elem!1)),
% 2.62/2.80 inference(unit_resolution,[status(thm)],[3122, 8828])).
% 2.62/2.80 tff(8898,plain,
% 2.62/2.80 (((~b(s(s(elem!1)), z)) | (~b(s(s(s(z))), z)) | (~b(z, s(s(elem!1)))) | (~b(s(s(elem!1)), z)) | (~b(s(s(s(z))), z)) | (~b(s(s(s(z))), s(s(elem!1))))) <=> ((~b(z, s(s(elem!1)))) | (~b(s(s(elem!1)), z)) | (~b(s(s(s(z))), z)) | (~b(s(s(s(z))), s(s(elem!1)))))),
% 2.62/2.80 inference(rewrite,[status(thm)],[])).
% 2.62/2.80 tff(8899,plain,
% 2.62/2.80 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), z)) | (~b(s(s(s(z))), z)) | (~b(z, s(s(elem!1)))) | (~b(s(s(elem!1)), z)) | (~b(s(s(s(z))), z)) | (~b(s(s(s(z))), s(s(elem!1)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(elem!1)))) | (~b(s(s(elem!1)), z)) | (~b(s(s(s(z))), z)) | (~b(s(s(s(z))), s(s(elem!1))))))),
% 2.62/2.80 inference(monotonicity,[status(thm)],[8898])).
% 2.62/2.80 tff(8900,plain,
% 2.62/2.80 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), z)) | (~b(s(s(s(z))), z)) | (~b(z, s(s(elem!1)))) | (~b(s(s(elem!1)), z)) | (~b(s(s(s(z))), z)) | (~b(s(s(s(z))), s(s(elem!1)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(s(elem!1)))) | (~b(s(s(elem!1)), z)) | (~b(s(s(s(z))), z)) | (~b(s(s(s(z))), s(s(elem!1)))))),
% 2.62/2.80 inference(transitivity,[status(thm)],[8899, 4527])).
% 2.62/2.80 tff(8901,plain,
% 2.62/2.80 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), z)) | (~b(s(s(s(z))), z)) | (~b(z, s(s(elem!1)))) | (~b(s(s(elem!1)), z)) | (~b(s(s(s(z))), z)) | (~b(s(s(s(z))), s(s(elem!1)))))),
% 2.62/2.80 inference(quant_inst,[status(thm)],[])).
% 2.62/2.80 tff(8902,plain,
% 2.62/2.80 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(s(elem!1)))) | (~b(s(s(elem!1)), z)) | (~b(s(s(s(z))), z)) | (~b(s(s(s(z))), s(s(elem!1))))),
% 2.62/2.80 inference(modus_ponens,[status(thm)],[8901, 8900])).
% 2.62/2.80 tff(8903,plain,
% 2.62/2.80 (~b(s(s(s(z))), s(s(elem!1)))),
% 2.62/2.80 inference(unit_resolution,[status(thm)],[8902, 166, 8882, 8880, 8878])).
% 2.62/2.80 tff(8904,plain,
% 2.62/2.80 (b(s(s(s(z))), s(s(elem!1))) <=> b(s(s(s(z))), s(s(s(elem!1))))),
% 2.62/2.80 inference(monotonicity,[status(thm)],[8229])).
% 2.62/2.80 tff(8905,plain,
% 2.62/2.80 (b(s(s(s(z))), s(s(s(elem!1)))) <=> b(s(s(s(z))), s(s(elem!1)))),
% 2.62/2.80 inference(symmetry,[status(thm)],[8904])).
% 2.62/2.80 tff(8906,plain,
% 2.62/2.80 (b(s(s(s(z))), s(s(elem!1)))),
% 2.62/2.80 inference(modus_ponens,[status(thm)],[6552, 8905])).
% 2.62/2.80 tff(8907,assumption,(~b(s(s(s(z))), s(s(elem!1)))), introduced(assumption)).
% 2.62/2.80 tff(8908,plain,
% 2.62/2.80 ($false),
% 2.62/2.80 inference(unit_resolution,[status(thm)],[8907, 8906])).
% 2.62/2.80 tff(8909,plain,(b(s(s(s(z))), s(s(elem!1))) | (~b(s(s(s(z))), s(s(s(elem!1))))) | (~(s(s(s(elem!1))) = s(s(elem!1))))), inference(lemma,lemma(discharge,[]))).
% 2.62/2.80 tff(8910,plain,
% 2.62/2.80 (~b(s(s(s(z))), s(s(s(elem!1))))),
% 2.62/2.80 inference(unit_resolution,[status(thm)],[8909, 8903, 8822])).
% 2.62/2.80 tff(8911,plain,
% 2.62/2.80 (~b(s(s(s(z))), elem!1)),
% 2.62/2.80 inference(unit_resolution,[status(thm)],[4078, 8910, 8822])).
% 2.62/2.80 tff(8912,plain,
% 2.62/2.80 (r(s(s(s(z))), elem!1)),
% 2.62/2.80 inference(unit_resolution,[status(thm)],[2826, 8911, 8897])).
% 2.62/2.80 tff(8913,plain,
% 2.62/2.80 (r(s(s(s(z))), s(s(elem!1)))),
% 2.62/2.80 inference(modus_ponens,[status(thm)],[8912, 8896])).
% 2.62/2.80 tff(8914,plain,
% 2.62/2.80 (~r(s(s(z)), s(s(s(z))))),
% 2.62/2.80 inference(unit_resolution,[status(thm)],[4415, 197, 2692, 8812, 8913])).
% 2.62/2.80 tff(8915,plain,
% 2.62/2.80 (b(s(s(z)), s(s(s(z))))),
% 2.62/2.80 inference(unit_resolution,[status(thm)],[1730, 8914])).
% 2.62/2.80 tff(8916,plain,
% 2.62/2.80 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(elem!1)))) | (~b(s(s(elem!1)), s(z))) | (~b(s(s(z)), z)) | (~b(s(s(z)), s(z))) | (~b(s(s(s(z))), z)) | (~b(s(s(z)), s(s(s(z))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(s(elem!1)))) | (~b(s(s(elem!1)), s(z))) | (~b(s(s(z)), z)) | (~b(s(s(z)), s(z))) | (~b(s(s(s(z))), z)) | (~b(s(s(z)), s(s(s(z))))))),
% 2.62/2.80 inference(rewrite,[status(thm)],[])).
% 2.62/2.80 tff(8917,plain,
% 2.62/2.80 (((~b(s(s(elem!1)), s(z))) | (~b(s(s(z)), s(z))) | (~b(z, s(s(elem!1)))) | (~b(s(s(s(z))), z)) | (~b(s(s(z)), z)) | (~b(s(s(z)), s(s(s(z)))))) <=> ((~b(z, s(s(elem!1)))) | (~b(s(s(elem!1)), s(z))) | (~b(s(s(z)), z)) | (~b(s(s(z)), s(z))) | (~b(s(s(s(z))), z)) | (~b(s(s(z)), s(s(s(z))))))),
% 2.62/2.80 inference(rewrite,[status(thm)],[])).
% 2.62/2.80 tff(8918,plain,
% 2.62/2.80 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), s(z))) | (~b(s(s(z)), s(z))) | (~b(z, s(s(elem!1)))) | (~b(s(s(s(z))), z)) | (~b(s(s(z)), z)) | (~b(s(s(z)), s(s(s(z))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(elem!1)))) | (~b(s(s(elem!1)), s(z))) | (~b(s(s(z)), z)) | (~b(s(s(z)), s(z))) | (~b(s(s(s(z))), z)) | (~b(s(s(z)), s(s(s(z)))))))),
% 2.62/2.80 inference(monotonicity,[status(thm)],[8917])).
% 2.62/2.80 tff(8919,plain,
% 2.62/2.80 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), s(z))) | (~b(s(s(z)), s(z))) | (~b(z, s(s(elem!1)))) | (~b(s(s(s(z))), z)) | (~b(s(s(z)), z)) | (~b(s(s(z)), s(s(s(z))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(s(elem!1)))) | (~b(s(s(elem!1)), s(z))) | (~b(s(s(z)), z)) | (~b(s(s(z)), s(z))) | (~b(s(s(s(z))), z)) | (~b(s(s(z)), s(s(s(z))))))),
% 2.62/2.80 inference(transitivity,[status(thm)],[8918, 8916])).
% 2.62/2.80 tff(8920,plain,
% 2.62/2.80 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), s(z))) | (~b(s(s(z)), s(z))) | (~b(z, s(s(elem!1)))) | (~b(s(s(s(z))), z)) | (~b(s(s(z)), z)) | (~b(s(s(z)), s(s(s(z))))))),
% 2.62/2.80 inference(quant_inst,[status(thm)],[])).
% 2.62/2.80 tff(8921,plain,
% 2.62/2.80 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(s(elem!1)))) | (~b(s(s(elem!1)), s(z))) | (~b(s(s(z)), z)) | (~b(s(s(z)), s(z))) | (~b(s(s(s(z))), z)) | (~b(s(s(z)), s(s(s(z)))))),
% 2.62/2.80 inference(modus_ponens,[status(thm)],[8920, 8919])).
% 2.62/2.80 tff(8922,plain,
% 2.62/2.80 ((~b(s(s(z)), z)) | (~b(s(s(z)), s(s(s(z)))))),
% 2.62/2.80 inference(unit_resolution,[status(thm)],[8921, 166, 8882, 310, 2682, 8878])).
% 2.62/2.80 tff(8923,plain,
% 2.62/2.80 (~b(s(s(z)), z)),
% 2.62/2.80 inference(unit_resolution,[status(thm)],[8922, 8915])).
% 2.62/2.80 tff(8924,plain,
% 2.62/2.80 (r(s(s(z)), z)),
% 2.62/2.80 inference(unit_resolution,[status(thm)],[186, 8923])).
% 2.62/2.80 tff(8925,plain,
% 2.62/2.80 (~r(s(s(s(s(z)))), z)),
% 2.62/2.80 inference(unit_resolution,[status(thm)],[7728, 8924, 155, 97, 2682, 8831])).
% 2.62/2.80 tff(8926,plain,
% 2.62/2.80 (b(s(s(s(s(z)))), z)),
% 2.62/2.80 inference(unit_resolution,[status(thm)],[3266, 8925])).
% 2.62/2.80 tff(8927,plain,
% 2.62/2.80 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(elem!1)))) | (~b(s(s(elem!1)), z)) | (~b(s(s(s(z))), z)) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(s(z)))), z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(s(elem!1)))) | (~b(s(s(elem!1)), z)) | (~b(s(s(s(z))), z)) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(s(z)))), z)))),
% 2.62/2.80 inference(rewrite,[status(thm)],[])).
% 2.62/2.80 tff(8928,plain,
% 2.62/2.80 (((~b(s(s(elem!1)), z)) | (~b(s(s(s(s(z)))), z)) | (~b(z, s(s(elem!1)))) | (~b(s(s(s(z))), z)) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(s(z)))), s(s(s(z)))))) <=> ((~b(z, s(s(elem!1)))) | (~b(s(s(elem!1)), z)) | (~b(s(s(s(z))), z)) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(s(z)))), z)))),
% 2.62/2.80 inference(rewrite,[status(thm)],[])).
% 2.62/2.80 tff(8929,plain,
% 2.62/2.80 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), z)) | (~b(s(s(s(s(z)))), z)) | (~b(z, s(s(elem!1)))) | (~b(s(s(s(z))), z)) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(s(z)))), s(s(s(z))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(elem!1)))) | (~b(s(s(elem!1)), z)) | (~b(s(s(s(z))), z)) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(s(z)))), z))))),
% 2.62/2.80 inference(monotonicity,[status(thm)],[8928])).
% 2.62/2.80 tff(8930,plain,
% 2.62/2.80 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), z)) | (~b(s(s(s(s(z)))), z)) | (~b(z, s(s(elem!1)))) | (~b(s(s(s(z))), z)) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(s(z)))), s(s(s(z))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(s(elem!1)))) | (~b(s(s(elem!1)), z)) | (~b(s(s(s(z))), z)) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(s(z)))), z)))),
% 2.62/2.80 inference(transitivity,[status(thm)],[8929, 8927])).
% 2.62/2.80 tff(8931,plain,
% 2.62/2.80 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), z)) | (~b(s(s(s(s(z)))), z)) | (~b(z, s(s(elem!1)))) | (~b(s(s(s(z))), z)) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(s(z)))), s(s(s(z))))))),
% 2.62/2.80 inference(quant_inst,[status(thm)],[])).
% 2.62/2.80 tff(8932,plain,
% 2.62/2.80 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(s(elem!1)))) | (~b(s(s(elem!1)), z)) | (~b(s(s(s(z))), z)) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(s(z)))), z))),
% 2.62/2.80 inference(modus_ponens,[status(thm)],[8931, 8930])).
% 2.62/2.80 tff(8933,plain,
% 2.62/2.80 (~b(s(s(s(s(z)))), s(s(s(z))))),
% 2.62/2.80 inference(unit_resolution,[status(thm)],[8932, 166, 8882, 8880, 8878, 8926])).
% 2.62/2.80 tff(8934,plain,
% 2.62/2.80 (r(s(s(s(s(z)))), s(s(s(z))))),
% 2.62/2.80 inference(unit_resolution,[status(thm)],[4662, 8933])).
% 2.62/2.80 tff(8935,plain,
% 2.62/2.80 (b(z, s(s(s(elem!1))))),
% 2.62/2.80 inference(unit_resolution,[status(thm)],[8327, 8822, 8882])).
% 2.62/2.80 tff(8936,plain,
% 2.62/2.80 (~b(s(s(s(z))), s(s(s(s(z)))))),
% 2.62/2.80 inference(unit_resolution,[status(thm)],[7772, 8926, 95, 8935, 8878])).
% 2.62/2.80 tff(8937,plain,
% 2.62/2.80 (r(s(s(s(z))), s(s(s(s(z)))))),
% 2.62/2.80 inference(unit_resolution,[status(thm)],[2233, 8936])).
% 2.62/2.80 tff(8938,plain,
% 2.62/2.80 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(z)))), s(s(s(z))))) | (~r(s(s(s(z))), s(s(s(s(z)))))) | (~r(s(s(elem!1)), s(s(s(z))))) | (~r(s(s(elem!1)), s(s(s(s(z)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(s(z)))), s(s(s(z))))) | (~r(s(s(s(z))), s(s(s(s(z)))))) | (~r(s(s(elem!1)), s(s(s(z))))) | (~r(s(s(elem!1)), s(s(s(s(z)))))))),
% 2.62/2.80 inference(rewrite,[status(thm)],[])).
% 2.62/2.80 tff(8939,plain,
% 2.62/2.80 (((~r(s(s(s(z))), s(s(s(s(z)))))) | (~r(s(s(s(s(z)))), s(s(s(z))))) | (~r(s(s(elem!1)), s(s(s(z))))) | (~r(s(s(elem!1)), s(s(s(s(z))))))) <=> ((~r(s(s(s(s(z)))), s(s(s(z))))) | (~r(s(s(s(z))), s(s(s(s(z)))))) | (~r(s(s(elem!1)), s(s(s(z))))) | (~r(s(s(elem!1)), s(s(s(s(z)))))))),
% 2.62/2.80 inference(rewrite,[status(thm)],[])).
% 2.62/2.80 tff(8940,plain,
% 2.62/2.80 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(z))), s(s(s(s(z)))))) | (~r(s(s(s(s(z)))), s(s(s(z))))) | (~r(s(s(elem!1)), s(s(s(z))))) | (~r(s(s(elem!1)), s(s(s(s(z)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(z)))), s(s(s(z))))) | (~r(s(s(s(z))), s(s(s(s(z)))))) | (~r(s(s(elem!1)), s(s(s(z))))) | (~r(s(s(elem!1)), s(s(s(s(z))))))))),
% 2.62/2.80 inference(monotonicity,[status(thm)],[8939])).
% 2.62/2.80 tff(8941,plain,
% 2.62/2.80 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(z))), s(s(s(s(z)))))) | (~r(s(s(s(s(z)))), s(s(s(z))))) | (~r(s(s(elem!1)), s(s(s(z))))) | (~r(s(s(elem!1)), s(s(s(s(z)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(s(z)))), s(s(s(z))))) | (~r(s(s(s(z))), s(s(s(s(z)))))) | (~r(s(s(elem!1)), s(s(s(z))))) | (~r(s(s(elem!1)), s(s(s(s(z)))))))),
% 2.62/2.80 inference(transitivity,[status(thm)],[8940, 8938])).
% 2.62/2.81 tff(8942,plain,
% 2.62/2.81 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(z))), s(s(s(s(z)))))) | (~r(s(s(s(s(z)))), s(s(s(z))))) | (~r(s(s(elem!1)), s(s(s(z))))) | (~r(s(s(elem!1)), s(s(s(s(z)))))))),
% 2.62/2.81 inference(quant_inst,[status(thm)],[])).
% 2.62/2.81 tff(8943,plain,
% 2.62/2.81 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(s(z)))), s(s(s(z))))) | (~r(s(s(s(z))), s(s(s(s(z)))))) | (~r(s(s(elem!1)), s(s(s(z))))) | (~r(s(s(elem!1)), s(s(s(s(z))))))),
% 2.62/2.81 inference(modus_ponens,[status(thm)],[8942, 8941])).
% 2.62/2.81 tff(8944,plain,
% 2.62/2.81 (~r(s(s(elem!1)), s(s(s(s(z)))))),
% 2.62/2.81 inference(unit_resolution,[status(thm)],[8943, 197, 8937, 8934, 8890])).
% 2.62/2.81 tff(8945,plain,
% 2.62/2.81 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(elem!1)))) | (~b(s(s(elem!1)), z)) | (~b(s(s(elem!1)), s(z))) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(elem!1)), s(s(s(s(z)))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(s(elem!1)))) | (~b(s(s(elem!1)), z)) | (~b(s(s(elem!1)), s(z))) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(elem!1)), s(s(s(s(z)))))))),
% 2.62/2.81 inference(rewrite,[status(thm)],[])).
% 2.62/2.81 tff(8946,plain,
% 2.62/2.81 (((~b(s(s(elem!1)), s(z))) | (~b(s(s(elem!1)), s(z))) | (~b(z, s(s(elem!1)))) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(elem!1)), z)) | (~b(s(s(elem!1)), s(s(s(s(z))))))) <=> ((~b(z, s(s(elem!1)))) | (~b(s(s(elem!1)), z)) | (~b(s(s(elem!1)), s(z))) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(elem!1)), s(s(s(s(z)))))))),
% 2.62/2.81 inference(rewrite,[status(thm)],[])).
% 2.62/2.81 tff(8947,plain,
% 2.62/2.81 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), s(z))) | (~b(s(s(elem!1)), s(z))) | (~b(z, s(s(elem!1)))) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(elem!1)), z)) | (~b(s(s(elem!1)), s(s(s(s(z)))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(elem!1)))) | (~b(s(s(elem!1)), z)) | (~b(s(s(elem!1)), s(z))) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(elem!1)), s(s(s(s(z))))))))),
% 2.62/2.81 inference(monotonicity,[status(thm)],[8946])).
% 2.62/2.81 tff(8948,plain,
% 2.62/2.81 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), s(z))) | (~b(s(s(elem!1)), s(z))) | (~b(z, s(s(elem!1)))) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(elem!1)), z)) | (~b(s(s(elem!1)), s(s(s(s(z)))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(s(elem!1)))) | (~b(s(s(elem!1)), z)) | (~b(s(s(elem!1)), s(z))) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(elem!1)), s(s(s(s(z)))))))),
% 2.62/2.81 inference(transitivity,[status(thm)],[8947, 8945])).
% 2.62/2.81 tff(8949,plain,
% 2.62/2.81 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), s(z))) | (~b(s(s(elem!1)), s(z))) | (~b(z, s(s(elem!1)))) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(elem!1)), z)) | (~b(s(s(elem!1)), s(s(s(s(z)))))))),
% 2.62/2.81 inference(quant_inst,[status(thm)],[])).
% 2.62/2.81 tff(8950,plain,
% 2.62/2.81 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(s(elem!1)))) | (~b(s(s(elem!1)), z)) | (~b(s(s(elem!1)), s(z))) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(elem!1)), s(s(s(s(z))))))),
% 2.62/2.81 inference(modus_ponens,[status(thm)],[8949, 8948])).
% 2.62/2.81 tff(8951,plain,
% 2.62/2.81 (~b(s(s(elem!1)), s(s(s(s(z)))))),
% 2.62/2.81 inference(unit_resolution,[status(thm)],[8950, 166, 8882, 310, 8880, 8926])).
% 2.62/2.81 tff(8952,plain,
% 2.62/2.81 (((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((s(s(elem!1)) = s(s(s(s(z))))) | b(s(s(elem!1)), s(s(s(s(z))))) | r(s(s(elem!1)), s(s(s(s(z))))))) <=> ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (s(s(elem!1)) = s(s(s(s(z))))) | b(s(s(elem!1)), s(s(s(s(z))))) | r(s(s(elem!1)), s(s(s(s(z))))))),
% 2.62/2.81 inference(rewrite,[status(thm)],[])).
% 2.62/2.81 tff(8953,plain,
% 2.62/2.81 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((s(s(elem!1)) = s(s(s(s(z))))) | b(s(s(elem!1)), s(s(s(s(z))))) | r(s(s(elem!1)), s(s(s(s(z))))))),
% 2.62/2.81 inference(quant_inst,[status(thm)],[])).
% 2.62/2.81 tff(8954,plain,
% 2.62/2.81 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (s(s(elem!1)) = s(s(s(s(z))))) | b(s(s(elem!1)), s(s(s(s(z))))) | r(s(s(elem!1)), s(s(s(s(z)))))),
% 2.62/2.81 inference(modus_ponens,[status(thm)],[8953, 8952])).
% 2.62/2.81 tff(8955,plain,
% 2.62/2.81 (s(s(elem!1)) = s(s(s(s(z))))),
% 2.62/2.81 inference(unit_resolution,[status(thm)],[8954, 79, 8951, 8944])).
% 2.62/2.81 tff(8956,plain,
% 2.62/2.81 (elem!1 = s(s(s(s(z))))),
% 2.62/2.81 inference(transitivity,[status(thm)],[1170, 8894, 38, 8892, 8822, 8955])).
% 2.62/2.81 tff(8957,plain,
% 2.62/2.81 (s(s(s(s(elem!1)))) = s(s(s(elem!1)))),
% 2.62/2.81 inference(monotonicity,[status(thm)],[8822])).
% 2.62/2.81 tff(8958,plain,
% 2.62/2.81 (s(s(s(elem!1))) = s(s(s(s(elem!1))))),
% 2.62/2.81 inference(symmetry,[status(thm)],[8957])).
% 2.62/2.81 tff(8959,plain,
% 2.62/2.81 (s(s(elem!1)) = s(s(s(elem!1)))),
% 2.62/2.81 inference(symmetry,[status(thm)],[8822])).
% 2.62/2.81 tff(8960,plain,
% 2.62/2.81 (s(s(elem!1)) = s(s(s(s(elem!1))))),
% 2.62/2.81 inference(transitivity,[status(thm)],[8959, 8958])).
% 2.62/2.81 tff(8961,plain,
% 2.62/2.81 (~(elem!1 = s(s(s(s(z)))))),
% 2.62/2.81 inference(unit_resolution,[status(thm)],[5489, 8960])).
% 2.62/2.81 tff(8962,plain,
% 2.62/2.81 ($false),
% 2.62/2.81 inference(unit_resolution,[status(thm)],[8961, 8956])).
% 2.62/2.81 tff(8963,plain,((~r(s(z), z)) | (~b(s(s(elem!1)), s(z))) | (~r(z, s(s(z)))) | (~r(z, s(z))) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(z), s(s(elem!1)))) | r(s(s(s(elem!1))), z) | (s(s(z)) = s(s(elem!1)))), inference(lemma,lemma(discharge,[]))).
% 2.62/2.81 tff(8964,plain,
% 2.62/2.81 (~r(s(z), z)),
% 2.62/2.81 inference(unit_resolution,[status(thm)],[8963, 52, 155, 323, 96, 376, 86, 310])).
% 2.62/2.81 tff(8965,plain,
% 2.62/2.81 (b(s(z), z)),
% 2.62/2.81 inference(unit_resolution,[status(thm)],[230, 8964])).
% 2.62/2.81 tff(8966,plain,
% 2.62/2.81 (s(s(elem!1)) = s(s(s(elem!1)))),
% 2.62/2.81 inference(unit_resolution,[status(thm)],[2253, 8965, 155, 323, 310])).
% 2.62/2.81 tff(8967,plain,
% 2.62/2.81 (b(s(s(elem!1)), s(s(z))) <=> b(s(s(s(elem!1))), s(s(z)))),
% 2.62/2.81 inference(monotonicity,[status(thm)],[8966])).
% 2.62/2.81 tff(8968,plain,
% 2.62/2.81 (~b(z, s(s(elem!1)))),
% 2.62/2.81 inference(unit_resolution,[status(thm)],[8791, 8965, 310, 376])).
% 2.62/2.81 tff(8969,plain,
% 2.62/2.81 (r(z, s(s(elem!1)))),
% 2.62/2.81 inference(unit_resolution,[status(thm)],[1795, 8968])).
% 2.62/2.81 tff(8970,plain,
% 2.62/2.81 (~b(z, s(s(s(elem!1))))),
% 2.62/2.81 inference(unit_resolution,[status(thm)],[4345, 8968, 8966])).
% 2.62/2.81 tff(8971,plain,
% 2.62/2.81 (r(z, s(s(s(elem!1))))),
% 2.62/2.81 inference(unit_resolution,[status(thm)],[261, 8970])).
% 2.62/2.81 tff(8972,plain,
% 2.62/2.81 (s(s(s(elem!1))) = s(s(elem!1))),
% 2.62/2.81 inference(symmetry,[status(thm)],[8966])).
% 2.62/2.81 tff(8973,plain,
% 2.62/2.81 (s(s(s(s(elem!1)))) = s(s(s(elem!1)))),
% 2.62/2.81 inference(monotonicity,[status(thm)],[8972])).
% 2.62/2.81 tff(8974,plain,
% 2.62/2.81 (b(s(s(s(s(elem!1)))), z) <=> b(s(s(s(elem!1))), z)),
% 2.62/2.81 inference(monotonicity,[status(thm)],[8973])).
% 2.62/2.81 tff(8975,plain,
% 2.62/2.81 (b(s(s(s(elem!1))), z) <=> b(s(s(s(s(elem!1)))), z)),
% 2.62/2.81 inference(symmetry,[status(thm)],[8974])).
% 2.62/2.81 tff(8976,plain,
% 2.62/2.81 (b(s(s(s(s(elem!1)))), z)),
% 2.62/2.81 inference(modus_ponens,[status(thm)],[95, 8975])).
% 2.62/2.81 tff(8977,plain,
% 2.62/2.81 (s(s(s(elem!1))) = s(elem!1)),
% 2.62/2.81 inference(unit_resolution,[status(thm)],[2594, 8966])).
% 2.62/2.81 tff(8978,plain,
% 2.62/2.81 (s(elem!1) = s(s(s(elem!1)))),
% 2.62/2.81 inference(symmetry,[status(thm)],[8977])).
% 2.62/2.81 tff(8979,plain,
% 2.62/2.81 (b(s(elem!1), z) <=> b(s(s(s(elem!1))), z)),
% 2.62/2.81 inference(monotonicity,[status(thm)],[8978])).
% 2.62/2.81 tff(8980,plain,
% 2.62/2.81 (b(s(s(s(elem!1))), z) <=> b(s(elem!1), z)),
% 2.62/2.81 inference(symmetry,[status(thm)],[8979])).
% 2.62/2.81 tff(8981,plain,
% 2.62/2.81 (b(s(elem!1), z)),
% 2.62/2.81 inference(modus_ponens,[status(thm)],[95, 8980])).
% 2.62/2.81 tff(8982,plain,
% 2.62/2.81 (b(s(s(s(s(elem!1)))), s(z)) <=> b(s(s(s(elem!1))), s(z))),
% 2.62/2.81 inference(monotonicity,[status(thm)],[8973])).
% 2.62/2.81 tff(8983,plain,
% 2.62/2.81 (b(s(s(s(elem!1))), s(z)) <=> b(s(s(s(s(elem!1)))), s(z))),
% 2.62/2.81 inference(symmetry,[status(thm)],[8982])).
% 2.62/2.81 tff(8984,plain,
% 2.62/2.81 (b(s(s(s(s(elem!1)))), s(z))),
% 2.62/2.81 inference(modus_ponens,[status(thm)],[96, 8983])).
% 2.62/2.81 tff(8985,plain,
% 2.62/2.81 (~r(s(s(s(elem!1))), s(s(z)))),
% 2.62/2.81 inference(unit_resolution,[status(thm)],[1588, 392, 155, 282])).
% 2.62/2.81 tff(8986,plain,
% 2.62/2.81 (b(s(s(s(elem!1))), s(s(z)))),
% 2.62/2.81 inference(unit_resolution,[status(thm)],[218, 8985])).
% 2.62/2.81 tff(8987,plain,
% 2.62/2.81 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(z))) | (~r(s(s(z)), s(z))) | (~r(z, s(s(z)))) | (~r(s(z), s(s(s(z))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, s(z))) | (~r(s(s(z)), s(z))) | (~r(z, s(s(z)))) | (~r(s(z), s(s(s(z))))))),
% 2.62/2.81 inference(rewrite,[status(thm)],[])).
% 2.62/2.81 tff(8988,plain,
% 2.62/2.81 (((~r(s(z), s(s(s(z))))) | (~r(s(s(z)), s(z))) | (~r(z, s(z))) | (~r(z, s(s(z))))) <=> ((~r(z, s(z))) | (~r(s(s(z)), s(z))) | (~r(z, s(s(z)))) | (~r(s(z), s(s(s(z))))))),
% 2.62/2.81 inference(rewrite,[status(thm)],[])).
% 2.62/2.81 tff(8989,plain,
% 2.62/2.81 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(s(s(z))))) | (~r(s(s(z)), s(z))) | (~r(z, s(z))) | (~r(z, s(s(z)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(z))) | (~r(s(s(z)), s(z))) | (~r(z, s(s(z)))) | (~r(s(z), s(s(s(z)))))))),
% 2.62/2.81 inference(monotonicity,[status(thm)],[8988])).
% 2.62/2.81 tff(8990,plain,
% 2.62/2.81 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(s(s(z))))) | (~r(s(s(z)), s(z))) | (~r(z, s(z))) | (~r(z, s(s(z)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, s(z))) | (~r(s(s(z)), s(z))) | (~r(z, s(s(z)))) | (~r(s(z), s(s(s(z))))))),
% 2.62/2.81 inference(transitivity,[status(thm)],[8989, 8987])).
% 2.62/2.81 tff(8991,plain,
% 2.62/2.81 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(s(s(z))))) | (~r(s(s(z)), s(z))) | (~r(z, s(z))) | (~r(z, s(s(z)))))),
% 2.62/2.81 inference(quant_inst,[status(thm)],[])).
% 2.62/2.81 tff(8992,plain,
% 2.62/2.81 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, s(z))) | (~r(s(s(z)), s(z))) | (~r(z, s(s(z)))) | (~r(s(z), s(s(s(z)))))),
% 2.62/2.81 inference(modus_ponens,[status(thm)],[8991, 8990])).
% 2.62/2.81 tff(8993,plain,
% 2.62/2.81 ($false),
% 2.62/2.81 inference(unit_resolution,[status(thm)],[8992, 197, 155, 323, 392, 1653])).
% 2.62/2.81 tff(8994,plain,((~r(s(z), s(s(s(z))))) | (~r(z, s(s(z)))) | (~r(z, s(z))) | (~r(s(s(z)), s(z)))), inference(lemma,lemma(discharge,[]))).
% 2.62/2.81 tff(8995,plain,
% 2.62/2.81 (~r(s(z), s(s(s(z))))),
% 2.62/2.81 inference(unit_resolution,[status(thm)],[8994, 392, 323, 155])).
% 2.62/2.81 tff(8996,plain,
% 2.62/2.81 (b(s(z), s(s(s(z))))),
% 2.62/2.81 inference(unit_resolution,[status(thm)],[1674, 8995])).
% 2.62/2.81 tff(8997,plain,
% 2.62/2.81 (b(s(z), s(elem!1)) <=> b(s(z), s(s(s(elem!1))))),
% 2.62/2.81 inference(monotonicity,[status(thm)],[3116])).
% 2.62/2.81 tff(8998,plain,
% 2.62/2.81 (b(s(z), s(s(s(elem!1)))) <=> b(s(z), s(elem!1))),
% 2.62/2.81 inference(symmetry,[status(thm)],[8997])).
% 2.62/2.81 tff(8999,plain,
% 2.62/2.81 (b(s(z), s(elem!1))),
% 2.62/2.81 inference(modus_ponens,[status(thm)],[5555, 8998])).
% 2.62/2.81 tff(9000,plain,
% 2.62/2.81 (b(s(s(s(s(elem!1)))), s(s(s(z)))) <=> b(s(s(s(elem!1))), s(s(s(z))))),
% 2.62/2.81 inference(monotonicity,[status(thm)],[6471])).
% 2.62/2.81 tff(9001,plain,
% 2.62/2.81 (b(s(s(s(elem!1))), s(s(s(z)))) <=> b(s(s(s(s(elem!1)))), s(s(s(z))))),
% 2.62/2.81 inference(symmetry,[status(thm)],[9000])).
% 2.62/2.81 tff(9002,plain,
% 2.62/2.81 (b(elem!1, s(s(s(z)))) <=> b(s(s(s(s(elem!1)))), s(s(s(z))))),
% 2.62/2.81 inference(transitivity,[status(thm)],[8223, 9001])).
% 2.62/2.81 tff(9003,plain,
% 2.62/2.81 (~r(s(s(elem!1)), s(s(z)))),
% 2.62/2.81 inference(unit_resolution,[status(thm)],[401, 392, 155, 365])).
% 2.62/2.81 tff(9004,plain,
% 2.62/2.81 (r(s(s(z)), s(s(elem!1)))),
% 2.62/2.81 inference(unit_resolution,[status(thm)],[5300, 9003, 376, 8632, 52])).
% 2.62/2.81 tff(9005,plain,
% 2.62/2.81 (~r(elem!1, s(s(s(z))))),
% 2.62/2.81 inference(unit_resolution,[status(thm)],[1614, 9004, 155, 365, 6567])).
% 2.62/2.81 tff(9006,plain,
% 2.62/2.81 (b(elem!1, s(s(s(z))))),
% 2.62/2.81 inference(unit_resolution,[status(thm)],[1619, 9005, 8222])).
% 2.62/2.81 tff(9007,plain,
% 2.62/2.81 (b(s(s(s(s(elem!1)))), s(s(s(z))))),
% 2.62/2.81 inference(modus_ponens,[status(thm)],[9006, 9002])).
% 2.62/2.81 tff(9008,assumption,(b(s(s(s(s(elem!1)))), s(s(s(z))))), introduced(assumption)).
% 2.62/2.81 tff(9009,plain,
% 2.62/2.81 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), z)) | (~b(s(z), s(elem!1))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(s(elem!1)))), s(z))) | (~b(s(s(s(s(elem!1)))), z)) | (~b(s(s(s(s(elem!1)))), s(s(s(z))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(elem!1), z)) | (~b(s(z), s(elem!1))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(s(elem!1)))), s(z))) | (~b(s(s(s(s(elem!1)))), z)) | (~b(s(s(s(s(elem!1)))), s(s(s(z))))))),
% 2.62/2.81 inference(rewrite,[status(thm)],[])).
% 2.62/2.81 tff(9010,plain,
% 2.62/2.81 (((~b(s(elem!1), z)) | (~b(s(s(s(s(elem!1)))), z)) | (~b(s(z), s(elem!1))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(s(elem!1)))), s(z))) | (~b(s(s(s(s(elem!1)))), s(s(s(z)))))) <=> ((~b(s(elem!1), z)) | (~b(s(z), s(elem!1))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(s(elem!1)))), s(z))) | (~b(s(s(s(s(elem!1)))), z)) | (~b(s(s(s(s(elem!1)))), s(s(s(z))))))),
% 2.62/2.81 inference(rewrite,[status(thm)],[])).
% 2.62/2.81 tff(9011,plain,
% 2.62/2.81 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), z)) | (~b(s(s(s(s(elem!1)))), z)) | (~b(s(z), s(elem!1))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(s(elem!1)))), s(z))) | (~b(s(s(s(s(elem!1)))), s(s(s(z))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), z)) | (~b(s(z), s(elem!1))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(s(elem!1)))), s(z))) | (~b(s(s(s(s(elem!1)))), z)) | (~b(s(s(s(s(elem!1)))), s(s(s(z)))))))),
% 2.62/2.81 inference(monotonicity,[status(thm)],[9010])).
% 2.62/2.81 tff(9012,plain,
% 2.62/2.81 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), z)) | (~b(s(s(s(s(elem!1)))), z)) | (~b(s(z), s(elem!1))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(s(elem!1)))), s(z))) | (~b(s(s(s(s(elem!1)))), s(s(s(z))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(elem!1), z)) | (~b(s(z), s(elem!1))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(s(elem!1)))), s(z))) | (~b(s(s(s(s(elem!1)))), z)) | (~b(s(s(s(s(elem!1)))), s(s(s(z))))))),
% 2.62/2.81 inference(transitivity,[status(thm)],[9011, 9009])).
% 2.62/2.81 tff(9013,plain,
% 2.62/2.81 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), z)) | (~b(s(s(s(s(elem!1)))), z)) | (~b(s(z), s(elem!1))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(s(elem!1)))), s(z))) | (~b(s(s(s(s(elem!1)))), s(s(s(z))))))),
% 2.62/2.81 inference(quant_inst,[status(thm)],[])).
% 2.62/2.81 tff(9014,plain,
% 2.62/2.81 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(elem!1), z)) | (~b(s(z), s(elem!1))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(s(elem!1)))), s(z))) | (~b(s(s(s(s(elem!1)))), z)) | (~b(s(s(s(s(elem!1)))), s(s(s(z)))))),
% 2.62/2.81 inference(modus_ponens,[status(thm)],[9013, 9012])).
% 2.62/2.81 tff(9015,plain,
% 2.62/2.81 ($false),
% 2.62/2.81 inference(unit_resolution,[status(thm)],[9014, 166, 2747, 1211, 1402, 3240, 1326, 9008])).
% 2.62/2.81 tff(9016,plain,((~b(s(s(s(z))), s(z))) | (~b(s(elem!1), z)) | (~b(s(z), s(elem!1))) | (~b(s(s(s(s(elem!1)))), s(z))) | (~b(s(s(s(s(elem!1)))), z)) | (~b(s(s(s(s(elem!1)))), s(s(s(z)))))), inference(lemma,lemma(discharge,[]))).
% 2.62/2.81 tff(9017,plain,
% 2.62/2.81 (~b(s(s(s(z))), s(z))),
% 2.62/2.81 inference(unit_resolution,[status(thm)],[9016, 9007, 1326, 8999, 1402, 2747])).
% 2.62/2.81 tff(9018,plain,
% 2.62/2.81 (r(s(s(s(z))), s(z))),
% 2.62/2.81 inference(unit_resolution,[status(thm)],[1763, 9017])).
% 2.62/2.81 tff(9019,plain,
% 2.62/2.81 (~r(s(s(s(z))), s(s(z)))),
% 2.62/2.81 inference(unit_resolution,[status(thm)],[1685, 1677, 155, 392])).
% 2.62/2.81 tff(9020,plain,
% 2.62/2.81 (b(s(s(s(z))), s(s(z)))),
% 2.62/2.81 inference(unit_resolution,[status(thm)],[1010, 9019])).
% 2.62/2.81 tff(9021,plain,
% 2.62/2.81 (~b(s(s(z)), s(s(s(z))))),
% 2.62/2.81 inference(unit_resolution,[status(thm)],[996, 9020, 988, 556])).
% 2.62/2.81 tff(9022,plain,
% 2.62/2.81 (r(s(s(z)), s(s(s(z))))),
% 2.62/2.81 inference(unit_resolution,[status(thm)],[1730, 9021])).
% 2.62/2.81 tff(9023,plain,
% 2.62/2.81 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(s(z))))) | (~r(s(s(z)), s(s(s(z))))) | (~r(z, s(s(z)))) | (~r(s(s(s(z))), s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, s(s(s(z))))) | (~r(s(s(z)), s(s(s(z))))) | (~r(z, s(s(z)))) | (~r(s(s(s(z))), s(z))))),
% 2.62/2.81 inference(rewrite,[status(thm)],[])).
% 2.62/2.81 tff(9024,plain,
% 2.62/2.81 (((~r(s(s(s(z))), s(z))) | (~r(s(s(z)), s(s(s(z))))) | (~r(z, s(s(s(z))))) | (~r(z, s(s(z))))) <=> ((~r(z, s(s(s(z))))) | (~r(s(s(z)), s(s(s(z))))) | (~r(z, s(s(z)))) | (~r(s(s(s(z))), s(z))))),
% 2.62/2.81 inference(rewrite,[status(thm)],[])).
% 2.62/2.81 tff(9025,plain,
% 2.62/2.81 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(z))), s(z))) | (~r(s(s(z)), s(s(s(z))))) | (~r(z, s(s(s(z))))) | (~r(z, s(s(z)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(s(z))))) | (~r(s(s(z)), s(s(s(z))))) | (~r(z, s(s(z)))) | (~r(s(s(s(z))), s(z)))))),
% 2.62/2.81 inference(monotonicity,[status(thm)],[9024])).
% 2.62/2.81 tff(9026,plain,
% 2.62/2.81 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(z))), s(z))) | (~r(s(s(z)), s(s(s(z))))) | (~r(z, s(s(s(z))))) | (~r(z, s(s(z)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, s(s(s(z))))) | (~r(s(s(z)), s(s(s(z))))) | (~r(z, s(s(z)))) | (~r(s(s(s(z))), s(z))))),
% 2.62/2.81 inference(transitivity,[status(thm)],[9025, 9023])).
% 2.62/2.81 tff(9027,plain,
% 2.62/2.81 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(z))), s(z))) | (~r(s(s(z)), s(s(s(z))))) | (~r(z, s(s(s(z))))) | (~r(z, s(s(z)))))),
% 2.62/2.81 inference(quant_inst,[status(thm)],[])).
% 2.62/2.81 tff(9028,plain,
% 2.62/2.81 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, s(s(s(z))))) | (~r(s(s(z)), s(s(s(z))))) | (~r(z, s(s(z)))) | (~r(s(s(s(z))), s(z)))),
% 2.62/2.81 inference(modus_ponens,[status(thm)],[9027, 9026])).
% 2.62/2.81 tff(9029,plain,
% 2.62/2.81 ($false),
% 2.62/2.81 inference(unit_resolution,[status(thm)],[9028, 197, 155, 1677, 1746, 9022])).
% 2.62/2.81 tff(9030,plain,((~r(z, s(s(s(z))))) | (~r(z, s(s(z)))) | (~r(s(s(s(z))), s(z))) | (~b(s(z), s(s(s(z))))) | (~b(s(z), s(s(z)))) | (~r(s(s(z)), s(z)))), inference(lemma,lemma(discharge,[]))).
% 2.62/2.81 tff(9031,plain,
% 2.62/2.81 (~r(z, s(s(s(z))))),
% 2.62/2.81 inference(unit_resolution,[status(thm)],[9030, 9018, 155, 8996, 8632, 392])).
% 2.62/2.81 tff(9032,plain,
% 2.62/2.81 (b(z, s(s(s(z))))),
% 2.62/2.81 inference(unit_resolution,[status(thm)],[1697, 9031])).
% 2.62/2.81 tff(9033,plain,
% 2.62/2.81 (~r(s(z), s(s(s(z))))),
% 2.62/2.81 inference(unit_resolution,[status(thm)],[1661, 866, 323, 392])).
% 2.62/2.81 tff(9034,plain,
% 2.62/2.81 (b(s(z), s(s(s(z))))),
% 2.62/2.81 inference(unit_resolution,[status(thm)],[1674, 9033])).
% 2.62/2.81 tff(9035,assumption,(b(elem!1, s(s(s(z))))), introduced(assumption)).
% 2.62/2.81 tff(9036,plain,
% 2.62/2.81 (b(s(s(s(s(elem!1)))), s(s(s(z))))),
% 2.62/2.81 inference(modus_ponens,[status(thm)],[9035, 1543])).
% 2.62/2.81 tff(9037,plain,
% 2.62/2.81 (~b(s(s(s(z))), s(z))),
% 2.62/2.81 inference(unit_resolution,[status(thm)],[9016, 9036, 1211, 1402, 1326, 2747])).
% 2.62/2.81 tff(9038,plain,
% 2.62/2.81 (r(s(s(s(z))), s(z))),
% 2.62/2.81 inference(unit_resolution,[status(thm)],[1763, 9037])).
% 2.62/2.81 tff(9039,plain,
% 2.62/2.81 (~r(s(s(s(z))), z)),
% 2.62/2.81 inference(unit_resolution,[status(thm)],[1741, 1732, 866, 155])).
% 2.62/2.81 tff(9040,plain,
% 2.62/2.81 (b(s(s(s(z))), z)),
% 2.62/2.81 inference(unit_resolution,[status(thm)],[1713, 9039])).
% 2.62/2.81 tff(9041,plain,
% 2.62/2.81 (~b(z, s(s(s(z))))),
% 2.62/2.81 inference(unit_resolution,[status(thm)],[1708, 9040, 53, 988])).
% 2.62/2.81 tff(9042,plain,
% 2.62/2.81 (r(z, s(s(s(z))))),
% 2.62/2.81 inference(unit_resolution,[status(thm)],[1697, 9041])).
% 2.62/2.82 tff(9043,plain,
% 2.62/2.82 ($false),
% 2.62/2.82 inference(unit_resolution,[status(thm)],[1752, 197, 866, 9042, 9038, 1732])).
% 2.62/2.82 tff(9044,plain,((~r(s(s(z)), s(s(s(z))))) | (~r(s(s(z)), z)) | (~b(s(z), s(elem!1))) | (~b(s(s(s(s(elem!1)))), s(z))) | (~b(s(s(s(s(elem!1)))), z)) | (~b(s(elem!1), z)) | (~b(elem!1, s(s(s(z))))) | (~(s(s(elem!1)) = s(s(s(s(elem!1)))))) | (~b(s(z), z)) | (~b(s(z), s(s(s(z))))) | (~r(z, s(s(z))))), inference(lemma,lemma(discharge,[]))).
% 2.62/2.82 tff(9045,plain,
% 2.62/2.82 (~r(s(s(z)), s(s(s(z))))),
% 2.62/2.82 inference(unit_resolution,[status(thm)],[9044, 9034, 155, 1211, 1402, 2747, 1326, 1153, 53, 9035, 866])).
% 2.62/2.82 tff(9046,plain,
% 2.62/2.82 (b(s(s(z)), s(s(s(z))))),
% 2.62/2.82 inference(unit_resolution,[status(thm)],[1730, 9045])).
% 2.62/2.82 tff(9047,plain,
% 2.62/2.82 (~r(s(s(s(z))), s(s(z)))),
% 2.62/2.82 inference(unit_resolution,[status(thm)],[1719, 9034, 155, 53, 866, 392])).
% 2.62/2.82 tff(9048,plain,
% 2.62/2.82 (b(s(s(s(z))), s(s(z)))),
% 2.62/2.82 inference(unit_resolution,[status(thm)],[1010, 9047])).
% 2.62/2.82 tff(9049,plain,
% 2.62/2.82 ($false),
% 2.62/2.82 inference(unit_resolution,[status(thm)],[996, 9048, 9046, 9034, 8632])).
% 2.62/2.82 tff(9050,plain,((~r(s(s(z)), z)) | (~r(z, s(s(z)))) | (~b(s(z), z)) | (~r(s(s(z)), s(z))) | (~b(s(z), s(elem!1))) | (~b(s(s(s(s(elem!1)))), s(z))) | (~b(s(elem!1), z)) | (~b(s(s(s(s(elem!1)))), z)) | (~(s(s(elem!1)) = s(s(s(s(elem!1)))))) | (~b(elem!1, s(s(s(z))))) | (~r(z, s(z)))), inference(lemma,lemma(discharge,[]))).
% 2.62/2.82 tff(9051,plain,
% 2.62/2.82 (~r(s(s(z)), z)),
% 2.62/2.82 inference(unit_resolution,[status(thm)],[9050, 392, 53, 155, 8999, 1402, 2747, 1326, 6567, 9006, 323])).
% 2.62/2.82 tff(9052,plain,
% 2.62/2.82 (b(s(s(z)), z)),
% 2.62/2.82 inference(unit_resolution,[status(thm)],[186, 9051])).
% 2.62/2.82 tff(9053,plain,
% 2.62/2.82 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(s(z)))) | (~b(s(z), s(s(z)))) | (~b(s(s(z)), z)) | (~b(s(z), s(s(s(z))))) | (~b(z, s(s(s(z))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(s(z)))) | (~b(s(z), s(s(z)))) | (~b(s(s(z)), z)) | (~b(s(z), s(s(s(z))))) | (~b(z, s(s(s(z))))))),
% 2.62/2.82 inference(rewrite,[status(thm)],[])).
% 2.62/2.82 tff(9054,plain,
% 2.62/2.82 (((~b(z, s(s(s(z))))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(z)), z)) | (~b(s(s(s(elem!1))), s(s(z)))) | (~b(s(z), s(s(z)))) | (~b(s(z), s(s(s(elem!1)))))) <=> ((~b(s(z), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(s(z)))) | (~b(s(z), s(s(z)))) | (~b(s(s(z)), z)) | (~b(s(z), s(s(s(z))))) | (~b(z, s(s(s(z))))))),
% 2.62/2.82 inference(rewrite,[status(thm)],[])).
% 2.62/2.82 tff(9055,plain,
% 2.62/2.82 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(s(z))))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(z)), z)) | (~b(s(s(s(elem!1))), s(s(z)))) | (~b(s(z), s(s(z)))) | (~b(s(z), s(s(s(elem!1))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(s(z)))) | (~b(s(z), s(s(z)))) | (~b(s(s(z)), z)) | (~b(s(z), s(s(s(z))))) | (~b(z, s(s(s(z)))))))),
% 2.62/2.82 inference(monotonicity,[status(thm)],[9054])).
% 2.62/2.82 tff(9056,plain,
% 2.62/2.82 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(s(z))))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(z)), z)) | (~b(s(s(s(elem!1))), s(s(z)))) | (~b(s(z), s(s(z)))) | (~b(s(z), s(s(s(elem!1))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(s(z)))) | (~b(s(z), s(s(z)))) | (~b(s(s(z)), z)) | (~b(s(z), s(s(s(z))))) | (~b(z, s(s(s(z))))))),
% 2.62/2.82 inference(transitivity,[status(thm)],[9055, 9053])).
% 2.62/2.82 tff(9057,plain,
% 2.62/2.82 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(s(z))))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(z)), z)) | (~b(s(s(s(elem!1))), s(s(z)))) | (~b(s(z), s(s(z)))) | (~b(s(z), s(s(s(elem!1))))))),
% 2.62/2.82 inference(quant_inst,[status(thm)],[])).
% 2.62/2.82 tff(9058,plain,
% 2.62/2.82 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(s(z)))) | (~b(s(z), s(s(z)))) | (~b(s(s(z)), z)) | (~b(s(z), s(s(s(z))))) | (~b(z, s(s(s(z)))))),
% 2.62/2.82 inference(modus_ponens,[status(thm)],[9057, 9056])).
% 2.62/2.82 tff(9059,plain,
% 2.62/2.82 ($false),
% 2.62/2.82 inference(unit_resolution,[status(thm)],[9058, 166, 5555, 8632, 9052, 8996, 9032, 8986])).
% 2.62/2.82 tff(9060,plain,((~r(s(s(z)), s(z))) | (~r(z, s(s(z)))) | (~r(z, s(z))) | (~b(s(z), z)) | (~b(s(s(s(s(elem!1)))), s(z))) | (~b(s(elem!1), z)) | (~b(s(s(s(s(elem!1)))), z)) | (~(s(s(elem!1)) = s(s(s(elem!1))))) | (~r(z, s(s(elem!1)))) | (~b(s(z), s(s(elem!1)))) | (s(s(z)) = s(s(elem!1))) | (~r(z, s(s(s(elem!1)))))), inference(lemma,lemma(discharge,[]))).
% 2.62/2.82 tff(9061,plain,
% 2.62/2.82 (~r(s(s(z)), s(z))),
% 2.62/2.82 inference(unit_resolution,[status(thm)],[9060, 8965, 323, 155, 8984, 8981, 8976, 8966, 8969, 376, 52, 8971])).
% 2.62/2.82 tff(9062,plain,
% 2.62/2.82 (b(s(s(z)), s(z))),
% 2.62/2.82 inference(unit_resolution,[status(thm)],[308, 9061])).
% 2.62/2.82 tff(9063,plain,
% 2.62/2.82 (~b(s(s(z)), s(s(elem!1)))),
% 2.62/2.82 inference(unit_resolution,[status(thm)],[454, 9062, 376, 310])).
% 2.62/2.82 tff(9064,plain,
% 2.62/2.82 (b(s(s(elem!1)), s(s(z)))),
% 2.62/2.82 inference(unit_resolution,[status(thm)],[2079, 9063, 155, 52, 8969])).
% 2.62/2.82 tff(9065,plain,
% 2.62/2.82 (b(s(s(s(elem!1))), s(s(z)))),
% 2.62/2.82 inference(modus_ponens,[status(thm)],[9064, 8967])).
% 2.62/2.82 tff(9066,plain,
% 2.62/2.82 (b(s(z), s(s(s(elem!1))))),
% 2.62/2.82 inference(unit_resolution,[status(thm)],[5500, 8966, 376])).
% 2.62/2.82 tff(9067,plain,
% 2.62/2.82 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(s(z)))) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(s(z)), s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(s(z)))) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(s(z)), s(z))))),
% 2.62/2.82 inference(rewrite,[status(thm)],[])).
% 2.62/2.82 tff(9068,plain,
% 2.62/2.82 (((~b(s(s(s(elem!1))), s(z))) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(z), s(s(s(elem!1))))) | (~b(s(s(z)), s(z))) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(s(s(elem!1))), s(s(z))))) <=> ((~b(s(z), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(s(z)))) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(s(z)), s(z))))),
% 2.62/2.82 inference(rewrite,[status(thm)],[])).
% 2.62/2.82 tff(9069,plain,
% 2.62/2.82 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), s(z))) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(z), s(s(s(elem!1))))) | (~b(s(s(z)), s(z))) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(s(s(elem!1))), s(s(z)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(s(z)))) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(s(z)), s(z)))))),
% 2.62/2.82 inference(monotonicity,[status(thm)],[9068])).
% 2.62/2.82 tff(9070,plain,
% 2.62/2.82 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), s(z))) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(z), s(s(s(elem!1))))) | (~b(s(s(z)), s(z))) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(s(s(elem!1))), s(s(z)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(s(z)))) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(s(z)), s(z))))),
% 2.62/2.82 inference(transitivity,[status(thm)],[9069, 9067])).
% 2.62/2.82 tff(9071,plain,
% 2.62/2.82 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), s(z))) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(z), s(s(s(elem!1))))) | (~b(s(s(z)), s(z))) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(s(s(elem!1))), s(s(z)))))),
% 2.62/2.82 inference(quant_inst,[status(thm)],[])).
% 2.62/2.82 tff(9072,plain,
% 2.62/2.82 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(s(z)))) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(s(z)), s(z)))),
% 2.62/2.82 inference(modus_ponens,[status(thm)],[9071, 9070])).
% 2.62/2.82 tff(9073,plain,
% 2.62/2.82 ($false),
% 2.62/2.82 inference(unit_resolution,[status(thm)],[9072, 166, 9066, 96, 9062, 9065])).
% 2.62/2.82 tff(9074,plain,((s(s(z)) = s(s(elem!1))) | (~b(s(s(s(elem!1))), s(z))) | (~r(z, s(s(z)))) | (~b(s(z), s(s(elem!1)))) | (~b(s(s(elem!1)), s(z))) | (~r(z, s(z))) | r(s(s(s(elem!1))), z)), inference(lemma,lemma(discharge,[]))).
% 2.62/2.82 tff(9075,plain,
% 2.62/2.82 (s(s(z)) = s(s(elem!1))),
% 2.62/2.82 inference(unit_resolution,[status(thm)],[9074, 8809, 152, 96, 310, 8408, 8807])).
% 2.62/2.82 tff(9076,plain,
% 2.62/2.82 (s(elem!1) = s(z)),
% 2.62/2.82 inference(unit_resolution,[status(thm)],[43, 9075])).
% 2.62/2.82 tff(9077,plain,
% 2.62/2.82 (z = elem!1),
% 2.62/2.82 inference(unit_resolution,[status(thm)],[30, 9076])).
% 2.62/2.82 tff(9078,plain,
% 2.62/2.82 (~(s(s(s(s(s(s(elem!1)))))) = elem!1)),
% 2.62/2.82 inference(unit_resolution,[status(thm)],[4897, 9077])).
% 2.62/2.82 tff(9079,plain,
% 2.62/2.82 (elem!1 = z),
% 2.62/2.82 inference(symmetry,[status(thm)],[9077])).
% 2.62/2.82 tff(9080,plain,
% 2.62/2.82 ((s(s(elem!1)) = elem!1) <=> (s(s(elem!1)) = z)),
% 2.62/2.82 inference(monotonicity,[status(thm)],[9079])).
% 2.62/2.82 tff(9081,plain,
% 2.62/2.82 ((s(s(elem!1)) = z) <=> (s(s(elem!1)) = elem!1)),
% 2.62/2.82 inference(symmetry,[status(thm)],[9080])).
% 2.62/2.82 tff(9082,plain,
% 2.62/2.82 ((~(s(s(elem!1)) = z)) <=> (~(s(s(elem!1)) = elem!1))),
% 2.62/2.82 inference(monotonicity,[status(thm)],[9081])).
% 2.62/2.82 tff(9083,plain,
% 2.62/2.82 (~(s(s(elem!1)) = elem!1)),
% 2.62/2.82 inference(modus_ponens,[status(thm)],[108, 9082])).
% 2.62/2.82 tff(9084,plain,
% 2.62/2.82 ((s(s(s(s(elem!1)))) = z) <=> (s(s(s(s(elem!1)))) = elem!1)),
% 2.62/2.82 inference(monotonicity,[status(thm)],[9077])).
% 2.62/2.82 tff(9085,plain,
% 2.62/2.82 ((~(s(s(s(s(elem!1)))) = z)) <=> (~(s(s(s(s(elem!1)))) = elem!1))),
% 2.62/2.82 inference(monotonicity,[status(thm)],[9084])).
% 2.62/2.82 tff(9086,plain,
% 2.62/2.82 (~(s(s(s(s(elem!1)))) = elem!1)),
% 2.62/2.82 inference(modus_ponens,[status(thm)],[626, 9085])).
% 2.62/2.82 tff(9087,plain,
% 2.62/2.82 (s(s(s(z))) = s(s(s(elem!1)))),
% 2.62/2.82 inference(monotonicity,[status(thm)],[9075])).
% 2.62/2.82 tff(9088,plain,
% 2.62/2.82 ((s(s(s(s(elem!1)))) = s(s(s(z)))) <=> (s(s(s(s(elem!1)))) = s(s(s(elem!1))))),
% 2.62/2.82 inference(monotonicity,[status(thm)],[9087])).
% 2.62/2.82 tff(9089,plain,
% 2.62/2.82 ((s(s(s(s(elem!1)))) = s(s(s(z)))) <=> (s(s(s(elem!1))) = s(s(s(s(elem!1)))))),
% 2.62/2.82 inference(transitivity,[status(thm)],[9088, 1191])).
% 2.62/2.82 tff(9090,plain,
% 2.62/2.82 ((~(s(s(s(s(elem!1)))) = s(s(s(z))))) <=> (~(s(s(s(elem!1))) = s(s(s(s(elem!1))))))),
% 2.62/2.82 inference(monotonicity,[status(thm)],[9089])).
% 2.62/2.82 tff(9091,plain,
% 2.62/2.82 (~(s(s(s(elem!1))) = s(s(s(s(elem!1)))))),
% 2.62/2.82 inference(modus_ponens,[status(thm)],[5112, 9090])).
% 2.62/2.82 tff(9092,plain,
% 2.62/2.82 ((s(s(s(s(elem!1)))) = s(s(z))) <=> (s(s(s(s(elem!1)))) = s(s(elem!1)))),
% 2.62/2.82 inference(monotonicity,[status(thm)],[9075])).
% 2.62/2.82 tff(9093,plain,
% 2.62/2.82 ((s(s(s(s(elem!1)))) = s(s(z))) <=> (s(s(elem!1)) = s(s(s(s(elem!1)))))),
% 2.62/2.82 inference(transitivity,[status(thm)],[9092, 123])).
% 2.62/2.82 tff(9094,plain,
% 2.62/2.82 ((~(s(s(s(s(elem!1)))) = s(s(z)))) <=> (~(s(s(elem!1)) = s(s(s(s(elem!1))))))),
% 2.62/2.82 inference(monotonicity,[status(thm)],[9093])).
% 2.62/2.82 tff(9095,plain,
% 2.62/2.82 (~(s(s(elem!1)) = s(s(s(s(elem!1)))))),
% 2.62/2.82 inference(modus_ponens,[status(thm)],[733, 9094])).
% 2.62/2.82 tff(9096,plain,
% 2.62/2.82 ((s(s(s(s(elem!1)))) = s(s(z))) <=> (s(s(s(s(elem!1)))) = s(s(elem!1)))),
% 2.62/2.82 inference(transitivity,[status(thm)],[9093, 124])).
% 2.62/2.82 tff(9097,plain,
% 2.62/2.82 ((~(s(s(s(s(elem!1)))) = s(s(z)))) <=> (~(s(s(s(s(elem!1)))) = s(s(elem!1))))),
% 2.62/2.82 inference(monotonicity,[status(thm)],[9096])).
% 2.62/2.82 tff(9098,plain,
% 2.62/2.82 (~(s(s(s(s(elem!1)))) = s(s(elem!1)))),
% 2.62/2.82 inference(modus_ponens,[status(thm)],[733, 9097])).
% 2.62/2.82 tff(9099,plain,
% 2.62/2.82 (~b(s(s(s(elem!1))), s(s(elem!1)))),
% 2.62/2.82 inference(unit_resolution,[status(thm)],[1858, 310, 96, 8809])).
% 2.62/2.82 tff(9100,plain,
% 2.62/2.82 ((s(s(z)) = s(s(s(elem!1)))) <=> (s(s(elem!1)) = s(s(s(elem!1))))),
% 2.62/2.82 inference(monotonicity,[status(thm)],[9075])).
% 2.62/2.82 tff(9101,plain,
% 2.62/2.82 ((s(s(z)) = s(s(s(elem!1)))) <=> (s(s(s(elem!1))) = s(s(elem!1)))),
% 2.62/2.82 inference(transitivity,[status(thm)],[9100, 3341])).
% 2.62/2.82 tff(9102,plain,
% 2.62/2.82 ((~(s(s(z)) = s(s(s(elem!1))))) <=> (~(s(s(s(elem!1))) = s(s(elem!1))))),
% 2.62/2.82 inference(monotonicity,[status(thm)],[9101])).
% 2.62/2.82 tff(9103,plain,
% 2.62/2.82 (~(s(s(s(elem!1))) = s(s(elem!1)))),
% 2.62/2.82 inference(modus_ponens,[status(thm)],[209, 9102])).
% 2.62/2.82 tff(9104,plain,
% 2.62/2.82 (r(s(s(s(elem!1))), s(s(elem!1)))),
% 2.62/2.82 inference(unit_resolution,[status(thm)],[889, 9103, 9099])).
% 2.62/2.82 tff(9105,plain,
% 2.62/2.82 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(elem!1)))) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(s(elem!1)), s(z))) | (~b(s(s(s(elem!1))), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), s(s(elem!1)))) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(s(elem!1)), s(z))) | (~b(s(s(s(elem!1))), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), s(z))))),
% 2.62/2.82 inference(rewrite,[status(thm)],[])).
% 2.62/2.82 tff(9106,plain,
% 2.62/2.82 (((~b(s(s(elem!1)), s(z))) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(z), s(s(elem!1)))) | (~b(s(s(s(s(elem!1)))), s(z))) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(s(s(elem!1))), s(s(s(s(elem!1))))))) <=> ((~b(s(z), s(s(elem!1)))) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(s(elem!1)), s(z))) | (~b(s(s(s(elem!1))), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), s(z))))),
% 2.62/2.82 inference(rewrite,[status(thm)],[])).
% 2.62/2.82 tff(9107,plain,
% 2.62/2.82 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), s(z))) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(z), s(s(elem!1)))) | (~b(s(s(s(s(elem!1)))), s(z))) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(s(s(elem!1))), s(s(s(s(elem!1)))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(elem!1)))) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(s(elem!1)), s(z))) | (~b(s(s(s(elem!1))), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), s(z)))))),
% 2.62/2.82 inference(monotonicity,[status(thm)],[9106])).
% 2.62/2.82 tff(9108,plain,
% 2.62/2.82 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), s(z))) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(z), s(s(elem!1)))) | (~b(s(s(s(s(elem!1)))), s(z))) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(s(s(elem!1))), s(s(s(s(elem!1)))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), s(s(elem!1)))) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(s(elem!1)), s(z))) | (~b(s(s(s(elem!1))), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), s(z))))),
% 2.62/2.82 inference(transitivity,[status(thm)],[9107, 9105])).
% 2.62/2.82 tff(9109,plain,
% 2.62/2.82 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), s(z))) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(z), s(s(elem!1)))) | (~b(s(s(s(s(elem!1)))), s(z))) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(s(s(elem!1))), s(s(s(s(elem!1)))))))),
% 2.62/2.82 inference(quant_inst,[status(thm)],[])).
% 2.62/2.82 tff(9110,plain,
% 2.62/2.82 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), s(s(elem!1)))) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(s(elem!1)), s(z))) | (~b(s(s(s(elem!1))), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), s(z)))),
% 2.62/2.82 inference(modus_ponens,[status(thm)],[9109, 9108])).
% 2.62/2.82 tff(9111,plain,
% 2.62/2.82 (~b(s(s(s(elem!1))), s(s(s(s(elem!1)))))),
% 2.62/2.82 inference(unit_resolution,[status(thm)],[9110, 166, 376, 96, 310, 1402])).
% 2.62/2.82 tff(9112,plain,
% 2.62/2.82 (r(s(s(s(elem!1))), s(s(s(s(elem!1)))))),
% 2.62/2.82 inference(unit_resolution,[status(thm)],[696, 9111, 361])).
% 2.62/2.82 tff(9113,plain,
% 2.62/2.82 (~b(s(s(s(s(elem!1)))), s(s(elem!1)))),
% 2.62/2.82 inference(unit_resolution,[status(thm)],[804, 166, 376, 310, 1402])).
% 2.62/2.82 tff(9114,plain,
% 2.62/2.82 (r(s(s(s(s(elem!1)))), s(s(elem!1)))),
% 2.62/2.82 inference(unit_resolution,[status(thm)],[813, 9113, 806])).
% 2.62/2.82 tff(9115,plain,
% 2.62/2.82 (~b(s(s(elem!1)), s(s(s(s(elem!1)))))),
% 2.62/2.82 inference(unit_resolution,[status(thm)],[822, 166, 376, 310, 1402])).
% 2.62/2.82 tff(9116,plain,
% 2.62/2.82 (r(s(s(elem!1)), s(s(s(s(elem!1)))))),
% 2.62/2.82 inference(unit_resolution,[status(thm)],[827, 9115, 2395])).
% 2.62/2.82 tff(9117,plain,
% 2.62/2.82 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), s(s(elem!1)))) | (~r(s(s(s(elem!1))), s(s(s(s(elem!1)))))) | (~r(s(s(s(s(elem!1)))), s(s(elem!1)))) | (~r(s(s(elem!1)), s(s(s(s(elem!1)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(elem!1))), s(s(elem!1)))) | (~r(s(s(s(elem!1))), s(s(s(s(elem!1)))))) | (~r(s(s(s(s(elem!1)))), s(s(elem!1)))) | (~r(s(s(elem!1)), s(s(s(s(elem!1)))))))),
% 2.62/2.82 inference(rewrite,[status(thm)],[])).
% 2.62/2.82 tff(9118,plain,
% 2.62/2.82 (((~r(s(s(s(s(elem!1)))), s(s(elem!1)))) | (~r(s(s(elem!1)), s(s(s(s(elem!1)))))) | (~r(s(s(s(elem!1))), s(s(s(s(elem!1)))))) | (~r(s(s(s(elem!1))), s(s(elem!1))))) <=> ((~r(s(s(s(elem!1))), s(s(elem!1)))) | (~r(s(s(s(elem!1))), s(s(s(s(elem!1)))))) | (~r(s(s(s(s(elem!1)))), s(s(elem!1)))) | (~r(s(s(elem!1)), s(s(s(s(elem!1)))))))),
% 2.62/2.82 inference(rewrite,[status(thm)],[])).
% 2.62/2.82 tff(9119,plain,
% 2.62/2.82 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(elem!1)))), s(s(elem!1)))) | (~r(s(s(elem!1)), s(s(s(s(elem!1)))))) | (~r(s(s(s(elem!1))), s(s(s(s(elem!1)))))) | (~r(s(s(s(elem!1))), s(s(elem!1)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), s(s(elem!1)))) | (~r(s(s(s(elem!1))), s(s(s(s(elem!1)))))) | (~r(s(s(s(s(elem!1)))), s(s(elem!1)))) | (~r(s(s(elem!1)), s(s(s(s(elem!1))))))))),
% 2.62/2.82 inference(monotonicity,[status(thm)],[9118])).
% 2.62/2.82 tff(9120,plain,
% 2.62/2.82 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(elem!1)))), s(s(elem!1)))) | (~r(s(s(elem!1)), s(s(s(s(elem!1)))))) | (~r(s(s(s(elem!1))), s(s(s(s(elem!1)))))) | (~r(s(s(s(elem!1))), s(s(elem!1)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(elem!1))), s(s(elem!1)))) | (~r(s(s(s(elem!1))), s(s(s(s(elem!1)))))) | (~r(s(s(s(s(elem!1)))), s(s(elem!1)))) | (~r(s(s(elem!1)), s(s(s(s(elem!1)))))))),
% 2.62/2.82 inference(transitivity,[status(thm)],[9119, 9117])).
% 2.62/2.82 tff(9121,plain,
% 2.62/2.82 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(elem!1)))), s(s(elem!1)))) | (~r(s(s(elem!1)), s(s(s(s(elem!1)))))) | (~r(s(s(s(elem!1))), s(s(s(s(elem!1)))))) | (~r(s(s(s(elem!1))), s(s(elem!1)))))),
% 2.62/2.82 inference(quant_inst,[status(thm)],[])).
% 2.62/2.82 tff(9122,plain,
% 2.62/2.82 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(elem!1))), s(s(elem!1)))) | (~r(s(s(s(elem!1))), s(s(s(s(elem!1)))))) | (~r(s(s(s(s(elem!1)))), s(s(elem!1)))) | (~r(s(s(elem!1)), s(s(s(s(elem!1))))))),
% 2.62/2.82 inference(modus_ponens,[status(thm)],[9121, 9120])).
% 2.62/2.82 tff(9123,plain,
% 2.62/2.82 ($false),
% 2.62/2.82 inference(unit_resolution,[status(thm)],[9122, 197, 905, 9116, 9114, 9112])).
% 2.62/2.82 tff(9124,plain,((~b(s(s(s(s(elem!1)))), s(z))) | (~r(s(s(s(elem!1))), s(s(elem!1)))) | (s(s(s(s(elem!1)))) = s(s(elem!1))) | (s(s(elem!1)) = s(s(s(s(elem!1))))) | (s(s(s(elem!1))) = s(s(s(s(elem!1))))) | (~b(s(z), s(s(elem!1)))) | (~b(s(s(elem!1)), s(z))) | (~b(s(s(s(elem!1))), s(z)))), inference(lemma,lemma(discharge,[]))).
% 2.62/2.83 tff(9125,plain,
% 2.62/2.83 (~b(s(s(s(s(elem!1)))), s(z))),
% 2.62/2.83 inference(unit_resolution,[status(thm)],[9124, 9104, 9098, 9095, 9091, 8809, 310, 96])).
% 2.62/2.83 tff(9126,plain,
% 2.62/2.83 (r(s(s(s(s(elem!1)))), s(z))),
% 2.62/2.83 inference(unit_resolution,[status(thm)],[661, 9125])).
% 2.62/2.83 tff(9127,plain,
% 2.62/2.83 (r(s(z), z) <=> r(s(z), elem!1)),
% 2.62/2.83 inference(monotonicity,[status(thm)],[9077])).
% 2.62/2.83 tff(9128,plain,
% 2.62/2.83 ((~(s(s(z)) = s(s(s(elem!1))))) <=> (~(s(s(elem!1)) = s(s(s(elem!1)))))),
% 2.62/2.83 inference(monotonicity,[status(thm)],[9100])).
% 2.62/2.83 tff(9129,plain,
% 2.62/2.83 (~(s(s(elem!1)) = s(s(s(elem!1))))),
% 2.62/2.83 inference(modus_ponens,[status(thm)],[209, 9128])).
% 2.62/2.83 tff(9130,plain,
% 2.62/2.83 (~b(s(z), z)),
% 2.62/2.83 inference(unit_resolution,[status(thm)],[2253, 9129, 152, 8408, 310])).
% 2.62/2.83 tff(9131,plain,
% 2.62/2.83 (r(s(z), z)),
% 2.62/2.83 inference(unit_resolution,[status(thm)],[230, 9130])).
% 2.62/2.83 tff(9132,plain,
% 2.62/2.83 (r(s(z), elem!1)),
% 2.62/2.83 inference(modus_ponens,[status(thm)],[9131, 9127])).
% 2.62/2.83 tff(9133,plain,
% 2.62/2.83 (r(elem!1, s(z))),
% 2.62/2.83 inference(unit_resolution,[status(thm)],[741, 9077, 8408])).
% 2.62/2.83 tff(9134,plain,
% 2.62/2.83 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), elem!1)) | (~r(elem!1, s(z))) | (~r(s(s(s(s(elem!1)))), s(z))) | (~r(s(s(s(s(elem!1)))), elem!1)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(z), elem!1)) | (~r(elem!1, s(z))) | (~r(s(s(s(s(elem!1)))), s(z))) | (~r(s(s(s(s(elem!1)))), elem!1)))),
% 2.62/2.83 inference(rewrite,[status(thm)],[])).
% 2.62/2.83 tff(9135,plain,
% 2.62/2.83 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), elem!1)) | (~r(elem!1, s(z))) | (~r(s(s(s(s(elem!1)))), s(z))) | (~r(s(s(s(s(elem!1)))), elem!1)))),
% 2.62/2.83 inference(quant_inst,[status(thm)],[])).
% 2.62/2.83 tff(9136,plain,
% 2.62/2.83 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(z), elem!1)) | (~r(elem!1, s(z))) | (~r(s(s(s(s(elem!1)))), s(z))) | (~r(s(s(s(s(elem!1)))), elem!1))),
% 2.62/2.83 inference(modus_ponens,[status(thm)],[9135, 9134])).
% 2.62/2.83 tff(9137,plain,
% 2.62/2.83 (~r(s(s(s(s(elem!1)))), elem!1)),
% 2.62/2.83 inference(unit_resolution,[status(thm)],[9136, 197, 9133, 9132, 9126])).
% 2.62/2.83 tff(9138,plain,
% 2.62/2.83 (b(s(s(s(s(elem!1)))), elem!1)),
% 2.62/2.83 inference(unit_resolution,[status(thm)],[719, 9137, 9086])).
% 2.62/2.83 tff(9139,plain,
% 2.62/2.83 ((s(s(s(s(elem!1)))) = z) <=> (elem!1 = s(s(s(s(elem!1)))))),
% 2.62/2.83 inference(transitivity,[status(thm)],[9084, 2287])).
% 2.62/2.83 tff(9140,plain,
% 2.62/2.83 ((~(s(s(s(s(elem!1)))) = z)) <=> (~(elem!1 = s(s(s(s(elem!1))))))),
% 2.62/2.83 inference(monotonicity,[status(thm)],[9139])).
% 2.62/2.83 tff(9141,plain,
% 2.62/2.83 (~(elem!1 = s(s(s(s(elem!1)))))),
% 2.62/2.83 inference(modus_ponens,[status(thm)],[626, 9140])).
% 2.62/2.83 tff(9142,plain,
% 2.62/2.83 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(s(s(s(elem!1)))))) | (~r(s(z), elem!1)) | (~r(elem!1, s(z))) | (~r(s(s(s(s(elem!1)))), s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(elem!1, s(s(s(s(elem!1)))))) | (~r(s(z), elem!1)) | (~r(elem!1, s(z))) | (~r(s(s(s(s(elem!1)))), s(z))))),
% 2.62/2.83 inference(rewrite,[status(thm)],[])).
% 2.62/2.83 tff(9143,plain,
% 2.62/2.83 (((~r(s(z), elem!1)) | (~r(s(s(s(s(elem!1)))), s(z))) | (~r(elem!1, s(z))) | (~r(elem!1, s(s(s(s(elem!1))))))) <=> ((~r(elem!1, s(s(s(s(elem!1)))))) | (~r(s(z), elem!1)) | (~r(elem!1, s(z))) | (~r(s(s(s(s(elem!1)))), s(z))))),
% 2.62/2.83 inference(rewrite,[status(thm)],[])).
% 2.62/2.83 tff(9144,plain,
% 2.62/2.83 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), elem!1)) | (~r(s(s(s(s(elem!1)))), s(z))) | (~r(elem!1, s(z))) | (~r(elem!1, s(s(s(s(elem!1)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(s(s(s(elem!1)))))) | (~r(s(z), elem!1)) | (~r(elem!1, s(z))) | (~r(s(s(s(s(elem!1)))), s(z)))))),
% 2.62/2.83 inference(monotonicity,[status(thm)],[9143])).
% 2.62/2.83 tff(9145,plain,
% 2.62/2.83 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), elem!1)) | (~r(s(s(s(s(elem!1)))), s(z))) | (~r(elem!1, s(z))) | (~r(elem!1, s(s(s(s(elem!1)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(elem!1, s(s(s(s(elem!1)))))) | (~r(s(z), elem!1)) | (~r(elem!1, s(z))) | (~r(s(s(s(s(elem!1)))), s(z))))),
% 2.62/2.83 inference(transitivity,[status(thm)],[9144, 9142])).
% 2.62/2.83 tff(9146,plain,
% 2.62/2.83 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), elem!1)) | (~r(s(s(s(s(elem!1)))), s(z))) | (~r(elem!1, s(z))) | (~r(elem!1, s(s(s(s(elem!1)))))))),
% 2.62/2.83 inference(quant_inst,[status(thm)],[])).
% 2.62/2.83 tff(9147,plain,
% 2.62/2.83 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(elem!1, s(s(s(s(elem!1)))))) | (~r(s(z), elem!1)) | (~r(elem!1, s(z))) | (~r(s(s(s(s(elem!1)))), s(z)))),
% 2.62/2.83 inference(modus_ponens,[status(thm)],[9146, 9145])).
% 2.62/2.83 tff(9148,plain,
% 2.62/2.83 (~r(elem!1, s(s(s(s(elem!1)))))),
% 2.62/2.83 inference(unit_resolution,[status(thm)],[9147, 197, 9133, 9132, 9126])).
% 2.62/2.83 tff(9149,plain,
% 2.62/2.83 (b(elem!1, s(s(s(s(elem!1)))))),
% 2.62/2.83 inference(unit_resolution,[status(thm)],[2427, 9148, 9141])).
% 2.62/2.83 tff(9150,plain,
% 2.62/2.83 ((s(s(s(s(elem!1)))) = s(s(s(z)))) <=> (s(s(s(s(elem!1)))) = s(s(s(elem!1))))),
% 2.62/2.83 inference(transitivity,[status(thm)],[9089, 3797])).
% 2.62/2.83 tff(9151,plain,
% 2.62/2.83 ((~(s(s(s(s(elem!1)))) = s(s(s(z))))) <=> (~(s(s(s(s(elem!1)))) = s(s(s(elem!1)))))),
% 2.62/2.83 inference(monotonicity,[status(thm)],[9150])).
% 2.62/2.83 tff(9152,plain,
% 2.62/2.83 (~(s(s(s(s(elem!1)))) = s(s(s(elem!1))))),
% 2.62/2.83 inference(modus_ponens,[status(thm)],[5112, 9151])).
% 2.62/2.83 tff(9153,plain,
% 2.62/2.83 ((s(s(s(elem!1))) = z) <=> (s(s(s(elem!1))) = elem!1)),
% 2.62/2.83 inference(monotonicity,[status(thm)],[9077])).
% 2.62/2.83 tff(9154,plain,
% 2.62/2.83 ((s(s(s(elem!1))) = z) <=> (elem!1 = s(s(s(elem!1))))),
% 2.62/2.83 inference(transitivity,[status(thm)],[9153, 5406])).
% 2.62/2.83 tff(9155,plain,
% 2.62/2.83 ((~(s(s(s(elem!1))) = z)) <=> (~(elem!1 = s(s(s(elem!1)))))),
% 2.62/2.83 inference(monotonicity,[status(thm)],[9154])).
% 2.62/2.83 tff(9156,plain,
% 2.62/2.83 (~(elem!1 = s(s(s(elem!1))))),
% 2.62/2.83 inference(modus_ponens,[status(thm)],[89, 9155])).
% 2.62/2.83 tff(9157,plain,
% 2.62/2.83 (~b(s(s(elem!1)), s(s(s(elem!1))))),
% 2.62/2.83 inference(unit_resolution,[status(thm)],[8544, 166, 8809, 96, 310])).
% 2.62/2.83 tff(9158,plain,
% 2.62/2.83 (r(s(s(elem!1)), s(s(s(elem!1))))),
% 2.62/2.83 inference(unit_resolution,[status(thm)],[461, 9129, 9157])).
% 2.62/2.83 tff(9159,plain,
% 2.62/2.83 (~b(z, s(s(elem!1)))),
% 2.62/2.83 inference(unit_resolution,[status(thm)],[2261, 9075, 125])).
% 2.62/2.83 tff(9160,plain,
% 2.62/2.83 (r(z, s(s(elem!1)))),
% 2.62/2.83 inference(unit_resolution,[status(thm)],[1795, 9159])).
% 2.62/2.83 tff(9161,plain,
% 2.62/2.83 (~r(z, s(s(s(elem!1))))),
% 2.62/2.83 inference(unit_resolution,[status(thm)],[1956, 9104, 9160, 9158])).
% 2.62/2.83 tff(9162,plain,
% 2.62/2.83 (~r(elem!1, s(s(s(elem!1))))),
% 2.62/2.83 inference(unit_resolution,[status(thm)],[5446, 9161, 9077])).
% 2.62/2.83 tff(9163,plain,
% 2.62/2.83 (b(elem!1, s(s(s(elem!1))))),
% 2.62/2.83 inference(unit_resolution,[status(thm)],[5451, 9162, 9156])).
% 2.62/2.83 tff(9164,plain,
% 2.62/2.83 (b(s(s(s(elem!1))), elem!1)),
% 2.62/2.83 inference(unit_resolution,[status(thm)],[634, 9077, 8808])).
% 2.62/2.83 tff(9165,plain,
% 2.62/2.83 (~b(s(s(s(s(elem!1)))), s(s(s(elem!1))))),
% 2.62/2.83 inference(unit_resolution,[status(thm)],[2912, 9149, 9164, 9163])).
% 2.62/2.83 tff(9166,plain,
% 2.62/2.83 (r(s(s(s(s(elem!1)))), s(s(s(elem!1))))),
% 2.62/2.83 inference(unit_resolution,[status(thm)],[1065, 9165, 9152])).
% 2.62/2.83 tff(9167,plain,
% 2.62/2.83 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), s(s(elem!1)))) | (~r(s(s(elem!1)), s(s(s(elem!1))))) | (~r(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~r(s(s(elem!1)), s(s(s(s(elem!1)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(elem!1))), s(s(elem!1)))) | (~r(s(s(elem!1)), s(s(s(elem!1))))) | (~r(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~r(s(s(elem!1)), s(s(s(s(elem!1)))))))),
% 2.62/2.83 inference(rewrite,[status(thm)],[])).
% 2.62/2.83 tff(9168,plain,
% 2.62/2.83 (((~r(s(s(s(elem!1))), s(s(elem!1)))) | (~r(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(elem!1))))))) <=> ((~r(s(s(s(elem!1))), s(s(elem!1)))) | (~r(s(s(elem!1)), s(s(s(elem!1))))) | (~r(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~r(s(s(elem!1)), s(s(s(s(elem!1)))))))),
% 2.62/2.83 inference(rewrite,[status(thm)],[])).
% 2.62/2.83 tff(9169,plain,
% 2.62/2.83 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), s(s(elem!1)))) | (~r(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(elem!1)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), s(s(elem!1)))) | (~r(s(s(elem!1)), s(s(s(elem!1))))) | (~r(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~r(s(s(elem!1)), s(s(s(s(elem!1))))))))),
% 2.62/2.83 inference(monotonicity,[status(thm)],[9168])).
% 2.62/2.83 tff(9170,plain,
% 2.62/2.83 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), s(s(elem!1)))) | (~r(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(elem!1)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(elem!1))), s(s(elem!1)))) | (~r(s(s(elem!1)), s(s(s(elem!1))))) | (~r(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~r(s(s(elem!1)), s(s(s(s(elem!1)))))))),
% 2.62/2.83 inference(transitivity,[status(thm)],[9169, 9167])).
% 2.62/2.83 tff(9171,plain,
% 2.62/2.83 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), s(s(elem!1)))) | (~r(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(elem!1)))))))),
% 2.62/2.83 inference(quant_inst,[status(thm)],[])).
% 2.62/2.83 tff(9172,plain,
% 2.62/2.83 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(elem!1))), s(s(elem!1)))) | (~r(s(s(elem!1)), s(s(s(elem!1))))) | (~r(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~r(s(s(elem!1)), s(s(s(s(elem!1))))))),
% 2.62/2.83 inference(modus_ponens,[status(thm)],[9171, 9170])).
% 2.62/2.83 tff(9173,plain,
% 2.62/2.83 (~r(s(s(elem!1)), s(s(s(s(elem!1)))))),
% 2.62/2.83 inference(unit_resolution,[status(thm)],[9172, 197, 9158, 9104, 9166])).
% 2.62/2.83 tff(9174,plain,
% 2.62/2.83 (b(s(s(elem!1)), s(s(s(s(elem!1)))))),
% 2.62/2.83 inference(unit_resolution,[status(thm)],[827, 9173, 9095])).
% 2.62/2.83 tff(9175,plain,
% 2.62/2.83 (~b(s(s(elem!1)), elem!1)),
% 2.62/2.83 inference(unit_resolution,[status(thm)],[1126, 9174, 9149, 9138])).
% 2.62/2.83 tff(9176,plain,
% 2.62/2.83 (r(s(s(elem!1)), elem!1)),
% 2.62/2.83 inference(unit_resolution,[status(thm)],[784, 9175, 9083])).
% 2.62/2.83 tff(9177,plain,
% 2.62/2.83 (~(s(s(s(s(s(s(elem!1)))))) = s(s(elem!1)))),
% 2.62/2.83 inference(unit_resolution,[status(thm)],[4986, 9076])).
% 2.62/2.83 tff(9178,assumption,(r(s(s(s(s(s(s(elem!1)))))), elem!1)), introduced(assumption)).
% 2.62/2.83 tff(9179,assumption,(r(s(s(s(s(s(s(elem!1)))))), s(s(elem!1)))), introduced(assumption)).
% 2.62/2.83 tff(9180,plain,
% 2.62/2.83 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(z))) | (~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, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(elem!1, s(z))) | (~r(s(s(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)))))),
% 2.62/2.83 inference(rewrite,[status(thm)],[])).
% 2.62/2.83 tff(9181,plain,
% 2.62/2.83 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(z))) | (~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)))))),
% 2.62/2.83 inference(quant_inst,[status(thm)],[])).
% 2.62/2.83 tff(9182,plain,
% 2.62/2.83 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(elem!1, s(z))) | (~r(s(s(elem!1)), elem!1)) | (~r(s(s(s(s(s(s(elem!1)))))), elem!1)) | (~r(s(s(s(s(s(s(elem!1)))))), s(s(elem!1))))),
% 2.62/2.83 inference(modus_ponens,[status(thm)],[9181, 9180])).
% 2.62/2.83 tff(9183,plain,
% 2.62/2.83 ($false),
% 2.62/2.83 inference(unit_resolution,[status(thm)],[9182, 197, 744, 768, 9178, 9179])).
% 2.62/2.83 tff(9184,plain,((~r(s(s(s(s(s(s(elem!1)))))), s(s(elem!1)))) | (~r(elem!1, s(z))) | (~r(s(s(elem!1)), elem!1)) | (~r(s(s(s(s(s(s(elem!1)))))), elem!1))), inference(lemma,lemma(discharge,[]))).
% 2.62/2.83 tff(9185,plain,
% 2.62/2.83 (~r(s(s(s(s(s(s(elem!1)))))), s(s(elem!1)))),
% 2.62/2.83 inference(unit_resolution,[status(thm)],[9184, 9178, 768, 744])).
% 2.62/2.83 tff(9186,plain,
% 2.62/2.83 (((~![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))))),
% 2.62/2.83 inference(rewrite,[status(thm)],[])).
% 2.62/2.83 tff(9187,plain,
% 2.62/2.83 ((~![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))))),
% 2.62/2.83 inference(quant_inst,[status(thm)],[])).
% 2.62/2.83 tff(9188,plain,
% 2.62/2.83 ((~![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)))),
% 2.62/2.83 inference(modus_ponens,[status(thm)],[9187, 9186])).
% 2.62/2.83 tff(9189,plain,
% 2.62/2.83 (b(s(s(s(s(s(s(elem!1)))))), s(s(elem!1)))),
% 2.62/2.83 inference(unit_resolution,[status(thm)],[9188, 79, 4993, 9185])).
% 2.62/2.83 tff(9190,plain,
% 2.62/2.83 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(elem!1)))) | (~b(s(s(elem!1)), s(z))) | (~b(s(s(s(s(s(s(elem!1)))))), s(s(elem!1)))) | (~b(s(s(s(s(s(s(elem!1)))))), s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), s(s(elem!1)))) | (~b(s(s(elem!1)), s(z))) | (~b(s(s(s(s(s(s(elem!1)))))), s(s(elem!1)))) | (~b(s(s(s(s(s(s(elem!1)))))), s(z))))),
% 2.62/2.83 inference(rewrite,[status(thm)],[])).
% 2.62/2.83 tff(9191,plain,
% 2.62/2.83 (((~b(s(z), s(s(elem!1)))) | (~b(s(s(s(s(s(s(elem!1)))))), s(s(elem!1)))) | (~b(s(s(elem!1)), s(z))) | (~b(s(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)))))), s(z)))) <=> ((~b(s(z), s(s(elem!1)))) | (~b(s(s(elem!1)), s(z))) | (~b(s(s(s(s(s(s(elem!1)))))), s(s(elem!1)))) | (~b(s(s(s(s(s(s(elem!1)))))), s(z))))),
% 2.62/2.83 inference(rewrite,[status(thm)],[])).
% 2.62/2.83 tff(9192,plain,
% 2.62/2.83 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(elem!1)))) | (~b(s(s(s(s(s(s(elem!1)))))), s(s(elem!1)))) | (~b(s(s(elem!1)), s(z))) | (~b(s(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)))))), s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(elem!1)))) | (~b(s(s(elem!1)), s(z))) | (~b(s(s(s(s(s(s(elem!1)))))), s(s(elem!1)))) | (~b(s(s(s(s(s(s(elem!1)))))), s(z)))))),
% 2.62/2.83 inference(monotonicity,[status(thm)],[9191])).
% 2.62/2.83 tff(9193,plain,
% 2.62/2.83 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(elem!1)))) | (~b(s(s(s(s(s(s(elem!1)))))), s(s(elem!1)))) | (~b(s(s(elem!1)), s(z))) | (~b(s(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)))))), s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), s(s(elem!1)))) | (~b(s(s(elem!1)), s(z))) | (~b(s(s(s(s(s(s(elem!1)))))), s(s(elem!1)))) | (~b(s(s(s(s(s(s(elem!1)))))), s(z))))),
% 2.62/2.83 inference(transitivity,[status(thm)],[9192, 9190])).
% 2.62/2.83 tff(9194,plain,
% 2.62/2.83 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(elem!1)))) | (~b(s(s(s(s(s(s(elem!1)))))), s(s(elem!1)))) | (~b(s(s(elem!1)), s(z))) | (~b(s(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)))))), s(z))))),
% 2.62/2.83 inference(quant_inst,[status(thm)],[])).
% 2.62/2.83 tff(9195,plain,
% 2.62/2.83 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), s(s(elem!1)))) | (~b(s(s(elem!1)), s(z))) | (~b(s(s(s(s(s(s(elem!1)))))), s(s(elem!1)))) | (~b(s(s(s(s(s(s(elem!1)))))), s(z)))),
% 2.62/2.83 inference(modus_ponens,[status(thm)],[9194, 9193])).
% 2.62/2.83 tff(9196,plain,
% 2.62/2.83 (~b(s(s(s(s(s(s(elem!1)))))), s(z))),
% 2.62/2.83 inference(unit_resolution,[status(thm)],[9195, 166, 376, 310, 9189])).
% 2.62/2.83 tff(9197,plain,
% 2.62/2.83 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(z))) | (~r(s(z), elem!1)) | (~r(s(s(s(s(s(s(elem!1)))))), elem!1)) | (~r(s(s(s(s(s(s(elem!1)))))), s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(elem!1, s(z))) | (~r(s(z), elem!1)) | (~r(s(s(s(s(s(s(elem!1)))))), elem!1)) | (~r(s(s(s(s(s(s(elem!1)))))), s(z))))),
% 2.62/2.83 inference(rewrite,[status(thm)],[])).
% 2.62/2.83 tff(9198,plain,
% 2.62/2.83 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(z))) | (~r(s(z), elem!1)) | (~r(s(s(s(s(s(s(elem!1)))))), elem!1)) | (~r(s(s(s(s(s(s(elem!1)))))), s(z))))),
% 2.62/2.83 inference(quant_inst,[status(thm)],[])).
% 2.62/2.83 tff(9199,plain,
% 2.62/2.83 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(elem!1, s(z))) | (~r(s(z), elem!1)) | (~r(s(s(s(s(s(s(elem!1)))))), elem!1)) | (~r(s(s(s(s(s(s(elem!1)))))), s(z)))),
% 2.62/2.83 inference(modus_ponens,[status(thm)],[9198, 9197])).
% 2.62/2.83 tff(9200,plain,
% 2.62/2.83 (~r(s(s(s(s(s(s(elem!1)))))), s(z))),
% 2.62/2.83 inference(unit_resolution,[status(thm)],[9199, 197, 744, 2381, 9178])).
% 2.62/2.83 tff(9201,plain,
% 2.62/2.83 (((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((s(s(s(s(s(s(elem!1)))))) = s(z)) | b(s(s(s(s(s(s(elem!1)))))), s(z)) | r(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(elem!1)))))) = s(z)) | b(s(s(s(s(s(s(elem!1)))))), s(z)) | r(s(s(s(s(s(s(elem!1)))))), s(z)))),
% 2.62/2.83 inference(rewrite,[status(thm)],[])).
% 2.62/2.83 tff(9202,plain,
% 2.62/2.83 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((s(s(s(s(s(s(elem!1)))))) = s(z)) | b(s(s(s(s(s(s(elem!1)))))), s(z)) | r(s(s(s(s(s(s(elem!1)))))), s(z)))),
% 2.62/2.83 inference(quant_inst,[status(thm)],[])).
% 2.62/2.83 tff(9203,plain,
% 2.62/2.83 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (s(s(s(s(s(s(elem!1)))))) = s(z)) | b(s(s(s(s(s(s(elem!1)))))), s(z)) | r(s(s(s(s(s(s(elem!1)))))), s(z))),
% 2.62/2.83 inference(modus_ponens,[status(thm)],[9202, 9201])).
% 2.62/2.83 tff(9204,plain,
% 2.62/2.83 ($false),
% 2.62/2.83 inference(unit_resolution,[status(thm)],[9203, 79, 5014, 9200, 9196])).
% 2.62/2.83 tff(9205,plain,((~r(s(s(s(s(s(s(elem!1)))))), elem!1)) | (~b(s(z), s(s(elem!1)))) | (~b(s(s(elem!1)), s(z))) | (~r(elem!1, s(z))) | (~r(s(z), elem!1)) | (s(s(s(s(s(s(elem!1)))))) = s(s(elem!1))) | (~r(s(s(elem!1)), elem!1))), inference(lemma,lemma(discharge,[]))).
% 2.62/2.83 tff(9206,plain,
% 2.62/2.83 (~r(s(s(s(s(s(s(elem!1)))))), elem!1)),
% 2.62/2.83 inference(unit_resolution,[status(thm)],[9205, 8809, 310, 9133, 9132, 9177, 9176])).
% 2.62/2.83 tff(9207,assumption,(~(s(s(s(s(s(s(elem!1)))))) = elem!1)), introduced(assumption)).
% 2.62/2.83 tff(9208,assumption,(~b(s(s(s(s(s(s(elem!1)))))), elem!1)), introduced(assumption)).
% 2.62/2.83 tff(9209,assumption,(~r(s(s(s(s(s(s(elem!1)))))), elem!1)), introduced(assumption)).
% 2.62/2.83 tff(9210,plain,
% 2.62/2.83 (((~![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))),
% 2.62/2.83 inference(rewrite,[status(thm)],[])).
% 2.62/2.84 tff(9211,plain,
% 2.62/2.84 ((~![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))),
% 2.62/2.84 inference(quant_inst,[status(thm)],[])).
% 2.62/2.84 tff(9212,plain,
% 2.62/2.84 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (s(s(s(s(s(s(elem!1)))))) = elem!1) | b(s(s(s(s(s(s(elem!1)))))), elem!1) | r(s(s(s(s(s(s(elem!1)))))), elem!1)),
% 2.62/2.84 inference(modus_ponens,[status(thm)],[9211, 9210])).
% 2.62/2.84 tff(9213,plain,
% 2.62/2.84 ($false),
% 2.62/2.84 inference(unit_resolution,[status(thm)],[9212, 79, 9209, 9208, 9207])).
% 2.62/2.84 tff(9214,plain,(r(s(s(s(s(s(s(elem!1)))))), elem!1) | b(s(s(s(s(s(s(elem!1)))))), elem!1) | (s(s(s(s(s(s(elem!1)))))) = elem!1)), inference(lemma,lemma(discharge,[]))).
% 2.62/2.84 tff(9215,plain,
% 2.62/2.84 (b(s(s(s(s(s(s(elem!1)))))), elem!1)),
% 2.62/2.84 inference(unit_resolution,[status(thm)],[9214, 9206, 9078])).
% 2.62/2.84 tff(9216,plain,
% 2.62/2.84 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(s(s(elem!1))))) | (~b(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(elem!1)))))), s(s(s(elem!1))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(s(s(elem!1))))) | (~b(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(elem!1)))))), s(s(s(elem!1))))))),
% 2.62/2.84 inference(rewrite,[status(thm)],[])).
% 2.62/2.84 tff(9217,plain,
% 2.62/2.84 (((~b(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(elem!1))), 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)))))) <=> ((~b(elem!1, s(s(s(elem!1))))) | (~b(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(elem!1)))))), s(s(s(elem!1))))))),
% 2.62/2.84 inference(rewrite,[status(thm)],[])).
% 2.62/2.84 tff(9218,plain,
% 2.62/2.84 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), elem!1)) | (~b(s(s(s(s(s(s(elem!1)))))), elem!1)) | (~b(elem!1, s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(s(s(s(s(s(elem!1)))))), elem!1)) | (~b(s(s(s(s(s(s(elem!1)))))), s(s(s(elem!1))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(s(s(elem!1))))) | (~b(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(elem!1)))))), s(s(s(elem!1)))))))),
% 2.62/2.84 inference(monotonicity,[status(thm)],[9217])).
% 2.62/2.84 tff(9219,plain,
% 2.62/2.84 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), elem!1)) | (~b(s(s(s(s(s(s(elem!1)))))), elem!1)) | (~b(elem!1, s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(s(s(s(s(s(elem!1)))))), elem!1)) | (~b(s(s(s(s(s(s(elem!1)))))), s(s(s(elem!1))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(s(s(elem!1))))) | (~b(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(elem!1)))))), s(s(s(elem!1))))))),
% 2.62/2.84 inference(transitivity,[status(thm)],[9218, 9216])).
% 2.62/2.84 tff(9220,plain,
% 2.62/2.84 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), elem!1)) | (~b(s(s(s(s(s(s(elem!1)))))), elem!1)) | (~b(elem!1, s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(s(s(s(s(s(elem!1)))))), elem!1)) | (~b(s(s(s(s(s(s(elem!1)))))), s(s(s(elem!1))))))),
% 2.62/2.84 inference(quant_inst,[status(thm)],[])).
% 2.62/2.84 tff(9221,plain,
% 2.62/2.84 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(s(s(elem!1))))) | (~b(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(elem!1)))))), s(s(s(elem!1)))))),
% 2.62/2.84 inference(modus_ponens,[status(thm)],[9220, 9219])).
% 2.62/2.84 tff(9222,plain,
% 2.62/2.84 (~b(s(s(s(s(s(s(elem!1)))))), s(s(s(elem!1))))),
% 2.62/2.84 inference(unit_resolution,[status(thm)],[9221, 166, 9163, 9164, 9215])).
% 2.62/2.84 tff(9223,plain,
% 2.62/2.84 (~(s(s(s(s(s(s(elem!1)))))) = s(s(s(elem!1))))),
% 2.62/2.84 inference(unit_resolution,[status(thm)],[4922, 9076])).
% 2.62/2.84 tff(9224,plain,
% 2.62/2.84 (((~![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)))))),
% 2.62/2.84 inference(rewrite,[status(thm)],[])).
% 2.62/2.84 tff(9225,plain,
% 2.62/2.84 ((~![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)))))),
% 2.62/2.84 inference(quant_inst,[status(thm)],[])).
% 2.62/2.84 tff(9226,plain,
% 2.62/2.84 ((~![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))))),
% 2.62/2.84 inference(modus_ponens,[status(thm)],[9225, 9224])).
% 2.62/2.84 tff(9227,plain,
% 2.62/2.84 (r(s(s(s(s(s(s(elem!1)))))), s(s(s(elem!1))))),
% 2.62/2.84 inference(unit_resolution,[status(thm)],[9226, 79, 9223, 9222])).
% 2.62/2.84 tff(9228,plain,
% 2.62/2.84 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(s(s(s(elem!1)))), elem!1)) | (~b(s(s(s(s(s(s(elem!1)))))), elem!1)) | (~b(s(s(s(s(elem!1)))), s(s(s(s(s(s(elem!1)))))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(s(s(s(elem!1)))), elem!1)) | (~b(s(s(s(s(s(s(elem!1)))))), elem!1)) | (~b(s(s(s(s(elem!1)))), s(s(s(s(s(s(elem!1)))))))))),
% 2.62/2.84 inference(rewrite,[status(thm)],[])).
% 2.62/2.84 tff(9229,plain,
% 2.62/2.84 (((~b(s(s(s(elem!1))), elem!1)) | (~b(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)))))), elem!1)) | (~b(s(s(s(s(elem!1)))), elem!1)) | (~b(s(s(s(s(elem!1)))), s(s(s(s(s(s(elem!1))))))))) <=> ((~b(elem!1, s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(s(s(s(elem!1)))), elem!1)) | (~b(s(s(s(s(s(s(elem!1)))))), elem!1)) | (~b(s(s(s(s(elem!1)))), s(s(s(s(s(s(elem!1)))))))))),
% 2.62/2.84 inference(rewrite,[status(thm)],[])).
% 2.62/2.84 tff(9230,plain,
% 2.62/2.84 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), elem!1)) | (~b(s(s(s(s(elem!1)))), 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(elem!1)))), elem!1)) | (~b(s(s(s(s(elem!1)))), s(s(s(s(s(s(elem!1)))))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(s(s(s(elem!1)))), elem!1)) | (~b(s(s(s(s(s(s(elem!1)))))), elem!1)) | (~b(s(s(s(s(elem!1)))), s(s(s(s(s(s(elem!1))))))))))),
% 2.62/2.84 inference(monotonicity,[status(thm)],[9229])).
% 2.62/2.84 tff(9231,plain,
% 2.62/2.84 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), elem!1)) | (~b(s(s(s(s(elem!1)))), 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(elem!1)))), elem!1)) | (~b(s(s(s(s(elem!1)))), s(s(s(s(s(s(elem!1)))))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(s(s(s(elem!1)))), elem!1)) | (~b(s(s(s(s(s(s(elem!1)))))), elem!1)) | (~b(s(s(s(s(elem!1)))), s(s(s(s(s(s(elem!1)))))))))),
% 2.62/2.84 inference(transitivity,[status(thm)],[9230, 9228])).
% 2.62/2.84 tff(9232,plain,
% 2.62/2.84 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), elem!1)) | (~b(s(s(s(s(elem!1)))), 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(elem!1)))), elem!1)) | (~b(s(s(s(s(elem!1)))), s(s(s(s(s(s(elem!1)))))))))),
% 2.62/2.84 inference(quant_inst,[status(thm)],[])).
% 2.62/2.84 tff(9233,plain,
% 2.62/2.84 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(s(s(s(elem!1)))), elem!1)) | (~b(s(s(s(s(s(s(elem!1)))))), elem!1)) | (~b(s(s(s(s(elem!1)))), s(s(s(s(s(s(elem!1))))))))),
% 2.62/2.84 inference(modus_ponens,[status(thm)],[9232, 9231])).
% 2.62/2.84 tff(9234,plain,
% 2.62/2.84 (~b(s(s(s(s(elem!1)))), s(s(s(s(s(s(elem!1)))))))),
% 2.62/2.84 inference(unit_resolution,[status(thm)],[9233, 166, 9163, 9164, 9138, 9215])).
% 2.62/2.84 tff(9235,assumption,(s(s(s(s(elem!1)))) = s(s(s(s(s(s(elem!1))))))), introduced(assumption)).
% 2.62/2.84 tff(9236,plain,
% 2.62/2.84 (s(s(s(s(s(s(elem!1)))))) = s(s(s(s(elem!1))))),
% 2.62/2.84 inference(symmetry,[status(thm)],[9235])).
% 2.62/2.84 tff(9237,plain,
% 2.62/2.84 (inj_0(s(s(s(s(s(s(elem!1))))))) = inj_0(s(s(s(s(elem!1)))))),
% 2.62/2.84 inference(monotonicity,[status(thm)],[9236])).
% 2.62/2.84 tff(9238,plain,
% 2.62/2.84 (inj_0(s(s(s(s(elem!1))))) = inj_0(s(s(s(s(s(s(elem!1)))))))),
% 2.62/2.84 inference(symmetry,[status(thm)],[9237])).
% 2.62/2.84 tff(9239,plain,
% 2.62/2.84 (s(s(s(elem!1))) = s(s(s(s(s(elem!1)))))),
% 2.62/2.84 inference(transitivity,[status(thm)],[653, 9238, 4910])).
% 2.62/2.84 tff(9240,plain,
% 2.62/2.84 (inj_0(s(s(s(elem!1)))) = inj_0(s(s(s(s(s(elem!1))))))),
% 2.62/2.84 inference(monotonicity,[status(thm)],[9239])).
% 2.62/2.84 tff(9241,plain,
% 2.62/2.84 (s(s(elem!1)) = s(s(s(s(elem!1))))),
% 2.62/2.84 inference(transitivity,[status(thm)],[105, 9240, 4918])).
% 2.62/2.84 tff(9242,plain,
% 2.62/2.84 ($false),
% 2.62/2.84 inference(unit_resolution,[status(thm)],[2395, 9241])).
% 2.62/2.84 tff(9243,plain,((~(s(s(s(s(elem!1)))) = s(s(s(s(s(s(elem!1)))))))) | (s(s(elem!1)) = s(s(s(s(elem!1)))))), inference(lemma,lemma(discharge,[]))).
% 2.62/2.84 tff(9244,plain,
% 2.62/2.84 (~(s(s(s(s(elem!1)))) = s(s(s(s(s(s(elem!1)))))))),
% 2.62/2.84 inference(unit_resolution,[status(thm)],[9243, 9095])).
% 2.62/2.84 tff(9245,plain,
% 2.62/2.84 (((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((s(s(s(s(elem!1)))) = s(s(s(s(s(s(elem!1))))))) | b(s(s(s(s(elem!1)))), s(s(s(s(s(s(elem!1))))))) | r(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(elem!1)))) = s(s(s(s(s(s(elem!1))))))) | b(s(s(s(s(elem!1)))), s(s(s(s(s(s(elem!1))))))) | r(s(s(s(s(elem!1)))), s(s(s(s(s(s(elem!1))))))))),
% 2.62/2.84 inference(rewrite,[status(thm)],[])).
% 2.62/2.84 tff(9246,plain,
% 2.62/2.84 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((s(s(s(s(elem!1)))) = s(s(s(s(s(s(elem!1))))))) | b(s(s(s(s(elem!1)))), s(s(s(s(s(s(elem!1))))))) | r(s(s(s(s(elem!1)))), s(s(s(s(s(s(elem!1))))))))),
% 2.62/2.84 inference(quant_inst,[status(thm)],[])).
% 2.62/2.84 tff(9247,plain,
% 2.62/2.84 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (s(s(s(s(elem!1)))) = s(s(s(s(s(s(elem!1))))))) | b(s(s(s(s(elem!1)))), s(s(s(s(s(s(elem!1))))))) | r(s(s(s(s(elem!1)))), s(s(s(s(s(s(elem!1)))))))),
% 2.62/2.84 inference(modus_ponens,[status(thm)],[9246, 9245])).
% 2.62/2.84 tff(9248,plain,
% 2.62/2.84 (r(s(s(s(s(elem!1)))), s(s(s(s(s(s(elem!1)))))))),
% 2.62/2.84 inference(unit_resolution,[status(thm)],[9247, 79, 9244, 9234])).
% 2.62/2.84 tff(9249,plain,
% 2.62/2.84 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), s(s(elem!1)))) | (~r(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~r(s(s(s(s(elem!1)))), s(s(s(s(s(s(elem!1)))))))) | (~r(s(s(s(s(s(s(elem!1)))))), s(s(s(elem!1))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(elem!1))), s(s(elem!1)))) | (~r(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~r(s(s(s(s(elem!1)))), s(s(s(s(s(s(elem!1)))))))) | (~r(s(s(s(s(s(s(elem!1)))))), s(s(s(elem!1))))))),
% 2.62/2.84 inference(rewrite,[status(thm)],[])).
% 2.62/2.84 tff(9250,plain,
% 2.62/2.84 (((~r(s(s(s(elem!1))), s(s(elem!1)))) | (~r(s(s(s(s(s(s(elem!1)))))), s(s(s(elem!1))))) | (~r(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~r(s(s(s(s(elem!1)))), s(s(s(s(s(s(elem!1))))))))) <=> ((~r(s(s(s(elem!1))), s(s(elem!1)))) | (~r(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~r(s(s(s(s(elem!1)))), s(s(s(s(s(s(elem!1)))))))) | (~r(s(s(s(s(s(s(elem!1)))))), s(s(s(elem!1))))))),
% 2.62/2.84 inference(rewrite,[status(thm)],[])).
% 2.62/2.84 tff(9251,plain,
% 2.62/2.84 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), s(s(elem!1)))) | (~r(s(s(s(s(s(s(elem!1)))))), s(s(s(elem!1))))) | (~r(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~r(s(s(s(s(elem!1)))), s(s(s(s(s(s(elem!1)))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), s(s(elem!1)))) | (~r(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~r(s(s(s(s(elem!1)))), s(s(s(s(s(s(elem!1)))))))) | (~r(s(s(s(s(s(s(elem!1)))))), s(s(s(elem!1)))))))),
% 2.62/2.84 inference(monotonicity,[status(thm)],[9250])).
% 2.62/2.84 tff(9252,plain,
% 2.62/2.84 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), s(s(elem!1)))) | (~r(s(s(s(s(s(s(elem!1)))))), s(s(s(elem!1))))) | (~r(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~r(s(s(s(s(elem!1)))), s(s(s(s(s(s(elem!1)))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(elem!1))), s(s(elem!1)))) | (~r(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~r(s(s(s(s(elem!1)))), s(s(s(s(s(s(elem!1)))))))) | (~r(s(s(s(s(s(s(elem!1)))))), s(s(s(elem!1))))))),
% 2.62/2.84 inference(transitivity,[status(thm)],[9251, 9249])).
% 2.62/2.84 tff(9253,plain,
% 2.62/2.84 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), s(s(elem!1)))) | (~r(s(s(s(s(s(s(elem!1)))))), s(s(s(elem!1))))) | (~r(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~r(s(s(s(s(elem!1)))), s(s(s(s(s(s(elem!1)))))))))),
% 2.62/2.84 inference(quant_inst,[status(thm)],[])).
% 2.62/2.84 tff(9254,plain,
% 2.62/2.84 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(elem!1))), s(s(elem!1)))) | (~r(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~r(s(s(s(s(elem!1)))), s(s(s(s(s(s(elem!1)))))))) | (~r(s(s(s(s(s(s(elem!1)))))), s(s(s(elem!1)))))),
% 2.62/2.84 inference(modus_ponens,[status(thm)],[9253, 9252])).
% 2.62/2.84 tff(9255,plain,
% 2.62/2.84 ($false),
% 2.62/2.84 inference(unit_resolution,[status(thm)],[9254, 197, 9104, 9166, 9248, 9227])).
% 2.62/2.84 tff(9256,plain,((~b(s(s(elem!1)), s(z))) | (~b(s(s(s(elem!1))), s(z))) | b(z, s(s(z)))), inference(lemma,lemma(discharge,[]))).
% 2.62/2.84 tff(9257,plain,
% 2.62/2.84 (~b(s(s(elem!1)), s(z))),
% 2.62/2.84 inference(unit_resolution,[status(thm)],[9256, 96, 125])).
% 2.62/2.84 tff(9258,plain,
% 2.62/2.84 (~(s(s(elem!1)) = s(s(s(elem!1))))),
% 2.62/2.84 inference(unit_resolution,[status(thm)],[4570, 9257, 96])).
% 2.62/2.84 tff(9259,plain,
% 2.62/2.84 (~(s(s(s(elem!1))) = s(s(elem!1)))),
% 2.62/2.84 inference(unit_resolution,[status(thm)],[50, 9258])).
% 2.62/2.84 tff(9260,plain,
% 2.62/2.84 (r(s(s(elem!1)), s(z))),
% 2.62/2.84 inference(unit_resolution,[status(thm)],[1912, 9257])).
% 2.62/2.84 tff(9261,plain,
% 2.62/2.84 (~r(z, s(s(elem!1)))),
% 2.62/2.84 inference(unit_resolution,[status(thm)],[8600, 311, 8408, 9260])).
% 2.62/2.84 tff(9262,plain,
% 2.62/2.84 (b(z, s(s(elem!1)))),
% 2.62/2.84 inference(unit_resolution,[status(thm)],[1795, 9261])).
% 2.62/2.84 tff(9263,plain,
% 2.62/2.84 (~(s(s(z)) = s(s(elem!1)))),
% 2.62/2.84 inference(unit_resolution,[status(thm)],[2261, 9262, 125])).
% 2.62/2.84 tff(9264,plain,
% 2.62/2.84 (~(s(s(elem!1)) = s(s(z)))),
% 2.62/2.84 inference(unit_resolution,[status(thm)],[131, 9263])).
% 2.62/2.84 tff(9265,plain,
% 2.62/2.84 (~(s(s(s(elem!1))) = s(s(s(z))))),
% 2.62/2.84 inference(unit_resolution,[status(thm)],[139, 9264])).
% 2.62/2.84 tff(9266,plain,
% 2.62/2.84 (~r(s(s(z)), s(z))),
% 2.62/2.84 inference(unit_resolution,[status(thm)],[8578, 311, 152, 8408])).
% 2.62/2.84 tff(9267,plain,
% 2.62/2.84 (b(s(s(z)), s(z))),
% 2.62/2.84 inference(unit_resolution,[status(thm)],[308, 9266])).
% 2.62/2.84 tff(9268,plain,
% 2.62/2.84 (~r(s(s(elem!1)), z)),
% 2.62/2.84 inference(unit_resolution,[status(thm)],[8590, 311, 8408, 9260])).
% 2.62/2.84 tff(9269,plain,
% 2.62/2.84 (b(s(s(elem!1)), z)),
% 2.62/2.84 inference(unit_resolution,[status(thm)],[608, 9268])).
% 2.62/2.84 tff(9270,plain,
% 2.62/2.84 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(z, s(s(elem!1)))) | (~b(s(s(elem!1)), z)) | (~b(s(s(s(elem!1))), z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(z, s(s(elem!1)))) | (~b(s(s(elem!1)), z)) | (~b(s(s(s(elem!1))), z)))),
% 2.62/2.84 inference(rewrite,[status(thm)],[])).
% 2.62/2.84 tff(9271,plain,
% 2.62/2.84 (((~b(s(s(elem!1)), z)) | (~b(s(s(s(elem!1))), z)) | (~b(z, s(s(elem!1)))) | (~b(s(s(elem!1)), z)) | (~b(s(s(s(elem!1))), z)) | (~b(s(s(s(elem!1))), s(s(elem!1))))) <=> ((~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(z, s(s(elem!1)))) | (~b(s(s(elem!1)), z)) | (~b(s(s(s(elem!1))), z)))),
% 2.62/2.84 inference(rewrite,[status(thm)],[])).
% 2.62/2.84 tff(9272,plain,
% 2.62/2.84 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), z)) | (~b(s(s(s(elem!1))), z)) | (~b(z, s(s(elem!1)))) | (~b(s(s(elem!1)), z)) | (~b(s(s(s(elem!1))), z)) | (~b(s(s(s(elem!1))), s(s(elem!1)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(z, s(s(elem!1)))) | (~b(s(s(elem!1)), z)) | (~b(s(s(s(elem!1))), z))))),
% 2.62/2.84 inference(monotonicity,[status(thm)],[9271])).
% 2.62/2.84 tff(9273,plain,
% 2.62/2.84 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), z)) | (~b(s(s(s(elem!1))), z)) | (~b(z, s(s(elem!1)))) | (~b(s(s(elem!1)), z)) | (~b(s(s(s(elem!1))), z)) | (~b(s(s(s(elem!1))), s(s(elem!1)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(z, s(s(elem!1)))) | (~b(s(s(elem!1)), z)) | (~b(s(s(s(elem!1))), z)))),
% 2.62/2.84 inference(transitivity,[status(thm)],[9272, 9270])).
% 2.62/2.84 tff(9274,plain,
% 2.62/2.84 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), z)) | (~b(s(s(s(elem!1))), z)) | (~b(z, s(s(elem!1)))) | (~b(s(s(elem!1)), z)) | (~b(s(s(s(elem!1))), z)) | (~b(s(s(s(elem!1))), s(s(elem!1)))))),
% 2.62/2.84 inference(quant_inst,[status(thm)],[])).
% 2.62/2.84 tff(9275,plain,
% 2.62/2.84 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(z, s(s(elem!1)))) | (~b(s(s(elem!1)), z)) | (~b(s(s(s(elem!1))), z))),
% 2.62/2.84 inference(modus_ponens,[status(thm)],[9274, 9273])).
% 2.62/2.84 tff(9276,plain,
% 2.62/2.84 (~b(s(s(s(elem!1))), s(s(elem!1)))),
% 2.62/2.84 inference(unit_resolution,[status(thm)],[9275, 166, 9262, 8808, 9269])).
% 2.62/2.84 tff(9277,plain,
% 2.62/2.84 (r(s(s(s(elem!1))), s(s(elem!1)))),
% 2.62/2.84 inference(unit_resolution,[status(thm)],[889, 9276, 9259])).
% 2.62/2.84 tff(9278,plain,
% 2.62/2.84 (~b(s(s(elem!1)), s(s(s(elem!1))))),
% 2.62/2.84 inference(unit_resolution,[status(thm)],[3593, 9262, 8808, 9269])).
% 2.62/2.84 tff(9279,plain,
% 2.62/2.84 (r(s(s(elem!1)), s(s(s(elem!1))))),
% 2.62/2.84 inference(unit_resolution,[status(thm)],[461, 9278, 9258])).
% 2.62/2.84 tff(9280,plain,
% 2.62/2.84 (~r(s(z), s(s(s(elem!1))))),
% 2.62/2.84 inference(unit_resolution,[status(thm)],[2949, 9277, 311, 9279])).
% 2.62/2.84 tff(9281,plain,
% 2.62/2.84 (b(s(z), s(s(s(elem!1))))),
% 2.62/2.84 inference(unit_resolution,[status(thm)],[116, 9280])).
% 2.62/2.84 tff(9282,plain,
% 2.62/2.84 (~b(s(s(z)), s(s(s(elem!1))))),
% 2.62/2.84 inference(unit_resolution,[status(thm)],[271, 9281, 96, 9267])).
% 2.62/2.84 tff(9283,plain,
% 2.62/2.84 (r(s(s(z)), s(s(s(elem!1))))),
% 2.62/2.84 inference(unit_resolution,[status(thm)],[279, 9282])).
% 2.62/2.84 tff(9284,plain,
% 2.62/2.84 (~r(s(s(z)), s(s(elem!1)))),
% 2.62/2.84 inference(unit_resolution,[status(thm)],[8677, 9283, 9260, 9277])).
% 2.62/2.84 tff(9285,plain,
% 2.62/2.84 (b(s(s(z)), s(s(elem!1)))),
% 2.62/2.84 inference(unit_resolution,[status(thm)],[390, 9284, 9263])).
% 2.62/2.84 tff(9286,plain,
% 2.62/2.84 (((~b(z, s(s(elem!1)))) | (~b(s(s(z)), s(s(elem!1)))) | (~b(s(s(elem!1)), z)) | (~b(z, s(s(elem!1)))) | (~b(s(s(z)), s(s(elem!1)))) | (~b(s(s(z)), z))) <=> ((~b(z, s(s(elem!1)))) | (~b(s(s(elem!1)), z)) | (~b(s(s(z)), s(s(elem!1)))) | (~b(s(s(z)), z)))),
% 2.62/2.84 inference(rewrite,[status(thm)],[])).
% 2.62/2.84 tff(9287,plain,
% 2.62/2.84 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(elem!1)))) | (~b(s(s(z)), s(s(elem!1)))) | (~b(s(s(elem!1)), z)) | (~b(z, s(s(elem!1)))) | (~b(s(s(z)), s(s(elem!1)))) | (~b(s(s(z)), z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(elem!1)))) | (~b(s(s(elem!1)), z)) | (~b(s(s(z)), s(s(elem!1)))) | (~b(s(s(z)), z))))),
% 2.62/2.84 inference(monotonicity,[status(thm)],[9286])).
% 2.62/2.84 tff(9288,plain,
% 2.62/2.84 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(elem!1)))) | (~b(s(s(z)), s(s(elem!1)))) | (~b(s(s(elem!1)), z)) | (~b(z, s(s(elem!1)))) | (~b(s(s(z)), s(s(elem!1)))) | (~b(s(s(z)), z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(s(elem!1)))) | (~b(s(s(elem!1)), z)) | (~b(s(s(z)), s(s(elem!1)))) | (~b(s(s(z)), z)))),
% 2.62/2.84 inference(transitivity,[status(thm)],[9287, 4600])).
% 2.62/2.84 tff(9289,plain,
% 2.62/2.84 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(elem!1)))) | (~b(s(s(z)), s(s(elem!1)))) | (~b(s(s(elem!1)), z)) | (~b(z, s(s(elem!1)))) | (~b(s(s(z)), s(s(elem!1)))) | (~b(s(s(z)), z)))),
% 2.62/2.84 inference(quant_inst,[status(thm)],[])).
% 2.62/2.84 tff(9290,plain,
% 2.62/2.84 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(s(elem!1)))) | (~b(s(s(elem!1)), z)) | (~b(s(s(z)), s(s(elem!1)))) | (~b(s(s(z)), z))),
% 2.62/2.84 inference(modus_ponens,[status(thm)],[9289, 9288])).
% 2.62/2.84 tff(9291,plain,
% 2.62/2.84 (~b(s(s(z)), z)),
% 2.62/2.84 inference(unit_resolution,[status(thm)],[9290, 166, 9262, 9269, 9285])).
% 2.62/2.84 tff(9292,plain,
% 2.62/2.84 (r(s(s(z)), z)),
% 2.62/2.84 inference(unit_resolution,[status(thm)],[186, 9291])).
% 2.62/2.84 tff(9293,plain,
% 2.62/2.84 (~b(s(s(s(elem!1))), s(s(z)))),
% 2.62/2.84 inference(unit_resolution,[status(thm)],[9072, 166, 9281, 96, 9267])).
% 2.62/2.84 tff(9294,plain,
% 2.62/2.84 (r(s(s(s(elem!1))), s(s(z)))),
% 2.62/2.84 inference(unit_resolution,[status(thm)],[218, 9293])).
% 2.62/2.84 tff(9295,plain,
% 2.62/2.84 (~r(z, s(s(s(elem!1))))),
% 2.62/2.84 inference(unit_resolution,[status(thm)],[6933, 197, 152, 9283, 9294])).
% 2.62/2.84 tff(9296,plain,
% 2.62/2.84 (b(z, s(s(s(elem!1))))),
% 2.62/2.84 inference(unit_resolution,[status(thm)],[261, 9295])).
% 2.62/2.84 tff(9297,plain,
% 2.62/2.84 (~b(s(z), z)),
% 2.62/2.84 inference(unit_resolution,[status(thm)],[1470, 9296, 8808, 9281])).
% 2.62/2.84 tff(9298,plain,
% 2.62/2.84 (r(s(z), z)),
% 2.62/2.84 inference(unit_resolution,[status(thm)],[230, 9297])).
% 2.62/2.84 tff(9299,plain,
% 2.62/2.84 (~r(s(s(s(z))), z)),
% 2.62/2.84 inference(unit_resolution,[status(thm)],[8122, 9298, 152, 9292, 9267])).
% 2.62/2.84 tff(9300,plain,
% 2.62/2.84 (b(s(s(s(z))), z)),
% 2.62/2.84 inference(unit_resolution,[status(thm)],[1713, 9299])).
% 2.62/2.84 tff(9301,plain,
% 2.62/2.84 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(elem!1)))) | (~b(s(s(elem!1)), z)) | (~b(s(s(s(elem!1))), z)) | (~b(s(s(s(z))), z)) | (~b(s(s(s(elem!1))), s(s(s(z))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(s(elem!1)))) | (~b(s(s(elem!1)), z)) | (~b(s(s(s(elem!1))), z)) | (~b(s(s(s(z))), z)) | (~b(s(s(s(elem!1))), s(s(s(z))))))),
% 2.62/2.85 inference(rewrite,[status(thm)],[])).
% 2.62/2.85 tff(9302,plain,
% 2.62/2.85 (((~b(s(s(elem!1)), z)) | (~b(s(s(s(elem!1))), z)) | (~b(z, s(s(elem!1)))) | (~b(s(s(s(z))), z)) | (~b(s(s(s(elem!1))), z)) | (~b(s(s(s(elem!1))), s(s(s(z)))))) <=> ((~b(z, s(s(elem!1)))) | (~b(s(s(elem!1)), z)) | (~b(s(s(s(elem!1))), z)) | (~b(s(s(s(z))), z)) | (~b(s(s(s(elem!1))), s(s(s(z))))))),
% 2.62/2.85 inference(rewrite,[status(thm)],[])).
% 2.62/2.85 tff(9303,plain,
% 2.62/2.85 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), z)) | (~b(s(s(s(elem!1))), z)) | (~b(z, s(s(elem!1)))) | (~b(s(s(s(z))), z)) | (~b(s(s(s(elem!1))), z)) | (~b(s(s(s(elem!1))), s(s(s(z))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(elem!1)))) | (~b(s(s(elem!1)), z)) | (~b(s(s(s(elem!1))), z)) | (~b(s(s(s(z))), z)) | (~b(s(s(s(elem!1))), s(s(s(z)))))))),
% 2.62/2.85 inference(monotonicity,[status(thm)],[9302])).
% 2.62/2.85 tff(9304,plain,
% 2.62/2.85 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), z)) | (~b(s(s(s(elem!1))), z)) | (~b(z, s(s(elem!1)))) | (~b(s(s(s(z))), z)) | (~b(s(s(s(elem!1))), z)) | (~b(s(s(s(elem!1))), s(s(s(z))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(s(elem!1)))) | (~b(s(s(elem!1)), z)) | (~b(s(s(s(elem!1))), z)) | (~b(s(s(s(z))), z)) | (~b(s(s(s(elem!1))), s(s(s(z))))))),
% 2.62/2.85 inference(transitivity,[status(thm)],[9303, 9301])).
% 2.62/2.85 tff(9305,plain,
% 2.62/2.85 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), z)) | (~b(s(s(s(elem!1))), z)) | (~b(z, s(s(elem!1)))) | (~b(s(s(s(z))), z)) | (~b(s(s(s(elem!1))), z)) | (~b(s(s(s(elem!1))), s(s(s(z))))))),
% 2.62/2.85 inference(quant_inst,[status(thm)],[])).
% 2.62/2.85 tff(9306,plain,
% 2.62/2.85 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(s(elem!1)))) | (~b(s(s(elem!1)), z)) | (~b(s(s(s(elem!1))), z)) | (~b(s(s(s(z))), z)) | (~b(s(s(s(elem!1))), s(s(s(z)))))),
% 2.62/2.85 inference(modus_ponens,[status(thm)],[9305, 9304])).
% 2.62/2.85 tff(9307,plain,
% 2.62/2.85 (~b(s(s(s(elem!1))), s(s(s(z))))),
% 2.62/2.85 inference(unit_resolution,[status(thm)],[9306, 166, 9262, 8808, 9269, 9300])).
% 2.62/2.85 tff(9308,plain,
% 2.62/2.85 (r(s(s(s(elem!1))), s(s(s(z))))),
% 2.62/2.85 inference(unit_resolution,[status(thm)],[3574, 9307, 9265])).
% 2.62/2.85 tff(9309,plain,
% 2.62/2.85 (~r(s(z), s(s(z)))),
% 2.62/2.85 inference(unit_resolution,[status(thm)],[331, 9283, 152, 8408])).
% 2.62/2.85 tff(9310,plain,
% 2.62/2.85 (b(s(z), s(s(z)))),
% 2.62/2.85 inference(unit_resolution,[status(thm)],[427, 9309])).
% 2.62/2.85 tff(9311,plain,
% 2.62/2.85 (~r(s(s(s(s(z)))), z)),
% 2.62/2.85 inference(unit_resolution,[status(thm)],[7728, 9298, 152, 9292, 9267, 9310])).
% 2.62/2.85 tff(9312,plain,
% 2.62/2.85 (b(s(s(s(s(z)))), z)),
% 2.62/2.85 inference(unit_resolution,[status(thm)],[3266, 9311])).
% 2.62/2.85 tff(9313,plain,
% 2.62/2.85 (~b(s(s(s(s(z)))), s(s(s(z))))),
% 2.62/2.85 inference(unit_resolution,[status(thm)],[8932, 166, 9262, 9269, 9300, 9312])).
% 2.62/2.85 tff(9314,plain,
% 2.62/2.85 (r(s(s(s(s(z)))), s(s(s(z))))),
% 2.62/2.85 inference(unit_resolution,[status(thm)],[4662, 9313])).
% 2.62/2.85 tff(9315,plain,
% 2.62/2.85 (~b(s(s(s(z))), s(s(s(s(z)))))),
% 2.62/2.85 inference(unit_resolution,[status(thm)],[7772, 9312, 8808, 9296, 9300])).
% 2.62/2.85 tff(9316,plain,
% 2.62/2.85 (r(s(s(s(z))), s(s(s(s(z)))))),
% 2.62/2.85 inference(unit_resolution,[status(thm)],[2233, 9315])).
% 2.62/2.85 tff(9317,plain,
% 2.62/2.85 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), s(s(s(z))))) | (~r(s(s(s(s(z)))), s(s(s(z))))) | (~r(s(s(s(z))), s(s(s(s(z)))))) | (~r(s(s(s(elem!1))), s(s(s(s(z)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(elem!1))), s(s(s(z))))) | (~r(s(s(s(s(z)))), s(s(s(z))))) | (~r(s(s(s(z))), s(s(s(s(z)))))) | (~r(s(s(s(elem!1))), s(s(s(s(z)))))))),
% 2.62/2.85 inference(rewrite,[status(thm)],[])).
% 2.62/2.85 tff(9318,plain,
% 2.62/2.85 (((~r(s(s(s(z))), s(s(s(s(z)))))) | (~r(s(s(s(s(z)))), s(s(s(z))))) | (~r(s(s(s(elem!1))), s(s(s(z))))) | (~r(s(s(s(elem!1))), s(s(s(s(z))))))) <=> ((~r(s(s(s(elem!1))), s(s(s(z))))) | (~r(s(s(s(s(z)))), s(s(s(z))))) | (~r(s(s(s(z))), s(s(s(s(z)))))) | (~r(s(s(s(elem!1))), s(s(s(s(z)))))))),
% 2.62/2.85 inference(rewrite,[status(thm)],[])).
% 2.62/2.85 tff(9319,plain,
% 2.62/2.85 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(z))), s(s(s(s(z)))))) | (~r(s(s(s(s(z)))), s(s(s(z))))) | (~r(s(s(s(elem!1))), s(s(s(z))))) | (~r(s(s(s(elem!1))), s(s(s(s(z)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), s(s(s(z))))) | (~r(s(s(s(s(z)))), s(s(s(z))))) | (~r(s(s(s(z))), s(s(s(s(z)))))) | (~r(s(s(s(elem!1))), s(s(s(s(z))))))))),
% 2.62/2.85 inference(monotonicity,[status(thm)],[9318])).
% 2.62/2.85 tff(9320,plain,
% 2.62/2.85 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(z))), s(s(s(s(z)))))) | (~r(s(s(s(s(z)))), s(s(s(z))))) | (~r(s(s(s(elem!1))), s(s(s(z))))) | (~r(s(s(s(elem!1))), s(s(s(s(z)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(elem!1))), s(s(s(z))))) | (~r(s(s(s(s(z)))), s(s(s(z))))) | (~r(s(s(s(z))), s(s(s(s(z)))))) | (~r(s(s(s(elem!1))), s(s(s(s(z)))))))),
% 2.62/2.85 inference(transitivity,[status(thm)],[9319, 9317])).
% 2.62/2.85 tff(9321,plain,
% 2.62/2.85 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(z))), s(s(s(s(z)))))) | (~r(s(s(s(s(z)))), s(s(s(z))))) | (~r(s(s(s(elem!1))), s(s(s(z))))) | (~r(s(s(s(elem!1))), s(s(s(s(z)))))))),
% 2.62/2.85 inference(quant_inst,[status(thm)],[])).
% 2.62/2.85 tff(9322,plain,
% 2.62/2.85 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(elem!1))), s(s(s(z))))) | (~r(s(s(s(s(z)))), s(s(s(z))))) | (~r(s(s(s(z))), s(s(s(s(z)))))) | (~r(s(s(s(elem!1))), s(s(s(s(z))))))),
% 2.62/2.85 inference(modus_ponens,[status(thm)],[9321, 9320])).
% 2.62/2.85 tff(9323,plain,
% 2.62/2.85 (~r(s(s(s(elem!1))), s(s(s(s(z)))))),
% 2.62/2.85 inference(unit_resolution,[status(thm)],[9322, 197, 9316, 9314, 9308])).
% 2.62/2.85 tff(9324,plain,
% 2.62/2.85 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(elem!1)))) | (~b(s(s(elem!1)), z)) | (~b(s(s(s(elem!1))), z)) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(elem!1))), s(s(s(s(z)))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(s(elem!1)))) | (~b(s(s(elem!1)), z)) | (~b(s(s(s(elem!1))), z)) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(elem!1))), s(s(s(s(z)))))))),
% 2.62/2.85 inference(rewrite,[status(thm)],[])).
% 2.62/2.85 tff(9325,plain,
% 2.62/2.85 (((~b(s(s(elem!1)), z)) | (~b(s(s(s(elem!1))), z)) | (~b(z, s(s(elem!1)))) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(elem!1))), z)) | (~b(s(s(s(elem!1))), s(s(s(s(z))))))) <=> ((~b(z, s(s(elem!1)))) | (~b(s(s(elem!1)), z)) | (~b(s(s(s(elem!1))), z)) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(elem!1))), s(s(s(s(z)))))))),
% 2.62/2.85 inference(rewrite,[status(thm)],[])).
% 2.62/2.85 tff(9326,plain,
% 2.62/2.85 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), z)) | (~b(s(s(s(elem!1))), z)) | (~b(z, s(s(elem!1)))) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(elem!1))), z)) | (~b(s(s(s(elem!1))), s(s(s(s(z)))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(elem!1)))) | (~b(s(s(elem!1)), z)) | (~b(s(s(s(elem!1))), z)) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(elem!1))), s(s(s(s(z))))))))),
% 2.62/2.85 inference(monotonicity,[status(thm)],[9325])).
% 2.62/2.85 tff(9327,plain,
% 2.62/2.85 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), z)) | (~b(s(s(s(elem!1))), z)) | (~b(z, s(s(elem!1)))) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(elem!1))), z)) | (~b(s(s(s(elem!1))), s(s(s(s(z)))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(s(elem!1)))) | (~b(s(s(elem!1)), z)) | (~b(s(s(s(elem!1))), z)) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(elem!1))), s(s(s(s(z)))))))),
% 2.62/2.85 inference(transitivity,[status(thm)],[9326, 9324])).
% 2.62/2.85 tff(9328,plain,
% 2.62/2.85 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), z)) | (~b(s(s(s(elem!1))), z)) | (~b(z, s(s(elem!1)))) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(elem!1))), z)) | (~b(s(s(s(elem!1))), s(s(s(s(z)))))))),
% 2.62/2.85 inference(quant_inst,[status(thm)],[])).
% 2.62/2.85 tff(9329,plain,
% 2.62/2.85 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(s(elem!1)))) | (~b(s(s(elem!1)), z)) | (~b(s(s(s(elem!1))), z)) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(elem!1))), s(s(s(s(z))))))),
% 2.62/2.85 inference(modus_ponens,[status(thm)],[9328, 9327])).
% 2.62/2.85 tff(9330,plain,
% 2.62/2.85 (~b(s(s(s(elem!1))), s(s(s(s(z)))))),
% 2.62/2.85 inference(unit_resolution,[status(thm)],[9329, 166, 9262, 8808, 9269, 9312])).
% 2.62/2.85 tff(9331,plain,
% 2.62/2.85 (((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((s(s(s(elem!1))) = s(s(s(s(z))))) | b(s(s(s(elem!1))), s(s(s(s(z))))) | r(s(s(s(elem!1))), s(s(s(s(z))))))) <=> ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (s(s(s(elem!1))) = s(s(s(s(z))))) | b(s(s(s(elem!1))), s(s(s(s(z))))) | r(s(s(s(elem!1))), s(s(s(s(z))))))),
% 2.62/2.85 inference(rewrite,[status(thm)],[])).
% 2.62/2.85 tff(9332,plain,
% 2.62/2.85 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((s(s(s(elem!1))) = s(s(s(s(z))))) | b(s(s(s(elem!1))), s(s(s(s(z))))) | r(s(s(s(elem!1))), s(s(s(s(z))))))),
% 2.62/2.85 inference(quant_inst,[status(thm)],[])).
% 2.62/2.85 tff(9333,plain,
% 2.62/2.85 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (s(s(s(elem!1))) = s(s(s(s(z))))) | b(s(s(s(elem!1))), s(s(s(s(z))))) | r(s(s(s(elem!1))), s(s(s(s(z)))))),
% 2.62/2.85 inference(modus_ponens,[status(thm)],[9332, 9331])).
% 2.62/2.85 tff(9334,plain,
% 2.62/2.85 ((s(s(s(elem!1))) = s(s(s(s(z))))) | r(s(s(s(elem!1))), s(s(s(s(z)))))),
% 2.62/2.85 inference(unit_resolution,[status(thm)],[9333, 79, 9330])).
% 2.62/2.85 tff(9335,plain,
% 2.62/2.85 (s(s(s(elem!1))) = s(s(s(s(z))))),
% 2.62/2.85 inference(unit_resolution,[status(thm)],[9334, 9323])).
% 2.62/2.85 tff(9336,plain,
% 2.62/2.85 (s(s(s(s(elem!1)))) = s(s(s(s(s(z)))))),
% 2.62/2.85 inference(monotonicity,[status(thm)],[9335])).
% 2.62/2.85 tff(9337,plain,
% 2.62/2.85 (s(s(s(s(s(z))))) = s(s(s(s(elem!1))))),
% 2.62/2.85 inference(symmetry,[status(thm)],[9336])).
% 2.62/2.85 tff(9338,plain,
% 2.62/2.85 (r(s(s(s(s(s(z))))), s(s(z))) <=> r(s(s(s(s(elem!1)))), s(s(z)))),
% 2.62/2.85 inference(monotonicity,[status(thm)],[9337])).
% 2.62/2.85 tff(9339,plain,
% 2.62/2.85 (r(s(s(s(s(elem!1)))), s(s(z))) <=> r(s(s(s(s(s(z))))), s(s(z)))),
% 2.62/2.85 inference(symmetry,[status(thm)],[9338])).
% 2.62/2.85 tff(9340,plain,
% 2.62/2.85 (b(s(s(s(s(s(z))))), s(s(z))) <=> b(s(s(s(s(elem!1)))), s(s(z)))),
% 2.62/2.85 inference(monotonicity,[status(thm)],[9337])).
% 2.62/2.85 tff(9341,plain,
% 2.62/2.85 ((~b(s(s(s(s(s(z))))), s(s(z)))) <=> (~b(s(s(s(s(elem!1)))), s(s(z))))),
% 2.62/2.85 inference(monotonicity,[status(thm)],[9340])).
% 2.62/2.85 tff(9342,plain,
% 2.62/2.85 (b(s(s(s(s(s(z))))), s(z)) <=> b(s(s(s(s(elem!1)))), s(z))),
% 2.62/2.85 inference(monotonicity,[status(thm)],[9337])).
% 2.62/2.85 tff(9343,plain,
% 2.62/2.85 (b(s(s(s(s(elem!1)))), s(z)) <=> b(s(s(s(s(s(z))))), s(z))),
% 2.62/2.85 inference(symmetry,[status(thm)],[9342])).
% 2.62/2.85 tff(9344,plain,
% 2.62/2.85 (inj_0(s(s(s(elem!1)))) = inj_0(s(s(s(s(z)))))),
% 2.62/2.85 inference(monotonicity,[status(thm)],[9335])).
% 2.62/2.85 tff(9345,plain,
% 2.62/2.85 (s(s(elem!1)) = s(s(s(z)))),
% 2.62/2.85 inference(transitivity,[status(thm)],[105, 9344, 2223])).
% 2.62/2.85 tff(9346,plain,
% 2.62/2.85 (r(s(s(elem!1)), s(z)) <=> r(s(s(s(z))), s(z))),
% 2.62/2.85 inference(monotonicity,[status(thm)],[9345])).
% 2.62/2.85 tff(9347,plain,
% 2.62/2.85 (r(s(s(s(z))), s(z))),
% 2.62/2.85 inference(modus_ponens,[status(thm)],[9260, 9346])).
% 2.62/2.85 tff(9348,assumption,(s(s(s(elem!1))) = s(s(s(s(z))))), introduced(assumption)).
% 2.62/2.85 tff(9349,plain,
% 2.62/2.85 (s(s(s(s(elem!1)))) = s(s(s(s(s(z)))))),
% 2.62/2.85 inference(monotonicity,[status(thm)],[9348])).
% 2.62/2.85 tff(9350,plain,
% 2.62/2.85 (s(s(s(s(s(z))))) = s(s(s(s(elem!1))))),
% 2.62/2.85 inference(symmetry,[status(thm)],[9349])).
% 2.62/2.85 tff(9351,plain,
% 2.62/2.85 (inj_0(s(s(s(elem!1)))) = inj_0(s(s(s(s(z)))))),
% 2.62/2.85 inference(monotonicity,[status(thm)],[9348])).
% 2.62/2.85 tff(9352,plain,
% 2.62/2.85 (inj_0(s(s(s(s(z))))) = inj_0(s(s(s(elem!1))))),
% 2.62/2.85 inference(symmetry,[status(thm)],[9351])).
% 2.62/2.85 tff(9353,plain,
% 2.62/2.85 (s(s(s(z))) = s(s(elem!1))),
% 2.62/2.85 inference(transitivity,[status(thm)],[3277, 9352, 104])).
% 2.62/2.85 tff(9354,plain,
% 2.62/2.85 (r(s(s(s(z))), s(s(s(s(s(z)))))) <=> r(s(s(elem!1)), s(s(s(s(elem!1)))))),
% 2.62/2.85 inference(monotonicity,[status(thm)],[9353, 9350])).
% 2.62/2.85 tff(9355,plain,
% 2.62/2.85 (r(s(s(elem!1)), s(s(s(s(elem!1))))) <=> r(s(s(s(z))), s(s(s(s(s(z))))))),
% 2.62/2.85 inference(symmetry,[status(thm)],[9354])).
% 2.62/2.85 tff(9356,plain,
% 2.62/2.85 ((s(s(s(s(elem!1)))) = s(s(s(z)))) <=> (s(s(s(s(elem!1)))) = s(s(elem!1)))),
% 2.62/2.85 inference(monotonicity,[status(thm)],[9353])).
% 2.62/2.85 tff(9357,plain,
% 2.62/2.85 ((s(s(s(s(elem!1)))) = s(s(s(z)))) <=> (s(s(elem!1)) = s(s(s(s(elem!1)))))),
% 2.62/2.85 inference(transitivity,[status(thm)],[9356, 123])).
% 2.62/2.85 tff(9358,plain,
% 2.62/2.85 ((~(s(s(s(s(elem!1)))) = s(s(s(z))))) <=> (~(s(s(elem!1)) = s(s(s(s(elem!1))))))),
% 2.62/2.85 inference(monotonicity,[status(thm)],[9357])).
% 2.62/2.85 tff(9359,plain,
% 2.62/2.85 (~(s(s(elem!1)) = s(s(s(s(elem!1)))))),
% 2.62/2.85 inference(modus_ponens,[status(thm)],[5112, 9358])).
% 2.62/2.85 tff(9360,plain,
% 2.62/2.85 (~b(s(s(elem!1)), s(s(s(s(elem!1)))))),
% 2.62/2.85 inference(unit_resolution,[status(thm)],[3073, 700, 323, 311, 1820])).
% 2.62/2.85 tff(9361,plain,
% 2.62/2.85 (r(s(s(elem!1)), s(s(s(s(elem!1)))))),
% 2.62/2.85 inference(unit_resolution,[status(thm)],[827, 9360, 9359])).
% 2.62/2.85 tff(9362,plain,
% 2.62/2.85 (r(s(s(s(z))), s(s(s(s(s(z))))))),
% 2.62/2.85 inference(modus_ponens,[status(thm)],[9361, 9355])).
% 2.62/2.85 tff(9363,plain,
% 2.62/2.85 (r(s(s(s(s(elem!1)))), s(z)) <=> r(s(s(s(s(s(z))))), s(z))),
% 2.62/2.85 inference(monotonicity,[status(thm)],[9349])).
% 2.62/2.85 tff(9364,plain,
% 2.62/2.85 (r(s(s(s(s(s(z))))), s(z))),
% 2.62/2.85 inference(modus_ponens,[status(thm)],[700, 9363])).
% 2.62/2.85 tff(9365,plain,
% 2.62/2.85 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), z)) | (~r(s(s(s(z))), s(z))) | (~r(s(s(s(s(s(z))))), s(z))) | (~r(s(s(s(z))), s(s(s(s(s(z))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(z), z)) | (~r(s(s(s(z))), s(z))) | (~r(s(s(s(s(s(z))))), s(z))) | (~r(s(s(s(z))), s(s(s(s(s(z))))))))),
% 2.62/2.85 inference(rewrite,[status(thm)],[])).
% 2.62/2.85 tff(9366,plain,
% 2.62/2.85 (((~r(s(z), z)) | (~r(s(s(s(s(s(z))))), s(z))) | (~r(s(s(s(z))), s(z))) | (~r(s(s(s(z))), s(s(s(s(s(z)))))))) <=> ((~r(s(z), z)) | (~r(s(s(s(z))), s(z))) | (~r(s(s(s(s(s(z))))), s(z))) | (~r(s(s(s(z))), s(s(s(s(s(z))))))))),
% 2.62/2.85 inference(rewrite,[status(thm)],[])).
% 2.62/2.85 tff(9367,plain,
% 2.62/2.85 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), z)) | (~r(s(s(s(s(s(z))))), s(z))) | (~r(s(s(s(z))), s(z))) | (~r(s(s(s(z))), s(s(s(s(s(z))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), z)) | (~r(s(s(s(z))), s(z))) | (~r(s(s(s(s(s(z))))), s(z))) | (~r(s(s(s(z))), s(s(s(s(s(z)))))))))),
% 2.62/2.85 inference(monotonicity,[status(thm)],[9366])).
% 2.62/2.85 tff(9368,plain,
% 2.62/2.85 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), z)) | (~r(s(s(s(s(s(z))))), s(z))) | (~r(s(s(s(z))), s(z))) | (~r(s(s(s(z))), s(s(s(s(s(z))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(z), z)) | (~r(s(s(s(z))), s(z))) | (~r(s(s(s(s(s(z))))), s(z))) | (~r(s(s(s(z))), s(s(s(s(s(z))))))))),
% 2.62/2.85 inference(transitivity,[status(thm)],[9367, 9365])).
% 2.62/2.85 tff(9369,plain,
% 2.62/2.85 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), z)) | (~r(s(s(s(s(s(z))))), s(z))) | (~r(s(s(s(z))), s(z))) | (~r(s(s(s(z))), s(s(s(s(s(z))))))))),
% 2.62/2.85 inference(quant_inst,[status(thm)],[])).
% 2.62/2.85 tff(9370,plain,
% 2.62/2.85 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(z), z)) | (~r(s(s(s(z))), s(z))) | (~r(s(s(s(s(s(z))))), s(z))) | (~r(s(s(s(z))), s(s(s(s(s(z)))))))),
% 2.62/2.85 inference(modus_ponens,[status(thm)],[9369, 9368])).
% 2.62/2.85 tff(9371,plain,
% 2.62/2.85 (~r(s(s(s(z))), s(s(s(s(s(z))))))),
% 2.62/2.85 inference(unit_resolution,[status(thm)],[9370, 197, 97, 1746, 9364])).
% 2.62/2.85 tff(9372,plain,
% 2.62/2.85 ($false),
% 2.62/2.85 inference(unit_resolution,[status(thm)],[9371, 9362])).
% 2.62/2.85 tff(9373,plain,((~r(s(s(s(s(elem!1)))), s(z))) | (~(s(s(s(elem!1))) = s(s(s(s(z)))))) | (~r(s(z), z)) | (~r(s(s(s(z))), s(z))) | (~r(z, s(z))) | (~r(s(z), s(s(elem!1)))) | (~b(z, s(s(elem!1))))), inference(lemma,lemma(discharge,[]))).
% 2.62/2.85 tff(9374,plain,
% 2.62/2.85 (~r(s(s(s(s(elem!1)))), s(z))),
% 2.62/2.85 inference(unit_resolution,[status(thm)],[9373, 9335, 9298, 9347, 8408, 311, 9262])).
% 2.62/2.85 tff(9375,plain,
% 2.62/2.85 (b(s(s(s(s(elem!1)))), s(z))),
% 2.62/2.85 inference(unit_resolution,[status(thm)],[661, 9374])).
% 2.62/2.85 tff(9376,plain,
% 2.62/2.85 (b(s(s(s(s(s(z))))), s(z))),
% 2.62/2.85 inference(modus_ponens,[status(thm)],[9375, 9343])).
% 2.62/2.85 tff(9377,plain,
% 2.62/2.85 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(z)))) | (~b(s(s(z)), s(z))) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(s(s(s(s(s(z))))), s(s(z)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), s(s(z)))) | (~b(s(s(z)), s(z))) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(s(s(s(s(s(z))))), s(s(z)))))),
% 2.62/2.85 inference(rewrite,[status(thm)],[])).
% 2.62/2.85 tff(9378,plain,
% 2.62/2.85 (((~b(s(s(z)), s(z))) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(s(z), s(s(z)))) | (~b(s(s(z)), s(z))) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(s(s(s(s(s(z))))), s(s(z))))) <=> ((~b(s(z), s(s(z)))) | (~b(s(s(z)), s(z))) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(s(s(s(s(s(z))))), s(s(z)))))),
% 2.62/2.85 inference(rewrite,[status(thm)],[])).
% 2.62/2.85 tff(9379,plain,
% 2.62/2.85 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), s(z))) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(s(z), s(s(z)))) | (~b(s(s(z)), s(z))) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(s(s(s(s(s(z))))), s(s(z)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(z)))) | (~b(s(s(z)), s(z))) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(s(s(s(s(s(z))))), s(s(z))))))),
% 2.62/2.85 inference(monotonicity,[status(thm)],[9378])).
% 2.62/2.85 tff(9380,plain,
% 2.62/2.85 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), s(z))) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(s(z), s(s(z)))) | (~b(s(s(z)), s(z))) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(s(s(s(s(s(z))))), s(s(z)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), s(s(z)))) | (~b(s(s(z)), s(z))) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(s(s(s(s(s(z))))), s(s(z)))))),
% 2.62/2.85 inference(transitivity,[status(thm)],[9379, 9377])).
% 2.62/2.85 tff(9381,plain,
% 2.62/2.85 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), s(z))) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(s(z), s(s(z)))) | (~b(s(s(z)), s(z))) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(s(s(s(s(s(z))))), s(s(z)))))),
% 2.62/2.85 inference(quant_inst,[status(thm)],[])).
% 2.62/2.85 tff(9382,plain,
% 2.62/2.85 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), s(s(z)))) | (~b(s(s(z)), s(z))) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(s(s(s(s(s(z))))), s(s(z))))),
% 2.62/2.85 inference(modus_ponens,[status(thm)],[9381, 9380])).
% 2.62/2.86 tff(9383,plain,
% 2.62/2.86 ((~b(s(s(s(s(s(z))))), s(z))) | (~b(s(s(s(s(s(z))))), s(s(z))))),
% 2.62/2.86 inference(unit_resolution,[status(thm)],[9382, 166, 9310, 9267])).
% 2.62/2.86 tff(9384,plain,
% 2.62/2.86 (~b(s(s(s(s(s(z))))), s(s(z)))),
% 2.62/2.86 inference(unit_resolution,[status(thm)],[9383, 9376])).
% 2.62/2.86 tff(9385,plain,
% 2.62/2.86 (~b(s(s(s(s(elem!1)))), s(s(z)))),
% 2.62/2.86 inference(modus_ponens,[status(thm)],[9384, 9341])).
% 2.62/2.86 tff(9386,plain,
% 2.62/2.86 (r(s(s(s(s(elem!1)))), s(s(z)))),
% 2.62/2.86 inference(unit_resolution,[status(thm)],[1299, 9385])).
% 2.62/2.86 tff(9387,plain,
% 2.62/2.86 (r(s(s(s(s(s(z))))), s(s(z)))),
% 2.62/2.86 inference(modus_ponens,[status(thm)],[9386, 9339])).
% 2.62/2.86 tff(9388,plain,
% 2.62/2.86 (s(s(s(s(z)))) = s(s(s(elem!1)))),
% 2.62/2.86 inference(symmetry,[status(thm)],[9335])).
% 2.62/2.86 tff(9389,plain,
% 2.62/2.86 (r(s(s(s(s(s(z))))), s(s(s(s(z))))) <=> r(s(s(s(s(elem!1)))), s(s(s(elem!1))))),
% 2.62/2.86 inference(monotonicity,[status(thm)],[9337, 9388])).
% 2.62/2.86 tff(9390,plain,
% 2.62/2.86 (r(s(s(s(s(elem!1)))), s(s(s(elem!1)))) <=> r(s(s(s(s(s(z))))), s(s(s(s(z)))))),
% 2.62/2.86 inference(symmetry,[status(thm)],[9389])).
% 2.62/2.86 tff(9391,plain,
% 2.62/2.86 (~(s(s(s(elem!1))) = s(s(s(s(elem!1)))))),
% 2.62/2.86 inference(unit_resolution,[status(thm)],[357, 9258])).
% 2.62/2.86 tff(9392,plain,
% 2.62/2.86 (~(s(s(s(s(elem!1)))) = s(s(s(elem!1))))),
% 2.62/2.86 inference(unit_resolution,[status(thm)],[363, 9391])).
% 2.62/2.86 tff(9393,plain,
% 2.62/2.86 (b(s(s(s(s(elem!1)))), s(s(s(elem!1)))) <=> b(s(s(s(s(elem!1)))), s(s(s(s(z)))))),
% 2.62/2.86 inference(monotonicity,[status(thm)],[9335])).
% 2.62/2.86 tff(9394,plain,
% 2.62/2.86 (b(s(s(s(s(elem!1)))), s(s(s(s(z))))) <=> b(s(s(s(s(elem!1)))), s(s(s(elem!1))))),
% 2.62/2.86 inference(symmetry,[status(thm)],[9393])).
% 2.62/2.86 tff(9395,plain,
% 2.62/2.86 (b(s(s(s(s(s(z))))), s(s(s(s(z))))) <=> b(s(s(s(s(elem!1)))), s(s(s(s(z)))))),
% 2.62/2.86 inference(monotonicity,[status(thm)],[9337])).
% 2.62/2.86 tff(9396,plain,
% 2.62/2.86 (b(s(s(s(s(s(z))))), s(s(s(s(z))))) <=> b(s(s(s(s(elem!1)))), s(s(s(elem!1))))),
% 2.62/2.86 inference(transitivity,[status(thm)],[9395, 9394])).
% 2.62/2.86 tff(9397,plain,
% 2.62/2.86 ((~b(s(s(s(s(s(z))))), s(s(s(s(z)))))) <=> (~b(s(s(s(s(elem!1)))), s(s(s(elem!1)))))),
% 2.62/2.86 inference(monotonicity,[status(thm)],[9396])).
% 2.62/2.86 tff(9398,plain,
% 2.62/2.86 (b(s(s(s(elem!1))), s(z)) <=> b(s(s(s(s(z)))), s(z))),
% 2.62/2.86 inference(monotonicity,[status(thm)],[9335])).
% 2.62/2.86 tff(9399,plain,
% 2.62/2.86 (b(s(s(s(s(z)))), s(z))),
% 2.62/2.86 inference(modus_ponens,[status(thm)],[96, 9398])).
% 2.62/2.86 tff(9400,plain,
% 2.62/2.86 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(z)))) | (~b(s(s(z)), s(z))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~b(s(s(s(s(s(z))))), s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), s(s(z)))) | (~b(s(s(z)), s(z))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~b(s(s(s(s(s(z))))), s(z))))),
% 2.62/2.86 inference(rewrite,[status(thm)],[])).
% 2.62/2.86 tff(9401,plain,
% 2.62/2.86 (((~b(s(s(z)), s(z))) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(s(z), s(s(z)))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(s(s(s(s(s(z))))), s(s(s(s(z))))))) <=> ((~b(s(z), s(s(z)))) | (~b(s(s(z)), s(z))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~b(s(s(s(s(s(z))))), s(z))))),
% 2.62/2.86 inference(rewrite,[status(thm)],[])).
% 2.62/2.86 tff(9402,plain,
% 2.62/2.86 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), s(z))) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(s(z), s(s(z)))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(s(s(s(s(s(z))))), s(s(s(s(z)))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(z)))) | (~b(s(s(z)), s(z))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~b(s(s(s(s(s(z))))), s(z)))))),
% 2.62/2.86 inference(monotonicity,[status(thm)],[9401])).
% 2.62/2.86 tff(9403,plain,
% 2.62/2.86 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), s(z))) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(s(z), s(s(z)))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(s(s(s(s(s(z))))), s(s(s(s(z)))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), s(s(z)))) | (~b(s(s(z)), s(z))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~b(s(s(s(s(s(z))))), s(z))))),
% 2.62/2.86 inference(transitivity,[status(thm)],[9402, 9400])).
% 2.62/2.86 tff(9404,plain,
% 2.62/2.86 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), s(z))) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(s(z), s(s(z)))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(s(s(s(s(s(z))))), s(s(s(s(z)))))))),
% 2.62/2.86 inference(quant_inst,[status(thm)],[])).
% 2.62/2.86 tff(9405,plain,
% 2.62/2.86 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), s(s(z)))) | (~b(s(s(z)), s(z))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~b(s(s(s(s(s(z))))), s(z)))),
% 2.62/2.86 inference(modus_ponens,[status(thm)],[9404, 9403])).
% 2.62/2.86 tff(9406,plain,
% 2.62/2.86 ((~b(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~b(s(s(s(s(s(z))))), s(z)))),
% 2.62/2.86 inference(unit_resolution,[status(thm)],[9405, 166, 9310, 9267, 9399])).
% 2.62/2.86 tff(9407,plain,
% 2.62/2.86 (~b(s(s(s(s(s(z))))), s(s(s(s(z)))))),
% 2.62/2.86 inference(unit_resolution,[status(thm)],[9406, 9376])).
% 2.62/2.86 tff(9408,plain,
% 2.62/2.86 (~b(s(s(s(s(elem!1)))), s(s(s(elem!1))))),
% 2.62/2.86 inference(modus_ponens,[status(thm)],[9407, 9397])).
% 2.62/2.86 tff(9409,plain,
% 2.62/2.86 (r(s(s(s(s(elem!1)))), s(s(s(elem!1))))),
% 2.62/2.86 inference(unit_resolution,[status(thm)],[1065, 9408, 9392])).
% 2.62/2.86 tff(9410,plain,
% 2.62/2.86 (r(s(s(s(s(s(z))))), s(s(s(s(z)))))),
% 2.62/2.86 inference(modus_ponens,[status(thm)],[9409, 9390])).
% 2.62/2.86 tff(9411,plain,
% 2.62/2.86 (r(s(s(s(elem!1))), s(s(z))) <=> r(s(s(s(s(z)))), s(s(z)))),
% 2.62/2.86 inference(monotonicity,[status(thm)],[9335])).
% 2.62/2.86 tff(9412,plain,
% 2.62/2.86 (r(s(s(s(s(z)))), s(s(z)))),
% 2.62/2.86 inference(modus_ponens,[status(thm)],[9294, 9411])).
% 2.62/2.86 tff(9413,plain,
% 2.62/2.86 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(z)), z)) | (~r(s(s(s(s(z)))), s(s(z)))) | (~r(s(s(s(s(s(z))))), s(s(z)))) | (~r(s(s(s(s(s(z))))), s(s(s(s(z)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(z)), z)) | (~r(s(s(s(s(z)))), s(s(z)))) | (~r(s(s(s(s(s(z))))), s(s(z)))) | (~r(s(s(s(s(s(z))))), s(s(s(s(z)))))))),
% 2.62/2.86 inference(rewrite,[status(thm)],[])).
% 2.62/2.86 tff(9414,plain,
% 2.62/2.86 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(z)), z)) | (~r(s(s(s(s(z)))), s(s(z)))) | (~r(s(s(s(s(s(z))))), s(s(z)))) | (~r(s(s(s(s(s(z))))), s(s(s(s(z)))))))),
% 2.62/2.86 inference(quant_inst,[status(thm)],[])).
% 2.62/2.86 tff(9415,plain,
% 2.62/2.86 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(z)), z)) | (~r(s(s(s(s(z)))), s(s(z)))) | (~r(s(s(s(s(s(z))))), s(s(z)))) | (~r(s(s(s(s(s(z))))), s(s(s(s(z))))))),
% 2.62/2.86 inference(modus_ponens,[status(thm)],[9414, 9413])).
% 2.62/2.86 tff(9416,plain,
% 2.62/2.86 (~r(s(s(s(s(s(z))))), s(s(z)))),
% 2.62/2.86 inference(unit_resolution,[status(thm)],[9415, 197, 9292, 9412, 9410])).
% 2.62/2.86 tff(9417,plain,
% 2.62/2.86 ($false),
% 2.62/2.86 inference(unit_resolution,[status(thm)],[9416, 9387])).
% 2.62/2.86 tff(9418,plain,((~r(s(z), s(s(elem!1)))) | (~b(s(s(s(elem!1))), s(z))) | b(z, s(s(z)))), inference(lemma,lemma(discharge,[]))).
% 2.62/2.86 tff(9419,plain,
% 2.62/2.86 (~r(s(z), s(s(elem!1)))),
% 2.62/2.86 inference(unit_resolution,[status(thm)],[9418, 96, 125])).
% 2.62/2.86 tff(9420,plain,
% 2.62/2.86 (b(s(z), s(s(elem!1)))),
% 2.62/2.86 inference(unit_resolution,[status(thm)],[84, 9419])).
% 2.62/2.86 tff(9421,plain,
% 2.62/2.86 (~b(s(s(elem!1)), s(s(s(elem!1))))),
% 2.62/2.86 inference(unit_resolution,[status(thm)],[7367, 9420, 96, 8808, 9259])).
% 2.62/2.86 tff(9422,plain,
% 2.62/2.86 (r(s(s(elem!1)), s(s(s(elem!1))))),
% 2.62/2.86 inference(unit_resolution,[status(thm)],[461, 9421, 9258])).
% 2.62/2.86 tff(9423,plain,
% 2.62/2.86 (~r(s(s(elem!1)), z)),
% 2.62/2.86 inference(unit_resolution,[status(thm)],[8490, 97, 323, 4577])).
% 2.62/2.86 tff(9424,plain,
% 2.62/2.86 (b(s(s(elem!1)), z)),
% 2.62/2.86 inference(unit_resolution,[status(thm)],[608, 9423])).
% 2.62/2.86 tff(9425,plain,
% 2.62/2.86 (~r(z, s(s(elem!1)))),
% 2.62/2.86 inference(unit_resolution,[status(thm)],[8426, 97, 323, 4577])).
% 2.62/2.86 tff(9426,plain,
% 2.62/2.86 (b(z, s(s(elem!1)))),
% 2.62/2.86 inference(unit_resolution,[status(thm)],[1795, 9425])).
% 2.62/2.86 tff(9427,plain,
% 2.62/2.86 (~b(s(s(s(elem!1))), s(s(elem!1)))),
% 2.62/2.86 inference(unit_resolution,[status(thm)],[9275, 166, 9426, 121, 9424])).
% 2.62/2.86 tff(9428,plain,
% 2.62/2.86 (r(s(s(s(elem!1))), s(s(elem!1)))),
% 2.62/2.86 inference(unit_resolution,[status(thm)],[889, 9427, 1863])).
% 2.62/2.86 tff(9429,plain,
% 2.62/2.86 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), z)) | (~b(s(s(s(elem!1))), s(s(z)))) | (~b(s(z), s(s(elem!1)))) | (~b(s(s(s(elem!1))), z)) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(s(z)), s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(elem!1)), z)) | (~b(s(s(s(elem!1))), s(s(z)))) | (~b(s(z), s(s(elem!1)))) | (~b(s(s(s(elem!1))), z)) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(s(z)), s(z))))),
% 2.62/2.86 inference(rewrite,[status(thm)],[])).
% 2.62/2.86 tff(9430,plain,
% 2.62/2.86 (((~b(s(s(elem!1)), z)) | (~b(s(s(s(elem!1))), z)) | (~b(s(z), s(s(elem!1)))) | (~b(s(s(z)), s(z))) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(s(s(elem!1))), s(s(z))))) <=> ((~b(s(s(elem!1)), z)) | (~b(s(s(s(elem!1))), s(s(z)))) | (~b(s(z), s(s(elem!1)))) | (~b(s(s(s(elem!1))), z)) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(s(z)), s(z))))),
% 2.62/2.86 inference(rewrite,[status(thm)],[])).
% 2.62/2.86 tff(9431,plain,
% 2.62/2.86 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), z)) | (~b(s(s(s(elem!1))), z)) | (~b(s(z), s(s(elem!1)))) | (~b(s(s(z)), s(z))) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(s(s(elem!1))), s(s(z)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), z)) | (~b(s(s(s(elem!1))), s(s(z)))) | (~b(s(z), s(s(elem!1)))) | (~b(s(s(s(elem!1))), z)) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(s(z)), s(z)))))),
% 2.62/2.86 inference(monotonicity,[status(thm)],[9430])).
% 2.62/2.86 tff(9432,plain,
% 2.62/2.86 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), z)) | (~b(s(s(s(elem!1))), z)) | (~b(s(z), s(s(elem!1)))) | (~b(s(s(z)), s(z))) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(s(s(elem!1))), s(s(z)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(elem!1)), z)) | (~b(s(s(s(elem!1))), s(s(z)))) | (~b(s(z), s(s(elem!1)))) | (~b(s(s(s(elem!1))), z)) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(s(z)), s(z))))),
% 2.62/2.86 inference(transitivity,[status(thm)],[9431, 9429])).
% 2.62/2.86 tff(9433,plain,
% 2.62/2.86 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), z)) | (~b(s(s(s(elem!1))), z)) | (~b(s(z), s(s(elem!1)))) | (~b(s(s(z)), s(z))) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(s(s(elem!1))), s(s(z)))))),
% 2.62/2.86 inference(quant_inst,[status(thm)],[])).
% 2.62/2.86 tff(9434,plain,
% 2.62/2.86 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(elem!1)), z)) | (~b(s(s(s(elem!1))), s(s(z)))) | (~b(s(z), s(s(elem!1)))) | (~b(s(s(s(elem!1))), z)) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(s(z)), s(z)))),
% 2.62/2.86 inference(modus_ponens,[status(thm)],[9433, 9432])).
% 2.62/2.86 tff(9435,plain,
% 2.62/2.86 (~b(s(s(s(elem!1))), s(s(z)))),
% 2.62/2.86 inference(unit_resolution,[status(thm)],[9434, 166, 376, 96, 121, 9424, 156])).
% 2.62/2.86 tff(9436,plain,
% 2.62/2.86 (r(s(s(s(elem!1))), s(s(z)))),
% 2.62/2.86 inference(unit_resolution,[status(thm)],[218, 9435])).
% 2.62/2.86 tff(9437,plain,
% 2.62/2.86 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(elem!1)), s(z))) | (~r(s(s(z)), s(s(elem!1)))) | (~r(s(s(s(elem!1))), s(s(elem!1)))) | (~r(s(s(s(elem!1))), s(s(z)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(elem!1)), s(z))) | (~r(s(s(z)), s(s(elem!1)))) | (~r(s(s(s(elem!1))), s(s(elem!1)))) | (~r(s(s(s(elem!1))), s(s(z)))))),
% 2.62/2.86 inference(rewrite,[status(thm)],[])).
% 2.62/2.86 tff(9438,plain,
% 2.62/2.86 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(elem!1)), s(z))) | (~r(s(s(z)), s(s(elem!1)))) | (~r(s(s(s(elem!1))), s(s(elem!1)))) | (~r(s(s(s(elem!1))), s(s(z)))))),
% 2.62/2.86 inference(quant_inst,[status(thm)],[])).
% 2.62/2.86 tff(9439,plain,
% 2.62/2.86 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(elem!1)), s(z))) | (~r(s(s(z)), s(s(elem!1)))) | (~r(s(s(s(elem!1))), s(s(elem!1)))) | (~r(s(s(s(elem!1))), s(s(z))))),
% 2.62/2.86 inference(modus_ponens,[status(thm)],[9438, 9437])).
% 2.62/2.86 tff(9440,plain,
% 2.62/2.86 ($false),
% 2.62/2.86 inference(unit_resolution,[status(thm)],[9439, 197, 4577, 333, 905, 464])).
% 2.62/2.86 tff(9441,plain,((~r(s(s(z)), s(s(elem!1)))) | (~r(s(s(elem!1)), s(z))) | (~r(s(s(s(elem!1))), s(s(elem!1)))) | (~r(s(s(s(elem!1))), s(s(z))))), inference(lemma,lemma(discharge,[]))).
% 2.62/2.86 tff(9442,plain,
% 2.62/2.86 (~r(s(s(z)), s(s(elem!1)))),
% 2.62/2.86 inference(unit_resolution,[status(thm)],[9441, 9436, 4577, 9428])).
% 2.62/2.86 tff(9443,plain,
% 2.62/2.86 (b(s(s(z)), s(s(elem!1)))),
% 2.62/2.86 inference(unit_resolution,[status(thm)],[390, 9442, 52])).
% 2.62/2.86 tff(9444,plain,
% 2.62/2.86 (~r(s(z), s(s(s(elem!1))))),
% 2.62/2.86 inference(unit_resolution,[status(thm)],[7376, 9428, 4577, 377])).
% 2.62/2.86 tff(9445,plain,
% 2.62/2.86 (b(s(z), s(s(s(elem!1))))),
% 2.62/2.86 inference(unit_resolution,[status(thm)],[116, 9444])).
% 2.62/2.86 tff(9446,plain,
% 2.62/2.86 (~b(s(s(z)), s(s(s(elem!1))))),
% 2.62/2.86 inference(unit_resolution,[status(thm)],[271, 9445, 96, 156])).
% 2.62/2.86 tff(9447,plain,
% 2.62/2.86 (r(s(s(z)), s(s(s(elem!1))))),
% 2.62/2.86 inference(unit_resolution,[status(thm)],[279, 9446])).
% 2.62/2.86 tff(9448,plain,
% 2.62/2.86 (~r(s(z), s(s(z)))),
% 2.62/2.86 inference(unit_resolution,[status(thm)],[331, 9447, 155, 323])).
% 2.62/2.86 tff(9449,plain,
% 2.62/2.86 (b(s(z), s(s(z)))),
% 2.62/2.86 inference(unit_resolution,[status(thm)],[427, 9448])).
% 2.62/2.86 tff(9450,plain,
% 2.62/2.86 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(elem!1)))) | (~b(s(s(elem!1)), z)) | (~b(s(z), s(s(elem!1)))) | (~b(s(z), s(s(z)))) | (~b(s(s(z)), s(s(elem!1)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(s(elem!1)))) | (~b(s(s(elem!1)), z)) | (~b(s(z), s(s(elem!1)))) | (~b(s(z), s(s(z)))) | (~b(s(s(z)), s(s(elem!1)))))),
% 2.62/2.86 inference(rewrite,[status(thm)],[])).
% 2.62/2.86 tff(9451,plain,
% 2.62/2.86 (((~b(z, s(s(elem!1)))) | (~b(s(z), s(s(elem!1)))) | (~b(s(s(elem!1)), z)) | (~b(s(s(z)), s(s(elem!1)))) | (~b(s(z), s(s(elem!1)))) | (~b(s(z), s(s(z))))) <=> ((~b(z, s(s(elem!1)))) | (~b(s(s(elem!1)), z)) | (~b(s(z), s(s(elem!1)))) | (~b(s(z), s(s(z)))) | (~b(s(s(z)), s(s(elem!1)))))),
% 2.62/2.86 inference(rewrite,[status(thm)],[])).
% 2.62/2.86 tff(9452,plain,
% 2.62/2.86 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(elem!1)))) | (~b(s(z), s(s(elem!1)))) | (~b(s(s(elem!1)), z)) | (~b(s(s(z)), s(s(elem!1)))) | (~b(s(z), s(s(elem!1)))) | (~b(s(z), s(s(z)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(elem!1)))) | (~b(s(s(elem!1)), z)) | (~b(s(z), s(s(elem!1)))) | (~b(s(z), s(s(z)))) | (~b(s(s(z)), s(s(elem!1))))))),
% 2.62/2.86 inference(monotonicity,[status(thm)],[9451])).
% 2.62/2.86 tff(9453,plain,
% 2.62/2.86 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(elem!1)))) | (~b(s(z), s(s(elem!1)))) | (~b(s(s(elem!1)), z)) | (~b(s(s(z)), s(s(elem!1)))) | (~b(s(z), s(s(elem!1)))) | (~b(s(z), s(s(z)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(s(elem!1)))) | (~b(s(s(elem!1)), z)) | (~b(s(z), s(s(elem!1)))) | (~b(s(z), s(s(z)))) | (~b(s(s(z)), s(s(elem!1)))))),
% 2.62/2.86 inference(transitivity,[status(thm)],[9452, 9450])).
% 2.62/2.86 tff(9454,plain,
% 2.62/2.86 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(elem!1)))) | (~b(s(z), s(s(elem!1)))) | (~b(s(s(elem!1)), z)) | (~b(s(s(z)), s(s(elem!1)))) | (~b(s(z), s(s(elem!1)))) | (~b(s(z), s(s(z)))))),
% 2.62/2.86 inference(quant_inst,[status(thm)],[])).
% 2.62/2.86 tff(9455,plain,
% 2.62/2.86 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(s(elem!1)))) | (~b(s(s(elem!1)), z)) | (~b(s(z), s(s(elem!1)))) | (~b(s(z), s(s(z)))) | (~b(s(s(z)), s(s(elem!1))))),
% 2.62/2.86 inference(modus_ponens,[status(thm)],[9454, 9453])).
% 2.62/2.86 tff(9456,plain,
% 2.62/2.86 ($false),
% 2.62/2.86 inference(unit_resolution,[status(thm)],[9455, 166, 376, 9426, 9449, 9424, 9443])).
% 2.62/2.86 tff(9457,plain,((~r(s(z), z)) | (~b(s(z), s(s(elem!1)))) | (~r(z, s(s(z)))) | (~r(z, s(z))) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(s(z)), s(z))) | (s(s(z)) = s(s(elem!1))) | (~r(s(s(elem!1)), s(z))) | (~r(s(s(elem!1)), s(s(s(elem!1))))) | (s(s(s(elem!1))) = s(s(elem!1))) | (~b(s(s(s(elem!1))), z))), inference(lemma,lemma(discharge,[]))).
% 2.62/2.86 tff(9458,plain,
% 2.62/2.86 (~r(s(z), z)),
% 2.62/2.86 inference(unit_resolution,[status(thm)],[9457, 156, 155, 323, 96, 376, 52, 4577, 377, 1863, 121])).
% 2.62/2.86 tff(9459,plain,
% 2.62/2.86 (b(s(z), z)),
% 2.62/2.86 inference(unit_resolution,[status(thm)],[230, 9458])).
% 2.62/2.86 tff(9460,plain,
% 2.62/2.86 (~r(s(z), s(s(s(elem!1))))),
% 2.62/2.86 inference(unit_resolution,[status(thm)],[8626, 365, 323, 4577])).
% 2.62/2.86 tff(9461,plain,
% 2.62/2.86 (b(s(z), s(s(s(elem!1))))),
% 2.62/2.86 inference(unit_resolution,[status(thm)],[116, 9460])).
% 2.62/2.86 tff(9462,plain,
% 2.62/2.86 (~b(s(s(z)), s(s(s(elem!1))))),
% 2.62/2.86 inference(unit_resolution,[status(thm)],[271, 9461, 96, 156])).
% 2.62/2.86 tff(9463,plain,
% 2.62/2.86 (r(s(s(z)), s(s(s(elem!1))))),
% 2.62/2.86 inference(unit_resolution,[status(thm)],[279, 9462])).
% 2.62/2.86 tff(9464,plain,
% 2.62/2.86 (~r(s(s(elem!1)), s(s(z)))),
% 2.62/2.86 inference(unit_resolution,[status(thm)],[539, 9463, 155, 365])).
% 2.62/2.86 tff(9465,plain,
% 2.62/2.86 (~r(s(z), s(s(z)))),
% 2.62/2.86 inference(unit_resolution,[status(thm)],[331, 9463, 155, 323])).
% 2.62/2.86 tff(9466,plain,
% 2.62/2.86 (b(s(z), s(s(z)))),
% 2.62/2.86 inference(unit_resolution,[status(thm)],[427, 9465])).
% 2.62/2.86 tff(9467,plain,
% 2.62/2.86 ($false),
% 2.62/2.86 inference(unit_resolution,[status(thm)],[5300, 9466, 9464, 376, 52, 8633])).
% 2.62/2.86 tff(9468,plain,((~r(z, s(s(elem!1)))) | (~b(s(z), s(s(elem!1)))) | (s(s(z)) = s(s(elem!1))) | (~r(z, s(s(z)))) | (~r(z, s(z))) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(s(z)), s(z))) | (~r(s(s(elem!1)), s(z)))), inference(lemma,lemma(discharge,[]))).
% 2.62/2.86 tff(9469,plain,
% 2.62/2.86 (~r(z, s(s(elem!1)))),
% 2.62/2.86 inference(unit_resolution,[status(thm)],[9468, 156, 52, 155, 323, 96, 376, 4577])).
% 2.62/2.86 tff(9470,plain,
% 2.62/2.86 (b(z, s(s(elem!1)))),
% 2.62/2.86 inference(unit_resolution,[status(thm)],[1795, 9469])).
% 2.62/2.86 tff(9471,plain,
% 2.62/2.86 (~b(s(s(elem!1)), z)),
% 2.62/2.86 inference(unit_resolution,[status(thm)],[5377, 9470, 376, 9459])).
% 2.62/2.86 tff(9472,plain,
% 2.62/2.86 (r(s(s(elem!1)), z)),
% 2.62/2.86 inference(unit_resolution,[status(thm)],[608, 9471])).
% 2.62/2.86 tff(9473,plain,
% 2.62/2.86 (~r(s(z), s(s(z)))),
% 2.62/2.86 inference(unit_resolution,[status(thm)],[8620, 9472, 4577, 323])).
% 2.62/2.86 tff(9474,plain,
% 2.62/2.86 (b(s(z), s(s(z)))),
% 2.62/2.86 inference(unit_resolution,[status(thm)],[427, 9473])).
% 2.62/2.86 tff(9475,plain,
% 2.62/2.86 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), z)) | (~b(s(s(s(elem!1))), s(s(z)))) | (~b(s(s(s(elem!1))), z)) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(z), s(s(z)))) | (~b(s(s(z)), s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), z)) | (~b(s(s(s(elem!1))), s(s(z)))) | (~b(s(s(s(elem!1))), z)) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(z), s(s(z)))) | (~b(s(s(z)), s(z))))),
% 2.62/2.87 inference(rewrite,[status(thm)],[])).
% 2.62/2.87 tff(9476,plain,
% 2.62/2.87 (((~b(s(z), z)) | (~b(s(s(s(elem!1))), z)) | (~b(s(s(z)), s(z))) | (~b(s(z), s(s(z)))) | (~b(s(s(s(elem!1))), s(s(z)))) | (~b(s(s(s(elem!1))), s(z)))) <=> ((~b(s(z), z)) | (~b(s(s(s(elem!1))), s(s(z)))) | (~b(s(s(s(elem!1))), z)) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(z), s(s(z)))) | (~b(s(s(z)), s(z))))),
% 2.62/2.87 inference(rewrite,[status(thm)],[])).
% 2.62/2.87 tff(9477,plain,
% 2.62/2.87 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), z)) | (~b(s(s(s(elem!1))), z)) | (~b(s(s(z)), s(z))) | (~b(s(z), s(s(z)))) | (~b(s(s(s(elem!1))), s(s(z)))) | (~b(s(s(s(elem!1))), s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), z)) | (~b(s(s(s(elem!1))), s(s(z)))) | (~b(s(s(s(elem!1))), z)) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(z), s(s(z)))) | (~b(s(s(z)), s(z)))))),
% 2.62/2.87 inference(monotonicity,[status(thm)],[9476])).
% 2.62/2.87 tff(9478,plain,
% 2.62/2.87 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), z)) | (~b(s(s(s(elem!1))), z)) | (~b(s(s(z)), s(z))) | (~b(s(z), s(s(z)))) | (~b(s(s(s(elem!1))), s(s(z)))) | (~b(s(s(s(elem!1))), s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), z)) | (~b(s(s(s(elem!1))), s(s(z)))) | (~b(s(s(s(elem!1))), z)) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(z), s(s(z)))) | (~b(s(s(z)), s(z))))),
% 2.62/2.87 inference(transitivity,[status(thm)],[9477, 9475])).
% 2.62/2.87 tff(9479,plain,
% 2.62/2.87 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), z)) | (~b(s(s(s(elem!1))), z)) | (~b(s(s(z)), s(z))) | (~b(s(z), s(s(z)))) | (~b(s(s(s(elem!1))), s(s(z)))) | (~b(s(s(s(elem!1))), s(z))))),
% 2.62/2.87 inference(quant_inst,[status(thm)],[])).
% 2.62/2.87 tff(9480,plain,
% 2.62/2.87 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), z)) | (~b(s(s(s(elem!1))), s(s(z)))) | (~b(s(s(s(elem!1))), z)) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(z), s(s(z)))) | (~b(s(s(z)), s(z)))),
% 2.62/2.87 inference(modus_ponens,[status(thm)],[9479, 9478])).
% 2.62/2.87 tff(9481,plain,
% 2.62/2.87 (~b(s(s(s(elem!1))), s(s(z)))),
% 2.62/2.87 inference(unit_resolution,[status(thm)],[9480, 166, 9459, 9474, 96, 121, 156])).
% 2.62/2.87 tff(9482,plain,
% 2.62/2.87 (r(s(s(s(elem!1))), s(s(z)))),
% 2.62/2.87 inference(unit_resolution,[status(thm)],[218, 9481])).
% 2.62/2.87 tff(9483,plain,
% 2.62/2.87 (~b(s(s(z)), s(s(s(elem!1))))),
% 2.62/2.87 inference(unit_resolution,[status(thm)],[4503, 166, 9474, 96, 156])).
% 2.62/2.87 tff(9484,plain,
% 2.62/2.87 (r(s(s(z)), s(s(s(elem!1))))),
% 2.62/2.87 inference(unit_resolution,[status(thm)],[279, 9483])).
% 2.62/2.87 tff(9485,plain,
% 2.62/2.87 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(elem!1)), s(s(s(elem!1))))) | (~r(s(s(z)), s(s(elem!1)))) | (~r(s(s(z)), s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), s(s(z)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(elem!1)), s(s(s(elem!1))))) | (~r(s(s(z)), s(s(elem!1)))) | (~r(s(s(z)), s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), s(s(z)))))),
% 2.62/2.87 inference(rewrite,[status(thm)],[])).
% 2.62/2.87 tff(9486,plain,
% 2.62/2.87 (((~r(s(s(s(elem!1))), s(s(z)))) | (~r(s(s(elem!1)), s(s(s(elem!1))))) | (~r(s(s(z)), s(s(s(elem!1))))) | (~r(s(s(z)), s(s(elem!1))))) <=> ((~r(s(s(elem!1)), s(s(s(elem!1))))) | (~r(s(s(z)), s(s(elem!1)))) | (~r(s(s(z)), s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), s(s(z)))))),
% 2.62/2.87 inference(rewrite,[status(thm)],[])).
% 2.62/2.87 tff(9487,plain,
% 2.62/2.87 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), s(s(z)))) | (~r(s(s(elem!1)), s(s(s(elem!1))))) | (~r(s(s(z)), s(s(s(elem!1))))) | (~r(s(s(z)), s(s(elem!1)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(elem!1)), s(s(s(elem!1))))) | (~r(s(s(z)), s(s(elem!1)))) | (~r(s(s(z)), s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), s(s(z))))))),
% 2.62/2.87 inference(monotonicity,[status(thm)],[9486])).
% 2.62/2.87 tff(9488,plain,
% 2.62/2.87 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), s(s(z)))) | (~r(s(s(elem!1)), s(s(s(elem!1))))) | (~r(s(s(z)), s(s(s(elem!1))))) | (~r(s(s(z)), s(s(elem!1)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(elem!1)), s(s(s(elem!1))))) | (~r(s(s(z)), s(s(elem!1)))) | (~r(s(s(z)), s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), s(s(z)))))),
% 2.62/2.87 inference(transitivity,[status(thm)],[9487, 9485])).
% 2.62/2.87 tff(9489,plain,
% 2.62/2.87 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), s(s(z)))) | (~r(s(s(elem!1)), s(s(s(elem!1))))) | (~r(s(s(z)), s(s(s(elem!1))))) | (~r(s(s(z)), s(s(elem!1)))))),
% 2.62/2.87 inference(quant_inst,[status(thm)],[])).
% 2.62/2.87 tff(9490,plain,
% 2.62/2.87 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(elem!1)), s(s(s(elem!1))))) | (~r(s(s(z)), s(s(elem!1)))) | (~r(s(s(z)), s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), s(s(z))))),
% 2.62/2.87 inference(modus_ponens,[status(thm)],[9489, 9488])).
% 2.62/2.87 tff(9491,plain,
% 2.62/2.87 (~r(s(s(z)), s(s(elem!1)))),
% 2.62/2.87 inference(unit_resolution,[status(thm)],[9490, 197, 377, 9484, 9482])).
% 2.62/2.87 tff(9492,plain,
% 2.62/2.87 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(elem!1)), s(s(s(elem!1))))) | (~r(s(s(elem!1)), s(s(z)))) | (~r(s(s(z)), s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), s(s(z)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(elem!1)), s(s(s(elem!1))))) | (~r(s(s(elem!1)), s(s(z)))) | (~r(s(s(z)), s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), s(s(z)))))),
% 2.62/2.87 inference(rewrite,[status(thm)],[])).
% 2.62/2.87 tff(9493,plain,
% 2.62/2.87 (((~r(s(s(s(elem!1))), s(s(z)))) | (~r(s(s(z)), s(s(s(elem!1))))) | (~r(s(s(elem!1)), s(s(s(elem!1))))) | (~r(s(s(elem!1)), s(s(z))))) <=> ((~r(s(s(elem!1)), s(s(s(elem!1))))) | (~r(s(s(elem!1)), s(s(z)))) | (~r(s(s(z)), s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), s(s(z)))))),
% 2.62/2.87 inference(rewrite,[status(thm)],[])).
% 2.62/2.87 tff(9494,plain,
% 2.62/2.87 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), s(s(z)))) | (~r(s(s(z)), s(s(s(elem!1))))) | (~r(s(s(elem!1)), s(s(s(elem!1))))) | (~r(s(s(elem!1)), s(s(z)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(elem!1)), s(s(s(elem!1))))) | (~r(s(s(elem!1)), s(s(z)))) | (~r(s(s(z)), s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), s(s(z))))))),
% 2.62/2.87 inference(monotonicity,[status(thm)],[9493])).
% 2.62/2.87 tff(9495,plain,
% 2.62/2.87 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), s(s(z)))) | (~r(s(s(z)), s(s(s(elem!1))))) | (~r(s(s(elem!1)), s(s(s(elem!1))))) | (~r(s(s(elem!1)), s(s(z)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(elem!1)), s(s(s(elem!1))))) | (~r(s(s(elem!1)), s(s(z)))) | (~r(s(s(z)), s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), s(s(z)))))),
% 2.62/2.87 inference(transitivity,[status(thm)],[9494, 9492])).
% 2.62/2.87 tff(9496,plain,
% 2.62/2.87 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), s(s(z)))) | (~r(s(s(z)), s(s(s(elem!1))))) | (~r(s(s(elem!1)), s(s(s(elem!1))))) | (~r(s(s(elem!1)), s(s(z)))))),
% 2.62/2.87 inference(quant_inst,[status(thm)],[])).
% 2.62/2.87 tff(9497,plain,
% 2.62/2.87 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(elem!1)), s(s(s(elem!1))))) | (~r(s(s(elem!1)), s(s(z)))) | (~r(s(s(z)), s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), s(s(z))))),
% 2.62/2.87 inference(modus_ponens,[status(thm)],[9496, 9495])).
% 2.62/2.87 tff(9498,plain,
% 2.62/2.87 (~r(s(s(elem!1)), s(s(z)))),
% 2.62/2.87 inference(unit_resolution,[status(thm)],[9497, 197, 377, 9484, 9482])).
% 2.62/2.87 tff(9499,plain,
% 2.62/2.87 ($false),
% 2.62/2.87 inference(unit_resolution,[status(thm)],[5300, 9498, 9491, 376, 52, 9474])).
% 2.62/2.87 tff(9500,plain,((~b(s(s(z)), s(z))) | (~b(s(z), s(s(elem!1)))) | (s(s(z)) = s(s(elem!1))) | (~r(s(s(elem!1)), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(s(s(elem!1))), z)) | (~r(s(s(elem!1)), s(z))) | (~r(z, s(z))) | (~r(z, s(s(z)))) | (s(s(s(elem!1))) = s(s(elem!1)))), inference(lemma,lemma(discharge,[]))).
% 2.62/2.87 tff(9501,plain,
% 2.62/2.87 (~b(s(s(z)), s(z))),
% 2.62/2.87 inference(unit_resolution,[status(thm)],[9500, 52, 376, 377, 96, 121, 4577, 323, 155, 1863])).
% 2.62/2.87 tff(9502,plain,
% 2.62/2.87 (r(s(s(z)), s(z))),
% 2.62/2.87 inference(unit_resolution,[status(thm)],[308, 9501])).
% 2.62/2.87 tff(9503,plain,
% 2.62/2.87 (~r(s(z), z)),
% 2.62/2.87 inference(unit_resolution,[status(thm)],[2680, 9502, 155, 323])).
% 2.62/2.87 tff(9504,plain,
% 2.62/2.87 (b(s(z), z)),
% 2.62/2.87 inference(unit_resolution,[status(thm)],[230, 9503])).
% 2.62/2.87 tff(9505,plain,
% 2.62/2.87 (~r(z, s(s(elem!1)))),
% 2.62/2.87 inference(unit_resolution,[status(thm)],[443, 9502, 155, 323, 377, 132])).
% 2.62/2.87 tff(9506,plain,
% 2.62/2.87 (b(z, s(s(elem!1)))),
% 2.62/2.87 inference(unit_resolution,[status(thm)],[1795, 9505])).
% 2.62/2.87 tff(9507,plain,
% 2.62/2.87 (~b(s(s(elem!1)), z)),
% 2.62/2.87 inference(unit_resolution,[status(thm)],[5377, 9506, 376, 9504])).
% 2.62/2.87 tff(9508,plain,
% 2.62/2.87 (r(s(s(elem!1)), z)),
% 2.62/2.87 inference(unit_resolution,[status(thm)],[608, 9507])).
% 2.62/2.87 tff(9509,plain,
% 2.62/2.87 (~r(s(z), s(s(z)))),
% 2.62/2.87 inference(unit_resolution,[status(thm)],[553, 9502, 155, 323])).
% 2.62/2.87 tff(9510,plain,
% 2.62/2.87 (b(s(z), s(s(z)))),
% 2.62/2.87 inference(unit_resolution,[status(thm)],[427, 9509])).
% 2.62/2.87 tff(9511,plain,
% 2.62/2.87 (~r(s(s(elem!1)), s(s(z)))),
% 2.62/2.87 inference(unit_resolution,[status(thm)],[8642, 9508, 155, 9502])).
% 2.62/2.87 tff(9512,plain,
% 2.62/2.87 (r(s(s(z)), s(s(elem!1)))),
% 2.62/2.87 inference(unit_resolution,[status(thm)],[5300, 9511, 376, 52, 9510])).
% 2.62/2.87 tff(9513,plain,
% 2.62/2.87 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(z))) | (~r(s(s(elem!1)), z)) | (~r(s(s(z)), z)) | (~r(s(s(z)), s(s(elem!1)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, s(z))) | (~r(s(s(elem!1)), z)) | (~r(s(s(z)), z)) | (~r(s(s(z)), s(s(elem!1)))))),
% 2.62/2.87 inference(rewrite,[status(thm)],[])).
% 2.62/2.87 tff(9514,plain,
% 2.62/2.87 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(z))) | (~r(s(s(elem!1)), z)) | (~r(s(s(z)), z)) | (~r(s(s(z)), s(s(elem!1)))))),
% 2.62/2.87 inference(quant_inst,[status(thm)],[])).
% 2.62/2.87 tff(9515,plain,
% 2.62/2.87 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, s(z))) | (~r(s(s(elem!1)), z)) | (~r(s(s(z)), z)) | (~r(s(s(z)), s(s(elem!1))))),
% 2.62/2.87 inference(modus_ponens,[status(thm)],[9514, 9513])).
% 2.62/2.87 tff(9516,plain,
% 2.62/2.87 ($false),
% 2.62/2.87 inference(unit_resolution,[status(thm)],[9515, 197, 323, 333, 1970, 866])).
% 2.62/2.87 tff(9517,plain,((~r(s(s(z)), z)) | (~r(z, s(z))) | (~r(s(s(z)), s(s(elem!1)))) | (~r(s(s(elem!1)), z))), inference(lemma,lemma(discharge,[]))).
% 2.62/2.87 tff(9518,plain,
% 2.62/2.87 (~r(s(s(z)), z)),
% 2.62/2.87 inference(unit_resolution,[status(thm)],[9517, 9512, 323, 9508])).
% 2.62/2.87 tff(9519,plain,
% 2.62/2.87 (b(s(s(z)), z)),
% 2.62/2.87 inference(unit_resolution,[status(thm)],[186, 9518])).
% 2.62/2.87 tff(9520,plain,
% 2.62/2.87 (b(s(s(elem!1)), s(s(z)))),
% 2.62/2.87 inference(unit_resolution,[status(thm)],[441, 9511, 132])).
% 2.62/2.87 tff(9521,plain,
% 2.62/2.87 (~r(s(z), s(s(s(elem!1))))),
% 2.62/2.87 inference(unit_resolution,[status(thm)],[6892, 9512, 4577, 9502])).
% 2.62/2.87 tff(9522,plain,
% 2.62/2.87 (b(s(z), s(s(s(elem!1))))),
% 2.62/2.87 inference(unit_resolution,[status(thm)],[116, 9521])).
% 2.62/2.87 tff(9523,plain,
% 2.62/2.87 (~r(s(z), s(s(s(z))))),
% 2.62/2.87 inference(unit_resolution,[status(thm)],[8994, 9502, 323, 155])).
% 2.62/2.87 tff(9524,plain,
% 2.62/2.87 (b(s(z), s(s(s(z))))),
% 2.62/2.87 inference(unit_resolution,[status(thm)],[1674, 9523])).
% 2.62/2.87 tff(9525,plain,
% 2.62/2.87 (~b(s(s(z)), s(s(s(elem!1))))),
% 2.62/2.87 inference(unit_resolution,[status(thm)],[8665, 9522, 96, 9510, 9524])).
% 2.62/2.87 tff(9526,plain,
% 2.62/2.87 (r(s(s(z)), s(s(s(elem!1))))),
% 2.62/2.87 inference(unit_resolution,[status(thm)],[279, 9525])).
% 2.62/2.87 tff(9527,plain,
% 2.62/2.87 (~r(s(s(s(elem!1))), s(s(elem!1)))),
% 2.62/2.87 inference(unit_resolution,[status(thm)],[8677, 9526, 4577, 9512])).
% 2.62/2.87 tff(9528,plain,
% 2.62/2.87 (b(s(s(s(elem!1))), s(s(elem!1)))),
% 2.62/2.87 inference(unit_resolution,[status(thm)],[889, 9527, 1863])).
% 2.62/2.87 tff(9529,plain,
% 2.62/2.87 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(z), z)) | (~b(s(z), s(s(s(elem!1))))) | (~b(s(z), s(s(elem!1)))) | (~b(s(s(elem!1)), s(s(z)))) | (~b(s(s(z)), z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(z), z)) | (~b(s(z), s(s(s(elem!1))))) | (~b(s(z), s(s(elem!1)))) | (~b(s(s(elem!1)), s(s(z)))) | (~b(s(s(z)), z)))),
% 2.62/2.87 inference(rewrite,[status(thm)],[])).
% 2.62/2.87 tff(9530,plain,
% 2.62/2.87 (((~b(s(s(z)), z)) | (~b(s(z), z)) | (~b(s(s(elem!1)), s(s(z)))) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(z), s(s(elem!1)))) | (~b(s(z), s(s(s(elem!1)))))) <=> ((~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(z), z)) | (~b(s(z), s(s(s(elem!1))))) | (~b(s(z), s(s(elem!1)))) | (~b(s(s(elem!1)), s(s(z)))) | (~b(s(s(z)), z)))),
% 2.62/2.87 inference(rewrite,[status(thm)],[])).
% 2.62/2.87 tff(9531,plain,
% 2.62/2.87 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), z)) | (~b(s(z), z)) | (~b(s(s(elem!1)), s(s(z)))) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(z), s(s(elem!1)))) | (~b(s(z), s(s(s(elem!1))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(z), z)) | (~b(s(z), s(s(s(elem!1))))) | (~b(s(z), s(s(elem!1)))) | (~b(s(s(elem!1)), s(s(z)))) | (~b(s(s(z)), z))))),
% 2.62/2.87 inference(monotonicity,[status(thm)],[9530])).
% 2.62/2.87 tff(9532,plain,
% 2.62/2.87 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), z)) | (~b(s(z), z)) | (~b(s(s(elem!1)), s(s(z)))) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(z), s(s(elem!1)))) | (~b(s(z), s(s(s(elem!1))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(z), z)) | (~b(s(z), s(s(s(elem!1))))) | (~b(s(z), s(s(elem!1)))) | (~b(s(s(elem!1)), s(s(z)))) | (~b(s(s(z)), z)))),
% 2.62/2.87 inference(transitivity,[status(thm)],[9531, 9529])).
% 2.62/2.87 tff(9533,plain,
% 2.62/2.87 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), z)) | (~b(s(z), z)) | (~b(s(s(elem!1)), s(s(z)))) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(z), s(s(elem!1)))) | (~b(s(z), s(s(s(elem!1))))))),
% 2.62/2.87 inference(quant_inst,[status(thm)],[])).
% 2.62/2.87 tff(9534,plain,
% 2.62/2.87 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(z), z)) | (~b(s(z), s(s(s(elem!1))))) | (~b(s(z), s(s(elem!1)))) | (~b(s(s(elem!1)), s(s(z)))) | (~b(s(s(z)), z))),
% 2.62/2.87 inference(modus_ponens,[status(thm)],[9533, 9532])).
% 2.62/2.87 tff(9535,plain,
% 2.62/2.87 ($false),
% 2.62/2.87 inference(unit_resolution,[status(thm)],[9534, 166, 376, 9528, 9522, 9504, 9520, 9519])).
% 2.62/2.87 tff(9536,plain,((s(s(z)) = s(s(elem!1))) | (~b(s(z), s(s(elem!1)))) | (s(s(s(elem!1))) = s(s(elem!1))) | (~r(s(s(elem!1)), s(z))) | (~b(s(s(s(elem!1))), s(z))) | (~r(z, s(z))) | (~r(z, s(s(z)))) | (~r(s(s(elem!1)), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), z))), inference(lemma,lemma(discharge,[]))).
% 2.62/2.87 tff(9537,plain,
% 2.62/2.87 (s(s(z)) = s(s(elem!1))),
% 2.62/2.87 inference(unit_resolution,[status(thm)],[9536, 9420, 9259, 9260, 96, 8408, 152, 9422, 8808])).
% 2.62/2.87 tff(9538,plain,
% 2.62/2.87 (s(elem!1) = s(z)),
% 2.62/2.87 inference(unit_resolution,[status(thm)],[43, 9537])).
% 2.62/2.87 tff(9539,plain,
% 2.62/2.87 (z = elem!1),
% 2.62/2.87 inference(unit_resolution,[status(thm)],[30, 9538])).
% 2.62/2.87 tff(9540,plain,
% 2.62/2.87 ((s(s(s(s(elem!1)))) = z) <=> (s(s(s(s(elem!1)))) = elem!1)),
% 2.62/2.87 inference(monotonicity,[status(thm)],[9539])).
% 2.62/2.87 tff(9541,plain,
% 2.62/2.87 ((s(s(s(s(elem!1)))) = z) <=> (elem!1 = s(s(s(s(elem!1)))))),
% 2.62/2.87 inference(transitivity,[status(thm)],[9540, 2287])).
% 2.62/2.87 tff(9542,plain,
% 2.62/2.87 ((~(s(s(s(s(elem!1)))) = z)) <=> (~(elem!1 = s(s(s(s(elem!1))))))),
% 2.62/2.87 inference(monotonicity,[status(thm)],[9541])).
% 2.62/2.87 tff(9543,plain,
% 2.62/2.87 (~(elem!1 = s(s(s(s(elem!1)))))),
% 2.62/2.87 inference(modus_ponens,[status(thm)],[626, 9542])).
% 2.62/2.87 tff(9544,plain,
% 2.62/2.87 (b(s(z), z) <=> b(s(z), elem!1)),
% 2.62/2.87 inference(monotonicity,[status(thm)],[9539])).
% 2.62/2.87 tff(9545,plain,
% 2.62/2.87 (~b(z, s(s(elem!1)))),
% 2.62/2.87 inference(unit_resolution,[status(thm)],[2261, 9537, 125])).
% 2.62/2.87 tff(9546,plain,
% 2.62/2.87 (r(z, s(s(elem!1)))),
% 2.62/2.87 inference(unit_resolution,[status(thm)],[1795, 9545])).
% 2.62/2.87 tff(9547,plain,
% 2.62/2.87 (~r(s(z), z)),
% 2.62/2.87 inference(unit_resolution,[status(thm)],[8426, 9546, 8408, 9260])).
% 2.62/2.87 tff(9548,plain,
% 2.62/2.87 (b(s(z), z)),
% 2.62/2.87 inference(unit_resolution,[status(thm)],[230, 9547])).
% 2.62/2.87 tff(9549,plain,
% 2.62/2.87 (b(s(z), elem!1)),
% 2.62/2.87 inference(modus_ponens,[status(thm)],[9548, 9544])).
% 2.62/2.87 tff(9550,plain,
% 2.62/2.87 (~r(s(z), s(s(s(elem!1))))),
% 2.62/2.87 inference(unit_resolution,[status(thm)],[8626, 9546, 8408, 9260])).
% 2.62/2.87 tff(9551,plain,
% 2.62/2.87 (b(s(z), s(s(s(elem!1))))),
% 2.62/2.87 inference(unit_resolution,[status(thm)],[116, 9550])).
% 2.62/2.87 tff(9552,plain,
% 2.62/2.87 (~b(z, s(s(s(elem!1))))),
% 2.62/2.87 inference(unit_resolution,[status(thm)],[1470, 9551, 8808, 9548])).
% 2.62/2.87 tff(9553,plain,
% 2.62/2.87 (r(z, s(s(s(elem!1))))),
% 2.62/2.87 inference(unit_resolution,[status(thm)],[261, 9552])).
% 2.62/2.87 tff(9554,plain,
% 2.62/2.87 (~r(s(s(s(elem!1))), s(s(elem!1)))),
% 2.62/2.87 inference(unit_resolution,[status(thm)],[1956, 9553, 9546, 9422])).
% 2.62/2.87 tff(9555,plain,
% 2.62/2.87 (b(s(s(s(elem!1))), s(s(elem!1)))),
% 2.62/2.87 inference(unit_resolution,[status(thm)],[889, 9554, 9259])).
% 2.62/2.87 tff(9556,plain,
% 2.62/2.87 (r(elem!1, s(z))),
% 2.62/2.87 inference(unit_resolution,[status(thm)],[741, 9539, 8408])).
% 2.62/2.87 tff(9557,plain,
% 2.62/2.87 (r(elem!1, s(s(z))) <=> r(z, s(s(elem!1)))),
% 2.62/2.87 inference(monotonicity,[status(thm)],[752, 34])).
% 2.62/2.87 tff(9558,plain,
% 2.62/2.87 (r(z, s(s(elem!1))) <=> r(elem!1, s(s(z)))),
% 2.62/2.87 inference(symmetry,[status(thm)],[9557])).
% 2.62/2.87 tff(9559,plain,
% 2.62/2.87 (r(elem!1, s(s(z)))),
% 2.62/2.87 inference(modus_ponens,[status(thm)],[365, 9558])).
% 2.62/2.87 tff(9560,plain,
% 2.62/2.87 (r(elem!1, s(s(elem!1))) <=> r(elem!1, s(s(z)))),
% 2.62/2.87 inference(monotonicity,[status(thm)],[6344])).
% 2.62/2.87 tff(9561,plain,
% 2.62/2.87 (r(elem!1, s(s(z))) <=> r(elem!1, s(s(elem!1)))),
% 2.62/2.87 inference(symmetry,[status(thm)],[9560])).
% 2.62/2.87 tff(9562,plain,
% 2.62/2.87 (r(elem!1, s(s(elem!1)))),
% 2.62/2.87 inference(modus_ponens,[status(thm)],[6194, 9561])).
% 2.62/2.87 tff(9563,assumption,(~r(elem!1, s(s(elem!1)))), introduced(assumption)).
% 2.62/2.87 tff(9564,plain,
% 2.62/2.87 ($false),
% 2.62/2.87 inference(unit_resolution,[status(thm)],[9563, 9562])).
% 2.62/2.87 tff(9565,plain,(r(elem!1, s(s(elem!1))) | (~r(elem!1, s(s(z)))) | (~(s(s(z)) = s(s(elem!1))))), inference(lemma,lemma(discharge,[]))).
% 2.62/2.87 tff(9566,plain,
% 2.62/2.87 (r(elem!1, s(s(elem!1)))),
% 2.62/2.87 inference(unit_resolution,[status(thm)],[9565, 9559, 34])).
% 2.62/2.87 tff(9567,plain,
% 2.62/2.87 (s(s(s(s(elem!1)))) = s(elem!1)),
% 2.62/2.87 inference(transitivity,[status(thm)],[651, 13])).
% 2.62/2.87 tff(9568,plain,
% 2.62/2.87 (inj_0(s(s(s(s(elem!1))))) = inj_0(s(elem!1))),
% 2.62/2.87 inference(monotonicity,[status(thm)],[9567])).
% 2.62/2.87 tff(9569,plain,
% 2.62/2.87 (inj_0(s(elem!1)) = inj_0(s(s(s(s(elem!1)))))),
% 2.62/2.87 inference(symmetry,[status(thm)],[9568])).
% 2.62/2.87 tff(9570,plain,
% 2.62/2.87 (elem!1 = s(s(s(elem!1)))),
% 2.62/2.87 inference(transitivity,[status(thm)],[1170, 9569, 352])).
% 2.62/2.87 tff(9571,plain,
% 2.62/2.87 ($false),
% 2.62/2.87 inference(unit_resolution,[status(thm)],[7751, 9570])).
% 2.62/2.87 tff(9572,plain,((~(s(s(s(s(elem!1)))) = s(z))) | (~(z = elem!1))), inference(lemma,lemma(discharge,[]))).
% 2.62/2.87 tff(9573,plain,
% 2.62/2.87 (~(s(s(s(s(elem!1)))) = s(z))),
% 2.62/2.88 inference(unit_resolution,[status(thm)],[9572, 620])).
% 2.62/2.88 tff(9574,plain,
% 2.62/2.88 (~(s(z) = s(s(s(s(elem!1)))))),
% 2.62/2.88 inference(unit_resolution,[status(thm)],[675, 9573])).
% 2.62/2.88 tff(9575,plain,
% 2.62/2.88 (r(z, s(s(s(elem!1)))) <=> r(elem!1, s(s(s(elem!1))))),
% 2.62/2.88 inference(monotonicity,[status(thm)],[620])).
% 2.62/2.88 tff(9576,plain,
% 2.62/2.88 (r(elem!1, s(s(s(elem!1))))),
% 2.62/2.88 inference(modus_ponens,[status(thm)],[282, 9575])).
% 2.62/2.88 tff(9577,plain,
% 2.62/2.88 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(s(elem!1)))) | (~r(elem!1, s(s(s(elem!1))))) | (~r(s(s(elem!1)), s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), s(s(s(s(elem!1)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(elem!1, s(s(elem!1)))) | (~r(elem!1, s(s(s(elem!1))))) | (~r(s(s(elem!1)), s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), s(s(s(s(elem!1)))))))),
% 2.62/2.88 inference(rewrite,[status(thm)],[])).
% 2.62/2.88 tff(9578,plain,
% 2.62/2.88 (((~r(s(s(s(elem!1))), s(s(s(s(elem!1)))))) | (~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(elem!1, s(s(s(elem!1))))) | (~r(s(s(elem!1)), s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), s(s(s(s(elem!1)))))))),
% 2.62/2.88 inference(rewrite,[status(thm)],[])).
% 2.62/2.88 tff(9579,plain,
% 2.62/2.88 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), s(s(s(s(elem!1)))))) | (~r(s(s(elem!1)), s(s(s(elem!1))))) | (~r(elem!1, s(s(s(elem!1))))) | (~r(elem!1, s(s(elem!1)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(s(elem!1)))) | (~r(elem!1, s(s(s(elem!1))))) | (~r(s(s(elem!1)), s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), s(s(s(s(elem!1))))))))),
% 2.62/2.88 inference(monotonicity,[status(thm)],[9578])).
% 2.62/2.88 tff(9580,plain,
% 2.62/2.88 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), s(s(s(s(elem!1)))))) | (~r(s(s(elem!1)), s(s(s(elem!1))))) | (~r(elem!1, s(s(s(elem!1))))) | (~r(elem!1, s(s(elem!1)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(elem!1, s(s(elem!1)))) | (~r(elem!1, s(s(s(elem!1))))) | (~r(s(s(elem!1)), s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), s(s(s(s(elem!1)))))))),
% 2.62/2.88 inference(transitivity,[status(thm)],[9579, 9577])).
% 2.62/2.88 tff(9581,plain,
% 2.62/2.88 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), s(s(s(s(elem!1)))))) | (~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)))))),
% 2.62/2.88 inference(quant_inst,[status(thm)],[])).
% 2.62/2.88 tff(9582,plain,
% 2.62/2.88 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(elem!1, s(s(elem!1)))) | (~r(elem!1, s(s(s(elem!1))))) | (~r(s(s(elem!1)), s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), s(s(s(s(elem!1))))))),
% 2.62/2.88 inference(modus_ponens,[status(thm)],[9581, 9580])).
% 2.62/2.88 tff(9583,plain,
% 2.62/2.88 ($false),
% 2.62/2.88 inference(unit_resolution,[status(thm)],[9582, 197, 942, 377, 698, 1027])).
% 2.62/2.88 tff(9584,plain,((~r(s(s(s(elem!1))), s(s(s(s(elem!1)))))) | (~r(elem!1, s(s(s(elem!1))))) | (~r(s(s(elem!1)), s(s(s(elem!1))))) | (~r(elem!1, s(s(elem!1))))), inference(lemma,lemma(discharge,[]))).
% 2.62/2.88 tff(9585,plain,
% 2.62/2.88 (~r(s(s(s(elem!1))), s(s(s(s(elem!1)))))),
% 2.62/2.88 inference(unit_resolution,[status(thm)],[9584, 9576, 377, 9566])).
% 2.62/2.88 tff(9586,plain,
% 2.62/2.88 (b(s(s(s(elem!1))), s(s(s(s(elem!1)))))),
% 2.62/2.88 inference(unit_resolution,[status(thm)],[694, 79, 361, 9585])).
% 2.62/2.88 tff(9587,plain,
% 2.62/2.88 (r(s(s(s(s(elem!1)))), s(s(elem!1))) <=> r(s(s(s(s(elem!1)))), s(s(z)))),
% 2.62/2.88 inference(symmetry,[status(thm)],[4863])).
% 2.62/2.88 tff(9588,plain,
% 2.62/2.88 ((~r(s(s(s(s(elem!1)))), s(s(elem!1)))) <=> (~r(s(s(s(s(elem!1)))), s(s(z))))),
% 2.62/2.88 inference(monotonicity,[status(thm)],[9587])).
% 2.62/2.88 tff(9589,plain,
% 2.62/2.88 (b(s(s(elem!1)), elem!1)),
% 2.62/2.88 inference(modus_ponens,[status(thm)],[592, 5412])).
% 2.62/2.88 tff(9590,plain,
% 2.62/2.88 ((s(s(s(s(elem!1)))) = elem!1) <=> (s(s(s(s(elem!1)))) = z)),
% 2.62/2.88 inference(monotonicity,[status(thm)],[752])).
% 2.62/2.88 tff(9591,plain,
% 2.62/2.88 ((s(s(s(s(elem!1)))) = z) <=> (s(s(s(s(elem!1)))) = elem!1)),
% 2.62/2.88 inference(symmetry,[status(thm)],[9590])).
% 2.62/2.88 tff(9592,plain,
% 2.62/2.88 ((~(s(s(s(s(elem!1)))) = z)) <=> (~(s(s(s(s(elem!1)))) = elem!1))),
% 2.62/2.88 inference(monotonicity,[status(thm)],[9591])).
% 2.62/2.88 tff(9593,plain,
% 2.62/2.88 (~(s(s(s(s(elem!1)))) = elem!1)),
% 2.62/2.88 inference(modus_ponens,[status(thm)],[626, 9592])).
% 2.62/2.88 tff(9594,plain,
% 2.62/2.88 ((~r(elem!1, s(s(elem!1)))) | (~r(s(s(s(s(elem!1)))), elem!1))),
% 2.62/2.88 inference(unit_resolution,[status(thm)],[6447, 197, 4577, 3408])).
% 2.62/2.88 tff(9595,plain,
% 2.62/2.88 (~r(s(s(s(s(elem!1)))), elem!1)),
% 2.62/2.88 inference(unit_resolution,[status(thm)],[9594, 9562])).
% 2.62/2.88 tff(9596,plain,
% 2.62/2.88 ((s(s(s(s(elem!1)))) = elem!1) | b(s(s(s(s(elem!1)))), elem!1)),
% 2.62/2.88 inference(unit_resolution,[status(thm)],[717, 79, 9595])).
% 2.62/2.88 tff(9597,plain,
% 2.62/2.88 (b(s(s(s(s(elem!1)))), elem!1)),
% 2.62/2.88 inference(unit_resolution,[status(thm)],[9596, 9593])).
% 2.62/2.88 tff(9598,plain,
% 2.62/2.88 ((elem!1 = s(s(s(s(elem!1))))) <=> (z = s(s(s(s(elem!1)))))),
% 2.62/2.88 inference(monotonicity,[status(thm)],[752])).
% 2.62/2.88 tff(9599,plain,
% 2.62/2.88 ((elem!1 = s(s(s(s(elem!1))))) <=> (s(s(s(s(elem!1)))) = z)),
% 2.62/2.88 inference(transitivity,[status(thm)],[9598, 1483])).
% 2.62/2.88 tff(9600,plain,
% 2.62/2.88 ((s(s(s(s(elem!1)))) = z) <=> (elem!1 = s(s(s(s(elem!1)))))),
% 2.62/2.88 inference(symmetry,[status(thm)],[9599])).
% 2.62/2.88 tff(9601,plain,
% 2.62/2.88 ((~(s(s(s(s(elem!1)))) = z)) <=> (~(elem!1 = s(s(s(s(elem!1))))))),
% 2.62/2.88 inference(monotonicity,[status(thm)],[9600])).
% 2.62/2.88 tff(9602,plain,
% 2.62/2.88 (~(elem!1 = s(s(s(s(elem!1)))))),
% 2.62/2.88 inference(modus_ponens,[status(thm)],[626, 9601])).
% 2.62/2.88 tff(9603,plain,
% 2.62/2.88 ((~r(elem!1, s(s(s(s(elem!1)))))) | (~r(elem!1, s(s(elem!1))))),
% 2.62/2.88 inference(unit_resolution,[status(thm)],[6435, 197, 4577, 3408])).
% 2.62/2.88 tff(9604,plain,
% 2.62/2.88 (~r(elem!1, s(s(s(s(elem!1)))))),
% 2.62/2.88 inference(unit_resolution,[status(thm)],[9603, 9562])).
% 2.62/2.88 tff(9605,plain,
% 2.62/2.88 ((elem!1 = s(s(s(s(elem!1))))) | b(elem!1, s(s(s(s(elem!1)))))),
% 2.62/2.88 inference(unit_resolution,[status(thm)],[2425, 79, 9604])).
% 2.62/2.88 tff(9606,plain,
% 2.62/2.88 (b(elem!1, s(s(s(s(elem!1)))))),
% 2.62/2.88 inference(unit_resolution,[status(thm)],[9605, 9602])).
% 2.62/2.88 tff(9607,plain,
% 2.62/2.88 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), elem!1)) | (~b(s(z), s(s(elem!1)))) | (~b(s(z), elem!1)) | (~b(s(s(s(s(elem!1)))), elem!1)) | (~b(elem!1, s(s(s(s(elem!1)))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(elem!1)), elem!1)) | (~b(s(z), s(s(elem!1)))) | (~b(s(z), elem!1)) | (~b(s(s(s(s(elem!1)))), elem!1)) | (~b(elem!1, s(s(s(s(elem!1)))))))),
% 2.62/2.88 inference(rewrite,[status(thm)],[])).
% 2.62/2.88 tff(9608,plain,
% 2.62/2.88 (((~b(s(s(s(s(elem!1)))), elem!1)) | (~b(s(z), elem!1)) | (~b(elem!1, s(s(s(s(elem!1)))))) | (~b(s(s(elem!1)), elem!1)) | (~b(s(z), elem!1)) | (~b(s(z), s(s(elem!1))))) <=> ((~b(s(s(elem!1)), elem!1)) | (~b(s(z), s(s(elem!1)))) | (~b(s(z), elem!1)) | (~b(s(s(s(s(elem!1)))), elem!1)) | (~b(elem!1, s(s(s(s(elem!1)))))))),
% 2.62/2.88 inference(rewrite,[status(thm)],[])).
% 2.62/2.88 tff(9609,plain,
% 2.62/2.88 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(elem!1)))), elem!1)) | (~b(s(z), elem!1)) | (~b(elem!1, s(s(s(s(elem!1)))))) | (~b(s(s(elem!1)), elem!1)) | (~b(s(z), elem!1)) | (~b(s(z), s(s(elem!1)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), elem!1)) | (~b(s(z), s(s(elem!1)))) | (~b(s(z), elem!1)) | (~b(s(s(s(s(elem!1)))), elem!1)) | (~b(elem!1, s(s(s(s(elem!1))))))))),
% 2.62/2.88 inference(monotonicity,[status(thm)],[9608])).
% 2.62/2.88 tff(9610,plain,
% 2.62/2.88 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(elem!1)))), elem!1)) | (~b(s(z), elem!1)) | (~b(elem!1, s(s(s(s(elem!1)))))) | (~b(s(s(elem!1)), elem!1)) | (~b(s(z), elem!1)) | (~b(s(z), s(s(elem!1)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(elem!1)), elem!1)) | (~b(s(z), s(s(elem!1)))) | (~b(s(z), elem!1)) | (~b(s(s(s(s(elem!1)))), elem!1)) | (~b(elem!1, s(s(s(s(elem!1)))))))),
% 2.62/2.88 inference(transitivity,[status(thm)],[9609, 9607])).
% 2.62/2.88 tff(9611,plain,
% 2.62/2.88 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(elem!1)))), elem!1)) | (~b(s(z), elem!1)) | (~b(elem!1, s(s(s(s(elem!1)))))) | (~b(s(s(elem!1)), elem!1)) | (~b(s(z), elem!1)) | (~b(s(z), s(s(elem!1)))))),
% 2.62/2.88 inference(quant_inst,[status(thm)],[])).
% 2.62/2.88 tff(9612,plain,
% 2.62/2.88 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(elem!1)), elem!1)) | (~b(s(z), s(s(elem!1)))) | (~b(s(z), elem!1)) | (~b(s(s(s(s(elem!1)))), elem!1)) | (~b(elem!1, s(s(s(s(elem!1))))))),
% 2.62/2.88 inference(modus_ponens,[status(thm)],[9611, 9610])).
% 2.62/2.88 tff(9613,plain,
% 2.62/2.88 ($false),
% 2.62/2.88 inference(unit_resolution,[status(thm)],[9612, 166, 376, 786, 642, 9606, 9597])).
% 2.62/2.88 tff(9614,plain,((~r(s(s(s(s(elem!1)))), s(s(elem!1)))) | (~b(s(z), s(s(elem!1)))) | (~b(s(s(elem!1)), elem!1)) | (~b(s(z), elem!1)) | (~r(s(s(elem!1)), s(z))) | (~r(elem!1, s(s(z)))) | (~(s(s(z)) = s(s(elem!1))))), inference(lemma,lemma(discharge,[]))).
% 2.62/2.88 tff(9615,plain,
% 2.62/2.88 (~r(s(s(s(s(elem!1)))), s(s(elem!1)))),
% 2.62/2.88 inference(unit_resolution,[status(thm)],[9614, 9589, 376, 637, 4577, 9559, 34])).
% 2.62/2.88 tff(9616,plain,
% 2.62/2.88 (~r(s(s(s(s(elem!1)))), s(s(z)))),
% 2.62/2.88 inference(modus_ponens,[status(thm)],[9615, 9588])).
% 2.62/2.88 tff(9617,plain,
% 2.62/2.88 (b(s(s(s(s(elem!1)))), s(s(z)))),
% 2.62/2.88 inference(unit_resolution,[status(thm)],[1299, 9616])).
% 2.62/2.88 tff(9618,plain,
% 2.62/2.88 (b(s(s(s(s(elem!1)))), s(s(elem!1)))),
% 2.62/2.88 inference(modus_ponens,[status(thm)],[9617, 2154])).
% 2.62/2.88 tff(9619,plain,
% 2.62/2.88 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), elem!1)) | (~b(s(z), s(s(s(elem!1))))) | (~b(s(s(s(s(elem!1)))), s(s(elem!1)))) | (~b(s(z), elem!1)) | (~b(s(s(s(elem!1))), s(s(s(s(elem!1)))))) | (~b(s(z), s(s(s(s(elem!1)))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(elem!1)), elem!1)) | (~b(s(z), s(s(s(elem!1))))) | (~b(s(s(s(s(elem!1)))), s(s(elem!1)))) | (~b(s(z), elem!1)) | (~b(s(s(s(elem!1))), s(s(s(s(elem!1)))))) | (~b(s(z), s(s(s(s(elem!1)))))))),
% 2.62/2.88 inference(rewrite,[status(thm)],[])).
% 2.62/2.88 tff(9620,plain,
% 2.62/2.88 (((~b(s(s(elem!1)), elem!1)) | (~b(s(z), elem!1)) | (~b(s(s(s(s(elem!1)))), s(s(elem!1)))) | (~b(s(s(s(elem!1))), s(s(s(s(elem!1)))))) | (~b(s(z), s(s(s(s(elem!1)))))) | (~b(s(z), s(s(s(elem!1)))))) <=> ((~b(s(s(elem!1)), elem!1)) | (~b(s(z), s(s(s(elem!1))))) | (~b(s(s(s(s(elem!1)))), s(s(elem!1)))) | (~b(s(z), elem!1)) | (~b(s(s(s(elem!1))), s(s(s(s(elem!1)))))) | (~b(s(z), s(s(s(s(elem!1)))))))),
% 2.62/2.88 inference(rewrite,[status(thm)],[])).
% 2.62/2.88 tff(9621,plain,
% 2.62/2.88 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), elem!1)) | (~b(s(z), elem!1)) | (~b(s(s(s(s(elem!1)))), s(s(elem!1)))) | (~b(s(s(s(elem!1))), s(s(s(s(elem!1)))))) | (~b(s(z), s(s(s(s(elem!1)))))) | (~b(s(z), s(s(s(elem!1))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), elem!1)) | (~b(s(z), s(s(s(elem!1))))) | (~b(s(s(s(s(elem!1)))), s(s(elem!1)))) | (~b(s(z), elem!1)) | (~b(s(s(s(elem!1))), s(s(s(s(elem!1)))))) | (~b(s(z), s(s(s(s(elem!1))))))))),
% 2.62/2.88 inference(monotonicity,[status(thm)],[9620])).
% 2.62/2.88 tff(9622,plain,
% 2.62/2.88 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), elem!1)) | (~b(s(z), elem!1)) | (~b(s(s(s(s(elem!1)))), s(s(elem!1)))) | (~b(s(s(s(elem!1))), s(s(s(s(elem!1)))))) | (~b(s(z), s(s(s(s(elem!1)))))) | (~b(s(z), s(s(s(elem!1))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(elem!1)), elem!1)) | (~b(s(z), s(s(s(elem!1))))) | (~b(s(s(s(s(elem!1)))), s(s(elem!1)))) | (~b(s(z), elem!1)) | (~b(s(s(s(elem!1))), s(s(s(s(elem!1)))))) | (~b(s(z), s(s(s(s(elem!1)))))))),
% 2.62/2.88 inference(transitivity,[status(thm)],[9621, 9619])).
% 2.62/2.88 tff(9623,plain,
% 2.62/2.88 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), elem!1)) | (~b(s(z), elem!1)) | (~b(s(s(s(s(elem!1)))), s(s(elem!1)))) | (~b(s(s(s(elem!1))), s(s(s(s(elem!1)))))) | (~b(s(z), s(s(s(s(elem!1)))))) | (~b(s(z), s(s(s(elem!1))))))),
% 2.62/2.88 inference(quant_inst,[status(thm)],[])).
% 2.62/2.88 tff(9624,plain,
% 2.62/2.88 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(elem!1)), elem!1)) | (~b(s(z), s(s(s(elem!1))))) | (~b(s(s(s(s(elem!1)))), s(s(elem!1)))) | (~b(s(z), elem!1)) | (~b(s(s(s(elem!1))), s(s(s(s(elem!1)))))) | (~b(s(z), s(s(s(s(elem!1))))))),
% 2.62/2.88 inference(modus_ponens,[status(thm)],[9623, 9622])).
% 2.62/2.88 tff(9625,plain,
% 2.62/2.88 (~b(s(z), s(s(s(s(elem!1)))))),
% 2.62/2.88 inference(unit_resolution,[status(thm)],[9624, 166, 9589, 241, 637, 9618, 9586])).
% 2.62/2.88 tff(9626,plain,
% 2.62/2.88 (r(s(z), s(s(s(s(elem!1)))))),
% 2.62/2.88 inference(unit_resolution,[status(thm)],[680, 9625, 9574])).
% 2.62/2.88 tff(9627,plain,
% 2.62/2.88 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(s(elem!1)))) | (~r(s(s(elem!1)), s(z))) | (~r(elem!1, s(z))) | (~r(s(z), s(s(s(s(elem!1)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(elem!1, s(s(elem!1)))) | (~r(s(s(elem!1)), s(z))) | (~r(elem!1, s(z))) | (~r(s(z), s(s(s(s(elem!1)))))))),
% 2.62/2.88 inference(rewrite,[status(thm)],[])).
% 2.62/2.88 tff(9628,plain,
% 2.62/2.88 (((~r(s(z), s(s(s(s(elem!1)))))) | (~r(s(s(elem!1)), s(z))) | (~r(elem!1, s(z))) | (~r(elem!1, s(s(elem!1))))) <=> ((~r(elem!1, s(s(elem!1)))) | (~r(s(s(elem!1)), s(z))) | (~r(elem!1, s(z))) | (~r(s(z), s(s(s(s(elem!1)))))))),
% 2.62/2.88 inference(rewrite,[status(thm)],[])).
% 2.62/2.88 tff(9629,plain,
% 2.62/2.88 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(s(s(s(elem!1)))))) | (~r(s(s(elem!1)), s(z))) | (~r(elem!1, s(z))) | (~r(elem!1, s(s(elem!1)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(s(elem!1)))) | (~r(s(s(elem!1)), s(z))) | (~r(elem!1, s(z))) | (~r(s(z), s(s(s(s(elem!1))))))))),
% 2.62/2.88 inference(monotonicity,[status(thm)],[9628])).
% 2.62/2.88 tff(9630,plain,
% 2.62/2.88 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(s(s(s(elem!1)))))) | (~r(s(s(elem!1)), s(z))) | (~r(elem!1, s(z))) | (~r(elem!1, s(s(elem!1)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(elem!1, s(s(elem!1)))) | (~r(s(s(elem!1)), s(z))) | (~r(elem!1, s(z))) | (~r(s(z), s(s(s(s(elem!1)))))))),
% 2.62/2.88 inference(transitivity,[status(thm)],[9629, 9627])).
% 2.62/2.88 tff(9631,plain,
% 2.62/2.88 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(s(s(s(elem!1)))))) | (~r(s(s(elem!1)), s(z))) | (~r(elem!1, s(z))) | (~r(elem!1, s(s(elem!1)))))),
% 2.62/2.88 inference(quant_inst,[status(thm)],[])).
% 2.62/2.88 tff(9632,plain,
% 2.62/2.88 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(elem!1, s(s(elem!1)))) | (~r(s(s(elem!1)), s(z))) | (~r(elem!1, s(z))) | (~r(s(z), s(s(s(s(elem!1))))))),
% 2.62/2.88 inference(modus_ponens,[status(thm)],[9631, 9630])).
% 2.62/2.88 tff(9633,plain,
% 2.62/2.88 ($false),
% 2.62/2.88 inference(unit_resolution,[status(thm)],[9632, 197, 742, 4577, 9626, 9566])).
% 2.62/2.88 tff(9634,plain,((~(s(s(z)) = s(s(elem!1)))) | (~r(s(s(elem!1)), s(z))) | (~b(s(z), s(s(s(elem!1))))) | (s(s(s(elem!1))) = s(s(s(s(elem!1))))) | (~r(s(s(elem!1)), s(s(s(elem!1))))) | (~b(s(z), s(s(elem!1)))) | (~r(z, s(s(s(elem!1))))) | (~r(z, s(s(elem!1)))) | (~b(s(s(elem!1)), z)) | (~b(s(z), z)) | (~r(z, s(z)))), inference(lemma,lemma(discharge,[]))).
% 2.62/2.88 tff(9635,plain,
% 2.62/2.88 (~b(s(s(elem!1)), z)),
% 2.62/2.88 inference(unit_resolution,[status(thm)],[9634, 9553, 9391, 9422, 9420, 9260, 9537, 9546, 9551, 9548, 8408])).
% 2.62/2.88 tff(9636,plain,
% 2.62/2.88 (r(s(s(elem!1)), z)),
% 2.62/2.88 inference(unit_resolution,[status(thm)],[608, 9635])).
% 2.62/2.88 tff(9637,plain,
% 2.62/2.88 (r(s(s(elem!1)), elem!1)),
% 2.62/2.88 inference(unit_resolution,[status(thm)],[3398, 9636, 9539])).
% 2.62/2.88 tff(9638,plain,
% 2.62/2.88 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(elem!1)), elem!1)) | (~r(s(s(elem!1)), s(z))) | (~r(elem!1, s(z))) | (~r(s(z), s(s(s(s(elem!1)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(elem!1)), elem!1)) | (~r(s(s(elem!1)), s(z))) | (~r(elem!1, s(z))) | (~r(s(z), s(s(s(s(elem!1)))))))),
% 2.62/2.88 inference(rewrite,[status(thm)],[])).
% 2.62/2.88 tff(9639,plain,
% 2.62/2.88 (((~r(s(z), s(s(s(s(elem!1)))))) | (~r(elem!1, s(z))) | (~r(s(s(elem!1)), s(z))) | (~r(s(s(elem!1)), elem!1))) <=> ((~r(s(s(elem!1)), elem!1)) | (~r(s(s(elem!1)), s(z))) | (~r(elem!1, s(z))) | (~r(s(z), s(s(s(s(elem!1)))))))),
% 2.62/2.88 inference(rewrite,[status(thm)],[])).
% 2.62/2.88 tff(9640,plain,
% 2.62/2.88 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(s(s(s(elem!1)))))) | (~r(elem!1, s(z))) | (~r(s(s(elem!1)), s(z))) | (~r(s(s(elem!1)), elem!1)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(elem!1)), elem!1)) | (~r(s(s(elem!1)), s(z))) | (~r(elem!1, s(z))) | (~r(s(z), s(s(s(s(elem!1))))))))),
% 2.62/2.88 inference(monotonicity,[status(thm)],[9639])).
% 2.62/2.88 tff(9641,plain,
% 2.62/2.88 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(s(s(s(elem!1)))))) | (~r(elem!1, s(z))) | (~r(s(s(elem!1)), s(z))) | (~r(s(s(elem!1)), elem!1)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(elem!1)), elem!1)) | (~r(s(s(elem!1)), s(z))) | (~r(elem!1, s(z))) | (~r(s(z), s(s(s(s(elem!1)))))))),
% 2.62/2.88 inference(transitivity,[status(thm)],[9640, 9638])).
% 2.62/2.88 tff(9642,plain,
% 2.62/2.88 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(s(s(s(elem!1)))))) | (~r(elem!1, s(z))) | (~r(s(s(elem!1)), s(z))) | (~r(s(s(elem!1)), elem!1)))),
% 2.62/2.88 inference(quant_inst,[status(thm)],[])).
% 2.62/2.88 tff(9643,plain,
% 2.62/2.88 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(elem!1)), elem!1)) | (~r(s(s(elem!1)), s(z))) | (~r(elem!1, s(z))) | (~r(s(z), s(s(s(s(elem!1))))))),
% 2.62/2.88 inference(modus_ponens,[status(thm)],[9642, 9641])).
% 2.62/2.88 tff(9644,plain,
% 2.62/2.88 ($false),
% 2.62/2.88 inference(unit_resolution,[status(thm)],[9643, 197, 744, 4577, 768, 699])).
% 2.62/2.88 tff(9645,plain,((~r(s(z), s(s(s(s(elem!1)))))) | (~r(elem!1, s(z))) | (~r(s(s(elem!1)), s(z))) | (~r(s(s(elem!1)), elem!1))), inference(lemma,lemma(discharge,[]))).
% 2.62/2.88 tff(9646,plain,
% 2.62/2.88 (~r(s(z), s(s(s(s(elem!1)))))),
% 2.62/2.88 inference(unit_resolution,[status(thm)],[9645, 9637, 9260, 9556])).
% 2.62/2.88 tff(9647,plain,
% 2.62/2.88 (b(s(z), s(s(s(s(elem!1)))))),
% 2.62/2.88 inference(unit_resolution,[status(thm)],[681, 9646])).
% 2.62/2.88 tff(9648,plain,
% 2.62/2.88 ((~(s(s(s(s(elem!1)))) = z)) <=> (~(s(s(s(s(elem!1)))) = elem!1))),
% 2.62/2.88 inference(monotonicity,[status(thm)],[9540])).
% 2.62/2.88 tff(9649,plain,
% 2.62/2.88 (~(s(s(s(s(elem!1)))) = elem!1)),
% 2.62/2.88 inference(modus_ponens,[status(thm)],[626, 9648])).
% 2.62/2.88 tff(9650,plain,
% 2.62/2.88 (b(s(s(s(elem!1))), elem!1)),
% 2.62/2.88 inference(unit_resolution,[status(thm)],[634, 9539, 8808])).
% 2.62/2.89 tff(9651,plain,
% 2.62/2.89 ((s(s(s(s(elem!1)))) = s(s(z))) <=> (s(s(s(s(elem!1)))) = s(s(elem!1)))),
% 2.62/2.89 inference(monotonicity,[status(thm)],[9537])).
% 2.62/2.89 tff(9652,plain,
% 2.62/2.89 ((s(s(s(s(elem!1)))) = s(s(z))) <=> (s(s(elem!1)) = s(s(s(s(elem!1)))))),
% 2.62/2.89 inference(transitivity,[status(thm)],[9651, 123])).
% 2.62/2.89 tff(9653,plain,
% 2.62/2.89 ((~(s(s(s(s(elem!1)))) = s(s(z)))) <=> (~(s(s(elem!1)) = s(s(s(s(elem!1))))))),
% 2.62/2.89 inference(monotonicity,[status(thm)],[9652])).
% 2.62/2.89 tff(9654,plain,
% 2.62/2.89 (~(s(s(elem!1)) = s(s(s(s(elem!1)))))),
% 2.62/2.89 inference(modus_ponens,[status(thm)],[733, 9653])).
% 2.62/2.89 tff(9655,plain,
% 2.62/2.89 ((s(s(s(s(elem!1)))) = s(s(z))) <=> (s(s(s(s(elem!1)))) = s(s(elem!1)))),
% 2.62/2.89 inference(transitivity,[status(thm)],[9652, 124])).
% 2.62/2.89 tff(9656,plain,
% 2.62/2.89 ((~(s(s(s(s(elem!1)))) = s(s(z)))) <=> (~(s(s(s(s(elem!1)))) = s(s(elem!1))))),
% 2.62/2.89 inference(monotonicity,[status(thm)],[9655])).
% 2.62/2.89 tff(9657,plain,
% 2.62/2.89 (~(s(s(s(s(elem!1)))) = s(s(elem!1)))),
% 2.62/2.89 inference(modus_ponens,[status(thm)],[733, 9656])).
% 2.62/2.89 tff(9658,plain,
% 2.62/2.89 (r(z, s(s(elem!1))) <=> r(elem!1, s(s(elem!1)))),
% 2.62/2.89 inference(monotonicity,[status(thm)],[9539])).
% 2.62/2.89 tff(9659,plain,
% 2.62/2.89 (r(elem!1, s(s(elem!1)))),
% 2.62/2.89 inference(modus_ponens,[status(thm)],[9546, 9658])).
% 2.62/2.89 tff(9660,plain,
% 2.62/2.89 (~r(s(s(s(s(elem!1)))), elem!1)),
% 2.62/2.89 inference(unit_resolution,[status(thm)],[7911, 3408, 768, 1027])).
% 2.62/2.89 tff(9661,plain,
% 2.62/2.89 (b(s(s(s(s(elem!1)))), elem!1)),
% 2.62/2.89 inference(unit_resolution,[status(thm)],[719, 9660, 712])).
% 2.62/2.89 tff(9662,plain,
% 2.62/2.89 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(z), elem!1)) | (~b(s(s(s(s(elem!1)))), elem!1)) | (~b(elem!1, s(s(s(s(elem!1)))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(z), elem!1)) | (~b(s(s(s(s(elem!1)))), elem!1)) | (~b(elem!1, s(s(s(s(elem!1)))))))),
% 2.62/2.89 inference(rewrite,[status(thm)],[])).
% 2.62/2.89 tff(9663,plain,
% 2.62/2.89 (((~b(s(s(s(s(elem!1)))), elem!1)) | (~b(s(z), elem!1)) | (~b(elem!1, s(s(s(s(elem!1)))))) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(z), elem!1)) | (~b(s(z), s(s(s(elem!1)))))) <=> ((~b(s(z), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(z), elem!1)) | (~b(s(s(s(s(elem!1)))), elem!1)) | (~b(elem!1, s(s(s(s(elem!1)))))))),
% 2.62/2.89 inference(rewrite,[status(thm)],[])).
% 2.62/2.89 tff(9664,plain,
% 2.62/2.89 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(elem!1)))), elem!1)) | (~b(s(z), elem!1)) | (~b(elem!1, s(s(s(s(elem!1)))))) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(z), elem!1)) | (~b(s(z), s(s(s(elem!1))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(z), elem!1)) | (~b(s(s(s(s(elem!1)))), elem!1)) | (~b(elem!1, s(s(s(s(elem!1))))))))),
% 2.62/2.89 inference(monotonicity,[status(thm)],[9663])).
% 2.62/2.89 tff(9665,plain,
% 2.62/2.89 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(elem!1)))), elem!1)) | (~b(s(z), elem!1)) | (~b(elem!1, s(s(s(s(elem!1)))))) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(z), elem!1)) | (~b(s(z), s(s(s(elem!1))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(z), elem!1)) | (~b(s(s(s(s(elem!1)))), elem!1)) | (~b(elem!1, s(s(s(s(elem!1)))))))),
% 2.62/2.89 inference(transitivity,[status(thm)],[9664, 9662])).
% 2.62/2.89 tff(9666,plain,
% 2.62/2.89 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(elem!1)))), elem!1)) | (~b(s(z), elem!1)) | (~b(elem!1, s(s(s(s(elem!1)))))) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(z), elem!1)) | (~b(s(z), s(s(s(elem!1))))))),
% 2.62/2.89 inference(quant_inst,[status(thm)],[])).
% 2.62/2.89 tff(9667,plain,
% 2.62/2.89 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(z), elem!1)) | (~b(s(s(s(s(elem!1)))), elem!1)) | (~b(elem!1, s(s(s(s(elem!1))))))),
% 2.62/2.89 inference(modus_ponens,[status(thm)],[9666, 9665])).
% 2.62/2.89 tff(9668,plain,
% 2.62/2.89 ($false),
% 2.62/2.89 inference(unit_resolution,[status(thm)],[9667, 166, 241, 642, 641, 1108, 640])).
% 2.62/2.89 tff(9669,plain,((~b(s(s(s(s(elem!1)))), elem!1)) | (~b(s(z), s(s(s(elem!1))))) | (~b(s(z), elem!1)) | (~b(s(s(s(elem!1))), elem!1)) | (~b(elem!1, s(s(s(s(elem!1))))))), inference(lemma,lemma(discharge,[]))).
% 2.62/2.89 tff(9670,plain,
% 2.62/2.89 (~b(elem!1, s(s(s(s(elem!1)))))),
% 2.62/2.89 inference(unit_resolution,[status(thm)],[9669, 9661, 641, 241, 642])).
% 2.62/2.89 tff(9671,plain,
% 2.62/2.89 (r(elem!1, s(s(s(s(elem!1)))))),
% 2.62/2.89 inference(unit_resolution,[status(thm)],[2427, 9670, 2422])).
% 2.62/2.89 tff(9672,plain,
% 2.62/2.89 ($false),
% 2.62/2.89 inference(unit_resolution,[status(thm)],[6435, 197, 4577, 3408, 9671, 1027])).
% 2.62/2.89 tff(9673,plain,((~r(s(s(s(s(elem!1)))), s(s(elem!1)))) | (~r(s(s(elem!1)), s(z))) | (~r(elem!1, s(s(elem!1)))) | (elem!1 = s(s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(z), s(s(s(elem!1))))) | (~b(s(z), elem!1)) | (s(s(s(s(elem!1)))) = elem!1) | (~r(s(s(elem!1)), elem!1))), inference(lemma,lemma(discharge,[]))).
% 2.62/2.89 tff(9674,plain,
% 2.62/2.89 (~r(s(s(s(s(elem!1)))), s(s(elem!1)))),
% 2.62/2.89 inference(unit_resolution,[status(thm)],[9673, 9260, 9659, 9543, 9650, 9551, 9549, 9649, 9637])).
% 2.62/2.89 tff(9675,plain,
% 2.62/2.89 (b(s(s(s(s(elem!1)))), s(s(elem!1)))),
% 2.62/2.89 inference(unit_resolution,[status(thm)],[813, 9674, 9657])).
% 2.62/2.89 tff(9676,plain,
% 2.62/2.89 ($false),
% 2.62/2.89 inference(unit_resolution,[status(thm)],[7785, 166, 376, 1046, 1327, 3457])).
% 2.62/2.89 tff(9677,plain,((~b(s(s(s(s(elem!1)))), s(s(elem!1)))) | (~b(s(z), s(s(elem!1)))) | (~b(s(s(elem!1)), s(s(s(s(elem!1)))))) | (~b(s(z), s(s(s(s(elem!1))))))), inference(lemma,lemma(discharge,[]))).
% 2.62/2.89 tff(9678,plain,
% 2.62/2.89 (~b(s(s(elem!1)), s(s(s(s(elem!1)))))),
% 2.62/2.89 inference(unit_resolution,[status(thm)],[9677, 9675, 9420, 9647])).
% 2.62/2.89 tff(9679,plain,
% 2.62/2.89 (r(s(s(elem!1)), s(s(s(s(elem!1)))))),
% 2.62/2.89 inference(unit_resolution,[status(thm)],[827, 9678, 9654])).
% 2.62/2.89 tff(9680,plain,
% 2.62/2.89 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(elem!1)), elem!1)) | (~r(elem!1, s(z))) | (~r(s(s(s(s(elem!1)))), elem!1)) | (~r(s(s(elem!1)), s(s(s(s(elem!1)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(elem!1)), elem!1)) | (~r(elem!1, s(z))) | (~r(s(s(s(s(elem!1)))), elem!1)) | (~r(s(s(elem!1)), s(s(s(s(elem!1)))))))),
% 2.62/2.89 inference(rewrite,[status(thm)],[])).
% 2.62/2.89 tff(9681,plain,
% 2.62/2.89 (((~r(elem!1, s(z))) | (~r(s(s(s(s(elem!1)))), elem!1)) | (~r(s(s(elem!1)), elem!1)) | (~r(s(s(elem!1)), s(s(s(s(elem!1))))))) <=> ((~r(s(s(elem!1)), elem!1)) | (~r(elem!1, s(z))) | (~r(s(s(s(s(elem!1)))), elem!1)) | (~r(s(s(elem!1)), s(s(s(s(elem!1)))))))),
% 2.62/2.89 inference(rewrite,[status(thm)],[])).
% 2.62/2.89 tff(9682,plain,
% 2.62/2.89 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(z))) | (~r(s(s(s(s(elem!1)))), elem!1)) | (~r(s(s(elem!1)), elem!1)) | (~r(s(s(elem!1)), s(s(s(s(elem!1)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(elem!1)), elem!1)) | (~r(elem!1, s(z))) | (~r(s(s(s(s(elem!1)))), elem!1)) | (~r(s(s(elem!1)), s(s(s(s(elem!1))))))))),
% 2.62/2.89 inference(monotonicity,[status(thm)],[9681])).
% 2.62/2.89 tff(9683,plain,
% 2.62/2.89 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(z))) | (~r(s(s(s(s(elem!1)))), elem!1)) | (~r(s(s(elem!1)), elem!1)) | (~r(s(s(elem!1)), s(s(s(s(elem!1)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(elem!1)), elem!1)) | (~r(elem!1, s(z))) | (~r(s(s(s(s(elem!1)))), elem!1)) | (~r(s(s(elem!1)), s(s(s(s(elem!1)))))))),
% 2.62/2.89 inference(transitivity,[status(thm)],[9682, 9680])).
% 2.62/2.89 tff(9684,plain,
% 2.62/2.89 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(z))) | (~r(s(s(s(s(elem!1)))), elem!1)) | (~r(s(s(elem!1)), elem!1)) | (~r(s(s(elem!1)), s(s(s(s(elem!1)))))))),
% 2.62/2.89 inference(quant_inst,[status(thm)],[])).
% 2.62/2.89 tff(9685,plain,
% 2.62/2.89 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(elem!1)), elem!1)) | (~r(elem!1, s(z))) | (~r(s(s(s(s(elem!1)))), elem!1)) | (~r(s(s(elem!1)), s(s(s(s(elem!1))))))),
% 2.62/2.89 inference(modus_ponens,[status(thm)],[9684, 9683])).
% 2.62/2.89 tff(9686,plain,
% 2.62/2.89 ($false),
% 2.62/2.89 inference(unit_resolution,[status(thm)],[9685, 197, 744, 768, 561, 743])).
% 2.62/2.89 tff(9687,plain,((~r(s(s(s(s(elem!1)))), elem!1)) | (~r(elem!1, s(z))) | (~r(s(s(elem!1)), elem!1)) | (~r(s(s(elem!1)), s(s(s(s(elem!1))))))), inference(lemma,lemma(discharge,[]))).
% 2.62/2.89 tff(9688,plain,
% 2.62/2.89 (~r(s(s(s(s(elem!1)))), elem!1)),
% 2.62/2.89 inference(unit_resolution,[status(thm)],[9687, 561, 768, 744])).
% 2.62/2.89 tff(9689,plain,
% 2.62/2.89 (b(s(s(s(s(elem!1)))), elem!1)),
% 2.62/2.89 inference(unit_resolution,[status(thm)],[719, 9688, 712])).
% 2.62/2.89 tff(9690,plain,
% 2.62/2.89 (~b(elem!1, s(s(s(s(elem!1)))))),
% 2.62/2.89 inference(unit_resolution,[status(thm)],[9669, 9689, 642, 641, 241])).
% 2.62/2.89 tff(9691,plain,
% 2.62/2.89 (r(elem!1, s(s(s(s(elem!1)))))),
% 2.62/2.89 inference(unit_resolution,[status(thm)],[2427, 9690, 2422])).
% 2.62/2.89 tff(9692,plain,
% 2.62/2.89 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(s(s(s(elem!1)))))) | (~r(s(s(elem!1)), elem!1)) | (~r(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~r(s(s(elem!1)), s(s(s(s(elem!1)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(elem!1, s(s(s(s(elem!1)))))) | (~r(s(s(elem!1)), elem!1)) | (~r(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~r(s(s(elem!1)), s(s(s(s(elem!1)))))))),
% 2.62/2.89 inference(rewrite,[status(thm)],[])).
% 2.62/2.89 tff(9693,plain,
% 2.62/2.89 (((~r(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~r(elem!1, s(s(s(s(elem!1)))))) | (~r(s(s(elem!1)), s(s(s(s(elem!1)))))) | (~r(s(s(elem!1)), elem!1))) <=> ((~r(elem!1, s(s(s(s(elem!1)))))) | (~r(s(s(elem!1)), elem!1)) | (~r(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~r(s(s(elem!1)), s(s(s(s(elem!1)))))))),
% 2.62/2.89 inference(rewrite,[status(thm)],[])).
% 2.62/2.89 tff(9694,plain,
% 2.62/2.89 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~r(elem!1, s(s(s(s(elem!1)))))) | (~r(s(s(elem!1)), s(s(s(s(elem!1)))))) | (~r(s(s(elem!1)), elem!1)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(s(s(s(elem!1)))))) | (~r(s(s(elem!1)), elem!1)) | (~r(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~r(s(s(elem!1)), s(s(s(s(elem!1))))))))),
% 2.62/2.89 inference(monotonicity,[status(thm)],[9693])).
% 2.62/2.89 tff(9695,plain,
% 2.62/2.89 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~r(elem!1, s(s(s(s(elem!1)))))) | (~r(s(s(elem!1)), s(s(s(s(elem!1)))))) | (~r(s(s(elem!1)), elem!1)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(elem!1, s(s(s(s(elem!1)))))) | (~r(s(s(elem!1)), elem!1)) | (~r(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~r(s(s(elem!1)), s(s(s(s(elem!1)))))))),
% 2.62/2.89 inference(transitivity,[status(thm)],[9694, 9692])).
% 2.62/2.89 tff(9696,plain,
% 2.62/2.89 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~r(elem!1, s(s(s(s(elem!1)))))) | (~r(s(s(elem!1)), s(s(s(s(elem!1)))))) | (~r(s(s(elem!1)), elem!1)))),
% 2.62/2.89 inference(quant_inst,[status(thm)],[])).
% 2.62/2.89 tff(9697,plain,
% 2.62/2.89 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(elem!1, s(s(s(s(elem!1)))))) | (~r(s(s(elem!1)), elem!1)) | (~r(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~r(s(s(elem!1)), s(s(s(s(elem!1))))))),
% 2.62/2.89 inference(modus_ponens,[status(thm)],[9696, 9695])).
% 2.62/2.89 tff(9698,plain,
% 2.62/2.89 ($false),
% 2.62/2.89 inference(unit_resolution,[status(thm)],[9697, 197, 768, 561, 1048, 9691])).
% 2.62/2.89 tff(9699,plain,((~r(s(s(elem!1)), s(s(s(s(elem!1)))))) | (~r(s(s(elem!1)), elem!1)) | (~r(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (elem!1 = s(s(s(s(elem!1))))) | (~b(s(z), elem!1)) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(z), s(s(s(elem!1))))) | (s(s(s(s(elem!1)))) = elem!1) | (~r(elem!1, s(z)))), inference(lemma,lemma(discharge,[]))).
% 2.62/2.89 tff(9700,plain,
% 2.62/2.89 (~r(s(s(s(s(elem!1)))), s(s(s(elem!1))))),
% 2.62/2.89 inference(unit_resolution,[status(thm)],[9699, 9679, 9650, 9543, 9551, 9637, 9549, 9649, 9556])).
% 2.62/2.89 tff(9701,plain,
% 2.62/2.89 (b(s(s(s(s(elem!1)))), s(s(s(elem!1))))),
% 2.62/2.89 inference(unit_resolution,[status(thm)],[1065, 9700, 9392])).
% 2.62/2.89 tff(9702,plain,
% 2.62/2.89 (~b(elem!1, s(s(s(s(elem!1)))))),
% 2.62/2.89 inference(unit_resolution,[status(thm)],[6387, 9701, 9647, 9420, 9555, 9549])).
% 2.62/2.89 tff(9703,plain,
% 2.62/2.89 (r(elem!1, s(s(s(s(elem!1)))))),
% 2.62/2.89 inference(unit_resolution,[status(thm)],[2427, 9702, 9543])).
% 2.62/2.89 tff(9704,plain,
% 2.62/2.89 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(s(elem!1))))) | (~r(z, s(s(elem!1)))) | (~r(s(s(elem!1)), s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), s(s(s(s(elem!1)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, s(s(s(elem!1))))) | (~r(z, s(s(elem!1)))) | (~r(s(s(elem!1)), s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), s(s(s(s(elem!1)))))))),
% 2.62/2.89 inference(rewrite,[status(thm)],[])).
% 2.62/2.89 tff(9705,plain,
% 2.62/2.89 (((~r(s(s(s(elem!1))), s(s(s(s(elem!1)))))) | (~r(s(s(elem!1)), s(s(s(elem!1))))) | (~r(z, s(s(s(elem!1))))) | (~r(z, s(s(elem!1))))) <=> ((~r(z, s(s(s(elem!1))))) | (~r(z, s(s(elem!1)))) | (~r(s(s(elem!1)), s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), s(s(s(s(elem!1)))))))),
% 2.62/2.89 inference(rewrite,[status(thm)],[])).
% 2.62/2.89 tff(9706,plain,
% 2.62/2.89 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), s(s(s(s(elem!1)))))) | (~r(s(s(elem!1)), s(s(s(elem!1))))) | (~r(z, s(s(s(elem!1))))) | (~r(z, s(s(elem!1)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(s(elem!1))))) | (~r(z, s(s(elem!1)))) | (~r(s(s(elem!1)), s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), s(s(s(s(elem!1))))))))),
% 2.62/2.89 inference(monotonicity,[status(thm)],[9705])).
% 2.62/2.89 tff(9707,plain,
% 2.62/2.89 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), s(s(s(s(elem!1)))))) | (~r(s(s(elem!1)), s(s(s(elem!1))))) | (~r(z, s(s(s(elem!1))))) | (~r(z, s(s(elem!1)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, s(s(s(elem!1))))) | (~r(z, s(s(elem!1)))) | (~r(s(s(elem!1)), s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), s(s(s(s(elem!1)))))))),
% 2.62/2.89 inference(transitivity,[status(thm)],[9706, 9704])).
% 2.62/2.89 tff(9708,plain,
% 2.62/2.89 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), s(s(s(s(elem!1)))))) | (~r(s(s(elem!1)), s(s(s(elem!1))))) | (~r(z, s(s(s(elem!1))))) | (~r(z, s(s(elem!1)))))),
% 2.62/2.89 inference(quant_inst,[status(thm)],[])).
% 2.62/2.89 tff(9709,plain,
% 2.62/2.89 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, s(s(s(elem!1))))) | (~r(z, s(s(elem!1)))) | (~r(s(s(elem!1)), s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), s(s(s(s(elem!1))))))),
% 2.62/2.89 inference(modus_ponens,[status(thm)],[9708, 9707])).
% 2.62/2.89 tff(9710,plain,
% 2.62/2.89 ($false),
% 2.62/2.89 inference(unit_resolution,[status(thm)],[9709, 197, 377, 365, 282, 698])).
% 2.62/2.89 tff(9711,plain,((~r(s(s(s(elem!1))), s(s(s(s(elem!1)))))) | (~r(s(s(elem!1)), s(s(s(elem!1))))) | (~r(z, s(s(elem!1)))) | (~r(z, s(s(s(elem!1)))))), inference(lemma,lemma(discharge,[]))).
% 2.62/2.89 tff(9712,plain,
% 2.62/2.89 (~r(s(s(s(elem!1))), s(s(s(s(elem!1)))))),
% 2.62/2.89 inference(unit_resolution,[status(thm)],[9711, 9553, 9546, 9422])).
% 2.62/2.89 tff(9713,plain,
% 2.62/2.89 (b(s(s(s(elem!1))), s(s(s(s(elem!1)))))),
% 2.62/2.89 inference(unit_resolution,[status(thm)],[696, 9712, 9391])).
% 2.62/2.89 tff(9714,plain,
% 2.62/2.89 (~b(s(s(s(s(elem!1)))), s(z))),
% 2.62/2.89 inference(unit_resolution,[status(thm)],[5130, 9713, 96, 9551])).
% 2.62/2.89 tff(9715,plain,
% 2.62/2.89 (r(s(s(s(s(elem!1)))), s(z))),
% 2.62/2.89 inference(unit_resolution,[status(thm)],[661, 9714])).
% 2.62/2.89 tff(9716,plain,
% 2.62/2.89 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(s(s(s(elem!1)))))) | (~r(s(s(elem!1)), elem!1)) | (~r(s(s(s(s(elem!1)))), s(z))) | (~r(s(s(elem!1)), s(s(s(s(elem!1)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(elem!1, s(s(s(s(elem!1)))))) | (~r(s(s(elem!1)), elem!1)) | (~r(s(s(s(s(elem!1)))), s(z))) | (~r(s(s(elem!1)), s(s(s(s(elem!1)))))))),
% 2.62/2.89 inference(rewrite,[status(thm)],[])).
% 2.62/2.89 tff(9717,plain,
% 2.62/2.89 (((~r(s(s(s(s(elem!1)))), s(z))) | (~r(elem!1, s(s(s(s(elem!1)))))) | (~r(s(s(elem!1)), s(s(s(s(elem!1)))))) | (~r(s(s(elem!1)), elem!1))) <=> ((~r(elem!1, s(s(s(s(elem!1)))))) | (~r(s(s(elem!1)), elem!1)) | (~r(s(s(s(s(elem!1)))), s(z))) | (~r(s(s(elem!1)), s(s(s(s(elem!1)))))))),
% 2.62/2.89 inference(rewrite,[status(thm)],[])).
% 2.62/2.89 tff(9718,plain,
% 2.62/2.89 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(elem!1)))), s(z))) | (~r(elem!1, s(s(s(s(elem!1)))))) | (~r(s(s(elem!1)), s(s(s(s(elem!1)))))) | (~r(s(s(elem!1)), elem!1)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(s(s(s(elem!1)))))) | (~r(s(s(elem!1)), elem!1)) | (~r(s(s(s(s(elem!1)))), s(z))) | (~r(s(s(elem!1)), s(s(s(s(elem!1))))))))),
% 2.62/2.89 inference(monotonicity,[status(thm)],[9717])).
% 2.62/2.89 tff(9719,plain,
% 2.62/2.89 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(elem!1)))), s(z))) | (~r(elem!1, s(s(s(s(elem!1)))))) | (~r(s(s(elem!1)), s(s(s(s(elem!1)))))) | (~r(s(s(elem!1)), elem!1)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(elem!1, s(s(s(s(elem!1)))))) | (~r(s(s(elem!1)), elem!1)) | (~r(s(s(s(s(elem!1)))), s(z))) | (~r(s(s(elem!1)), s(s(s(s(elem!1)))))))),
% 2.62/2.89 inference(transitivity,[status(thm)],[9718, 9716])).
% 2.62/2.89 tff(9720,plain,
% 2.62/2.89 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(elem!1)))), s(z))) | (~r(elem!1, s(s(s(s(elem!1)))))) | (~r(s(s(elem!1)), s(s(s(s(elem!1)))))) | (~r(s(s(elem!1)), elem!1)))),
% 2.62/2.89 inference(quant_inst,[status(thm)],[])).
% 2.62/2.89 tff(9721,plain,
% 2.62/2.89 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(elem!1, s(s(s(s(elem!1)))))) | (~r(s(s(elem!1)), elem!1)) | (~r(s(s(s(s(elem!1)))), s(z))) | (~r(s(s(elem!1)), s(s(s(s(elem!1))))))),
% 2.62/2.89 inference(modus_ponens,[status(thm)],[9720, 9719])).
% 2.62/2.89 tff(9722,plain,
% 2.62/2.89 ($false),
% 2.62/2.89 inference(unit_resolution,[status(thm)],[9721, 197, 9637, 9679, 9715, 9703])).
% 2.62/2.89 tff(9723,plain,((~b(s(s(s(elem!1))), s(z))) | b(z, s(s(z)))), inference(lemma,lemma(discharge,[]))).
% 2.62/2.89 tff(9724,plain,
% 2.62/2.89 (~b(s(s(s(elem!1))), s(z))),
% 2.62/2.89 inference(unit_resolution,[status(thm)],[9723, 125])).
% 2.62/2.89 tff(9725,plain,
% 2.62/2.89 (~(s(s(elem!1)) = s(s(s(elem!1))))),
% 2.62/2.89 inference(unit_resolution,[status(thm)],[3849, 310, 9724])).
% 2.62/2.89 tff(9726,plain,
% 2.62/2.89 (~(s(s(s(elem!1))) = s(s(elem!1)))),
% 2.62/2.89 inference(unit_resolution,[status(thm)],[50, 9725])).
% 2.62/2.89 tff(9727,plain,
% 2.62/2.89 (r(s(s(s(elem!1))), s(z))),
% 2.62/2.89 inference(unit_resolution,[status(thm)],[1849, 9724])).
% 2.62/2.89 tff(9728,plain,
% 2.62/2.89 (~b(s(z), z)),
% 2.62/2.89 inference(unit_resolution,[status(thm)],[1843, 310, 152, 8408, 9727, 9725])).
% 2.62/2.89 tff(9729,plain,
% 2.62/2.89 (r(s(z), z)),
% 2.62/2.89 inference(unit_resolution,[status(thm)],[230, 9728])).
% 2.62/2.89 tff(9730,plain,
% 2.62/2.89 (~(s(s(s(elem!1))) = s(s(s(s(elem!1)))))),
% 2.62/2.89 inference(unit_resolution,[status(thm)],[357, 9725])).
% 2.62/2.89 tff(9731,plain,
% 2.62/2.89 (~r(s(s(elem!1)), s(s(s(elem!1))))),
% 2.62/2.89 inference(unit_resolution,[status(thm)],[2919, 9730, 125, 8408, 9727, 310, 9729, 9726])).
% 2.62/2.89 tff(9732,plain,
% 2.62/2.89 (b(s(s(elem!1)), s(s(s(elem!1))))),
% 2.62/2.89 inference(unit_resolution,[status(thm)],[461, 9731, 9725])).
% 2.62/2.89 tff(9733,plain,
% 2.62/2.89 (~r(s(s(s(elem!1))), z)),
% 2.62/2.89 inference(unit_resolution,[status(thm)],[5698, 9729, 152, 9727])).
% 2.62/2.89 tff(9734,plain,
% 2.62/2.89 (b(s(s(s(elem!1))), z)),
% 2.62/2.89 inference(unit_resolution,[status(thm)],[94, 9733])).
% 2.62/2.89 tff(9735,plain,
% 2.62/2.89 (~r(z, s(s(s(elem!1))))),
% 2.62/2.89 inference(unit_resolution,[status(thm)],[2613, 9729, 8408, 9727])).
% 2.62/2.89 tff(9736,plain,
% 2.62/2.89 (b(z, s(s(s(elem!1))))),
% 2.62/2.89 inference(unit_resolution,[status(thm)],[261, 9735])).
% 2.62/2.89 tff(9737,plain,
% 2.62/2.89 (~b(s(s(elem!1)), z)),
% 2.62/2.89 inference(unit_resolution,[status(thm)],[600, 9736, 9734, 9732])).
% 2.62/2.89 tff(9738,plain,
% 2.62/2.89 (r(s(s(elem!1)), z)),
% 2.62/2.89 inference(unit_resolution,[status(thm)],[608, 9737])).
% 2.62/2.89 tff(9739,plain,
% 2.62/2.89 (~r(z, s(s(elem!1)))),
% 2.62/2.89 inference(unit_resolution,[status(thm)],[8600, 323, 311, 4577])).
% 2.62/2.89 tff(9740,plain,
% 2.62/2.89 (b(z, s(s(elem!1)))),
% 2.62/2.89 inference(unit_resolution,[status(thm)],[1795, 9739])).
% 2.62/2.89 tff(9741,plain,
% 2.62/2.89 (s(s(elem!1)) = s(s(s(elem!1)))),
% 2.62/2.89 inference(unit_resolution,[status(thm)],[1834, 9740, 6719, 4457, 6723])).
% 2.62/2.89 tff(9742,plain,
% 2.62/2.89 (~(s(s(s(z))) = elem!1)),
% 2.62/2.89 inference(unit_resolution,[status(thm)],[3122, 9741])).
% 2.62/2.89 tff(9743,plain,
% 2.62/2.89 (s(s(s(elem!1))) = s(elem!1)),
% 2.62/2.89 inference(unit_resolution,[status(thm)],[2594, 9741])).
% 2.62/2.89 tff(9744,plain,
% 2.62/2.89 (s(elem!1) = s(s(s(elem!1)))),
% 2.62/2.89 inference(symmetry,[status(thm)],[9743])).
% 2.62/2.89 tff(9745,plain,
% 2.62/2.89 (inj_0(s(elem!1)) = inj_0(s(s(s(elem!1))))),
% 2.62/2.89 inference(monotonicity,[status(thm)],[9744])).
% 2.62/2.89 tff(9746,plain,
% 2.62/2.89 (elem!1 = s(s(s(elem!1)))),
% 2.62/2.89 inference(transitivity,[status(thm)],[1170, 9745, 104, 9741])).
% 2.62/2.89 tff(9747,plain,
% 2.62/2.89 (b(z, elem!1) <=> b(z, s(s(s(elem!1))))),
% 2.62/2.89 inference(monotonicity,[status(thm)],[9746])).
% 2.62/2.89 tff(9748,plain,
% 2.62/2.89 (b(z, s(s(s(elem!1)))) <=> b(z, elem!1)),
% 2.62/2.89 inference(symmetry,[status(thm)],[9747])).
% 2.62/2.89 tff(9749,plain,
% 2.62/2.89 (b(z, elem!1)),
% 2.62/2.89 inference(modus_ponens,[status(thm)],[4457, 9748])).
% 2.62/2.89 tff(9750,plain,
% 2.62/2.89 (r(elem!1, z) <=> r(s(s(s(elem!1))), z)),
% 2.62/2.89 inference(monotonicity,[status(thm)],[6548])).
% 2.62/2.89 tff(9751,assumption,(r(elem!1, z)), introduced(assumption)).
% 2.62/2.89 tff(9752,plain,
% 2.62/2.89 (r(s(s(s(elem!1))), z)),
% 2.62/2.89 inference(modus_ponens,[status(thm)],[9751, 9750])).
% 2.62/2.89 tff(9753,plain,
% 2.62/2.89 ($false),
% 2.62/2.89 inference(unit_resolution,[status(thm)],[86, 9752])).
% 2.62/2.89 tff(9754,plain,((~r(elem!1, z)) | r(s(s(s(elem!1))), z) | (~(s(s(elem!1)) = s(s(s(elem!1)))))), inference(lemma,lemma(discharge,[]))).
% 2.62/2.89 tff(9755,plain,
% 2.62/2.89 (~r(elem!1, z)),
% 2.62/2.89 inference(unit_resolution,[status(thm)],[9754, 9741, 4454])).
% 2.62/2.89 tff(9756,plain,
% 2.62/2.89 (~(s(s(z)) = s(s(elem!1)))),
% 2.62/2.89 inference(unit_resolution,[status(thm)],[2261, 9740, 125])).
% 2.62/2.89 tff(9757,plain,
% 2.62/2.89 (~(s(s(elem!1)) = s(s(z)))),
% 2.62/2.89 inference(unit_resolution,[status(thm)],[131, 9756])).
% 2.62/2.89 tff(9758,plain,
% 2.62/2.89 (~(z = elem!1)),
% 2.62/2.89 inference(unit_resolution,[status(thm)],[17, 9757])).
% 2.62/2.89 tff(9759,plain,
% 2.62/2.89 (~(elem!1 = z)),
% 2.62/2.89 inference(unit_resolution,[status(thm)],[1151, 9758])).
% 2.62/2.89 tff(9760,plain,
% 2.62/2.89 (b(elem!1, z)),
% 2.62/2.89 inference(unit_resolution,[status(thm)],[1239, 9759, 9755])).
% 2.62/2.89 tff(9761,plain,
% 2.62/2.89 (r(elem!1, s(z)) <=> r(s(s(s(elem!1))), s(z))),
% 2.62/2.89 inference(monotonicity,[status(thm)],[9746])).
% 2.62/2.89 tff(9762,plain,
% 2.62/2.89 (r(s(s(s(elem!1))), s(z)) <=> r(elem!1, s(z))),
% 2.62/2.89 inference(symmetry,[status(thm)],[9761])).
% 2.62/2.89 tff(9763,plain,
% 2.62/2.89 (r(elem!1, s(z))),
% 2.62/2.89 inference(modus_ponens,[status(thm)],[350, 9762])).
% 2.62/2.89 tff(9764,plain,
% 2.62/2.89 (~(s(s(s(elem!1))) = s(s(s(z))))),
% 2.62/2.89 inference(unit_resolution,[status(thm)],[139, 9757])).
% 2.62/2.89 tff(9765,plain,
% 2.62/2.89 (~r(s(s(z)), z)),
% 2.62/2.89 inference(unit_resolution,[status(thm)],[2959, 120, 155, 323])).
% 2.62/2.89 tff(9766,plain,
% 2.62/2.89 (~b(s(s(z)), z)),
% 2.62/2.89 inference(unit_resolution,[status(thm)],[3176, 120, 323, 311, 350])).
% 2.62/2.89 tff(9767,plain,
% 2.62/2.89 ($false),
% 2.62/2.89 inference(unit_resolution,[status(thm)],[186, 9766, 9765])).
% 2.72/2.90 tff(9768,plain,((~r(s(z), s(s(z)))) | (~r(z, s(z))) | (~r(s(z), s(s(elem!1)))) | (~r(s(s(s(elem!1))), s(z))) | (~r(z, s(s(z))))), inference(lemma,lemma(discharge,[]))).
% 2.72/2.90 tff(9769,plain,
% 2.72/2.90 (~r(s(z), s(s(z)))),
% 2.72/2.90 inference(unit_resolution,[status(thm)],[9768, 323, 311, 350, 152])).
% 2.72/2.90 tff(9770,plain,
% 2.72/2.90 (b(s(z), s(s(z)))),
% 2.72/2.90 inference(unit_resolution,[status(thm)],[427, 9769])).
% 2.72/2.90 tff(9771,plain,
% 2.72/2.90 (r(s(z), s(elem!1)) <=> r(s(z), s(s(s(elem!1))))),
% 2.72/2.90 inference(monotonicity,[status(thm)],[9744])).
% 2.72/2.90 tff(9772,plain,
% 2.72/2.90 (r(s(z), s(s(s(elem!1)))) <=> r(s(z), s(elem!1))),
% 2.72/2.90 inference(symmetry,[status(thm)],[9771])).
% 2.72/2.90 tff(9773,plain,
% 2.72/2.90 (r(s(z), s(s(elem!1))) <=> r(s(z), s(s(s(elem!1))))),
% 2.72/2.90 inference(monotonicity,[status(thm)],[9741])).
% 2.72/2.90 tff(9774,plain,
% 2.72/2.90 (r(s(z), s(s(s(elem!1))))),
% 2.72/2.90 inference(modus_ponens,[status(thm)],[311, 9773])).
% 2.72/2.90 tff(9775,plain,
% 2.72/2.90 (r(s(z), s(elem!1))),
% 2.72/2.90 inference(modus_ponens,[status(thm)],[9774, 9772])).
% 2.72/2.90 tff(9776,plain,
% 2.72/2.90 (~r(s(s(z)), s(z))),
% 2.72/2.90 inference(unit_resolution,[status(thm)],[2095, 9775, 323, 152])).
% 2.72/2.90 tff(9777,plain,
% 2.72/2.90 (b(s(s(z)), s(z))),
% 2.72/2.90 inference(unit_resolution,[status(thm)],[308, 9776])).
% 2.72/2.90 tff(9778,plain,
% 2.72/2.90 (~r(s(z), z)),
% 2.72/2.90 inference(unit_resolution,[status(thm)],[8164, 9741, 4457, 4455, 9777, 152, 9770, 350, 311, 9764])).
% 2.72/2.90 tff(9779,plain,
% 2.72/2.90 (b(s(z), z)),
% 2.72/2.90 inference(unit_resolution,[status(thm)],[230, 9778])).
% 2.72/2.90 tff(9780,plain,
% 2.72/2.90 (~b(s(s(s(z))), z)),
% 2.72/2.90 inference(unit_resolution,[status(thm)],[5855, 9779, 9763, 9760, 9749, 9742])).
% 2.72/2.90 tff(9781,plain,
% 2.72/2.90 (r(s(s(s(z))), z)),
% 2.72/2.90 inference(unit_resolution,[status(thm)],[1713, 9780])).
% 2.72/2.90 tff(9782,plain,
% 2.72/2.90 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(s(elem!1))))) | (~b(s(z), z)) | (~b(s(s(s(elem!1))), z)) | (~b(s(z), s(s(z)))) | (~b(s(s(z)), z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(s(s(elem!1))))) | (~b(s(z), z)) | (~b(s(s(s(elem!1))), z)) | (~b(s(z), s(s(z)))) | (~b(s(s(z)), z)))),
% 2.72/2.90 inference(rewrite,[status(thm)],[])).
% 2.72/2.90 tff(9783,plain,
% 2.72/2.90 (((~b(s(s(s(elem!1))), z)) | (~b(s(z), z)) | (~b(z, s(s(s(elem!1))))) | (~b(s(s(z)), z)) | (~b(s(z), z)) | (~b(s(z), s(s(z))))) <=> ((~b(z, s(s(s(elem!1))))) | (~b(s(z), z)) | (~b(s(s(s(elem!1))), z)) | (~b(s(z), s(s(z)))) | (~b(s(s(z)), z)))),
% 2.72/2.90 inference(rewrite,[status(thm)],[])).
% 2.72/2.90 tff(9784,plain,
% 2.72/2.90 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), z)) | (~b(s(z), z)) | (~b(z, s(s(s(elem!1))))) | (~b(s(s(z)), z)) | (~b(s(z), z)) | (~b(s(z), s(s(z)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(s(elem!1))))) | (~b(s(z), z)) | (~b(s(s(s(elem!1))), z)) | (~b(s(z), s(s(z)))) | (~b(s(s(z)), z))))),
% 2.72/2.90 inference(monotonicity,[status(thm)],[9783])).
% 2.72/2.90 tff(9785,plain,
% 2.72/2.90 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), z)) | (~b(s(z), z)) | (~b(z, s(s(s(elem!1))))) | (~b(s(s(z)), z)) | (~b(s(z), z)) | (~b(s(z), s(s(z)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(s(s(elem!1))))) | (~b(s(z), z)) | (~b(s(s(s(elem!1))), z)) | (~b(s(z), s(s(z)))) | (~b(s(s(z)), z)))),
% 2.72/2.90 inference(transitivity,[status(thm)],[9784, 9782])).
% 2.72/2.90 tff(9786,plain,
% 2.72/2.90 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), z)) | (~b(s(z), z)) | (~b(z, s(s(s(elem!1))))) | (~b(s(s(z)), z)) | (~b(s(z), z)) | (~b(s(z), s(s(z)))))),
% 2.72/2.90 inference(quant_inst,[status(thm)],[])).
% 2.72/2.90 tff(9787,plain,
% 2.72/2.90 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(s(s(elem!1))))) | (~b(s(z), z)) | (~b(s(s(s(elem!1))), z)) | (~b(s(z), s(s(z)))) | (~b(s(s(z)), z))),
% 2.72/2.90 inference(modus_ponens,[status(thm)],[9786, 9785])).
% 2.72/2.90 tff(9788,plain,
% 2.72/2.90 ($false),
% 2.72/2.90 inference(unit_resolution,[status(thm)],[9787, 166, 240, 53, 556, 121, 122])).
% 2.72/2.90 tff(9789,plain,((~b(s(s(z)), z)) | (~b(z, s(s(s(elem!1))))) | (~b(s(z), z)) | (~b(s(z), s(s(z)))) | (~b(s(s(s(elem!1))), z))), inference(lemma,lemma(discharge,[]))).
% 2.72/2.90 tff(9790,plain,
% 2.72/2.90 (~b(s(s(z)), z)),
% 2.72/2.90 inference(unit_resolution,[status(thm)],[9789, 4457, 9779, 9770, 4455])).
% 2.72/2.90 tff(9791,plain,
% 2.72/2.90 (r(s(s(z)), z)),
% 2.72/2.90 inference(unit_resolution,[status(thm)],[186, 9790])).
% 2.72/2.90 tff(9792,plain,
% 2.72/2.90 (~r(s(s(s(z))), s(s(z)))),
% 2.72/2.90 inference(unit_resolution,[status(thm)],[1717, 197, 152, 9791, 9781])).
% 2.72/2.90 tff(9793,plain,
% 2.72/2.90 (b(s(s(s(z))), s(s(z)))),
% 2.72/2.90 inference(unit_resolution,[status(thm)],[1010, 9792])).
% 2.72/2.90 tff(9794,plain,
% 2.72/2.90 (((~b(s(z), s(s(z)))) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(s(z)), s(z))) | (~b(s(z), s(s(z)))) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(s(s(z))), s(z)))) <=> ((~b(s(z), s(s(z)))) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(z)), s(z))))),
% 2.72/2.90 inference(rewrite,[status(thm)],[])).
% 2.72/2.90 tff(9795,plain,
% 2.72/2.90 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(z)))) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(s(z)), s(z))) | (~b(s(z), s(s(z)))) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(s(s(z))), s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(z)))) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(z)), s(z)))))),
% 2.72/2.90 inference(monotonicity,[status(thm)],[9794])).
% 2.72/2.90 tff(9796,plain,
% 2.72/2.90 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(z)))) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(s(z)), s(z))) | (~b(s(z), s(s(z)))) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(s(s(z))), s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), s(s(z)))) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(z)), s(z))))),
% 2.72/2.90 inference(transitivity,[status(thm)],[9795, 8139])).
% 2.72/2.90 tff(9797,plain,
% 2.72/2.90 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(z)))) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(s(z)), s(z))) | (~b(s(z), s(s(z)))) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(s(s(z))), s(z))))),
% 2.72/2.90 inference(quant_inst,[status(thm)],[])).
% 2.72/2.90 tff(9798,plain,
% 2.72/2.90 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), s(s(z)))) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(z)), s(z)))),
% 2.72/2.90 inference(modus_ponens,[status(thm)],[9797, 9796])).
% 2.72/2.90 tff(9799,plain,
% 2.72/2.90 (~b(s(s(s(z))), s(z))),
% 2.72/2.90 inference(unit_resolution,[status(thm)],[9798, 166, 9770, 9777, 9793])).
% 2.72/2.90 tff(9800,plain,
% 2.72/2.90 (r(s(s(s(z))), s(z))),
% 2.72/2.90 inference(unit_resolution,[status(thm)],[1763, 9799])).
% 2.72/2.90 tff(9801,plain,
% 2.72/2.90 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(z))) | (~r(s(z), s(s(s(elem!1))))) | (~r(s(s(s(z))), z)) | (~r(s(s(s(z))), s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, s(z))) | (~r(s(z), s(s(s(elem!1))))) | (~r(s(s(s(z))), z)) | (~r(s(s(s(z))), s(z))))),
% 2.72/2.90 inference(rewrite,[status(thm)],[])).
% 2.72/2.90 tff(9802,plain,
% 2.72/2.90 (((~r(s(z), s(s(s(elem!1))))) | (~r(z, s(z))) | (~r(s(s(s(z))), s(z))) | (~r(s(s(s(z))), z))) <=> ((~r(z, s(z))) | (~r(s(z), s(s(s(elem!1))))) | (~r(s(s(s(z))), z)) | (~r(s(s(s(z))), s(z))))),
% 2.72/2.90 inference(rewrite,[status(thm)],[])).
% 2.72/2.90 tff(9803,plain,
% 2.72/2.90 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(s(s(elem!1))))) | (~r(z, s(z))) | (~r(s(s(s(z))), s(z))) | (~r(s(s(s(z))), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(z))) | (~r(s(z), s(s(s(elem!1))))) | (~r(s(s(s(z))), z)) | (~r(s(s(s(z))), s(z)))))),
% 2.72/2.90 inference(monotonicity,[status(thm)],[9802])).
% 2.72/2.90 tff(9804,plain,
% 2.72/2.90 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(s(s(elem!1))))) | (~r(z, s(z))) | (~r(s(s(s(z))), s(z))) | (~r(s(s(s(z))), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, s(z))) | (~r(s(z), s(s(s(elem!1))))) | (~r(s(s(s(z))), z)) | (~r(s(s(s(z))), s(z))))),
% 2.72/2.90 inference(transitivity,[status(thm)],[9803, 9801])).
% 2.72/2.90 tff(9805,plain,
% 2.72/2.90 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(s(s(elem!1))))) | (~r(z, s(z))) | (~r(s(s(s(z))), s(z))) | (~r(s(s(s(z))), z)))),
% 2.72/2.90 inference(quant_inst,[status(thm)],[])).
% 2.72/2.90 tff(9806,plain,
% 2.72/2.90 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, s(z))) | (~r(s(z), s(s(s(elem!1))))) | (~r(s(s(s(z))), z)) | (~r(s(s(s(z))), s(z)))),
% 2.72/2.90 inference(modus_ponens,[status(thm)],[9805, 9804])).
% 2.72/2.90 tff(9807,plain,
% 2.72/2.90 ($false),
% 2.72/2.90 inference(unit_resolution,[status(thm)],[9806, 197, 323, 9774, 9800, 9781])).
% 2.72/2.90 tff(9808,plain,((~r(z, s(z))) | (~r(s(s(s(elem!1))), s(z))) | (~r(s(z), s(s(elem!1)))) | b(z, s(s(z))) | (~r(s(s(elem!1)), s(z)))), inference(lemma,lemma(discharge,[]))).
% 2.72/2.90 tff(9809,plain,
% 2.72/2.90 (~r(s(s(elem!1)), s(z))),
% 2.72/2.90 inference(unit_resolution,[status(thm)],[9808, 85, 8408, 125, 9727])).
% 2.72/2.90 tff(9810,plain,
% 2.72/2.90 ($false),
% 2.72/2.90 inference(unit_resolution,[status(thm)],[1912, 9809, 4557])).
% 2.72/2.90 tff(9811,plain,(b(s(z), s(s(elem!1))) | b(z, s(s(z)))), inference(lemma,lemma(discharge,[]))).
% 2.72/2.90 tff(9812,plain,
% 2.72/2.90 (b(s(z), s(s(elem!1)))),
% 2.72/2.90 inference(unit_resolution,[status(thm)],[9811, 125])).
% 2.72/2.90 tff(9813,plain,
% 2.72/2.90 (~r(s(s(z)), s(z))),
% 2.72/2.90 inference(unit_resolution,[status(thm)],[2680, 9729, 152, 8408])).
% 2.72/2.90 tff(9814,plain,
% 2.72/2.90 (b(s(s(z)), s(z))),
% 2.72/2.90 inference(unit_resolution,[status(thm)],[308, 9813])).
% 2.72/2.90 tff(9815,plain,
% 2.72/2.90 (~b(s(s(z)), s(s(elem!1)))),
% 2.72/2.90 inference(unit_resolution,[status(thm)],[454, 9814, 9812, 310])).
% 2.72/2.90 tff(9816,plain,
% 2.72/2.90 (r(s(s(z)), s(s(elem!1)))),
% 2.72/2.90 inference(unit_resolution,[status(thm)],[390, 9815, 52])).
% 2.72/2.90 tff(9817,plain,
% 2.72/2.90 (~b(s(s(elem!1)), s(s(z)))),
% 2.72/2.90 inference(unit_resolution,[status(thm)],[549, 9732, 9812, 310, 9814])).
% 2.72/2.90 tff(9818,plain,
% 2.72/2.90 (r(s(s(elem!1)), s(s(z)))),
% 2.72/2.90 inference(unit_resolution,[status(thm)],[441, 9817, 132])).
% 2.72/2.90 tff(9819,plain,
% 2.72/2.90 ($false),
% 2.72/2.90 inference(unit_resolution,[status(thm)],[2740, 197, 9818, 152, 9816, 9738])).
% 2.72/2.90 tff(9820,plain,((~b(s(s(elem!1)), s(z))) | (s(s(z)) = s(s(elem!1))) | b(z, s(s(z)))), inference(lemma,lemma(discharge,[]))).
% 2.72/2.90 tff(9821,plain,
% 2.72/2.90 (~b(s(s(elem!1)), s(z))),
% 2.72/2.90 inference(unit_resolution,[status(thm)],[9820, 52, 125])).
% 2.72/2.90 tff(9822,plain,
% 2.72/2.90 (r(s(s(elem!1)), s(z))),
% 2.72/2.90 inference(unit_resolution,[status(thm)],[1912, 9821])).
% 2.72/2.90 tff(9823,plain,
% 2.72/2.90 (~b(s(s(elem!1)), z)),
% 2.72/2.90 inference(unit_resolution,[status(thm)],[5377, 1820, 376, 53])).
% 2.72/2.90 tff(9824,plain,
% 2.72/2.90 (r(s(s(elem!1)), z)),
% 2.72/2.90 inference(unit_resolution,[status(thm)],[608, 9823])).
% 2.72/2.90 tff(9825,plain,
% 2.72/2.90 (~r(s(z), s(s(z)))),
% 2.72/2.90 inference(unit_resolution,[status(thm)],[8620, 9824, 4577, 323])).
% 2.72/2.90 tff(9826,plain,
% 2.72/2.90 (b(s(z), s(s(z)))),
% 2.72/2.90 inference(unit_resolution,[status(thm)],[427, 9825])).
% 2.72/2.90 tff(9827,plain,
% 2.72/2.90 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(z))) | (~r(s(s(elem!1)), z)) | (~r(s(z), s(s(s(elem!1))))) | (~r(s(s(elem!1)), s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, s(z))) | (~r(s(s(elem!1)), z)) | (~r(s(z), s(s(s(elem!1))))) | (~r(s(s(elem!1)), s(z))))),
% 2.72/2.90 inference(rewrite,[status(thm)],[])).
% 2.72/2.90 tff(9828,plain,
% 2.72/2.90 (((~r(s(z), s(s(s(elem!1))))) | (~r(z, s(z))) | (~r(s(s(elem!1)), s(z))) | (~r(s(s(elem!1)), z))) <=> ((~r(z, s(z))) | (~r(s(s(elem!1)), z)) | (~r(s(z), s(s(s(elem!1))))) | (~r(s(s(elem!1)), s(z))))),
% 2.72/2.90 inference(rewrite,[status(thm)],[])).
% 2.72/2.90 tff(9829,plain,
% 2.72/2.90 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(s(s(elem!1))))) | (~r(z, s(z))) | (~r(s(s(elem!1)), s(z))) | (~r(s(s(elem!1)), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(z))) | (~r(s(s(elem!1)), z)) | (~r(s(z), s(s(s(elem!1))))) | (~r(s(s(elem!1)), s(z)))))),
% 2.72/2.90 inference(monotonicity,[status(thm)],[9828])).
% 2.72/2.90 tff(9830,plain,
% 2.72/2.90 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(s(s(elem!1))))) | (~r(z, s(z))) | (~r(s(s(elem!1)), s(z))) | (~r(s(s(elem!1)), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, s(z))) | (~r(s(s(elem!1)), z)) | (~r(s(z), s(s(s(elem!1))))) | (~r(s(s(elem!1)), s(z))))),
% 2.72/2.90 inference(transitivity,[status(thm)],[9829, 9827])).
% 2.72/2.90 tff(9831,plain,
% 2.72/2.90 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(s(s(elem!1))))) | (~r(z, s(z))) | (~r(s(s(elem!1)), s(z))) | (~r(s(s(elem!1)), z)))),
% 2.72/2.90 inference(quant_inst,[status(thm)],[])).
% 2.72/2.90 tff(9832,plain,
% 2.72/2.90 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, s(z))) | (~r(s(s(elem!1)), z)) | (~r(s(z), s(s(s(elem!1))))) | (~r(s(s(elem!1)), s(z)))),
% 2.72/2.90 inference(modus_ponens,[status(thm)],[9831, 9830])).
% 2.72/2.90 tff(9833,plain,
% 2.72/2.90 ($false),
% 2.72/2.90 inference(unit_resolution,[status(thm)],[9832, 197, 323, 4577, 119, 1970])).
% 2.72/2.90 tff(9834,plain,((~r(s(z), s(s(s(elem!1))))) | (~r(z, s(z))) | (~r(s(s(elem!1)), s(z))) | (~r(s(s(elem!1)), z))), inference(lemma,lemma(discharge,[]))).
% 2.72/2.90 tff(9835,plain,
% 2.72/2.90 (~r(s(z), s(s(s(elem!1))))),
% 2.72/2.90 inference(unit_resolution,[status(thm)],[9834, 9824, 4577, 323])).
% 2.72/2.90 tff(9836,plain,
% 2.72/2.90 (b(s(z), s(s(s(elem!1))))),
% 2.72/2.90 inference(unit_resolution,[status(thm)],[116, 9835])).
% 2.72/2.90 tff(9837,plain,
% 2.72/2.90 ($false),
% 2.72/2.90 inference(unit_resolution,[status(thm)],[6023, 197, 154, 155, 377, 1970])).
% 2.72/2.90 tff(9838,plain,((~r(s(s(elem!1)), s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), z)) | (~r(z, s(s(z)))) | (~r(s(s(elem!1)), z))), inference(lemma,lemma(discharge,[]))).
% 2.72/2.90 tff(9839,plain,
% 2.72/2.90 (~r(s(s(elem!1)), s(s(s(elem!1))))),
% 2.72/2.90 inference(unit_resolution,[status(thm)],[9838, 154, 155, 1970])).
% 2.72/2.90 tff(9840,plain,
% 2.72/2.90 (r(s(s(s(elem!1))), s(s(elem!1)))),
% 2.72/2.90 inference(unit_resolution,[status(thm)],[6040, 9839, 241, 376, 1863])).
% 2.72/2.90 tff(9841,plain,
% 2.72/2.90 ($false),
% 2.72/2.90 inference(unit_resolution,[status(thm)],[1884, 197, 154, 155, 9840, 1970])).
% 2.72/2.90 tff(9842,plain,((~r(s(s(s(elem!1))), z)) | (~r(z, s(s(z)))) | (~r(s(s(elem!1)), z)) | (~b(s(z), s(s(s(elem!1))))) | (~b(s(z), s(s(elem!1)))) | (s(s(s(elem!1))) = s(s(elem!1)))), inference(lemma,lemma(discharge,[]))).
% 2.72/2.90 tff(9843,plain,
% 2.72/2.90 (~r(s(s(s(elem!1))), z)),
% 2.72/2.90 inference(unit_resolution,[status(thm)],[9842, 1863, 1970, 241, 376, 155])).
% 2.72/2.90 tff(9844,plain,
% 2.72/2.90 (b(s(s(s(elem!1))), z)),
% 2.72/2.90 inference(unit_resolution,[status(thm)],[94, 9843])).
% 2.72/2.90 tff(9845,plain,
% 2.72/2.90 (~b(z, s(s(s(elem!1))))),
% 2.72/2.90 inference(unit_resolution,[status(thm)],[1470, 121, 53, 241])).
% 2.72/2.90 tff(9846,plain,
% 2.72/2.90 (r(z, s(s(s(elem!1))))),
% 2.72/2.90 inference(unit_resolution,[status(thm)],[261, 9845])).
% 2.72/2.90 tff(9847,plain,
% 2.72/2.90 (~r(z, s(s(elem!1)))),
% 2.72/2.90 inference(unit_resolution,[status(thm)],[933, 282, 350, 377])).
% 2.72/2.90 tff(9848,plain,
% 2.72/2.90 (b(z, s(s(elem!1)))),
% 2.72/2.90 inference(unit_resolution,[status(thm)],[1795, 9847])).
% 2.72/2.90 tff(9849,plain,
% 2.72/2.90 (~r(s(s(elem!1)), z)),
% 2.72/2.90 inference(unit_resolution,[status(thm)],[7278, 282, 350, 377])).
% 2.72/2.90 tff(9850,plain,
% 2.72/2.90 (b(s(s(elem!1)), z)),
% 2.72/2.90 inference(unit_resolution,[status(thm)],[608, 9849])).
% 2.72/2.90 tff(9851,plain,
% 2.72/2.90 ($false),
% 2.72/2.90 inference(unit_resolution,[status(thm)],[5377, 9850, 9848, 376, 53])).
% 2.72/2.90 tff(9852,plain,((~r(z, s(s(s(elem!1))))) | (~b(s(z), s(s(elem!1)))) | (~b(s(z), z)) | (~r(s(s(s(elem!1))), s(z))) | (~r(s(s(elem!1)), s(s(s(elem!1)))))), inference(lemma,lemma(discharge,[]))).
% 2.72/2.90 tff(9853,plain,
% 2.72/2.90 (~r(s(s(elem!1)), s(s(s(elem!1))))),
% 2.72/2.90 inference(unit_resolution,[status(thm)],[9852, 9846, 350, 53, 376])).
% 2.72/2.90 tff(9854,plain,
% 2.72/2.90 (b(s(s(elem!1)), s(s(s(elem!1))))),
% 2.72/2.90 inference(unit_resolution,[status(thm)],[461, 9853, 45])).
% 2.72/2.90 tff(9855,plain,
% 2.72/2.90 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(s(z), z)) | (~b(s(z), s(s(elem!1)))) | (~b(s(s(s(elem!1))), z)) | (~b(s(z), s(s(z)))) | (~b(s(s(z)), s(s(elem!1)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(s(z), z)) | (~b(s(z), s(s(elem!1)))) | (~b(s(s(s(elem!1))), z)) | (~b(s(z), s(s(z)))) | (~b(s(s(z)), s(s(elem!1)))))),
% 2.72/2.90 inference(rewrite,[status(thm)],[])).
% 2.72/2.90 tff(9856,plain,
% 2.72/2.90 (((~b(s(s(s(elem!1))), z)) | (~b(s(z), z)) | (~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(s(s(z)), s(s(elem!1)))) | (~b(s(z), s(s(elem!1)))) | (~b(s(z), s(s(z))))) <=> ((~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(s(z), z)) | (~b(s(z), s(s(elem!1)))) | (~b(s(s(s(elem!1))), z)) | (~b(s(z), s(s(z)))) | (~b(s(s(z)), s(s(elem!1)))))),
% 2.72/2.90 inference(rewrite,[status(thm)],[])).
% 2.72/2.90 tff(9857,plain,
% 2.72/2.90 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), z)) | (~b(s(z), z)) | (~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(s(s(z)), s(s(elem!1)))) | (~b(s(z), s(s(elem!1)))) | (~b(s(z), s(s(z)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(s(z), z)) | (~b(s(z), s(s(elem!1)))) | (~b(s(s(s(elem!1))), z)) | (~b(s(z), s(s(z)))) | (~b(s(s(z)), s(s(elem!1))))))),
% 2.72/2.90 inference(monotonicity,[status(thm)],[9856])).
% 2.72/2.90 tff(9858,plain,
% 2.72/2.90 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), z)) | (~b(s(z), z)) | (~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(s(s(z)), s(s(elem!1)))) | (~b(s(z), s(s(elem!1)))) | (~b(s(z), s(s(z)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(s(z), z)) | (~b(s(z), s(s(elem!1)))) | (~b(s(s(s(elem!1))), z)) | (~b(s(z), s(s(z)))) | (~b(s(s(z)), s(s(elem!1)))))),
% 2.72/2.90 inference(transitivity,[status(thm)],[9857, 9855])).
% 2.72/2.90 tff(9859,plain,
% 2.72/2.90 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), z)) | (~b(s(z), z)) | (~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(s(s(z)), s(s(elem!1)))) | (~b(s(z), s(s(elem!1)))) | (~b(s(z), s(s(z)))))),
% 2.72/2.90 inference(quant_inst,[status(thm)],[])).
% 2.72/2.90 tff(9860,plain,
% 2.72/2.90 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(s(z), z)) | (~b(s(z), s(s(elem!1)))) | (~b(s(s(s(elem!1))), z)) | (~b(s(z), s(s(z)))) | (~b(s(s(z)), s(s(elem!1))))),
% 2.72/2.90 inference(modus_ponens,[status(thm)],[9859, 9858])).
% 2.72/2.90 tff(9861,plain,
% 2.72/2.90 ($false),
% 2.72/2.90 inference(unit_resolution,[status(thm)],[9860, 166, 376, 9854, 53, 556, 121, 446])).
% 2.72/2.90 tff(9862,plain,((~b(s(s(s(elem!1))), z)) | (~b(s(z), s(s(elem!1)))) | (~b(s(z), z)) | (~b(s(z), s(s(z)))) | (~b(s(s(z)), s(s(elem!1)))) | (s(s(elem!1)) = s(s(s(elem!1)))) | (~r(s(s(s(elem!1))), s(z))) | (~b(s(z), s(s(s(elem!1)))))), inference(lemma,lemma(discharge,[]))).
% 2.72/2.91 tff(9863,plain,
% 2.72/2.91 (~b(s(s(z)), s(s(elem!1)))),
% 2.72/2.91 inference(unit_resolution,[status(thm)],[9862, 9844, 53, 556, 376, 6029, 350, 241])).
% 2.72/2.91 tff(9864,plain,
% 2.72/2.91 (r(s(s(z)), s(s(elem!1)))),
% 2.72/2.91 inference(unit_resolution,[status(thm)],[390, 9863, 52])).
% 2.72/2.91 tff(9865,plain,
% 2.72/2.91 (~b(z, s(s(s(elem!1))))),
% 2.72/2.91 inference(unit_resolution,[status(thm)],[1470, 9844, 53, 241])).
% 2.72/2.91 tff(9866,plain,
% 2.72/2.91 (r(z, s(s(s(elem!1))))),
% 2.72/2.91 inference(unit_resolution,[status(thm)],[261, 9865])).
% 2.72/2.91 tff(9867,plain,
% 2.72/2.91 (~r(s(s(elem!1)), s(s(s(elem!1))))),
% 2.72/2.91 inference(unit_resolution,[status(thm)],[9852, 9866, 350, 53, 376])).
% 2.72/2.91 tff(9868,plain,
% 2.72/2.91 (r(s(s(s(elem!1))), s(s(elem!1)))),
% 2.72/2.91 inference(unit_resolution,[status(thm)],[6040, 9867, 241, 376, 1863])).
% 2.72/2.91 tff(9869,plain,
% 2.72/2.91 (~r(s(s(s(elem!1))), s(s(z)))),
% 2.72/2.91 inference(unit_resolution,[status(thm)],[9441, 9868, 4577, 9864])).
% 2.72/2.91 tff(9870,plain,
% 2.72/2.91 (b(s(s(elem!1)), s(s(s(elem!1))))),
% 2.72/2.91 inference(unit_resolution,[status(thm)],[461, 9867, 6029])).
% 2.72/2.91 tff(9871,plain,
% 2.72/2.91 (~r(s(s(z)), s(s(s(elem!1))))),
% 2.72/2.91 inference(unit_resolution,[status(thm)],[8677, 9868, 4577, 9864])).
% 2.72/2.91 tff(9872,plain,
% 2.72/2.91 (~b(s(s(elem!1)), s(s(z)))),
% 2.72/2.91 inference(unit_resolution,[status(thm)],[501, 9871, 9870, 9869])).
% 2.72/2.91 tff(9873,plain,
% 2.72/2.91 (r(s(s(elem!1)), s(s(z)))),
% 2.72/2.91 inference(unit_resolution,[status(thm)],[441, 9872, 132])).
% 2.72/2.91 tff(9874,plain,
% 2.72/2.91 ($false),
% 2.72/2.91 inference(unit_resolution,[status(thm)],[2740, 197, 9873, 155, 9864, 1970])).
% 2.72/2.91 tff(9875,plain,((s(s(s(elem!1))) = s(s(elem!1))) | (~r(z, s(s(z)))) | (~r(s(s(elem!1)), z)) | (~r(s(s(elem!1)), s(z))) | (~b(s(z), s(s(s(elem!1))))) | (~b(s(z), s(s(elem!1)))) | (~r(s(s(s(elem!1))), s(z))) | (~b(s(z), z)) | (s(s(z)) = s(s(elem!1))) | (~b(s(z), s(s(z))))), inference(lemma,lemma(discharge,[]))).
% 2.72/2.91 tff(9876,plain,
% 2.72/2.91 (s(s(s(elem!1))) = s(s(elem!1))),
% 2.72/2.91 inference(unit_resolution,[status(thm)],[9875, 9824, 155, 4577, 9836, 376, 350, 53, 52, 9826])).
% 2.72/2.91 tff(9877,plain,
% 2.72/2.91 ((s(s(s(elem!1))) = s(s(s(z)))) <=> (s(s(elem!1)) = s(s(s(z))))),
% 2.72/2.91 inference(monotonicity,[status(thm)],[9876])).
% 2.72/2.91 tff(9878,plain,
% 2.72/2.91 ((s(s(s(elem!1))) = s(s(s(z)))) <=> (s(s(s(z))) = s(s(elem!1)))),
% 2.72/2.91 inference(transitivity,[status(thm)],[9877, 4437])).
% 2.72/2.91 tff(9879,plain,
% 2.72/2.91 ((~(s(s(s(elem!1))) = s(s(s(z))))) <=> (~(s(s(s(z))) = s(s(elem!1))))),
% 2.72/2.91 inference(monotonicity,[status(thm)],[9878])).
% 2.72/2.91 tff(9880,plain,
% 2.72/2.91 (~(s(s(s(z))) = s(s(elem!1)))),
% 2.72/2.91 inference(modus_ponens,[status(thm)],[140, 9879])).
% 2.72/2.91 tff(9881,plain,
% 2.72/2.91 (s(s(elem!1)) = s(s(s(elem!1)))),
% 2.72/2.91 inference(unit_resolution,[status(thm)],[50, 9876])).
% 2.72/2.91 tff(9882,plain,
% 2.72/2.91 (r(s(s(s(elem!1))), z)),
% 2.72/2.91 inference(unit_resolution,[status(thm)],[2974, 9881, 9824])).
% 2.72/2.91 tff(9883,plain,
% 2.72/2.91 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), z)) | (~r(s(s(s(elem!1))), s(z))) | (~r(z, s(z))) | (~r(s(z), s(s(s(z))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(elem!1))), z)) | (~r(s(s(s(elem!1))), s(z))) | (~r(z, s(z))) | (~r(s(z), s(s(s(z))))))),
% 2.72/2.91 inference(rewrite,[status(thm)],[])).
% 2.72/2.91 tff(9884,plain,
% 2.72/2.91 (((~r(s(z), s(s(s(z))))) | (~r(z, s(z))) | (~r(s(s(s(elem!1))), s(z))) | (~r(s(s(s(elem!1))), z))) <=> ((~r(s(s(s(elem!1))), z)) | (~r(s(s(s(elem!1))), s(z))) | (~r(z, s(z))) | (~r(s(z), s(s(s(z))))))),
% 2.72/2.91 inference(rewrite,[status(thm)],[])).
% 2.72/2.91 tff(9885,plain,
% 2.72/2.91 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(s(s(z))))) | (~r(z, s(z))) | (~r(s(s(s(elem!1))), s(z))) | (~r(s(s(s(elem!1))), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), z)) | (~r(s(s(s(elem!1))), s(z))) | (~r(z, s(z))) | (~r(s(z), s(s(s(z)))))))),
% 2.72/2.91 inference(monotonicity,[status(thm)],[9884])).
% 2.72/2.91 tff(9886,plain,
% 2.72/2.91 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(s(s(z))))) | (~r(z, s(z))) | (~r(s(s(s(elem!1))), s(z))) | (~r(s(s(s(elem!1))), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(elem!1))), z)) | (~r(s(s(s(elem!1))), s(z))) | (~r(z, s(z))) | (~r(s(z), s(s(s(z))))))),
% 2.72/2.91 inference(transitivity,[status(thm)],[9885, 9883])).
% 2.72/2.91 tff(9887,plain,
% 2.72/2.91 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(s(s(z))))) | (~r(z, s(z))) | (~r(s(s(s(elem!1))), s(z))) | (~r(s(s(s(elem!1))), z)))),
% 2.72/2.91 inference(quant_inst,[status(thm)],[])).
% 2.72/2.91 tff(9888,plain,
% 2.72/2.91 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(elem!1))), z)) | (~r(s(s(s(elem!1))), s(z))) | (~r(z, s(z))) | (~r(s(z), s(s(s(z)))))),
% 2.72/2.91 inference(modus_ponens,[status(thm)],[9887, 9886])).
% 2.72/2.91 tff(9889,plain,
% 2.72/2.91 ($false),
% 2.72/2.91 inference(unit_resolution,[status(thm)],[9888, 197, 154, 350, 323, 1653])).
% 2.72/2.91 tff(9890,plain,((~r(s(z), s(s(s(z))))) | (~r(s(s(s(elem!1))), z)) | (~r(s(s(s(elem!1))), s(z))) | (~r(z, s(z)))), inference(lemma,lemma(discharge,[]))).
% 2.72/2.91 tff(9891,plain,
% 2.72/2.91 (~r(s(z), s(s(s(z))))),
% 2.72/2.91 inference(unit_resolution,[status(thm)],[9890, 9882, 350, 323])).
% 2.72/2.91 tff(9892,plain,
% 2.72/2.91 (b(s(z), s(s(s(z))))),
% 2.72/2.91 inference(unit_resolution,[status(thm)],[1674, 9891])).
% 2.72/2.91 tff(9893,plain,
% 2.72/2.91 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(z)))) | (~r(s(s(elem!1)), z)) | (~r(s(s(s(z))), z)) | (~r(s(s(s(z))), s(s(elem!1)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, s(s(z)))) | (~r(s(s(elem!1)), z)) | (~r(s(s(s(z))), z)) | (~r(s(s(s(z))), s(s(elem!1)))))),
% 2.72/2.91 inference(rewrite,[status(thm)],[])).
% 2.72/2.91 tff(9894,plain,
% 2.72/2.91 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(z)))) | (~r(s(s(elem!1)), z)) | (~r(s(s(s(z))), z)) | (~r(s(s(s(z))), s(s(elem!1)))))),
% 2.72/2.91 inference(quant_inst,[status(thm)],[])).
% 2.72/2.91 tff(9895,plain,
% 2.72/2.91 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, s(s(z)))) | (~r(s(s(elem!1)), z)) | (~r(s(s(s(z))), z)) | (~r(s(s(s(z))), s(s(elem!1))))),
% 2.72/2.91 inference(modus_ponens,[status(thm)],[9894, 9893])).
% 2.72/2.91 tff(9896,plain,
% 2.72/2.91 (~r(s(s(s(z))), s(s(elem!1)))),
% 2.72/2.91 inference(unit_resolution,[status(thm)],[9895, 197, 155, 1970, 1733])).
% 2.72/2.91 tff(9897,plain,
% 2.72/2.91 ($false),
% 2.72/2.91 inference(unit_resolution,[status(thm)],[5552, 7177, 9896, 988, 376, 5534])).
% 2.72/2.91 tff(9898,plain,((~r(s(s(s(z))), z)) | (~b(s(z), s(s(s(z))))) | (~b(s(z), s(s(elem!1)))) | (s(s(s(z))) = s(s(elem!1))) | (~r(z, s(s(z)))) | (~r(s(s(elem!1)), z))), inference(lemma,lemma(discharge,[]))).
% 2.72/2.91 tff(9899,plain,
% 2.72/2.91 (~r(s(s(s(z))), z)),
% 2.72/2.91 inference(unit_resolution,[status(thm)],[9898, 9892, 376, 9880, 155, 9824])).
% 2.72/2.91 tff(9900,plain,
% 2.72/2.91 (b(s(s(s(z))), z)),
% 2.72/2.91 inference(unit_resolution,[status(thm)],[1713, 9899])).
% 2.72/2.91 tff(9901,plain,
% 2.72/2.91 (s(s(s(elem!1))) = s(elem!1)),
% 2.72/2.91 inference(unit_resolution,[status(thm)],[2594, 9881])).
% 2.72/2.91 tff(9902,plain,
% 2.72/2.91 (s(elem!1) = s(s(s(elem!1)))),
% 2.72/2.91 inference(symmetry,[status(thm)],[9901])).
% 2.72/2.91 tff(9903,plain,
% 2.72/2.91 (s(elem!1) = s(s(elem!1))),
% 2.72/2.91 inference(transitivity,[status(thm)],[9902, 9876])).
% 2.72/2.91 tff(9904,plain,
% 2.72/2.91 (inj_0(s(elem!1)) = inj_0(s(s(elem!1)))),
% 2.72/2.91 inference(monotonicity,[status(thm)],[9903])).
% 2.72/2.91 tff(9905,plain,
% 2.72/2.91 (elem!1 = s(s(elem!1))),
% 2.72/2.91 inference(transitivity,[status(thm)],[1170, 9904, 38, 9902, 9876])).
% 2.72/2.91 tff(9906,plain,
% 2.72/2.91 (b(z, elem!1) <=> b(z, s(s(elem!1)))),
% 2.72/2.91 inference(monotonicity,[status(thm)],[9905])).
% 2.72/2.91 tff(9907,plain,
% 2.72/2.91 (b(z, s(s(elem!1))) <=> b(z, elem!1)),
% 2.72/2.91 inference(symmetry,[status(thm)],[9906])).
% 2.72/2.91 tff(9908,plain,
% 2.72/2.91 (b(z, elem!1)),
% 2.72/2.91 inference(modus_ponens,[status(thm)],[1820, 9907])).
% 2.72/2.91 tff(9909,plain,
% 2.72/2.91 (b(s(z), s(s(elem!1))) <=> b(s(z), elem!1)),
% 2.72/2.91 inference(monotonicity,[status(thm)],[3649])).
% 2.72/2.91 tff(9910,plain,
% 2.72/2.91 (b(s(z), elem!1) <=> b(s(z), s(s(elem!1)))),
% 2.72/2.91 inference(symmetry,[status(thm)],[9909])).
% 2.72/2.91 tff(9911,plain,
% 2.72/2.91 ((~b(s(z), elem!1)) <=> (~b(s(z), s(s(elem!1))))),
% 2.72/2.91 inference(monotonicity,[status(thm)],[9910])).
% 2.72/2.91 tff(9912,assumption,(~b(s(z), elem!1)), introduced(assumption)).
% 2.72/2.91 tff(9913,plain,
% 2.72/2.91 (~b(s(z), s(s(elem!1)))),
% 2.72/2.91 inference(modus_ponens,[status(thm)],[9912, 9911])).
% 2.72/2.91 tff(9914,plain,
% 2.72/2.91 ($false),
% 2.72/2.91 inference(unit_resolution,[status(thm)],[376, 9913])).
% 2.72/2.91 tff(9915,plain,((~(s(s(s(elem!1))) = s(elem!1))) | (~b(s(z), s(s(elem!1)))) | b(s(z), elem!1)), inference(lemma,lemma(discharge,[]))).
% 2.72/2.91 tff(9916,plain,
% 2.72/2.91 (b(s(z), elem!1)),
% 2.72/2.91 inference(unit_resolution,[status(thm)],[9915, 9901, 376])).
% 2.72/2.91 tff(9917,plain,
% 2.72/2.91 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(z)))) | (~b(s(z), elem!1)) | (~b(z, elem!1)) | (~b(s(s(s(z))), z)) | (~b(s(z), s(s(s(z))))) | (~b(s(s(z)), s(s(s(z))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), s(s(z)))) | (~b(s(z), elem!1)) | (~b(z, elem!1)) | (~b(s(s(s(z))), z)) | (~b(s(z), s(s(s(z))))) | (~b(s(s(z)), s(s(s(z))))))),
% 2.72/2.91 inference(rewrite,[status(thm)],[])).
% 2.72/2.91 tff(9918,plain,
% 2.72/2.91 (((~b(z, elem!1)) | (~b(s(z), elem!1)) | (~b(s(s(s(z))), z)) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(z), s(s(s(z))))) | (~b(s(z), s(s(z))))) <=> ((~b(s(z), s(s(z)))) | (~b(s(z), elem!1)) | (~b(z, elem!1)) | (~b(s(s(s(z))), z)) | (~b(s(z), s(s(s(z))))) | (~b(s(s(z)), s(s(s(z))))))),
% 2.72/2.91 inference(rewrite,[status(thm)],[])).
% 2.72/2.91 tff(9919,plain,
% 2.72/2.91 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, elem!1)) | (~b(s(z), elem!1)) | (~b(s(s(s(z))), z)) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(z), s(s(s(z))))) | (~b(s(z), s(s(z)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(z)))) | (~b(s(z), elem!1)) | (~b(z, elem!1)) | (~b(s(s(s(z))), z)) | (~b(s(z), s(s(s(z))))) | (~b(s(s(z)), s(s(s(z)))))))),
% 2.72/2.91 inference(monotonicity,[status(thm)],[9918])).
% 2.72/2.91 tff(9920,plain,
% 2.72/2.91 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, elem!1)) | (~b(s(z), elem!1)) | (~b(s(s(s(z))), z)) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(z), s(s(s(z))))) | (~b(s(z), s(s(z)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), s(s(z)))) | (~b(s(z), elem!1)) | (~b(z, elem!1)) | (~b(s(s(s(z))), z)) | (~b(s(z), s(s(s(z))))) | (~b(s(s(z)), s(s(s(z))))))),
% 2.72/2.91 inference(transitivity,[status(thm)],[9919, 9917])).
% 2.72/2.91 tff(9921,plain,
% 2.72/2.91 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, elem!1)) | (~b(s(z), elem!1)) | (~b(s(s(s(z))), z)) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(z), s(s(s(z))))) | (~b(s(z), s(s(z)))))),
% 2.72/2.91 inference(quant_inst,[status(thm)],[])).
% 2.72/2.91 tff(9922,plain,
% 2.72/2.91 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), s(s(z)))) | (~b(s(z), elem!1)) | (~b(z, elem!1)) | (~b(s(s(s(z))), z)) | (~b(s(z), s(s(s(z))))) | (~b(s(s(z)), s(s(s(z)))))),
% 2.72/2.91 inference(modus_ponens,[status(thm)],[9921, 9920])).
% 2.72/2.91 tff(9923,plain,
% 2.72/2.91 ($false),
% 2.72/2.91 inference(unit_resolution,[status(thm)],[9922, 166, 2517, 556, 642, 988, 986, 1699])).
% 2.72/2.91 tff(9924,plain,((~b(s(s(s(z))), z)) | (~b(z, elem!1)) | (~b(s(z), s(s(z)))) | (~b(s(z), elem!1)) | (~b(s(z), s(s(s(z))))) | (~b(s(s(z)), s(s(s(z)))))), inference(lemma,lemma(discharge,[]))).
% 2.72/2.91 tff(9925,plain,
% 2.72/2.91 (~b(s(s(z)), s(s(s(z))))),
% 2.72/2.91 inference(unit_resolution,[status(thm)],[9924, 9900, 9826, 9916, 9892, 9908])).
% 2.72/2.91 tff(9926,plain,
% 2.72/2.91 (r(s(s(z)), s(s(s(z))))),
% 2.72/2.91 inference(unit_resolution,[status(thm)],[1730, 9925])).
% 2.72/2.91 tff(9927,plain,
% 2.72/2.91 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(elem!1)), z)) | (~r(s(s(elem!1)), s(s(z)))) | (~r(s(s(z)), s(s(s(z))))) | (~r(z, s(s(z)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(elem!1)), z)) | (~r(s(s(elem!1)), s(s(z)))) | (~r(s(s(z)), s(s(s(z))))) | (~r(z, s(s(z)))))),
% 2.72/2.91 inference(rewrite,[status(thm)],[])).
% 2.72/2.91 tff(9928,plain,
% 2.72/2.91 (((~r(s(s(z)), s(s(s(z))))) | (~r(z, s(s(z)))) | (~r(s(s(elem!1)), s(s(z)))) | (~r(s(s(elem!1)), z))) <=> ((~r(s(s(elem!1)), z)) | (~r(s(s(elem!1)), s(s(z)))) | (~r(s(s(z)), s(s(s(z))))) | (~r(z, s(s(z)))))),
% 2.72/2.91 inference(rewrite,[status(thm)],[])).
% 2.72/2.91 tff(9929,plain,
% 2.72/2.91 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(z)), s(s(s(z))))) | (~r(z, s(s(z)))) | (~r(s(s(elem!1)), s(s(z)))) | (~r(s(s(elem!1)), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(elem!1)), z)) | (~r(s(s(elem!1)), s(s(z)))) | (~r(s(s(z)), s(s(s(z))))) | (~r(z, s(s(z))))))),
% 2.72/2.91 inference(monotonicity,[status(thm)],[9928])).
% 2.72/2.91 tff(9930,plain,
% 2.72/2.91 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(z)), s(s(s(z))))) | (~r(z, s(s(z)))) | (~r(s(s(elem!1)), s(s(z)))) | (~r(s(s(elem!1)), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(elem!1)), z)) | (~r(s(s(elem!1)), s(s(z)))) | (~r(s(s(z)), s(s(s(z))))) | (~r(z, s(s(z)))))),
% 2.72/2.91 inference(transitivity,[status(thm)],[9929, 9927])).
% 2.72/2.91 tff(9931,plain,
% 2.72/2.91 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(z)), s(s(s(z))))) | (~r(z, s(s(z)))) | (~r(s(s(elem!1)), s(s(z)))) | (~r(s(s(elem!1)), z)))),
% 2.72/2.91 inference(quant_inst,[status(thm)],[])).
% 2.72/2.91 tff(9932,plain,
% 2.72/2.91 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(elem!1)), z)) | (~r(s(s(elem!1)), s(s(z)))) | (~r(s(s(z)), s(s(s(z))))) | (~r(z, s(s(z))))),
% 2.72/2.91 inference(modus_ponens,[status(thm)],[9931, 9930])).
% 2.72/2.91 tff(9933,plain,
% 2.72/2.91 ($false),
% 2.72/2.91 inference(unit_resolution,[status(thm)],[9932, 197, 393, 155, 1970, 1732])).
% 2.72/2.91 tff(9934,plain,((~r(s(s(z)), s(s(s(z))))) | (~r(s(s(elem!1)), s(s(z)))) | (~r(z, s(s(z)))) | (~r(s(s(elem!1)), z))), inference(lemma,lemma(discharge,[]))).
% 2.72/2.91 tff(9935,plain,
% 2.72/2.91 (~r(s(s(elem!1)), s(s(z)))),
% 2.72/2.91 inference(unit_resolution,[status(thm)],[9934, 9926, 155, 9824])).
% 2.72/2.91 tff(9936,plain,
% 2.72/2.91 (b(s(s(elem!1)), s(s(z)))),
% 2.72/2.91 inference(unit_resolution,[status(thm)],[441, 9935, 132])).
% 2.72/2.91 tff(9937,plain,
% 2.72/2.91 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(elem!1)))) | (~b(s(z), z)) | (~b(s(s(elem!1)), s(s(z)))) | (~b(s(z), s(s(z)))) | (~b(s(s(s(z))), z)) | (~b(s(z), s(s(s(z))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(s(elem!1)))) | (~b(s(z), z)) | (~b(s(s(elem!1)), s(s(z)))) | (~b(s(z), s(s(z)))) | (~b(s(s(s(z))), z)) | (~b(s(z), s(s(s(z))))))),
% 2.72/2.91 inference(rewrite,[status(thm)],[])).
% 2.72/2.91 tff(9938,plain,
% 2.72/2.91 (((~b(s(s(elem!1)), s(s(z)))) | (~b(s(z), s(s(z)))) | (~b(z, s(s(elem!1)))) | (~b(s(s(s(z))), z)) | (~b(s(z), z)) | (~b(s(z), s(s(s(z)))))) <=> ((~b(z, s(s(elem!1)))) | (~b(s(z), z)) | (~b(s(s(elem!1)), s(s(z)))) | (~b(s(z), s(s(z)))) | (~b(s(s(s(z))), z)) | (~b(s(z), s(s(s(z))))))),
% 2.72/2.91 inference(rewrite,[status(thm)],[])).
% 2.72/2.91 tff(9939,plain,
% 2.72/2.91 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), s(s(z)))) | (~b(s(z), s(s(z)))) | (~b(z, s(s(elem!1)))) | (~b(s(s(s(z))), z)) | (~b(s(z), z)) | (~b(s(z), s(s(s(z))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(elem!1)))) | (~b(s(z), z)) | (~b(s(s(elem!1)), s(s(z)))) | (~b(s(z), s(s(z)))) | (~b(s(s(s(z))), z)) | (~b(s(z), s(s(s(z)))))))),
% 2.72/2.91 inference(monotonicity,[status(thm)],[9938])).
% 2.72/2.91 tff(9940,plain,
% 2.72/2.91 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), s(s(z)))) | (~b(s(z), s(s(z)))) | (~b(z, s(s(elem!1)))) | (~b(s(s(s(z))), z)) | (~b(s(z), z)) | (~b(s(z), s(s(s(z))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(s(elem!1)))) | (~b(s(z), z)) | (~b(s(s(elem!1)), s(s(z)))) | (~b(s(z), s(s(z)))) | (~b(s(s(s(z))), z)) | (~b(s(z), s(s(s(z))))))),
% 2.72/2.91 inference(transitivity,[status(thm)],[9939, 9937])).
% 2.72/2.91 tff(9941,plain,
% 2.72/2.91 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), s(s(z)))) | (~b(s(z), s(s(z)))) | (~b(z, s(s(elem!1)))) | (~b(s(s(s(z))), z)) | (~b(s(z), z)) | (~b(s(z), s(s(s(z))))))),
% 2.72/2.91 inference(quant_inst,[status(thm)],[])).
% 2.72/2.91 tff(9942,plain,
% 2.72/2.91 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(s(elem!1)))) | (~b(s(z), z)) | (~b(s(s(elem!1)), s(s(z)))) | (~b(s(z), s(s(z)))) | (~b(s(s(s(z))), z)) | (~b(s(z), s(s(s(z)))))),
% 2.72/2.91 inference(modus_ponens,[status(thm)],[9941, 9940])).
% 2.72/2.91 tff(9943,plain,
% 2.72/2.91 ($false),
% 2.72/2.91 inference(unit_resolution,[status(thm)],[9942, 166, 1820, 53, 9936, 9826, 9892, 9900])).
% 2.72/2.91 tff(9944,plain,((~b(z, s(s(elem!1)))) | (~b(s(z), z)) | (~r(z, s(s(z)))) | (~b(s(z), s(s(elem!1)))) | (~r(s(s(s(elem!1))), s(z))) | (~r(z, s(z))) | (~r(s(s(elem!1)), s(z))) | (s(s(z)) = s(s(elem!1)))), inference(lemma,lemma(discharge,[]))).
% 2.72/2.91 tff(9945,plain,
% 2.72/2.91 (~b(z, s(s(elem!1)))),
% 2.72/2.91 inference(unit_resolution,[status(thm)],[9944, 53, 155, 376, 350, 323, 4577, 52])).
% 2.72/2.91 tff(9946,plain,
% 2.72/2.91 (r(z, s(s(elem!1)))),
% 2.72/2.91 inference(unit_resolution,[status(thm)],[1795, 9945])).
% 2.72/2.91 tff(9947,plain,
% 2.72/2.91 (~r(s(s(z)), s(s(elem!1)))),
% 2.72/2.91 inference(unit_resolution,[status(thm)],[5997, 9946, 155, 4577])).
% 2.72/2.91 tff(9948,plain,
% 2.72/2.91 (~r(s(z), s(s(s(elem!1))))),
% 2.72/2.91 inference(unit_resolution,[status(thm)],[8626, 9946, 323, 4577])).
% 2.72/2.91 tff(9949,plain,
% 2.72/2.91 (b(s(z), s(s(s(elem!1))))),
% 2.72/2.91 inference(unit_resolution,[status(thm)],[116, 9948])).
% 2.72/2.91 tff(9950,plain,
% 2.72/2.91 (b(s(s(z)), s(s(elem!1)))),
% 2.72/2.91 inference(unit_resolution,[status(thm)],[390, 2288, 52])).
% 2.72/2.91 tff(9951,plain,
% 2.72/2.91 (~r(s(z), s(s(z)))),
% 2.72/2.91 inference(unit_resolution,[status(thm)],[980, 9846, 323, 350])).
% 2.72/2.91 tff(9952,plain,
% 2.72/2.91 (b(s(z), s(s(z)))),
% 2.72/2.91 inference(unit_resolution,[status(thm)],[427, 9951])).
% 2.72/2.91 tff(9953,plain,
% 2.72/2.91 (s(s(elem!1)) = s(s(s(elem!1)))),
% 2.72/2.91 inference(unit_resolution,[status(thm)],[9862, 9952, 53, 9950, 376, 121, 350, 241])).
% 2.72/2.91 tff(9954,plain,
% 2.72/2.91 (s(s(s(elem!1))) = s(s(elem!1))),
% 2.72/2.91 inference(symmetry,[status(thm)],[9953])).
% 2.72/2.91 tff(9955,plain,
% 2.72/2.91 (r(s(s(s(z))), s(s(s(elem!1)))) <=> r(s(s(s(z))), s(s(elem!1)))),
% 2.72/2.91 inference(monotonicity,[status(thm)],[9954])).
% 2.72/2.91 tff(9956,plain,
% 2.72/2.91 (r(s(s(s(z))), s(s(elem!1))) <=> r(s(s(s(z))), s(s(s(elem!1))))),
% 2.72/2.91 inference(symmetry,[status(thm)],[9955])).
% 2.72/2.91 tff(9957,plain,
% 2.72/2.91 (s(s(s(elem!1))) = s(elem!1)),
% 2.72/2.91 inference(unit_resolution,[status(thm)],[2594, 9953])).
% 2.72/2.91 tff(9958,plain,
% 2.72/2.91 (s(elem!1) = s(s(s(elem!1)))),
% 2.72/2.91 inference(symmetry,[status(thm)],[9957])).
% 2.72/2.91 tff(9959,plain,
% 2.72/2.91 (inj_0(s(elem!1)) = inj_0(s(s(s(elem!1))))),
% 2.72/2.91 inference(monotonicity,[status(thm)],[9958])).
% 2.72/2.91 tff(9960,plain,
% 2.72/2.91 (elem!1 = s(s(elem!1))),
% 2.72/2.91 inference(transitivity,[status(thm)],[1170, 9959, 104])).
% 2.72/2.91 tff(9961,plain,
% 2.72/2.91 (r(s(s(s(z))), elem!1) <=> r(s(s(s(z))), s(s(elem!1)))),
% 2.72/2.91 inference(monotonicity,[status(thm)],[9960])).
% 2.72/2.91 tff(9962,plain,
% 2.72/2.91 (~(s(s(s(z))) = elem!1)),
% 2.72/2.91 inference(unit_resolution,[status(thm)],[3122, 9953])).
% 2.72/2.91 tff(9963,plain,
% 2.72/2.92 (s(s(s(elem!1))) = s(s(elem!1))),
% 2.72/2.92 inference(unit_resolution,[status(thm)],[4030, 9953])).
% 2.72/2.92 tff(9964,plain,
% 2.72/2.92 (r(s(s(elem!1)), s(s(z))) <=> r(s(s(s(elem!1))), s(s(z)))),
% 2.72/2.92 inference(monotonicity,[status(thm)],[9953])).
% 2.72/2.92 tff(9965,plain,
% 2.72/2.92 (r(s(s(elem!1)), s(s(z)))),
% 2.72/2.92 inference(unit_resolution,[status(thm)],[5300, 9952, 376, 52, 2288])).
% 2.72/2.92 tff(9966,plain,
% 2.72/2.92 (r(s(s(s(elem!1))), s(s(z)))),
% 2.72/2.92 inference(modus_ponens,[status(thm)],[9965, 9964])).
% 2.72/2.92 tff(9967,plain,
% 2.72/2.92 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), s(s(z)))) | (~r(s(s(z)), s(s(s(z))))) | (~r(z, s(s(z)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), s(s(z)))) | (~r(s(s(z)), s(s(s(z))))) | (~r(z, s(s(z)))))),
% 2.72/2.92 inference(rewrite,[status(thm)],[])).
% 2.72/2.92 tff(9968,plain,
% 2.72/2.92 (((~r(s(s(z)), s(s(s(z))))) | (~r(s(s(s(elem!1))), s(s(z)))) | (~r(z, s(s(z)))) | (~r(z, s(s(s(elem!1)))))) <=> ((~r(z, s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), s(s(z)))) | (~r(s(s(z)), s(s(s(z))))) | (~r(z, s(s(z)))))),
% 2.72/2.92 inference(rewrite,[status(thm)],[])).
% 2.72/2.92 tff(9969,plain,
% 2.72/2.92 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(z)), s(s(s(z))))) | (~r(s(s(s(elem!1))), s(s(z)))) | (~r(z, s(s(z)))) | (~r(z, s(s(s(elem!1))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), s(s(z)))) | (~r(s(s(z)), s(s(s(z))))) | (~r(z, s(s(z))))))),
% 2.72/2.92 inference(monotonicity,[status(thm)],[9968])).
% 2.72/2.92 tff(9970,plain,
% 2.72/2.92 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(z)), s(s(s(z))))) | (~r(s(s(s(elem!1))), s(s(z)))) | (~r(z, s(s(z)))) | (~r(z, s(s(s(elem!1))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), s(s(z)))) | (~r(s(s(z)), s(s(s(z))))) | (~r(z, s(s(z)))))),
% 2.72/2.92 inference(transitivity,[status(thm)],[9969, 9967])).
% 2.72/2.92 tff(9971,plain,
% 2.72/2.92 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(z)), s(s(s(z))))) | (~r(s(s(s(elem!1))), s(s(z)))) | (~r(z, s(s(z)))) | (~r(z, s(s(s(elem!1))))))),
% 2.72/2.92 inference(quant_inst,[status(thm)],[])).
% 2.72/2.92 tff(9972,plain,
% 2.72/2.92 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), s(s(z)))) | (~r(s(s(z)), s(s(s(z))))) | (~r(z, s(s(z))))),
% 2.72/2.92 inference(modus_ponens,[status(thm)],[9971, 9970])).
% 2.72/2.92 tff(9973,plain,
% 2.72/2.92 ($false),
% 2.72/2.92 inference(unit_resolution,[status(thm)],[9972, 197, 155, 282, 464, 1732])).
% 2.72/2.92 tff(9974,plain,((~r(s(s(z)), s(s(s(z))))) | (~r(z, s(s(z)))) | (~r(z, s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), s(s(z))))), inference(lemma,lemma(discharge,[]))).
% 2.72/2.92 tff(9975,plain,
% 2.72/2.92 (~r(s(s(z)), s(s(s(z))))),
% 2.72/2.92 inference(unit_resolution,[status(thm)],[9974, 9846, 155, 9966])).
% 2.72/2.92 tff(9976,plain,
% 2.72/2.92 (b(s(s(z)), s(s(s(z))))),
% 2.72/2.92 inference(unit_resolution,[status(thm)],[1730, 9975])).
% 2.72/2.92 tff(9977,plain,
% 2.72/2.92 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), s(z))) | (~r(z, s(z))) | (~r(s(z), s(s(s(z))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), s(z))) | (~r(z, s(z))) | (~r(s(z), s(s(s(z))))))),
% 2.72/2.92 inference(rewrite,[status(thm)],[])).
% 2.72/2.92 tff(9978,plain,
% 2.72/2.92 (((~r(s(z), s(s(s(z))))) | (~r(s(s(s(elem!1))), s(z))) | (~r(z, s(z))) | (~r(z, s(s(s(elem!1)))))) <=> ((~r(z, s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), s(z))) | (~r(z, s(z))) | (~r(s(z), s(s(s(z))))))),
% 2.72/2.92 inference(rewrite,[status(thm)],[])).
% 2.72/2.92 tff(9979,plain,
% 2.72/2.92 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(s(s(z))))) | (~r(s(s(s(elem!1))), s(z))) | (~r(z, s(z))) | (~r(z, s(s(s(elem!1))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), s(z))) | (~r(z, s(z))) | (~r(s(z), s(s(s(z)))))))),
% 2.72/2.92 inference(monotonicity,[status(thm)],[9978])).
% 2.72/2.92 tff(9980,plain,
% 2.72/2.92 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(s(s(z))))) | (~r(s(s(s(elem!1))), s(z))) | (~r(z, s(z))) | (~r(z, s(s(s(elem!1))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), s(z))) | (~r(z, s(z))) | (~r(s(z), s(s(s(z))))))),
% 2.72/2.92 inference(transitivity,[status(thm)],[9979, 9977])).
% 2.72/2.92 tff(9981,plain,
% 2.72/2.92 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(s(s(z))))) | (~r(s(s(s(elem!1))), s(z))) | (~r(z, s(z))) | (~r(z, s(s(s(elem!1))))))),
% 2.72/2.92 inference(quant_inst,[status(thm)],[])).
% 2.72/2.92 tff(9982,plain,
% 2.72/2.92 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), s(z))) | (~r(z, s(z))) | (~r(s(z), s(s(s(z)))))),
% 2.72/2.92 inference(modus_ponens,[status(thm)],[9981, 9980])).
% 2.72/2.92 tff(9983,plain,
% 2.72/2.92 ($false),
% 2.72/2.92 inference(unit_resolution,[status(thm)],[9982, 197, 350, 323, 282, 1653])).
% 2.72/2.92 tff(9984,plain,((~r(s(z), s(s(s(z))))) | (~r(s(s(s(elem!1))), s(z))) | (~r(z, s(z))) | (~r(z, s(s(s(elem!1)))))), inference(lemma,lemma(discharge,[]))).
% 2.72/2.92 tff(9985,plain,
% 2.72/2.92 (~r(s(z), s(s(s(z))))),
% 2.72/2.92 inference(unit_resolution,[status(thm)],[9984, 9846, 323, 350])).
% 2.72/2.92 tff(9986,plain,
% 2.72/2.92 (b(s(z), s(s(s(z))))),
% 2.72/2.92 inference(unit_resolution,[status(thm)],[1674, 9985])).
% 2.72/2.92 tff(9987,plain,
% 2.72/2.92 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), z)) | (~b(s(s(s(elem!1))), z)) | (~b(s(z), s(s(z)))) | (~b(s(s(s(z))), s(s(s(elem!1))))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(z)), s(s(s(z))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), z)) | (~b(s(s(s(elem!1))), z)) | (~b(s(z), s(s(z)))) | (~b(s(s(s(z))), s(s(s(elem!1))))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(z)), s(s(s(z))))))),
% 2.72/2.92 inference(rewrite,[status(thm)],[])).
% 2.72/2.92 tff(9988,plain,
% 2.72/2.92 (((~b(s(s(s(elem!1))), z)) | (~b(s(z), z)) | (~b(s(s(s(z))), s(s(s(elem!1))))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(z), s(s(s(z))))) | (~b(s(z), s(s(z))))) <=> ((~b(s(z), z)) | (~b(s(s(s(elem!1))), z)) | (~b(s(z), s(s(z)))) | (~b(s(s(s(z))), s(s(s(elem!1))))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(z)), s(s(s(z))))))),
% 2.72/2.92 inference(rewrite,[status(thm)],[])).
% 2.72/2.92 tff(9989,plain,
% 2.72/2.92 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), z)) | (~b(s(z), z)) | (~b(s(s(s(z))), s(s(s(elem!1))))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(z), s(s(s(z))))) | (~b(s(z), s(s(z)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), z)) | (~b(s(s(s(elem!1))), z)) | (~b(s(z), s(s(z)))) | (~b(s(s(s(z))), s(s(s(elem!1))))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(z)), s(s(s(z)))))))),
% 2.72/2.92 inference(monotonicity,[status(thm)],[9988])).
% 2.72/2.92 tff(9990,plain,
% 2.72/2.92 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), z)) | (~b(s(z), z)) | (~b(s(s(s(z))), s(s(s(elem!1))))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(z), s(s(s(z))))) | (~b(s(z), s(s(z)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), z)) | (~b(s(s(s(elem!1))), z)) | (~b(s(z), s(s(z)))) | (~b(s(s(s(z))), s(s(s(elem!1))))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(z)), s(s(s(z))))))),
% 2.72/2.92 inference(transitivity,[status(thm)],[9989, 9987])).
% 2.72/2.92 tff(9991,plain,
% 2.72/2.92 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), z)) | (~b(s(z), z)) | (~b(s(s(s(z))), s(s(s(elem!1))))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(z), s(s(s(z))))) | (~b(s(z), s(s(z)))))),
% 2.72/2.92 inference(quant_inst,[status(thm)],[])).
% 2.72/2.92 tff(9992,plain,
% 2.72/2.92 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), z)) | (~b(s(s(s(elem!1))), z)) | (~b(s(z), s(s(z)))) | (~b(s(s(s(z))), s(s(s(elem!1))))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(z)), s(s(s(z)))))),
% 2.72/2.92 inference(modus_ponens,[status(thm)],[9991, 9990])).
% 2.72/2.92 tff(9993,plain,
% 2.72/2.92 ($false),
% 2.72/2.92 inference(unit_resolution,[status(thm)],[9992, 166, 53, 556, 121, 6552, 988, 986])).
% 2.72/2.92 tff(9994,plain,((~b(s(s(s(z))), s(s(s(elem!1))))) | (~b(s(z), z)) | (~b(s(z), s(s(z)))) | (~b(s(s(s(elem!1))), z)) | (~b(s(z), s(s(s(z))))) | (~b(s(s(z)), s(s(s(z)))))), inference(lemma,lemma(discharge,[]))).
% 2.72/2.92 tff(9995,plain,
% 2.72/2.92 (~b(s(s(s(z))), s(s(s(elem!1))))),
% 2.72/2.92 inference(unit_resolution,[status(thm)],[9994, 9952, 53, 121, 9986, 9976])).
% 2.72/2.92 tff(9996,plain,
% 2.72/2.92 (~b(s(s(s(z))), elem!1)),
% 2.72/2.92 inference(unit_resolution,[status(thm)],[4078, 9995, 9963])).
% 2.72/2.92 tff(9997,plain,
% 2.72/2.92 (r(s(s(s(z))), elem!1)),
% 2.72/2.92 inference(unit_resolution,[status(thm)],[2826, 9996, 9962])).
% 2.72/2.92 tff(9998,plain,
% 2.72/2.92 (r(s(s(s(z))), s(s(elem!1)))),
% 2.72/2.92 inference(modus_ponens,[status(thm)],[9997, 9961])).
% 2.72/2.92 tff(9999,plain,
% 2.72/2.92 (r(s(s(s(z))), s(s(s(elem!1))))),
% 2.72/2.92 inference(modus_ponens,[status(thm)],[9998, 9956])).
% 2.72/2.92 tff(10000,plain,
% 2.72/2.92 (r(s(s(s(z))), s(s(s(elem!1))))),
% 2.72/2.92 inference(modus_ponens,[status(thm)],[4409, 4024])).
% 2.72/2.92 tff(10001,plain,
% 2.72/2.92 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(z))), s(s(s(elem!1))))) | (~r(z, s(s(s(elem!1))))) | (~r(z, s(s(s(z))))) | (~r(s(s(s(elem!1))), s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(z))), s(s(s(elem!1))))) | (~r(z, s(s(s(elem!1))))) | (~r(z, s(s(s(z))))) | (~r(s(s(s(elem!1))), s(z))))),
% 2.72/2.92 inference(rewrite,[status(thm)],[])).
% 2.72/2.92 tff(10002,plain,
% 2.72/2.92 (((~r(s(s(s(elem!1))), s(z))) | (~r(s(s(s(z))), s(s(s(elem!1))))) | (~r(z, s(s(s(elem!1))))) | (~r(z, s(s(s(z)))))) <=> ((~r(s(s(s(z))), s(s(s(elem!1))))) | (~r(z, s(s(s(elem!1))))) | (~r(z, s(s(s(z))))) | (~r(s(s(s(elem!1))), s(z))))),
% 2.72/2.92 inference(rewrite,[status(thm)],[])).
% 2.72/2.92 tff(10003,plain,
% 2.72/2.92 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), s(z))) | (~r(s(s(s(z))), s(s(s(elem!1))))) | (~r(z, s(s(s(elem!1))))) | (~r(z, s(s(s(z))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(z))), s(s(s(elem!1))))) | (~r(z, s(s(s(elem!1))))) | (~r(z, s(s(s(z))))) | (~r(s(s(s(elem!1))), s(z)))))),
% 2.72/2.92 inference(monotonicity,[status(thm)],[10002])).
% 2.72/2.92 tff(10004,plain,
% 2.72/2.92 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), s(z))) | (~r(s(s(s(z))), s(s(s(elem!1))))) | (~r(z, s(s(s(elem!1))))) | (~r(z, s(s(s(z))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(z))), s(s(s(elem!1))))) | (~r(z, s(s(s(elem!1))))) | (~r(z, s(s(s(z))))) | (~r(s(s(s(elem!1))), s(z))))),
% 2.72/2.92 inference(transitivity,[status(thm)],[10003, 10001])).
% 2.72/2.92 tff(10005,plain,
% 2.72/2.92 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), s(z))) | (~r(s(s(s(z))), s(s(s(elem!1))))) | (~r(z, s(s(s(elem!1))))) | (~r(z, s(s(s(z))))))),
% 2.72/2.92 inference(quant_inst,[status(thm)],[])).
% 2.72/2.92 tff(10006,plain,
% 2.72/2.92 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(z))), s(s(s(elem!1))))) | (~r(z, s(s(s(elem!1))))) | (~r(z, s(s(s(z))))) | (~r(s(s(s(elem!1))), s(z)))),
% 2.72/2.92 inference(modus_ponens,[status(thm)],[10005, 10004])).
% 2.72/2.92 tff(10007,plain,
% 2.72/2.92 (~r(s(s(s(z))), s(s(s(elem!1))))),
% 2.72/2.92 inference(unit_resolution,[status(thm)],[10006, 197, 350, 282, 1677])).
% 2.72/2.92 tff(10008,plain,
% 2.72/2.92 ($false),
% 2.72/2.92 inference(unit_resolution,[status(thm)],[10007, 10000])).
% 2.72/2.92 tff(10009,plain,((~r(s(s(s(z))), s(s(elem!1)))) | (~(s(s(elem!1)) = s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), s(z))) | (~r(z, s(s(s(elem!1))))) | (~r(z, s(s(s(z)))))), inference(lemma,lemma(discharge,[]))).
% 2.72/2.92 tff(10010,plain,
% 2.72/2.92 (~r(z, s(s(s(z))))),
% 2.72/2.92 inference(unit_resolution,[status(thm)],[10009, 9998, 350, 9846, 9953])).
% 2.72/2.92 tff(10011,plain,
% 2.72/2.92 (b(z, s(s(s(z))))),
% 2.72/2.92 inference(unit_resolution,[status(thm)],[1697, 10010])).
% 2.72/2.92 tff(10012,plain,
% 2.72/2.92 (~b(s(s(s(z))), z)),
% 2.72/2.92 inference(unit_resolution,[status(thm)],[1708, 10011, 53, 9986])).
% 2.72/2.92 tff(10013,plain,
% 2.72/2.92 (r(s(s(s(z))), z)),
% 2.72/2.92 inference(unit_resolution,[status(thm)],[1713, 10012])).
% 2.72/2.92 tff(10014,plain,
% 2.72/2.92 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(z))), s(s(s(elem!1))))) | (~r(z, s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), s(z))) | (~r(s(s(s(z))), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(z))), s(s(s(elem!1))))) | (~r(z, s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), s(z))) | (~r(s(s(s(z))), z)))),
% 2.72/2.92 inference(rewrite,[status(thm)],[])).
% 2.72/2.92 tff(10015,plain,
% 2.72/2.92 (((~r(s(s(s(elem!1))), s(z))) | (~r(z, s(s(s(elem!1))))) | (~r(s(s(s(z))), s(s(s(elem!1))))) | (~r(s(s(s(z))), z))) <=> ((~r(s(s(s(z))), s(s(s(elem!1))))) | (~r(z, s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), s(z))) | (~r(s(s(s(z))), z)))),
% 2.72/2.92 inference(rewrite,[status(thm)],[])).
% 2.72/2.92 tff(10016,plain,
% 2.72/2.92 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), s(z))) | (~r(z, s(s(s(elem!1))))) | (~r(s(s(s(z))), s(s(s(elem!1))))) | (~r(s(s(s(z))), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(z))), s(s(s(elem!1))))) | (~r(z, s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), s(z))) | (~r(s(s(s(z))), z))))),
% 2.72/2.92 inference(monotonicity,[status(thm)],[10015])).
% 2.72/2.92 tff(10017,plain,
% 2.72/2.92 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), s(z))) | (~r(z, s(s(s(elem!1))))) | (~r(s(s(s(z))), s(s(s(elem!1))))) | (~r(s(s(s(z))), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(z))), s(s(s(elem!1))))) | (~r(z, s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), s(z))) | (~r(s(s(s(z))), z)))),
% 2.72/2.92 inference(transitivity,[status(thm)],[10016, 10014])).
% 2.72/2.92 tff(10018,plain,
% 2.72/2.92 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), s(z))) | (~r(z, s(s(s(elem!1))))) | (~r(s(s(s(z))), s(s(s(elem!1))))) | (~r(s(s(s(z))), z)))),
% 2.72/2.92 inference(quant_inst,[status(thm)],[])).
% 2.72/2.92 tff(10019,plain,
% 2.72/2.92 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(z))), s(s(s(elem!1))))) | (~r(z, s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), s(z))) | (~r(s(s(s(z))), z))),
% 2.72/2.92 inference(modus_ponens,[status(thm)],[10018, 10017])).
% 2.72/2.92 tff(10020,plain,
% 2.72/2.92 ((~r(s(s(s(z))), s(s(s(elem!1))))) | (~r(s(s(s(z))), z))),
% 2.72/2.92 inference(unit_resolution,[status(thm)],[10019, 197, 350, 9846])).
% 2.72/2.92 tff(10021,plain,
% 2.72/2.92 (~r(s(s(s(z))), s(s(s(elem!1))))),
% 2.72/2.92 inference(unit_resolution,[status(thm)],[10020, 10013])).
% 2.72/2.92 tff(10022,plain,
% 2.72/2.92 ($false),
% 2.72/2.92 inference(unit_resolution,[status(thm)],[10021, 9999])).
% 2.72/2.92 tff(10023,plain,((~b(s(s(s(elem!1))), z)) | (~r(s(s(s(elem!1))), s(z))) | (~b(s(z), z)) | (~r(z, s(s(z)))) | (~r(z, s(z))) | (~b(s(z), s(s(elem!1)))) | (~b(s(z), s(s(s(elem!1))))) | (s(s(z)) = s(s(elem!1))) | r(s(s(z)), s(s(elem!1)))), inference(lemma,lemma(discharge,[]))).
% 2.72/2.93 tff(10024,plain,
% 2.72/2.93 (~b(s(s(s(elem!1))), z)),
% 2.72/2.93 inference(unit_resolution,[status(thm)],[10023, 53, 350, 155, 323, 376, 9949, 52, 9947])).
% 2.72/2.93 tff(10025,plain,
% 2.72/2.93 (r(s(s(s(elem!1))), z)),
% 2.72/2.93 inference(unit_resolution,[status(thm)],[94, 10024])).
% 2.72/2.93 tff(10026,plain,
% 2.72/2.93 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), z)) | (~r(s(s(s(elem!1))), s(z))) | (~r(z, s(z))) | (~r(s(z), s(s(z)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(elem!1))), z)) | (~r(s(s(s(elem!1))), s(z))) | (~r(z, s(z))) | (~r(s(z), s(s(z)))))),
% 2.72/2.93 inference(rewrite,[status(thm)],[])).
% 2.72/2.93 tff(10027,plain,
% 2.72/2.93 (((~r(s(z), s(s(z)))) | (~r(z, s(z))) | (~r(s(s(s(elem!1))), s(z))) | (~r(s(s(s(elem!1))), z))) <=> ((~r(s(s(s(elem!1))), z)) | (~r(s(s(s(elem!1))), s(z))) | (~r(z, s(z))) | (~r(s(z), s(s(z)))))),
% 2.72/2.93 inference(rewrite,[status(thm)],[])).
% 2.72/2.93 tff(10028,plain,
% 2.72/2.93 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(s(z)))) | (~r(z, s(z))) | (~r(s(s(s(elem!1))), s(z))) | (~r(s(s(s(elem!1))), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), z)) | (~r(s(s(s(elem!1))), s(z))) | (~r(z, s(z))) | (~r(s(z), s(s(z))))))),
% 2.72/2.93 inference(monotonicity,[status(thm)],[10027])).
% 2.72/2.93 tff(10029,plain,
% 2.72/2.93 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(s(z)))) | (~r(z, s(z))) | (~r(s(s(s(elem!1))), s(z))) | (~r(s(s(s(elem!1))), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(elem!1))), z)) | (~r(s(s(s(elem!1))), s(z))) | (~r(z, s(z))) | (~r(s(z), s(s(z)))))),
% 2.72/2.93 inference(transitivity,[status(thm)],[10028, 10026])).
% 2.72/2.93 tff(10030,plain,
% 2.72/2.93 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(s(z)))) | (~r(z, s(z))) | (~r(s(s(s(elem!1))), s(z))) | (~r(s(s(s(elem!1))), z)))),
% 2.72/2.93 inference(quant_inst,[status(thm)],[])).
% 2.72/2.93 tff(10031,plain,
% 2.72/2.93 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(elem!1))), z)) | (~r(s(s(s(elem!1))), s(z))) | (~r(z, s(z))) | (~r(s(z), s(s(z))))),
% 2.72/2.93 inference(modus_ponens,[status(thm)],[10030, 10029])).
% 2.72/2.93 tff(10032,plain,
% 2.72/2.93 ($false),
% 2.72/2.93 inference(unit_resolution,[status(thm)],[10031, 197, 154, 120, 350, 323])).
% 2.72/2.93 tff(10033,plain,((~r(s(z), s(s(z)))) | (~r(s(s(s(elem!1))), z)) | (~r(s(s(s(elem!1))), s(z))) | (~r(z, s(z)))), inference(lemma,lemma(discharge,[]))).
% 2.72/2.93 tff(10034,plain,
% 2.72/2.93 (~r(s(z), s(s(z)))),
% 2.72/2.93 inference(unit_resolution,[status(thm)],[10033, 10025, 323, 350])).
% 2.72/2.93 tff(10035,plain,
% 2.72/2.93 (b(s(z), s(s(z)))),
% 2.72/2.93 inference(unit_resolution,[status(thm)],[427, 10034])).
% 2.72/2.93 tff(10036,plain,
% 2.72/2.93 (r(s(s(elem!1)), s(s(z)))),
% 2.72/2.93 inference(unit_resolution,[status(thm)],[5300, 10035, 376, 52, 9947])).
% 2.72/2.93 tff(10037,plain,
% 2.72/2.93 (~r(s(s(z)), s(s(s(elem!1))))),
% 2.72/2.93 inference(unit_resolution,[status(thm)],[539, 10036, 155, 9946])).
% 2.72/2.93 tff(10038,plain,
% 2.72/2.93 (b(s(s(z)), s(s(s(elem!1))))),
% 2.72/2.93 inference(unit_resolution,[status(thm)],[279, 10037])).
% 2.72/2.93 tff(10039,plain,
% 2.72/2.93 (~r(s(z), s(s(s(z))))),
% 2.72/2.93 inference(unit_resolution,[status(thm)],[9890, 10025, 350, 323])).
% 2.72/2.93 tff(10040,plain,
% 2.72/2.93 (b(s(z), s(s(s(z))))),
% 2.72/2.93 inference(unit_resolution,[status(thm)],[1674, 10039])).
% 2.72/2.93 tff(10041,plain,
% 2.72/2.93 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(elem!1)))) | (~r(s(s(elem!1)), s(s(z)))) | (~r(s(s(z)), s(s(s(z))))) | (~r(z, s(s(z)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, s(s(elem!1)))) | (~r(s(s(elem!1)), s(s(z)))) | (~r(s(s(z)), s(s(s(z))))) | (~r(z, s(s(z)))))),
% 2.72/2.93 inference(rewrite,[status(thm)],[])).
% 2.72/2.93 tff(10042,plain,
% 2.72/2.93 (((~r(s(s(z)), s(s(s(z))))) | (~r(s(s(elem!1)), s(s(z)))) | (~r(z, s(s(z)))) | (~r(z, s(s(elem!1))))) <=> ((~r(z, s(s(elem!1)))) | (~r(s(s(elem!1)), s(s(z)))) | (~r(s(s(z)), s(s(s(z))))) | (~r(z, s(s(z)))))),
% 2.72/2.93 inference(rewrite,[status(thm)],[])).
% 2.72/2.93 tff(10043,plain,
% 2.72/2.93 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(z)), s(s(s(z))))) | (~r(s(s(elem!1)), s(s(z)))) | (~r(z, s(s(z)))) | (~r(z, s(s(elem!1)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(elem!1)))) | (~r(s(s(elem!1)), s(s(z)))) | (~r(s(s(z)), s(s(s(z))))) | (~r(z, s(s(z))))))),
% 2.72/2.93 inference(monotonicity,[status(thm)],[10042])).
% 2.72/2.93 tff(10044,plain,
% 2.72/2.93 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(z)), s(s(s(z))))) | (~r(s(s(elem!1)), s(s(z)))) | (~r(z, s(s(z)))) | (~r(z, s(s(elem!1)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, s(s(elem!1)))) | (~r(s(s(elem!1)), s(s(z)))) | (~r(s(s(z)), s(s(s(z))))) | (~r(z, s(s(z)))))),
% 2.72/2.93 inference(transitivity,[status(thm)],[10043, 10041])).
% 2.72/2.93 tff(10045,plain,
% 2.72/2.93 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(z)), s(s(s(z))))) | (~r(s(s(elem!1)), s(s(z)))) | (~r(z, s(s(z)))) | (~r(z, s(s(elem!1)))))),
% 2.72/2.93 inference(quant_inst,[status(thm)],[])).
% 2.72/2.93 tff(10046,plain,
% 2.72/2.93 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, s(s(elem!1)))) | (~r(s(s(elem!1)), s(s(z)))) | (~r(s(s(z)), s(s(s(z))))) | (~r(z, s(s(z))))),
% 2.72/2.93 inference(modus_ponens,[status(thm)],[10045, 10044])).
% 2.72/2.93 tff(10047,plain,
% 2.72/2.93 ($false),
% 2.72/2.93 inference(unit_resolution,[status(thm)],[10046, 197, 393, 155, 365, 1732])).
% 2.72/2.93 tff(10048,plain,((~r(s(s(z)), s(s(s(z))))) | (~r(s(s(elem!1)), s(s(z)))) | (~r(z, s(s(z)))) | (~r(z, s(s(elem!1))))), inference(lemma,lemma(discharge,[]))).
% 2.72/2.93 tff(10049,plain,
% 2.72/2.93 (~r(s(s(z)), s(s(s(z))))),
% 2.72/2.93 inference(unit_resolution,[status(thm)],[10048, 10036, 155, 9946])).
% 2.72/2.93 tff(10050,plain,
% 2.72/2.93 (b(s(s(z)), s(s(s(z))))),
% 2.72/2.93 inference(unit_resolution,[status(thm)],[1730, 10049])).
% 2.72/2.93 tff(10051,plain,
% 2.72/2.93 (~b(s(s(s(z))), s(s(z)))),
% 2.72/2.93 inference(unit_resolution,[status(thm)],[996, 10050, 10040, 10035])).
% 2.72/2.93 tff(10052,plain,
% 2.72/2.93 (r(s(s(s(z))), s(s(z)))),
% 2.72/2.93 inference(unit_resolution,[status(thm)],[1010, 10051])).
% 2.72/2.93 tff(10053,plain,
% 2.72/2.93 ((s(s(s(z))) = s(s(s(elem!1)))) <=> (s(s(s(elem!1))) = s(s(s(z))))),
% 2.72/2.93 inference(commutativity,[status(thm)],[])).
% 2.72/2.93 tff(10054,plain,
% 2.72/2.93 ((s(s(s(elem!1))) = s(s(s(z)))) <=> (s(s(s(z))) = s(s(s(elem!1))))),
% 2.72/2.93 inference(symmetry,[status(thm)],[10053])).
% 2.72/2.93 tff(10055,plain,
% 2.72/2.93 ((~(s(s(s(elem!1))) = s(s(s(z))))) <=> (~(s(s(s(z))) = s(s(s(elem!1)))))),
% 2.72/2.93 inference(monotonicity,[status(thm)],[10054])).
% 2.72/2.93 tff(10056,plain,
% 2.72/2.93 (~(s(s(s(z))) = s(s(s(elem!1))))),
% 2.72/2.93 inference(modus_ponens,[status(thm)],[3567, 10055])).
% 2.72/2.93 tff(10057,plain,
% 2.72/2.93 (((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((s(s(s(z))) = s(s(s(elem!1)))) | b(s(s(s(z))), s(s(s(elem!1)))) | r(s(s(s(z))), s(s(s(elem!1)))))) <=> ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (s(s(s(z))) = s(s(s(elem!1)))) | b(s(s(s(z))), s(s(s(elem!1)))) | r(s(s(s(z))), s(s(s(elem!1)))))),
% 2.72/2.93 inference(rewrite,[status(thm)],[])).
% 2.72/2.93 tff(10058,plain,
% 2.72/2.93 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((s(s(s(z))) = s(s(s(elem!1)))) | b(s(s(s(z))), s(s(s(elem!1)))) | r(s(s(s(z))), s(s(s(elem!1)))))),
% 2.72/2.93 inference(quant_inst,[status(thm)],[])).
% 2.72/2.93 tff(10059,plain,
% 2.72/2.93 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (s(s(s(z))) = s(s(s(elem!1)))) | b(s(s(s(z))), s(s(s(elem!1)))) | r(s(s(s(z))), s(s(s(elem!1))))),
% 2.72/2.93 inference(modus_ponens,[status(thm)],[10058, 10057])).
% 2.72/2.93 tff(10060,plain,
% 2.72/2.93 ((s(s(s(z))) = s(s(s(elem!1)))) | b(s(s(s(z))), s(s(s(elem!1))))),
% 2.72/2.93 inference(unit_resolution,[status(thm)],[10059, 79, 5510])).
% 2.72/2.93 tff(10061,plain,
% 2.72/2.93 (b(s(s(s(z))), s(s(s(elem!1))))),
% 2.72/2.93 inference(unit_resolution,[status(thm)],[10060, 10056])).
% 2.72/2.93 tff(10062,plain,
% 2.72/2.93 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(s(elem!1))))) | (~b(s(s(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, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), s(s(s(elem!1))))) | (~b(s(s(s(z))), s(s(s(elem!1))))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(elem!1))), s(s(s(z))))))),
% 2.72/2.93 inference(rewrite,[status(thm)],[])).
% 2.72/2.93 tff(10063,plain,
% 2.72/2.93 (((~b(s(s(s(z))), s(s(s(elem!1))))) | (~b(s(z), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(s(s(z))))) | (~b(s(s(s(z))), s(s(s(elem!1))))) | (~b(s(z), s(s(s(elem!1))))) | (~b(s(z), s(s(s(z)))))) <=> ((~b(s(z), s(s(s(elem!1))))) | (~b(s(s(s(z))), s(s(s(elem!1))))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(elem!1))), s(s(s(z))))))),
% 2.72/2.93 inference(rewrite,[status(thm)],[])).
% 2.72/2.93 tff(10064,plain,
% 2.72/2.93 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), s(s(s(elem!1))))) | (~b(s(z), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(s(s(z))))) | (~b(s(s(s(z))), s(s(s(elem!1))))) | (~b(s(z), s(s(s(elem!1))))) | (~b(s(z), s(s(s(z))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(s(elem!1))))) | (~b(s(s(s(z))), s(s(s(elem!1))))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(elem!1))), s(s(s(z)))))))),
% 2.72/2.93 inference(monotonicity,[status(thm)],[10063])).
% 2.72/2.93 tff(10065,plain,
% 2.72/2.93 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), s(s(s(elem!1))))) | (~b(s(z), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(s(s(z))))) | (~b(s(s(s(z))), s(s(s(elem!1))))) | (~b(s(z), s(s(s(elem!1))))) | (~b(s(z), s(s(s(z))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), s(s(s(elem!1))))) | (~b(s(s(s(z))), s(s(s(elem!1))))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(elem!1))), s(s(s(z))))))),
% 2.72/2.93 inference(transitivity,[status(thm)],[10064, 10062])).
% 2.72/2.93 tff(10066,plain,
% 2.72/2.93 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), s(s(s(elem!1))))) | (~b(s(z), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(s(s(z))))) | (~b(s(s(s(z))), s(s(s(elem!1))))) | (~b(s(z), s(s(s(elem!1))))) | (~b(s(z), s(s(s(z))))))),
% 2.72/2.93 inference(quant_inst,[status(thm)],[])).
% 2.72/2.93 tff(10067,plain,
% 2.72/2.93 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), s(s(s(elem!1))))) | (~b(s(s(s(z))), s(s(s(elem!1))))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(elem!1))), s(s(s(z)))))),
% 2.72/2.93 inference(modus_ponens,[status(thm)],[10066, 10065])).
% 2.72/2.93 tff(10068,plain,
% 2.72/2.93 ($false),
% 2.72/2.93 inference(unit_resolution,[status(thm)],[10067, 166, 241, 10061, 988, 5506])).
% 2.72/2.93 tff(10069,plain,((~r(s(s(s(z))), z)) | (~b(s(z), s(s(s(elem!1))))) | (~b(s(z), s(s(s(z))))) | (s(s(s(elem!1))) = s(s(s(z)))) | (~r(s(s(s(elem!1))), z)) | (~r(z, s(s(z))))), inference(lemma,lemma(discharge,[]))).
% 2.72/2.93 tff(10070,plain,
% 2.72/2.93 (~r(s(s(s(z))), z)),
% 2.72/2.93 inference(unit_resolution,[status(thm)],[10069, 9949, 10040, 140, 10025, 155])).
% 2.72/2.93 tff(10071,plain,
% 2.72/2.93 (b(s(s(s(z))), z)),
% 2.72/2.93 inference(unit_resolution,[status(thm)],[1713, 10070])).
% 2.72/2.93 tff(10072,plain,
% 2.72/2.93 (~b(z, s(s(s(z))))),
% 2.72/2.93 inference(unit_resolution,[status(thm)],[1708, 10071, 53, 10040])).
% 2.72/2.93 tff(10073,plain,
% 2.72/2.93 (r(z, s(s(s(z))))),
% 2.72/2.93 inference(unit_resolution,[status(thm)],[1697, 10072])).
% 2.72/2.93 tff(10074,plain,
% 2.72/2.93 (~b(z, s(s(s(elem!1))))),
% 2.72/2.93 inference(unit_resolution,[status(thm)],[4345, 4066, 1790])).
% 2.72/2.93 tff(10075,plain,
% 2.72/2.93 (r(z, s(s(s(elem!1))))),
% 2.72/2.93 inference(unit_resolution,[status(thm)],[261, 10074])).
% 2.72/2.93 tff(10076,plain,
% 2.72/2.93 (~r(s(s(s(z))), s(s(elem!1)))),
% 2.72/2.93 inference(unit_resolution,[status(thm)],[10009, 10075, 350, 1677, 4066])).
% 2.72/2.93 tff(10077,plain,
% 2.72/2.93 ((s(s(s(elem!1))) = s(s(s(z)))) <=> (s(s(elem!1)) = s(s(s(z))))),
% 2.72/2.93 inference(monotonicity,[status(thm)],[47])).
% 2.72/2.93 tff(10078,plain,
% 2.72/2.93 ((s(s(s(elem!1))) = s(s(s(z)))) <=> (s(s(s(z))) = s(s(elem!1)))),
% 2.72/2.93 inference(transitivity,[status(thm)],[10077, 4437])).
% 2.72/2.93 tff(10079,plain,
% 2.72/2.93 ((~(s(s(s(elem!1))) = s(s(s(z))))) <=> (~(s(s(s(z))) = s(s(elem!1))))),
% 2.72/2.93 inference(monotonicity,[status(thm)],[10078])).
% 2.72/2.93 tff(10080,plain,
% 2.72/2.93 (~(s(s(s(z))) = s(s(elem!1)))),
% 2.72/2.93 inference(modus_ponens,[status(thm)],[3567, 10079])).
% 2.72/2.93 tff(10081,plain,
% 2.72/2.93 (r(s(s(elem!1)), s(s(s(z))))),
% 2.72/2.93 inference(unit_resolution,[status(thm)],[5552, 10080, 988, 376, 10076])).
% 2.72/2.93 tff(10082,plain,
% 2.72/2.93 (r(s(s(s(elem!1))), z) <=> r(s(s(elem!1)), z)),
% 2.72/2.93 inference(monotonicity,[status(thm)],[47])).
% 2.72/2.93 tff(10083,plain,
% 2.72/2.93 (r(s(s(elem!1)), z)),
% 2.72/2.93 inference(modus_ponens,[status(thm)],[154, 10082])).
% 2.72/2.93 tff(10084,plain,
% 2.72/2.93 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(s(z))))) | (~r(s(s(elem!1)), z)) | (~r(s(s(s(z))), s(s(z)))) | (~r(s(s(elem!1)), s(s(s(z))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, s(s(s(z))))) | (~r(s(s(elem!1)), z)) | (~r(s(s(s(z))), s(s(z)))) | (~r(s(s(elem!1)), s(s(s(z))))))),
% 2.72/2.93 inference(rewrite,[status(thm)],[])).
% 2.72/2.93 tff(10085,plain,
% 2.72/2.93 (((~r(s(s(s(z))), s(s(z)))) | (~r(z, s(s(s(z))))) | (~r(s(s(elem!1)), s(s(s(z))))) | (~r(s(s(elem!1)), z))) <=> ((~r(z, s(s(s(z))))) | (~r(s(s(elem!1)), z)) | (~r(s(s(s(z))), s(s(z)))) | (~r(s(s(elem!1)), s(s(s(z))))))),
% 2.72/2.93 inference(rewrite,[status(thm)],[])).
% 2.72/2.93 tff(10086,plain,
% 2.72/2.93 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(z))), s(s(z)))) | (~r(z, s(s(s(z))))) | (~r(s(s(elem!1)), s(s(s(z))))) | (~r(s(s(elem!1)), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(s(z))))) | (~r(s(s(elem!1)), z)) | (~r(s(s(s(z))), s(s(z)))) | (~r(s(s(elem!1)), s(s(s(z)))))))),
% 2.72/2.93 inference(monotonicity,[status(thm)],[10085])).
% 2.72/2.93 tff(10087,plain,
% 2.72/2.93 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(z))), s(s(z)))) | (~r(z, s(s(s(z))))) | (~r(s(s(elem!1)), s(s(s(z))))) | (~r(s(s(elem!1)), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, s(s(s(z))))) | (~r(s(s(elem!1)), z)) | (~r(s(s(s(z))), s(s(z)))) | (~r(s(s(elem!1)), s(s(s(z))))))),
% 2.72/2.93 inference(transitivity,[status(thm)],[10086, 10084])).
% 2.72/2.93 tff(10088,plain,
% 2.72/2.93 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(z))), s(s(z)))) | (~r(z, s(s(s(z))))) | (~r(s(s(elem!1)), s(s(s(z))))) | (~r(s(s(elem!1)), z)))),
% 2.72/2.93 inference(quant_inst,[status(thm)],[])).
% 2.72/2.93 tff(10089,plain,
% 2.72/2.93 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, s(s(s(z))))) | (~r(s(s(elem!1)), z)) | (~r(s(s(s(z))), s(s(z)))) | (~r(s(s(elem!1)), s(s(s(z)))))),
% 2.72/2.93 inference(modus_ponens,[status(thm)],[10088, 10087])).
% 2.72/2.93 tff(10090,plain,
% 2.72/2.93 ($false),
% 2.72/2.93 inference(unit_resolution,[status(thm)],[10089, 197, 10083, 1677, 1676, 10081])).
% 2.72/2.93 tff(10091,plain,((~(s(s(s(elem!1))) = s(s(elem!1)))) | (~r(z, s(s(s(z))))) | (~r(s(s(s(z))), s(s(z)))) | (~b(s(z), s(s(s(z))))) | (~b(s(z), s(s(elem!1)))) | (s(s(s(elem!1))) = s(s(s(z)))) | (~r(s(s(s(elem!1))), z)) | (~r(s(s(s(elem!1))), s(z))) | b(z, s(s(elem!1)))), inference(lemma,lemma(discharge,[]))).
% 2.72/2.93 tff(10092,plain,
% 2.72/2.93 (~(s(s(s(elem!1))) = s(s(elem!1)))),
% 2.72/2.93 inference(unit_resolution,[status(thm)],[10091, 10073, 10052, 10040, 376, 140, 10025, 350, 9945])).
% 2.72/2.93 tff(10093,plain,
% 2.72/2.93 (~r(s(s(elem!1)), z)),
% 2.72/2.93 inference(unit_resolution,[status(thm)],[9842, 10092, 10025, 9949, 376, 155])).
% 2.72/2.93 tff(10094,plain,
% 2.72/2.93 (b(s(s(elem!1)), z)),
% 2.72/2.93 inference(unit_resolution,[status(thm)],[608, 10093])).
% 2.72/2.93 tff(10095,plain,
% 2.72/2.93 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), z)) | (~r(s(s(s(elem!1))), s(s(elem!1)))) | (~r(z, s(s(elem!1)))) | (~r(s(s(elem!1)), s(s(z)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(elem!1))), z)) | (~r(s(s(s(elem!1))), s(s(elem!1)))) | (~r(z, s(s(elem!1)))) | (~r(s(s(elem!1)), s(s(z)))))),
% 2.72/2.93 inference(rewrite,[status(thm)],[])).
% 2.72/2.93 tff(10096,plain,
% 2.72/2.93 (((~r(s(s(elem!1)), s(s(z)))) | (~r(z, s(s(elem!1)))) | (~r(s(s(s(elem!1))), s(s(elem!1)))) | (~r(s(s(s(elem!1))), z))) <=> ((~r(s(s(s(elem!1))), z)) | (~r(s(s(s(elem!1))), s(s(elem!1)))) | (~r(z, s(s(elem!1)))) | (~r(s(s(elem!1)), s(s(z)))))),
% 2.72/2.93 inference(rewrite,[status(thm)],[])).
% 2.72/2.93 tff(10097,plain,
% 2.72/2.93 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(elem!1)), s(s(z)))) | (~r(z, s(s(elem!1)))) | (~r(s(s(s(elem!1))), s(s(elem!1)))) | (~r(s(s(s(elem!1))), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), z)) | (~r(s(s(s(elem!1))), s(s(elem!1)))) | (~r(z, s(s(elem!1)))) | (~r(s(s(elem!1)), s(s(z))))))),
% 2.72/2.93 inference(monotonicity,[status(thm)],[10096])).
% 2.72/2.93 tff(10098,plain,
% 2.72/2.93 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(elem!1)), s(s(z)))) | (~r(z, s(s(elem!1)))) | (~r(s(s(s(elem!1))), s(s(elem!1)))) | (~r(s(s(s(elem!1))), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(elem!1))), z)) | (~r(s(s(s(elem!1))), s(s(elem!1)))) | (~r(z, s(s(elem!1)))) | (~r(s(s(elem!1)), s(s(z)))))),
% 2.72/2.93 inference(transitivity,[status(thm)],[10097, 10095])).
% 2.72/2.93 tff(10099,plain,
% 2.72/2.93 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(elem!1)), s(s(z)))) | (~r(z, s(s(elem!1)))) | (~r(s(s(s(elem!1))), s(s(elem!1)))) | (~r(s(s(s(elem!1))), z)))),
% 2.72/2.93 inference(quant_inst,[status(thm)],[])).
% 2.72/2.93 tff(10100,plain,
% 2.72/2.93 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(elem!1))), z)) | (~r(s(s(s(elem!1))), s(s(elem!1)))) | (~r(z, s(s(elem!1)))) | (~r(s(s(elem!1)), s(s(z))))),
% 2.72/2.93 inference(modus_ponens,[status(thm)],[10099, 10098])).
% 2.72/2.93 tff(10101,plain,
% 2.72/2.93 ($false),
% 2.72/2.93 inference(unit_resolution,[status(thm)],[10100, 197, 154, 393, 365, 905])).
% 2.72/2.93 tff(10102,plain,((~r(s(s(s(elem!1))), s(s(elem!1)))) | (~r(s(s(s(elem!1))), z)) | (~r(s(s(elem!1)), s(s(z)))) | (~r(z, s(s(elem!1))))), inference(lemma,lemma(discharge,[]))).
% 2.72/2.93 tff(10103,plain,
% 2.72/2.93 (~r(s(s(s(elem!1))), s(s(elem!1)))),
% 2.72/2.93 inference(unit_resolution,[status(thm)],[10102, 10025, 10036, 9946])).
% 2.72/2.93 tff(10104,plain,
% 2.72/2.93 (b(s(s(s(elem!1))), s(s(elem!1)))),
% 2.72/2.93 inference(unit_resolution,[status(thm)],[889, 10092, 10103])).
% 2.72/2.93 tff(10105,plain,
% 2.72/2.93 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(z), z)) | (~b(s(z), s(s(s(elem!1))))) | (~b(s(s(elem!1)), z)) | (~b(s(z), s(s(z)))) | (~b(s(s(z)), s(s(s(elem!1))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(z), z)) | (~b(s(z), s(s(s(elem!1))))) | (~b(s(s(elem!1)), z)) | (~b(s(z), s(s(z)))) | (~b(s(s(z)), s(s(s(elem!1))))))),
% 2.72/2.93 inference(rewrite,[status(thm)],[])).
% 2.72/2.93 tff(10106,plain,
% 2.72/2.93 (((~b(s(s(elem!1)), z)) | (~b(s(z), z)) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(s(z)), s(s(s(elem!1))))) | (~b(s(z), s(s(s(elem!1))))) | (~b(s(z), s(s(z))))) <=> ((~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(z), z)) | (~b(s(z), s(s(s(elem!1))))) | (~b(s(s(elem!1)), z)) | (~b(s(z), s(s(z)))) | (~b(s(s(z)), s(s(s(elem!1))))))),
% 2.72/2.93 inference(rewrite,[status(thm)],[])).
% 2.72/2.93 tff(10107,plain,
% 2.72/2.93 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), z)) | (~b(s(z), z)) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(s(z)), s(s(s(elem!1))))) | (~b(s(z), s(s(s(elem!1))))) | (~b(s(z), s(s(z)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(z), z)) | (~b(s(z), s(s(s(elem!1))))) | (~b(s(s(elem!1)), z)) | (~b(s(z), s(s(z)))) | (~b(s(s(z)), s(s(s(elem!1)))))))),
% 2.72/2.93 inference(monotonicity,[status(thm)],[10106])).
% 2.72/2.93 tff(10108,plain,
% 2.72/2.93 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), z)) | (~b(s(z), z)) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(s(z)), s(s(s(elem!1))))) | (~b(s(z), s(s(s(elem!1))))) | (~b(s(z), s(s(z)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(z), z)) | (~b(s(z), s(s(s(elem!1))))) | (~b(s(s(elem!1)), z)) | (~b(s(z), s(s(z)))) | (~b(s(s(z)), s(s(s(elem!1))))))),
% 2.72/2.93 inference(transitivity,[status(thm)],[10107, 10105])).
% 2.72/2.93 tff(10109,plain,
% 2.72/2.93 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), z)) | (~b(s(z), z)) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(s(z)), s(s(s(elem!1))))) | (~b(s(z), s(s(s(elem!1))))) | (~b(s(z), s(s(z)))))),
% 2.72/2.93 inference(quant_inst,[status(thm)],[])).
% 2.72/2.93 tff(10110,plain,
% 2.72/2.93 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(z), z)) | (~b(s(z), s(s(s(elem!1))))) | (~b(s(s(elem!1)), z)) | (~b(s(z), s(s(z)))) | (~b(s(s(z)), s(s(s(elem!1)))))),
% 2.72/2.93 inference(modus_ponens,[status(thm)],[10109, 10108])).
% 2.72/2.93 tff(10111,plain,
% 2.72/2.93 ($false),
% 2.72/2.93 inference(unit_resolution,[status(thm)],[10110, 166, 10104, 9949, 53, 10035, 10094, 10038])).
% 2.72/2.93 tff(10112,plain,((~b(s(z), z)) | (~b(s(z), s(s(elem!1)))) | (~r(z, s(s(z)))) | (~r(s(s(s(elem!1))), s(z))) | (s(s(z)) = s(s(elem!1))) | (~r(z, s(z))) | (~r(s(s(elem!1)), s(z)))), inference(lemma,lemma(discharge,[]))).
% 2.72/2.93 tff(10113,plain,
% 2.72/2.93 (~b(s(z), z)),
% 2.72/2.93 inference(unit_resolution,[status(thm)],[10112, 52, 152, 9727, 9812, 8408, 9822])).
% 2.72/2.93 tff(10114,plain,
% 2.72/2.93 (r(s(z), z)),
% 2.72/2.93 inference(unit_resolution,[status(thm)],[230, 10113])).
% 2.72/2.93 tff(10115,plain,
% 2.72/2.93 (~r(s(s(z)), s(z))),
% 2.72/2.93 inference(unit_resolution,[status(thm)],[2680, 10114, 152, 8408])).
% 2.72/2.93 tff(10116,plain,
% 2.72/2.93 (b(s(s(z)), s(z))),
% 2.72/2.93 inference(unit_resolution,[status(thm)],[308, 10115])).
% 2.72/2.93 tff(10117,plain,
% 2.72/2.93 (~r(s(s(s(elem!1))), z)),
% 2.72/2.93 inference(unit_resolution,[status(thm)],[5698, 10114, 152, 9727])).
% 2.72/2.93 tff(10118,plain,
% 2.72/2.93 (b(s(s(s(elem!1))), z)),
% 2.72/2.93 inference(unit_resolution,[status(thm)],[94, 10117])).
% 2.72/2.93 tff(10119,plain,
% 2.72/2.93 (~r(z, s(s(s(elem!1))))),
% 2.72/2.93 inference(unit_resolution,[status(thm)],[2613, 10114, 8408, 9727])).
% 2.72/2.93 tff(10120,plain,
% 2.72/2.93 (b(z, s(s(s(elem!1))))),
% 2.72/2.93 inference(unit_resolution,[status(thm)],[261, 10119])).
% 2.72/2.93 tff(10121,plain,
% 2.72/2.93 (b(z, s(s(elem!1)))),
% 2.72/2.93 inference(unit_resolution,[status(thm)],[7965, 4577, 240, 350, 97])).
% 2.72/2.93 tff(10122,plain,
% 2.72/2.93 (~r(s(s(elem!1)), z)),
% 2.72/2.93 inference(unit_resolution,[status(thm)],[8490, 4577, 97, 323])).
% 2.72/2.93 tff(10123,plain,
% 2.72/2.93 (b(s(s(elem!1)), z)),
% 2.72/2.93 inference(unit_resolution,[status(thm)],[608, 10122])).
% 2.72/2.93 tff(10124,plain,
% 2.72/2.93 (~b(s(s(elem!1)), s(s(s(elem!1))))),
% 2.72/2.93 inference(unit_resolution,[status(thm)],[3593, 10123, 10121, 121])).
% 2.72/2.93 tff(10125,plain,
% 2.72/2.93 (r(s(s(elem!1)), s(s(s(elem!1))))),
% 2.72/2.93 inference(unit_resolution,[status(thm)],[461, 10124, 45])).
% 2.72/2.94 tff(10126,plain,
% 2.72/2.94 ($false),
% 2.72/2.94 inference(unit_resolution,[status(thm)],[7419, 197, 350, 4577, 97, 10125])).
% 2.72/2.94 tff(10127,plain,((~r(s(s(elem!1)), s(z))) | (~r(s(s(s(elem!1))), s(z))) | (~r(s(z), z)) | (s(s(elem!1)) = s(s(s(elem!1)))) | (~b(s(s(s(elem!1))), z)) | (~r(z, s(z))) | (~b(z, s(s(s(elem!1)))))), inference(lemma,lemma(discharge,[]))).
% 2.72/2.94 tff(10128,plain,
% 2.72/2.94 (s(s(elem!1)) = s(s(s(elem!1)))),
% 2.72/2.94 inference(unit_resolution,[status(thm)],[10127, 10118, 8408, 9727, 9822, 10114, 10120])).
% 2.72/2.94 tff(10129,plain,
% 2.72/2.94 (~b(s(s(z)), z)),
% 2.72/2.94 inference(unit_resolution,[status(thm)],[8117, 10128, 152, 9727, 10114, 10120, 10116, 10118])).
% 2.72/2.94 tff(10130,plain,
% 2.72/2.94 (r(s(s(z)), z)),
% 2.72/2.94 inference(unit_resolution,[status(thm)],[186, 10129])).
% 2.72/2.94 tff(10131,plain,
% 2.72/2.94 (~r(s(s(s(z))), z)),
% 2.72/2.94 inference(unit_resolution,[status(thm)],[8122, 10130, 152, 10114, 10116])).
% 2.72/2.94 tff(10132,plain,
% 2.72/2.94 (b(s(s(s(z))), z)),
% 2.72/2.94 inference(unit_resolution,[status(thm)],[1713, 10131])).
% 2.72/2.94 tff(10133,plain,
% 2.72/2.94 (~b(s(s(s(elem!1))), s(s(s(z))))),
% 2.72/2.94 inference(unit_resolution,[status(thm)],[7286, 166, 10120, 10118, 10132])).
% 2.72/2.94 tff(10134,plain,
% 2.72/2.94 (r(s(s(s(elem!1))), s(s(s(z))))),
% 2.72/2.94 inference(unit_resolution,[status(thm)],[3574, 10133, 140])).
% 2.72/2.94 tff(10135,plain,
% 2.72/2.94 ((s(s(elem!1)) = s(s(s(s(elem!1))))) <=> (s(s(s(elem!1))) = s(s(s(s(elem!1)))))),
% 2.72/2.94 inference(monotonicity,[status(thm)],[10128])).
% 2.72/2.94 tff(10136,plain,
% 2.72/2.94 ((s(s(s(elem!1))) = s(s(s(s(elem!1))))) <=> (s(s(elem!1)) = s(s(s(s(elem!1)))))),
% 2.72/2.94 inference(symmetry,[status(thm)],[10135])).
% 2.72/2.94 tff(10137,plain,
% 2.72/2.94 (s(s(s(elem!1))) = s(elem!1)),
% 2.72/2.94 inference(unit_resolution,[status(thm)],[2594, 10128])).
% 2.72/2.94 tff(10138,plain,
% 2.72/2.94 ($false),
% 2.72/2.94 inference(unit_resolution,[status(thm)],[767, 3649])).
% 2.72/2.94 tff(10139,plain,((~(s(s(s(elem!1))) = s(elem!1))) | (s(s(elem!1)) = elem!1)), inference(lemma,lemma(discharge,[]))).
% 2.72/2.94 tff(10140,plain,
% 2.72/2.94 (s(s(elem!1)) = elem!1),
% 2.72/2.94 inference(unit_resolution,[status(thm)],[10139, 10137])).
% 2.72/2.94 tff(10141,plain,
% 2.72/2.94 (b(s(s(elem!1)), s(z)) <=> b(elem!1, s(z))),
% 2.72/2.94 inference(monotonicity,[status(thm)],[2559])).
% 2.72/2.94 tff(10142,plain,
% 2.72/2.94 (b(elem!1, s(z)) <=> b(s(s(elem!1)), s(z))),
% 2.72/2.94 inference(symmetry,[status(thm)],[10141])).
% 2.72/2.94 tff(10143,plain,
% 2.72/2.94 (b(s(s(elem!1)), s(z))),
% 2.72/2.94 inference(modus_ponens,[status(thm)],[1212, 10142])).
% 2.72/2.94 tff(10144,plain,
% 2.72/2.94 ($false),
% 2.72/2.94 inference(unit_resolution,[status(thm)],[4568, 10143])).
% 2.72/2.94 tff(10145,plain,((~(s(s(elem!1)) = elem!1)) | b(s(s(elem!1)), s(z)) | (~b(elem!1, s(z)))), inference(lemma,lemma(discharge,[]))).
% 2.72/2.94 tff(10146,plain,
% 2.72/2.94 (~b(elem!1, s(z))),
% 2.72/2.94 inference(unit_resolution,[status(thm)],[10145, 10140, 9821])).
% 2.72/2.94 tff(10147,plain,
% 2.72/2.94 (b(s(s(s(s(elem!1)))), s(z)) <=> b(s(s(s(elem!1))), s(z))),
% 2.72/2.94 inference(monotonicity,[status(thm)],[6471])).
% 2.72/2.94 tff(10148,plain,
% 2.72/2.94 (b(s(s(s(elem!1))), s(z)) <=> b(s(s(s(s(elem!1)))), s(z))),
% 2.72/2.94 inference(symmetry,[status(thm)],[10147])).
% 2.72/2.94 tff(10149,plain,
% 2.72/2.94 ((~b(s(s(s(elem!1))), s(z))) <=> (~b(s(s(s(s(elem!1)))), s(z)))),
% 2.72/2.94 inference(monotonicity,[status(thm)],[10148])).
% 2.72/2.94 tff(10150,plain,
% 2.72/2.94 (s(s(elem!1)) = elem!1),
% 2.72/2.94 inference(unit_resolution,[status(thm)],[10139, 3115])).
% 2.72/2.94 tff(10151,plain,
% 2.72/2.94 (elem!1 = s(s(elem!1))),
% 2.72/2.94 inference(symmetry,[status(thm)],[10150])).
% 2.72/2.94 tff(10152,plain,
% 2.72/2.94 (elem!1 = s(s(s(elem!1)))),
% 2.72/2.94 inference(transitivity,[status(thm)],[10151, 334])).
% 2.72/2.94 tff(10153,plain,
% 2.72/2.94 (b(elem!1, s(z)) <=> b(s(s(s(elem!1))), s(z))),
% 2.72/2.94 inference(monotonicity,[status(thm)],[10152])).
% 2.72/2.94 tff(10154,plain,
% 2.72/2.94 ((~b(elem!1, s(z))) <=> (~b(s(s(s(elem!1))), s(z)))),
% 2.72/2.94 inference(monotonicity,[status(thm)],[10153])).
% 2.72/2.94 tff(10155,plain,
% 2.72/2.94 (~b(s(s(s(elem!1))), s(z))),
% 2.72/2.94 inference(modus_ponens,[status(thm)],[2527, 10154])).
% 2.72/2.94 tff(10156,plain,
% 2.72/2.94 (~b(s(s(s(s(elem!1)))), s(z))),
% 2.72/2.94 inference(modus_ponens,[status(thm)],[10155, 10149])).
% 2.72/2.94 tff(10157,plain,
% 2.72/2.94 ($false),
% 2.72/2.94 inference(unit_resolution,[status(thm)],[1402, 10156])).
% 2.72/2.94 tff(10158,plain,((~(s(s(elem!1)) = s(s(s(elem!1))))) | (~b(s(s(s(s(elem!1)))), s(z))) | b(elem!1, s(z))), inference(lemma,lemma(discharge,[]))).
% 2.72/2.94 tff(10159,plain,
% 2.72/2.94 (~b(s(s(s(s(elem!1)))), s(z))),
% 2.72/2.94 inference(unit_resolution,[status(thm)],[10158, 10146, 10128])).
% 2.72/2.94 tff(10160,plain,
% 2.72/2.94 (r(s(s(s(s(elem!1)))), s(z))),
% 2.72/2.94 inference(unit_resolution,[status(thm)],[661, 10159])).
% 2.72/2.94 tff(10161,plain,
% 2.72/2.94 (s(s(s(s(elem!1)))) = s(s(s(elem!1)))),
% 2.72/2.94 inference(unit_resolution,[status(thm)],[2669, 10160, 8408, 9727, 10114])).
% 2.72/2.94 tff(10162,plain,
% 2.72/2.94 (s(s(s(elem!1))) = s(s(s(s(elem!1))))),
% 2.72/2.94 inference(unit_resolution,[status(thm)],[363, 10161])).
% 2.72/2.94 tff(10163,plain,
% 2.72/2.94 (s(s(elem!1)) = s(s(s(s(elem!1))))),
% 2.72/2.94 inference(modus_ponens,[status(thm)],[10162, 10136])).
% 2.72/2.94 tff(10164,plain,
% 2.72/2.94 (~(elem!1 = s(s(s(s(z)))))),
% 2.72/2.94 inference(unit_resolution,[status(thm)],[5489, 10163])).
% 2.72/2.94 tff(10165,plain,
% 2.72/2.94 (s(elem!1) = s(s(s(elem!1)))),
% 2.72/2.94 inference(symmetry,[status(thm)],[10137])).
% 2.72/2.94 tff(10166,plain,
% 2.72/2.94 (inj_0(s(elem!1)) = inj_0(s(s(s(elem!1))))),
% 2.72/2.94 inference(monotonicity,[status(thm)],[10165])).
% 2.72/2.94 tff(10167,plain,
% 2.72/2.94 (elem!1 = s(s(s(elem!1)))),
% 2.72/2.94 inference(transitivity,[status(thm)],[1170, 10166, 104, 10128])).
% 2.72/2.94 tff(10168,plain,
% 2.72/2.94 (b(elem!1, s(s(s(s(z))))) <=> b(s(s(s(elem!1))), s(s(s(s(z)))))),
% 2.72/2.94 inference(monotonicity,[status(thm)],[10167])).
% 2.72/2.94 tff(10169,plain,
% 2.72/2.94 (b(s(s(s(elem!1))), s(s(s(s(z))))) <=> b(elem!1, s(s(s(s(z)))))),
% 2.72/2.94 inference(symmetry,[status(thm)],[10168])).
% 2.72/2.94 tff(10170,plain,
% 2.72/2.94 ((~b(s(s(s(elem!1))), s(s(s(s(z)))))) <=> (~b(elem!1, s(s(s(s(z))))))),
% 2.72/2.94 inference(monotonicity,[status(thm)],[10169])).
% 2.72/2.94 tff(10171,plain,
% 2.72/2.94 (~r(s(z), s(s(z)))),
% 2.72/2.94 inference(unit_resolution,[status(thm)],[2959, 10130, 152, 8408])).
% 2.72/2.94 tff(10172,plain,
% 2.72/2.94 (b(s(z), s(s(z)))),
% 2.72/2.94 inference(unit_resolution,[status(thm)],[427, 10171])).
% 2.72/2.94 tff(10173,plain,
% 2.72/2.94 (~r(s(s(s(s(z)))), z)),
% 2.72/2.94 inference(unit_resolution,[status(thm)],[7728, 10172, 152, 10114, 10116, 10130])).
% 2.72/2.94 tff(10174,plain,
% 2.72/2.94 (b(s(s(s(s(z)))), z)),
% 2.72/2.94 inference(unit_resolution,[status(thm)],[3266, 10173])).
% 2.72/2.94 tff(10175,plain,
% 2.72/2.94 (~b(s(s(s(elem!1))), s(s(s(s(z)))))),
% 2.72/2.94 inference(unit_resolution,[status(thm)],[8159, 166, 10120, 10118, 10174])).
% 2.72/2.94 tff(10176,plain,
% 2.72/2.94 (~b(elem!1, s(s(s(s(z)))))),
% 2.72/2.94 inference(modus_ponens,[status(thm)],[10175, 10170])).
% 2.72/2.94 tff(10177,plain,
% 2.72/2.94 (r(elem!1, s(s(s(s(z)))))),
% 2.72/2.94 inference(unit_resolution,[status(thm)],[1098, 10176, 10164])).
% 2.72/2.94 tff(10178,plain,
% 2.72/2.94 (r(s(s(s(elem!1))), s(s(s(s(z)))))),
% 2.72/2.94 inference(unit_resolution,[status(thm)],[5665, 10177, 10128])).
% 2.72/2.94 tff(10179,plain,
% 2.72/2.94 (~b(s(s(s(s(z)))), s(s(s(z))))),
% 2.72/2.94 inference(unit_resolution,[status(thm)],[8134, 166, 10120, 10118, 10132, 10174])).
% 2.72/2.94 tff(10180,plain,
% 2.72/2.94 (r(s(s(s(s(z)))), s(s(s(z))))),
% 2.72/2.94 inference(unit_resolution,[status(thm)],[4662, 10179])).
% 2.72/2.94 tff(10181,plain,
% 2.72/2.94 (~b(s(s(s(z))), s(s(s(s(z)))))),
% 2.72/2.94 inference(unit_resolution,[status(thm)],[7772, 10174, 10120, 10118, 10132])).
% 2.72/2.94 tff(10182,plain,
% 2.72/2.94 (r(s(s(s(z))), s(s(s(s(z)))))),
% 2.72/2.94 inference(unit_resolution,[status(thm)],[2233, 10181])).
% 2.72/2.94 tff(10183,plain,
% 2.72/2.94 ($false),
% 2.72/2.94 inference(unit_resolution,[status(thm)],[9322, 197, 10182, 10180, 10178, 10134])).
% 2.72/2.94 tff(10184,plain,((s(s(z)) = s(s(elem!1))) | b(z, s(s(z)))), inference(lemma,lemma(discharge,[]))).
% 2.72/2.94 tff(10185,plain,
% 2.72/2.94 (s(s(z)) = s(s(elem!1))),
% 2.72/2.94 inference(unit_resolution,[status(thm)],[10184, 125])).
% 2.72/2.94 tff(10186,plain,
% 2.72/2.94 ((s(s(s(s(elem!1)))) = s(s(z))) <=> (s(s(s(s(elem!1)))) = s(s(elem!1)))),
% 2.72/2.94 inference(monotonicity,[status(thm)],[10185])).
% 2.72/2.94 tff(10187,plain,
% 2.72/2.94 ((s(s(s(s(elem!1)))) = s(s(z))) <=> (s(s(elem!1)) = s(s(s(s(elem!1)))))),
% 2.72/2.94 inference(transitivity,[status(thm)],[10186, 123])).
% 2.72/2.94 tff(10188,plain,
% 2.72/2.94 ((s(s(s(s(elem!1)))) = s(s(z))) <=> (s(s(s(s(elem!1)))) = s(s(elem!1)))),
% 2.72/2.94 inference(transitivity,[status(thm)],[10187, 124])).
% 2.72/2.94 tff(10189,plain,
% 2.72/2.94 ((~(s(s(s(s(elem!1)))) = s(s(z)))) <=> (~(s(s(s(s(elem!1)))) = s(s(elem!1))))),
% 2.72/2.94 inference(monotonicity,[status(thm)],[10188])).
% 2.72/2.94 tff(10190,plain,
% 2.72/2.94 (~(s(s(s(s(elem!1)))) = s(s(elem!1)))),
% 2.72/2.94 inference(modus_ponens,[status(thm)],[733, 10189])).
% 2.72/2.94 tff(10191,plain,
% 2.72/2.94 ((s(s(z)) = s(s(s(elem!1)))) <=> (s(s(elem!1)) = s(s(s(elem!1))))),
% 2.72/2.94 inference(monotonicity,[status(thm)],[10185])).
% 2.72/2.94 tff(10192,plain,
% 2.72/2.94 ((~(s(s(z)) = s(s(s(elem!1))))) <=> (~(s(s(elem!1)) = s(s(s(elem!1)))))),
% 2.72/2.94 inference(monotonicity,[status(thm)],[10191])).
% 2.72/2.94 tff(10193,plain,
% 2.72/2.94 (~(s(s(elem!1)) = s(s(s(elem!1))))),
% 2.72/2.94 inference(modus_ponens,[status(thm)],[209, 10192])).
% 2.72/2.94 tff(10194,plain,
% 2.72/2.94 (s(elem!1) = s(z)),
% 2.72/2.94 inference(unit_resolution,[status(thm)],[43, 10185])).
% 2.72/2.94 tff(10195,plain,
% 2.72/2.94 (z = elem!1),
% 2.72/2.94 inference(unit_resolution,[status(thm)],[30, 10194])).
% 2.72/2.94 tff(10196,plain,
% 2.72/2.94 (b(s(z), z) <=> b(s(z), elem!1)),
% 2.72/2.94 inference(monotonicity,[status(thm)],[10195])).
% 2.72/2.94 tff(10197,plain,
% 2.72/2.94 (~(s(s(s(s(s(s(elem!1)))))) = elem!1)),
% 2.72/2.94 inference(unit_resolution,[status(thm)],[4897, 10195])).
% 2.72/2.94 tff(10198,plain,
% 2.72/2.94 (elem!1 = z),
% 2.72/2.94 inference(symmetry,[status(thm)],[10195])).
% 2.72/2.94 tff(10199,plain,
% 2.72/2.94 ((s(s(elem!1)) = elem!1) <=> (s(s(elem!1)) = z)),
% 2.72/2.94 inference(monotonicity,[status(thm)],[10198])).
% 2.72/2.94 tff(10200,plain,
% 2.72/2.94 ((s(s(elem!1)) = z) <=> (s(s(elem!1)) = elem!1)),
% 2.72/2.94 inference(symmetry,[status(thm)],[10199])).
% 2.72/2.94 tff(10201,plain,
% 2.72/2.94 ((~(s(s(elem!1)) = z)) <=> (~(s(s(elem!1)) = elem!1))),
% 2.72/2.94 inference(monotonicity,[status(thm)],[10200])).
% 2.72/2.94 tff(10202,plain,
% 2.72/2.94 (~(s(s(elem!1)) = elem!1)),
% 2.72/2.94 inference(modus_ponens,[status(thm)],[108, 10201])).
% 2.72/2.94 tff(10203,plain,
% 2.72/2.94 ((s(s(s(elem!1))) = z) <=> (s(s(s(elem!1))) = elem!1)),
% 2.72/2.94 inference(monotonicity,[status(thm)],[10195])).
% 2.72/2.94 tff(10204,plain,
% 2.72/2.94 ((s(s(s(elem!1))) = z) <=> (elem!1 = s(s(s(elem!1))))),
% 2.72/2.94 inference(transitivity,[status(thm)],[10203, 5406])).
% 2.72/2.94 tff(10205,plain,
% 2.72/2.94 ((~(s(s(s(elem!1))) = z)) <=> (~(elem!1 = s(s(s(elem!1)))))),
% 2.72/2.94 inference(monotonicity,[status(thm)],[10204])).
% 2.72/2.94 tff(10206,plain,
% 2.72/2.94 (~(elem!1 = s(s(s(elem!1))))),
% 2.72/2.94 inference(modus_ponens,[status(thm)],[89, 10205])).
% 2.72/2.94 tff(10207,plain,
% 2.72/2.94 (~r(z, s(s(s(elem!1))))),
% 2.72/2.94 inference(unit_resolution,[status(thm)],[2613, 97, 8408, 9727])).
% 2.72/2.94 tff(10208,plain,
% 2.72/2.94 (~r(elem!1, s(s(s(elem!1))))),
% 2.72/2.94 inference(unit_resolution,[status(thm)],[5446, 10207, 10195])).
% 2.72/2.94 tff(10209,plain,
% 2.72/2.94 (b(elem!1, s(s(s(elem!1))))),
% 2.72/2.94 inference(unit_resolution,[status(thm)],[5451, 10208, 10206])).
% 2.72/2.94 tff(10210,plain,
% 2.72/2.94 (b(s(s(s(elem!1))), elem!1)),
% 2.72/2.94 inference(unit_resolution,[status(thm)],[634, 121, 10195])).
% 2.72/2.94 tff(10211,plain,
% 2.72/2.94 ((s(s(z)) = s(s(s(elem!1)))) <=> (s(s(s(elem!1))) = s(s(elem!1)))),
% 2.72/2.94 inference(transitivity,[status(thm)],[10191, 3341])).
% 2.72/2.94 tff(10212,plain,
% 2.72/2.94 ((~(s(s(z)) = s(s(s(elem!1))))) <=> (~(s(s(s(elem!1))) = s(s(elem!1))))),
% 2.72/2.94 inference(monotonicity,[status(thm)],[10211])).
% 2.72/2.94 tff(10213,plain,
% 2.72/2.94 (~(s(s(s(elem!1))) = s(s(elem!1)))),
% 2.72/2.94 inference(modus_ponens,[status(thm)],[209, 10212])).
% 2.72/2.94 tff(10214,plain,
% 2.72/2.94 (s(s(s(z))) = s(s(s(elem!1)))),
% 2.72/2.94 inference(monotonicity,[status(thm)],[10185])).
% 2.72/2.94 tff(10215,plain,
% 2.72/2.94 ((s(s(s(s(elem!1)))) = s(s(s(z)))) <=> (s(s(s(s(elem!1)))) = s(s(s(elem!1))))),
% 2.72/2.94 inference(monotonicity,[status(thm)],[10214])).
% 2.72/2.94 tff(10216,plain,
% 2.72/2.94 ((s(s(s(s(elem!1)))) = s(s(s(z)))) <=> (s(s(s(elem!1))) = s(s(s(s(elem!1)))))),
% 2.72/2.94 inference(transitivity,[status(thm)],[10215, 1191])).
% 2.72/2.94 tff(10217,plain,
% 2.72/2.94 ((~(s(s(s(s(elem!1)))) = s(s(s(z))))) <=> (~(s(s(s(elem!1))) = s(s(s(s(elem!1))))))),
% 2.72/2.94 inference(monotonicity,[status(thm)],[10216])).
% 2.72/2.94 tff(10218,plain,
% 2.72/2.94 (~(s(s(s(elem!1))) = s(s(s(s(elem!1)))))),
% 2.72/2.94 inference(modus_ponens,[status(thm)],[5112, 10217])).
% 2.72/2.94 tff(10219,plain,
% 2.72/2.94 (~b(z, s(s(elem!1)))),
% 2.72/2.94 inference(unit_resolution,[status(thm)],[2261, 10185, 125])).
% 2.72/2.94 tff(10220,plain,
% 2.72/2.94 (r(z, s(s(elem!1)))),
% 2.72/2.94 inference(unit_resolution,[status(thm)],[1795, 10219])).
% 2.72/2.94 tff(10221,plain,
% 2.72/2.94 (~r(s(s(elem!1)), s(z))),
% 2.72/2.94 inference(unit_resolution,[status(thm)],[8426, 97, 8408, 10220])).
% 2.72/2.94 tff(10222,plain,
% 2.72/2.94 (b(s(s(elem!1)), s(z))),
% 2.72/2.94 inference(unit_resolution,[status(thm)],[1912, 10221])).
% 2.72/2.94 tff(10223,plain,
% 2.72/2.94 (~r(s(s(elem!1)), s(s(s(elem!1))))),
% 2.72/2.94 inference(unit_resolution,[status(thm)],[2919, 10222, 125, 8408, 9727, 10218, 97, 10213])).
% 2.72/2.94 tff(10224,plain,
% 2.72/2.94 (b(s(s(elem!1)), s(s(s(elem!1))))),
% 2.72/2.94 inference(unit_resolution,[status(thm)],[461, 10223, 10193])).
% 2.72/2.94 tff(10225,plain,
% 2.72/2.94 (~b(s(s(elem!1)), elem!1)),
% 2.72/2.94 inference(unit_resolution,[status(thm)],[794, 10224, 10210, 10209])).
% 2.72/2.94 tff(10226,plain,
% 2.72/2.94 (r(s(s(elem!1)), elem!1)),
% 2.72/2.94 inference(unit_resolution,[status(thm)],[784, 10225, 10202])).
% 2.72/2.94 tff(10227,plain,
% 2.72/2.94 (~(s(s(s(s(s(s(elem!1)))))) = s(s(elem!1)))),
% 2.72/2.94 inference(unit_resolution,[status(thm)],[4986, 10194])).
% 2.72/2.94 tff(10228,plain,
% 2.72/2.94 (r(elem!1, s(z))),
% 2.72/2.94 inference(unit_resolution,[status(thm)],[741, 10195, 8408])).
% 2.72/2.94 tff(10229,plain,
% 2.72/2.94 (r(s(z), z) <=> r(s(z), elem!1)),
% 2.72/2.94 inference(monotonicity,[status(thm)],[10195])).
% 2.72/2.94 tff(10230,plain,
% 2.72/2.94 (r(s(z), elem!1)),
% 2.72/2.94 inference(modus_ponens,[status(thm)],[97, 10229])).
% 2.72/2.94 tff(10231,plain,
% 2.72/2.94 (~r(s(s(s(s(s(s(elem!1)))))), elem!1)),
% 2.72/2.94 inference(unit_resolution,[status(thm)],[9205, 10230, 9812, 10228, 10222, 10227, 10226])).
% 2.72/2.94 tff(10232,plain,
% 2.72/2.94 (b(s(s(s(s(s(s(elem!1)))))), elem!1)),
% 2.72/2.94 inference(unit_resolution,[status(thm)],[9214, 10231, 10197])).
% 2.72/2.94 tff(10233,plain,
% 2.72/2.94 ((s(s(s(s(elem!1)))) = z) <=> (s(s(s(s(elem!1)))) = elem!1)),
% 2.72/2.94 inference(monotonicity,[status(thm)],[10195])).
% 2.72/2.94 tff(10234,plain,
% 2.72/2.94 ((~(s(s(s(s(elem!1)))) = z)) <=> (~(s(s(s(s(elem!1)))) = elem!1))),
% 2.72/2.94 inference(monotonicity,[status(thm)],[10233])).
% 2.72/2.94 tff(10235,plain,
% 2.72/2.94 (~(s(s(s(s(elem!1)))) = elem!1)),
% 2.72/2.94 inference(modus_ponens,[status(thm)],[626, 10234])).
% 2.72/2.94 tff(10236,plain,
% 2.72/2.94 ((~(s(s(s(s(elem!1)))) = s(s(z)))) <=> (~(s(s(elem!1)) = s(s(s(s(elem!1))))))),
% 2.72/2.94 inference(monotonicity,[status(thm)],[10187])).
% 2.72/2.94 tff(10237,plain,
% 2.72/2.94 (~(s(s(elem!1)) = s(s(s(s(elem!1)))))),
% 2.72/2.94 inference(modus_ponens,[status(thm)],[733, 10236])).
% 2.72/2.94 tff(10238,plain,
% 2.72/2.94 ((s(s(s(s(elem!1)))) = s(s(s(z)))) <=> (s(s(s(s(elem!1)))) = s(s(s(elem!1))))),
% 2.72/2.94 inference(transitivity,[status(thm)],[10216, 3797])).
% 2.72/2.94 tff(10239,plain,
% 2.72/2.94 ((~(s(s(s(s(elem!1)))) = s(s(s(z))))) <=> (~(s(s(s(s(elem!1)))) = s(s(s(elem!1)))))),
% 2.72/2.94 inference(monotonicity,[status(thm)],[10238])).
% 2.72/2.94 tff(10240,plain,
% 2.72/2.94 (~(s(s(s(s(elem!1)))) = s(s(s(elem!1))))),
% 2.72/2.94 inference(modus_ponens,[status(thm)],[5112, 10239])).
% 2.72/2.94 tff(10241,plain,
% 2.72/2.94 (~r(s(s(s(s(elem!1)))), s(z))),
% 2.72/2.94 inference(unit_resolution,[status(thm)],[2669, 97, 8408, 9727, 10240])).
% 2.72/2.94 tff(10242,plain,
% 2.72/2.94 (b(s(s(s(s(elem!1)))), s(z))),
% 2.72/2.94 inference(unit_resolution,[status(thm)],[661, 10241])).
% 2.72/2.94 tff(10243,plain,
% 2.72/2.94 (~b(s(s(elem!1)), s(s(s(s(elem!1)))))),
% 2.72/2.94 inference(unit_resolution,[status(thm)],[1410, 10224, 9812, 10222, 10242])).
% 2.72/2.94 tff(10244,plain,
% 2.72/2.94 (r(s(s(elem!1)), s(s(s(s(elem!1)))))),
% 2.72/2.94 inference(unit_resolution,[status(thm)],[827, 10243, 10237])).
% 2.72/2.94 tff(10245,plain,
% 2.72/2.94 (~r(s(s(s(s(elem!1)))), elem!1)),
% 2.72/2.94 inference(unit_resolution,[status(thm)],[9687, 10244, 10226, 10228])).
% 2.72/2.94 tff(10246,plain,
% 2.72/2.94 (b(s(s(s(s(elem!1)))), elem!1)),
% 2.72/2.94 inference(unit_resolution,[status(thm)],[719, 10245, 10235])).
% 2.72/2.94 tff(10247,plain,
% 2.72/2.94 (~b(s(s(s(s(elem!1)))), s(s(s(s(s(s(elem!1)))))))),
% 2.72/2.94 inference(unit_resolution,[status(thm)],[9233, 166, 10209, 10210, 10246, 10232])).
% 2.72/2.94 tff(10248,plain,
% 2.72/2.94 (~(s(s(s(s(elem!1)))) = s(s(s(s(s(s(elem!1)))))))),
% 2.72/2.94 inference(unit_resolution,[status(thm)],[9243, 10237])).
% 2.72/2.94 tff(10249,plain,
% 2.72/2.94 (s(s(s(s(z)))) = s(s(s(s(elem!1))))),
% 2.72/2.94 inference(monotonicity,[status(thm)],[10214])).
% 2.72/2.94 tff(10250,plain,
% 2.72/2.94 (s(s(s(s(elem!1)))) = s(s(s(s(z))))),
% 2.72/2.94 inference(symmetry,[status(thm)],[10249])).
% 2.72/2.94 tff(10251,plain,
% 2.72/2.94 (r(s(s(s(elem!1))), s(s(s(s(elem!1))))) <=> r(s(s(s(elem!1))), s(s(s(s(z)))))),
% 2.72/2.94 inference(monotonicity,[status(thm)],[10250])).
% 2.72/2.94 tff(10252,plain,
% 2.72/2.94 (r(s(s(s(elem!1))), s(s(s(s(z))))) <=> r(s(s(s(elem!1))), s(s(s(s(elem!1)))))),
% 2.72/2.94 inference(symmetry,[status(thm)],[10251])).
% 2.72/2.94 tff(10253,plain,
% 2.72/2.94 (r(s(s(s(z))), s(s(s(s(z))))) <=> r(s(s(s(elem!1))), s(s(s(s(z)))))),
% 2.72/2.94 inference(monotonicity,[status(thm)],[10214])).
% 2.72/2.94 tff(10254,plain,
% 2.72/2.94 (r(s(s(s(z))), s(s(s(s(z))))) <=> r(s(s(s(elem!1))), s(s(s(s(elem!1)))))),
% 2.72/2.94 inference(transitivity,[status(thm)],[10253, 10252])).
% 2.72/2.94 tff(10255,plain,
% 2.72/2.94 (~b(s(s(z)), z)),
% 2.72/2.94 inference(unit_resolution,[status(thm)],[8754, 10225, 10185])).
% 2.72/2.94 tff(10256,plain,
% 2.72/2.94 (r(s(s(z)), z)),
% 2.72/2.94 inference(unit_resolution,[status(thm)],[186, 10255])).
% 2.72/2.94 tff(10257,plain,
% 2.72/2.94 (~r(s(s(s(z))), z)),
% 2.72/2.94 inference(unit_resolution,[status(thm)],[8122, 10256, 152, 97, 8410])).
% 2.72/2.94 tff(10258,plain,
% 2.72/2.94 (b(s(s(s(z))), z)),
% 2.72/2.94 inference(unit_resolution,[status(thm)],[1713, 10257])).
% 2.72/2.94 tff(10259,plain,
% 2.72/2.94 (b(z, s(s(s(elem!1))))),
% 2.72/2.94 inference(unit_resolution,[status(thm)],[261, 10207])).
% 2.72/2.94 tff(10260,plain,
% 2.72/2.94 (b(s(z), s(s(z)))),
% 2.72/2.94 inference(unit_resolution,[status(thm)],[5435, 10185, 9812])).
% 2.72/2.94 tff(10261,plain,
% 2.72/2.94 (~r(s(s(s(s(z)))), z)),
% 2.72/2.94 inference(unit_resolution,[status(thm)],[7728, 10256, 152, 10260, 97, 8410])).
% 2.72/2.94 tff(10262,plain,
% 2.72/2.94 (b(s(s(s(s(z)))), z)),
% 2.72/2.94 inference(unit_resolution,[status(thm)],[3266, 10261])).
% 2.72/2.94 tff(10263,plain,
% 2.72/2.94 (~b(s(s(s(z))), s(s(s(s(z)))))),
% 2.72/2.94 inference(unit_resolution,[status(thm)],[7772, 10262, 10259, 121, 10258])).
% 2.72/2.94 tff(10264,plain,
% 2.72/2.94 (r(s(s(s(z))), s(s(s(s(z)))))),
% 2.72/2.94 inference(unit_resolution,[status(thm)],[2233, 10263])).
% 2.72/2.94 tff(10265,plain,
% 2.72/2.94 (r(s(s(s(elem!1))), s(s(s(s(elem!1)))))),
% 2.72/2.94 inference(modus_ponens,[status(thm)],[10264, 10254])).
% 2.72/2.94 tff(10266,plain,
% 2.72/2.94 (~b(s(s(s(s(elem!1)))), s(s(elem!1)))),
% 2.72/2.94 inference(unit_resolution,[status(thm)],[804, 166, 9812, 10222, 10242])).
% 2.72/2.94 tff(10267,plain,
% 2.72/2.94 (r(s(s(s(s(elem!1)))), s(s(elem!1)))),
% 2.72/2.94 inference(unit_resolution,[status(thm)],[813, 10266, 10190])).
% 2.72/2.94 tff(10268,plain,
% 2.72/2.94 (~r(s(s(s(elem!1))), s(s(elem!1)))),
% 2.72/2.94 inference(unit_resolution,[status(thm)],[9122, 197, 10244, 10267, 10265])).
% 2.72/2.94 tff(10269,plain,
% 2.72/2.94 (b(s(s(s(elem!1))), s(s(elem!1)))),
% 2.72/2.94 inference(unit_resolution,[status(thm)],[889, 10268, 10213])).
% 2.72/2.94 tff(10270,assumption,(b(s(s(s(s(s(s(elem!1)))))), s(s(s(elem!1))))), introduced(assumption)).
% 2.72/2.94 tff(10271,assumption,(b(s(s(s(s(s(s(elem!1)))))), elem!1)), introduced(assumption)).
% 2.72/2.94 tff(10272,plain,
% 2.72/2.94 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), 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)))))), s(s(s(elem!1))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), 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)))))), s(s(s(elem!1))))))),
% 2.72/2.94 inference(rewrite,[status(thm)],[])).
% 2.72/2.94 tff(10273,plain,
% 2.72/2.94 (((~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(s(elem!1))), s(s(elem!1)))) | (~b(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(elem!1)))))), elem!1))) <=> ((~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(elem!1, s(s(s(elem!1))))) | (~b(s(s(s(s(s(s(elem!1)))))), elem!1)) | (~b(s(s(s(s(s(s(elem!1)))))), s(s(s(elem!1))))))),
% 2.72/2.94 inference(rewrite,[status(thm)],[])).
% 2.72/2.94 tff(10274,plain,
% 2.72/2.94 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(s(s(s(s(s(s(elem!1)))))), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(elem!1, s(s(s(elem!1))))) | (~b(s(s(s(s(s(s(elem!1)))))), s(s(s(elem!1))))) | (~b(s(s(s(s(s(s(elem!1)))))), elem!1)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), 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)))))), s(s(s(elem!1)))))))),
% 2.72/2.94 inference(monotonicity,[status(thm)],[10273])).
% 2.72/2.94 tff(10275,plain,
% 2.72/2.94 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(s(s(s(s(s(s(elem!1)))))), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(elem!1, s(s(s(elem!1))))) | (~b(s(s(s(s(s(s(elem!1)))))), s(s(s(elem!1))))) | (~b(s(s(s(s(s(s(elem!1)))))), elem!1)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), 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)))))), s(s(s(elem!1))))))),
% 2.72/2.94 inference(transitivity,[status(thm)],[10274, 10272])).
% 2.72/2.94 tff(10276,plain,
% 2.72/2.94 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(s(s(s(s(s(s(elem!1)))))), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(elem!1, s(s(s(elem!1))))) | (~b(s(s(s(s(s(s(elem!1)))))), s(s(s(elem!1))))) | (~b(s(s(s(s(s(s(elem!1)))))), elem!1)))),
% 2.72/2.94 inference(quant_inst,[status(thm)],[])).
% 2.72/2.94 tff(10277,plain,
% 2.72/2.94 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(elem!1, s(s(s(elem!1))))) | (~b(s(s(s(s(s(s(elem!1)))))), elem!1)) | (~b(s(s(s(s(s(s(elem!1)))))), s(s(s(elem!1)))))),
% 2.72/2.94 inference(modus_ponens,[status(thm)],[10276, 10275])).
% 2.72/2.94 tff(10278,plain,
% 2.72/2.94 ($false),
% 2.72/2.94 inference(unit_resolution,[status(thm)],[10277, 166, 463, 839, 643, 10271, 10270])).
% 2.72/2.94 tff(10279,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(s(elem!1))), s(s(elem!1)))) | (~b(elem!1, s(s(s(elem!1))))) | (~b(s(s(s(s(s(s(elem!1)))))), elem!1))), inference(lemma,lemma(discharge,[]))).
% 2.72/2.94 tff(10280,plain,
% 2.72/2.94 (~b(s(s(s(s(s(s(elem!1)))))), s(s(s(elem!1))))),
% 2.72/2.94 inference(unit_resolution,[status(thm)],[10279, 10224, 10269, 10209, 10232])).
% 2.72/2.94 tff(10281,plain,
% 2.72/2.94 (~(s(s(s(s(s(s(elem!1)))))) = s(s(s(elem!1))))),
% 2.72/2.94 inference(unit_resolution,[status(thm)],[4922, 10194])).
% 2.72/2.94 tff(10282,plain,
% 2.72/2.94 (r(s(s(s(s(s(s(elem!1)))))), s(s(s(elem!1))))),
% 2.72/2.94 inference(unit_resolution,[status(thm)],[9226, 79, 10281, 10280])).
% 2.72/2.94 tff(10283,plain,
% 2.72/2.94 (~b(s(s(s(s(elem!1)))), s(s(s(elem!1))))),
% 2.72/2.94 inference(unit_resolution,[status(thm)],[7737, 166, 10209, 10210, 10246])).
% 2.72/2.94 tff(10284,plain,
% 2.72/2.94 (r(s(s(s(s(elem!1)))), s(s(s(elem!1))))),
% 2.72/2.94 inference(unit_resolution,[status(thm)],[1065, 10283, 10240])).
% 2.72/2.94 tff(10285,plain,
% 2.72/2.94 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), s(z))) | (~r(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~r(s(s(s(s(elem!1)))), s(s(s(s(s(s(elem!1)))))))) | (~r(s(s(s(s(s(s(elem!1)))))), s(s(s(elem!1))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(elem!1))), s(z))) | (~r(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~r(s(s(s(s(elem!1)))), s(s(s(s(s(s(elem!1)))))))) | (~r(s(s(s(s(s(s(elem!1)))))), s(s(s(elem!1))))))),
% 2.72/2.94 inference(rewrite,[status(thm)],[])).
% 2.72/2.94 tff(10286,plain,
% 2.72/2.94 (((~r(s(s(s(elem!1))), s(z))) | (~r(s(s(s(s(s(s(elem!1)))))), s(s(s(elem!1))))) | (~r(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~r(s(s(s(s(elem!1)))), s(s(s(s(s(s(elem!1))))))))) <=> ((~r(s(s(s(elem!1))), s(z))) | (~r(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~r(s(s(s(s(elem!1)))), s(s(s(s(s(s(elem!1)))))))) | (~r(s(s(s(s(s(s(elem!1)))))), s(s(s(elem!1))))))),
% 2.72/2.94 inference(rewrite,[status(thm)],[])).
% 2.72/2.94 tff(10287,plain,
% 2.72/2.94 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), s(z))) | (~r(s(s(s(s(s(s(elem!1)))))), s(s(s(elem!1))))) | (~r(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~r(s(s(s(s(elem!1)))), s(s(s(s(s(s(elem!1)))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), s(z))) | (~r(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~r(s(s(s(s(elem!1)))), s(s(s(s(s(s(elem!1)))))))) | (~r(s(s(s(s(s(s(elem!1)))))), s(s(s(elem!1)))))))),
% 2.72/2.94 inference(monotonicity,[status(thm)],[10286])).
% 2.72/2.95 tff(10288,plain,
% 2.72/2.95 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), s(z))) | (~r(s(s(s(s(s(s(elem!1)))))), s(s(s(elem!1))))) | (~r(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~r(s(s(s(s(elem!1)))), s(s(s(s(s(s(elem!1)))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(elem!1))), s(z))) | (~r(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~r(s(s(s(s(elem!1)))), s(s(s(s(s(s(elem!1)))))))) | (~r(s(s(s(s(s(s(elem!1)))))), s(s(s(elem!1))))))),
% 2.72/2.95 inference(transitivity,[status(thm)],[10287, 10285])).
% 2.72/2.95 tff(10289,plain,
% 2.72/2.95 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), s(z))) | (~r(s(s(s(s(s(s(elem!1)))))), s(s(s(elem!1))))) | (~r(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~r(s(s(s(s(elem!1)))), s(s(s(s(s(s(elem!1)))))))))),
% 2.72/2.95 inference(quant_inst,[status(thm)],[])).
% 2.72/2.95 tff(10290,plain,
% 2.72/2.95 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(elem!1))), s(z))) | (~r(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~r(s(s(s(s(elem!1)))), s(s(s(s(s(s(elem!1)))))))) | (~r(s(s(s(s(s(s(elem!1)))))), s(s(s(elem!1)))))),
% 2.72/2.95 inference(modus_ponens,[status(thm)],[10289, 10288])).
% 2.72/2.95 tff(10291,plain,
% 2.72/2.95 (~r(s(s(s(s(elem!1)))), s(s(s(s(s(s(elem!1)))))))),
% 2.72/2.95 inference(unit_resolution,[status(thm)],[10290, 197, 9727, 10284, 10282])).
% 2.72/2.95 tff(10292,plain,
% 2.72/2.95 ($false),
% 2.72/2.95 inference(unit_resolution,[status(thm)],[9247, 79, 10291, 10248, 10247])).
% 2.72/2.95 tff(10293,plain,((~r(s(z), z)) | (~b(s(s(s(elem!1))), z)) | b(z, s(s(z)))), inference(lemma,lemma(discharge,[]))).
% 2.72/2.95 tff(10294,plain,
% 2.72/2.95 (~r(s(z), z)),
% 2.72/2.95 inference(unit_resolution,[status(thm)],[10293, 121, 125])).
% 2.72/2.95 tff(10295,plain,
% 2.72/2.95 (b(s(z), z)),
% 2.72/2.95 inference(unit_resolution,[status(thm)],[230, 10294])).
% 2.72/2.95 tff(10296,plain,
% 2.72/2.95 (b(s(z), elem!1)),
% 2.72/2.95 inference(modus_ponens,[status(thm)],[10295, 10196])).
% 2.72/2.95 tff(10297,plain,
% 2.72/2.95 (~b(s(s(elem!1)), s(z))),
% 2.72/2.95 inference(unit_resolution,[status(thm)],[2253, 10295, 152, 8408, 10193])).
% 2.72/2.95 tff(10298,plain,
% 2.72/2.95 (r(s(s(elem!1)), s(z))),
% 2.72/2.95 inference(unit_resolution,[status(thm)],[1912, 10297])).
% 2.72/2.95 tff(10299,plain,
% 2.72/2.95 (~r(s(z), s(s(s(elem!1))))),
% 2.72/2.95 inference(unit_resolution,[status(thm)],[8626, 10298, 8408, 10220])).
% 2.72/2.95 tff(10300,plain,
% 2.72/2.95 (b(s(z), s(s(s(elem!1))))),
% 2.72/2.95 inference(unit_resolution,[status(thm)],[116, 10299])).
% 2.72/2.95 tff(10301,plain,
% 2.72/2.95 (~b(z, s(s(s(elem!1))))),
% 2.72/2.95 inference(unit_resolution,[status(thm)],[1470, 10300, 121, 10295])).
% 2.72/2.95 tff(10302,plain,
% 2.72/2.95 (r(z, s(s(s(elem!1))))),
% 2.72/2.95 inference(unit_resolution,[status(thm)],[261, 10301])).
% 2.72/2.95 tff(10303,plain,
% 2.72/2.95 (~r(s(z), s(s(s(s(elem!1)))))),
% 2.72/2.95 inference(unit_resolution,[status(thm)],[1480, 10302, 8408, 9727])).
% 2.72/2.95 tff(10304,plain,
% 2.72/2.95 (b(s(z), s(s(s(s(elem!1)))))),
% 2.72/2.95 inference(unit_resolution,[status(thm)],[681, 10303])).
% 2.72/2.95 tff(10305,plain,
% 2.72/2.95 (~r(s(s(elem!1)), s(s(s(elem!1))))),
% 2.72/2.95 inference(unit_resolution,[status(thm)],[9852, 10302, 9727, 10295, 9812])).
% 2.72/2.95 tff(10306,plain,
% 2.72/2.95 (r(s(s(s(elem!1))), s(s(elem!1)))),
% 2.72/2.95 inference(unit_resolution,[status(thm)],[6040, 10305, 10213, 9812, 10300])).
% 2.72/2.95 tff(10307,plain,
% 2.72/2.95 (~r(s(s(elem!1)), s(s(s(s(elem!1)))))),
% 2.72/2.95 inference(unit_resolution,[status(thm)],[1536, 10306, 10220, 10302])).
% 2.72/2.95 tff(10308,plain,
% 2.72/2.95 (b(s(s(elem!1)), s(s(s(s(elem!1)))))),
% 2.72/2.95 inference(unit_resolution,[status(thm)],[827, 10307, 10237])).
% 2.72/2.95 tff(10309,plain,
% 2.72/2.95 (~b(s(s(s(s(elem!1)))), s(s(elem!1)))),
% 2.72/2.95 inference(unit_resolution,[status(thm)],[9677, 10308, 9812, 10304])).
% 2.72/2.95 tff(10310,plain,
% 2.72/2.95 (r(s(s(s(s(elem!1)))), s(s(elem!1)))),
% 2.72/2.95 inference(unit_resolution,[status(thm)],[813, 10309, 10190])).
% 2.72/2.95 tff(10311,plain,
% 2.72/2.95 (r(elem!1, s(s(z))) <=> r(elem!1, s(s(elem!1)))),
% 2.72/2.95 inference(monotonicity,[status(thm)],[10185])).
% 2.72/2.95 tff(10312,plain,
% 2.72/2.95 (r(elem!1, s(s(elem!1))) <=> r(elem!1, s(s(z)))),
% 2.72/2.95 inference(symmetry,[status(thm)],[10311])).
% 2.72/2.95 tff(10313,plain,
% 2.72/2.95 (r(z, s(s(elem!1))) <=> r(elem!1, s(s(elem!1)))),
% 2.72/2.95 inference(monotonicity,[status(thm)],[10195])).
% 2.72/2.95 tff(10314,plain,
% 2.72/2.95 (r(z, s(s(elem!1))) <=> r(elem!1, s(s(z)))),
% 2.72/2.95 inference(transitivity,[status(thm)],[10313, 10312])).
% 2.72/2.95 tff(10315,plain,
% 2.72/2.95 (r(elem!1, s(s(z)))),
% 2.72/2.95 inference(modus_ponens,[status(thm)],[10220, 10314])).
% 2.72/2.95 tff(10316,plain,
% 2.72/2.95 (r(s(s(s(elem!1))), s(s(z)))),
% 2.72/2.95 inference(unit_resolution,[status(thm)],[3454, 10306, 10185])).
% 2.72/2.95 tff(10317,plain,
% 2.72/2.95 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(s(elem!1))))) | (~r(s(s(z)), z)) | (~r(s(s(s(elem!1))), s(s(z)))) | (~r(z, s(s(z)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, s(s(s(elem!1))))) | (~r(s(s(z)), z)) | (~r(s(s(s(elem!1))), s(s(z)))) | (~r(z, s(s(z)))))),
% 2.72/2.95 inference(rewrite,[status(thm)],[])).
% 2.72/2.95 tff(10318,plain,
% 2.72/2.95 (((~r(s(s(z)), z)) | (~r(s(s(s(elem!1))), s(s(z)))) | (~r(z, s(s(z)))) | (~r(z, s(s(s(elem!1)))))) <=> ((~r(z, s(s(s(elem!1))))) | (~r(s(s(z)), z)) | (~r(s(s(s(elem!1))), s(s(z)))) | (~r(z, s(s(z)))))),
% 2.72/2.95 inference(rewrite,[status(thm)],[])).
% 2.72/2.95 tff(10319,plain,
% 2.72/2.95 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(z)), z)) | (~r(s(s(s(elem!1))), s(s(z)))) | (~r(z, s(s(z)))) | (~r(z, s(s(s(elem!1))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(s(elem!1))))) | (~r(s(s(z)), z)) | (~r(s(s(s(elem!1))), s(s(z)))) | (~r(z, s(s(z))))))),
% 2.72/2.95 inference(monotonicity,[status(thm)],[10318])).
% 2.72/2.95 tff(10320,plain,
% 2.72/2.95 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(z)), z)) | (~r(s(s(s(elem!1))), s(s(z)))) | (~r(z, s(s(z)))) | (~r(z, s(s(s(elem!1))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, s(s(s(elem!1))))) | (~r(s(s(z)), z)) | (~r(s(s(s(elem!1))), s(s(z)))) | (~r(z, s(s(z)))))),
% 2.72/2.95 inference(transitivity,[status(thm)],[10319, 10317])).
% 2.72/2.95 tff(10321,plain,
% 2.72/2.95 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(z)), z)) | (~r(s(s(s(elem!1))), s(s(z)))) | (~r(z, s(s(z)))) | (~r(z, s(s(s(elem!1))))))),
% 2.72/2.95 inference(quant_inst,[status(thm)],[])).
% 2.72/2.95 tff(10322,plain,
% 2.72/2.95 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, s(s(s(elem!1))))) | (~r(s(s(z)), z)) | (~r(s(s(s(elem!1))), s(s(z)))) | (~r(z, s(s(z))))),
% 2.72/2.95 inference(modus_ponens,[status(thm)],[10321, 10320])).
% 2.72/2.95 tff(10323,plain,
% 2.72/2.95 ($false),
% 2.72/2.95 inference(unit_resolution,[status(thm)],[10322, 197, 155, 282, 866, 464])).
% 2.72/2.95 tff(10324,plain,((~r(s(s(z)), z)) | (~r(z, s(s(z)))) | (~r(z, s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), s(s(z))))), inference(lemma,lemma(discharge,[]))).
% 2.72/2.95 tff(10325,plain,
% 2.72/2.95 (~r(s(s(z)), z)),
% 2.72/2.95 inference(unit_resolution,[status(thm)],[10324, 10316, 152, 10302])).
% 2.72/2.95 tff(10326,plain,
% 2.72/2.95 (b(s(s(z)), z)),
% 2.72/2.95 inference(unit_resolution,[status(thm)],[186, 10325])).
% 2.72/2.95 tff(10327,plain,
% 2.72/2.95 (b(s(s(elem!1)), elem!1)),
% 2.72/2.95 inference(unit_resolution,[status(thm)],[8754, 10326, 10185])).
% 2.72/2.95 tff(10328,plain,
% 2.72/2.95 (~b(s(z), elem!1)),
% 2.72/2.95 inference(unit_resolution,[status(thm)],[9614, 10327, 10298, 9812, 10315, 10310, 10185])).
% 2.72/2.95 tff(10329,plain,
% 2.72/2.95 ($false),
% 2.72/2.95 inference(unit_resolution,[status(thm)],[10328, 10296])).
% 2.72/2.95 tff(10330,plain,((~b(s(s(s(elem!1))), z)) | b(z, s(s(z)))), inference(lemma,lemma(discharge,[]))).
% 2.72/2.95 tff(10331,plain,
% 2.72/2.95 (~b(s(s(s(elem!1))), z)),
% 2.72/2.95 inference(unit_resolution,[status(thm)],[10330, 125])).
% 2.72/2.95 tff(10332,plain,
% 2.72/2.95 (r(s(s(s(elem!1))), z)),
% 2.72/2.95 inference(unit_resolution,[status(thm)],[94, 10331])).
% 2.72/2.95 tff(10333,plain,
% 2.72/2.95 (~r(s(z), z)),
% 2.72/2.95 inference(unit_resolution,[status(thm)],[5698, 10332, 152, 9727])).
% 2.72/2.95 tff(10334,plain,
% 2.72/2.95 (b(s(z), z)),
% 2.72/2.95 inference(unit_resolution,[status(thm)],[230, 10333])).
% 2.72/2.95 tff(10335,plain,
% 2.72/2.95 (~b(s(s(elem!1)), s(z))),
% 2.72/2.95 inference(unit_resolution,[status(thm)],[2253, 10334, 152, 8408, 10193])).
% 2.72/2.95 tff(10336,plain,
% 2.72/2.95 (r(s(s(elem!1)), s(z))),
% 2.72/2.95 inference(unit_resolution,[status(thm)],[1912, 10335])).
% 2.72/2.95 tff(10337,assumption,(s(z) = elem!1), introduced(assumption)).
% 2.72/2.95 tff(10338,plain,
% 2.72/2.95 (r(elem!1, s(z)) <=> r(elem!1, elem!1)),
% 2.72/2.95 inference(monotonicity,[status(thm)],[10337])).
% 2.72/2.95 tff(10339,plain,
% 2.72/2.95 (r(elem!1, elem!1) <=> r(elem!1, s(z))),
% 2.72/2.95 inference(symmetry,[status(thm)],[10338])).
% 2.72/2.95 tff(10340,plain,
% 2.72/2.95 ((~r(elem!1, elem!1)) <=> (~r(elem!1, s(z)))),
% 2.72/2.95 inference(monotonicity,[status(thm)],[10339])).
% 2.72/2.95 tff(10341,plain,
% 2.72/2.95 ((~![X: $i] : (~r(X, X))) | (~r(elem!1, elem!1))),
% 2.72/2.95 inference(quant_inst,[status(thm)],[])).
% 2.72/2.95 tff(10342,plain,
% 2.72/2.95 (~r(elem!1, elem!1)),
% 2.72/2.95 inference(unit_resolution,[status(thm)],[10341, 3147])).
% 2.72/2.95 tff(10343,plain,
% 2.72/2.95 (~r(elem!1, s(z))),
% 2.72/2.95 inference(modus_ponens,[status(thm)],[10342, 10340])).
% 2.72/2.95 tff(10344,plain,
% 2.72/2.95 ($false),
% 2.72/2.95 inference(unit_resolution,[status(thm)],[744, 10343])).
% 2.72/2.95 tff(10345,plain,((~(s(z) = elem!1)) | (~r(elem!1, s(z)))), inference(lemma,lemma(discharge,[]))).
% 2.72/2.95 tff(10346,plain,
% 2.72/2.95 (~(s(z) = elem!1)),
% 2.72/2.95 inference(unit_resolution,[status(thm)],[10345, 10228])).
% 2.72/2.95 tff(10347,plain,
% 2.72/2.95 ((s(z) = elem!1) <=> (elem!1 = s(z))),
% 2.72/2.95 inference(commutativity,[status(thm)],[])).
% 2.72/2.95 tff(10348,plain,
% 2.72/2.95 ((elem!1 = s(z)) <=> (s(z) = elem!1)),
% 2.72/2.95 inference(symmetry,[status(thm)],[10347])).
% 2.72/2.95 tff(10349,plain,
% 2.72/2.95 (s(z) = elem!1),
% 2.72/2.95 inference(modus_ponens,[status(thm)],[2528, 10348])).
% 2.72/2.95 tff(10350,assumption,(~(s(z) = elem!1)), introduced(assumption)).
% 2.72/2.95 tff(10351,plain,
% 2.72/2.95 ($false),
% 2.72/2.95 inference(unit_resolution,[status(thm)],[10350, 10349])).
% 2.72/2.95 tff(10352,plain,((~(elem!1 = s(z))) | (s(z) = elem!1)), inference(lemma,lemma(discharge,[]))).
% 2.72/2.95 tff(10353,plain,
% 2.72/2.95 (~(elem!1 = s(z))),
% 2.72/2.95 inference(unit_resolution,[status(thm)],[10352, 10346])).
% 2.72/2.95 tff(10354,plain,
% 2.72/2.95 (b(z, s(z)) <=> b(elem!1, s(z))),
% 2.72/2.95 inference(monotonicity,[status(thm)],[10195])).
% 2.72/2.95 tff(10355,plain,
% 2.72/2.95 ((~b(z, s(z))) <=> (~b(elem!1, s(z)))),
% 2.72/2.95 inference(monotonicity,[status(thm)],[10354])).
% 2.72/2.95 tff(10356,plain,
% 2.72/2.95 (~b(elem!1, s(z))),
% 2.72/2.95 inference(modus_ponens,[status(thm)],[8407, 10355])).
% 2.72/2.95 tff(10357,plain,
% 2.72/2.95 (r(s(s(s(elem!1))), elem!1)),
% 2.72/2.95 inference(unit_resolution,[status(thm)],[966, 10332, 10195])).
% 2.72/2.95 tff(10358,assumption,(~(elem!1 = s(z))), introduced(assumption)).
% 2.72/2.95 tff(10359,plain,
% 2.72/2.95 (elem!1 = s(z)),
% 2.72/2.95 inference(modus_ponens,[status(thm)],[10337, 10347])).
% 2.72/2.95 tff(10360,plain,
% 2.72/2.95 ($false),
% 2.72/2.95 inference(unit_resolution,[status(thm)],[10358, 10359])).
% 2.72/2.95 tff(10361,plain,((~(s(z) = elem!1)) | (elem!1 = s(z))), inference(lemma,lemma(discharge,[]))).
% 2.72/2.95 tff(10362,plain,
% 2.72/2.95 (~(s(z) = elem!1)),
% 2.72/2.95 inference(unit_resolution,[status(thm)],[10361, 10358])).
% 2.72/2.95 tff(10363,plain,
% 2.72/2.95 (((~![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))),
% 2.72/2.95 inference(rewrite,[status(thm)],[])).
% 2.72/2.95 tff(10364,plain,
% 2.72/2.95 ((~![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))),
% 2.72/2.95 inference(quant_inst,[status(thm)],[])).
% 2.72/2.95 tff(10365,plain,
% 2.72/2.95 ((~![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)),
% 2.72/2.95 inference(modus_ponens,[status(thm)],[10364, 10363])).
% 2.72/2.95 tff(10366,plain,
% 2.72/2.95 ((s(z) = elem!1) | r(s(z), elem!1)),
% 2.72/2.95 inference(unit_resolution,[status(thm)],[10365, 79, 9912])).
% 2.72/2.95 tff(10367,plain,
% 2.72/2.95 (r(s(z), elem!1)),
% 2.72/2.95 inference(unit_resolution,[status(thm)],[10366, 10362])).
% 2.72/2.95 tff(10368,plain,
% 2.72/2.95 (r(elem!1, s(z))),
% 2.72/2.95 inference(unit_resolution,[status(thm)],[2539, 10358, 2527])).
% 2.72/2.95 tff(10369,plain,
% 2.72/2.95 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), s(z))) | (~r(s(z), elem!1)) | (~r(s(s(s(elem!1))), elem!1)) | (~r(elem!1, s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(elem!1))), s(z))) | (~r(s(z), elem!1)) | (~r(s(s(s(elem!1))), elem!1)) | (~r(elem!1, s(z))))),
% 2.72/2.95 inference(rewrite,[status(thm)],[])).
% 2.72/2.95 tff(10370,plain,
% 2.72/2.95 (((~r(s(z), elem!1)) | (~r(elem!1, s(z))) | (~r(s(s(s(elem!1))), s(z))) | (~r(s(s(s(elem!1))), elem!1))) <=> ((~r(s(s(s(elem!1))), s(z))) | (~r(s(z), elem!1)) | (~r(s(s(s(elem!1))), elem!1)) | (~r(elem!1, s(z))))),
% 2.72/2.95 inference(rewrite,[status(thm)],[])).
% 2.72/2.95 tff(10371,plain,
% 2.72/2.95 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), elem!1)) | (~r(elem!1, s(z))) | (~r(s(s(s(elem!1))), s(z))) | (~r(s(s(s(elem!1))), elem!1)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), s(z))) | (~r(s(z), elem!1)) | (~r(s(s(s(elem!1))), elem!1)) | (~r(elem!1, s(z)))))),
% 2.72/2.95 inference(monotonicity,[status(thm)],[10370])).
% 2.72/2.95 tff(10372,plain,
% 2.72/2.95 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), elem!1)) | (~r(elem!1, s(z))) | (~r(s(s(s(elem!1))), s(z))) | (~r(s(s(s(elem!1))), elem!1)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(elem!1))), s(z))) | (~r(s(z), elem!1)) | (~r(s(s(s(elem!1))), elem!1)) | (~r(elem!1, s(z))))),
% 2.72/2.95 inference(transitivity,[status(thm)],[10371, 10369])).
% 2.72/2.95 tff(10373,plain,
% 2.72/2.95 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), elem!1)) | (~r(elem!1, s(z))) | (~r(s(s(s(elem!1))), s(z))) | (~r(s(s(s(elem!1))), elem!1)))),
% 2.72/2.95 inference(quant_inst,[status(thm)],[])).
% 2.72/2.95 tff(10374,plain,
% 2.72/2.95 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(elem!1))), s(z))) | (~r(s(z), elem!1)) | (~r(s(s(s(elem!1))), elem!1)) | (~r(elem!1, s(z)))),
% 2.72/2.95 inference(modus_ponens,[status(thm)],[10373, 10372])).
% 2.72/2.95 tff(10375,plain,
% 2.72/2.95 ($false),
% 2.72/2.95 inference(unit_resolution,[status(thm)],[10374, 197, 350, 10368, 10367, 1013])).
% 2.72/2.95 tff(10376,plain,((elem!1 = s(z)) | (~r(s(s(s(elem!1))), s(z))) | (~r(s(s(s(elem!1))), elem!1)) | b(s(z), elem!1) | b(elem!1, s(z))), inference(lemma,lemma(discharge,[]))).
% 2.72/2.95 tff(10377,plain,
% 2.72/2.95 (b(s(z), elem!1)),
% 2.72/2.95 inference(unit_resolution,[status(thm)],[10376, 10357, 9727, 10356, 10353])).
% 2.72/2.95 tff(10378,plain,
% 2.72/2.95 (~r(s(z), s(s(s(z))))),
% 2.72/2.95 inference(unit_resolution,[status(thm)],[9890, 10332, 9727, 8408])).
% 2.72/2.95 tff(10379,plain,
% 2.72/2.95 (b(s(z), s(s(s(z))))),
% 2.72/2.95 inference(unit_resolution,[status(thm)],[1674, 10378])).
% 2.72/2.95 tff(10380,plain,
% 2.72/2.95 (b(s(s(s(z))), z) <=> b(s(s(s(z))), elem!1)),
% 2.72/2.95 inference(monotonicity,[status(thm)],[10195])).
% 2.72/2.95 tff(10381,plain,
% 2.72/2.95 (b(s(s(s(z))), elem!1) <=> b(s(s(s(z))), z)),
% 2.72/2.95 inference(symmetry,[status(thm)],[10380])).
% 2.72/2.95 tff(10382,plain,
% 2.72/2.95 (b(s(s(s(z))), elem!1) <=> b(s(s(s(elem!1))), elem!1)),
% 2.72/2.95 inference(monotonicity,[status(thm)],[10214])).
% 2.72/2.95 tff(10383,plain,
% 2.72/2.95 (b(s(s(s(elem!1))), elem!1) <=> b(s(s(s(z))), elem!1)),
% 2.72/2.95 inference(symmetry,[status(thm)],[10382])).
% 2.72/2.95 tff(10384,plain,
% 2.72/2.95 (b(s(s(s(elem!1))), z) <=> b(s(s(s(elem!1))), elem!1)),
% 2.72/2.95 inference(monotonicity,[status(thm)],[10195])).
% 2.72/2.95 tff(10385,plain,
% 2.72/2.95 (b(s(s(s(elem!1))), z) <=> b(s(s(s(z))), z)),
% 2.72/2.95 inference(transitivity,[status(thm)],[10384, 10383, 10381])).
% 2.72/2.95 tff(10386,plain,
% 2.72/2.95 ((~b(s(s(s(elem!1))), z)) <=> (~b(s(s(s(z))), z))),
% 2.72/2.95 inference(monotonicity,[status(thm)],[10385])).
% 2.72/2.95 tff(10387,plain,
% 2.72/2.95 (~b(s(s(s(z))), z)),
% 2.72/2.95 inference(modus_ponens,[status(thm)],[10331, 10386])).
% 2.72/2.95 tff(10388,plain,
% 2.72/2.95 (r(s(s(s(z))), z)),
% 2.72/2.95 inference(unit_resolution,[status(thm)],[1713, 10387])).
% 2.72/2.95 tff(10389,plain,
% 2.72/2.95 (~r(s(s(z)), z)),
% 2.72/2.95 inference(unit_resolution,[status(thm)],[8748, 10388, 8408, 10379, 10260])).
% 2.72/2.95 tff(10390,plain,
% 2.72/2.95 (b(s(s(z)), z)),
% 2.72/2.95 inference(unit_resolution,[status(thm)],[186, 10389])).
% 2.72/2.95 tff(10391,plain,
% 2.72/2.95 (b(s(s(elem!1)), elem!1)),
% 2.72/2.95 inference(unit_resolution,[status(thm)],[8754, 10390, 10185])).
% 2.72/2.95 tff(10392,plain,
% 2.72/2.95 (~r(s(s(s(s(elem!1)))), s(s(elem!1)))),
% 2.72/2.95 inference(unit_resolution,[status(thm)],[9614, 10391, 10377, 9812, 10315, 10336, 10185])).
% 2.72/2.95 tff(10393,plain,
% 2.72/2.95 (b(s(s(s(s(elem!1)))), s(s(elem!1)))),
% 2.72/2.95 inference(unit_resolution,[status(thm)],[813, 10392, 10190])).
% 2.72/2.95 tff(10394,plain,
% 2.72/2.95 (b(s(elem!1), z)),
% 2.72/2.95 inference(unit_resolution,[status(thm)],[8702, 10334, 10195])).
% 2.72/2.95 tff(10395,plain,
% 2.72/2.95 (~r(s(z), s(s(s(elem!1))))),
% 2.72/2.95 inference(unit_resolution,[status(thm)],[8626, 10336, 8408, 10220])).
% 2.72/2.95 tff(10396,plain,
% 2.72/2.95 (b(s(z), s(s(s(elem!1))))),
% 2.72/2.95 inference(unit_resolution,[status(thm)],[116, 10395])).
% 2.72/2.95 tff(10397,plain,
% 2.72/2.95 (b(s(elem!1), s(s(s(elem!1))))),
% 2.72/2.95 inference(unit_resolution,[status(thm)],[8725, 10396, 10195])).
% 2.72/2.95 tff(10398,plain,
% 2.72/2.95 (r(s(s(s(z))), s(z)) <=> r(s(s(s(elem!1))), s(z))),
% 2.72/2.95 inference(monotonicity,[status(thm)],[10214])).
% 2.72/2.95 tff(10399,plain,
% 2.72/2.95 (r(s(s(s(elem!1))), s(z)) <=> r(s(s(s(z))), s(z))),
% 2.72/2.95 inference(symmetry,[status(thm)],[10398])).
% 2.72/2.95 tff(10400,plain,
% 2.72/2.95 (r(s(s(s(z))), s(z))),
% 2.72/2.95 inference(modus_ponens,[status(thm)],[9727, 10399])).
% 2.72/2.95 tff(10401,plain,
% 2.72/2.95 (r(s(s(z)), s(z)) <=> r(s(s(elem!1)), s(z))),
% 2.72/2.95 inference(monotonicity,[status(thm)],[10185])).
% 2.72/2.95 tff(10402,plain,
% 2.72/2.95 (r(s(s(elem!1)), s(z)) <=> r(s(s(z)), s(z))),
% 2.72/2.95 inference(symmetry,[status(thm)],[10401])).
% 2.72/2.95 tff(10403,plain,
% 2.72/2.95 (r(s(s(z)), s(z))),
% 2.72/2.95 inference(modus_ponens,[status(thm)],[10336, 10402])).
% 2.72/2.95 tff(10404,plain,
% 2.72/2.95 (~r(z, s(s(s(z))))),
% 2.72/2.95 inference(unit_resolution,[status(thm)],[9030, 10403, 152, 10379, 10260, 10400])).
% 2.72/2.95 tff(10405,plain,
% 2.72/2.95 (b(z, s(s(s(z))))),
% 2.72/2.95 inference(unit_resolution,[status(thm)],[1697, 10404])).
% 2.72/2.95 tff(10406,plain,
% 2.72/2.95 (b(z, s(s(s(elem!1))))),
% 2.72/2.95 inference(unit_resolution,[status(thm)],[4844, 10405, 10185])).
% 2.72/2.95 tff(10407,plain,
% 2.72/2.95 (b(s(elem!1), elem!1) <=> b(s(z), elem!1)),
% 2.72/2.95 inference(monotonicity,[status(thm)],[10194])).
% 2.72/2.95 tff(10408,plain,
% 2.72/2.95 (b(s(z), elem!1) <=> b(s(elem!1), elem!1)),
% 2.72/2.95 inference(symmetry,[status(thm)],[10407])).
% 2.72/2.95 tff(10409,plain,
% 2.72/2.95 (b(s(elem!1), elem!1)),
% 2.72/2.95 inference(modus_ponens,[status(thm)],[10377, 10408])).
% 2.72/2.95 tff(10410,plain,
% 2.72/2.95 (~b(s(s(s(elem!1))), s(s(elem!1)))),
% 2.72/2.95 inference(unit_resolution,[status(thm)],[8762, 10391, 10409, 10406, 10397, 10394])).
% 2.72/2.95 tff(10411,plain,
% 2.72/2.95 (r(s(s(s(elem!1))), s(s(elem!1)))),
% 2.72/2.95 inference(unit_resolution,[status(thm)],[889, 10410, 10213])).
% 2.72/2.95 tff(10412,plain,
% 2.72/2.95 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), s(s(elem!1)))) | (~r(s(s(s(elem!1))), s(z))) | (~r(s(s(elem!1)), s(z))) | (~r(s(z), s(s(s(s(elem!1)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(elem!1))), s(s(elem!1)))) | (~r(s(s(s(elem!1))), s(z))) | (~r(s(s(elem!1)), s(z))) | (~r(s(z), s(s(s(s(elem!1)))))))),
% 2.72/2.95 inference(rewrite,[status(thm)],[])).
% 2.72/2.95 tff(10413,plain,
% 2.72/2.95 (((~r(s(z), s(s(s(s(elem!1)))))) | (~r(s(s(elem!1)), s(z))) | (~r(s(s(s(elem!1))), s(z))) | (~r(s(s(s(elem!1))), s(s(elem!1))))) <=> ((~r(s(s(s(elem!1))), s(s(elem!1)))) | (~r(s(s(s(elem!1))), s(z))) | (~r(s(s(elem!1)), s(z))) | (~r(s(z), s(s(s(s(elem!1)))))))),
% 2.72/2.95 inference(rewrite,[status(thm)],[])).
% 2.72/2.95 tff(10414,plain,
% 2.72/2.95 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(s(s(s(elem!1)))))) | (~r(s(s(elem!1)), s(z))) | (~r(s(s(s(elem!1))), s(z))) | (~r(s(s(s(elem!1))), s(s(elem!1)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), s(s(elem!1)))) | (~r(s(s(s(elem!1))), s(z))) | (~r(s(s(elem!1)), s(z))) | (~r(s(z), s(s(s(s(elem!1))))))))),
% 2.72/2.95 inference(monotonicity,[status(thm)],[10413])).
% 2.72/2.95 tff(10415,plain,
% 2.72/2.95 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(s(s(s(elem!1)))))) | (~r(s(s(elem!1)), s(z))) | (~r(s(s(s(elem!1))), s(z))) | (~r(s(s(s(elem!1))), s(s(elem!1)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(elem!1))), s(s(elem!1)))) | (~r(s(s(s(elem!1))), s(z))) | (~r(s(s(elem!1)), s(z))) | (~r(s(z), s(s(s(s(elem!1)))))))),
% 2.72/2.95 inference(transitivity,[status(thm)],[10414, 10412])).
% 2.72/2.95 tff(10416,plain,
% 2.72/2.95 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(s(s(s(elem!1)))))) | (~r(s(s(elem!1)), s(z))) | (~r(s(s(s(elem!1))), s(z))) | (~r(s(s(s(elem!1))), s(s(elem!1)))))),
% 2.72/2.95 inference(quant_inst,[status(thm)],[])).
% 2.72/2.95 tff(10417,plain,
% 2.72/2.95 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(elem!1))), s(s(elem!1)))) | (~r(s(s(s(elem!1))), s(z))) | (~r(s(s(elem!1)), s(z))) | (~r(s(z), s(s(s(s(elem!1))))))),
% 2.72/2.95 inference(modus_ponens,[status(thm)],[10416, 10415])).
% 2.72/2.95 tff(10418,plain,
% 2.72/2.95 ($false),
% 2.72/2.95 inference(unit_resolution,[status(thm)],[10417, 197, 350, 4577, 905, 699])).
% 2.72/2.95 tff(10419,plain,((~r(s(z), s(s(s(s(elem!1)))))) | (~r(s(s(s(elem!1))), s(z))) | (~r(s(s(elem!1)), s(z))) | (~r(s(s(s(elem!1))), s(s(elem!1))))), inference(lemma,lemma(discharge,[]))).
% 2.72/2.95 tff(10420,plain,
% 2.72/2.95 (~r(s(z), s(s(s(s(elem!1)))))),
% 2.72/2.95 inference(unit_resolution,[status(thm)],[10419, 10411, 9727, 10336])).
% 2.72/2.95 tff(10421,plain,
% 2.72/2.95 (b(s(z), s(s(s(s(elem!1)))))),
% 2.72/2.95 inference(unit_resolution,[status(thm)],[681, 10420])).
% 2.72/2.95 tff(10422,plain,
% 2.72/2.95 (b(s(s(z)), s(s(elem!1))) <=> b(s(s(elem!1)), s(s(elem!1)))),
% 2.72/2.95 inference(monotonicity,[status(thm)],[10185])).
% 2.72/2.95 tff(10423,plain,
% 2.72/2.95 (b(s(s(elem!1)), s(s(elem!1))) <=> b(s(s(z)), s(s(elem!1)))),
% 2.72/2.95 inference(symmetry,[status(thm)],[10422])).
% 2.72/2.95 tff(10424,plain,
% 2.72/2.95 ((~b(s(s(elem!1)), s(s(elem!1)))) <=> (~b(s(s(z)), s(s(elem!1))))),
% 2.72/2.95 inference(monotonicity,[status(thm)],[10423])).
% 2.72/2.95 tff(10425,plain,
% 2.72/2.95 (^[X: $i] : refl((~b(X, X)) <=> (~b(X, X)))),
% 2.72/2.95 inference(bind,[status(th)],[])).
% 2.72/2.95 tff(10426,plain,
% 2.72/2.95 (![X: $i] : (~b(X, X)) <=> ![X: $i] : (~b(X, X))),
% 2.72/2.95 inference(quant_intro,[status(thm)],[10425])).
% 2.72/2.95 tff(10427,plain,
% 2.72/2.95 (![X: $i] : (~b(X, X)) <=> ![X: $i] : (~b(X, X))),
% 2.72/2.95 inference(rewrite,[status(thm)],[])).
% 2.72/2.95 tff(10428,axiom,(![X: $i] : (~b(X, X))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','bi')).
% 2.72/2.95 tff(10429,plain,
% 2.72/2.95 (![X: $i] : (~b(X, X))),
% 2.72/2.95 inference(modus_ponens,[status(thm)],[10428, 10427])).
% 2.72/2.95 tff(10430,plain,(
% 2.72/2.95 ![X: $i] : (~b(X, X))),
% 2.72/2.95 inference(skolemize,[status(sab)],[10429])).
% 2.72/2.95 tff(10431,plain,
% 2.72/2.95 (![X: $i] : (~b(X, X))),
% 2.72/2.95 inference(modus_ponens,[status(thm)],[10430, 10426])).
% 2.72/2.95 tff(10432,plain,
% 2.72/2.95 ((~![X: $i] : (~b(X, X))) | (~b(s(s(elem!1)), s(s(elem!1))))),
% 2.72/2.95 inference(quant_inst,[status(thm)],[])).
% 2.72/2.95 tff(10433,plain,
% 2.72/2.95 (~b(s(s(elem!1)), s(s(elem!1)))),
% 2.72/2.95 inference(unit_resolution,[status(thm)],[10432, 10431])).
% 2.72/2.95 tff(10434,plain,
% 2.72/2.95 (~b(s(s(z)), s(s(elem!1)))),
% 2.72/2.95 inference(modus_ponens,[status(thm)],[10433, 10424])).
% 2.72/2.95 tff(10435,plain,
% 2.72/2.95 (~r(s(s(z)), s(s(elem!1)))),
% 2.72/2.95 inference(unit_resolution,[status(thm)],[569, 561, 155, 365])).
% 2.72/2.95 tff(10436,plain,
% 2.72/2.95 (s(s(z)) = s(s(elem!1))),
% 2.72/2.95 inference(unit_resolution,[status(thm)],[390, 10435, 2072])).
% 2.72/2.95 tff(10437,plain,
% 2.72/2.95 (s(elem!1) = s(z)),
% 2.72/2.95 inference(unit_resolution,[status(thm)],[43, 10436])).
% 2.72/2.95 tff(10438,plain,
% 2.72/2.95 (z = elem!1),
% 2.72/2.95 inference(unit_resolution,[status(thm)],[30, 10437])).
% 2.72/2.95 tff(10439,plain,
% 2.72/2.95 (r(z, s(s(elem!1))) <=> r(elem!1, s(s(elem!1)))),
% 2.72/2.95 inference(monotonicity,[status(thm)],[10438])).
% 2.72/2.95 tff(10440,plain,
% 2.72/2.95 (r(elem!1, s(s(elem!1))) <=> r(z, s(s(elem!1)))),
% 2.72/2.95 inference(symmetry,[status(thm)],[10439])).
% 2.72/2.95 tff(10441,plain,
% 2.72/2.95 ((~r(elem!1, s(s(elem!1)))) <=> (~r(z, s(s(elem!1))))),
% 2.72/2.95 inference(monotonicity,[status(thm)],[10440])).
% 2.72/2.95 tff(10442,plain,
% 2.72/2.95 (r(s(s(s(elem!1))), elem!1)),
% 2.72/2.95 inference(unit_resolution,[status(thm)],[966, 10438, 154])).
% 2.72/2.95 tff(10443,plain,
% 2.72/2.95 (~r(elem!1, s(s(elem!1)))),
% 2.72/2.95 inference(unit_resolution,[status(thm)],[1376, 10442, 905, 561])).
% 2.72/2.95 tff(10444,plain,
% 2.72/2.95 (~r(z, s(s(elem!1)))),
% 2.72/2.95 inference(modus_ponens,[status(thm)],[10443, 10441])).
% 2.72/2.95 tff(10445,plain,
% 2.72/2.95 ($false),
% 2.72/2.95 inference(unit_resolution,[status(thm)],[365, 10444])).
% 2.72/2.95 tff(10446,plain,((~r(s(s(elem!1)), s(s(s(s(elem!1)))))) | (~r(z, s(s(elem!1)))) | (~r(s(s(s(elem!1))), s(s(elem!1)))) | (~r(s(s(s(elem!1))), z)) | b(s(s(z)), s(s(elem!1))) | (~r(z, s(s(z))))), inference(lemma,lemma(discharge,[]))).
% 2.72/2.96 tff(10447,plain,
% 2.72/2.96 (~r(s(s(elem!1)), s(s(s(s(elem!1)))))),
% 2.72/2.96 inference(unit_resolution,[status(thm)],[10446, 10411, 152, 10220, 10434, 10332])).
% 2.72/2.96 tff(10448,plain,
% 2.72/2.96 (b(s(s(elem!1)), s(s(s(s(elem!1)))))),
% 2.72/2.96 inference(unit_resolution,[status(thm)],[827, 10447, 10237])).
% 2.72/2.96 tff(10449,plain,
% 2.72/2.96 ($false),
% 2.72/2.96 inference(unit_resolution,[status(thm)],[9677, 10448, 10421, 9812, 10393])).
% 2.72/2.96 tff(10450,plain,(b(z, s(s(z)))), inference(lemma,lemma(discharge,[]))).
% 2.72/2.96 tff(10451,assumption,(b(z, s(s(z)))), introduced(assumption)).
% 2.72/2.96 tff(10452,plain,
% 2.72/2.96 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(z)))) | (~b(s(s(s(elem!1))), s(s(z)))) | (~b(s(s(s(elem!1))), z)) | (~b(s(s(z)), z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(s(z)))) | (~b(s(s(s(elem!1))), s(s(z)))) | (~b(s(s(s(elem!1))), z)) | (~b(s(s(z)), z)))),
% 2.72/2.96 inference(rewrite,[status(thm)],[])).
% 2.72/2.96 tff(10453,plain,
% 2.72/2.96 (((~b(s(s(z)), z)) | (~b(s(s(s(elem!1))), z)) | (~b(z, s(s(z)))) | (~b(s(s(z)), z)) | (~b(s(s(s(elem!1))), z)) | (~b(s(s(s(elem!1))), s(s(z))))) <=> ((~b(z, s(s(z)))) | (~b(s(s(s(elem!1))), s(s(z)))) | (~b(s(s(s(elem!1))), z)) | (~b(s(s(z)), z)))),
% 2.72/2.96 inference(rewrite,[status(thm)],[])).
% 2.72/2.96 tff(10454,plain,
% 2.72/2.96 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), z)) | (~b(s(s(s(elem!1))), z)) | (~b(z, s(s(z)))) | (~b(s(s(z)), z)) | (~b(s(s(s(elem!1))), z)) | (~b(s(s(s(elem!1))), s(s(z)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(z)))) | (~b(s(s(s(elem!1))), s(s(z)))) | (~b(s(s(s(elem!1))), z)) | (~b(s(s(z)), z))))),
% 2.72/2.96 inference(monotonicity,[status(thm)],[10453])).
% 2.72/2.96 tff(10455,plain,
% 2.72/2.96 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), z)) | (~b(s(s(s(elem!1))), z)) | (~b(z, s(s(z)))) | (~b(s(s(z)), z)) | (~b(s(s(s(elem!1))), z)) | (~b(s(s(s(elem!1))), s(s(z)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(s(z)))) | (~b(s(s(s(elem!1))), s(s(z)))) | (~b(s(s(s(elem!1))), z)) | (~b(s(s(z)), z)))),
% 2.72/2.96 inference(transitivity,[status(thm)],[10454, 10452])).
% 2.72/2.96 tff(10456,plain,
% 2.72/2.96 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), z)) | (~b(s(s(s(elem!1))), z)) | (~b(z, s(s(z)))) | (~b(s(s(z)), z)) | (~b(s(s(s(elem!1))), z)) | (~b(s(s(s(elem!1))), s(s(z)))))),
% 2.72/2.96 inference(quant_inst,[status(thm)],[])).
% 2.72/2.96 tff(10457,plain,
% 2.72/2.96 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(s(z)))) | (~b(s(s(s(elem!1))), s(s(z)))) | (~b(s(s(s(elem!1))), z)) | (~b(s(s(z)), z))),
% 2.72/2.96 inference(modus_ponens,[status(thm)],[10456, 10455])).
% 2.72/2.96 tff(10458,plain,
% 2.72/2.96 ($false),
% 2.72/2.96 inference(unit_resolution,[status(thm)],[10457, 166, 10451, 121, 122, 2060])).
% 2.72/2.96 tff(10459,plain,((~b(s(s(z)), z)) | (~b(z, s(s(z)))) | (~b(s(s(s(elem!1))), z)) | (~b(s(s(s(elem!1))), s(s(z))))), inference(lemma,lemma(discharge,[]))).
% 2.72/2.96 tff(10460,plain,
% 2.72/2.96 ((~b(s(s(z)), z)) | (~b(s(s(s(elem!1))), z)) | (~b(s(s(s(elem!1))), s(s(z))))),
% 2.72/2.96 inference(unit_resolution,[status(thm)],[10459, 10450])).
% 2.72/2.96 tff(10461,plain,
% 2.72/2.96 (~b(s(s(s(elem!1))), s(s(z)))),
% 2.72/2.96 inference(unit_resolution,[status(thm)],[10460, 122, 121])).
% 2.72/2.96 tff(10462,plain,
% 2.72/2.96 (r(s(s(s(elem!1))), s(s(z)))),
% 2.72/2.96 inference(unit_resolution,[status(thm)],[218, 10461])).
% 2.72/2.96 tff(10463,plain,
% 2.72/2.96 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(z)))) | (~b(s(s(s(elem!1))), z)) | (~b(s(s(z)), z)) | (~b(s(s(z)), s(s(s(elem!1))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(s(z)))) | (~b(s(s(s(elem!1))), z)) | (~b(s(s(z)), z)) | (~b(s(s(z)), s(s(s(elem!1))))))),
% 2.72/2.96 inference(rewrite,[status(thm)],[])).
% 2.72/2.96 tff(10464,plain,
% 2.72/2.96 (((~b(s(s(z)), z)) | (~b(s(s(z)), z)) | (~b(z, s(s(z)))) | (~b(s(s(s(elem!1))), z)) | (~b(s(s(z)), z)) | (~b(s(s(z)), s(s(s(elem!1)))))) <=> ((~b(z, s(s(z)))) | (~b(s(s(s(elem!1))), z)) | (~b(s(s(z)), z)) | (~b(s(s(z)), s(s(s(elem!1))))))),
% 2.72/2.96 inference(rewrite,[status(thm)],[])).
% 2.72/2.96 tff(10465,plain,
% 2.72/2.96 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), z)) | (~b(s(s(z)), z)) | (~b(z, s(s(z)))) | (~b(s(s(s(elem!1))), z)) | (~b(s(s(z)), z)) | (~b(s(s(z)), s(s(s(elem!1))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(z)))) | (~b(s(s(s(elem!1))), z)) | (~b(s(s(z)), z)) | (~b(s(s(z)), s(s(s(elem!1)))))))),
% 2.72/2.96 inference(monotonicity,[status(thm)],[10464])).
% 2.72/2.96 tff(10466,plain,
% 2.72/2.96 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), z)) | (~b(s(s(z)), z)) | (~b(z, s(s(z)))) | (~b(s(s(s(elem!1))), z)) | (~b(s(s(z)), z)) | (~b(s(s(z)), s(s(s(elem!1))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(s(z)))) | (~b(s(s(s(elem!1))), z)) | (~b(s(s(z)), z)) | (~b(s(s(z)), s(s(s(elem!1))))))),
% 2.72/2.96 inference(transitivity,[status(thm)],[10465, 10463])).
% 2.72/2.96 tff(10467,plain,
% 2.72/2.96 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), z)) | (~b(s(s(z)), z)) | (~b(z, s(s(z)))) | (~b(s(s(s(elem!1))), z)) | (~b(s(s(z)), z)) | (~b(s(s(z)), s(s(s(elem!1))))))),
% 2.72/2.96 inference(quant_inst,[status(thm)],[])).
% 2.72/2.96 tff(10468,plain,
% 2.72/2.96 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(s(z)))) | (~b(s(s(s(elem!1))), z)) | (~b(s(s(z)), z)) | (~b(s(s(z)), s(s(s(elem!1)))))),
% 2.72/2.96 inference(modus_ponens,[status(thm)],[10467, 10466])).
% 2.72/2.96 tff(10469,plain,
% 2.72/2.96 (~b(s(s(z)), s(s(s(elem!1))))),
% 2.72/2.96 inference(unit_resolution,[status(thm)],[10468, 166, 10450, 121, 122])).
% 2.72/2.96 tff(10470,plain,
% 2.72/2.96 (r(s(s(z)), s(s(s(elem!1))))),
% 2.72/2.96 inference(unit_resolution,[status(thm)],[279, 10469])).
% 2.72/2.96 tff(10471,plain,
% 2.72/2.96 (((~r(s(s(z)), s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), s(s(z)))) | (~r(s(z), s(s(z)))) | (~r(s(z), s(s(s(elem!1)))))) <=> ((~r(s(z), s(s(s(elem!1))))) | (~r(s(z), s(s(z)))) | (~r(s(s(z)), s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), s(s(z)))))),
% 2.72/2.96 inference(rewrite,[status(thm)],[])).
% 2.72/2.96 tff(10472,plain,
% 2.72/2.96 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(z)), s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), s(s(z)))) | (~r(s(z), s(s(z)))) | (~r(s(z), s(s(s(elem!1))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(s(s(elem!1))))) | (~r(s(z), s(s(z)))) | (~r(s(s(z)), s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), s(s(z))))))),
% 2.72/2.96 inference(monotonicity,[status(thm)],[10471])).
% 2.72/2.96 tff(10473,plain,
% 2.72/2.96 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(z)), s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), s(s(z)))) | (~r(s(z), s(s(z)))) | (~r(s(z), s(s(s(elem!1))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(z), s(s(s(elem!1))))) | (~r(s(z), s(s(z)))) | (~r(s(s(z)), s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), s(s(z)))))),
% 2.72/2.96 inference(transitivity,[status(thm)],[10472, 3548])).
% 2.72/2.96 tff(10474,plain,
% 2.72/2.96 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(z)), s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), s(s(z)))) | (~r(s(z), s(s(z)))) | (~r(s(z), s(s(s(elem!1))))))),
% 2.72/2.96 inference(quant_inst,[status(thm)],[])).
% 2.72/2.96 tff(10475,plain,
% 2.72/2.96 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(z), s(s(s(elem!1))))) | (~r(s(z), s(s(z)))) | (~r(s(s(z)), s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), s(s(z))))),
% 2.72/2.96 inference(modus_ponens,[status(thm)],[10474, 10473])).
% 2.72/2.96 tff(10476,plain,
% 2.72/2.96 ($false),
% 2.72/2.96 inference(unit_resolution,[status(thm)],[10475, 197, 120, 119, 10470, 10462])).
% 2.72/2.96 tff(10477,plain,((~b(s(s(z)), z)) | (~r(s(z), s(s(z)))) | (~r(s(z), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), z))), inference(lemma,lemma(discharge,[]))).
% 2.72/2.96 tff(10478,plain,
% 2.72/2.96 (~b(s(s(z)), z)),
% 2.72/2.96 inference(unit_resolution,[status(thm)],[10477, 120, 119, 95])).
% 2.72/2.96 tff(10479,plain,
% 2.72/2.96 (r(s(s(z)), z)),
% 2.72/2.96 inference(unit_resolution,[status(thm)],[186, 10478])).
% 2.72/2.96 tff(10480,plain,
% 2.72/2.96 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, elem!1)) | (~r(s(z), z)) | (~r(s(z), s(s(z)))) | (~r(s(s(z)), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, elem!1)) | (~r(s(z), z)) | (~r(s(z), s(s(z)))) | (~r(s(s(z)), z)))),
% 2.72/2.96 inference(rewrite,[status(thm)],[])).
% 2.72/2.96 tff(10481,plain,
% 2.72/2.96 (((~r(z, elem!1)) | (~r(s(s(z)), z)) | (~r(s(z), z)) | (~r(s(z), s(s(z))))) <=> ((~r(z, elem!1)) | (~r(s(z), z)) | (~r(s(z), s(s(z)))) | (~r(s(s(z)), z)))),
% 2.72/2.96 inference(rewrite,[status(thm)],[])).
% 2.72/2.96 tff(10482,plain,
% 2.72/2.96 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, elem!1)) | (~r(s(s(z)), z)) | (~r(s(z), z)) | (~r(s(z), s(s(z)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, elem!1)) | (~r(s(z), z)) | (~r(s(z), s(s(z)))) | (~r(s(s(z)), z))))),
% 2.72/2.96 inference(monotonicity,[status(thm)],[10481])).
% 2.72/2.96 tff(10483,plain,
% 2.72/2.96 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, elem!1)) | (~r(s(s(z)), z)) | (~r(s(z), z)) | (~r(s(z), s(s(z)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, elem!1)) | (~r(s(z), z)) | (~r(s(z), s(s(z)))) | (~r(s(s(z)), z)))),
% 2.72/2.96 inference(transitivity,[status(thm)],[10482, 10480])).
% 2.72/2.96 tff(10484,plain,
% 2.72/2.96 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, elem!1)) | (~r(s(s(z)), z)) | (~r(s(z), z)) | (~r(s(z), s(s(z)))))),
% 2.72/2.96 inference(quant_inst,[status(thm)],[])).
% 2.72/2.96 tff(10485,plain,
% 2.72/2.96 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, elem!1)) | (~r(s(z), z)) | (~r(s(z), s(s(z)))) | (~r(s(s(z)), z))),
% 2.72/2.96 inference(modus_ponens,[status(thm)],[10484, 10483])).
% 2.72/2.96 tff(10486,plain,
% 2.72/2.96 ($false),
% 2.72/2.96 inference(unit_resolution,[status(thm)],[10485, 197, 2481, 120, 97, 866])).
% 2.72/2.96 tff(10487,plain,((~r(z, elem!1)) | (~r(s(z), s(s(z)))) | (~r(s(z), z)) | (~r(s(s(z)), z))), inference(lemma,lemma(discharge,[]))).
% 2.72/2.96 tff(10488,plain,
% 2.72/2.96 (~r(z, elem!1)),
% 2.72/2.96 inference(unit_resolution,[status(thm)],[10487, 10479, 97, 120])).
% 2.72/2.96 tff(10489,plain,
% 2.72/2.96 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(s(elem!1))))) | (~r(s(z), z)) | (~r(s(z), s(s(z)))) | (~r(s(s(z)), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, s(s(s(elem!1))))) | (~r(s(z), z)) | (~r(s(z), s(s(z)))) | (~r(s(s(z)), z)))),
% 2.72/2.96 inference(rewrite,[status(thm)],[])).
% 2.72/2.96 tff(10490,plain,
% 2.72/2.96 (((~r(z, s(s(s(elem!1))))) | (~r(s(s(z)), z)) | (~r(s(z), z)) | (~r(s(z), s(s(z))))) <=> ((~r(z, s(s(s(elem!1))))) | (~r(s(z), z)) | (~r(s(z), s(s(z)))) | (~r(s(s(z)), z)))),
% 2.72/2.96 inference(rewrite,[status(thm)],[])).
% 2.72/2.96 tff(10491,plain,
% 2.72/2.96 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(s(elem!1))))) | (~r(s(s(z)), z)) | (~r(s(z), z)) | (~r(s(z), s(s(z)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(s(elem!1))))) | (~r(s(z), z)) | (~r(s(z), s(s(z)))) | (~r(s(s(z)), z))))),
% 2.72/2.96 inference(monotonicity,[status(thm)],[10490])).
% 2.72/2.96 tff(10492,plain,
% 2.72/2.96 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(s(elem!1))))) | (~r(s(s(z)), z)) | (~r(s(z), z)) | (~r(s(z), s(s(z)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, s(s(s(elem!1))))) | (~r(s(z), z)) | (~r(s(z), s(s(z)))) | (~r(s(s(z)), z)))),
% 2.72/2.96 inference(transitivity,[status(thm)],[10491, 10489])).
% 2.72/2.96 tff(10493,plain,
% 2.72/2.96 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(s(elem!1))))) | (~r(s(s(z)), z)) | (~r(s(z), z)) | (~r(s(z), s(s(z)))))),
% 2.72/2.96 inference(quant_inst,[status(thm)],[])).
% 2.72/2.96 tff(10494,plain,
% 2.72/2.96 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, s(s(s(elem!1))))) | (~r(s(z), z)) | (~r(s(z), s(s(z)))) | (~r(s(s(z)), z))),
% 2.72/2.96 inference(modus_ponens,[status(thm)],[10493, 10492])).
% 2.72/2.96 tff(10495,plain,
% 2.72/2.96 ($false),
% 2.72/2.96 inference(unit_resolution,[status(thm)],[10494, 197, 120, 97, 282, 866])).
% 2.72/2.96 tff(10496,plain,((~r(z, s(s(s(elem!1))))) | (~r(s(z), s(s(z)))) | (~r(s(z), z)) | (~r(s(s(z)), z))), inference(lemma,lemma(discharge,[]))).
% 2.72/2.96 tff(10497,plain,
% 2.72/2.96 (~r(z, s(s(s(elem!1))))),
% 2.72/2.96 inference(unit_resolution,[status(thm)],[10496, 10479, 97, 120])).
% 2.72/2.96 tff(10498,plain,
% 2.72/2.96 (b(z, s(s(s(elem!1))))),
% 2.72/2.96 inference(unit_resolution,[status(thm)],[261, 10497])).
% 2.72/2.96 tff(10499,plain,
% 2.72/2.96 (~r(z, s(s(elem!1)))),
% 2.72/2.96 inference(unit_resolution,[status(thm)],[2359, 10479, 97, 120])).
% 2.72/2.96 tff(10500,plain,
% 2.72/2.96 (b(z, s(s(elem!1)))),
% 2.72/2.96 inference(unit_resolution,[status(thm)],[1795, 10499])).
% 2.72/2.96 tff(10501,plain,
% 2.72/2.96 (~r(s(s(elem!1)), s(s(s(elem!1))))),
% 2.72/2.96 inference(unit_resolution,[status(thm)],[2949, 905, 311, 119])).
% 2.72/2.96 tff(10502,plain,
% 2.72/2.96 (b(s(s(elem!1)), s(s(s(elem!1))))),
% 2.72/2.96 inference(unit_resolution,[status(thm)],[461, 10501, 45])).
% 2.72/2.96 tff(10503,plain,
% 2.72/2.96 (~r(s(s(elem!1)), elem!1)),
% 2.72/2.96 inference(unit_resolution,[status(thm)],[2508, 905, 311, 119])).
% 2.72/2.96 tff(10504,plain,
% 2.72/2.96 (~b(s(s(elem!1)), z)),
% 2.72/2.96 inference(unit_resolution,[status(thm)],[3593, 10502, 1820, 121])).
% 2.72/2.96 tff(10505,plain,
% 2.72/2.96 (r(s(s(elem!1)), z)),
% 2.72/2.96 inference(unit_resolution,[status(thm)],[608, 10504])).
% 2.72/2.96 tff(10506,plain,
% 2.72/2.96 (~(z = elem!1)),
% 2.72/2.96 inference(unit_resolution,[status(thm)],[3398, 10505, 10503])).
% 2.72/2.96 tff(10507,plain,
% 2.72/2.96 (b(z, elem!1)),
% 2.72/2.96 inference(unit_resolution,[status(thm)],[2514, 10506, 2510])).
% 2.72/2.96 tff(10508,plain,
% 2.72/2.96 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(z, s(s(s(elem!1))))) | (~b(z, s(s(elem!1)))) | (~b(s(s(s(elem!1))), z)) | (~b(z, elem!1)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(z, s(s(s(elem!1))))) | (~b(z, s(s(elem!1)))) | (~b(s(s(s(elem!1))), z)) | (~b(z, elem!1)))),
% 2.72/2.96 inference(rewrite,[status(thm)],[])).
% 2.72/2.96 tff(10509,plain,
% 2.72/2.96 (((~b(z, elem!1)) | (~b(z, elem!1)) | (~b(s(s(s(elem!1))), z)) | (~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(z, s(s(s(elem!1))))) | (~b(z, s(s(elem!1))))) <=> ((~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(z, s(s(s(elem!1))))) | (~b(z, s(s(elem!1)))) | (~b(s(s(s(elem!1))), z)) | (~b(z, elem!1)))),
% 2.72/2.96 inference(rewrite,[status(thm)],[])).
% 2.72/2.96 tff(10510,plain,
% 2.72/2.96 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, elem!1)) | (~b(z, elem!1)) | (~b(s(s(s(elem!1))), z)) | (~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(z, s(s(s(elem!1))))) | (~b(z, s(s(elem!1)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(z, s(s(s(elem!1))))) | (~b(z, s(s(elem!1)))) | (~b(s(s(s(elem!1))), z)) | (~b(z, elem!1))))),
% 2.72/2.96 inference(monotonicity,[status(thm)],[10509])).
% 2.72/2.96 tff(10511,plain,
% 2.72/2.96 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, elem!1)) | (~b(z, elem!1)) | (~b(s(s(s(elem!1))), z)) | (~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(z, s(s(s(elem!1))))) | (~b(z, s(s(elem!1)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(z, s(s(s(elem!1))))) | (~b(z, s(s(elem!1)))) | (~b(s(s(s(elem!1))), z)) | (~b(z, elem!1)))),
% 2.72/2.96 inference(transitivity,[status(thm)],[10510, 10508])).
% 2.72/2.96 tff(10512,plain,
% 2.72/2.96 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, elem!1)) | (~b(z, elem!1)) | (~b(s(s(s(elem!1))), z)) | (~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(z, s(s(s(elem!1))))) | (~b(z, s(s(elem!1)))))),
% 2.72/2.96 inference(quant_inst,[status(thm)],[])).
% 2.72/2.96 tff(10513,plain,
% 2.72/2.96 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(z, s(s(s(elem!1))))) | (~b(z, s(s(elem!1)))) | (~b(s(s(s(elem!1))), z)) | (~b(z, elem!1))),
% 2.72/2.96 inference(modus_ponens,[status(thm)],[10512, 10511])).
% 2.72/2.96 tff(10514,plain,
% 2.72/2.96 ($false),
% 2.72/2.96 inference(unit_resolution,[status(thm)],[10513, 166, 10507, 10502, 240, 1820, 121])).
% 2.72/2.96 tff(10515,plain,((~r(s(s(s(elem!1))), s(s(elem!1)))) | (~b(z, s(s(s(elem!1))))) | (~b(z, s(s(elem!1)))) | (~b(s(s(s(elem!1))), z)) | r(z, elem!1) | (s(s(elem!1)) = s(s(s(elem!1)))) | (~r(s(z), s(s(elem!1)))) | (~r(s(z), s(s(s(elem!1)))))), inference(lemma,lemma(discharge,[]))).
% 2.72/2.96 tff(10516,plain,
% 2.72/2.96 (~r(s(s(s(elem!1))), s(s(elem!1)))),
% 2.72/2.96 inference(unit_resolution,[status(thm)],[10515, 45, 1820, 121, 2510, 240, 311, 119])).
% 2.72/2.96 tff(10517,plain,
% 2.72/2.96 (r(s(s(elem!1)), s(s(s(elem!1))))),
% 2.72/2.96 inference(unit_resolution,[status(thm)],[1834, 10516, 1820, 240, 45])).
% 2.72/2.96 tff(10518,plain,
% 2.72/2.96 (~r(s(s(s(elem!1))), s(s(z)))),
% 2.72/2.96 inference(unit_resolution,[status(thm)],[2939, 10517, 311, 119])).
% 2.72/2.96 tff(10519,plain,
% 2.72/2.96 (b(s(s(s(elem!1))), s(s(z)))),
% 2.72/2.96 inference(unit_resolution,[status(thm)],[218, 10518])).
% 2.72/2.96 tff(10520,plain,
% 2.72/2.96 (~r(s(s(z)), s(s(elem!1)))),
% 2.72/2.96 inference(unit_resolution,[status(thm)],[4253, 10519, 311, 96, 10517])).
% 2.72/2.96 tff(10521,plain,
% 2.72/2.96 (r(s(s(elem!1)), s(z))),
% 2.72/2.96 inference(unit_resolution,[status(thm)],[1912, 4568])).
% 2.72/2.96 tff(10522,plain,
% 2.72/2.96 (~r(z, s(s(s(elem!1))))),
% 2.72/2.96 inference(unit_resolution,[status(thm)],[10496, 866, 97, 120])).
% 2.72/2.96 tff(10523,plain,
% 2.72/2.96 (b(z, s(s(s(elem!1))))),
% 2.72/2.96 inference(unit_resolution,[status(thm)],[261, 10522])).
% 2.72/2.96 tff(10524,plain,
% 2.72/2.96 (~r(z, s(s(elem!1)))),
% 2.72/2.96 inference(unit_resolution,[status(thm)],[2359, 866, 97, 120])).
% 2.72/2.96 tff(10525,plain,
% 2.72/2.96 (b(z, s(s(elem!1)))),
% 2.72/2.96 inference(unit_resolution,[status(thm)],[1795, 10524])).
% 2.72/2.96 tff(10526,plain,
% 2.72/2.96 (r(s(s(z)), s(s(s(elem!1)))) <=> r(s(s(elem!1)), s(s(s(elem!1))))),
% 2.72/2.96 inference(monotonicity,[status(thm)],[34])).
% 2.72/2.96 tff(10527,plain,
% 2.72/2.96 (r(s(s(elem!1)), s(s(s(elem!1)))) <=> r(s(s(z)), s(s(s(elem!1))))),
% 2.72/2.96 inference(symmetry,[status(thm)],[10526])).
% 2.72/2.96 tff(10528,plain,
% 2.72/2.96 ((~(s(s(z)) = s(s(s(elem!1))))) <=> (~(s(s(elem!1)) = s(s(s(elem!1)))))),
% 2.72/2.96 inference(monotonicity,[status(thm)],[3342])).
% 2.72/2.96 tff(10529,plain,
% 2.72/2.96 (~(s(s(elem!1)) = s(s(s(elem!1))))),
% 2.72/2.96 inference(modus_ponens,[status(thm)],[209, 10528])).
% 2.72/2.97 tff(10530,plain,
% 2.72/2.97 (r(s(z), s(s(z))) <=> r(s(z), s(s(elem!1)))),
% 2.72/2.97 inference(monotonicity,[status(thm)],[34])).
% 2.72/2.97 tff(10531,plain,
% 2.72/2.97 (r(s(z), s(s(elem!1)))),
% 2.72/2.97 inference(modus_ponens,[status(thm)],[120, 10530])).
% 2.72/2.97 tff(10532,plain,
% 2.72/2.97 (~r(s(s(s(elem!1))), s(z))),
% 2.72/2.97 inference(unit_resolution,[status(thm)],[6958, 10531, 10525, 10523, 4577, 10529])).
% 2.72/2.97 tff(10533,plain,
% 2.72/2.97 (b(s(s(s(elem!1))), s(z))),
% 2.72/2.97 inference(unit_resolution,[status(thm)],[1849, 10532])).
% 2.72/2.97 tff(10534,plain,
% 2.72/2.97 (b(elem!1, s(s(s(elem!1))))),
% 2.72/2.97 inference(modus_ponens,[status(thm)],[10523, 638])).
% 2.72/2.97 tff(10535,plain,
% 2.72/2.97 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(z))) | (~b(s(z), s(s(s(elem!1))))) | (~b(elem!1, s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(z))) | (~b(s(z), s(s(s(elem!1))))) | (~b(elem!1, s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(z))))),
% 2.72/2.97 inference(rewrite,[status(thm)],[])).
% 2.72/2.97 tff(10536,plain,
% 2.72/2.97 (((~b(s(z), s(s(s(elem!1))))) | (~b(elem!1, s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(z), s(s(s(elem!1))))) | (~b(elem!1, s(s(s(elem!1))))) | (~b(elem!1, s(z)))) <=> ((~b(elem!1, s(z))) | (~b(s(z), s(s(s(elem!1))))) | (~b(elem!1, s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(z))))),
% 2.72/2.97 inference(rewrite,[status(thm)],[])).
% 2.72/2.97 tff(10537,plain,
% 2.72/2.97 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(s(elem!1))))) | (~b(elem!1, s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(z), s(s(s(elem!1))))) | (~b(elem!1, s(s(s(elem!1))))) | (~b(elem!1, s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(z))) | (~b(s(z), s(s(s(elem!1))))) | (~b(elem!1, s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(z)))))),
% 2.72/2.97 inference(monotonicity,[status(thm)],[10536])).
% 2.72/2.97 tff(10538,plain,
% 2.72/2.97 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(s(elem!1))))) | (~b(elem!1, s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(z), s(s(s(elem!1))))) | (~b(elem!1, s(s(s(elem!1))))) | (~b(elem!1, s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(z))) | (~b(s(z), s(s(s(elem!1))))) | (~b(elem!1, s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(z))))),
% 2.72/2.97 inference(transitivity,[status(thm)],[10537, 10535])).
% 2.72/2.97 tff(10539,plain,
% 2.72/2.97 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(s(elem!1))))) | (~b(elem!1, s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(z), s(s(s(elem!1))))) | (~b(elem!1, s(s(s(elem!1))))) | (~b(elem!1, s(z))))),
% 2.72/2.97 inference(quant_inst,[status(thm)],[])).
% 2.72/2.97 tff(10540,plain,
% 2.72/2.97 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(z))) | (~b(s(z), s(s(s(elem!1))))) | (~b(elem!1, s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(z)))),
% 2.72/2.97 inference(modus_ponens,[status(thm)],[10539, 10538])).
% 2.72/2.97 tff(10541,plain,
% 2.72/2.97 ($false),
% 2.72/2.97 inference(unit_resolution,[status(thm)],[10540, 166, 643, 241, 96, 1212])).
% 2.72/2.97 tff(10542,plain,((~b(s(z), s(s(s(elem!1))))) | (~b(elem!1, s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(z))) | (~b(elem!1, s(z)))), inference(lemma,lemma(discharge,[]))).
% 2.72/2.97 tff(10543,plain,
% 2.72/2.97 (~b(s(z), s(s(s(elem!1))))),
% 2.72/2.97 inference(unit_resolution,[status(thm)],[10542, 10534, 10533, 5417])).
% 2.72/2.97 tff(10544,plain,
% 2.72/2.97 (r(s(z), s(s(s(elem!1))))),
% 2.72/2.97 inference(unit_resolution,[status(thm)],[116, 10543])).
% 2.72/2.97 tff(10545,plain,
% 2.72/2.97 (r(s(s(elem!1)), z)),
% 2.72/2.97 inference(modus_ponens,[status(thm)],[866, 6286])).
% 2.72/2.97 tff(10546,plain,
% 2.72/2.97 (r(s(s(elem!1)), elem!1)),
% 2.72/2.97 inference(modus_ponens,[status(thm)],[10545, 6285])).
% 2.72/2.97 tff(10547,plain,
% 2.72/2.97 (~r(s(s(s(elem!1))), s(s(elem!1)))),
% 2.72/2.97 inference(unit_resolution,[status(thm)],[2508, 10544, 10531, 10546])).
% 2.72/2.97 tff(10548,plain,
% 2.72/2.97 (b(s(s(s(elem!1))), s(s(elem!1)))),
% 2.72/2.97 inference(unit_resolution,[status(thm)],[889, 10547, 3345])).
% 2.72/2.97 tff(10549,plain,
% 2.72/2.97 (~b(s(s(elem!1)), s(s(s(elem!1))))),
% 2.72/2.97 inference(unit_resolution,[status(thm)],[2349, 10548, 97, 10525, 10544])).
% 2.72/2.97 tff(10550,plain,
% 2.72/2.97 (r(s(s(elem!1)), s(s(s(elem!1))))),
% 2.72/2.97 inference(unit_resolution,[status(thm)],[461, 10549, 10529])).
% 2.72/2.97 tff(10551,plain,
% 2.72/2.97 (r(s(s(z)), s(s(s(elem!1))))),
% 2.72/2.97 inference(modus_ponens,[status(thm)],[10550, 10527])).
% 2.72/2.97 tff(10552,plain,
% 2.72/2.97 (~r(s(s(z)), s(s(s(elem!1))))),
% 2.72/2.97 inference(unit_resolution,[status(thm)],[2304, 10544, 154, 120])).
% 2.72/2.97 tff(10553,plain,
% 2.72/2.97 ($false),
% 2.72/2.97 inference(unit_resolution,[status(thm)],[10552, 10551])).
% 2.72/2.97 tff(10554,plain,((~(s(s(z)) = s(s(elem!1)))) | (~r(s(z), z)) | (~r(s(s(s(elem!1))), z)) | (~r(s(z), s(s(z)))) | (~r(s(s(elem!1)), s(z))) | (~b(z, s(z))) | (~r(s(s(z)), z))), inference(lemma,lemma(discharge,[]))).
% 2.72/2.97 tff(10555,plain,
% 2.72/2.97 (~(s(s(z)) = s(s(elem!1)))),
% 2.72/2.97 inference(unit_resolution,[status(thm)],[10554, 154, 97, 120, 10521, 118, 866])).
% 2.72/2.97 tff(10556,plain,
% 2.72/2.97 (b(s(s(z)), s(s(elem!1)))),
% 2.72/2.97 inference(unit_resolution,[status(thm)],[390, 10555, 2288])).
% 2.72/2.97 tff(10557,plain,
% 2.72/2.97 (~r(s(s(s(elem!1))), s(s(z)))),
% 2.72/2.97 inference(unit_resolution,[status(thm)],[874, 350, 120, 866])).
% 2.72/2.97 tff(10558,plain,
% 2.72/2.97 (b(s(s(s(elem!1))), s(s(z)))),
% 2.72/2.97 inference(unit_resolution,[status(thm)],[216, 79, 10557, 211])).
% 2.72/2.97 tff(10559,plain,
% 2.72/2.97 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), s(z))) | (~r(s(s(elem!1)), s(s(s(elem!1))))) | (~r(s(s(elem!1)), s(z))) | (~r(s(z), s(s(z)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(elem!1))), s(z))) | (~r(s(s(elem!1)), s(s(s(elem!1))))) | (~r(s(s(elem!1)), s(z))) | (~r(s(z), s(s(z)))))),
% 2.72/2.97 inference(rewrite,[status(thm)],[])).
% 2.72/2.97 tff(10560,plain,
% 2.72/2.97 (((~r(s(z), s(s(z)))) | (~r(s(s(s(elem!1))), s(z))) | (~r(s(s(elem!1)), s(z))) | (~r(s(s(elem!1)), s(s(s(elem!1)))))) <=> ((~r(s(s(s(elem!1))), s(z))) | (~r(s(s(elem!1)), s(s(s(elem!1))))) | (~r(s(s(elem!1)), s(z))) | (~r(s(z), s(s(z)))))),
% 2.72/2.97 inference(rewrite,[status(thm)],[])).
% 2.72/2.97 tff(10561,plain,
% 2.72/2.97 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(s(z)))) | (~r(s(s(s(elem!1))), s(z))) | (~r(s(s(elem!1)), s(z))) | (~r(s(s(elem!1)), s(s(s(elem!1))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), s(z))) | (~r(s(s(elem!1)), s(s(s(elem!1))))) | (~r(s(s(elem!1)), s(z))) | (~r(s(z), s(s(z))))))),
% 2.72/2.97 inference(monotonicity,[status(thm)],[10560])).
% 2.72/2.97 tff(10562,plain,
% 2.72/2.97 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(s(z)))) | (~r(s(s(s(elem!1))), s(z))) | (~r(s(s(elem!1)), s(z))) | (~r(s(s(elem!1)), s(s(s(elem!1))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(elem!1))), s(z))) | (~r(s(s(elem!1)), s(s(s(elem!1))))) | (~r(s(s(elem!1)), s(z))) | (~r(s(z), s(s(z)))))),
% 2.72/2.97 inference(transitivity,[status(thm)],[10561, 10559])).
% 2.72/2.97 tff(10563,plain,
% 2.72/2.97 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(s(z)))) | (~r(s(s(s(elem!1))), s(z))) | (~r(s(s(elem!1)), s(z))) | (~r(s(s(elem!1)), s(s(s(elem!1))))))),
% 2.72/2.97 inference(quant_inst,[status(thm)],[])).
% 2.72/2.97 tff(10564,plain,
% 2.72/2.97 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(elem!1))), s(z))) | (~r(s(s(elem!1)), s(s(s(elem!1))))) | (~r(s(s(elem!1)), s(z))) | (~r(s(z), s(s(z))))),
% 2.72/2.97 inference(modus_ponens,[status(thm)],[10563, 10562])).
% 2.72/2.97 tff(10565,plain,
% 2.72/2.97 (~r(s(s(elem!1)), s(s(s(elem!1))))),
% 2.72/2.97 inference(unit_resolution,[status(thm)],[10564, 197, 120, 350, 4577])).
% 2.72/2.97 tff(10566,plain,
% 2.72/2.97 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(s(z)))) | (~r(s(s(elem!1)), s(z))) | (~r(s(s(s(elem!1))), s(z))) | (~r(s(s(s(elem!1))), s(s(elem!1)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(z), s(s(z)))) | (~r(s(s(elem!1)), s(z))) | (~r(s(s(s(elem!1))), s(z))) | (~r(s(s(s(elem!1))), s(s(elem!1)))))),
% 2.72/2.97 inference(rewrite,[status(thm)],[])).
% 2.72/2.97 tff(10567,plain,
% 2.72/2.97 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(s(z)))) | (~r(s(s(elem!1)), s(z))) | (~r(s(s(s(elem!1))), s(z))) | (~r(s(s(s(elem!1))), s(s(elem!1)))))),
% 2.72/2.97 inference(quant_inst,[status(thm)],[])).
% 2.72/2.97 tff(10568,plain,
% 2.72/2.97 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(z), s(s(z)))) | (~r(s(s(elem!1)), s(z))) | (~r(s(s(s(elem!1))), s(z))) | (~r(s(s(s(elem!1))), s(s(elem!1))))),
% 2.72/2.97 inference(modus_ponens,[status(thm)],[10567, 10566])).
% 2.72/2.97 tff(10569,plain,
% 2.72/2.97 (~r(s(s(s(elem!1))), s(s(elem!1)))),
% 2.72/2.97 inference(unit_resolution,[status(thm)],[10568, 197, 120, 350, 4577])).
% 2.72/2.97 tff(10570,plain,
% 2.72/2.97 (s(s(elem!1)) = s(s(s(elem!1)))),
% 2.72/2.97 inference(unit_resolution,[status(thm)],[1834, 10569, 240, 1820, 10565])).
% 2.72/2.97 tff(10571,plain,
% 2.72/2.97 (b(s(s(z)), s(s(s(elem!1))))),
% 2.72/2.97 inference(unit_resolution,[status(thm)],[6647, 10570, 446])).
% 2.72/2.97 tff(10572,plain,
% 2.72/2.97 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(z)))) | (~b(z, s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(s(z)))) | (~b(s(s(z)), s(s(s(elem!1))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(s(z)))) | (~b(z, s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(s(z)))) | (~b(s(s(z)), s(s(s(elem!1))))))),
% 2.72/2.97 inference(rewrite,[status(thm)],[])).
% 2.72/2.97 tff(10573,plain,
% 2.72/2.97 (((~b(s(s(s(elem!1))), s(s(z)))) | (~b(z, s(s(z)))) | (~b(s(s(z)), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(s(z)))) | (~b(z, s(s(z)))) | (~b(z, s(s(s(elem!1)))))) <=> ((~b(z, s(s(z)))) | (~b(z, s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(s(z)))) | (~b(s(s(z)), s(s(s(elem!1))))))),
% 2.72/2.97 inference(rewrite,[status(thm)],[])).
% 2.72/2.97 tff(10574,plain,
% 2.72/2.97 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), s(s(z)))) | (~b(z, s(s(z)))) | (~b(s(s(z)), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(s(z)))) | (~b(z, s(s(z)))) | (~b(z, s(s(s(elem!1))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(z)))) | (~b(z, s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(s(z)))) | (~b(s(s(z)), s(s(s(elem!1)))))))),
% 2.72/2.97 inference(monotonicity,[status(thm)],[10573])).
% 2.72/2.97 tff(10575,plain,
% 2.72/2.97 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), s(s(z)))) | (~b(z, s(s(z)))) | (~b(s(s(z)), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(s(z)))) | (~b(z, s(s(z)))) | (~b(z, s(s(s(elem!1))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(s(z)))) | (~b(z, s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(s(z)))) | (~b(s(s(z)), s(s(s(elem!1))))))),
% 2.72/2.97 inference(transitivity,[status(thm)],[10574, 10572])).
% 2.72/2.97 tff(10576,plain,
% 2.72/2.97 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), s(s(z)))) | (~b(z, s(s(z)))) | (~b(s(s(z)), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(s(z)))) | (~b(z, s(s(z)))) | (~b(z, s(s(s(elem!1))))))),
% 2.72/2.97 inference(quant_inst,[status(thm)],[])).
% 2.72/2.97 tff(10577,plain,
% 2.72/2.97 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(s(z)))) | (~b(z, s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(s(z)))) | (~b(s(s(z)), s(s(s(elem!1)))))),
% 2.72/2.97 inference(modus_ponens,[status(thm)],[10576, 10575])).
% 2.72/2.97 tff(10578,plain,
% 2.72/2.97 ($false),
% 2.72/2.97 inference(unit_resolution,[status(thm)],[10577, 166, 240, 10451, 10571, 10558])).
% 2.72/2.97 tff(10579,plain,((~r(s(s(s(elem!1))), s(z))) | (~b(z, s(s(s(elem!1))))) | (~b(z, s(s(z)))) | (~r(s(z), s(s(z)))) | (~r(s(s(z)), z)) | (~b(s(s(z)), s(s(elem!1)))) | (~b(z, s(s(elem!1)))) | (~r(s(s(elem!1)), s(z)))), inference(lemma,lemma(discharge,[]))).
% 2.72/2.97 tff(10580,plain,
% 2.72/2.97 (~r(s(s(s(elem!1))), s(z))),
% 2.72/2.97 inference(unit_resolution,[status(thm)],[10579, 10556, 10451, 120, 866, 10523, 10525, 10521])).
% 2.72/2.97 tff(10581,plain,
% 2.72/2.97 (b(s(s(s(elem!1))), s(z))),
% 2.72/2.97 inference(unit_resolution,[status(thm)],[1849, 10580])).
% 2.72/2.97 tff(10582,plain,
% 2.72/2.97 (~b(s(z), s(s(s(elem!1))))),
% 2.72/2.97 inference(unit_resolution,[status(thm)],[249, 10581, 10523, 118])).
% 2.72/2.97 tff(10583,plain,
% 2.72/2.97 (r(s(z), s(s(s(elem!1))))),
% 2.72/2.97 inference(unit_resolution,[status(thm)],[116, 10582])).
% 2.72/2.97 tff(10584,plain,
% 2.72/2.97 (~r(s(s(elem!1)), s(s(s(elem!1))))),
% 2.72/2.97 inference(unit_resolution,[status(thm)],[5310, 10583, 10521, 154])).
% 2.72/2.97 tff(10585,plain,
% 2.72/2.97 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(z, s(s(z)))) | (~b(z, s(s(elem!1)))) | (~b(s(s(s(elem!1))), s(z))) | (~b(z, s(z))) | (~b(s(s(z)), s(s(elem!1)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(z, s(s(z)))) | (~b(z, s(s(elem!1)))) | (~b(s(s(s(elem!1))), s(z))) | (~b(z, s(z))) | (~b(s(s(z)), s(s(elem!1)))))),
% 2.72/2.97 inference(rewrite,[status(thm)],[])).
% 2.72/2.97 tff(10586,plain,
% 2.72/2.97 (((~b(s(s(s(elem!1))), s(z))) | (~b(z, s(z))) | (~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(s(s(z)), s(s(elem!1)))) | (~b(z, s(s(elem!1)))) | (~b(z, s(s(z))))) <=> ((~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(z, s(s(z)))) | (~b(z, s(s(elem!1)))) | (~b(s(s(s(elem!1))), s(z))) | (~b(z, s(z))) | (~b(s(s(z)), s(s(elem!1)))))),
% 2.72/2.97 inference(rewrite,[status(thm)],[])).
% 2.72/2.97 tff(10587,plain,
% 2.72/2.97 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), s(z))) | (~b(z, s(z))) | (~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(s(s(z)), s(s(elem!1)))) | (~b(z, s(s(elem!1)))) | (~b(z, s(s(z)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(z, s(s(z)))) | (~b(z, s(s(elem!1)))) | (~b(s(s(s(elem!1))), s(z))) | (~b(z, s(z))) | (~b(s(s(z)), s(s(elem!1))))))),
% 2.72/2.97 inference(monotonicity,[status(thm)],[10586])).
% 2.72/2.97 tff(10588,plain,
% 2.72/2.97 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), s(z))) | (~b(z, s(z))) | (~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(s(s(z)), s(s(elem!1)))) | (~b(z, s(s(elem!1)))) | (~b(z, s(s(z)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(z, s(s(z)))) | (~b(z, s(s(elem!1)))) | (~b(s(s(s(elem!1))), s(z))) | (~b(z, s(z))) | (~b(s(s(z)), s(s(elem!1)))))),
% 2.72/2.97 inference(transitivity,[status(thm)],[10587, 10585])).
% 2.72/2.97 tff(10589,plain,
% 2.72/2.97 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), s(z))) | (~b(z, s(z))) | (~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(s(s(z)), s(s(elem!1)))) | (~b(z, s(s(elem!1)))) | (~b(z, s(s(z)))))),
% 2.72/2.97 inference(quant_inst,[status(thm)],[])).
% 2.72/2.97 tff(10590,plain,
% 2.72/2.97 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(z, s(s(z)))) | (~b(z, s(s(elem!1)))) | (~b(s(s(s(elem!1))), s(z))) | (~b(z, s(z))) | (~b(s(s(z)), s(s(elem!1))))),
% 2.72/2.97 inference(modus_ponens,[status(thm)],[10589, 10588])).
% 2.72/2.97 tff(10591,plain,
% 2.72/2.97 ($false),
% 2.72/2.97 inference(unit_resolution,[status(thm)],[10590, 166, 463, 1820, 10451, 96, 118, 446])).
% 2.72/2.97 tff(10592,plain,((~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(z, s(s(elem!1)))) | (~b(z, s(s(z)))) | (~b(s(s(s(elem!1))), s(z))) | (~b(z, s(z))) | (~b(s(s(z)), s(s(elem!1))))), inference(lemma,lemma(discharge,[]))).
% 2.72/2.97 tff(10593,plain,
% 2.72/2.97 (~b(s(s(elem!1)), s(s(s(elem!1))))),
% 2.72/2.97 inference(unit_resolution,[status(thm)],[10592, 10581, 10451, 10525, 118, 10556])).
% 2.72/2.97 tff(10594,plain,
% 2.72/2.97 (s(s(elem!1)) = s(s(s(elem!1)))),
% 2.72/2.97 inference(unit_resolution,[status(thm)],[461, 10593, 10584])).
% 2.72/2.97 tff(10595,plain,
% 2.72/2.97 (b(s(s(elem!1)), s(z)) <=> b(s(s(s(elem!1))), s(z))),
% 2.72/2.97 inference(monotonicity,[status(thm)],[10594])).
% 2.72/2.97 tff(10596,plain,
% 2.72/2.97 (b(s(s(s(elem!1))), s(z)) <=> b(s(s(elem!1)), s(z))),
% 2.72/2.97 inference(symmetry,[status(thm)],[10595])).
% 2.72/2.97 tff(10597,plain,
% 2.72/2.97 (b(s(s(elem!1)), s(z))),
% 2.72/2.97 inference(modus_ponens,[status(thm)],[10581, 10596])).
% 2.72/2.97 tff(10598,plain,
% 2.72/2.97 ($false),
% 2.72/2.97 inference(unit_resolution,[status(thm)],[4568, 10597])).
% 2.72/2.97 tff(10599,plain,((~r(s(s(s(elem!1))), z)) | b(s(s(elem!1)), s(z)) | (~b(z, s(s(z)))) | (~b(z, s(z))) | (~r(s(z), s(s(z)))) | (~r(s(s(z)), z)) | r(s(s(z)), s(s(elem!1))) | (~r(s(z), z))), inference(lemma,lemma(discharge,[]))).
% 2.72/2.97 tff(10600,plain,
% 2.72/2.97 (~r(s(s(s(elem!1))), z)),
% 2.72/2.97 inference(unit_resolution,[status(thm)],[10599, 866, 10451, 118, 120, 4568, 2288, 97])).
% 2.72/2.97 tff(10601,plain,
% 2.72/2.97 (b(s(s(s(elem!1))), z)),
% 2.72/2.97 inference(unit_resolution,[status(thm)],[94, 10600])).
% 2.72/2.97 tff(10602,plain,
% 2.72/2.97 (~b(s(s(z)), s(s(elem!1)))),
% 2.72/2.97 inference(unit_resolution,[status(thm)],[10579, 350, 10451, 120, 866, 240, 1820, 4577])).
% 2.72/2.97 tff(10603,plain,
% 2.72/2.97 (s(s(z)) = s(s(elem!1))),
% 2.72/2.97 inference(unit_resolution,[status(thm)],[390, 10602, 2288])).
% 2.72/2.97 tff(10604,plain,
% 2.72/2.97 (r(s(z), s(s(z))) <=> r(s(z), s(s(elem!1)))),
% 2.72/2.97 inference(monotonicity,[status(thm)],[10603])).
% 2.72/2.97 tff(10605,plain,
% 2.72/2.97 (r(s(z), s(s(elem!1)))),
% 2.72/2.97 inference(modus_ponens,[status(thm)],[120, 10604])).
% 2.72/2.97 tff(10606,plain,
% 2.72/2.97 ((s(s(z)) = s(s(s(elem!1)))) <=> (s(s(elem!1)) = s(s(s(elem!1))))),
% 2.72/2.97 inference(monotonicity,[status(thm)],[10603])).
% 2.72/2.97 tff(10607,plain,
% 2.72/2.97 ((~(s(s(z)) = s(s(s(elem!1))))) <=> (~(s(s(elem!1)) = s(s(s(elem!1)))))),
% 2.72/2.97 inference(monotonicity,[status(thm)],[10606])).
% 2.72/2.97 tff(10608,plain,
% 2.72/2.97 (~(s(s(elem!1)) = s(s(s(elem!1))))),
% 2.72/2.97 inference(modus_ponens,[status(thm)],[209, 10607])).
% 2.72/2.97 tff(10609,plain,
% 2.72/2.97 ($false),
% 2.72/2.97 inference(unit_resolution,[status(thm)],[6958, 10608, 10605, 1820, 240, 4577, 350])).
% 2.72/2.97 tff(10610,plain,((~r(s(s(s(elem!1))), s(z))) | (~b(z, s(s(elem!1)))) | (~b(z, s(s(s(elem!1))))) | (~r(s(s(elem!1)), s(z))) | (~r(s(z), s(s(z)))) | r(s(s(z)), s(s(elem!1))) | (~b(z, s(s(z)))) | (~r(s(s(z)), z))), inference(lemma,lemma(discharge,[]))).
% 2.72/2.97 tff(10611,plain,
% 2.72/2.97 (~r(s(s(s(elem!1))), s(z))),
% 2.72/2.97 inference(unit_resolution,[status(thm)],[10610, 10525, 10523, 10521, 120, 2288, 10451, 866])).
% 2.72/2.97 tff(10612,plain,
% 2.72/2.97 (b(s(s(s(elem!1))), s(z))),
% 2.72/2.97 inference(unit_resolution,[status(thm)],[1849, 10611])).
% 2.72/2.97 tff(10613,plain,
% 2.72/2.97 (~(s(s(elem!1)) = s(s(s(elem!1))))),
% 2.72/2.97 inference(unit_resolution,[status(thm)],[4570, 10612, 4568])).
% 2.72/2.97 tff(10614,plain,
% 2.72/2.97 (~(s(s(s(elem!1))) = s(s(elem!1)))),
% 2.72/2.97 inference(unit_resolution,[status(thm)],[50, 10613])).
% 2.72/2.97 tff(10615,plain,
% 2.72/2.97 (~(s(s(s(elem!1))) = s(s(s(s(elem!1)))))),
% 2.72/2.97 inference(unit_resolution,[status(thm)],[357, 10613])).
% 2.72/2.97 tff(10616,plain,
% 2.72/2.97 (b(s(s(s(elem!1))), z) <=> b(s(s(s(elem!1))), elem!1)),
% 2.72/2.97 inference(monotonicity,[status(thm)],[620])).
% 2.72/2.97 tff(10617,plain,
% 2.72/2.97 (b(s(s(s(elem!1))), elem!1)),
% 2.72/2.98 inference(modus_ponens,[status(thm)],[121, 10616])).
% 2.72/2.98 tff(10618,plain,
% 2.72/2.98 (~b(s(z), s(s(s(elem!1))))),
% 2.72/2.98 inference(unit_resolution,[status(thm)],[249, 96, 10523, 118])).
% 2.72/2.98 tff(10619,plain,
% 2.72/2.98 (r(s(z), s(s(s(elem!1))))),
% 2.72/2.98 inference(unit_resolution,[status(thm)],[116, 10618])).
% 2.72/2.98 tff(10620,plain,
% 2.72/2.98 (~r(s(s(s(elem!1))), s(s(elem!1)))),
% 2.72/2.98 inference(unit_resolution,[status(thm)],[2508, 10546, 10619, 10531])).
% 2.72/2.98 tff(10621,plain,
% 2.72/2.98 (b(s(s(s(elem!1))), s(s(elem!1)))),
% 2.72/2.98 inference(unit_resolution,[status(thm)],[889, 10620, 1863])).
% 2.72/2.98 tff(10622,plain,
% 2.72/2.98 (r(s(z), z) <=> r(s(z), elem!1)),
% 2.72/2.98 inference(monotonicity,[status(thm)],[620])).
% 2.72/2.98 tff(10623,plain,
% 2.72/2.98 (r(s(z), elem!1)),
% 2.72/2.98 inference(modus_ponens,[status(thm)],[97, 10622])).
% 2.72/2.98 tff(10624,plain,
% 2.72/2.98 (r(s(s(s(s(z)))), elem!1) <=> r(s(s(s(s(elem!1)))), elem!1)),
% 2.72/2.98 inference(monotonicity,[status(thm)],[1087])).
% 2.72/2.98 tff(10625,plain,
% 2.72/2.98 (r(s(s(s(s(z)))), z) <=> r(s(s(s(s(z)))), elem!1)),
% 2.72/2.98 inference(monotonicity,[status(thm)],[620])).
% 2.72/2.98 tff(10626,plain,
% 2.72/2.98 (r(s(s(s(s(z)))), z) <=> r(s(s(s(s(elem!1)))), elem!1)),
% 2.72/2.98 inference(transitivity,[status(thm)],[10625, 10624])).
% 2.72/2.98 tff(10627,plain,
% 2.72/2.98 (b(s(s(s(s(elem!1)))), elem!1) <=> b(s(s(s(s(z)))), elem!1)),
% 2.72/2.98 inference(monotonicity,[status(thm)],[2370])).
% 2.72/2.98 tff(10628,plain,
% 2.72/2.98 (b(s(s(s(s(elem!1)))), elem!1) <=> b(s(s(s(s(z)))), z)),
% 2.72/2.98 inference(transitivity,[status(thm)],[10627, 4665])).
% 2.72/2.98 tff(10629,plain,
% 2.72/2.98 ((~b(s(s(s(s(elem!1)))), elem!1)) <=> (~b(s(s(s(s(z)))), z))),
% 2.72/2.98 inference(monotonicity,[status(thm)],[10628])).
% 2.72/2.98 tff(10630,plain,
% 2.72/2.98 (~b(s(z), s(s(s(s(elem!1)))))),
% 2.72/2.98 inference(unit_resolution,[status(thm)],[3794, 1402, 1212, 96, 641])).
% 2.72/2.98 tff(10631,plain,
% 2.72/2.98 (r(s(z), s(s(s(s(elem!1)))))),
% 2.72/2.98 inference(unit_resolution,[status(thm)],[681, 10630])).
% 2.72/2.98 tff(10632,plain,
% 2.72/2.98 (b(elem!1, s(s(s(s(elem!1))))) <=> b(elem!1, s(s(s(s(z)))))),
% 2.72/2.98 inference(symmetry,[status(thm)],[1100])).
% 2.72/2.98 tff(10633,plain,
% 2.72/2.98 ((~b(elem!1, s(s(s(s(elem!1)))))) <=> (~b(elem!1, s(s(s(s(z))))))),
% 2.72/2.98 inference(monotonicity,[status(thm)],[10632])).
% 2.72/2.98 tff(10634,plain,
% 2.72/2.98 (~b(elem!1, s(s(s(s(elem!1)))))),
% 2.72/2.98 inference(unit_resolution,[status(thm)],[2912, 1107, 643, 641])).
% 2.72/2.98 tff(10635,plain,
% 2.72/2.98 (~b(elem!1, s(s(s(s(z)))))),
% 2.72/2.98 inference(modus_ponens,[status(thm)],[10634, 10633])).
% 2.72/2.98 tff(10636,plain,
% 2.72/2.98 (r(elem!1, s(s(s(s(z)))))),
% 2.72/2.98 inference(unit_resolution,[status(thm)],[1098, 10635, 1045])).
% 2.72/2.98 tff(10637,plain,
% 2.72/2.98 (r(elem!1, s(s(s(s(elem!1)))))),
% 2.72/2.98 inference(modus_ponens,[status(thm)],[10636, 1088])).
% 2.72/2.98 tff(10638,plain,
% 2.72/2.98 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(s(s(s(elem!1)))), elem!1)) | (~b(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~b(s(s(s(s(elem!1)))), s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(s(s(s(elem!1)))), elem!1)) | (~b(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~b(s(s(s(s(elem!1)))), s(z))))),
% 2.72/2.98 inference(rewrite,[status(thm)],[])).
% 2.72/2.98 tff(10639,plain,
% 2.72/2.98 (((~b(s(s(s(elem!1))), s(z))) | (~b(s(s(s(s(elem!1)))), s(z))) | (~b(elem!1, s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(s(s(s(elem!1)))), elem!1)) | (~b(s(s(s(s(elem!1)))), s(s(s(elem!1)))))) <=> ((~b(elem!1, s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(s(s(s(elem!1)))), elem!1)) | (~b(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~b(s(s(s(s(elem!1)))), s(z))))),
% 2.72/2.98 inference(rewrite,[status(thm)],[])).
% 2.72/2.98 tff(10640,plain,
% 2.72/2.98 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), s(z))) | (~b(s(s(s(s(elem!1)))), s(z))) | (~b(elem!1, s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(s(s(s(elem!1)))), elem!1)) | (~b(s(s(s(s(elem!1)))), s(s(s(elem!1))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(s(s(s(elem!1)))), elem!1)) | (~b(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~b(s(s(s(s(elem!1)))), s(z)))))),
% 2.72/2.98 inference(monotonicity,[status(thm)],[10639])).
% 2.72/2.98 tff(10641,plain,
% 2.72/2.98 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), s(z))) | (~b(s(s(s(s(elem!1)))), s(z))) | (~b(elem!1, s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(s(s(s(elem!1)))), elem!1)) | (~b(s(s(s(s(elem!1)))), s(s(s(elem!1))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(s(s(s(elem!1)))), elem!1)) | (~b(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~b(s(s(s(s(elem!1)))), s(z))))),
% 2.72/2.98 inference(transitivity,[status(thm)],[10640, 10638])).
% 2.72/2.98 tff(10642,plain,
% 2.72/2.98 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), s(z))) | (~b(s(s(s(s(elem!1)))), s(z))) | (~b(elem!1, s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(s(s(s(elem!1)))), elem!1)) | (~b(s(s(s(s(elem!1)))), s(s(s(elem!1))))))),
% 2.72/2.98 inference(quant_inst,[status(thm)],[])).
% 2.72/2.98 tff(10643,plain,
% 2.72/2.98 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(s(s(s(elem!1)))), elem!1)) | (~b(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~b(s(s(s(s(elem!1)))), s(z)))),
% 2.72/2.98 inference(modus_ponens,[status(thm)],[10642, 10641])).
% 2.72/2.98 tff(10644,plain,
% 2.72/2.98 ((~b(s(s(s(s(elem!1)))), elem!1)) | (~b(s(s(s(s(elem!1)))), s(s(s(elem!1)))))),
% 2.72/2.98 inference(unit_resolution,[status(thm)],[10643, 166, 643, 96, 1402, 641])).
% 2.72/2.98 tff(10645,plain,
% 2.72/2.98 (~b(s(s(s(s(elem!1)))), elem!1)),
% 2.72/2.98 inference(unit_resolution,[status(thm)],[10644, 1107])).
% 2.72/2.98 tff(10646,plain,
% 2.72/2.98 (~b(s(s(s(s(z)))), z)),
% 2.72/2.98 inference(modus_ponens,[status(thm)],[10645, 10629])).
% 2.72/2.98 tff(10647,plain,
% 2.72/2.98 (r(s(s(s(s(z)))), z)),
% 2.72/2.98 inference(unit_resolution,[status(thm)],[3266, 10646])).
% 2.72/2.98 tff(10648,plain,
% 2.72/2.98 (r(s(s(s(s(elem!1)))), elem!1)),
% 2.72/2.98 inference(modus_ponens,[status(thm)],[10647, 10626])).
% 2.72/2.98 tff(10649,plain,
% 2.72/2.98 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(s(s(s(elem!1)))))) | (~r(s(z), elem!1)) | (~r(s(z), s(s(s(s(elem!1)))))) | (~r(s(s(s(s(elem!1)))), elem!1)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(elem!1, s(s(s(s(elem!1)))))) | (~r(s(z), elem!1)) | (~r(s(z), s(s(s(s(elem!1)))))) | (~r(s(s(s(s(elem!1)))), elem!1)))),
% 2.72/2.98 inference(rewrite,[status(thm)],[])).
% 2.72/2.98 tff(10650,plain,
% 2.72/2.98 (((~r(s(s(s(s(elem!1)))), elem!1)) | (~r(elem!1, s(s(s(s(elem!1)))))) | (~r(s(z), s(s(s(s(elem!1)))))) | (~r(s(z), elem!1))) <=> ((~r(elem!1, s(s(s(s(elem!1)))))) | (~r(s(z), elem!1)) | (~r(s(z), s(s(s(s(elem!1)))))) | (~r(s(s(s(s(elem!1)))), elem!1)))),
% 2.72/2.98 inference(rewrite,[status(thm)],[])).
% 2.72/2.98 tff(10651,plain,
% 2.72/2.98 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(elem!1)))), elem!1)) | (~r(elem!1, s(s(s(s(elem!1)))))) | (~r(s(z), s(s(s(s(elem!1)))))) | (~r(s(z), elem!1)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(s(s(s(elem!1)))))) | (~r(s(z), elem!1)) | (~r(s(z), s(s(s(s(elem!1)))))) | (~r(s(s(s(s(elem!1)))), elem!1))))),
% 2.72/2.98 inference(monotonicity,[status(thm)],[10650])).
% 2.72/2.98 tff(10652,plain,
% 2.72/2.98 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(elem!1)))), elem!1)) | (~r(elem!1, s(s(s(s(elem!1)))))) | (~r(s(z), s(s(s(s(elem!1)))))) | (~r(s(z), elem!1)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(elem!1, s(s(s(s(elem!1)))))) | (~r(s(z), elem!1)) | (~r(s(z), s(s(s(s(elem!1)))))) | (~r(s(s(s(s(elem!1)))), elem!1)))),
% 2.72/2.98 inference(transitivity,[status(thm)],[10651, 10649])).
% 2.72/2.98 tff(10653,plain,
% 2.72/2.98 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(elem!1)))), elem!1)) | (~r(elem!1, s(s(s(s(elem!1)))))) | (~r(s(z), s(s(s(s(elem!1)))))) | (~r(s(z), elem!1)))),
% 2.72/2.98 inference(quant_inst,[status(thm)],[])).
% 2.72/2.98 tff(10654,plain,
% 2.72/2.98 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(elem!1, s(s(s(s(elem!1)))))) | (~r(s(z), elem!1)) | (~r(s(z), s(s(s(s(elem!1)))))) | (~r(s(s(s(s(elem!1)))), elem!1))),
% 2.72/2.98 inference(modus_ponens,[status(thm)],[10653, 10652])).
% 2.72/2.98 tff(10655,plain,
% 2.72/2.98 ($false),
% 2.72/2.98 inference(unit_resolution,[status(thm)],[10654, 197, 2381, 699, 10648, 10637])).
% 2.72/2.98 tff(10656,plain,((~b(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~r(s(z), elem!1)) | (~r(s(z), s(s(s(s(elem!1)))))) | (~(s(s(z)) = s(s(elem!1)))) | (~b(elem!1, s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(s(s(s(elem!1)))), s(z))) | (~b(s(s(s(elem!1))), elem!1))), inference(lemma,lemma(discharge,[]))).
% 2.72/2.98 tff(10657,plain,
% 2.72/2.98 (~b(s(s(s(s(elem!1)))), s(s(s(elem!1))))),
% 2.72/2.98 inference(unit_resolution,[status(thm)],[10656, 10631, 2381, 34, 643, 96, 1402, 641])).
% 2.72/2.98 tff(10658,plain,
% 2.72/2.98 (r(s(s(s(s(elem!1)))), s(s(s(elem!1))))),
% 2.72/2.98 inference(unit_resolution,[status(thm)],[1063, 79, 10657, 1038])).
% 2.72/2.98 tff(10659,plain,
% 2.72/2.98 (~r(s(s(s(elem!1))), s(s(s(s(elem!1)))))),
% 2.72/2.98 inference(unit_resolution,[status(thm)],[2125, 10631, 119, 10658])).
% 2.72/2.98 tff(10660,plain,
% 2.72/2.98 (b(s(s(s(elem!1))), s(s(s(s(elem!1)))))),
% 2.72/2.98 inference(unit_resolution,[status(thm)],[694, 79, 361, 10659])).
% 2.72/2.98 tff(10661,plain,
% 2.72/2.98 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(elem!1, s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(s(s(s(elem!1)))), elem!1)) | (~b(s(s(s(elem!1))), s(s(s(s(elem!1)))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(elem!1, s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(s(s(s(elem!1)))), elem!1)) | (~b(s(s(s(elem!1))), s(s(s(s(elem!1)))))))),
% 2.72/2.98 inference(rewrite,[status(thm)],[])).
% 2.72/2.98 tff(10662,plain,
% 2.72/2.98 (((~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(elem!1, s(s(s(elem!1))))) | (~b(s(s(s(s(elem!1)))), elem!1)) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(s(s(elem!1))), s(s(s(s(elem!1))))))) <=> ((~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(elem!1, s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(s(s(s(elem!1)))), elem!1)) | (~b(s(s(s(elem!1))), s(s(s(s(elem!1)))))))),
% 2.72/2.98 inference(rewrite,[status(thm)],[])).
% 2.72/2.98 tff(10663,plain,
% 2.72/2.98 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(elem!1, s(s(s(elem!1))))) | (~b(s(s(s(s(elem!1)))), elem!1)) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(s(s(elem!1))), s(s(s(s(elem!1)))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(elem!1, s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(s(s(s(elem!1)))), elem!1)) | (~b(s(s(s(elem!1))), s(s(s(s(elem!1))))))))),
% 2.72/2.98 inference(monotonicity,[status(thm)],[10662])).
% 2.72/2.98 tff(10664,plain,
% 2.72/2.98 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(elem!1, s(s(s(elem!1))))) | (~b(s(s(s(s(elem!1)))), elem!1)) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(s(s(elem!1))), s(s(s(s(elem!1)))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(elem!1, s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(s(s(s(elem!1)))), elem!1)) | (~b(s(s(s(elem!1))), s(s(s(s(elem!1)))))))),
% 2.72/2.98 inference(transitivity,[status(thm)],[10663, 10661])).
% 2.72/2.98 tff(10665,plain,
% 2.72/2.98 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(elem!1, s(s(s(elem!1))))) | (~b(s(s(s(s(elem!1)))), elem!1)) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(s(s(elem!1))), s(s(s(s(elem!1)))))))),
% 2.72/2.98 inference(quant_inst,[status(thm)],[])).
% 2.72/2.98 tff(10666,plain,
% 2.72/2.98 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(elem!1, s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(s(s(s(elem!1)))), elem!1)) | (~b(s(s(s(elem!1))), s(s(s(s(elem!1))))))),
% 2.72/2.98 inference(modus_ponens,[status(thm)],[10665, 10664])).
% 2.72/2.98 tff(10667,plain,
% 2.72/2.98 ($false),
% 2.72/2.98 inference(unit_resolution,[status(thm)],[10666, 166, 839, 643, 641, 1311, 640])).
% 2.72/2.98 tff(10668,plain,((~b(s(s(s(s(elem!1)))), elem!1)) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(elem!1, s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(s(s(elem!1))), s(s(s(s(elem!1))))))), inference(lemma,lemma(discharge,[]))).
% 2.72/2.98 tff(10669,plain,
% 2.72/2.98 (~b(s(s(s(s(elem!1)))), elem!1)),
% 2.72/2.98 inference(unit_resolution,[status(thm)],[10668, 10660, 643, 641, 839])).
% 2.72/2.98 tff(10670,plain,
% 2.72/2.98 (~b(s(s(s(s(z)))), z)),
% 2.72/2.98 inference(modus_ponens,[status(thm)],[10669, 10629])).
% 2.72/2.98 tff(10671,plain,
% 2.72/2.98 (r(s(s(s(s(z)))), z)),
% 2.72/2.98 inference(unit_resolution,[status(thm)],[3266, 10670])).
% 2.72/2.98 tff(10672,plain,
% 2.72/2.98 (r(s(s(s(s(elem!1)))), elem!1)),
% 2.72/2.98 inference(modus_ponens,[status(thm)],[10671, 10626])).
% 2.72/2.98 tff(10673,plain,
% 2.72/2.98 (~r(s(s(s(s(elem!1)))), s(s(elem!1)))),
% 2.72/2.98 inference(unit_resolution,[status(thm)],[4636, 10631, 4577, 311])).
% 2.72/2.98 tff(10674,plain,
% 2.72/2.98 (b(s(s(s(s(elem!1)))), s(s(elem!1)))),
% 2.72/2.98 inference(unit_resolution,[status(thm)],[813, 10673, 734])).
% 2.72/2.98 tff(10675,plain,
% 2.72/2.98 (r(elem!1, s(s(s(s(elem!1))))) <=> r(elem!1, s(s(s(s(z)))))),
% 2.72/2.98 inference(symmetry,[status(thm)],[1088])).
% 2.72/2.98 tff(10676,plain,
% 2.72/2.98 ((~r(elem!1, s(s(s(s(elem!1)))))) <=> (~r(elem!1, s(s(s(s(z))))))),
% 2.72/2.98 inference(monotonicity,[status(thm)],[10675])).
% 2.72/2.98 tff(10677,plain,
% 2.72/2.98 ($false),
% 2.72/2.98 inference(unit_resolution,[status(thm)],[10654, 197, 2381, 699, 743, 1047])).
% 2.72/2.98 tff(10678,plain,((~r(elem!1, s(s(s(s(elem!1)))))) | (~r(s(z), elem!1)) | (~r(s(z), s(s(s(s(elem!1)))))) | (~r(s(s(s(s(elem!1)))), elem!1))), inference(lemma,lemma(discharge,[]))).
% 2.72/2.98 tff(10679,plain,
% 2.72/2.98 (~r(elem!1, s(s(s(s(elem!1)))))),
% 2.72/2.98 inference(unit_resolution,[status(thm)],[10678, 10631, 2381, 10672])).
% 2.72/2.98 tff(10680,plain,
% 2.72/2.98 (~r(elem!1, s(s(s(s(z)))))),
% 2.72/2.98 inference(modus_ponens,[status(thm)],[10679, 10676])).
% 2.72/2.98 tff(10681,plain,
% 2.72/2.98 (b(elem!1, s(s(s(s(z)))))),
% 2.72/2.98 inference(unit_resolution,[status(thm)],[1098, 10680, 1045])).
% 2.72/2.98 tff(10682,plain,
% 2.72/2.98 (b(elem!1, s(s(s(s(elem!1)))))),
% 2.72/2.98 inference(modus_ponens,[status(thm)],[10681, 1100])).
% 2.72/2.98 tff(10683,plain,
% 2.72/2.98 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(elem!1)))), s(s(elem!1)))) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(s(elem!1)), s(s(s(s(elem!1)))))) | (~b(s(s(s(elem!1))), s(s(s(s(elem!1)))))) | (~b(elem!1, s(s(s(s(elem!1)))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(elem!1)))), s(s(elem!1)))) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(s(elem!1)), s(s(s(s(elem!1)))))) | (~b(s(s(s(elem!1))), s(s(s(s(elem!1)))))) | (~b(elem!1, s(s(s(s(elem!1)))))))),
% 2.72/2.98 inference(rewrite,[status(thm)],[])).
% 2.72/2.98 tff(10684,plain,
% 2.72/2.98 (((~b(s(s(elem!1)), s(s(s(s(elem!1)))))) | (~b(s(s(s(elem!1))), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), s(s(elem!1)))) | (~b(elem!1, s(s(s(s(elem!1)))))) | (~b(s(s(s(elem!1))), s(s(s(s(elem!1)))))) | (~b(s(s(s(elem!1))), elem!1))) <=> ((~b(s(s(s(s(elem!1)))), s(s(elem!1)))) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(s(elem!1)), s(s(s(s(elem!1)))))) | (~b(s(s(s(elem!1))), s(s(s(s(elem!1)))))) | (~b(elem!1, s(s(s(s(elem!1)))))))),
% 2.72/2.98 inference(rewrite,[status(thm)],[])).
% 2.72/2.98 tff(10685,plain,
% 2.72/2.98 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), s(s(s(s(elem!1)))))) | (~b(s(s(s(elem!1))), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), s(s(elem!1)))) | (~b(elem!1, s(s(s(s(elem!1)))))) | (~b(s(s(s(elem!1))), s(s(s(s(elem!1)))))) | (~b(s(s(s(elem!1))), elem!1)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(elem!1)))), s(s(elem!1)))) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(s(elem!1)), s(s(s(s(elem!1)))))) | (~b(s(s(s(elem!1))), s(s(s(s(elem!1)))))) | (~b(elem!1, s(s(s(s(elem!1))))))))),
% 2.72/2.98 inference(monotonicity,[status(thm)],[10684])).
% 2.72/2.98 tff(10686,plain,
% 2.72/2.98 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), s(s(s(s(elem!1)))))) | (~b(s(s(s(elem!1))), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), s(s(elem!1)))) | (~b(elem!1, s(s(s(s(elem!1)))))) | (~b(s(s(s(elem!1))), s(s(s(s(elem!1)))))) | (~b(s(s(s(elem!1))), elem!1)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(elem!1)))), s(s(elem!1)))) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(s(elem!1)), s(s(s(s(elem!1)))))) | (~b(s(s(s(elem!1))), s(s(s(s(elem!1)))))) | (~b(elem!1, s(s(s(s(elem!1)))))))),
% 2.72/2.98 inference(transitivity,[status(thm)],[10685, 10683])).
% 2.72/2.98 tff(10687,plain,
% 2.72/2.98 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), s(s(s(s(elem!1)))))) | (~b(s(s(s(elem!1))), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), s(s(elem!1)))) | (~b(elem!1, s(s(s(s(elem!1)))))) | (~b(s(s(s(elem!1))), s(s(s(s(elem!1)))))) | (~b(s(s(s(elem!1))), elem!1)))),
% 2.72/2.98 inference(quant_inst,[status(thm)],[])).
% 2.72/2.98 tff(10688,plain,
% 2.72/2.98 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(elem!1)))), s(s(elem!1)))) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(s(elem!1)), s(s(s(s(elem!1)))))) | (~b(s(s(s(elem!1))), s(s(s(s(elem!1)))))) | (~b(elem!1, s(s(s(s(elem!1))))))),
% 2.72/2.98 inference(modus_ponens,[status(thm)],[10687, 10686])).
% 2.72/2.98 tff(10689,plain,
% 2.72/2.98 ((~b(s(s(s(s(elem!1)))), s(s(elem!1)))) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(s(elem!1)), s(s(s(s(elem!1)))))) | (~b(s(s(s(elem!1))), s(s(s(s(elem!1)))))) | (~b(elem!1, s(s(s(s(elem!1))))))),
% 2.72/2.98 inference(unit_resolution,[status(thm)],[10688, 166])).
% 2.72/2.98 tff(10690,plain,
% 2.72/2.98 (~b(s(s(elem!1)), s(s(s(s(elem!1)))))),
% 2.72/2.98 inference(unit_resolution,[status(thm)],[10689, 10682, 641, 10674, 10660])).
% 2.72/2.98 tff(10691,plain,
% 2.72/2.98 (r(s(s(elem!1)), s(s(s(s(elem!1)))))),
% 2.72/2.98 inference(unit_resolution,[status(thm)],[827, 10690, 816])).
% 2.72/2.98 tff(10692,plain,
% 2.72/2.98 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(elem!1)), s(z))) | (~r(s(z), s(s(s(s(elem!1)))))) | (~r(s(s(s(s(elem!1)))), elem!1)) | (~r(s(s(elem!1)), s(s(s(s(elem!1)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(elem!1)), s(z))) | (~r(s(z), s(s(s(s(elem!1)))))) | (~r(s(s(s(s(elem!1)))), elem!1)) | (~r(s(s(elem!1)), s(s(s(s(elem!1)))))))),
% 2.72/2.99 inference(rewrite,[status(thm)],[])).
% 2.72/2.99 tff(10693,plain,
% 2.72/2.99 (((~r(s(s(s(s(elem!1)))), elem!1)) | (~r(s(z), s(s(s(s(elem!1)))))) | (~r(s(s(elem!1)), s(s(s(s(elem!1)))))) | (~r(s(s(elem!1)), s(z)))) <=> ((~r(s(s(elem!1)), s(z))) | (~r(s(z), s(s(s(s(elem!1)))))) | (~r(s(s(s(s(elem!1)))), elem!1)) | (~r(s(s(elem!1)), s(s(s(s(elem!1)))))))),
% 2.72/2.99 inference(rewrite,[status(thm)],[])).
% 2.72/2.99 tff(10694,plain,
% 2.72/2.99 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(elem!1)))), elem!1)) | (~r(s(z), s(s(s(s(elem!1)))))) | (~r(s(s(elem!1)), s(s(s(s(elem!1)))))) | (~r(s(s(elem!1)), s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(elem!1)), s(z))) | (~r(s(z), s(s(s(s(elem!1)))))) | (~r(s(s(s(s(elem!1)))), elem!1)) | (~r(s(s(elem!1)), s(s(s(s(elem!1))))))))),
% 2.72/2.99 inference(monotonicity,[status(thm)],[10693])).
% 2.72/2.99 tff(10695,plain,
% 2.72/2.99 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(elem!1)))), elem!1)) | (~r(s(z), s(s(s(s(elem!1)))))) | (~r(s(s(elem!1)), s(s(s(s(elem!1)))))) | (~r(s(s(elem!1)), s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(elem!1)), s(z))) | (~r(s(z), s(s(s(s(elem!1)))))) | (~r(s(s(s(s(elem!1)))), elem!1)) | (~r(s(s(elem!1)), s(s(s(s(elem!1)))))))),
% 2.72/2.99 inference(transitivity,[status(thm)],[10694, 10692])).
% 2.72/2.99 tff(10696,plain,
% 2.72/2.99 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(elem!1)))), elem!1)) | (~r(s(z), s(s(s(s(elem!1)))))) | (~r(s(s(elem!1)), s(s(s(s(elem!1)))))) | (~r(s(s(elem!1)), s(z))))),
% 2.72/2.99 inference(quant_inst,[status(thm)],[])).
% 2.72/2.99 tff(10697,plain,
% 2.72/2.99 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(elem!1)), s(z))) | (~r(s(z), s(s(s(s(elem!1)))))) | (~r(s(s(s(s(elem!1)))), elem!1)) | (~r(s(s(elem!1)), s(s(s(s(elem!1))))))),
% 2.72/2.99 inference(modus_ponens,[status(thm)],[10696, 10695])).
% 2.72/2.99 tff(10698,plain,
% 2.72/2.99 ($false),
% 2.72/2.99 inference(unit_resolution,[status(thm)],[10697, 197, 4577, 10691, 10631, 10672])).
% 2.72/2.99 tff(10699,plain,((~b(s(s(s(s(elem!1)))), s(z))) | (~r(s(s(elem!1)), s(z))) | (~b(s(s(s(elem!1))), elem!1)) | (~(s(s(z)) = s(s(elem!1)))) | (~r(s(z), elem!1)) | (~b(elem!1, s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (s(s(s(elem!1))) = s(s(s(s(elem!1))))) | (~r(s(z), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(z))) | (~r(s(z), s(s(elem!1)))) | (~b(elem!1, s(z)))), inference(lemma,lemma(discharge,[]))).
% 2.72/2.99 tff(10700,plain,
% 2.72/2.99 (~b(s(s(s(s(elem!1)))), s(z))),
% 2.72/2.99 inference(unit_resolution,[status(thm)],[10699, 10617, 4577, 34, 10623, 10534, 10621, 361, 10619, 96, 10531, 5417])).
% 2.72/2.99 tff(10701,plain,
% 2.72/2.99 (r(s(s(s(s(elem!1)))), s(z))),
% 2.72/2.99 inference(unit_resolution,[status(thm)],[661, 10700])).
% 2.72/2.99 tff(10702,plain,
% 2.72/2.99 (~r(s(s(s(s(elem!1)))), s(s(elem!1)))),
% 2.72/2.99 inference(unit_resolution,[status(thm)],[5796, 197, 10531, 4577, 10701])).
% 2.72/2.99 tff(10703,plain,
% 2.72/2.99 (b(s(s(s(s(elem!1)))), s(s(elem!1)))),
% 2.72/2.99 inference(unit_resolution,[status(thm)],[813, 10702, 734])).
% 2.72/2.99 tff(10704,plain,
% 2.72/2.99 (b(elem!1, s(s(elem!1))) <=> b(z, s(s(elem!1)))),
% 2.72/2.99 inference(monotonicity,[status(thm)],[752])).
% 2.72/2.99 tff(10705,plain,
% 2.72/2.99 (b(z, s(s(elem!1))) <=> b(elem!1, s(s(elem!1)))),
% 2.72/2.99 inference(symmetry,[status(thm)],[10704])).
% 2.72/2.99 tff(10706,plain,
% 2.72/2.99 (b(elem!1, s(s(elem!1)))),
% 2.72/2.99 inference(modus_ponens,[status(thm)],[10525, 10705])).
% 2.72/2.99 tff(10707,plain,
% 2.72/2.99 (~r(s(s(elem!1)), s(s(s(s(elem!1)))))),
% 2.72/2.99 inference(unit_resolution,[status(thm)],[5140, 197, 10531, 4577, 10701])).
% 2.72/2.99 tff(10708,plain,
% 2.72/2.99 (b(s(s(elem!1)), s(s(s(s(elem!1)))))),
% 2.72/2.99 inference(unit_resolution,[status(thm)],[827, 10707, 816])).
% 2.72/2.99 tff(10709,plain,
% 2.72/2.99 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(s(s(s(elem!1)))), s(s(elem!1)))) | (~b(elem!1, s(s(elem!1)))) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(s(elem!1)), s(s(s(s(elem!1)))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(s(s(s(elem!1)))), s(s(elem!1)))) | (~b(elem!1, s(s(elem!1)))) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(s(elem!1)), s(s(s(s(elem!1)))))))),
% 2.72/2.99 inference(rewrite,[status(thm)],[])).
% 2.72/2.99 tff(10710,plain,
% 2.72/2.99 (((~b(s(s(s(s(elem!1)))), s(s(elem!1)))) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(s(elem!1)), s(s(s(s(elem!1)))))) | (~b(elem!1, s(s(elem!1)))) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(s(s(elem!1))), elem!1))) <=> ((~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(s(s(s(elem!1)))), s(s(elem!1)))) | (~b(elem!1, s(s(elem!1)))) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(s(elem!1)), s(s(s(s(elem!1)))))))),
% 2.72/2.99 inference(rewrite,[status(thm)],[])).
% 2.72/2.99 tff(10711,plain,
% 2.72/2.99 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(elem!1)))), s(s(elem!1)))) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(s(elem!1)), s(s(s(s(elem!1)))))) | (~b(elem!1, s(s(elem!1)))) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(s(s(elem!1))), elem!1)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(s(s(s(elem!1)))), s(s(elem!1)))) | (~b(elem!1, s(s(elem!1)))) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(s(elem!1)), s(s(s(s(elem!1))))))))),
% 2.72/2.99 inference(monotonicity,[status(thm)],[10710])).
% 2.72/2.99 tff(10712,plain,
% 2.72/2.99 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(elem!1)))), s(s(elem!1)))) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(s(elem!1)), s(s(s(s(elem!1)))))) | (~b(elem!1, s(s(elem!1)))) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(s(s(elem!1))), elem!1)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(s(s(s(elem!1)))), s(s(elem!1)))) | (~b(elem!1, s(s(elem!1)))) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(s(elem!1)), s(s(s(s(elem!1)))))))),
% 2.72/2.99 inference(transitivity,[status(thm)],[10711, 10709])).
% 2.72/2.99 tff(10713,plain,
% 2.72/2.99 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(elem!1)))), s(s(elem!1)))) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(s(elem!1)), s(s(s(s(elem!1)))))) | (~b(elem!1, s(s(elem!1)))) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(s(s(elem!1))), elem!1)))),
% 2.72/2.99 inference(quant_inst,[status(thm)],[])).
% 2.72/2.99 tff(10714,plain,
% 2.72/2.99 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(s(s(s(elem!1)))), s(s(elem!1)))) | (~b(elem!1, s(s(elem!1)))) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(s(elem!1)), s(s(s(s(elem!1))))))),
% 2.72/2.99 inference(modus_ponens,[status(thm)],[10713, 10712])).
% 2.72/2.99 tff(10715,plain,
% 2.72/2.99 ($false),
% 2.72/2.99 inference(unit_resolution,[status(thm)],[10714, 166, 10621, 10708, 10706, 10703, 10617])).
% 2.72/2.99 tff(10716,plain,((~(s(s(z)) = s(s(elem!1)))) | (~r(s(s(elem!1)), s(z))) | (s(s(s(elem!1))) = s(s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(z))) | (s(s(s(elem!1))) = s(s(elem!1))) | (~b(s(s(s(elem!1))), z)) | (~r(s(z), z)) | (~b(z, s(z))) | (~r(s(s(z)), z)) | (~r(s(z), s(s(z))))), inference(lemma,lemma(discharge,[]))).
% 2.72/2.99 tff(10717,plain,
% 2.72/2.99 (~(s(s(z)) = s(s(elem!1)))),
% 2.72/2.99 inference(unit_resolution,[status(thm)],[10716, 10615, 10521, 10612, 10614, 10601, 97, 118, 866, 120])).
% 2.72/2.99 tff(10718,plain,
% 2.72/2.99 (~(s(s(elem!1)) = s(s(z)))),
% 2.72/2.99 inference(unit_resolution,[status(thm)],[131, 10717])).
% 2.72/2.99 tff(10719,plain,
% 2.72/2.99 (b(s(s(z)), s(s(elem!1)))),
% 2.72/2.99 inference(unit_resolution,[status(thm)],[390, 10717, 2288])).
% 2.72/2.99 tff(10720,plain,
% 2.72/2.99 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(z)))) | (~b(z, s(s(elem!1)))) | (~b(s(s(elem!1)), s(s(z)))) | (~b(s(s(z)), s(s(elem!1)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(s(z)))) | (~b(z, s(s(elem!1)))) | (~b(s(s(elem!1)), s(s(z)))) | (~b(s(s(z)), s(s(elem!1)))))),
% 2.72/2.99 inference(rewrite,[status(thm)],[])).
% 2.72/2.99 tff(10721,plain,
% 2.72/2.99 (((~b(s(s(elem!1)), s(s(z)))) | (~b(z, s(s(z)))) | (~b(s(s(z)), s(s(elem!1)))) | (~b(s(s(elem!1)), s(s(z)))) | (~b(z, s(s(z)))) | (~b(z, s(s(elem!1))))) <=> ((~b(z, s(s(z)))) | (~b(z, s(s(elem!1)))) | (~b(s(s(elem!1)), s(s(z)))) | (~b(s(s(z)), s(s(elem!1)))))),
% 2.72/2.99 inference(rewrite,[status(thm)],[])).
% 2.72/2.99 tff(10722,plain,
% 2.72/2.99 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), s(s(z)))) | (~b(z, s(s(z)))) | (~b(s(s(z)), s(s(elem!1)))) | (~b(s(s(elem!1)), s(s(z)))) | (~b(z, s(s(z)))) | (~b(z, s(s(elem!1)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(z)))) | (~b(z, s(s(elem!1)))) | (~b(s(s(elem!1)), s(s(z)))) | (~b(s(s(z)), s(s(elem!1))))))),
% 2.72/2.99 inference(monotonicity,[status(thm)],[10721])).
% 2.72/2.99 tff(10723,plain,
% 2.72/2.99 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), s(s(z)))) | (~b(z, s(s(z)))) | (~b(s(s(z)), s(s(elem!1)))) | (~b(s(s(elem!1)), s(s(z)))) | (~b(z, s(s(z)))) | (~b(z, s(s(elem!1)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(s(z)))) | (~b(z, s(s(elem!1)))) | (~b(s(s(elem!1)), s(s(z)))) | (~b(s(s(z)), s(s(elem!1)))))),
% 2.72/2.99 inference(transitivity,[status(thm)],[10722, 10720])).
% 2.72/2.99 tff(10724,plain,
% 2.72/2.99 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), s(s(z)))) | (~b(z, s(s(z)))) | (~b(s(s(z)), s(s(elem!1)))) | (~b(s(s(elem!1)), s(s(z)))) | (~b(z, s(s(z)))) | (~b(z, s(s(elem!1)))))),
% 2.72/2.99 inference(quant_inst,[status(thm)],[])).
% 2.72/2.99 tff(10725,plain,
% 2.72/2.99 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(s(z)))) | (~b(z, s(s(elem!1)))) | (~b(s(s(elem!1)), s(s(z)))) | (~b(s(s(z)), s(s(elem!1))))),
% 2.72/2.99 inference(modus_ponens,[status(thm)],[10724, 10723])).
% 2.72/2.99 tff(10726,plain,
% 2.72/2.99 ($false),
% 2.72/2.99 inference(unit_resolution,[status(thm)],[10725, 166, 1820, 405, 10451, 446])).
% 2.72/2.99 tff(10727,plain,((~b(s(s(elem!1)), s(s(z)))) | (~b(z, s(s(elem!1)))) | (~b(z, s(s(z)))) | (~b(s(s(z)), s(s(elem!1))))), inference(lemma,lemma(discharge,[]))).
% 2.72/2.99 tff(10728,plain,
% 2.72/2.99 (~b(s(s(elem!1)), s(s(z)))),
% 2.72/2.99 inference(unit_resolution,[status(thm)],[10727, 10525, 10451, 10719])).
% 2.72/2.99 tff(10729,plain,
% 2.72/2.99 (r(s(s(elem!1)), s(s(z)))),
% 2.72/2.99 inference(unit_resolution,[status(thm)],[441, 10728, 10718])).
% 2.72/2.99 tff(10730,plain,
% 2.72/2.99 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(elem!1)), s(z))) | (~r(s(z), s(s(z)))) | (~r(s(s(z)), z)) | (~r(s(s(elem!1)), s(s(z)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(elem!1)), s(z))) | (~r(s(z), s(s(z)))) | (~r(s(s(z)), z)) | (~r(s(s(elem!1)), s(s(z)))))),
% 2.72/2.99 inference(rewrite,[status(thm)],[])).
% 2.72/2.99 tff(10731,plain,
% 2.72/2.99 (((~r(s(s(z)), z)) | (~r(s(z), s(s(z)))) | (~r(s(s(elem!1)), s(s(z)))) | (~r(s(s(elem!1)), s(z)))) <=> ((~r(s(s(elem!1)), s(z))) | (~r(s(z), s(s(z)))) | (~r(s(s(z)), z)) | (~r(s(s(elem!1)), s(s(z)))))),
% 2.72/2.99 inference(rewrite,[status(thm)],[])).
% 2.72/2.99 tff(10732,plain,
% 2.72/2.99 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(z)), z)) | (~r(s(z), s(s(z)))) | (~r(s(s(elem!1)), s(s(z)))) | (~r(s(s(elem!1)), s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(elem!1)), s(z))) | (~r(s(z), s(s(z)))) | (~r(s(s(z)), z)) | (~r(s(s(elem!1)), s(s(z))))))),
% 2.72/2.99 inference(monotonicity,[status(thm)],[10731])).
% 2.72/2.99 tff(10733,plain,
% 2.72/2.99 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(z)), z)) | (~r(s(z), s(s(z)))) | (~r(s(s(elem!1)), s(s(z)))) | (~r(s(s(elem!1)), s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(elem!1)), s(z))) | (~r(s(z), s(s(z)))) | (~r(s(s(z)), z)) | (~r(s(s(elem!1)), s(s(z)))))),
% 2.72/2.99 inference(transitivity,[status(thm)],[10732, 10730])).
% 2.72/2.99 tff(10734,plain,
% 2.72/2.99 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(z)), z)) | (~r(s(z), s(s(z)))) | (~r(s(s(elem!1)), s(s(z)))) | (~r(s(s(elem!1)), s(z))))),
% 2.72/2.99 inference(quant_inst,[status(thm)],[])).
% 2.72/2.99 tff(10735,plain,
% 2.72/2.99 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(elem!1)), s(z))) | (~r(s(z), s(s(z)))) | (~r(s(s(z)), z)) | (~r(s(s(elem!1)), s(s(z))))),
% 2.72/2.99 inference(modus_ponens,[status(thm)],[10734, 10733])).
% 2.72/2.99 tff(10736,plain,
% 2.72/2.99 ($false),
% 2.72/2.99 inference(unit_resolution,[status(thm)],[10735, 197, 10729, 120, 10521, 866])).
% 2.72/2.99 tff(10737,plain,((~r(s(s(z)), z)) | (~r(s(z), s(s(z)))) | (~b(z, s(s(z)))) | r(s(s(z)), s(s(elem!1))) | (~r(s(z), z)) | (~b(z, s(z))) | b(s(s(elem!1)), s(z))), inference(lemma,lemma(discharge,[]))).
% 2.72/2.99 tff(10738,plain,
% 2.72/2.99 (~r(s(s(z)), z)),
% 2.72/2.99 inference(unit_resolution,[status(thm)],[10737, 118, 10451, 2288, 97, 120, 4568])).
% 2.72/2.99 tff(10739,plain,
% 2.72/2.99 (b(s(s(z)), z)),
% 2.72/2.99 inference(unit_resolution,[status(thm)],[186, 10738])).
% 2.72/2.99 tff(10740,plain,
% 2.72/2.99 (~b(s(s(s(elem!1))), s(s(z)))),
% 2.72/2.99 inference(unit_resolution,[status(thm)],[10457, 166, 10451, 121, 122])).
% 2.72/2.99 tff(10741,plain,
% 2.72/2.99 (r(s(s(s(elem!1))), s(s(z)))),
% 2.72/2.99 inference(unit_resolution,[status(thm)],[216, 79, 10740, 211])).
% 2.72/2.99 tff(10742,plain,
% 2.72/2.99 (~b(s(s(z)), s(s(s(elem!1))))),
% 2.72/2.99 inference(unit_resolution,[status(thm)],[10468, 166, 10451, 121, 122])).
% 2.72/2.99 tff(10743,plain,
% 2.72/2.99 (r(s(s(z)), s(s(s(elem!1))))),
% 2.72/2.99 inference(unit_resolution,[status(thm)],[277, 79, 10742, 209])).
% 2.72/2.99 tff(10744,plain,
% 2.72/2.99 ($false),
% 2.72/2.99 inference(unit_resolution,[status(thm)],[3174, 197, 120, 350, 10743, 10741])).
% 2.72/2.99 tff(10745,plain,((~b(s(s(s(elem!1))), z)) | (~r(s(z), s(s(z)))) | (~r(s(s(s(elem!1))), s(z))) | (~b(z, s(s(z)))) | (~b(s(s(z)), z))), inference(lemma,lemma(discharge,[]))).
% 2.72/2.99 tff(10746,plain,
% 2.72/2.99 (~b(s(s(s(elem!1))), z)),
% 2.72/2.99 inference(unit_resolution,[status(thm)],[10745, 350, 120, 10451, 122])).
% 2.72/2.99 tff(10747,plain,
% 2.72/2.99 (r(s(s(s(elem!1))), z)),
% 2.72/2.99 inference(unit_resolution,[status(thm)],[94, 10746])).
% 2.72/2.99 tff(10748,plain,
% 2.72/2.99 (r(s(s(s(elem!1))), elem!1)),
% 2.72/2.99 inference(unit_resolution,[status(thm)],[966, 620, 154])).
% 2.72/2.99 tff(10749,plain,
% 2.72/2.99 (~r(z, s(s(elem!1)))),
% 2.72/2.99 inference(unit_resolution,[status(thm)],[4466, 154, 350, 97])).
% 2.72/2.99 tff(10750,plain,
% 2.72/2.99 (b(z, s(s(elem!1)))),
% 2.72/2.99 inference(unit_resolution,[status(thm)],[1795, 10749])).
% 2.72/2.99 tff(10751,plain,
% 2.72/2.99 (b(elem!1, s(s(elem!1)))),
% 2.72/2.99 inference(modus_ponens,[status(thm)],[10750, 10705])).
% 2.72/2.99 tff(10752,plain,
% 2.72/2.99 (b(s(s(s(elem!1))), s(s(elem!1)))),
% 2.72/2.99 inference(unit_resolution,[status(thm)],[889, 3345, 1823])).
% 2.72/2.99 tff(10753,plain,
% 2.72/2.99 (b(s(s(elem!1)), s(s(s(elem!1))))),
% 2.72/2.99 inference(unit_resolution,[status(thm)],[461, 10529, 1821])).
% 2.72/2.99 tff(10754,plain,
% 2.72/2.99 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(elem!1, s(s(s(elem!1))))) | (~b(elem!1, s(s(elem!1)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(elem!1, s(s(s(elem!1))))) | (~b(elem!1, s(s(elem!1)))))),
% 2.72/2.99 inference(rewrite,[status(thm)],[])).
% 2.72/2.99 tff(10755,plain,
% 2.72/2.99 (((~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(elem!1, s(s(elem!1)))) | (~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(elem!1, s(s(elem!1)))) | (~b(elem!1, s(s(s(elem!1)))))) <=> ((~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(elem!1, s(s(s(elem!1))))) | (~b(elem!1, s(s(elem!1)))))),
% 2.72/2.99 inference(rewrite,[status(thm)],[])).
% 2.72/2.99 tff(10756,plain,
% 2.72/2.99 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(elem!1, s(s(elem!1)))) | (~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(elem!1, s(s(elem!1)))) | (~b(elem!1, s(s(s(elem!1))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(elem!1, s(s(s(elem!1))))) | (~b(elem!1, s(s(elem!1))))))),
% 2.72/2.99 inference(monotonicity,[status(thm)],[10755])).
% 2.72/2.99 tff(10757,plain,
% 2.72/2.99 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(elem!1, s(s(elem!1)))) | (~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(elem!1, s(s(elem!1)))) | (~b(elem!1, s(s(s(elem!1))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(elem!1, s(s(s(elem!1))))) | (~b(elem!1, s(s(elem!1)))))),
% 2.72/2.99 inference(transitivity,[status(thm)],[10756, 10754])).
% 2.72/2.99 tff(10758,plain,
% 2.72/2.99 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(elem!1, s(s(elem!1)))) | (~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(elem!1, s(s(elem!1)))) | (~b(elem!1, s(s(s(elem!1))))))),
% 2.72/2.99 inference(quant_inst,[status(thm)],[])).
% 2.72/2.99 tff(10759,plain,
% 2.72/2.99 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(elem!1, s(s(s(elem!1))))) | (~b(elem!1, s(s(elem!1))))),
% 2.72/2.99 inference(modus_ponens,[status(thm)],[10758, 10757])).
% 2.72/2.99 tff(10760,plain,
% 2.72/2.99 (~b(elem!1, s(s(s(elem!1))))),
% 2.72/2.99 inference(unit_resolution,[status(thm)],[10759, 166, 10753, 10752, 10751])).
% 2.72/2.99 tff(10761,plain,
% 2.72/2.99 (r(elem!1, s(s(s(elem!1))))),
% 2.72/2.99 inference(unit_resolution,[status(thm)],[5451, 10760, 6292])).
% 2.72/2.99 tff(10762,plain,
% 2.72/2.99 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), s(z))) | (~r(s(z), elem!1)) | (~r(elem!1, s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), elem!1)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(elem!1))), s(z))) | (~r(s(z), elem!1)) | (~r(elem!1, s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), elem!1)))),
% 2.72/2.99 inference(rewrite,[status(thm)],[])).
% 2.72/2.99 tff(10763,plain,
% 2.72/2.99 (((~r(elem!1, s(s(s(elem!1))))) | (~r(s(z), elem!1)) | (~r(s(s(s(elem!1))), elem!1)) | (~r(s(s(s(elem!1))), s(z)))) <=> ((~r(s(s(s(elem!1))), s(z))) | (~r(s(z), elem!1)) | (~r(elem!1, s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), elem!1)))),
% 2.72/2.99 inference(rewrite,[status(thm)],[])).
% 2.72/2.99 tff(10764,plain,
% 2.72/2.99 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(s(s(elem!1))))) | (~r(s(z), elem!1)) | (~r(s(s(s(elem!1))), elem!1)) | (~r(s(s(s(elem!1))), s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), s(z))) | (~r(s(z), elem!1)) | (~r(elem!1, s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), elem!1))))),
% 2.72/3.00 inference(monotonicity,[status(thm)],[10763])).
% 2.72/3.00 tff(10765,plain,
% 2.72/3.00 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(s(s(elem!1))))) | (~r(s(z), elem!1)) | (~r(s(s(s(elem!1))), elem!1)) | (~r(s(s(s(elem!1))), s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(elem!1))), s(z))) | (~r(s(z), elem!1)) | (~r(elem!1, s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), elem!1)))),
% 2.72/3.00 inference(transitivity,[status(thm)],[10764, 10762])).
% 2.72/3.00 tff(10766,plain,
% 2.72/3.00 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(s(s(elem!1))))) | (~r(s(z), elem!1)) | (~r(s(s(s(elem!1))), elem!1)) | (~r(s(s(s(elem!1))), s(z))))),
% 2.72/3.00 inference(quant_inst,[status(thm)],[])).
% 2.72/3.00 tff(10767,plain,
% 2.72/3.00 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(elem!1))), s(z))) | (~r(s(z), elem!1)) | (~r(elem!1, s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), elem!1))),
% 2.72/3.00 inference(modus_ponens,[status(thm)],[10766, 10765])).
% 2.72/3.00 tff(10768,plain,
% 2.72/3.00 ($false),
% 2.72/3.00 inference(unit_resolution,[status(thm)],[10767, 197, 350, 10623, 10761, 10748])).
% 2.72/3.00 tff(10769,plain,((~(s(s(z)) = s(s(elem!1)))) | (~r(s(s(s(elem!1))), s(z))) | r(s(s(s(elem!1))), s(s(elem!1))) | r(s(s(elem!1)), s(s(s(elem!1)))) | (~r(s(z), z)) | (~r(s(s(s(elem!1))), z))), inference(lemma,lemma(discharge,[]))).
% 2.72/3.00 tff(10770,plain,
% 2.72/3.00 (~(s(s(z)) = s(s(elem!1)))),
% 2.72/3.00 inference(unit_resolution,[status(thm)],[10769, 350, 10569, 10565, 97, 10747])).
% 2.72/3.00 tff(10771,plain,
% 2.72/3.00 (b(s(s(z)), s(s(elem!1)))),
% 2.72/3.00 inference(unit_resolution,[status(thm)],[390, 10770, 2288])).
% 2.72/3.00 tff(10772,plain,
% 2.72/3.00 (~(s(s(elem!1)) = s(s(z)))),
% 2.72/3.00 inference(unit_resolution,[status(thm)],[131, 10770])).
% 2.72/3.00 tff(10773,plain,
% 2.72/3.00 (~r(z, s(s(elem!1)))),
% 2.72/3.00 inference(unit_resolution,[status(thm)],[4466, 10747, 350, 97])).
% 2.72/3.00 tff(10774,plain,
% 2.72/3.00 (b(z, s(s(elem!1)))),
% 2.72/3.00 inference(unit_resolution,[status(thm)],[1795, 10773])).
% 2.72/3.00 tff(10775,plain,
% 2.72/3.00 (~b(s(s(elem!1)), s(s(z)))),
% 2.72/3.00 inference(unit_resolution,[status(thm)],[10727, 10771, 10451, 10774])).
% 2.72/3.00 tff(10776,plain,
% 2.72/3.00 (r(s(s(elem!1)), s(s(z)))),
% 2.72/3.00 inference(unit_resolution,[status(thm)],[441, 10775, 10772])).
% 2.72/3.00 tff(10777,plain,
% 2.72/3.00 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(elem!1)), s(z))) | (~r(s(z), s(s(z)))) | (~r(s(s(elem!1)), s(s(z)))) | (~r(s(s(z)), s(s(s(z))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(elem!1)), s(z))) | (~r(s(z), s(s(z)))) | (~r(s(s(elem!1)), s(s(z)))) | (~r(s(s(z)), s(s(s(z))))))),
% 2.72/3.00 inference(rewrite,[status(thm)],[])).
% 2.72/3.00 tff(10778,plain,
% 2.72/3.00 (((~r(s(s(z)), s(s(s(z))))) | (~r(s(z), s(s(z)))) | (~r(s(s(elem!1)), s(s(z)))) | (~r(s(s(elem!1)), s(z)))) <=> ((~r(s(s(elem!1)), s(z))) | (~r(s(z), s(s(z)))) | (~r(s(s(elem!1)), s(s(z)))) | (~r(s(s(z)), s(s(s(z))))))),
% 2.72/3.00 inference(rewrite,[status(thm)],[])).
% 2.72/3.00 tff(10779,plain,
% 2.72/3.00 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(z)), s(s(s(z))))) | (~r(s(z), s(s(z)))) | (~r(s(s(elem!1)), s(s(z)))) | (~r(s(s(elem!1)), s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(elem!1)), s(z))) | (~r(s(z), s(s(z)))) | (~r(s(s(elem!1)), s(s(z)))) | (~r(s(s(z)), s(s(s(z)))))))),
% 2.72/3.00 inference(monotonicity,[status(thm)],[10778])).
% 2.72/3.00 tff(10780,plain,
% 2.72/3.00 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(z)), s(s(s(z))))) | (~r(s(z), s(s(z)))) | (~r(s(s(elem!1)), s(s(z)))) | (~r(s(s(elem!1)), s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(elem!1)), s(z))) | (~r(s(z), s(s(z)))) | (~r(s(s(elem!1)), s(s(z)))) | (~r(s(s(z)), s(s(s(z))))))),
% 2.72/3.00 inference(transitivity,[status(thm)],[10779, 10777])).
% 2.72/3.00 tff(10781,plain,
% 2.72/3.00 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(z)), s(s(s(z))))) | (~r(s(z), s(s(z)))) | (~r(s(s(elem!1)), s(s(z)))) | (~r(s(s(elem!1)), s(z))))),
% 2.72/3.00 inference(quant_inst,[status(thm)],[])).
% 2.72/3.00 tff(10782,plain,
% 2.72/3.00 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(elem!1)), s(z))) | (~r(s(z), s(s(z)))) | (~r(s(s(elem!1)), s(s(z)))) | (~r(s(s(z)), s(s(s(z)))))),
% 2.72/3.00 inference(modus_ponens,[status(thm)],[10781, 10780])).
% 2.72/3.00 tff(10783,plain,
% 2.72/3.00 ($false),
% 2.72/3.00 inference(unit_resolution,[status(thm)],[10782, 197, 393, 120, 4577, 1732])).
% 2.72/3.00 tff(10784,plain,((~r(s(s(z)), s(s(s(z))))) | (~r(s(s(elem!1)), s(s(z)))) | (~r(s(z), s(s(z)))) | (~r(s(s(elem!1)), s(z)))), inference(lemma,lemma(discharge,[]))).
% 2.72/3.00 tff(10785,plain,
% 2.72/3.00 (~r(s(s(z)), s(s(s(z))))),
% 2.72/3.00 inference(unit_resolution,[status(thm)],[10784, 10776, 120, 4577])).
% 2.72/3.00 tff(10786,plain,
% 2.72/3.00 (b(s(s(z)), s(s(s(z))))),
% 2.72/3.00 inference(unit_resolution,[status(thm)],[1729, 10785, 1725])).
% 2.72/3.00 tff(10787,plain,
% 2.72/3.00 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(z)))) | (~b(s(s(z)), s(s(elem!1)))) | (~b(s(s(z)), z)) | (~b(s(s(s(z))), z)) | (~b(s(s(z)), s(s(s(z))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(s(z)))) | (~b(s(s(z)), s(s(elem!1)))) | (~b(s(s(z)), z)) | (~b(s(s(s(z))), z)) | (~b(s(s(z)), s(s(s(z))))))),
% 2.72/3.00 inference(rewrite,[status(thm)],[])).
% 2.72/3.00 tff(10788,plain,
% 2.72/3.00 (((~b(s(s(z)), s(s(elem!1)))) | (~b(s(s(z)), s(s(elem!1)))) | (~b(z, s(s(z)))) | (~b(s(s(s(z))), z)) | (~b(s(s(z)), z)) | (~b(s(s(z)), s(s(s(z)))))) <=> ((~b(z, s(s(z)))) | (~b(s(s(z)), s(s(elem!1)))) | (~b(s(s(z)), z)) | (~b(s(s(s(z))), z)) | (~b(s(s(z)), s(s(s(z))))))),
% 2.72/3.00 inference(rewrite,[status(thm)],[])).
% 2.72/3.00 tff(10789,plain,
% 2.72/3.00 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), s(s(elem!1)))) | (~b(s(s(z)), s(s(elem!1)))) | (~b(z, s(s(z)))) | (~b(s(s(s(z))), z)) | (~b(s(s(z)), z)) | (~b(s(s(z)), s(s(s(z))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(z)))) | (~b(s(s(z)), s(s(elem!1)))) | (~b(s(s(z)), z)) | (~b(s(s(s(z))), z)) | (~b(s(s(z)), s(s(s(z)))))))),
% 2.72/3.00 inference(monotonicity,[status(thm)],[10788])).
% 2.72/3.00 tff(10790,plain,
% 2.72/3.00 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), s(s(elem!1)))) | (~b(s(s(z)), s(s(elem!1)))) | (~b(z, s(s(z)))) | (~b(s(s(s(z))), z)) | (~b(s(s(z)), z)) | (~b(s(s(z)), s(s(s(z))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(s(z)))) | (~b(s(s(z)), s(s(elem!1)))) | (~b(s(s(z)), z)) | (~b(s(s(s(z))), z)) | (~b(s(s(z)), s(s(s(z))))))),
% 2.72/3.00 inference(transitivity,[status(thm)],[10789, 10787])).
% 2.72/3.00 tff(10791,plain,
% 2.72/3.00 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), s(s(elem!1)))) | (~b(s(s(z)), s(s(elem!1)))) | (~b(z, s(s(z)))) | (~b(s(s(s(z))), z)) | (~b(s(s(z)), z)) | (~b(s(s(z)), s(s(s(z))))))),
% 2.72/3.00 inference(quant_inst,[status(thm)],[])).
% 2.72/3.00 tff(10792,plain,
% 2.72/3.00 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(s(z)))) | (~b(s(s(z)), s(s(elem!1)))) | (~b(s(s(z)), z)) | (~b(s(s(s(z))), z)) | (~b(s(s(z)), s(s(s(z)))))),
% 2.72/3.00 inference(modus_ponens,[status(thm)],[10791, 10790])).
% 2.72/3.00 tff(10793,plain,
% 2.72/3.00 ($false),
% 2.72/3.00 inference(unit_resolution,[status(thm)],[10792, 166, 10451, 446, 122, 986, 1699])).
% 2.72/3.00 tff(10794,plain,((~b(s(s(s(z))), z)) | (~b(z, s(s(z)))) | (~b(s(s(z)), s(s(elem!1)))) | (~b(s(s(z)), z)) | (~b(s(s(z)), s(s(s(z)))))), inference(lemma,lemma(discharge,[]))).
% 2.72/3.00 tff(10795,plain,
% 2.72/3.00 (~b(s(s(s(z))), z)),
% 2.72/3.00 inference(unit_resolution,[status(thm)],[10794, 10771, 10451, 122, 10786])).
% 2.72/3.00 tff(10796,plain,
% 2.72/3.00 (r(s(s(s(z))), z)),
% 2.72/3.00 inference(unit_resolution,[status(thm)],[1713, 10795])).
% 2.72/3.00 tff(10797,plain,
% 2.72/3.00 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(s(z))))) | (~r(s(s(elem!1)), z)) | (~r(s(z), z)) | (~r(s(s(elem!1)), s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, s(s(s(z))))) | (~r(s(s(elem!1)), z)) | (~r(s(z), z)) | (~r(s(s(elem!1)), s(z))))),
% 2.72/3.00 inference(rewrite,[status(thm)],[])).
% 2.72/3.00 tff(10798,plain,
% 2.72/3.00 (((~r(z, s(s(s(z))))) | (~r(s(z), z)) | (~r(s(s(elem!1)), z)) | (~r(s(s(elem!1)), s(z)))) <=> ((~r(z, s(s(s(z))))) | (~r(s(s(elem!1)), z)) | (~r(s(z), z)) | (~r(s(s(elem!1)), s(z))))),
% 2.72/3.00 inference(rewrite,[status(thm)],[])).
% 2.72/3.00 tff(10799,plain,
% 2.72/3.00 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(s(z))))) | (~r(s(z), z)) | (~r(s(s(elem!1)), z)) | (~r(s(s(elem!1)), s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(s(z))))) | (~r(s(s(elem!1)), z)) | (~r(s(z), z)) | (~r(s(s(elem!1)), s(z)))))),
% 2.72/3.00 inference(monotonicity,[status(thm)],[10798])).
% 2.72/3.00 tff(10800,plain,
% 2.72/3.00 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(s(z))))) | (~r(s(z), z)) | (~r(s(s(elem!1)), z)) | (~r(s(s(elem!1)), s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, s(s(s(z))))) | (~r(s(s(elem!1)), z)) | (~r(s(z), z)) | (~r(s(s(elem!1)), s(z))))),
% 2.72/3.00 inference(transitivity,[status(thm)],[10799, 10797])).
% 2.72/3.00 tff(10801,plain,
% 2.72/3.00 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(s(z))))) | (~r(s(z), z)) | (~r(s(s(elem!1)), z)) | (~r(s(s(elem!1)), s(z))))),
% 2.72/3.00 inference(quant_inst,[status(thm)],[])).
% 2.72/3.00 tff(10802,plain,
% 2.72/3.00 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, s(s(s(z))))) | (~r(s(s(elem!1)), z)) | (~r(s(z), z)) | (~r(s(s(elem!1)), s(z)))),
% 2.72/3.00 inference(modus_ponens,[status(thm)],[10801, 10800])).
% 2.72/3.00 tff(10803,plain,
% 2.72/3.00 ($false),
% 2.72/3.00 inference(unit_resolution,[status(thm)],[10802, 197, 4577, 97, 1970, 1677])).
% 2.72/3.00 tff(10804,plain,((~r(z, s(s(s(z))))) | (~r(s(s(elem!1)), s(z))) | (~r(s(z), z)) | (~r(s(s(elem!1)), z))), inference(lemma,lemma(discharge,[]))).
% 2.72/3.00 tff(10805,plain,
% 2.72/3.00 (~r(z, s(s(s(z))))),
% 2.72/3.00 inference(unit_resolution,[status(thm)],[10804, 10083, 97, 4577])).
% 2.72/3.00 tff(10806,plain,
% 2.72/3.00 (b(z, s(s(s(z))))),
% 2.72/3.00 inference(unit_resolution,[status(thm)],[1696, 10805, 1692])).
% 2.72/3.00 tff(10807,plain,
% 2.72/3.00 (b(s(s(elem!1)), s(s(s(z)))) <=> b(elem!1, s(s(s(z))))),
% 2.72/3.00 inference(monotonicity,[status(thm)],[8230])).
% 2.72/3.00 tff(10808,plain,
% 2.72/3.00 (b(elem!1, s(s(s(z)))) <=> b(s(s(elem!1)), s(s(s(z))))),
% 2.72/3.00 inference(symmetry,[status(thm)],[10807])).
% 2.72/3.00 tff(10809,plain,
% 2.72/3.00 (~(s(s(s(z))) = elem!1)),
% 2.72/3.00 inference(unit_resolution,[status(thm)],[3122, 4066])).
% 2.72/3.00 tff(10810,plain,
% 2.72/3.00 (~(elem!1 = s(s(s(z))))),
% 2.72/3.00 inference(unit_resolution,[status(thm)],[1564, 10809])).
% 2.72/3.00 tff(10811,plain,
% 2.72/3.00 ((~r(s(s(elem!1)), s(s(s(z))))) <=> (~r(elem!1, s(s(s(z)))))),
% 2.72/3.00 inference(monotonicity,[status(thm)],[8231])).
% 2.72/3.00 tff(10812,plain,
% 2.72/3.00 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(elem!1)), s(z))) | (~r(s(z), s(s(z)))) | (~r(s(s(s(z))), s(z))) | (~r(s(s(elem!1)), s(s(s(z))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(elem!1)), s(z))) | (~r(s(z), s(s(z)))) | (~r(s(s(s(z))), s(z))) | (~r(s(s(elem!1)), s(s(s(z))))))),
% 2.72/3.00 inference(rewrite,[status(thm)],[])).
% 2.72/3.00 tff(10813,plain,
% 2.72/3.00 (((~r(s(z), s(s(z)))) | (~r(s(s(s(z))), s(z))) | (~r(s(s(elem!1)), s(z))) | (~r(s(s(elem!1)), s(s(s(z)))))) <=> ((~r(s(s(elem!1)), s(z))) | (~r(s(z), s(s(z)))) | (~r(s(s(s(z))), s(z))) | (~r(s(s(elem!1)), s(s(s(z))))))),
% 2.72/3.00 inference(rewrite,[status(thm)],[])).
% 2.72/3.00 tff(10814,plain,
% 2.72/3.00 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(s(z)))) | (~r(s(s(s(z))), s(z))) | (~r(s(s(elem!1)), s(z))) | (~r(s(s(elem!1)), s(s(s(z))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(elem!1)), s(z))) | (~r(s(z), s(s(z)))) | (~r(s(s(s(z))), s(z))) | (~r(s(s(elem!1)), s(s(s(z)))))))),
% 2.72/3.00 inference(monotonicity,[status(thm)],[10813])).
% 2.72/3.00 tff(10815,plain,
% 2.72/3.00 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(s(z)))) | (~r(s(s(s(z))), s(z))) | (~r(s(s(elem!1)), s(z))) | (~r(s(s(elem!1)), s(s(s(z))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(elem!1)), s(z))) | (~r(s(z), s(s(z)))) | (~r(s(s(s(z))), s(z))) | (~r(s(s(elem!1)), s(s(s(z))))))),
% 2.72/3.00 inference(transitivity,[status(thm)],[10814, 10812])).
% 2.72/3.00 tff(10816,plain,
% 2.72/3.00 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(s(z)))) | (~r(s(s(s(z))), s(z))) | (~r(s(s(elem!1)), s(z))) | (~r(s(s(elem!1)), s(s(s(z))))))),
% 2.72/3.00 inference(quant_inst,[status(thm)],[])).
% 2.72/3.00 tff(10817,plain,
% 2.72/3.00 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(elem!1)), s(z))) | (~r(s(z), s(s(z)))) | (~r(s(s(s(z))), s(z))) | (~r(s(s(elem!1)), s(s(s(z)))))),
% 2.72/3.00 inference(modus_ponens,[status(thm)],[10816, 10815])).
% 2.72/3.00 tff(10818,plain,
% 2.72/3.00 (~r(s(s(elem!1)), s(s(s(z))))),
% 2.72/3.00 inference(unit_resolution,[status(thm)],[10817, 197, 120, 4577, 1746])).
% 2.72/3.00 tff(10819,plain,
% 2.72/3.00 (~r(elem!1, s(s(s(z))))),
% 2.72/3.00 inference(modus_ponens,[status(thm)],[10818, 10811])).
% 2.72/3.00 tff(10820,plain,
% 2.72/3.00 (b(elem!1, s(s(s(z))))),
% 2.72/3.00 inference(unit_resolution,[status(thm)],[1619, 10819, 10810])).
% 2.72/3.00 tff(10821,plain,
% 2.72/3.00 (b(s(s(elem!1)), s(s(s(z))))),
% 2.72/3.00 inference(modus_ponens,[status(thm)],[10820, 10808])).
% 2.72/3.00 tff(10822,plain,
% 2.72/3.00 (elem!1 = s(s(s(elem!1)))),
% 2.72/3.00 inference(transitivity,[status(thm)],[1170, 4070, 38, 4068])).
% 2.72/3.00 tff(10823,plain,
% 2.72/3.00 (b(s(s(s(z))), elem!1) <=> b(s(s(s(z))), s(s(s(elem!1))))),
% 2.72/3.00 inference(monotonicity,[status(thm)],[10822])).
% 2.72/3.00 tff(10824,plain,
% 2.72/3.00 (b(s(s(s(z))), elem!1) <=> b(s(s(s(z))), s(s(elem!1)))),
% 2.72/3.00 inference(transitivity,[status(thm)],[10823, 8905])).
% 2.72/3.00 tff(10825,plain,
% 2.72/3.00 (r(s(s(s(z))), s(s(elem!1))) <=> r(s(s(s(z))), elem!1)),
% 2.72/3.00 inference(monotonicity,[status(thm)],[8230])).
% 2.72/3.00 tff(10826,plain,
% 2.72/3.00 ((~r(s(s(s(z))), s(s(elem!1)))) <=> (~r(s(s(s(z))), elem!1))),
% 2.72/3.00 inference(monotonicity,[status(thm)],[10825])).
% 2.72/3.00 tff(10827,plain,
% 2.72/3.00 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(s(z)))) | (~r(s(s(elem!1)), s(z))) | (~r(s(s(s(z))), s(z))) | (~r(s(s(s(z))), s(s(elem!1)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(z), s(s(z)))) | (~r(s(s(elem!1)), s(z))) | (~r(s(s(s(z))), s(z))) | (~r(s(s(s(z))), s(s(elem!1)))))),
% 2.72/3.00 inference(rewrite,[status(thm)],[])).
% 2.72/3.00 tff(10828,plain,
% 2.72/3.00 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(s(z)))) | (~r(s(s(elem!1)), s(z))) | (~r(s(s(s(z))), s(z))) | (~r(s(s(s(z))), s(s(elem!1)))))),
% 2.72/3.00 inference(quant_inst,[status(thm)],[])).
% 2.72/3.00 tff(10829,plain,
% 2.72/3.00 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(z), s(s(z)))) | (~r(s(s(elem!1)), s(z))) | (~r(s(s(s(z))), s(z))) | (~r(s(s(s(z))), s(s(elem!1))))),
% 2.72/3.00 inference(modus_ponens,[status(thm)],[10828, 10827])).
% 2.72/3.00 tff(10830,plain,
% 2.72/3.00 (~r(s(s(s(z))), s(s(elem!1)))),
% 2.72/3.00 inference(unit_resolution,[status(thm)],[10829, 197, 120, 4577, 1746])).
% 2.72/3.00 tff(10831,plain,
% 2.72/3.00 (~r(s(s(s(z))), elem!1)),
% 2.72/3.00 inference(modus_ponens,[status(thm)],[10830, 10826])).
% 2.72/3.00 tff(10832,plain,
% 2.72/3.00 (b(s(s(s(z))), elem!1)),
% 2.72/3.00 inference(unit_resolution,[status(thm)],[2826, 10831, 10809])).
% 2.72/3.00 tff(10833,plain,
% 2.72/3.00 (b(s(s(s(z))), s(s(elem!1)))),
% 2.72/3.00 inference(modus_ponens,[status(thm)],[10832, 10824])).
% 2.72/3.00 tff(10834,plain,
% 2.72/3.00 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(elem!1)))) | (~b(z, s(s(s(z))))) | (~b(s(s(elem!1)), s(s(s(z))))) | (~b(s(s(s(z))), s(s(elem!1)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(s(elem!1)))) | (~b(z, s(s(s(z))))) | (~b(s(s(elem!1)), s(s(s(z))))) | (~b(s(s(s(z))), s(s(elem!1)))))),
% 2.72/3.00 inference(rewrite,[status(thm)],[])).
% 2.72/3.00 tff(10835,plain,
% 2.72/3.00 (((~b(s(s(s(z))), s(s(elem!1)))) | (~b(z, s(s(elem!1)))) | (~b(s(s(elem!1)), s(s(s(z))))) | (~b(s(s(s(z))), s(s(elem!1)))) | (~b(z, s(s(elem!1)))) | (~b(z, s(s(s(z)))))) <=> ((~b(z, s(s(elem!1)))) | (~b(z, s(s(s(z))))) | (~b(s(s(elem!1)), s(s(s(z))))) | (~b(s(s(s(z))), s(s(elem!1)))))),
% 2.72/3.00 inference(rewrite,[status(thm)],[])).
% 2.72/3.00 tff(10836,plain,
% 2.72/3.00 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), s(s(elem!1)))) | (~b(z, s(s(elem!1)))) | (~b(s(s(elem!1)), s(s(s(z))))) | (~b(s(s(s(z))), s(s(elem!1)))) | (~b(z, s(s(elem!1)))) | (~b(z, s(s(s(z))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(elem!1)))) | (~b(z, s(s(s(z))))) | (~b(s(s(elem!1)), s(s(s(z))))) | (~b(s(s(s(z))), s(s(elem!1))))))),
% 2.72/3.00 inference(monotonicity,[status(thm)],[10835])).
% 2.72/3.00 tff(10837,plain,
% 2.72/3.00 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), s(s(elem!1)))) | (~b(z, s(s(elem!1)))) | (~b(s(s(elem!1)), s(s(s(z))))) | (~b(s(s(s(z))), s(s(elem!1)))) | (~b(z, s(s(elem!1)))) | (~b(z, s(s(s(z))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(s(elem!1)))) | (~b(z, s(s(s(z))))) | (~b(s(s(elem!1)), s(s(s(z))))) | (~b(s(s(s(z))), s(s(elem!1)))))),
% 2.72/3.00 inference(transitivity,[status(thm)],[10836, 10834])).
% 2.72/3.00 tff(10838,plain,
% 2.72/3.00 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), s(s(elem!1)))) | (~b(z, s(s(elem!1)))) | (~b(s(s(elem!1)), s(s(s(z))))) | (~b(s(s(s(z))), s(s(elem!1)))) | (~b(z, s(s(elem!1)))) | (~b(z, s(s(s(z))))))),
% 2.72/3.00 inference(quant_inst,[status(thm)],[])).
% 2.72/3.00 tff(10839,plain,
% 2.72/3.00 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(s(elem!1)))) | (~b(z, s(s(s(z))))) | (~b(s(s(elem!1)), s(s(s(z))))) | (~b(s(s(s(z))), s(s(elem!1))))),
% 2.72/3.00 inference(modus_ponens,[status(thm)],[10838, 10837])).
% 2.72/3.00 tff(10840,plain,
% 2.72/3.00 (~b(s(s(elem!1)), s(s(s(z))))),
% 2.72/3.00 inference(unit_resolution,[status(thm)],[10839, 166, 1820, 1700, 10833])).
% 2.72/3.00 tff(10841,plain,
% 2.72/3.00 ($false),
% 2.72/3.00 inference(unit_resolution,[status(thm)],[10840, 10821])).
% 2.72/3.00 tff(10842,plain,((~r(s(s(s(z))), s(z))) | (~(s(s(s(elem!1))) = s(s(elem!1)))) | (~b(z, s(s(elem!1)))) | (~b(z, s(s(s(z))))) | (~r(s(z), s(s(z)))) | (~r(s(s(elem!1)), s(z)))), inference(lemma,lemma(discharge,[]))).
% 2.72/3.01 tff(10843,plain,
% 2.72/3.01 (~r(s(s(s(z))), s(z))),
% 2.72/3.01 inference(unit_resolution,[status(thm)],[10842, 47, 10750, 10806, 120, 4577])).
% 2.72/3.01 tff(10844,plain,
% 2.72/3.01 (b(s(s(s(z))), s(z))),
% 2.72/3.01 inference(unit_resolution,[status(thm)],[1762, 10843, 1758])).
% 2.72/3.01 tff(10845,plain,
% 2.72/3.01 (~(s(s(z)) = s(s(elem!1)))),
% 2.72/3.01 inference(unit_resolution,[status(thm)],[10769, 350, 10569, 10565, 97, 154])).
% 2.72/3.01 tff(10846,plain,
% 2.72/3.01 (~(s(s(elem!1)) = s(s(z)))),
% 2.72/3.01 inference(unit_resolution,[status(thm)],[131, 10845])).
% 2.72/3.01 tff(10847,plain,
% 2.72/3.01 (~b(s(s(elem!1)), s(s(z)))),
% 2.72/3.01 inference(unit_resolution,[status(thm)],[10727, 446, 10451, 10750])).
% 2.72/3.01 tff(10848,plain,
% 2.72/3.01 (r(s(s(elem!1)), s(s(z)))),
% 2.72/3.01 inference(unit_resolution,[status(thm)],[441, 10847, 10846])).
% 2.72/3.01 tff(10849,plain,
% 2.72/3.01 (~r(s(s(z)), s(s(s(z))))),
% 2.72/3.01 inference(unit_resolution,[status(thm)],[10784, 10848, 120, 4577])).
% 2.72/3.01 tff(10850,plain,
% 2.72/3.01 (b(s(s(z)), s(s(s(z))))),
% 2.72/3.01 inference(unit_resolution,[status(thm)],[1729, 10849, 1725])).
% 2.72/3.01 tff(10851,plain,
% 2.72/3.01 (r(s(s(s(z))), elem!1) <=> r(s(s(s(z))), s(s(elem!1)))),
% 2.72/3.01 inference(symmetry,[status(thm)],[10825])).
% 2.72/3.01 tff(10852,plain,
% 2.72/3.01 (b(s(s(s(z))), s(s(s(elem!1)))) <=> b(s(s(s(z))), elem!1)),
% 2.72/3.01 inference(symmetry,[status(thm)],[10823])).
% 2.72/3.01 tff(10853,plain,
% 2.72/3.01 ((~b(s(s(s(z))), s(s(s(elem!1))))) <=> (~b(s(s(s(z))), elem!1))),
% 2.72/3.01 inference(monotonicity,[status(thm)],[10852])).
% 2.72/3.01 tff(10854,plain,
% 2.72/3.01 (r(s(s(s(elem!1))), s(s(z))) <=> r(s(s(elem!1)), s(s(z)))),
% 2.72/3.01 inference(monotonicity,[status(thm)],[47])).
% 2.72/3.01 tff(10855,plain,
% 2.72/3.01 (r(s(s(elem!1)), s(s(z))) <=> r(s(s(s(elem!1))), s(s(z)))),
% 2.72/3.01 inference(symmetry,[status(thm)],[10854])).
% 2.72/3.01 tff(10856,plain,
% 2.72/3.01 (r(s(s(s(elem!1))), s(s(z)))),
% 2.72/3.01 inference(modus_ponens,[status(thm)],[10848, 10855])).
% 2.72/3.01 tff(10857,plain,
% 2.72/3.01 (~r(s(s(z)), s(z))),
% 2.72/3.01 inference(unit_resolution,[status(thm)],[483, 10856, 350, 120])).
% 2.72/3.01 tff(10858,plain,
% 2.72/3.01 (b(s(s(z)), s(z))),
% 2.72/3.01 inference(unit_resolution,[status(thm)],[308, 10857])).
% 2.72/3.01 tff(10859,plain,
% 2.72/3.01 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(z)))) | (~b(z, s(s(elem!1)))) | (~b(z, s(z))) | (~b(s(s(z)), s(z))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(z))), s(s(elem!1)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(s(z)))) | (~b(z, s(s(elem!1)))) | (~b(z, s(z))) | (~b(s(s(z)), s(z))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(z))), s(s(elem!1)))))),
% 2.72/3.01 inference(rewrite,[status(thm)],[])).
% 2.72/3.01 tff(10860,plain,
% 2.72/3.01 (((~b(s(s(s(z))), s(s(elem!1)))) | (~b(z, s(s(elem!1)))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(z)), s(z))) | (~b(z, s(z))) | (~b(z, s(s(z))))) <=> ((~b(z, s(s(z)))) | (~b(z, s(s(elem!1)))) | (~b(z, s(z))) | (~b(s(s(z)), s(z))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(z))), s(s(elem!1)))))),
% 2.72/3.01 inference(rewrite,[status(thm)],[])).
% 2.72/3.01 tff(10861,plain,
% 2.72/3.01 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), s(s(elem!1)))) | (~b(z, s(s(elem!1)))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(z)), s(z))) | (~b(z, s(z))) | (~b(z, s(s(z)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(z)))) | (~b(z, s(s(elem!1)))) | (~b(z, s(z))) | (~b(s(s(z)), s(z))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(z))), s(s(elem!1))))))),
% 2.72/3.01 inference(monotonicity,[status(thm)],[10860])).
% 2.72/3.01 tff(10862,plain,
% 2.72/3.01 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), s(s(elem!1)))) | (~b(z, s(s(elem!1)))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(z)), s(z))) | (~b(z, s(z))) | (~b(z, s(s(z)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(s(z)))) | (~b(z, s(s(elem!1)))) | (~b(z, s(z))) | (~b(s(s(z)), s(z))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(z))), s(s(elem!1)))))),
% 2.72/3.01 inference(transitivity,[status(thm)],[10861, 10859])).
% 2.72/3.01 tff(10863,plain,
% 2.72/3.01 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), s(s(elem!1)))) | (~b(z, s(s(elem!1)))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(z)), s(z))) | (~b(z, s(z))) | (~b(z, s(s(z)))))),
% 2.72/3.01 inference(quant_inst,[status(thm)],[])).
% 2.72/3.01 tff(10864,plain,
% 2.72/3.01 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(s(z)))) | (~b(z, s(s(elem!1)))) | (~b(z, s(z))) | (~b(s(s(z)), s(z))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(z))), s(s(elem!1))))),
% 2.72/3.01 inference(modus_ponens,[status(thm)],[10863, 10862])).
% 2.72/3.01 tff(10865,plain,
% 2.72/3.01 ($false),
% 2.72/3.01 inference(unit_resolution,[status(thm)],[10864, 166, 1820, 10451, 118, 156, 988, 5540])).
% 2.72/3.01 tff(10866,plain,((~b(s(z), s(s(s(z))))) | (~b(z, s(s(elem!1)))) | (~b(z, s(s(z)))) | (~b(z, s(z))) | (~b(s(s(z)), s(z))) | (~b(s(s(s(z))), s(s(elem!1))))), inference(lemma,lemma(discharge,[]))).
% 2.72/3.01 tff(10867,plain,
% 2.72/3.01 (~b(s(z), s(s(s(z))))),
% 2.72/3.01 inference(unit_resolution,[status(thm)],[10866, 5540, 10451, 118, 156, 1820])).
% 2.72/3.01 tff(10868,plain,
% 2.72/3.01 (r(s(z), s(s(s(z))))),
% 2.72/3.01 inference(unit_resolution,[status(thm)],[1673, 10867, 1669])).
% 2.72/3.01 tff(10869,plain,
% 2.72/3.01 (~r(elem!1, s(s(s(z))))),
% 2.72/3.01 inference(unit_resolution,[status(thm)],[8242, 10868, 4577, 1733, 47])).
% 2.72/3.01 tff(10870,plain,
% 2.72/3.01 (b(elem!1, s(s(s(z))))),
% 2.72/3.01 inference(unit_resolution,[status(thm)],[1619, 10869, 10810])).
% 2.72/3.01 tff(10871,plain,
% 2.72/3.01 (b(s(s(elem!1)), s(s(s(z))))),
% 2.72/3.01 inference(modus_ponens,[status(thm)],[10870, 10808])).
% 2.72/3.01 tff(10872,plain,
% 2.72/3.01 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), s(s(elem!1)))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(elem!1)), s(s(s(z))))) | (~b(s(s(s(z))), s(s(elem!1)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(z)), s(s(elem!1)))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(elem!1)), s(s(s(z))))) | (~b(s(s(s(z))), s(s(elem!1)))))),
% 2.72/3.01 inference(rewrite,[status(thm)],[])).
% 2.72/3.01 tff(10873,plain,
% 2.72/3.01 (((~b(s(s(elem!1)), s(s(s(z))))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(s(z))), s(s(elem!1)))) | (~b(s(s(elem!1)), s(s(s(z))))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(z)), s(s(elem!1))))) <=> ((~b(s(s(z)), s(s(elem!1)))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(elem!1)), s(s(s(z))))) | (~b(s(s(s(z))), s(s(elem!1)))))),
% 2.72/3.01 inference(rewrite,[status(thm)],[])).
% 2.72/3.01 tff(10874,plain,
% 2.72/3.01 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), s(s(s(z))))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(s(z))), s(s(elem!1)))) | (~b(s(s(elem!1)), s(s(s(z))))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(z)), s(s(elem!1)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), s(s(elem!1)))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(elem!1)), s(s(s(z))))) | (~b(s(s(s(z))), s(s(elem!1))))))),
% 2.72/3.01 inference(monotonicity,[status(thm)],[10873])).
% 2.72/3.01 tff(10875,plain,
% 2.72/3.01 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), s(s(s(z))))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(s(z))), s(s(elem!1)))) | (~b(s(s(elem!1)), s(s(s(z))))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(z)), s(s(elem!1)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(z)), s(s(elem!1)))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(elem!1)), s(s(s(z))))) | (~b(s(s(s(z))), s(s(elem!1)))))),
% 2.72/3.01 inference(transitivity,[status(thm)],[10874, 10872])).
% 2.83/3.01 tff(10876,plain,
% 2.83/3.01 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), s(s(s(z))))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(s(z))), s(s(elem!1)))) | (~b(s(s(elem!1)), s(s(s(z))))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(z)), s(s(elem!1)))))),
% 2.83/3.01 inference(quant_inst,[status(thm)],[])).
% 2.83/3.01 tff(10877,plain,
% 2.83/3.01 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(z)), s(s(elem!1)))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(elem!1)), s(s(s(z))))) | (~b(s(s(s(z))), s(s(elem!1))))),
% 2.83/3.01 inference(modus_ponens,[status(thm)],[10876, 10875])).
% 2.83/3.01 tff(10878,plain,
% 2.83/3.01 (~b(s(s(elem!1)), s(s(s(z))))),
% 2.83/3.01 inference(unit_resolution,[status(thm)],[10877, 166, 446, 986, 5540])).
% 2.83/3.01 tff(10879,plain,
% 2.83/3.01 ($false),
% 2.83/3.01 inference(unit_resolution,[status(thm)],[10878, 10871])).
% 2.83/3.01 tff(10880,plain,((~b(s(s(s(z))), s(s(elem!1)))) | (~(s(s(s(elem!1))) = s(s(elem!1)))) | (~b(s(s(z)), s(s(elem!1)))) | (~b(s(s(z)), s(s(s(z))))) | (~r(s(s(elem!1)), s(z))) | (~r(s(s(s(z))), z)) | (~b(z, s(s(z)))) | (~b(z, s(z))) | (~b(s(s(z)), s(z))) | (~b(z, s(s(elem!1))))), inference(lemma,lemma(discharge,[]))).
% 2.83/3.01 tff(10881,plain,
% 2.83/3.01 (~b(s(s(s(z))), s(s(elem!1)))),
% 2.83/3.01 inference(unit_resolution,[status(thm)],[10880, 47, 446, 10850, 4577, 1733, 10451, 118, 10858, 10750])).
% 2.83/3.01 tff(10882,plain,
% 2.83/3.01 (~b(s(s(s(z))), s(s(s(elem!1))))),
% 2.83/3.01 inference(unit_resolution,[status(thm)],[8909, 10881, 47])).
% 2.83/3.01 tff(10883,plain,
% 2.83/3.01 (~b(s(s(s(z))), elem!1)),
% 2.83/3.01 inference(modus_ponens,[status(thm)],[10882, 10853])).
% 2.83/3.01 tff(10884,plain,
% 2.83/3.01 (r(s(s(s(z))), elem!1)),
% 2.83/3.01 inference(unit_resolution,[status(thm)],[2826, 10883, 10809])).
% 2.83/3.01 tff(10885,plain,
% 2.83/3.01 (r(s(s(s(z))), s(s(elem!1)))),
% 2.83/3.01 inference(modus_ponens,[status(thm)],[10884, 10851])).
% 2.83/3.01 tff(10886,plain,
% 2.83/3.01 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(z)))) | (~b(z, s(s(elem!1)))) | (~b(s(z), s(s(elem!1)))) | (~b(s(s(s(z))), s(z))) | (~b(z, s(s(s(z))))) | (~b(s(s(z)), s(s(s(z))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(s(z)))) | (~b(z, s(s(elem!1)))) | (~b(s(z), s(s(elem!1)))) | (~b(s(s(s(z))), s(z))) | (~b(z, s(s(s(z))))) | (~b(s(s(z)), s(s(s(z))))))),
% 2.83/3.01 inference(rewrite,[status(thm)],[])).
% 2.83/3.01 tff(10887,plain,
% 2.83/3.01 (((~b(s(z), s(s(elem!1)))) | (~b(z, s(s(elem!1)))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(z)), s(s(s(z))))) | (~b(z, s(s(s(z))))) | (~b(z, s(s(z))))) <=> ((~b(z, s(s(z)))) | (~b(z, s(s(elem!1)))) | (~b(s(z), s(s(elem!1)))) | (~b(s(s(s(z))), s(z))) | (~b(z, s(s(s(z))))) | (~b(s(s(z)), s(s(s(z))))))),
% 2.83/3.01 inference(rewrite,[status(thm)],[])).
% 2.83/3.01 tff(10888,plain,
% 2.83/3.01 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(elem!1)))) | (~b(z, s(s(elem!1)))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(z)), s(s(s(z))))) | (~b(z, s(s(s(z))))) | (~b(z, s(s(z)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(z)))) | (~b(z, s(s(elem!1)))) | (~b(s(z), s(s(elem!1)))) | (~b(s(s(s(z))), s(z))) | (~b(z, s(s(s(z))))) | (~b(s(s(z)), s(s(s(z)))))))),
% 2.83/3.01 inference(monotonicity,[status(thm)],[10887])).
% 2.83/3.01 tff(10889,plain,
% 2.83/3.01 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(elem!1)))) | (~b(z, s(s(elem!1)))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(z)), s(s(s(z))))) | (~b(z, s(s(s(z))))) | (~b(z, s(s(z)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(s(z)))) | (~b(z, s(s(elem!1)))) | (~b(s(z), s(s(elem!1)))) | (~b(s(s(s(z))), s(z))) | (~b(z, s(s(s(z))))) | (~b(s(s(z)), s(s(s(z))))))),
% 2.83/3.01 inference(transitivity,[status(thm)],[10888, 10886])).
% 2.83/3.01 tff(10890,plain,
% 2.83/3.01 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(elem!1)))) | (~b(z, s(s(elem!1)))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(z)), s(s(s(z))))) | (~b(z, s(s(s(z))))) | (~b(z, s(s(z)))))),
% 2.83/3.01 inference(quant_inst,[status(thm)],[])).
% 2.83/3.01 tff(10891,plain,
% 2.83/3.01 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(s(z)))) | (~b(z, s(s(elem!1)))) | (~b(s(z), s(s(elem!1)))) | (~b(s(s(s(z))), s(z))) | (~b(z, s(s(s(z))))) | (~b(s(s(z)), s(s(s(z)))))),
% 2.83/3.01 inference(modus_ponens,[status(thm)],[10890, 10889])).
% 2.83/3.01 tff(10892,plain,
% 2.83/3.01 ($false),
% 2.83/3.01 inference(unit_resolution,[status(thm)],[10891, 166, 376, 1820, 10451, 986, 1700, 3240])).
% 2.83/3.01 tff(10893,plain,((~b(s(s(s(z))), s(z))) | (~b(s(z), s(s(elem!1)))) | (~b(z, s(s(elem!1)))) | (~b(z, s(s(z)))) | (~b(s(s(z)), s(s(s(z))))) | (~b(z, s(s(s(z)))))), inference(lemma,lemma(discharge,[]))).
% 2.83/3.01 tff(10894,plain,
% 2.83/3.01 (~b(s(z), s(s(elem!1)))),
% 2.83/3.01 inference(unit_resolution,[status(thm)],[10893, 10844, 10750, 10451, 10850, 10806])).
% 2.83/3.01 tff(10895,plain,
% 2.83/3.01 (r(s(z), s(s(elem!1)))),
% 2.83/3.01 inference(unit_resolution,[status(thm)],[84, 10894])).
% 2.83/3.01 tff(10896,plain,
% 2.83/3.01 (~r(s(z), s(s(s(z))))),
% 2.83/3.01 inference(unit_resolution,[status(thm)],[4431, 197, 10895, 10848, 10885])).
% 2.83/3.01 tff(10897,plain,
% 2.83/3.01 (b(s(z), s(s(s(z))))),
% 2.83/3.01 inference(unit_resolution,[status(thm)],[1673, 10896, 1669])).
% 2.83/3.01 tff(10898,plain,
% 2.83/3.01 (((~b(s(z), s(s(s(z))))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(s(z))), s(z))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(z)), s(z)))) <=> ((~b(s(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))))))),
% 2.83/3.01 inference(rewrite,[status(thm)],[])).
% 2.83/3.01 tff(10899,plain,
% 2.83/3.01 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(s(z))))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(s(z))), s(z))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(z)), s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), s(z))) | (~b(s(s(z)), s(z))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(z)), s(s(s(z)))))))),
% 2.83/3.01 inference(monotonicity,[status(thm)],[10898])).
% 2.83/3.01 tff(10900,plain,
% 2.83/3.01 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(s(z))))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(s(z))), s(z))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(z)), s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(z)), s(z))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(z)), s(s(s(z))))))),
% 2.83/3.01 inference(transitivity,[status(thm)],[10899, 3241])).
% 2.83/3.01 tff(10901,plain,
% 2.83/3.01 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(s(z))))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(s(z))), s(z))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(z)), s(z))))),
% 2.83/3.01 inference(quant_inst,[status(thm)],[])).
% 2.83/3.01 tff(10902,plain,
% 2.83/3.01 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(z)), s(z))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(z)), s(s(s(z)))))),
% 2.83/3.01 inference(modus_ponens,[status(thm)],[10901, 10900])).
% 2.83/3.01 tff(10903,plain,
% 2.83/3.01 ($false),
% 2.83/3.01 inference(unit_resolution,[status(thm)],[10902, 166, 10858, 10897, 10850, 10844])).
% 2.83/3.01 tff(10904,plain,((~(s(s(s(elem!1))) = s(s(elem!1)))) | (~b(s(s(z)), s(s(elem!1)))) | (~r(s(s(elem!1)), s(z))) | (~r(s(s(s(z))), z)) | (~b(z, s(s(z)))) | (~b(z, s(z))) | (~r(s(z), s(s(z)))) | (~r(s(z), z)) | (~r(s(s(s(elem!1))), s(z))) | (~r(s(s(s(elem!1))), z))), inference(lemma,lemma(discharge,[]))).
% 2.83/3.02 tff(10905,plain,
% 2.83/3.02 (~(s(s(s(elem!1))) = s(s(elem!1)))),
% 2.83/3.02 inference(unit_resolution,[status(thm)],[10904, 10771, 4577, 10796, 10451, 118, 120, 97, 350, 10747])).
% 2.83/3.02 tff(10906,plain,
% 2.83/3.02 (b(s(s(s(elem!1))), s(s(elem!1)))),
% 2.83/3.02 inference(unit_resolution,[status(thm)],[889, 10905, 10569])).
% 2.83/3.02 tff(10907,plain,
% 2.83/3.02 ((~(s(s(s(elem!1))) = s(s(elem!1)))) <=> (~(s(s(elem!1)) = s(s(s(elem!1)))))),
% 2.83/3.02 inference(monotonicity,[status(thm)],[46])).
% 2.83/3.02 tff(10908,plain,
% 2.83/3.02 (~(s(s(elem!1)) = s(s(s(elem!1))))),
% 2.83/3.02 inference(modus_ponens,[status(thm)],[10905, 10907])).
% 2.83/3.02 tff(10909,plain,
% 2.83/3.02 (b(s(s(elem!1)), s(s(s(elem!1))))),
% 2.83/3.02 inference(unit_resolution,[status(thm)],[461, 10908, 10565])).
% 2.83/3.02 tff(10910,plain,
% 2.83/3.02 (~b(s(s(s(elem!1))), s(s(z)))),
% 2.83/3.02 inference(unit_resolution,[status(thm)],[2066, 166, 10909, 10906, 10771])).
% 2.83/3.02 tff(10911,plain,
% 2.83/3.02 (~r(s(z), s(s(s(elem!1))))),
% 2.83/3.02 inference(unit_resolution,[status(thm)],[2349, 10909, 97, 10774, 10906])).
% 2.83/3.02 tff(10912,plain,
% 2.83/3.02 (b(s(z), s(s(s(elem!1))))),
% 2.83/3.02 inference(unit_resolution,[status(thm)],[116, 10911])).
% 2.83/3.02 tff(10913,plain,
% 2.83/3.02 (((~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(s(z), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(s(z), s(s(s(elem!1))))) | (~b(s(z), s(s(elem!1))))) <=> ((~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(z), s(s(s(elem!1))))) | (~b(s(z), s(s(elem!1)))))),
% 2.83/3.02 inference(rewrite,[status(thm)],[])).
% 2.83/3.02 tff(10914,plain,
% 2.83/3.02 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(s(z), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(s(z), s(s(s(elem!1))))) | (~b(s(z), s(s(elem!1)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(z), s(s(s(elem!1))))) | (~b(s(z), s(s(elem!1))))))),
% 2.83/3.02 inference(monotonicity,[status(thm)],[10913])).
% 2.83/3.02 tff(10915,plain,
% 2.83/3.02 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(s(z), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(s(z), s(s(s(elem!1))))) | (~b(s(z), s(s(elem!1)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(z), s(s(s(elem!1))))) | (~b(s(z), s(s(elem!1)))))),
% 2.83/3.02 inference(transitivity,[status(thm)],[10914, 6031])).
% 2.83/3.02 tff(10916,plain,
% 2.83/3.02 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(s(z), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(s(z), s(s(s(elem!1))))) | (~b(s(z), s(s(elem!1)))))),
% 2.83/3.02 inference(quant_inst,[status(thm)],[])).
% 2.83/3.02 tff(10917,plain,
% 2.83/3.02 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(z), s(s(s(elem!1))))) | (~b(s(z), s(s(elem!1))))),
% 2.83/3.02 inference(modus_ponens,[status(thm)],[10916, 10915])).
% 2.83/3.02 tff(10918,plain,
% 2.83/3.02 (~b(s(z), s(s(elem!1)))),
% 2.83/3.02 inference(unit_resolution,[status(thm)],[10917, 166, 10909, 10906, 10912])).
% 2.83/3.02 tff(10919,plain,
% 2.83/3.02 (r(s(z), s(s(elem!1)))),
% 2.83/3.02 inference(unit_resolution,[status(thm)],[84, 10918])).
% 2.83/3.02 tff(10920,plain,
% 2.83/3.02 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(z), s(s(s(elem!1))))) | (~b(z, s(z))) | (~b(s(s(z)), s(s(elem!1)))) | (~b(s(s(z)), z)) | (~b(s(s(z)), s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(z), s(s(s(elem!1))))) | (~b(z, s(z))) | (~b(s(s(z)), s(s(elem!1)))) | (~b(s(s(z)), z)) | (~b(s(s(z)), s(z))))),
% 2.83/3.02 inference(rewrite,[status(thm)],[])).
% 2.83/3.02 tff(10921,plain,
% 2.83/3.02 (((~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(s(z)), s(s(elem!1)))) | (~b(s(z), s(s(s(elem!1))))) | (~b(z, s(z))) | (~b(s(s(z)), s(z))) | (~b(s(s(z)), z))) <=> ((~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(z), s(s(s(elem!1))))) | (~b(z, s(z))) | (~b(s(s(z)), s(s(elem!1)))) | (~b(s(s(z)), z)) | (~b(s(s(z)), s(z))))),
% 2.83/3.02 inference(rewrite,[status(thm)],[])).
% 2.83/3.02 tff(10922,plain,
% 2.83/3.02 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(s(z)), s(s(elem!1)))) | (~b(s(z), s(s(s(elem!1))))) | (~b(z, s(z))) | (~b(s(s(z)), s(z))) | (~b(s(s(z)), z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(z), s(s(s(elem!1))))) | (~b(z, s(z))) | (~b(s(s(z)), s(s(elem!1)))) | (~b(s(s(z)), z)) | (~b(s(s(z)), s(z)))))),
% 2.83/3.02 inference(monotonicity,[status(thm)],[10921])).
% 2.83/3.02 tff(10923,plain,
% 2.83/3.02 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(s(z)), s(s(elem!1)))) | (~b(s(z), s(s(s(elem!1))))) | (~b(z, s(z))) | (~b(s(s(z)), s(z))) | (~b(s(s(z)), z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(z), s(s(s(elem!1))))) | (~b(z, s(z))) | (~b(s(s(z)), s(s(elem!1)))) | (~b(s(s(z)), z)) | (~b(s(s(z)), s(z))))),
% 2.83/3.02 inference(transitivity,[status(thm)],[10922, 10920])).
% 2.83/3.02 tff(10924,plain,
% 2.83/3.02 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(s(z)), s(s(elem!1)))) | (~b(s(z), s(s(s(elem!1))))) | (~b(z, s(z))) | (~b(s(s(z)), s(z))) | (~b(s(s(z)), z)))),
% 2.83/3.02 inference(quant_inst,[status(thm)],[])).
% 2.83/3.02 tff(10925,plain,
% 2.83/3.02 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(z), s(s(s(elem!1))))) | (~b(z, s(z))) | (~b(s(s(z)), s(s(elem!1)))) | (~b(s(s(z)), z)) | (~b(s(s(z)), s(z)))),
% 2.83/3.02 inference(modus_ponens,[status(thm)],[10924, 10923])).
% 2.83/3.02 tff(10926,plain,
% 2.83/3.02 (~b(s(s(z)), s(z))),
% 2.83/3.02 inference(unit_resolution,[status(thm)],[10925, 166, 10906, 10912, 118, 10771, 122])).
% 2.83/3.02 tff(10927,plain,
% 2.83/3.02 (r(s(s(z)), s(z))),
% 2.83/3.02 inference(unit_resolution,[status(thm)],[308, 10926])).
% 2.83/3.02 tff(10928,plain,
% 2.83/3.02 (~r(s(s(s(elem!1))), s(s(z)))),
% 2.83/3.02 inference(unit_resolution,[status(thm)],[854, 10927, 350, 10919])).
% 2.83/3.02 tff(10929,plain,
% 2.83/3.02 ($false),
% 2.83/3.02 inference(unit_resolution,[status(thm)],[216, 79, 10928, 10910, 211])).
% 2.83/3.02 tff(10930,plain,((~r(s(s(s(elem!1))), s(z))) | (~b(z, s(z))) | (~b(s(s(z)), z)) | (~r(s(z), z)) | (~r(s(s(elem!1)), s(z))) | (~b(z, s(s(z)))) | (~r(s(z), s(s(z)))) | r(s(s(z)), s(s(elem!1)))), inference(lemma,lemma(discharge,[]))).
% 2.83/3.02 tff(10931,plain,
% 2.83/3.02 (~r(s(s(s(elem!1))), s(z))),
% 2.83/3.02 inference(unit_resolution,[status(thm)],[10930, 118, 10739, 97, 10521, 10451, 120, 2288])).
% 2.83/3.02 tff(10932,plain,
% 2.83/3.02 (b(s(s(s(elem!1))), s(z))),
% 2.83/3.02 inference(unit_resolution,[status(thm)],[1849, 10931])).
% 2.83/3.02 tff(10933,plain,
% 2.83/3.02 (~(s(s(elem!1)) = s(s(s(elem!1))))),
% 2.83/3.02 inference(unit_resolution,[status(thm)],[4570, 10932, 4568])).
% 2.83/3.02 tff(10934,plain,
% 2.83/3.02 ((~b(z, s(s(elem!1)))) <=> (~b(z, s(s(z))))),
% 2.83/3.02 inference(monotonicity,[status(thm)],[2258])).
% 2.83/3.02 tff(10935,plain,
% 2.83/3.02 (~b(z, s(s(z)))),
% 2.83/3.02 inference(modus_ponens,[status(thm)],[1790, 10934])).
% 2.83/3.02 tff(10936,plain,
% 2.83/3.02 ($false),
% 2.83/3.02 inference(unit_resolution,[status(thm)],[10451, 10935])).
% 2.83/3.02 tff(10937,plain,((~(s(s(z)) = s(s(elem!1)))) | (~b(z, s(s(z)))) | b(z, s(s(elem!1)))), inference(lemma,lemma(discharge,[]))).
% 2.83/3.02 tff(10938,plain,
% 2.83/3.02 (~(s(s(z)) = s(s(elem!1)))),
% 2.83/3.02 inference(unit_resolution,[status(thm)],[10937, 1790, 10451])).
% 2.83/3.02 tff(10939,plain,
% 2.83/3.02 (b(s(s(z)), s(s(elem!1)))),
% 2.83/3.02 inference(unit_resolution,[status(thm)],[390, 10938, 2288])).
% 2.83/3.02 tff(10940,plain,
% 2.83/3.02 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(z)))) | (~b(s(s(elem!1)), z)) | (~b(s(s(z)), s(s(elem!1)))) | (~b(s(s(z)), z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(s(z)))) | (~b(s(s(elem!1)), z)) | (~b(s(s(z)), s(s(elem!1)))) | (~b(s(s(z)), z)))),
% 2.83/3.02 inference(rewrite,[status(thm)],[])).
% 2.83/3.02 tff(10941,plain,
% 2.83/3.02 (((~b(s(s(z)), s(s(elem!1)))) | (~b(s(s(z)), s(s(elem!1)))) | (~b(z, s(s(z)))) | (~b(s(s(elem!1)), z)) | (~b(s(s(z)), z)) | (~b(s(s(z)), s(s(elem!1))))) <=> ((~b(z, s(s(z)))) | (~b(s(s(elem!1)), z)) | (~b(s(s(z)), s(s(elem!1)))) | (~b(s(s(z)), z)))),
% 2.83/3.02 inference(rewrite,[status(thm)],[])).
% 2.83/3.02 tff(10942,plain,
% 2.83/3.02 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), s(s(elem!1)))) | (~b(s(s(z)), s(s(elem!1)))) | (~b(z, s(s(z)))) | (~b(s(s(elem!1)), z)) | (~b(s(s(z)), z)) | (~b(s(s(z)), s(s(elem!1)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(z)))) | (~b(s(s(elem!1)), z)) | (~b(s(s(z)), s(s(elem!1)))) | (~b(s(s(z)), z))))),
% 2.83/3.02 inference(monotonicity,[status(thm)],[10941])).
% 2.83/3.02 tff(10943,plain,
% 2.83/3.02 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), s(s(elem!1)))) | (~b(s(s(z)), s(s(elem!1)))) | (~b(z, s(s(z)))) | (~b(s(s(elem!1)), z)) | (~b(s(s(z)), z)) | (~b(s(s(z)), s(s(elem!1)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(s(z)))) | (~b(s(s(elem!1)), z)) | (~b(s(s(z)), s(s(elem!1)))) | (~b(s(s(z)), z)))),
% 2.83/3.02 inference(transitivity,[status(thm)],[10942, 10940])).
% 2.83/3.02 tff(10944,plain,
% 2.83/3.02 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), s(s(elem!1)))) | (~b(s(s(z)), s(s(elem!1)))) | (~b(z, s(s(z)))) | (~b(s(s(elem!1)), z)) | (~b(s(s(z)), z)) | (~b(s(s(z)), s(s(elem!1)))))),
% 2.83/3.02 inference(quant_inst,[status(thm)],[])).
% 2.83/3.02 tff(10945,plain,
% 2.83/3.02 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(s(z)))) | (~b(s(s(elem!1)), z)) | (~b(s(s(z)), s(s(elem!1)))) | (~b(s(s(z)), z))),
% 2.83/3.02 inference(modus_ponens,[status(thm)],[10944, 10943])).
% 2.83/3.02 tff(10946,plain,
% 2.83/3.02 ($false),
% 2.83/3.02 inference(unit_resolution,[status(thm)],[10945, 166, 10451, 7963, 10939, 122])).
% 2.83/3.02 tff(10947,plain,(b(z, s(s(elem!1))) | (~b(z, s(s(z)))) | (~b(s(s(z)), z)) | (~r(s(z), z)) | (~r(s(s(elem!1)), s(z))) | r(s(s(z)), s(s(elem!1)))), inference(lemma,lemma(discharge,[]))).
% 2.83/3.02 tff(10948,plain,
% 2.83/3.02 (b(z, s(s(elem!1)))),
% 2.83/3.02 inference(unit_resolution,[status(thm)],[10947, 10739, 10451, 97, 10521, 2288])).
% 2.83/3.02 tff(10949,plain,
% 2.83/3.02 (b(s(s(elem!1)), elem!1)),
% 2.83/3.02 inference(modus_ponens,[status(thm)],[2963, 5412])).
% 2.83/3.02 tff(10950,plain,
% 2.83/3.02 (r(s(elem!1), elem!1) <=> r(s(z), elem!1)),
% 2.83/3.02 inference(monotonicity,[status(thm)],[619])).
% 2.83/3.02 tff(10951,plain,
% 2.83/3.02 (r(s(z), elem!1) <=> r(s(elem!1), elem!1)),
% 2.83/3.02 inference(symmetry,[status(thm)],[10950])).
% 2.83/3.02 tff(10952,plain,
% 2.83/3.02 (r(s(z), z) <=> r(s(elem!1), elem!1)),
% 2.83/3.02 inference(transitivity,[status(thm)],[10622, 10951])).
% 2.83/3.02 tff(10953,plain,
% 2.83/3.02 (r(s(elem!1), elem!1)),
% 2.83/3.02 inference(modus_ponens,[status(thm)],[97, 10952])).
% 2.83/3.02 tff(10954,plain,
% 2.83/3.02 (b(elem!1, s(s(elem!1)))),
% 2.83/3.02 inference(modus_ponens,[status(thm)],[1820, 10705])).
% 2.83/3.02 tff(10955,plain,
% 2.83/3.02 (r(elem!1, s(s(s(elem!1)))) <=> r(elem!1, s(s(s(z))))),
% 2.83/3.02 inference(symmetry,[status(thm)],[3741])).
% 2.83/3.02 tff(10956,plain,
% 2.83/3.02 (b(s(s(s(z))), z) <=> b(s(s(s(elem!1))), elem!1)),
% 2.83/3.02 inference(transitivity,[status(thm)],[7759, 7761])).
% 2.83/3.02 tff(10957,plain,
% 2.83/3.02 (r(s(s(s(elem!1))), z) <=> r(s(s(s(elem!1))), elem!1)),
% 2.83/3.02 inference(monotonicity,[status(thm)],[620])).
% 2.83/3.02 tff(10958,plain,
% 2.83/3.02 (r(s(s(s(elem!1))), z) <=> r(s(s(s(z))), z)),
% 2.83/3.02 inference(transitivity,[status(thm)],[10957, 6296, 6294])).
% 2.83/3.02 tff(10959,plain,
% 2.83/3.02 ((~r(s(s(s(elem!1))), z)) <=> (~r(s(s(s(z))), z))),
% 2.83/3.02 inference(monotonicity,[status(thm)],[10958])).
% 2.83/3.02 tff(10960,assumption,(b(elem!1, s(s(elem!1)))), introduced(assumption)).
% 2.83/3.02 tff(10961,plain,
% 2.83/3.02 (~r(s(z), s(s(s(elem!1))))),
% 2.83/3.02 inference(unit_resolution,[status(thm)],[5310, 154, 4577, 377])).
% 2.83/3.02 tff(10962,plain,
% 2.83/3.02 (b(s(z), s(s(s(elem!1))))),
% 2.83/3.02 inference(unit_resolution,[status(thm)],[116, 10961])).
% 2.83/3.02 tff(10963,plain,
% 2.83/3.02 (~b(elem!1, s(s(s(elem!1))))),
% 2.83/3.02 inference(unit_resolution,[status(thm)],[10542, 10962, 96, 1212])).
% 2.83/3.02 tff(10964,plain,
% 2.83/3.02 (r(elem!1, s(s(s(elem!1))))),
% 2.83/3.02 inference(unit_resolution,[status(thm)],[5451, 10963, 6292])).
% 2.83/3.02 tff(10965,plain,
% 2.83/3.02 (r(elem!1, s(s(s(z))))),
% 2.83/3.02 inference(modus_ponens,[status(thm)],[10964, 10955])).
% 2.83/3.02 tff(10966,plain,
% 2.83/3.02 (z = elem!1),
% 2.83/3.02 inference(unit_resolution,[status(thm)],[30, 21])).
% 2.83/3.02 tff(10967,plain,
% 2.83/3.02 ((s(s(s(s(elem!1)))) = z) <=> (s(s(s(s(elem!1)))) = elem!1)),
% 2.83/3.02 inference(monotonicity,[status(thm)],[10966])).
% 2.83/3.02 tff(10968,plain,
% 2.83/3.02 ((~(s(s(s(s(elem!1)))) = z)) <=> (~(s(s(s(s(elem!1)))) = elem!1))),
% 2.83/3.02 inference(monotonicity,[status(thm)],[10967])).
% 2.83/3.02 tff(10969,plain,
% 2.83/3.02 (~(s(s(s(s(elem!1)))) = elem!1)),
% 2.83/3.02 inference(modus_ponens,[status(thm)],[626, 10968])).
% 2.83/3.02 tff(10970,plain,
% 2.83/3.02 (r(s(s(s(s(elem!1)))), s(elem!1)) <=> r(s(s(s(s(elem!1)))), s(z))),
% 2.83/3.02 inference(monotonicity,[status(thm)],[21])).
% 2.83/3.02 tff(10971,plain,
% 2.83/3.02 (r(s(s(s(s(elem!1)))), s(z)) <=> r(s(s(s(s(elem!1)))), s(elem!1))),
% 2.83/3.02 inference(symmetry,[status(thm)],[10970])).
% 2.83/3.02 tff(10972,plain,
% 2.83/3.02 (r(s(s(s(s(elem!1)))), s(elem!1))),
% 2.83/3.02 inference(modus_ponens,[status(thm)],[700, 10971])).
% 2.83/3.02 tff(10973,plain,
% 2.83/3.02 (~r(s(s(s(s(elem!1)))), elem!1)),
% 2.83/3.02 inference(unit_resolution,[status(thm)],[3738, 10972, 3728, 1604])).
% 2.83/3.02 tff(10974,plain,
% 2.83/3.02 (b(s(s(s(s(elem!1)))), elem!1)),
% 2.83/3.02 inference(unit_resolution,[status(thm)],[717, 79, 10973, 10969])).
% 2.83/3.02 tff(10975,plain,
% 2.83/3.02 (~r(s(s(s(s(elem!1)))), s(s(elem!1)))),
% 2.83/3.02 inference(unit_resolution,[status(thm)],[4643, 700, 4577, 120])).
% 2.83/3.02 tff(10976,plain,
% 2.83/3.02 (b(s(s(s(s(elem!1)))), s(s(elem!1)))),
% 2.83/3.02 inference(unit_resolution,[status(thm)],[813, 10975, 806])).
% 2.83/3.02 tff(10977,plain,
% 2.83/3.02 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), elem!1)) | (~b(s(s(s(s(elem!1)))), s(s(elem!1)))) | (~b(elem!1, s(s(elem!1)))) | (~b(s(s(s(s(elem!1)))), elem!1)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(elem!1)), elem!1)) | (~b(s(s(s(s(elem!1)))), s(s(elem!1)))) | (~b(elem!1, s(s(elem!1)))) | (~b(s(s(s(s(elem!1)))), elem!1)))),
% 2.83/3.02 inference(rewrite,[status(thm)],[])).
% 2.83/3.02 tff(10978,plain,
% 2.83/3.02 (((~b(elem!1, s(s(elem!1)))) | (~b(s(s(s(s(elem!1)))), s(s(elem!1)))) | (~b(s(s(elem!1)), elem!1)) | (~b(elem!1, s(s(elem!1)))) | (~b(s(s(s(s(elem!1)))), s(s(elem!1)))) | (~b(s(s(s(s(elem!1)))), elem!1))) <=> ((~b(s(s(elem!1)), elem!1)) | (~b(s(s(s(s(elem!1)))), s(s(elem!1)))) | (~b(elem!1, s(s(elem!1)))) | (~b(s(s(s(s(elem!1)))), elem!1)))),
% 2.83/3.02 inference(rewrite,[status(thm)],[])).
% 2.83/3.02 tff(10979,plain,
% 2.83/3.02 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(s(elem!1)))) | (~b(s(s(s(s(elem!1)))), s(s(elem!1)))) | (~b(s(s(elem!1)), elem!1)) | (~b(elem!1, s(s(elem!1)))) | (~b(s(s(s(s(elem!1)))), s(s(elem!1)))) | (~b(s(s(s(s(elem!1)))), elem!1)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), elem!1)) | (~b(s(s(s(s(elem!1)))), s(s(elem!1)))) | (~b(elem!1, s(s(elem!1)))) | (~b(s(s(s(s(elem!1)))), elem!1))))),
% 2.83/3.02 inference(monotonicity,[status(thm)],[10978])).
% 2.83/3.02 tff(10980,plain,
% 2.83/3.02 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(s(elem!1)))) | (~b(s(s(s(s(elem!1)))), s(s(elem!1)))) | (~b(s(s(elem!1)), elem!1)) | (~b(elem!1, s(s(elem!1)))) | (~b(s(s(s(s(elem!1)))), s(s(elem!1)))) | (~b(s(s(s(s(elem!1)))), elem!1)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(elem!1)), elem!1)) | (~b(s(s(s(s(elem!1)))), s(s(elem!1)))) | (~b(elem!1, s(s(elem!1)))) | (~b(s(s(s(s(elem!1)))), elem!1)))),
% 2.83/3.02 inference(transitivity,[status(thm)],[10979, 10977])).
% 2.83/3.02 tff(10981,plain,
% 2.83/3.02 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(s(elem!1)))) | (~b(s(s(s(s(elem!1)))), s(s(elem!1)))) | (~b(s(s(elem!1)), elem!1)) | (~b(elem!1, s(s(elem!1)))) | (~b(s(s(s(s(elem!1)))), s(s(elem!1)))) | (~b(s(s(s(s(elem!1)))), elem!1)))),
% 2.83/3.02 inference(quant_inst,[status(thm)],[])).
% 2.83/3.02 tff(10982,plain,
% 2.83/3.02 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(elem!1)), elem!1)) | (~b(s(s(s(s(elem!1)))), s(s(elem!1)))) | (~b(elem!1, s(s(elem!1)))) | (~b(s(s(s(s(elem!1)))), elem!1))),
% 2.83/3.02 inference(modus_ponens,[status(thm)],[10981, 10980])).
% 2.83/3.02 tff(10983,plain,
% 2.83/3.02 ($false),
% 2.83/3.02 inference(unit_resolution,[status(thm)],[10982, 166, 786, 10960, 10976, 10974])).
% 2.83/3.02 tff(10984,plain,((~r(s(s(s(s(elem!1)))), s(z))) | (~b(s(s(elem!1)), elem!1)) | (~b(elem!1, s(s(elem!1)))) | (~r(s(elem!1), elem!1)) | (~r(elem!1, s(s(s(z))))) | (~(s(elem!1) = s(z))) | (s(s(s(s(elem!1)))) = s(s(elem!1))) | (~r(s(s(elem!1)), s(z))) | (~r(s(z), s(s(z))))), inference(lemma,lemma(discharge,[]))).
% 2.83/3.02 tff(10985,plain,
% 2.83/3.02 (~r(s(s(s(s(elem!1)))), s(z))),
% 2.83/3.02 inference(unit_resolution,[status(thm)],[10984, 10965, 10960, 3728, 786, 619, 734, 4577, 120])).
% 2.83/3.02 tff(10986,plain,
% 2.83/3.02 (b(s(s(s(s(elem!1)))), s(z))),
% 2.83/3.02 inference(unit_resolution,[status(thm)],[661, 10985])).
% 2.83/3.02 tff(10987,plain,
% 2.83/3.02 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(z))) | (~b(s(z), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(z))) | (~b(elem!1, s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(z))) | (~b(s(z), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(z))) | (~b(elem!1, s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), s(z))))),
% 2.83/3.02 inference(rewrite,[status(thm)],[])).
% 2.83/3.02 tff(10988,plain,
% 2.83/3.02 (((~b(s(s(s(elem!1))), s(z))) | (~b(elem!1, s(z))) | (~b(s(z), s(s(s(elem!1))))) | (~b(s(s(s(s(elem!1)))), s(z))) | (~b(elem!1, s(z))) | (~b(elem!1, s(s(s(s(elem!1))))))) <=> ((~b(elem!1, s(z))) | (~b(s(z), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(z))) | (~b(elem!1, s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), s(z))))),
% 2.83/3.02 inference(rewrite,[status(thm)],[])).
% 2.83/3.02 tff(10989,plain,
% 2.83/3.02 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), s(z))) | (~b(elem!1, s(z))) | (~b(s(z), s(s(s(elem!1))))) | (~b(s(s(s(s(elem!1)))), s(z))) | (~b(elem!1, s(z))) | (~b(elem!1, s(s(s(s(elem!1)))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(z))) | (~b(s(z), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(z))) | (~b(elem!1, s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), s(z)))))),
% 2.83/3.03 inference(monotonicity,[status(thm)],[10988])).
% 2.83/3.03 tff(10990,plain,
% 2.83/3.03 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), s(z))) | (~b(elem!1, s(z))) | (~b(s(z), s(s(s(elem!1))))) | (~b(s(s(s(s(elem!1)))), s(z))) | (~b(elem!1, s(z))) | (~b(elem!1, s(s(s(s(elem!1)))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(z))) | (~b(s(z), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(z))) | (~b(elem!1, s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), s(z))))),
% 2.83/3.03 inference(transitivity,[status(thm)],[10989, 10987])).
% 2.83/3.03 tff(10991,plain,
% 2.83/3.03 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), s(z))) | (~b(elem!1, s(z))) | (~b(s(z), s(s(s(elem!1))))) | (~b(s(s(s(s(elem!1)))), s(z))) | (~b(elem!1, s(z))) | (~b(elem!1, s(s(s(s(elem!1)))))))),
% 2.83/3.03 inference(quant_inst,[status(thm)],[])).
% 2.83/3.03 tff(10992,plain,
% 2.83/3.03 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(z))) | (~b(s(z), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(z))) | (~b(elem!1, s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), s(z)))),
% 2.83/3.03 inference(modus_ponens,[status(thm)],[10991, 10990])).
% 2.83/3.03 tff(10993,plain,
% 2.83/3.03 (~b(elem!1, s(s(s(s(elem!1)))))),
% 2.83/3.03 inference(unit_resolution,[status(thm)],[10992, 166, 10962, 96, 1212, 10986])).
% 2.83/3.03 tff(10994,plain,
% 2.83/3.03 (~b(elem!1, s(s(s(s(z)))))),
% 2.83/3.03 inference(modus_ponens,[status(thm)],[10993, 10633])).
% 2.83/3.03 tff(10995,plain,
% 2.83/3.03 (r(elem!1, s(s(s(s(z)))))),
% 2.83/3.03 inference(unit_resolution,[status(thm)],[1098, 10994, 1045])).
% 2.83/3.03 tff(10996,plain,
% 2.83/3.03 (r(elem!1, s(s(s(s(elem!1)))))),
% 2.83/3.03 inference(modus_ponens,[status(thm)],[10995, 1088])).
% 2.83/3.03 tff(10997,plain,
% 2.83/3.03 (~b(s(s(s(elem!1))), s(s(s(s(elem!1)))))),
% 2.83/3.03 inference(unit_resolution,[status(thm)],[5130, 10986, 96, 10962])).
% 2.83/3.03 tff(10998,plain,
% 2.83/3.03 (r(s(s(s(elem!1))), s(s(s(s(elem!1)))))),
% 2.83/3.03 inference(unit_resolution,[status(thm)],[696, 10997, 361])).
% 2.83/3.03 tff(10999,plain,
% 2.83/3.03 (r(s(s(s(elem!1))), elem!1)),
% 2.83/3.03 inference(unit_resolution,[status(thm)],[966, 154, 620])).
% 2.83/3.03 tff(11000,plain,
% 2.83/3.03 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(z))) | (~b(s(z), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(s(s(s(elem!1)))), elem!1)) | (~b(s(s(s(s(elem!1)))), s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(z))) | (~b(s(z), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(s(s(s(elem!1)))), elem!1)) | (~b(s(s(s(s(elem!1)))), s(z))))),
% 2.83/3.03 inference(rewrite,[status(thm)],[])).
% 2.83/3.03 tff(11001,plain,
% 2.83/3.03 (((~b(s(s(s(elem!1))), s(z))) | (~b(s(s(s(s(elem!1)))), s(z))) | (~b(s(z), s(s(s(elem!1))))) | (~b(elem!1, s(z))) | (~b(s(s(s(s(elem!1)))), s(z))) | (~b(s(s(s(s(elem!1)))), elem!1))) <=> ((~b(elem!1, s(z))) | (~b(s(z), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(s(s(s(elem!1)))), elem!1)) | (~b(s(s(s(s(elem!1)))), s(z))))),
% 2.83/3.03 inference(rewrite,[status(thm)],[])).
% 2.83/3.03 tff(11002,plain,
% 2.83/3.03 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), s(z))) | (~b(s(s(s(s(elem!1)))), s(z))) | (~b(s(z), s(s(s(elem!1))))) | (~b(elem!1, s(z))) | (~b(s(s(s(s(elem!1)))), s(z))) | (~b(s(s(s(s(elem!1)))), elem!1)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(z))) | (~b(s(z), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(s(s(s(elem!1)))), elem!1)) | (~b(s(s(s(s(elem!1)))), s(z)))))),
% 2.83/3.03 inference(monotonicity,[status(thm)],[11001])).
% 2.83/3.03 tff(11003,plain,
% 2.83/3.03 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), s(z))) | (~b(s(s(s(s(elem!1)))), s(z))) | (~b(s(z), s(s(s(elem!1))))) | (~b(elem!1, s(z))) | (~b(s(s(s(s(elem!1)))), s(z))) | (~b(s(s(s(s(elem!1)))), elem!1)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(z))) | (~b(s(z), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(s(s(s(elem!1)))), elem!1)) | (~b(s(s(s(s(elem!1)))), s(z))))),
% 2.83/3.03 inference(transitivity,[status(thm)],[11002, 11000])).
% 2.83/3.03 tff(11004,plain,
% 2.83/3.03 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), s(z))) | (~b(s(s(s(s(elem!1)))), s(z))) | (~b(s(z), s(s(s(elem!1))))) | (~b(elem!1, s(z))) | (~b(s(s(s(s(elem!1)))), s(z))) | (~b(s(s(s(s(elem!1)))), elem!1)))),
% 2.83/3.03 inference(quant_inst,[status(thm)],[])).
% 2.83/3.03 tff(11005,plain,
% 2.83/3.03 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(z))) | (~b(s(z), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(s(s(s(elem!1)))), elem!1)) | (~b(s(s(s(s(elem!1)))), s(z)))),
% 2.83/3.03 inference(modus_ponens,[status(thm)],[11004, 11003])).
% 2.83/3.03 tff(11006,plain,
% 2.83/3.03 (~b(s(s(s(s(elem!1)))), elem!1)),
% 2.83/3.03 inference(unit_resolution,[status(thm)],[11005, 166, 10962, 96, 1212, 10986])).
% 2.83/3.03 tff(11007,plain,
% 2.83/3.03 (r(s(s(s(s(elem!1)))), elem!1)),
% 2.83/3.03 inference(unit_resolution,[status(thm)],[717, 79, 11006, 627])).
% 2.83/3.03 tff(11008,plain,
% 2.83/3.03 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(s(s(s(elem!1)))))) | (~r(s(s(s(elem!1))), elem!1)) | (~r(s(s(s(elem!1))), s(s(s(s(elem!1)))))) | (~r(s(s(s(s(elem!1)))), elem!1)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(elem!1, s(s(s(s(elem!1)))))) | (~r(s(s(s(elem!1))), elem!1)) | (~r(s(s(s(elem!1))), s(s(s(s(elem!1)))))) | (~r(s(s(s(s(elem!1)))), elem!1)))),
% 2.83/3.03 inference(rewrite,[status(thm)],[])).
% 2.83/3.03 tff(11009,plain,
% 2.83/3.03 (((~r(s(s(s(s(elem!1)))), elem!1)) | (~r(elem!1, s(s(s(s(elem!1)))))) | (~r(s(s(s(elem!1))), s(s(s(s(elem!1)))))) | (~r(s(s(s(elem!1))), elem!1))) <=> ((~r(elem!1, s(s(s(s(elem!1)))))) | (~r(s(s(s(elem!1))), elem!1)) | (~r(s(s(s(elem!1))), s(s(s(s(elem!1)))))) | (~r(s(s(s(s(elem!1)))), elem!1)))),
% 2.83/3.03 inference(rewrite,[status(thm)],[])).
% 2.83/3.03 tff(11010,plain,
% 2.83/3.03 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(elem!1)))), elem!1)) | (~r(elem!1, s(s(s(s(elem!1)))))) | (~r(s(s(s(elem!1))), s(s(s(s(elem!1)))))) | (~r(s(s(s(elem!1))), elem!1)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(s(s(s(elem!1)))))) | (~r(s(s(s(elem!1))), elem!1)) | (~r(s(s(s(elem!1))), s(s(s(s(elem!1)))))) | (~r(s(s(s(s(elem!1)))), elem!1))))),
% 2.83/3.03 inference(monotonicity,[status(thm)],[11009])).
% 2.83/3.03 tff(11011,plain,
% 2.83/3.03 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(elem!1)))), elem!1)) | (~r(elem!1, s(s(s(s(elem!1)))))) | (~r(s(s(s(elem!1))), s(s(s(s(elem!1)))))) | (~r(s(s(s(elem!1))), elem!1)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(elem!1, s(s(s(s(elem!1)))))) | (~r(s(s(s(elem!1))), elem!1)) | (~r(s(s(s(elem!1))), s(s(s(s(elem!1)))))) | (~r(s(s(s(s(elem!1)))), elem!1)))),
% 2.83/3.03 inference(transitivity,[status(thm)],[11010, 11008])).
% 2.83/3.03 tff(11012,plain,
% 2.83/3.03 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(elem!1)))), elem!1)) | (~r(elem!1, s(s(s(s(elem!1)))))) | (~r(s(s(s(elem!1))), s(s(s(s(elem!1)))))) | (~r(s(s(s(elem!1))), elem!1)))),
% 2.83/3.03 inference(quant_inst,[status(thm)],[])).
% 2.83/3.03 tff(11013,plain,
% 2.83/3.03 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(elem!1, s(s(s(s(elem!1)))))) | (~r(s(s(s(elem!1))), elem!1)) | (~r(s(s(s(elem!1))), s(s(s(s(elem!1)))))) | (~r(s(s(s(s(elem!1)))), elem!1))),
% 2.83/3.03 inference(modus_ponens,[status(thm)],[11012, 11011])).
% 2.83/3.03 tff(11014,plain,
% 2.83/3.03 ($false),
% 2.83/3.03 inference(unit_resolution,[status(thm)],[11013, 197, 11007, 10999, 10998, 10996])).
% 2.83/3.03 tff(11015,plain,((~r(s(s(s(elem!1))), z)) | (~(s(s(z)) = s(s(elem!1)))) | (~b(s(s(s(elem!1))), s(z))) | (~b(elem!1, s(z))) | (s(s(s(elem!1))) = s(s(s(s(elem!1))))) | (~b(elem!1, s(s(elem!1)))) | (~r(s(elem!1), elem!1)) | (~b(s(s(elem!1)), elem!1)) | (~r(s(s(elem!1)), s(z))) | (~r(s(z), s(s(z)))) | (~r(s(s(elem!1)), s(s(s(elem!1)))))), inference(lemma,lemma(discharge,[]))).
% 2.83/3.03 tff(11016,plain,
% 2.83/3.03 (~r(s(s(s(elem!1))), z)),
% 2.83/3.03 inference(unit_resolution,[status(thm)],[11015, 377, 96, 5417, 361, 10960, 3728, 10949, 4577, 120, 34])).
% 2.83/3.03 tff(11017,plain,
% 2.83/3.03 (~r(s(s(s(z))), z)),
% 2.83/3.03 inference(modus_ponens,[status(thm)],[11016, 10959])).
% 2.83/3.03 tff(11018,plain,
% 2.83/3.03 (b(s(s(s(z))), z)),
% 2.83/3.03 inference(unit_resolution,[status(thm)],[1713, 11017])).
% 2.83/3.03 tff(11019,plain,
% 2.83/3.03 (b(s(s(s(elem!1))), elem!1)),
% 2.83/3.03 inference(modus_ponens,[status(thm)],[11018, 10956])).
% 2.83/3.03 tff(11020,plain,
% 2.83/3.03 (b(s(s(s(elem!1))), s(s(z))) <=> b(s(s(s(elem!1))), s(s(elem!1)))),
% 2.83/3.03 inference(monotonicity,[status(thm)],[34])).
% 2.83/3.03 tff(11021,plain,
% 2.83/3.03 ((~b(s(s(s(elem!1))), s(s(z)))) <=> (~b(s(s(s(elem!1))), s(s(elem!1))))),
% 2.83/3.03 inference(monotonicity,[status(thm)],[11020])).
% 2.83/3.03 tff(11022,plain,
% 2.83/3.03 (b(s(s(s(elem!1))), z)),
% 2.83/3.03 inference(unit_resolution,[status(thm)],[94, 11016])).
% 2.83/3.03 tff(11023,plain,
% 2.83/3.03 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(z)))) | (~b(s(s(s(elem!1))), s(s(z)))) | (~b(s(s(s(elem!1))), z)) | (~b(s(s(s(elem!1))), s(z))) | (~b(z, s(z))) | (~b(s(s(z)), z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(s(z)))) | (~b(s(s(s(elem!1))), s(s(z)))) | (~b(s(s(s(elem!1))), z)) | (~b(s(s(s(elem!1))), s(z))) | (~b(z, s(z))) | (~b(s(s(z)), z)))),
% 2.83/3.03 inference(rewrite,[status(thm)],[])).
% 2.83/3.03 tff(11024,plain,
% 2.83/3.03 (((~b(z, s(z))) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(s(z)), z)) | (~b(z, s(s(z)))) | (~b(s(s(s(elem!1))), s(s(z)))) | (~b(s(s(s(elem!1))), z))) <=> ((~b(z, s(s(z)))) | (~b(s(s(s(elem!1))), s(s(z)))) | (~b(s(s(s(elem!1))), z)) | (~b(s(s(s(elem!1))), s(z))) | (~b(z, s(z))) | (~b(s(s(z)), z)))),
% 2.83/3.03 inference(rewrite,[status(thm)],[])).
% 2.83/3.03 tff(11025,plain,
% 2.83/3.03 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(z))) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(s(z)), z)) | (~b(z, s(s(z)))) | (~b(s(s(s(elem!1))), s(s(z)))) | (~b(s(s(s(elem!1))), z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(z)))) | (~b(s(s(s(elem!1))), s(s(z)))) | (~b(s(s(s(elem!1))), z)) | (~b(s(s(s(elem!1))), s(z))) | (~b(z, s(z))) | (~b(s(s(z)), z))))),
% 2.83/3.03 inference(monotonicity,[status(thm)],[11024])).
% 2.83/3.03 tff(11026,plain,
% 2.83/3.03 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(z))) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(s(z)), z)) | (~b(z, s(s(z)))) | (~b(s(s(s(elem!1))), s(s(z)))) | (~b(s(s(s(elem!1))), z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(s(z)))) | (~b(s(s(s(elem!1))), s(s(z)))) | (~b(s(s(s(elem!1))), z)) | (~b(s(s(s(elem!1))), s(z))) | (~b(z, s(z))) | (~b(s(s(z)), z)))),
% 2.83/3.03 inference(transitivity,[status(thm)],[11025, 11023])).
% 2.83/3.03 tff(11027,plain,
% 2.83/3.03 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(z))) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(s(z)), z)) | (~b(z, s(s(z)))) | (~b(s(s(s(elem!1))), s(s(z)))) | (~b(s(s(s(elem!1))), z)))),
% 2.83/3.03 inference(quant_inst,[status(thm)],[])).
% 2.83/3.03 tff(11028,plain,
% 2.83/3.03 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(s(z)))) | (~b(s(s(s(elem!1))), s(s(z)))) | (~b(s(s(s(elem!1))), z)) | (~b(s(s(s(elem!1))), s(z))) | (~b(z, s(z))) | (~b(s(s(z)), z))),
% 2.83/3.03 inference(modus_ponens,[status(thm)],[11027, 11026])).
% 2.83/3.03 tff(11029,plain,
% 2.83/3.03 ((~b(s(s(s(elem!1))), s(s(z)))) | (~b(s(s(s(elem!1))), z))),
% 2.83/3.03 inference(unit_resolution,[status(thm)],[11028, 166, 10451, 96, 118, 122])).
% 2.83/3.03 tff(11030,plain,
% 2.83/3.03 (~b(s(s(s(elem!1))), s(s(z)))),
% 2.83/3.03 inference(unit_resolution,[status(thm)],[11029, 11022])).
% 2.83/3.03 tff(11031,plain,
% 2.83/3.03 (~b(s(s(s(elem!1))), s(s(elem!1)))),
% 2.83/3.03 inference(modus_ponens,[status(thm)],[11030, 11021])).
% 2.83/3.03 tff(11032,plain,
% 2.83/3.03 (r(s(s(s(elem!1))), s(s(elem!1)))),
% 2.83/3.03 inference(unit_resolution,[status(thm)],[889, 11031, 1863])).
% 2.83/3.03 tff(11033,plain,
% 2.83/3.03 (~r(s(z), s(s(s(elem!1))))),
% 2.83/3.03 inference(unit_resolution,[status(thm)],[7376, 11032, 4577, 377])).
% 2.83/3.03 tff(11034,plain,
% 2.83/3.03 (b(s(z), s(s(s(elem!1))))),
% 2.83/3.03 inference(unit_resolution,[status(thm)],[116, 11033])).
% 2.83/3.03 tff(11035,plain,
% 2.83/3.03 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(z))) | (~b(s(z), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(s(s(elem!1))), elem!1)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(z))) | (~b(s(z), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(s(s(elem!1))), elem!1)))),
% 2.83/3.03 inference(rewrite,[status(thm)],[])).
% 2.83/3.03 tff(11036,plain,
% 2.83/3.03 (((~b(s(s(s(elem!1))), elem!1)) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(z), s(s(s(elem!1))))) | (~b(elem!1, s(z))) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(s(s(elem!1))), elem!1))) <=> ((~b(elem!1, s(z))) | (~b(s(z), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(s(s(elem!1))), elem!1)))),
% 2.83/3.03 inference(rewrite,[status(thm)],[])).
% 2.83/3.03 tff(11037,plain,
% 2.83/3.03 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), elem!1)) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(z), s(s(s(elem!1))))) | (~b(elem!1, s(z))) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(s(s(elem!1))), elem!1)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(z))) | (~b(s(z), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(s(s(elem!1))), elem!1))))),
% 2.83/3.03 inference(monotonicity,[status(thm)],[11036])).
% 2.83/3.03 tff(11038,plain,
% 2.83/3.03 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), elem!1)) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(z), s(s(s(elem!1))))) | (~b(elem!1, s(z))) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(s(s(elem!1))), elem!1)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(z))) | (~b(s(z), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(s(s(elem!1))), elem!1)))),
% 2.83/3.03 inference(transitivity,[status(thm)],[11037, 11035])).
% 2.83/3.03 tff(11039,plain,
% 2.83/3.03 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), elem!1)) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(z), s(s(s(elem!1))))) | (~b(elem!1, s(z))) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(s(s(elem!1))), elem!1)))),
% 2.83/3.03 inference(quant_inst,[status(thm)],[])).
% 2.83/3.03 tff(11040,plain,
% 2.83/3.03 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(z))) | (~b(s(z), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(s(s(elem!1))), elem!1))),
% 2.83/3.03 inference(modus_ponens,[status(thm)],[11039, 11038])).
% 2.83/3.03 tff(11041,plain,
% 2.83/3.03 ($false),
% 2.83/3.03 inference(unit_resolution,[status(thm)],[11040, 166, 11034, 96, 5417, 11019])).
% 2.83/3.03 tff(11042,plain,((~r(s(s(elem!1)), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(z))) | (~(s(s(z)) = s(s(elem!1)))) | (~r(s(s(elem!1)), s(z))) | (s(s(s(elem!1))) = s(s(elem!1))) | (~b(z, s(s(z)))) | (~b(z, s(z))) | (~b(s(s(z)), z)) | (s(s(s(elem!1))) = s(s(s(s(elem!1))))) | (~b(elem!1, s(s(elem!1)))) | (~r(s(elem!1), elem!1)) | (~r(s(z), s(s(z))))), inference(lemma,lemma(discharge,[]))).
% 2.83/3.03 tff(11043,plain,
% 2.83/3.03 (~r(s(s(elem!1)), s(s(s(elem!1))))),
% 2.83/3.03 inference(unit_resolution,[status(thm)],[11042, 34, 96, 4577, 51, 10451, 118, 122, 358, 10954, 10953, 120])).
% 2.83/3.03 tff(11044,plain,
% 2.83/3.03 (b(s(s(elem!1)), s(s(s(elem!1))))),
% 2.83/3.03 inference(unit_resolution,[status(thm)],[461, 11043, 45])).
% 2.83/3.03 tff(11045,plain,
% 2.83/3.03 (~r(s(z), s(s(s(elem!1))))),
% 2.83/3.03 inference(unit_resolution,[status(thm)],[8455, 10531, 4577, 51, 97, 1820, 11044])).
% 2.83/3.03 tff(11046,plain,
% 2.83/3.03 (b(s(z), s(s(s(elem!1))))),
% 2.83/3.03 inference(unit_resolution,[status(thm)],[116, 11045])).
% 2.83/3.03 tff(11047,plain,
% 2.83/3.03 (~b(elem!1, s(s(s(elem!1))))),
% 2.83/3.03 inference(unit_resolution,[status(thm)],[10542, 11046, 96, 5417])).
% 2.83/3.03 tff(11048,plain,
% 2.83/3.03 (r(elem!1, s(s(s(elem!1))))),
% 2.83/3.03 inference(unit_resolution,[status(thm)],[5451, 11047, 6292])).
% 2.83/3.03 tff(11049,plain,
% 2.83/3.03 (r(elem!1, s(s(s(z))))),
% 2.83/3.03 inference(modus_ponens,[status(thm)],[11048, 10955])).
% 2.83/3.03 tff(11050,plain,
% 2.83/3.03 (~r(s(s(s(s(elem!1)))), s(z))),
% 2.83/3.03 inference(unit_resolution,[status(thm)],[10984, 11049, 10954, 10953, 10949, 619, 734, 4577, 120])).
% 2.83/3.03 tff(11051,plain,
% 2.83/3.03 (b(s(s(s(s(elem!1)))), s(z))),
% 2.83/3.03 inference(unit_resolution,[status(thm)],[661, 11050])).
% 2.83/3.03 tff(11052,plain,
% 2.83/3.03 (~b(elem!1, s(s(s(s(elem!1)))))),
% 2.83/3.03 inference(unit_resolution,[status(thm)],[10992, 166, 11046, 96, 5417, 11051])).
% 2.83/3.03 tff(11053,plain,
% 2.83/3.03 (~b(elem!1, s(s(s(s(z)))))),
% 2.83/3.03 inference(modus_ponens,[status(thm)],[11052, 10633])).
% 2.83/3.03 tff(11054,plain,
% 2.83/3.03 (r(elem!1, s(s(s(s(z)))))),
% 2.83/3.03 inference(unit_resolution,[status(thm)],[1098, 11053, 1045])).
% 2.83/3.03 tff(11055,plain,
% 2.83/3.03 (r(elem!1, s(s(s(s(elem!1)))))),
% 2.83/3.03 inference(modus_ponens,[status(thm)],[11054, 1088])).
% 2.83/3.03 tff(11056,plain,
% 2.83/3.03 (~b(s(s(s(elem!1))), s(s(s(s(elem!1)))))),
% 2.83/3.03 inference(unit_resolution,[status(thm)],[5130, 11051, 96, 11046])).
% 2.83/3.03 tff(11057,plain,
% 2.83/3.03 (r(s(s(s(elem!1))), s(s(s(s(elem!1)))))),
% 2.83/3.03 inference(unit_resolution,[status(thm)],[696, 11056, 358])).
% 2.83/3.03 tff(11058,plain,
% 2.83/3.03 (~b(s(s(s(elem!1))), z)),
% 2.83/3.03 inference(unit_resolution,[status(thm)],[3593, 11044, 1820, 2963])).
% 2.83/3.03 tff(11059,plain,
% 2.83/3.03 (r(s(s(s(elem!1))), z)),
% 2.83/3.03 inference(unit_resolution,[status(thm)],[94, 11058])).
% 2.83/3.03 tff(11060,plain,
% 2.83/3.03 (r(s(s(s(elem!1))), elem!1)),
% 2.83/3.03 inference(unit_resolution,[status(thm)],[966, 11059, 620])).
% 2.83/3.03 tff(11061,plain,
% 2.83/3.03 (~b(s(s(s(s(elem!1)))), elem!1)),
% 2.83/3.03 inference(unit_resolution,[status(thm)],[11005, 166, 11046, 96, 5417, 11051])).
% 2.83/3.03 tff(11062,plain,
% 2.83/3.03 (r(s(s(s(s(elem!1)))), elem!1)),
% 2.83/3.03 inference(unit_resolution,[status(thm)],[717, 79, 11061, 627])).
% 2.83/3.03 tff(11063,plain,
% 2.83/3.03 ($false),
% 2.83/3.03 inference(unit_resolution,[status(thm)],[11013, 197, 11062, 11060, 11057, 11055])).
% 2.83/3.03 tff(11064,plain,((~(s(s(z)) = s(s(elem!1)))) | (~b(s(s(s(elem!1))), s(z))) | (~r(s(s(elem!1)), s(z))) | (~r(s(z), s(s(z)))) | (~r(s(z), z)) | (~b(z, s(s(elem!1)))) | (s(s(elem!1)) = s(s(s(elem!1)))) | (~b(z, s(s(z)))) | (~b(z, s(z))) | (~b(s(s(z)), z))), inference(lemma,lemma(discharge,[]))).
% 2.83/3.04 tff(11065,plain,
% 2.83/3.04 (~(s(s(z)) = s(s(elem!1)))),
% 2.83/3.04 inference(unit_resolution,[status(thm)],[11064, 10932, 10521, 120, 97, 10948, 10933, 10451, 118, 10739])).
% 2.83/3.04 tff(11066,plain,
% 2.83/3.04 (b(s(s(z)), s(s(elem!1)))),
% 2.83/3.04 inference(unit_resolution,[status(thm)],[390, 11065, 2288])).
% 2.83/3.04 tff(11067,plain,
% 2.83/3.04 (~b(s(s(elem!1)), s(s(s(elem!1))))),
% 2.83/3.04 inference(unit_resolution,[status(thm)],[10592, 11066, 10451, 10932, 118, 10948])).
% 2.83/3.04 tff(11068,plain,
% 2.83/3.04 (r(s(s(elem!1)), s(s(s(elem!1))))),
% 2.83/3.04 inference(unit_resolution,[status(thm)],[461, 11067, 10933])).
% 2.83/3.04 tff(11069,plain,
% 2.83/3.04 (~(s(s(elem!1)) = s(s(z)))),
% 2.83/3.04 inference(unit_resolution,[status(thm)],[131, 11065])).
% 2.83/3.04 tff(11070,plain,
% 2.83/3.04 (~b(s(s(elem!1)), s(s(z)))),
% 2.83/3.04 inference(unit_resolution,[status(thm)],[10727, 11066, 10451, 10948])).
% 2.83/3.04 tff(11071,plain,
% 2.83/3.04 (r(s(s(elem!1)), s(s(z)))),
% 2.83/3.04 inference(unit_resolution,[status(thm)],[441, 11070, 11069])).
% 2.83/3.04 tff(11072,plain,
% 2.83/3.04 (~r(s(s(z)), s(z))),
% 2.83/3.04 inference(unit_resolution,[status(thm)],[5362, 11071, 120, 10521])).
% 2.83/3.04 tff(11073,plain,
% 2.83/3.04 (b(s(s(z)), s(z))),
% 2.83/3.04 inference(unit_resolution,[status(thm)],[308, 11072])).
% 2.83/3.04 tff(11074,plain,
% 2.83/3.04 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(z)))) | (~b(s(z), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(z))) | (~b(z, s(z))) | (~b(s(s(z)), s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(s(z)))) | (~b(s(z), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(z))) | (~b(z, s(z))) | (~b(s(s(z)), s(z))))),
% 2.83/3.04 inference(rewrite,[status(thm)],[])).
% 2.83/3.04 tff(11075,plain,
% 2.83/3.04 (((~b(s(s(s(elem!1))), s(z))) | (~b(z, s(z))) | (~b(s(z), s(s(s(elem!1))))) | (~b(s(s(z)), s(z))) | (~b(z, s(z))) | (~b(z, s(s(z))))) <=> ((~b(z, s(s(z)))) | (~b(s(z), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(z))) | (~b(z, s(z))) | (~b(s(s(z)), s(z))))),
% 2.83/3.04 inference(rewrite,[status(thm)],[])).
% 2.83/3.04 tff(11076,plain,
% 2.83/3.04 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), s(z))) | (~b(z, s(z))) | (~b(s(z), s(s(s(elem!1))))) | (~b(s(s(z)), s(z))) | (~b(z, s(z))) | (~b(z, s(s(z)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(z)))) | (~b(s(z), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(z))) | (~b(z, s(z))) | (~b(s(s(z)), s(z)))))),
% 2.83/3.04 inference(monotonicity,[status(thm)],[11075])).
% 2.83/3.04 tff(11077,plain,
% 2.83/3.04 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), s(z))) | (~b(z, s(z))) | (~b(s(z), s(s(s(elem!1))))) | (~b(s(s(z)), s(z))) | (~b(z, s(z))) | (~b(z, s(s(z)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(s(z)))) | (~b(s(z), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(z))) | (~b(z, s(z))) | (~b(s(s(z)), s(z))))),
% 2.83/3.04 inference(transitivity,[status(thm)],[11076, 11074])).
% 2.83/3.04 tff(11078,plain,
% 2.83/3.04 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), s(z))) | (~b(z, s(z))) | (~b(s(z), s(s(s(elem!1))))) | (~b(s(s(z)), s(z))) | (~b(z, s(z))) | (~b(z, s(s(z)))))),
% 2.83/3.04 inference(quant_inst,[status(thm)],[])).
% 2.83/3.04 tff(11079,plain,
% 2.83/3.04 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(s(z)))) | (~b(s(z), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(z))) | (~b(z, s(z))) | (~b(s(s(z)), s(z)))),
% 2.83/3.04 inference(modus_ponens,[status(thm)],[11078, 11077])).
% 2.83/3.04 tff(11080,plain,
% 2.83/3.04 ($false),
% 2.83/3.04 inference(unit_resolution,[status(thm)],[11079, 166, 241, 10451, 96, 118, 156])).
% 2.83/3.04 tff(11081,plain,((~b(s(z), s(s(s(elem!1))))) | (~b(z, s(s(z)))) | (~b(s(s(s(elem!1))), s(z))) | (~b(z, s(z))) | (~b(s(s(z)), s(z)))), inference(lemma,lemma(discharge,[]))).
% 2.83/3.04 tff(11082,plain,
% 2.83/3.04 (~b(s(z), s(s(s(elem!1))))),
% 2.83/3.04 inference(unit_resolution,[status(thm)],[11081, 10932, 10451, 118, 11073])).
% 2.83/3.04 tff(11083,plain,
% 2.83/3.04 (r(s(z), s(s(s(elem!1))))),
% 2.83/3.04 inference(unit_resolution,[status(thm)],[116, 11082])).
% 2.83/3.04 tff(11084,plain,
% 2.83/3.04 (~r(s(s(s(elem!1))), z)),
% 2.83/3.04 inference(unit_resolution,[status(thm)],[5310, 11083, 10521, 11068])).
% 2.83/3.04 tff(11085,plain,
% 2.83/3.04 (b(s(s(s(elem!1))), z)),
% 2.83/3.04 inference(unit_resolution,[status(thm)],[94, 11084])).
% 2.83/3.04 tff(11086,plain,
% 2.83/3.04 ((~b(s(s(s(elem!1))), s(s(z)))) | (~b(s(s(s(elem!1))), z))),
% 2.83/3.04 inference(unit_resolution,[status(thm)],[11028, 166, 10451, 10932, 118, 10739])).
% 2.83/3.04 tff(11087,plain,
% 2.83/3.04 (~b(s(s(s(elem!1))), s(s(z)))),
% 2.83/3.04 inference(unit_resolution,[status(thm)],[11086, 11085])).
% 2.83/3.04 tff(11088,plain,
% 2.83/3.04 (r(s(s(s(elem!1))), s(s(z)))),
% 2.83/3.04 inference(unit_resolution,[status(thm)],[216, 79, 11087, 211])).
% 2.83/3.04 tff(11089,plain,
% 2.83/3.04 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(s(s(elem!1))))) | (~r(s(s(elem!1)), s(s(s(elem!1))))) | (~r(s(s(elem!1)), s(z))) | (~r(s(s(s(elem!1))), s(s(z)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(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(s(s(elem!1))), s(s(z)))))),
% 2.83/3.04 inference(rewrite,[status(thm)],[])).
% 2.83/3.04 tff(11090,plain,
% 2.83/3.04 (((~r(s(s(s(elem!1))), s(s(z)))) | (~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(s(s(elem!1))))) | (~r(s(s(elem!1)), s(z))) | (~r(s(s(s(elem!1))), s(s(z)))))),
% 2.83/3.04 inference(rewrite,[status(thm)],[])).
% 2.83/3.04 tff(11091,plain,
% 2.83/3.04 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), s(s(z)))) | (~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, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(s(s(elem!1))))) | (~r(s(s(elem!1)), s(s(s(elem!1))))) | (~r(s(s(elem!1)), s(z))) | (~r(s(s(s(elem!1))), s(s(z))))))),
% 2.83/3.04 inference(monotonicity,[status(thm)],[11090])).
% 2.83/3.04 tff(11092,plain,
% 2.83/3.04 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), s(s(z)))) | (~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, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(z), s(s(s(elem!1))))) | (~r(s(s(elem!1)), s(s(s(elem!1))))) | (~r(s(s(elem!1)), s(z))) | (~r(s(s(s(elem!1))), s(s(z)))))),
% 2.83/3.04 inference(transitivity,[status(thm)],[11091, 11089])).
% 2.83/3.04 tff(11093,plain,
% 2.83/3.04 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), s(s(z)))) | (~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))))),
% 2.83/3.04 inference(quant_inst,[status(thm)],[])).
% 2.83/3.04 tff(11094,plain,
% 2.83/3.04 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(z), s(s(s(elem!1))))) | (~r(s(s(elem!1)), s(s(s(elem!1))))) | (~r(s(s(elem!1)), s(z))) | (~r(s(s(s(elem!1))), s(s(z))))),
% 2.83/3.04 inference(modus_ponens,[status(thm)],[11093, 11092])).
% 2.83/3.04 tff(11095,plain,
% 2.83/3.04 ($false),
% 2.83/3.04 inference(unit_resolution,[status(thm)],[11094, 197, 10521, 11068, 11083, 11088])).
% 2.83/3.04 tff(11096,plain,((~b(z, s(z))) | (~b(z, s(s(z)))) | (~r(s(z), s(s(z)))) | r(s(s(z)), s(s(elem!1))) | (~r(s(z), z)) | b(s(s(elem!1)), s(z))), inference(lemma,lemma(discharge,[]))).
% 2.83/3.04 tff(11097,plain,
% 2.83/3.04 (~b(z, s(z))),
% 2.83/3.04 inference(unit_resolution,[status(thm)],[11096, 120, 10451, 2288, 97, 4568])).
% 2.83/3.04 tff(11098,plain,
% 2.83/3.04 (r(z, s(z))),
% 2.83/3.04 inference(unit_resolution,[status(thm)],[321, 11097])).
% 2.83/3.04 tff(11099,plain,
% 2.83/3.04 (~r(s(s(elem!1)), z)),
% 2.83/3.04 inference(unit_resolution,[status(thm)],[8618, 197, 120, 11098, 10521])).
% 2.83/3.04 tff(11100,plain,
% 2.83/3.04 (b(s(s(elem!1)), z)),
% 2.83/3.04 inference(unit_resolution,[status(thm)],[608, 11099])).
% 2.83/3.04 tff(11101,plain,
% 2.83/3.04 (~r(z, s(s(elem!1)))),
% 2.83/3.04 inference(unit_resolution,[status(thm)],[8426, 11098, 10521, 97])).
% 2.83/3.04 tff(11102,plain,
% 2.83/3.04 (b(z, s(s(elem!1)))),
% 2.83/3.04 inference(unit_resolution,[status(thm)],[1795, 11101])).
% 2.83/3.04 tff(11103,plain,
% 2.83/3.04 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(z)))) | (~b(z, s(s(elem!1)))) | (~b(s(s(elem!1)), z)) | (~b(s(s(z)), s(s(elem!1)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(s(z)))) | (~b(z, s(s(elem!1)))) | (~b(s(s(elem!1)), z)) | (~b(s(s(z)), s(s(elem!1)))))),
% 2.83/3.04 inference(rewrite,[status(thm)],[])).
% 2.83/3.04 tff(11104,plain,
% 2.83/3.04 (((~b(z, s(s(elem!1)))) | (~b(z, s(s(elem!1)))) | (~b(s(s(elem!1)), z)) | (~b(s(s(z)), s(s(elem!1)))) | (~b(z, s(s(elem!1)))) | (~b(z, s(s(z))))) <=> ((~b(z, s(s(z)))) | (~b(z, s(s(elem!1)))) | (~b(s(s(elem!1)), z)) | (~b(s(s(z)), s(s(elem!1)))))),
% 2.83/3.04 inference(rewrite,[status(thm)],[])).
% 2.83/3.04 tff(11105,plain,
% 2.83/3.04 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(elem!1)))) | (~b(z, s(s(elem!1)))) | (~b(s(s(elem!1)), z)) | (~b(s(s(z)), s(s(elem!1)))) | (~b(z, s(s(elem!1)))) | (~b(z, s(s(z)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(z)))) | (~b(z, s(s(elem!1)))) | (~b(s(s(elem!1)), z)) | (~b(s(s(z)), s(s(elem!1))))))),
% 2.83/3.04 inference(monotonicity,[status(thm)],[11104])).
% 2.83/3.04 tff(11106,plain,
% 2.83/3.04 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(elem!1)))) | (~b(z, s(s(elem!1)))) | (~b(s(s(elem!1)), z)) | (~b(s(s(z)), s(s(elem!1)))) | (~b(z, s(s(elem!1)))) | (~b(z, s(s(z)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(s(z)))) | (~b(z, s(s(elem!1)))) | (~b(s(s(elem!1)), z)) | (~b(s(s(z)), s(s(elem!1)))))),
% 2.83/3.04 inference(transitivity,[status(thm)],[11105, 11103])).
% 2.83/3.04 tff(11107,plain,
% 2.83/3.04 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(elem!1)))) | (~b(z, s(s(elem!1)))) | (~b(s(s(elem!1)), z)) | (~b(s(s(z)), s(s(elem!1)))) | (~b(z, s(s(elem!1)))) | (~b(z, s(s(z)))))),
% 2.83/3.04 inference(quant_inst,[status(thm)],[])).
% 2.83/3.04 tff(11108,plain,
% 2.83/3.04 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(s(z)))) | (~b(z, s(s(elem!1)))) | (~b(s(s(elem!1)), z)) | (~b(s(s(z)), s(s(elem!1))))),
% 2.83/3.04 inference(modus_ponens,[status(thm)],[11107, 11106])).
% 2.83/3.04 tff(11109,plain,
% 2.83/3.04 ($false),
% 2.83/3.04 inference(unit_resolution,[status(thm)],[11108, 166, 1820, 10451, 592, 446])).
% 2.83/3.04 tff(11110,plain,((~b(s(s(z)), s(s(elem!1)))) | (~b(z, s(s(elem!1)))) | (~b(z, s(s(z)))) | (~b(s(s(elem!1)), z))), inference(lemma,lemma(discharge,[]))).
% 2.83/3.04 tff(11111,plain,
% 2.83/3.04 (~b(s(s(z)), s(s(elem!1)))),
% 2.83/3.04 inference(unit_resolution,[status(thm)],[11110, 11102, 10451, 11100])).
% 2.83/3.04 tff(11112,plain,
% 2.83/3.04 (s(s(z)) = s(s(elem!1))),
% 2.83/3.04 inference(unit_resolution,[status(thm)],[390, 11111, 2288])).
% 2.83/3.04 tff(11113,plain,
% 2.83/3.04 (s(elem!1) = s(z)),
% 2.83/3.04 inference(unit_resolution,[status(thm)],[43, 11112])).
% 2.83/3.04 tff(11114,plain,
% 2.83/3.04 (z = elem!1),
% 2.83/3.04 inference(unit_resolution,[status(thm)],[30, 11113])).
% 2.83/3.04 tff(11115,plain,
% 2.83/3.04 ((s(s(s(s(elem!1)))) = z) <=> (s(s(s(s(elem!1)))) = elem!1)),
% 2.83/3.04 inference(monotonicity,[status(thm)],[11114])).
% 2.83/3.04 tff(11116,plain,
% 2.83/3.04 ((~(s(s(s(s(elem!1)))) = z)) <=> (~(s(s(s(s(elem!1)))) = elem!1))),
% 2.83/3.04 inference(monotonicity,[status(thm)],[11115])).
% 2.83/3.04 tff(11117,plain,
% 2.83/3.04 (~(s(s(s(s(elem!1)))) = elem!1)),
% 2.83/3.04 inference(modus_ponens,[status(thm)],[626, 11116])).
% 2.83/3.04 tff(11118,plain,
% 2.83/3.04 (r(s(z), z) <=> r(s(z), elem!1)),
% 2.83/3.04 inference(monotonicity,[status(thm)],[11114])).
% 2.83/3.04 tff(11119,plain,
% 2.83/3.04 (r(s(z), elem!1)),
% 2.83/3.04 inference(modus_ponens,[status(thm)],[97, 11118])).
% 2.83/3.04 tff(11120,plain,
% 2.83/3.04 (r(s(elem!1), elem!1) <=> r(s(z), elem!1)),
% 2.83/3.04 inference(monotonicity,[status(thm)],[11113])).
% 2.83/3.04 tff(11121,plain,
% 2.83/3.04 (r(s(z), elem!1) <=> r(s(elem!1), elem!1)),
% 2.83/3.04 inference(symmetry,[status(thm)],[11120])).
% 2.83/3.04 tff(11122,plain,
% 2.83/3.04 (r(s(z), z) <=> r(s(elem!1), elem!1)),
% 2.83/3.04 inference(transitivity,[status(thm)],[11118, 11121])).
% 2.83/3.04 tff(11123,plain,
% 2.83/3.04 (r(s(elem!1), elem!1)),
% 2.83/3.04 inference(modus_ponens,[status(thm)],[97, 11122])).
% 2.83/3.04 tff(11124,plain,
% 2.83/3.04 (elem!1 = z),
% 2.83/3.04 inference(symmetry,[status(thm)],[11114])).
% 2.83/3.04 tff(11125,plain,
% 2.83/3.04 (b(elem!1, s(s(elem!1))) <=> b(z, s(s(elem!1)))),
% 2.83/3.04 inference(monotonicity,[status(thm)],[11124])).
% 2.83/3.04 tff(11126,plain,
% 2.83/3.04 (b(z, s(s(elem!1))) <=> b(elem!1, s(s(elem!1)))),
% 2.83/3.04 inference(symmetry,[status(thm)],[11125])).
% 2.83/3.04 tff(11127,plain,
% 2.83/3.04 (b(elem!1, s(s(elem!1)))),
% 2.83/3.04 inference(modus_ponens,[status(thm)],[11102, 11126])).
% 2.83/3.04 tff(11128,plain,
% 2.83/3.04 (r(elem!1, s(z))),
% 2.83/3.04 inference(unit_resolution,[status(thm)],[741, 11114, 11098])).
% 2.83/3.04 tff(11129,plain,
% 2.83/3.04 (b(s(s(elem!1)), z) <=> b(s(s(elem!1)), elem!1)),
% 2.83/3.04 inference(monotonicity,[status(thm)],[11114])).
% 2.83/3.04 tff(11130,plain,
% 2.83/3.04 (b(s(s(elem!1)), elem!1)),
% 2.83/3.04 inference(modus_ponens,[status(thm)],[11100, 11129])).
% 2.83/3.04 tff(11131,plain,
% 2.83/3.04 (~r(z, s(s(s(elem!1))))),
% 2.83/3.04 inference(unit_resolution,[status(thm)],[980, 350, 323, 120])).
% 2.83/3.04 tff(11132,plain,
% 2.83/3.04 (b(z, s(s(s(elem!1))))),
% 2.83/3.04 inference(unit_resolution,[status(thm)],[261, 11131])).
% 2.83/3.04 tff(11133,plain,
% 2.83/3.04 (~r(s(s(z)), z)),
% 2.83/3.04 inference(unit_resolution,[status(thm)],[10610, 11132, 350, 4577, 120, 2288, 10451, 1820])).
% 2.83/3.04 tff(11134,plain,
% 2.83/3.04 (b(s(s(z)), z)),
% 2.83/3.04 inference(unit_resolution,[status(thm)],[186, 11133])).
% 2.83/3.04 tff(11135,plain,
% 2.83/3.04 (~b(s(s(s(elem!1))), z)),
% 2.83/3.04 inference(unit_resolution,[status(thm)],[10745, 11134, 120, 10451, 350])).
% 2.83/3.04 tff(11136,plain,
% 2.83/3.04 (r(s(s(s(elem!1))), z)),
% 2.83/3.04 inference(unit_resolution,[status(thm)],[94, 11135])).
% 2.83/3.04 tff(11137,plain,
% 2.83/3.04 ($false),
% 2.83/3.04 inference(unit_resolution,[status(thm)],[10031, 197, 11136, 120, 350, 323])).
% 2.83/3.04 tff(11138,plain,((~r(s(s(s(elem!1))), s(z))) | (~r(s(z), s(s(z)))) | (~r(z, s(z))) | (~b(z, s(s(z)))) | (~r(s(s(elem!1)), s(z))) | r(s(s(z)), s(s(elem!1))) | (~b(z, s(s(elem!1))))), inference(lemma,lemma(discharge,[]))).
% 2.83/3.04 tff(11139,plain,
% 2.83/3.04 (~r(s(s(s(elem!1))), s(z))),
% 2.83/3.04 inference(unit_resolution,[status(thm)],[11138, 120, 11098, 10451, 10521, 2288, 11102])).
% 2.83/3.04 tff(11140,plain,
% 2.83/3.04 (b(s(s(s(elem!1))), s(z))),
% 2.83/3.04 inference(unit_resolution,[status(thm)],[1849, 11139])).
% 2.83/3.04 tff(11141,plain,
% 2.83/3.04 (r(s(z), s(s(z))) <=> r(s(z), s(s(elem!1)))),
% 2.83/3.04 inference(monotonicity,[status(thm)],[11112])).
% 2.83/3.04 tff(11142,plain,
% 2.83/3.04 (r(s(z), s(s(elem!1)))),
% 2.83/3.04 inference(modus_ponens,[status(thm)],[120, 11141])).
% 2.83/3.04 tff(11143,plain,
% 2.83/3.04 (~(s(s(elem!1)) = s(s(s(elem!1))))),
% 2.83/3.04 inference(unit_resolution,[status(thm)],[4570, 11140, 4568])).
% 2.83/3.04 tff(11144,plain,
% 2.83/3.04 (b(elem!1, s(s(elem!1))) <=> b(z, s(s(elem!1)))),
% 2.83/3.04 inference(monotonicity,[status(thm)],[4891])).
% 2.83/3.04 tff(11145,plain,
% 2.83/3.04 (b(z, s(s(elem!1))) <=> b(elem!1, s(s(elem!1)))),
% 2.83/3.04 inference(symmetry,[status(thm)],[11144])).
% 2.83/3.04 tff(11146,plain,
% 2.83/3.04 (b(elem!1, s(s(elem!1)))),
% 2.83/3.04 inference(modus_ponens,[status(thm)],[1820, 11145])).
% 2.83/3.04 tff(11147,plain,
% 2.83/3.04 (~b(s(s(elem!1)), s(s(s(elem!1))))),
% 2.83/3.04 inference(unit_resolution,[status(thm)],[8455, 119, 4577, 51, 97, 1820, 311])).
% 2.83/3.04 tff(11148,plain,
% 2.83/3.04 (r(s(s(elem!1)), s(s(s(elem!1))))),
% 2.83/3.04 inference(unit_resolution,[status(thm)],[461, 11147, 45])).
% 2.83/3.04 tff(11149,plain,
% 2.83/3.04 (~r(s(s(s(elem!1))), s(s(elem!1)))),
% 2.83/3.04 inference(unit_resolution,[status(thm)],[7376, 11148, 4577, 119])).
% 2.83/3.04 tff(11150,plain,
% 2.83/3.04 (b(s(s(s(elem!1))), s(s(elem!1)))),
% 2.83/3.04 inference(unit_resolution,[status(thm)],[889, 11149, 51])).
% 2.83/3.04 tff(11151,plain,
% 2.83/3.04 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), elem!1)) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(elem!1, s(s(elem!1)))) | (~b(s(s(s(elem!1))), elem!1)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(elem!1)), elem!1)) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(elem!1, s(s(elem!1)))) | (~b(s(s(s(elem!1))), elem!1)))),
% 2.83/3.04 inference(rewrite,[status(thm)],[])).
% 2.83/3.04 tff(11152,plain,
% 2.83/3.04 (((~b(elem!1, s(s(elem!1)))) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(s(elem!1)), elem!1)) | (~b(elem!1, s(s(elem!1)))) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(s(s(elem!1))), elem!1))) <=> ((~b(s(s(elem!1)), elem!1)) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(elem!1, s(s(elem!1)))) | (~b(s(s(s(elem!1))), elem!1)))),
% 2.83/3.04 inference(rewrite,[status(thm)],[])).
% 2.83/3.04 tff(11153,plain,
% 2.83/3.04 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(s(elem!1)))) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(s(elem!1)), elem!1)) | (~b(elem!1, s(s(elem!1)))) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(s(s(elem!1))), elem!1)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), elem!1)) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(elem!1, s(s(elem!1)))) | (~b(s(s(s(elem!1))), elem!1))))),
% 2.83/3.04 inference(monotonicity,[status(thm)],[11152])).
% 2.83/3.04 tff(11154,plain,
% 2.83/3.04 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(s(elem!1)))) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(s(elem!1)), elem!1)) | (~b(elem!1, s(s(elem!1)))) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(s(s(elem!1))), elem!1)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(elem!1)), elem!1)) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(elem!1, s(s(elem!1)))) | (~b(s(s(s(elem!1))), elem!1)))),
% 2.83/3.04 inference(transitivity,[status(thm)],[11153, 11151])).
% 2.83/3.04 tff(11155,plain,
% 2.83/3.04 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(s(elem!1)))) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(s(elem!1)), elem!1)) | (~b(elem!1, s(s(elem!1)))) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(s(s(elem!1))), elem!1)))),
% 2.83/3.04 inference(quant_inst,[status(thm)],[])).
% 2.83/3.04 tff(11156,plain,
% 2.83/3.04 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(elem!1)), elem!1)) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(elem!1, s(s(elem!1)))) | (~b(s(s(s(elem!1))), elem!1))),
% 2.83/3.04 inference(modus_ponens,[status(thm)],[11155, 11154])).
% 2.83/3.04 tff(11157,plain,
% 2.83/3.04 (~b(s(s(s(elem!1))), elem!1)),
% 2.83/3.04 inference(unit_resolution,[status(thm)],[11156, 166, 786, 11150, 11146])).
% 2.83/3.04 tff(11158,plain,
% 2.83/3.04 (~b(s(s(s(elem!1))), z)),
% 2.83/3.04 inference(modus_ponens,[status(thm)],[11157, 630])).
% 2.83/3.04 tff(11159,plain,
% 2.83/3.04 (~r(s(s(s(elem!1))), z)),
% 2.83/3.04 inference(unit_resolution,[status(thm)],[5310, 11148, 4577, 119])).
% 2.83/3.04 tff(11160,plain,
% 2.83/3.04 (b(s(s(s(elem!1))), z)),
% 2.83/3.04 inference(unit_resolution,[status(thm)],[94, 11159])).
% 2.83/3.04 tff(11161,plain,
% 2.83/3.04 ($false),
% 2.83/3.04 inference(unit_resolution,[status(thm)],[11160, 11158])).
% 2.83/3.04 tff(11162,plain,((~r(s(z), s(s(s(elem!1))))) | (~(z = elem!1)) | (~b(s(s(elem!1)), elem!1)) | (~r(s(s(elem!1)), s(z))) | (s(s(elem!1)) = s(s(s(elem!1)))) | (~r(s(z), z)) | (~b(z, s(s(elem!1)))) | (~r(s(z), s(s(elem!1))))), inference(lemma,lemma(discharge,[]))).
% 2.83/3.04 tff(11163,plain,
% 2.83/3.04 (~r(s(z), s(s(s(elem!1))))),
% 2.83/3.04 inference(unit_resolution,[status(thm)],[11162, 11114, 11130, 10521, 11143, 97, 11102, 11142])).
% 2.83/3.04 tff(11164,plain,
% 2.83/3.04 (b(s(z), s(s(s(elem!1))))),
% 2.83/3.04 inference(unit_resolution,[status(thm)],[116, 11163])).
% 2.83/3.04 tff(11165,plain,
% 2.83/3.04 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(z))) | (~r(s(z), elem!1)) | (~r(s(s(s(s(elem!1)))), elem!1)) | (~r(s(s(s(s(elem!1)))), s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(elem!1, s(z))) | (~r(s(z), elem!1)) | (~r(s(s(s(s(elem!1)))), elem!1)) | (~r(s(s(s(s(elem!1)))), s(z))))),
% 2.83/3.04 inference(rewrite,[status(thm)],[])).
% 2.83/3.04 tff(11166,plain,
% 2.83/3.04 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(z))) | (~r(s(z), elem!1)) | (~r(s(s(s(s(elem!1)))), elem!1)) | (~r(s(s(s(s(elem!1)))), s(z))))),
% 2.83/3.04 inference(quant_inst,[status(thm)],[])).
% 2.83/3.04 tff(11167,plain,
% 2.83/3.04 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(elem!1, s(z))) | (~r(s(z), elem!1)) | (~r(s(s(s(s(elem!1)))), elem!1)) | (~r(s(s(s(s(elem!1)))), s(z)))),
% 2.83/3.04 inference(modus_ponens,[status(thm)],[11166, 11165])).
% 2.83/3.04 tff(11168,plain,
% 2.83/3.04 (~r(s(s(s(s(elem!1)))), s(z))),
% 2.83/3.04 inference(unit_resolution,[status(thm)],[11167, 197, 744, 2381, 743])).
% 2.83/3.04 tff(11169,plain,
% 2.83/3.04 (b(s(s(s(s(elem!1)))), s(z))),
% 2.83/3.04 inference(unit_resolution,[status(thm)],[661, 11168])).
% 2.83/3.04 tff(11170,plain,
% 2.83/3.04 (~r(s(s(s(elem!1))), s(s(s(s(elem!1)))))),
% 2.83/3.04 inference(unit_resolution,[status(thm)],[1456, 197, 744, 743, 1013])).
% 2.83/3.04 tff(11171,plain,
% 2.83/3.04 (b(s(s(s(elem!1))), s(s(s(s(elem!1)))))),
% 2.83/3.04 inference(unit_resolution,[status(thm)],[696, 11170, 361])).
% 2.83/3.04 tff(11172,plain,
% 2.83/3.04 ($false),
% 2.83/3.04 inference(unit_resolution,[status(thm)],[5130, 11171, 11169, 96, 241])).
% 2.83/3.04 tff(11173,plain,((~r(s(s(s(s(elem!1)))), elem!1)) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(z), s(s(s(elem!1))))) | (s(s(s(elem!1))) = s(s(s(s(elem!1))))) | (~r(elem!1, s(z))) | (~r(s(s(s(elem!1))), elem!1)) | (~r(s(z), elem!1))), inference(lemma,lemma(discharge,[]))).
% 2.83/3.04 tff(11174,plain,
% 2.83/3.04 (~r(s(s(s(s(elem!1)))), elem!1)),
% 2.83/3.04 inference(unit_resolution,[status(thm)],[11173, 1013, 241, 358, 744, 96, 2381])).
% 2.83/3.04 tff(11175,plain,
% 2.83/3.04 (b(s(s(s(s(elem!1)))), elem!1)),
% 2.83/3.04 inference(unit_resolution,[status(thm)],[717, 79, 11174, 627])).
% 2.83/3.04 tff(11176,plain,
% 2.83/3.04 (((~b(s(s(elem!1)), elem!1)) | (~b(s(s(s(s(elem!1)))), elem!1)) | (~b(elem!1, s(s(elem!1)))) | (~b(s(s(elem!1)), elem!1)) | (~b(s(s(s(s(elem!1)))), elem!1)) | (~b(s(s(s(s(elem!1)))), s(s(elem!1))))) <=> ((~b(s(s(elem!1)), elem!1)) | (~b(s(s(s(s(elem!1)))), s(s(elem!1)))) | (~b(elem!1, s(s(elem!1)))) | (~b(s(s(s(s(elem!1)))), elem!1)))),
% 2.83/3.04 inference(rewrite,[status(thm)],[])).
% 2.83/3.04 tff(11177,plain,
% 2.83/3.04 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), elem!1)) | (~b(s(s(s(s(elem!1)))), elem!1)) | (~b(elem!1, s(s(elem!1)))) | (~b(s(s(elem!1)), elem!1)) | (~b(s(s(s(s(elem!1)))), elem!1)) | (~b(s(s(s(s(elem!1)))), s(s(elem!1)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), elem!1)) | (~b(s(s(s(s(elem!1)))), s(s(elem!1)))) | (~b(elem!1, s(s(elem!1)))) | (~b(s(s(s(s(elem!1)))), elem!1))))),
% 2.83/3.04 inference(monotonicity,[status(thm)],[11176])).
% 2.83/3.04 tff(11178,plain,
% 2.83/3.04 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), elem!1)) | (~b(s(s(s(s(elem!1)))), elem!1)) | (~b(elem!1, s(s(elem!1)))) | (~b(s(s(elem!1)), elem!1)) | (~b(s(s(s(s(elem!1)))), elem!1)) | (~b(s(s(s(s(elem!1)))), s(s(elem!1)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(elem!1)), elem!1)) | (~b(s(s(s(s(elem!1)))), s(s(elem!1)))) | (~b(elem!1, s(s(elem!1)))) | (~b(s(s(s(s(elem!1)))), elem!1)))),
% 2.83/3.04 inference(transitivity,[status(thm)],[11177, 10977])).
% 2.83/3.05 tff(11179,plain,
% 2.83/3.05 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), elem!1)) | (~b(s(s(s(s(elem!1)))), elem!1)) | (~b(elem!1, s(s(elem!1)))) | (~b(s(s(elem!1)), elem!1)) | (~b(s(s(s(s(elem!1)))), elem!1)) | (~b(s(s(s(s(elem!1)))), s(s(elem!1)))))),
% 2.83/3.05 inference(quant_inst,[status(thm)],[])).
% 2.83/3.05 tff(11180,plain,
% 2.83/3.05 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(elem!1)), elem!1)) | (~b(s(s(s(s(elem!1)))), s(s(elem!1)))) | (~b(elem!1, s(s(elem!1)))) | (~b(s(s(s(s(elem!1)))), elem!1))),
% 2.83/3.05 inference(modus_ponens,[status(thm)],[11179, 11178])).
% 2.83/3.05 tff(11181,plain,
% 2.83/3.05 (~b(s(s(s(s(elem!1)))), s(s(elem!1)))),
% 2.83/3.05 inference(unit_resolution,[status(thm)],[11180, 166, 786, 10960, 11175])).
% 2.83/3.05 tff(11182,plain,
% 2.83/3.05 (r(s(s(s(s(elem!1)))), s(s(elem!1)))),
% 2.83/3.05 inference(unit_resolution,[status(thm)],[813, 11181, 734])).
% 2.83/3.05 tff(11183,plain,
% 2.83/3.05 (~r(s(z), s(s(s(s(elem!1)))))),
% 2.83/3.05 inference(unit_resolution,[status(thm)],[4636, 11182, 4577, 10531])).
% 2.83/3.05 tff(11184,plain,
% 2.83/3.05 (b(s(z), s(s(s(s(elem!1)))))),
% 2.83/3.05 inference(unit_resolution,[status(thm)],[681, 11183])).
% 2.83/3.05 tff(11185,plain,
% 2.83/3.05 (~b(s(s(s(elem!1))), s(s(s(s(elem!1)))))),
% 2.83/3.05 inference(unit_resolution,[status(thm)],[5150, 11184, 241, 816, 10531, 4577, 734, 120, 96])).
% 2.83/3.05 tff(11186,plain,
% 2.83/3.05 (r(s(s(s(elem!1))), s(s(s(s(elem!1)))))),
% 2.83/3.05 inference(unit_resolution,[status(thm)],[696, 11185, 358])).
% 2.83/3.05 tff(11187,plain,
% 2.83/3.05 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), elem!1)) | (~b(elem!1, s(s(elem!1)))) | (~b(s(s(elem!1)), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), elem!1)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(elem!1)), elem!1)) | (~b(elem!1, s(s(elem!1)))) | (~b(s(s(elem!1)), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), elem!1)))),
% 2.83/3.05 inference(rewrite,[status(thm)],[])).
% 2.83/3.05 tff(11188,plain,
% 2.83/3.05 (((~b(s(s(elem!1)), elem!1)) | (~b(s(s(elem!1)), elem!1)) | (~b(elem!1, s(s(elem!1)))) | (~b(s(s(s(s(elem!1)))), elem!1)) | (~b(s(s(elem!1)), elem!1)) | (~b(s(s(elem!1)), s(s(s(s(elem!1))))))) <=> ((~b(s(s(elem!1)), elem!1)) | (~b(elem!1, s(s(elem!1)))) | (~b(s(s(elem!1)), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), elem!1)))),
% 2.83/3.05 inference(rewrite,[status(thm)],[])).
% 2.83/3.05 tff(11189,plain,
% 2.83/3.05 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), elem!1)) | (~b(s(s(elem!1)), elem!1)) | (~b(elem!1, s(s(elem!1)))) | (~b(s(s(s(s(elem!1)))), elem!1)) | (~b(s(s(elem!1)), elem!1)) | (~b(s(s(elem!1)), s(s(s(s(elem!1)))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), elem!1)) | (~b(elem!1, s(s(elem!1)))) | (~b(s(s(elem!1)), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), elem!1))))),
% 2.83/3.05 inference(monotonicity,[status(thm)],[11188])).
% 2.83/3.05 tff(11190,plain,
% 2.83/3.05 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), elem!1)) | (~b(s(s(elem!1)), elem!1)) | (~b(elem!1, s(s(elem!1)))) | (~b(s(s(s(s(elem!1)))), elem!1)) | (~b(s(s(elem!1)), elem!1)) | (~b(s(s(elem!1)), s(s(s(s(elem!1)))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(elem!1)), elem!1)) | (~b(elem!1, s(s(elem!1)))) | (~b(s(s(elem!1)), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), elem!1)))),
% 2.83/3.05 inference(transitivity,[status(thm)],[11189, 11187])).
% 2.83/3.05 tff(11191,plain,
% 2.83/3.05 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), elem!1)) | (~b(s(s(elem!1)), elem!1)) | (~b(elem!1, s(s(elem!1)))) | (~b(s(s(s(s(elem!1)))), elem!1)) | (~b(s(s(elem!1)), elem!1)) | (~b(s(s(elem!1)), s(s(s(s(elem!1)))))))),
% 2.83/3.05 inference(quant_inst,[status(thm)],[])).
% 2.83/3.05 tff(11192,plain,
% 2.83/3.05 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(elem!1)), elem!1)) | (~b(elem!1, s(s(elem!1)))) | (~b(s(s(elem!1)), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), elem!1))),
% 2.83/3.05 inference(modus_ponens,[status(thm)],[11191, 11190])).
% 2.83/3.05 tff(11193,plain,
% 2.83/3.05 (~b(s(s(elem!1)), s(s(s(s(elem!1)))))),
% 2.83/3.05 inference(unit_resolution,[status(thm)],[11192, 166, 786, 10960, 11175])).
% 2.83/3.05 tff(11194,plain,
% 2.83/3.05 (r(s(s(elem!1)), s(s(s(s(elem!1)))))),
% 2.83/3.05 inference(unit_resolution,[status(thm)],[827, 11193, 816])).
% 2.83/3.05 tff(11195,plain,
% 2.83/3.05 (~r(s(s(s(elem!1))), s(s(elem!1)))),
% 2.83/3.05 inference(unit_resolution,[status(thm)],[5160, 11182, 4577, 358, 241, 816, 10531, 734, 120, 96])).
% 2.83/3.05 tff(11196,plain,
% 2.83/3.05 (b(s(s(s(elem!1))), s(s(elem!1)))),
% 2.83/3.05 inference(unit_resolution,[status(thm)],[889, 11195, 51])).
% 2.83/3.05 tff(11197,plain,
% 2.83/3.05 (~(s(s(s(s(s(s(elem!1)))))) = elem!1)),
% 2.83/3.05 inference(unit_resolution,[status(thm)],[4897, 620])).
% 2.83/3.05 tff(11198,plain,
% 2.83/3.05 (~(s(s(s(s(s(s(elem!1)))))) = s(s(s(elem!1))))),
% 2.83/3.05 inference(unit_resolution,[status(thm)],[4922, 619])).
% 2.83/3.05 tff(11199,plain,
% 2.83/3.05 (b(s(s(s(s(s(s(elem!1)))))), s(z))),
% 2.83/3.05 inference(unit_resolution,[status(thm)],[9203, 79, 5014, 9200])).
% 2.83/3.05 tff(11200,plain,
% 2.83/3.05 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(z))) | (~r(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(elem!1)))))), s(s(s(elem!1))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(elem!1, s(z))) | (~r(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(elem!1)))))), s(s(s(elem!1))))))),
% 2.83/3.05 inference(rewrite,[status(thm)],[])).
% 2.83/3.05 tff(11201,plain,
% 2.83/3.05 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(z))) | (~r(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(elem!1)))))), s(s(s(elem!1))))))),
% 2.83/3.05 inference(quant_inst,[status(thm)],[])).
% 2.83/3.05 tff(11202,plain,
% 2.83/3.05 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(elem!1, s(z))) | (~r(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(elem!1)))))), s(s(s(elem!1)))))),
% 2.83/3.05 inference(modus_ponens,[status(thm)],[11201, 11200])).
% 2.83/3.05 tff(11203,plain,
% 2.83/3.05 (~r(s(s(s(s(s(s(elem!1)))))), s(s(s(elem!1))))),
% 2.83/3.05 inference(unit_resolution,[status(thm)],[11202, 197, 744, 9178, 1013])).
% 2.83/3.05 tff(11204,assumption,(~(s(s(s(s(s(s(elem!1)))))) = s(s(s(elem!1))))), introduced(assumption)).
% 2.83/3.05 tff(11205,plain,
% 2.83/3.05 (b(s(s(s(s(s(s(elem!1)))))), s(s(s(elem!1))))),
% 2.83/3.05 inference(unit_resolution,[status(thm)],[9226, 79, 11204, 11203])).
% 2.83/3.05 tff(11206,plain,
% 2.83/3.05 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(z), 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(elem!1)))))), s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(z), 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(elem!1)))))), s(z))))),
% 2.83/3.05 inference(rewrite,[status(thm)],[])).
% 2.83/3.05 tff(11207,plain,
% 2.83/3.05 (((~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(s(elem!1))), s(s(elem!1)))) | (~b(s(z), 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(elem!1)))))), s(z)))) <=> ((~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(z), 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(elem!1)))))), s(z))))),
% 2.83/3.05 inference(rewrite,[status(thm)],[])).
% 2.83/3.05 tff(11208,plain,
% 2.83/3.05 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(s(s(s(s(s(s(elem!1)))))), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(z), 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(elem!1)))))), s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(z), 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(elem!1)))))), s(z)))))),
% 2.83/3.05 inference(monotonicity,[status(thm)],[11207])).
% 2.83/3.05 tff(11209,plain,
% 2.83/3.05 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(s(s(s(s(s(s(elem!1)))))), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(z), 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(elem!1)))))), s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(z), 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(elem!1)))))), s(z))))),
% 2.83/3.05 inference(transitivity,[status(thm)],[11208, 11206])).
% 2.83/3.05 tff(11210,plain,
% 2.83/3.05 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(s(s(s(s(s(s(elem!1)))))), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(z), 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(elem!1)))))), s(z))))),
% 2.83/3.05 inference(quant_inst,[status(thm)],[])).
% 2.83/3.05 tff(11211,plain,
% 2.83/3.05 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(z), s(s(s(elem!1))))) | (~b(s(s(s(s(s(s(elem!1)))))), s(s(s(elem!1))))) | (~b(s(s(s(s(s(s(elem!1)))))), s(z)))),
% 2.83/3.05 inference(modus_ponens,[status(thm)],[11210, 11209])).
% 2.83/3.05 tff(11212,plain,
% 2.83/3.05 ($false),
% 2.83/3.05 inference(unit_resolution,[status(thm)],[11211, 166, 463, 839, 241, 11205, 11199])).
% 2.83/3.05 tff(11213,plain,((~r(s(s(s(s(s(s(elem!1)))))), elem!1)) | (~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(z), s(s(s(elem!1))))) | (s(s(s(s(s(s(elem!1)))))) = s(s(s(elem!1)))) | (~r(elem!1, s(z))) | (~r(s(s(s(elem!1))), elem!1)) | (~r(s(z), elem!1))), inference(lemma,lemma(discharge,[]))).
% 2.83/3.05 tff(11214,plain,
% 2.83/3.05 (~r(s(s(s(s(s(s(elem!1)))))), elem!1)),
% 2.83/3.05 inference(unit_resolution,[status(thm)],[11213, 839, 463, 241, 11198, 744, 1013, 2381])).
% 2.83/3.05 tff(11215,plain,
% 2.83/3.05 (b(s(s(s(s(s(s(elem!1)))))), elem!1)),
% 2.83/3.05 inference(unit_resolution,[status(thm)],[9214, 11214, 11197])).
% 2.83/3.05 tff(11216,plain,
% 2.83/3.05 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), elem!1)) | (~b(elem!1, s(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, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(elem!1)), elem!1)) | (~b(elem!1, s(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)))),
% 2.83/3.05 inference(rewrite,[status(thm)],[])).
% 2.83/3.05 tff(11217,plain,
% 2.83/3.05 (((~b(s(s(elem!1)), elem!1)) | (~b(s(s(s(s(s(s(elem!1)))))), elem!1)) | (~b(elem!1, s(s(elem!1)))) | (~b(s(s(elem!1)), elem!1)) | (~b(s(s(s(s(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(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)))),
% 2.83/3.05 inference(rewrite,[status(thm)],[])).
% 2.83/3.05 tff(11218,plain,
% 2.83/3.05 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), elem!1)) | (~b(s(s(s(s(s(s(elem!1)))))), elem!1)) | (~b(elem!1, 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(s(s(s(s(elem!1)))))), s(s(elem!1)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), elem!1)) | (~b(elem!1, s(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))))),
% 2.83/3.05 inference(monotonicity,[status(thm)],[11217])).
% 2.83/3.05 tff(11219,plain,
% 2.83/3.05 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), elem!1)) | (~b(s(s(s(s(s(s(elem!1)))))), elem!1)) | (~b(elem!1, 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(s(s(s(s(elem!1)))))), s(s(elem!1)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(elem!1)), elem!1)) | (~b(elem!1, s(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)))),
% 2.83/3.05 inference(transitivity,[status(thm)],[11218, 11216])).
% 2.83/3.05 tff(11220,plain,
% 2.83/3.05 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), elem!1)) | (~b(s(s(s(s(s(s(elem!1)))))), elem!1)) | (~b(elem!1, 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(s(s(s(s(elem!1)))))), s(s(elem!1)))))),
% 2.83/3.05 inference(quant_inst,[status(thm)],[])).
% 2.83/3.05 tff(11221,plain,
% 2.83/3.05 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(elem!1)), elem!1)) | (~b(elem!1, s(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))),
% 2.83/3.05 inference(modus_ponens,[status(thm)],[11220, 11219])).
% 2.83/3.05 tff(11222,plain,
% 2.83/3.05 (~b(s(s(s(s(s(s(elem!1)))))), s(s(elem!1)))),
% 2.83/3.05 inference(unit_resolution,[status(thm)],[11221, 166, 786, 10960, 11215])).
% 2.83/3.05 tff(11223,plain,
% 2.83/3.05 (r(s(s(s(s(s(s(elem!1)))))), s(s(elem!1)))),
% 2.83/3.05 inference(unit_resolution,[status(thm)],[9188, 79, 6328, 11222])).
% 2.83/3.05 tff(11224,plain,
% 2.83/3.05 (~b(elem!1, s(s(s(elem!1))))),
% 2.83/3.05 inference(unit_resolution,[status(thm)],[10759, 166, 463, 839, 10960])).
% 2.83/3.05 tff(11225,plain,
% 2.83/3.05 (r(elem!1, s(s(s(elem!1))))),
% 2.83/3.05 inference(unit_resolution,[status(thm)],[5451, 11224, 6292])).
% 2.83/3.05 tff(11226,plain,
% 2.83/3.05 (r(elem!1, s(s(s(z))))),
% 2.83/3.05 inference(modus_ponens,[status(thm)],[11225, 10955])).
% 2.83/3.05 tff(11227,plain,
% 2.83/3.05 (~r(s(s(s(s(elem!1)))), s(z))),
% 2.83/3.05 inference(unit_resolution,[status(thm)],[10984, 11226, 10960, 3728, 786, 619, 734, 4577, 120])).
% 2.83/3.05 tff(11228,plain,
% 2.83/3.05 (b(s(s(s(s(elem!1)))), s(z))),
% 2.83/3.05 inference(unit_resolution,[status(thm)],[661, 11227])).
% 2.83/3.05 tff(11229,plain,
% 2.83/3.05 (~b(s(s(s(elem!1))), s(s(s(s(elem!1)))))),
% 2.83/3.05 inference(unit_resolution,[status(thm)],[5130, 11228, 96, 241])).
% 2.83/3.05 tff(11230,plain,
% 2.83/3.05 (r(s(s(s(elem!1))), s(s(s(s(elem!1)))))),
% 2.83/3.05 inference(unit_resolution,[status(thm)],[696, 11229, 361])).
% 2.83/3.05 tff(11231,plain,
% 2.83/3.05 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~b(s(s(s(s(elem!1)))), s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~b(s(s(s(s(elem!1)))), s(z))))),
% 2.83/3.05 inference(rewrite,[status(thm)],[])).
% 2.83/3.05 tff(11232,plain,
% 2.83/3.05 (((~b(s(s(s(elem!1))), s(z))) | (~b(s(s(s(s(elem!1)))), s(z))) | (~b(s(z), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(s(s(s(elem!1)))), s(z))) | (~b(s(s(s(s(elem!1)))), s(s(s(elem!1)))))) <=> ((~b(s(z), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~b(s(s(s(s(elem!1)))), s(z))))),
% 2.83/3.05 inference(rewrite,[status(thm)],[])).
% 2.83/3.05 tff(11233,plain,
% 2.83/3.05 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), s(z))) | (~b(s(s(s(s(elem!1)))), s(z))) | (~b(s(z), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(s(s(s(elem!1)))), s(z))) | (~b(s(s(s(s(elem!1)))), s(s(s(elem!1))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~b(s(s(s(s(elem!1)))), s(z)))))),
% 2.83/3.05 inference(monotonicity,[status(thm)],[11232])).
% 2.83/3.05 tff(11234,plain,
% 2.83/3.05 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), s(z))) | (~b(s(s(s(s(elem!1)))), s(z))) | (~b(s(z), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(s(s(s(elem!1)))), s(z))) | (~b(s(s(s(s(elem!1)))), s(s(s(elem!1))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~b(s(s(s(s(elem!1)))), s(z))))),
% 2.83/3.05 inference(transitivity,[status(thm)],[11233, 11231])).
% 2.83/3.05 tff(11235,plain,
% 2.83/3.05 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), s(z))) | (~b(s(s(s(s(elem!1)))), s(z))) | (~b(s(z), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(s(s(s(elem!1)))), s(z))) | (~b(s(s(s(s(elem!1)))), s(s(s(elem!1))))))),
% 2.83/3.05 inference(quant_inst,[status(thm)],[])).
% 2.83/3.05 tff(11236,plain,
% 2.83/3.05 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~b(s(s(s(s(elem!1)))), s(z)))),
% 2.83/3.05 inference(modus_ponens,[status(thm)],[11235, 11234])).
% 2.83/3.05 tff(11237,plain,
% 2.83/3.05 (~b(s(s(s(s(elem!1)))), s(s(s(elem!1))))),
% 2.83/3.05 inference(unit_resolution,[status(thm)],[11236, 166, 241, 96, 11228])).
% 2.83/3.05 tff(11238,plain,
% 2.83/3.05 (r(s(s(s(s(elem!1)))), s(s(s(elem!1))))),
% 2.83/3.05 inference(unit_resolution,[status(thm)],[1063, 79, 11237, 1038])).
% 2.83/3.05 tff(11239,plain,
% 2.83/3.05 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), s(s(s(s(elem!1)))))) | (~r(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~r(s(s(s(s(elem!1)))), elem!1)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(elem!1, s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), s(s(s(s(elem!1)))))) | (~r(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~r(s(s(s(s(elem!1)))), elem!1)))),
% 2.83/3.05 inference(rewrite,[status(thm)],[])).
% 2.83/3.05 tff(11240,plain,
% 2.83/3.05 (((~r(s(s(s(elem!1))), s(s(s(s(elem!1)))))) | (~r(elem!1, s(s(s(elem!1))))) | (~r(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~r(s(s(s(s(elem!1)))), elem!1))) <=> ((~r(elem!1, s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), s(s(s(s(elem!1)))))) | (~r(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~r(s(s(s(s(elem!1)))), elem!1)))),
% 2.83/3.06 inference(rewrite,[status(thm)],[])).
% 2.83/3.06 tff(11241,plain,
% 2.83/3.06 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), s(s(s(s(elem!1)))))) | (~r(elem!1, s(s(s(elem!1))))) | (~r(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~r(s(s(s(s(elem!1)))), elem!1)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), s(s(s(s(elem!1)))))) | (~r(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~r(s(s(s(s(elem!1)))), elem!1))))),
% 2.83/3.06 inference(monotonicity,[status(thm)],[11240])).
% 2.83/3.06 tff(11242,plain,
% 2.83/3.06 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), s(s(s(s(elem!1)))))) | (~r(elem!1, s(s(s(elem!1))))) | (~r(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~r(s(s(s(s(elem!1)))), elem!1)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(elem!1, s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), s(s(s(s(elem!1)))))) | (~r(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~r(s(s(s(s(elem!1)))), elem!1)))),
% 2.83/3.06 inference(transitivity,[status(thm)],[11241, 11239])).
% 2.83/3.06 tff(11243,plain,
% 2.83/3.06 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), s(s(s(s(elem!1)))))) | (~r(elem!1, s(s(s(elem!1))))) | (~r(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~r(s(s(s(s(elem!1)))), elem!1)))),
% 2.83/3.06 inference(quant_inst,[status(thm)],[])).
% 2.83/3.06 tff(11244,plain,
% 2.83/3.06 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(elem!1, s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), s(s(s(s(elem!1)))))) | (~r(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~r(s(s(s(s(elem!1)))), elem!1))),
% 2.83/3.06 inference(modus_ponens,[status(thm)],[11243, 11242])).
% 2.83/3.06 tff(11245,plain,
% 2.83/3.06 (~r(s(s(s(s(elem!1)))), elem!1)),
% 2.83/3.06 inference(unit_resolution,[status(thm)],[11244, 197, 11225, 11238, 11230])).
% 2.83/3.06 tff(11246,plain,
% 2.83/3.06 (b(s(s(s(s(elem!1)))), elem!1)),
% 2.83/3.06 inference(unit_resolution,[status(thm)],[717, 79, 11245, 627])).
% 2.83/3.06 tff(11247,plain,
% 2.83/3.06 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), elem!1)) | (~b(elem!1, s(s(elem!1)))) | (~b(s(s(s(s(elem!1)))), elem!1)) | (~b(s(s(s(s(s(s(elem!1)))))), elem!1)) | (~b(s(s(s(s(elem!1)))), s(s(s(s(s(s(elem!1)))))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(elem!1)), elem!1)) | (~b(elem!1, s(s(elem!1)))) | (~b(s(s(s(s(elem!1)))), elem!1)) | (~b(s(s(s(s(s(s(elem!1)))))), elem!1)) | (~b(s(s(s(s(elem!1)))), s(s(s(s(s(s(elem!1)))))))))),
% 2.83/3.06 inference(rewrite,[status(thm)],[])).
% 2.83/3.06 tff(11248,plain,
% 2.83/3.06 (((~b(s(s(elem!1)), elem!1)) | (~b(s(s(s(s(elem!1)))), elem!1)) | (~b(elem!1, s(s(elem!1)))) | (~b(s(s(s(s(s(s(elem!1)))))), elem!1)) | (~b(s(s(s(s(elem!1)))), elem!1)) | (~b(s(s(s(s(elem!1)))), s(s(s(s(s(s(elem!1))))))))) <=> ((~b(s(s(elem!1)), elem!1)) | (~b(elem!1, s(s(elem!1)))) | (~b(s(s(s(s(elem!1)))), elem!1)) | (~b(s(s(s(s(s(s(elem!1)))))), elem!1)) | (~b(s(s(s(s(elem!1)))), s(s(s(s(s(s(elem!1)))))))))),
% 2.83/3.06 inference(rewrite,[status(thm)],[])).
% 2.83/3.06 tff(11249,plain,
% 2.83/3.06 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), elem!1)) | (~b(s(s(s(s(elem!1)))), elem!1)) | (~b(elem!1, s(s(elem!1)))) | (~b(s(s(s(s(s(s(elem!1)))))), elem!1)) | (~b(s(s(s(s(elem!1)))), elem!1)) | (~b(s(s(s(s(elem!1)))), s(s(s(s(s(s(elem!1)))))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), elem!1)) | (~b(elem!1, s(s(elem!1)))) | (~b(s(s(s(s(elem!1)))), elem!1)) | (~b(s(s(s(s(s(s(elem!1)))))), elem!1)) | (~b(s(s(s(s(elem!1)))), s(s(s(s(s(s(elem!1))))))))))),
% 2.83/3.06 inference(monotonicity,[status(thm)],[11248])).
% 2.83/3.06 tff(11250,plain,
% 2.83/3.06 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), elem!1)) | (~b(s(s(s(s(elem!1)))), elem!1)) | (~b(elem!1, s(s(elem!1)))) | (~b(s(s(s(s(s(s(elem!1)))))), elem!1)) | (~b(s(s(s(s(elem!1)))), elem!1)) | (~b(s(s(s(s(elem!1)))), s(s(s(s(s(s(elem!1)))))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(elem!1)), elem!1)) | (~b(elem!1, s(s(elem!1)))) | (~b(s(s(s(s(elem!1)))), elem!1)) | (~b(s(s(s(s(s(s(elem!1)))))), elem!1)) | (~b(s(s(s(s(elem!1)))), s(s(s(s(s(s(elem!1)))))))))),
% 2.83/3.06 inference(transitivity,[status(thm)],[11249, 11247])).
% 2.83/3.06 tff(11251,plain,
% 2.83/3.06 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), elem!1)) | (~b(s(s(s(s(elem!1)))), elem!1)) | (~b(elem!1, s(s(elem!1)))) | (~b(s(s(s(s(s(s(elem!1)))))), elem!1)) | (~b(s(s(s(s(elem!1)))), elem!1)) | (~b(s(s(s(s(elem!1)))), s(s(s(s(s(s(elem!1)))))))))),
% 2.83/3.06 inference(quant_inst,[status(thm)],[])).
% 2.83/3.06 tff(11252,plain,
% 2.83/3.06 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(elem!1)), elem!1)) | (~b(elem!1, s(s(elem!1)))) | (~b(s(s(s(s(elem!1)))), elem!1)) | (~b(s(s(s(s(s(s(elem!1)))))), elem!1)) | (~b(s(s(s(s(elem!1)))), s(s(s(s(s(s(elem!1))))))))),
% 2.83/3.06 inference(modus_ponens,[status(thm)],[11251, 11250])).
% 2.83/3.06 tff(11253,plain,
% 2.83/3.06 (~b(s(s(s(s(elem!1)))), s(s(s(s(s(s(elem!1)))))))),
% 2.83/3.06 inference(unit_resolution,[status(thm)],[11252, 166, 786, 10960, 11246, 11215])).
% 2.83/3.06 tff(11254,plain,
% 2.83/3.06 (~(s(s(s(s(elem!1)))) = s(s(s(s(s(s(elem!1)))))))),
% 2.83/3.06 inference(unit_resolution,[status(thm)],[9243, 816])).
% 2.83/3.06 tff(11255,plain,
% 2.83/3.06 (r(s(s(s(s(elem!1)))), s(s(s(s(s(s(elem!1)))))))),
% 2.83/3.06 inference(unit_resolution,[status(thm)],[9247, 79, 11254, 11253])).
% 2.83/3.06 tff(11256,plain,
% 2.83/3.06 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(s(s(s(s(elem!1)))), s(s(elem!1)))) | (~b(elem!1, s(s(elem!1)))) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(s(s(s(elem!1)))), elem!1)) | (~b(s(s(s(s(elem!1)))), s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(s(s(s(s(elem!1)))), s(s(elem!1)))) | (~b(elem!1, s(s(elem!1)))) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(s(s(s(elem!1)))), elem!1)) | (~b(s(s(s(s(elem!1)))), s(z))))),
% 2.83/3.06 inference(rewrite,[status(thm)],[])).
% 2.83/3.06 tff(11257,plain,
% 2.83/3.06 (((~b(s(s(s(elem!1))), s(z))) | (~b(s(s(s(s(elem!1)))), s(z))) | (~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(elem!1, s(s(elem!1)))) | (~b(s(s(s(s(elem!1)))), s(s(elem!1)))) | (~b(s(s(s(s(elem!1)))), elem!1))) <=> ((~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(s(s(s(s(elem!1)))), s(s(elem!1)))) | (~b(elem!1, s(s(elem!1)))) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(s(s(s(elem!1)))), elem!1)) | (~b(s(s(s(s(elem!1)))), s(z))))),
% 2.83/3.06 inference(rewrite,[status(thm)],[])).
% 2.83/3.06 tff(11258,plain,
% 2.83/3.06 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), s(z))) | (~b(s(s(s(s(elem!1)))), s(z))) | (~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(elem!1, s(s(elem!1)))) | (~b(s(s(s(s(elem!1)))), s(s(elem!1)))) | (~b(s(s(s(s(elem!1)))), elem!1)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(s(s(s(s(elem!1)))), s(s(elem!1)))) | (~b(elem!1, s(s(elem!1)))) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(s(s(s(elem!1)))), elem!1)) | (~b(s(s(s(s(elem!1)))), s(z)))))),
% 2.83/3.06 inference(monotonicity,[status(thm)],[11257])).
% 2.83/3.06 tff(11259,plain,
% 2.83/3.06 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), s(z))) | (~b(s(s(s(s(elem!1)))), s(z))) | (~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(elem!1, s(s(elem!1)))) | (~b(s(s(s(s(elem!1)))), s(s(elem!1)))) | (~b(s(s(s(s(elem!1)))), elem!1)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(s(s(s(s(elem!1)))), s(s(elem!1)))) | (~b(elem!1, s(s(elem!1)))) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(s(s(s(elem!1)))), elem!1)) | (~b(s(s(s(s(elem!1)))), s(z))))),
% 2.83/3.06 inference(transitivity,[status(thm)],[11258, 11256])).
% 2.83/3.06 tff(11260,plain,
% 2.83/3.06 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), s(z))) | (~b(s(s(s(s(elem!1)))), s(z))) | (~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(elem!1, s(s(elem!1)))) | (~b(s(s(s(s(elem!1)))), s(s(elem!1)))) | (~b(s(s(s(s(elem!1)))), elem!1)))),
% 2.83/3.06 inference(quant_inst,[status(thm)],[])).
% 2.83/3.06 tff(11261,plain,
% 2.83/3.06 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(s(s(s(s(elem!1)))), s(s(elem!1)))) | (~b(elem!1, s(s(elem!1)))) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(s(s(s(elem!1)))), elem!1)) | (~b(s(s(s(s(elem!1)))), s(z)))),
% 2.83/3.06 inference(modus_ponens,[status(thm)],[11260, 11259])).
% 2.83/3.06 tff(11262,plain,
% 2.83/3.06 ((~b(s(s(s(s(elem!1)))), s(s(elem!1)))) | (~b(s(s(s(s(elem!1)))), elem!1))),
% 2.83/3.06 inference(unit_resolution,[status(thm)],[11261, 166, 463, 96, 11228, 10960])).
% 2.83/3.06 tff(11263,plain,
% 2.83/3.06 (~b(s(s(s(s(elem!1)))), s(s(elem!1)))),
% 2.83/3.06 inference(unit_resolution,[status(thm)],[11262, 11246])).
% 2.83/3.06 tff(11264,plain,
% 2.83/3.06 (r(s(s(s(s(elem!1)))), s(s(elem!1)))),
% 2.83/3.06 inference(unit_resolution,[status(thm)],[813, 11263, 734])).
% 2.83/3.06 tff(11265,plain,
% 2.83/3.06 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(elem!1)), s(z))) | (~r(s(s(s(s(elem!1)))), s(s(elem!1)))) | (~r(s(s(s(s(elem!1)))), s(s(s(s(s(s(elem!1)))))))) | (~r(s(s(s(s(s(s(elem!1)))))), s(s(elem!1)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(elem!1)), s(z))) | (~r(s(s(s(s(elem!1)))), s(s(elem!1)))) | (~r(s(s(s(s(elem!1)))), s(s(s(s(s(s(elem!1)))))))) | (~r(s(s(s(s(s(s(elem!1)))))), s(s(elem!1)))))),
% 2.83/3.06 inference(rewrite,[status(thm)],[])).
% 2.83/3.06 tff(11266,plain,
% 2.83/3.06 (((~r(s(s(elem!1)), s(z))) | (~r(s(s(s(s(s(s(elem!1)))))), s(s(elem!1)))) | (~r(s(s(s(s(elem!1)))), s(s(elem!1)))) | (~r(s(s(s(s(elem!1)))), s(s(s(s(s(s(elem!1))))))))) <=> ((~r(s(s(elem!1)), s(z))) | (~r(s(s(s(s(elem!1)))), s(s(elem!1)))) | (~r(s(s(s(s(elem!1)))), s(s(s(s(s(s(elem!1)))))))) | (~r(s(s(s(s(s(s(elem!1)))))), s(s(elem!1)))))),
% 2.83/3.06 inference(rewrite,[status(thm)],[])).
% 2.83/3.06 tff(11267,plain,
% 2.83/3.06 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(elem!1)), s(z))) | (~r(s(s(s(s(s(s(elem!1)))))), s(s(elem!1)))) | (~r(s(s(s(s(elem!1)))), s(s(elem!1)))) | (~r(s(s(s(s(elem!1)))), s(s(s(s(s(s(elem!1)))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(elem!1)), s(z))) | (~r(s(s(s(s(elem!1)))), s(s(elem!1)))) | (~r(s(s(s(s(elem!1)))), s(s(s(s(s(s(elem!1)))))))) | (~r(s(s(s(s(s(s(elem!1)))))), s(s(elem!1))))))),
% 2.83/3.06 inference(monotonicity,[status(thm)],[11266])).
% 2.83/3.06 tff(11268,plain,
% 2.83/3.06 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(elem!1)), s(z))) | (~r(s(s(s(s(s(s(elem!1)))))), s(s(elem!1)))) | (~r(s(s(s(s(elem!1)))), s(s(elem!1)))) | (~r(s(s(s(s(elem!1)))), s(s(s(s(s(s(elem!1)))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(elem!1)), s(z))) | (~r(s(s(s(s(elem!1)))), s(s(elem!1)))) | (~r(s(s(s(s(elem!1)))), s(s(s(s(s(s(elem!1)))))))) | (~r(s(s(s(s(s(s(elem!1)))))), s(s(elem!1)))))),
% 2.83/3.06 inference(transitivity,[status(thm)],[11267, 11265])).
% 2.83/3.06 tff(11269,plain,
% 2.83/3.06 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(elem!1)), s(z))) | (~r(s(s(s(s(s(s(elem!1)))))), s(s(elem!1)))) | (~r(s(s(s(s(elem!1)))), s(s(elem!1)))) | (~r(s(s(s(s(elem!1)))), s(s(s(s(s(s(elem!1)))))))))),
% 2.83/3.06 inference(quant_inst,[status(thm)],[])).
% 2.83/3.06 tff(11270,plain,
% 2.83/3.06 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(elem!1)), s(z))) | (~r(s(s(s(s(elem!1)))), s(s(elem!1)))) | (~r(s(s(s(s(elem!1)))), s(s(s(s(s(s(elem!1)))))))) | (~r(s(s(s(s(s(s(elem!1)))))), s(s(elem!1))))),
% 2.83/3.06 inference(modus_ponens,[status(thm)],[11269, 11268])).
% 2.83/3.06 tff(11271,plain,
% 2.83/3.06 ($false),
% 2.83/3.06 inference(unit_resolution,[status(thm)],[11270, 197, 4577, 11264, 11255, 11223])).
% 2.83/3.06 tff(11272,plain,((~b(s(s(s(elem!1))), s(s(elem!1)))) | (~r(s(s(elem!1)), s(z))) | (~b(s(s(elem!1)), elem!1)) | (~b(elem!1, s(s(elem!1)))) | (~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(s(z), s(s(s(elem!1))))) | (~r(elem!1, s(z))) | (~r(s(s(s(elem!1))), elem!1)) | (~r(s(z), elem!1)) | (~b(s(s(s(elem!1))), s(z))) | (s(s(s(elem!1))) = s(s(s(s(elem!1))))) | (~r(s(elem!1), elem!1)) | (~r(s(z), s(s(z)))) | (~(s(s(z)) = s(s(elem!1))))), inference(lemma,lemma(discharge,[]))).
% 2.83/3.06 tff(11273,plain,
% 2.83/3.06 (~b(s(s(elem!1)), s(s(s(elem!1))))),
% 2.83/3.06 inference(unit_resolution,[status(thm)],[11272, 11196, 786, 10960, 4577, 241, 744, 1013, 2381, 96, 358, 3728, 120, 34])).
% 2.83/3.06 tff(11274,plain,
% 2.83/3.06 (r(s(s(elem!1)), s(s(s(elem!1))))),
% 2.83/3.06 inference(unit_resolution,[status(thm)],[461, 11273, 45])).
% 2.83/3.06 tff(11275,plain,
% 2.83/3.06 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(elem!1)), s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), s(s(s(s(elem!1)))))) | (~r(s(s(s(s(elem!1)))), s(s(elem!1)))) | (~r(s(s(elem!1)), s(s(s(s(elem!1)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(elem!1)), s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), s(s(s(s(elem!1)))))) | (~r(s(s(s(s(elem!1)))), s(s(elem!1)))) | (~r(s(s(elem!1)), s(s(s(s(elem!1)))))))),
% 2.83/3.06 inference(rewrite,[status(thm)],[])).
% 2.83/3.06 tff(11276,plain,
% 2.83/3.06 (((~r(s(s(s(s(elem!1)))), s(s(elem!1)))) | (~r(s(s(s(elem!1))), s(s(s(s(elem!1)))))) | (~r(s(s(elem!1)), s(s(s(s(elem!1)))))) | (~r(s(s(elem!1)), s(s(s(elem!1)))))) <=> ((~r(s(s(elem!1)), s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), s(s(s(s(elem!1)))))) | (~r(s(s(s(s(elem!1)))), s(s(elem!1)))) | (~r(s(s(elem!1)), s(s(s(s(elem!1)))))))),
% 2.83/3.06 inference(rewrite,[status(thm)],[])).
% 2.83/3.06 tff(11277,plain,
% 2.83/3.06 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(elem!1)))), s(s(elem!1)))) | (~r(s(s(s(elem!1))), s(s(s(s(elem!1)))))) | (~r(s(s(elem!1)), s(s(s(s(elem!1)))))) | (~r(s(s(elem!1)), s(s(s(elem!1))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(elem!1)), s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), s(s(s(s(elem!1)))))) | (~r(s(s(s(s(elem!1)))), s(s(elem!1)))) | (~r(s(s(elem!1)), s(s(s(s(elem!1))))))))),
% 2.83/3.06 inference(monotonicity,[status(thm)],[11276])).
% 2.83/3.06 tff(11278,plain,
% 2.83/3.06 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(elem!1)))), s(s(elem!1)))) | (~r(s(s(s(elem!1))), s(s(s(s(elem!1)))))) | (~r(s(s(elem!1)), s(s(s(s(elem!1)))))) | (~r(s(s(elem!1)), s(s(s(elem!1))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(elem!1)), s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), s(s(s(s(elem!1)))))) | (~r(s(s(s(s(elem!1)))), s(s(elem!1)))) | (~r(s(s(elem!1)), s(s(s(s(elem!1)))))))),
% 2.83/3.06 inference(transitivity,[status(thm)],[11277, 11275])).
% 2.83/3.06 tff(11279,plain,
% 2.83/3.06 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(elem!1)))), s(s(elem!1)))) | (~r(s(s(s(elem!1))), s(s(s(s(elem!1)))))) | (~r(s(s(elem!1)), s(s(s(s(elem!1)))))) | (~r(s(s(elem!1)), s(s(s(elem!1))))))),
% 2.83/3.06 inference(quant_inst,[status(thm)],[])).
% 2.83/3.06 tff(11280,plain,
% 2.83/3.06 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(elem!1)), s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), s(s(s(s(elem!1)))))) | (~r(s(s(s(s(elem!1)))), s(s(elem!1)))) | (~r(s(s(elem!1)), s(s(s(s(elem!1))))))),
% 2.83/3.06 inference(modus_ponens,[status(thm)],[11279, 11278])).
% 2.83/3.06 tff(11281,plain,
% 2.83/3.06 ($false),
% 2.83/3.06 inference(unit_resolution,[status(thm)],[11280, 197, 11274, 11194, 11182, 11186])).
% 2.83/3.06 tff(11282,plain,((~r(s(s(s(elem!1))), elem!1)) | (s(s(elem!1)) = s(s(s(elem!1)))) | (~b(s(s(elem!1)), elem!1)) | (~b(elem!1, s(s(elem!1)))) | (~r(s(s(elem!1)), s(z))) | (~b(s(z), s(s(s(elem!1))))) | (~r(elem!1, s(z))) | (~r(s(z), elem!1)) | (~b(s(s(s(elem!1))), s(z))) | (~r(s(elem!1), elem!1)) | (~r(s(z), s(s(z)))) | (~(s(s(z)) = s(s(elem!1))))), inference(lemma,lemma(discharge,[]))).
% 2.83/3.06 tff(11283,plain,
% 2.83/3.06 (~r(s(s(s(elem!1))), elem!1)),
% 2.83/3.06 inference(unit_resolution,[status(thm)],[11282, 11143, 11130, 11127, 10521, 11164, 11128, 11119, 11140, 11123, 120, 11112])).
% 2.83/3.06 tff(11284,plain,
% 2.83/3.06 (~r(s(s(s(elem!1))), z)),
% 2.83/3.06 inference(unit_resolution,[status(thm)],[966, 11283, 11114])).
% 2.83/3.06 tff(11285,plain,
% 2.83/3.06 (b(s(s(s(elem!1))), z)),
% 2.83/3.06 inference(unit_resolution,[status(thm)],[94, 11284])).
% 2.83/3.06 tff(11286,plain,
% 2.83/3.06 (b(s(s(s(elem!1))), elem!1)),
% 2.83/3.06 inference(unit_resolution,[status(thm)],[634, 11285, 11114])).
% 2.83/3.06 tff(11287,plain,
% 2.83/3.06 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(s(elem!1)))) | (~r(elem!1, s(z))) | (~r(s(s(s(s(elem!1)))), s(z))) | (~r(s(s(s(s(elem!1)))), elem!1)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(z), s(s(elem!1)))) | (~r(elem!1, s(z))) | (~r(s(s(s(s(elem!1)))), s(z))) | (~r(s(s(s(s(elem!1)))), elem!1)))),
% 2.83/3.06 inference(rewrite,[status(thm)],[])).
% 2.83/3.06 tff(11288,plain,
% 2.83/3.06 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(s(elem!1)))) | (~r(elem!1, s(z))) | (~r(s(s(s(s(elem!1)))), s(z))) | (~r(s(s(s(s(elem!1)))), elem!1)))),
% 2.83/3.06 inference(quant_inst,[status(thm)],[])).
% 2.83/3.06 tff(11289,plain,
% 2.83/3.06 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(z), s(s(elem!1)))) | (~r(elem!1, s(z))) | (~r(s(s(s(s(elem!1)))), s(z))) | (~r(s(s(s(s(elem!1)))), elem!1))),
% 2.83/3.06 inference(modus_ponens,[status(thm)],[11288, 11287])).
% 2.83/3.06 tff(11290,plain,
% 2.83/3.06 (~r(s(s(s(s(elem!1)))), elem!1)),
% 2.83/3.06 inference(unit_resolution,[status(thm)],[11289, 197, 10531, 744, 700])).
% 2.83/3.06 tff(11291,plain,
% 2.83/3.06 (b(s(s(s(s(elem!1)))), elem!1)),
% 2.83/3.06 inference(unit_resolution,[status(thm)],[717, 79, 11290, 627])).
% 2.83/3.06 tff(11292,plain,
% 2.83/3.06 (~r(s(s(elem!1)), s(s(s(s(elem!1)))))),
% 2.83/3.06 inference(unit_resolution,[status(thm)],[5140, 197, 10531, 4577, 700])).
% 2.83/3.06 tff(11293,plain,
% 2.83/3.06 (b(s(s(elem!1)), s(s(s(s(elem!1)))))),
% 2.83/3.06 inference(unit_resolution,[status(thm)],[827, 11292, 816])).
% 2.83/3.06 tff(11294,plain,
% 2.83/3.06 ((s(s(s(z))) = z) <=> (s(s(s(z))) = elem!1)),
% 2.83/3.06 inference(monotonicity,[status(thm)],[620])).
% 2.83/3.06 tff(11295,plain,
% 2.83/3.06 ((s(s(s(z))) = z) <=> (elem!1 = s(s(s(z))))),
% 2.83/3.06 inference(transitivity,[status(thm)],[11294, 1558])).
% 2.83/3.06 tff(11296,plain,
% 2.83/3.06 ((~(s(s(s(z))) = z)) <=> (~(elem!1 = s(s(s(z)))))),
% 2.83/3.06 inference(monotonicity,[status(thm)],[11295])).
% 2.83/3.06 tff(11297,plain,
% 2.83/3.06 (~(elem!1 = s(s(s(z))))),
% 2.83/3.06 inference(modus_ponens,[status(thm)],[1691, 11296])).
% 2.83/3.06 tff(11298,plain,
% 2.83/3.06 (~r(elem!1, s(s(s(z))))),
% 2.83/3.06 inference(unit_resolution,[status(thm)],[10984, 700, 10960, 3728, 786, 619, 734, 4577, 120])).
% 2.83/3.06 tff(11299,plain,
% 2.83/3.06 (b(elem!1, s(s(s(z))))),
% 2.83/3.06 inference(unit_resolution,[status(thm)],[1619, 11298, 11297])).
% 2.83/3.06 tff(11300,plain,
% 2.83/3.07 (b(elem!1, s(s(s(elem!1))))),
% 2.83/3.07 inference(modus_ponens,[status(thm)],[11299, 4839])).
% 2.83/3.07 tff(11301,plain,
% 2.83/3.07 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), elem!1)) | (~b(elem!1, s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(s(elem!1)), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), elem!1)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(elem!1)), elem!1)) | (~b(elem!1, s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(s(elem!1)), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), elem!1)))),
% 2.83/3.07 inference(rewrite,[status(thm)],[])).
% 2.83/3.07 tff(11302,plain,
% 2.83/3.07 (((~b(s(s(s(elem!1))), elem!1)) | (~b(s(s(elem!1)), elem!1)) | (~b(elem!1, s(s(s(elem!1))))) | (~b(s(s(s(s(elem!1)))), elem!1)) | (~b(s(s(elem!1)), elem!1)) | (~b(s(s(elem!1)), s(s(s(s(elem!1))))))) <=> ((~b(s(s(elem!1)), elem!1)) | (~b(elem!1, s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(s(elem!1)), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), elem!1)))),
% 2.83/3.07 inference(rewrite,[status(thm)],[])).
% 2.83/3.07 tff(11303,plain,
% 2.83/3.07 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), elem!1)) | (~b(s(s(elem!1)), elem!1)) | (~b(elem!1, s(s(s(elem!1))))) | (~b(s(s(s(s(elem!1)))), elem!1)) | (~b(s(s(elem!1)), elem!1)) | (~b(s(s(elem!1)), s(s(s(s(elem!1)))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), elem!1)) | (~b(elem!1, s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(s(elem!1)), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), elem!1))))),
% 2.83/3.07 inference(monotonicity,[status(thm)],[11302])).
% 2.83/3.07 tff(11304,plain,
% 2.83/3.07 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), elem!1)) | (~b(s(s(elem!1)), elem!1)) | (~b(elem!1, s(s(s(elem!1))))) | (~b(s(s(s(s(elem!1)))), elem!1)) | (~b(s(s(elem!1)), elem!1)) | (~b(s(s(elem!1)), s(s(s(s(elem!1)))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(elem!1)), elem!1)) | (~b(elem!1, s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(s(elem!1)), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), elem!1)))),
% 2.83/3.07 inference(transitivity,[status(thm)],[11303, 11301])).
% 2.83/3.07 tff(11305,plain,
% 2.83/3.07 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), elem!1)) | (~b(s(s(elem!1)), elem!1)) | (~b(elem!1, s(s(s(elem!1))))) | (~b(s(s(s(s(elem!1)))), elem!1)) | (~b(s(s(elem!1)), elem!1)) | (~b(s(s(elem!1)), s(s(s(s(elem!1)))))))),
% 2.83/3.07 inference(quant_inst,[status(thm)],[])).
% 2.83/3.07 tff(11306,plain,
% 2.83/3.07 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(elem!1)), elem!1)) | (~b(elem!1, s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(s(elem!1)), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), elem!1))),
% 2.83/3.07 inference(modus_ponens,[status(thm)],[11305, 11304])).
% 2.83/3.07 tff(11307,plain,
% 2.83/3.07 ($false),
% 2.83/3.07 inference(unit_resolution,[status(thm)],[11306, 166, 786, 11300, 11293, 641, 11291])).
% 2.83/3.07 tff(11308,plain,((~r(s(s(s(s(elem!1)))), s(z))) | (~b(s(s(elem!1)), elem!1)) | (~b(s(s(s(elem!1))), elem!1)) | (~r(s(s(elem!1)), s(z))) | (~r(elem!1, s(z))) | (~(s(s(z)) = s(s(elem!1)))) | (~b(elem!1, s(s(elem!1)))) | (~r(s(elem!1), elem!1)) | (~r(s(z), s(s(z))))), inference(lemma,lemma(discharge,[]))).
% 2.83/3.07 tff(11309,plain,
% 2.83/3.07 (~r(s(s(s(s(elem!1)))), s(z))),
% 2.83/3.07 inference(unit_resolution,[status(thm)],[11308, 11286, 11130, 10521, 11128, 11112, 11127, 11123, 120])).
% 2.83/3.07 tff(11310,plain,
% 2.83/3.07 (b(s(s(s(s(elem!1)))), s(z))),
% 2.83/3.07 inference(unit_resolution,[status(thm)],[661, 11309])).
% 2.83/3.07 tff(11311,plain,
% 2.83/3.07 ((s(s(s(s(elem!1)))) = s(s(z))) <=> (s(s(s(s(elem!1)))) = s(s(elem!1)))),
% 2.83/3.07 inference(monotonicity,[status(thm)],[11112])).
% 2.83/3.07 tff(11312,plain,
% 2.83/3.07 ((s(s(s(s(elem!1)))) = s(s(z))) <=> (s(s(elem!1)) = s(s(s(s(elem!1)))))),
% 2.83/3.07 inference(transitivity,[status(thm)],[11311, 123])).
% 2.83/3.07 tff(11313,plain,
% 2.83/3.07 ((~(s(s(s(s(elem!1)))) = s(s(z)))) <=> (~(s(s(elem!1)) = s(s(s(s(elem!1))))))),
% 2.83/3.07 inference(monotonicity,[status(thm)],[11312])).
% 2.83/3.07 tff(11314,plain,
% 2.83/3.07 (~(s(s(elem!1)) = s(s(s(s(elem!1)))))),
% 2.83/3.07 inference(modus_ponens,[status(thm)],[733, 11313])).
% 2.83/3.07 tff(11315,plain,
% 2.83/3.07 (~(s(s(s(s(elem!1)))) = s(s(s(s(s(s(elem!1)))))))),
% 2.83/3.07 inference(unit_resolution,[status(thm)],[9243, 11314])).
% 2.83/3.07 tff(11316,plain,
% 2.83/3.07 (~(s(s(s(s(s(s(elem!1)))))) = elem!1)),
% 2.83/3.07 inference(unit_resolution,[status(thm)],[4897, 11114])).
% 2.83/3.07 tff(11317,plain,
% 2.83/3.07 (~(s(s(s(s(s(s(elem!1)))))) = s(s(elem!1)))),
% 2.83/3.07 inference(unit_resolution,[status(thm)],[4986, 11113])).
% 2.83/3.07 tff(11318,plain,
% 2.83/3.07 (~(s(s(s(s(s(s(elem!1)))))) = s(s(s(elem!1))))),
% 2.83/3.07 inference(unit_resolution,[status(thm)],[4922, 11113])).
% 2.83/3.07 tff(11319,plain,
% 2.83/3.07 (~(s(s(s(elem!1))) = s(s(elem!1)))),
% 2.83/3.07 inference(unit_resolution,[status(thm)],[50, 11143])).
% 2.83/3.07 tff(11320,plain,
% 2.83/3.07 (((~b(s(s(elem!1)), elem!1)) | (~b(s(s(s(elem!1))), elem!1)) | (~b(elem!1, s(s(elem!1)))) | (~b(s(s(elem!1)), elem!1)) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(s(s(elem!1))), s(s(elem!1))))) <=> ((~b(s(s(elem!1)), elem!1)) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(elem!1, s(s(elem!1)))) | (~b(s(s(s(elem!1))), elem!1)))),
% 2.83/3.07 inference(rewrite,[status(thm)],[])).
% 2.83/3.07 tff(11321,plain,
% 2.83/3.07 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), elem!1)) | (~b(s(s(s(elem!1))), elem!1)) | (~b(elem!1, s(s(elem!1)))) | (~b(s(s(elem!1)), elem!1)) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(s(s(elem!1))), s(s(elem!1)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), elem!1)) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(elem!1, s(s(elem!1)))) | (~b(s(s(s(elem!1))), elem!1))))),
% 2.83/3.07 inference(monotonicity,[status(thm)],[11320])).
% 2.83/3.07 tff(11322,plain,
% 2.83/3.07 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), elem!1)) | (~b(s(s(s(elem!1))), elem!1)) | (~b(elem!1, s(s(elem!1)))) | (~b(s(s(elem!1)), elem!1)) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(s(s(elem!1))), s(s(elem!1)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(elem!1)), elem!1)) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(elem!1, s(s(elem!1)))) | (~b(s(s(s(elem!1))), elem!1)))),
% 2.83/3.07 inference(transitivity,[status(thm)],[11321, 11151])).
% 2.83/3.07 tff(11323,plain,
% 2.83/3.07 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), elem!1)) | (~b(s(s(s(elem!1))), elem!1)) | (~b(elem!1, s(s(elem!1)))) | (~b(s(s(elem!1)), elem!1)) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(s(s(elem!1))), s(s(elem!1)))))),
% 2.83/3.07 inference(quant_inst,[status(thm)],[])).
% 2.83/3.07 tff(11324,plain,
% 2.83/3.07 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(elem!1)), elem!1)) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(elem!1, s(s(elem!1)))) | (~b(s(s(s(elem!1))), elem!1))),
% 2.83/3.07 inference(modus_ponens,[status(thm)],[11323, 11322])).
% 2.83/3.07 tff(11325,plain,
% 2.83/3.07 (~b(s(s(s(elem!1))), s(s(elem!1)))),
% 2.83/3.07 inference(unit_resolution,[status(thm)],[11324, 166, 11130, 11127, 11286])).
% 2.83/3.07 tff(11326,plain,
% 2.83/3.07 (r(s(s(s(elem!1))), s(s(elem!1)))),
% 2.83/3.07 inference(unit_resolution,[status(thm)],[889, 11325, 11319])).
% 2.83/3.07 tff(11327,plain,
% 2.83/3.07 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), elem!1)) | (~b(elem!1, s(s(elem!1)))) | (~b(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(elem!1)))))), s(s(s(elem!1))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(elem!1)), elem!1)) | (~b(elem!1, s(s(elem!1)))) | (~b(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(elem!1)))))), s(s(s(elem!1))))))),
% 2.83/3.07 inference(rewrite,[status(thm)],[])).
% 2.83/3.07 tff(11328,plain,
% 2.83/3.07 (((~b(s(s(elem!1)), elem!1)) | (~b(s(s(s(s(s(s(elem!1)))))), elem!1)) | (~b(elem!1, s(s(elem!1)))) | (~b(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(elem!1)))))), s(s(s(elem!1)))))) <=> ((~b(s(s(elem!1)), elem!1)) | (~b(elem!1, s(s(elem!1)))) | (~b(s(s(s(elem!1))), 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))))))),
% 2.83/3.07 inference(rewrite,[status(thm)],[])).
% 2.83/3.07 tff(11329,plain,
% 2.83/3.07 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), elem!1)) | (~b(s(s(s(s(s(s(elem!1)))))), elem!1)) | (~b(elem!1, s(s(elem!1)))) | (~b(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(elem!1)))))), s(s(s(elem!1))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), elem!1)) | (~b(elem!1, s(s(elem!1)))) | (~b(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(elem!1)))))), s(s(s(elem!1)))))))),
% 2.83/3.07 inference(monotonicity,[status(thm)],[11328])).
% 2.83/3.07 tff(11330,plain,
% 2.83/3.07 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), elem!1)) | (~b(s(s(s(s(s(s(elem!1)))))), elem!1)) | (~b(elem!1, s(s(elem!1)))) | (~b(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(elem!1)))))), s(s(s(elem!1))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(elem!1)), elem!1)) | (~b(elem!1, s(s(elem!1)))) | (~b(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(elem!1)))))), s(s(s(elem!1))))))),
% 2.83/3.07 inference(transitivity,[status(thm)],[11329, 11327])).
% 2.83/3.07 tff(11331,plain,
% 2.83/3.07 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), elem!1)) | (~b(s(s(s(s(s(s(elem!1)))))), elem!1)) | (~b(elem!1, s(s(elem!1)))) | (~b(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(elem!1)))))), s(s(s(elem!1))))))),
% 2.83/3.07 inference(quant_inst,[status(thm)],[])).
% 2.83/3.07 tff(11332,plain,
% 2.83/3.07 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(elem!1)), elem!1)) | (~b(elem!1, s(s(elem!1)))) | (~b(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(elem!1)))))), s(s(s(elem!1)))))),
% 2.83/3.07 inference(modus_ponens,[status(thm)],[11331, 11330])).
% 2.83/3.07 tff(11333,plain,
% 2.83/3.07 (~b(s(s(s(s(s(s(elem!1)))))), s(s(s(elem!1))))),
% 2.83/3.07 inference(unit_resolution,[status(thm)],[11332, 166, 786, 10960, 641, 10271])).
% 2.83/3.07 tff(11334,plain,
% 2.83/3.07 (r(s(s(s(s(s(s(elem!1)))))), s(s(s(elem!1))))),
% 2.83/3.07 inference(unit_resolution,[status(thm)],[9226, 79, 11204, 11333])).
% 2.83/3.07 tff(11335,plain,
% 2.83/3.07 (~b(s(s(s(s(s(s(elem!1)))))), s(s(elem!1)))),
% 2.83/3.07 inference(unit_resolution,[status(thm)],[11221, 166, 786, 10960, 10271])).
% 2.83/3.07 tff(11336,plain,
% 2.83/3.07 (r(s(s(s(s(s(s(elem!1)))))), s(s(elem!1)))),
% 2.83/3.07 inference(unit_resolution,[status(thm)],[9188, 79, 4993, 11335])).
% 2.83/3.07 tff(11337,plain,
% 2.83/3.07 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(elem!1)), s(z))) | (~r(s(s(s(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)))))), s(s(s(elem!1))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(elem!1)), s(z))) | (~r(s(s(s(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)))))), s(s(s(elem!1))))))),
% 2.83/3.07 inference(rewrite,[status(thm)],[])).
% 2.83/3.07 tff(11338,plain,
% 2.83/3.07 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(elem!1)), s(z))) | (~r(s(s(s(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)))))), s(s(s(elem!1))))))),
% 2.83/3.07 inference(quant_inst,[status(thm)],[])).
% 2.83/3.07 tff(11339,plain,
% 2.83/3.07 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(elem!1)), s(z))) | (~r(s(s(s(elem!1))), s(s(elem!1)))) | (~r(s(s(s(s(s(s(elem!1)))))), s(s(elem!1)))) | (~r(s(s(s(s(s(s(elem!1)))))), s(s(s(elem!1)))))),
% 2.83/3.07 inference(modus_ponens,[status(thm)],[11338, 11337])).
% 2.83/3.07 tff(11340,plain,
% 2.83/3.07 ($false),
% 2.83/3.07 inference(unit_resolution,[status(thm)],[11339, 197, 4577, 905, 11336, 11334])).
% 2.83/3.07 tff(11341,plain,((~b(s(s(s(s(s(s(elem!1)))))), elem!1)) | (~r(s(s(elem!1)), s(z))) | (~r(s(s(s(elem!1))), s(s(elem!1)))) | (s(s(s(s(s(s(elem!1)))))) = s(s(s(elem!1)))) | (s(s(s(s(s(s(elem!1)))))) = s(s(elem!1))) | (~b(s(s(elem!1)), elem!1)) | (~b(elem!1, s(s(elem!1)))) | (~b(s(s(s(elem!1))), elem!1))), inference(lemma,lemma(discharge,[]))).
% 2.83/3.07 tff(11342,plain,
% 2.83/3.07 (~b(s(s(s(s(s(s(elem!1)))))), elem!1)),
% 2.83/3.07 inference(unit_resolution,[status(thm)],[11341, 11326, 11286, 11318, 11317, 11130, 11127, 10521])).
% 2.83/3.07 tff(11343,plain,
% 2.83/3.07 (r(s(s(s(s(s(s(elem!1)))))), elem!1)),
% 2.83/3.07 inference(unit_resolution,[status(thm)],[9214, 11342, 11316])).
% 2.83/3.07 tff(11344,assumption,(~(s(s(s(s(elem!1)))) = s(s(s(s(s(s(elem!1)))))))), introduced(assumption)).
% 2.83/3.07 tff(11345,plain,
% 2.83/3.07 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(z))) | (~r(s(s(s(s(elem!1)))), elem!1)) | (~r(s(s(s(s(elem!1)))), s(s(s(s(s(s(elem!1)))))))) | (~r(s(s(s(s(s(s(elem!1)))))), elem!1)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(elem!1, s(z))) | (~r(s(s(s(s(elem!1)))), elem!1)) | (~r(s(s(s(s(elem!1)))), s(s(s(s(s(s(elem!1)))))))) | (~r(s(s(s(s(s(s(elem!1)))))), elem!1)))),
% 2.83/3.07 inference(rewrite,[status(thm)],[])).
% 2.83/3.07 tff(11346,plain,
% 2.83/3.07 (((~r(elem!1, s(z))) | (~r(s(s(s(s(s(s(elem!1)))))), elem!1)) | (~r(s(s(s(s(elem!1)))), elem!1)) | (~r(s(s(s(s(elem!1)))), s(s(s(s(s(s(elem!1))))))))) <=> ((~r(elem!1, s(z))) | (~r(s(s(s(s(elem!1)))), elem!1)) | (~r(s(s(s(s(elem!1)))), s(s(s(s(s(s(elem!1)))))))) | (~r(s(s(s(s(s(s(elem!1)))))), elem!1)))),
% 2.83/3.07 inference(rewrite,[status(thm)],[])).
% 2.83/3.07 tff(11347,plain,
% 2.83/3.07 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(z))) | (~r(s(s(s(s(s(s(elem!1)))))), elem!1)) | (~r(s(s(s(s(elem!1)))), elem!1)) | (~r(s(s(s(s(elem!1)))), s(s(s(s(s(s(elem!1)))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(z))) | (~r(s(s(s(s(elem!1)))), elem!1)) | (~r(s(s(s(s(elem!1)))), s(s(s(s(s(s(elem!1)))))))) | (~r(s(s(s(s(s(s(elem!1)))))), elem!1))))),
% 2.83/3.07 inference(monotonicity,[status(thm)],[11346])).
% 2.83/3.07 tff(11348,plain,
% 2.83/3.07 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(z))) | (~r(s(s(s(s(s(s(elem!1)))))), elem!1)) | (~r(s(s(s(s(elem!1)))), elem!1)) | (~r(s(s(s(s(elem!1)))), s(s(s(s(s(s(elem!1)))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(elem!1, s(z))) | (~r(s(s(s(s(elem!1)))), elem!1)) | (~r(s(s(s(s(elem!1)))), s(s(s(s(s(s(elem!1)))))))) | (~r(s(s(s(s(s(s(elem!1)))))), elem!1)))),
% 2.83/3.07 inference(transitivity,[status(thm)],[11347, 11345])).
% 2.83/3.07 tff(11349,plain,
% 2.83/3.07 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(z))) | (~r(s(s(s(s(s(s(elem!1)))))), elem!1)) | (~r(s(s(s(s(elem!1)))), elem!1)) | (~r(s(s(s(s(elem!1)))), s(s(s(s(s(s(elem!1)))))))))),
% 2.83/3.07 inference(quant_inst,[status(thm)],[])).
% 2.83/3.07 tff(11350,plain,
% 2.83/3.07 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(elem!1, s(z))) | (~r(s(s(s(s(elem!1)))), elem!1)) | (~r(s(s(s(s(elem!1)))), s(s(s(s(s(s(elem!1)))))))) | (~r(s(s(s(s(s(s(elem!1)))))), elem!1))),
% 2.83/3.07 inference(modus_ponens,[status(thm)],[11349, 11348])).
% 2.83/3.07 tff(11351,plain,
% 2.83/3.07 (~r(s(s(s(s(elem!1)))), s(s(s(s(s(s(elem!1)))))))),
% 2.83/3.07 inference(unit_resolution,[status(thm)],[11350, 197, 744, 743, 9178])).
% 2.83/3.07 tff(11352,plain,
% 2.83/3.07 (b(s(s(s(s(elem!1)))), s(s(s(s(s(s(elem!1)))))))),
% 2.83/3.07 inference(unit_resolution,[status(thm)],[9247, 79, 11351, 11344])).
% 2.83/3.07 tff(11353,plain,
% 2.83/3.07 (~r(s(z), s(s(s(s(elem!1)))))),
% 2.83/3.07 inference(unit_resolution,[status(thm)],[2387, 197, 744, 2381, 743])).
% 2.83/3.07 tff(11354,plain,
% 2.83/3.07 (b(s(z), s(s(s(s(elem!1)))))),
% 2.83/3.07 inference(unit_resolution,[status(thm)],[681, 11353])).
% 2.83/3.07 tff(11355,plain,
% 2.83/3.07 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(elem!1)))), s(z))) | (~b(s(z), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(s(s(elem!1)))))), s(z))) | (~b(s(s(s(s(elem!1)))), s(s(s(s(s(s(elem!1)))))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(elem!1)))), s(z))) | (~b(s(z), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(s(s(elem!1)))))), s(z))) | (~b(s(s(s(s(elem!1)))), s(s(s(s(s(s(elem!1)))))))))),
% 2.83/3.07 inference(rewrite,[status(thm)],[])).
% 2.83/3.07 tff(11356,plain,
% 2.83/3.07 (((~b(s(s(s(s(elem!1)))), s(s(s(s(s(s(elem!1)))))))) | (~b(s(s(s(s(elem!1)))), s(s(s(s(s(s(elem!1)))))))) | (~b(s(z), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(s(s(elem!1)))))), s(z))) | (~b(s(s(s(s(elem!1)))), s(z))) | (~b(s(s(s(s(elem!1)))), s(s(s(s(s(s(elem!1))))))))) <=> ((~b(s(s(s(s(elem!1)))), s(z))) | (~b(s(z), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(s(s(elem!1)))))), s(z))) | (~b(s(s(s(s(elem!1)))), s(s(s(s(s(s(elem!1)))))))))),
% 2.83/3.07 inference(rewrite,[status(thm)],[])).
% 2.83/3.07 tff(11357,plain,
% 2.83/3.07 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(elem!1)))), s(s(s(s(s(s(elem!1)))))))) | (~b(s(s(s(s(elem!1)))), s(s(s(s(s(s(elem!1)))))))) | (~b(s(z), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(s(s(elem!1)))))), s(z))) | (~b(s(s(s(s(elem!1)))), s(z))) | (~b(s(s(s(s(elem!1)))), s(s(s(s(s(s(elem!1)))))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(elem!1)))), s(z))) | (~b(s(z), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(s(s(elem!1)))))), s(z))) | (~b(s(s(s(s(elem!1)))), s(s(s(s(s(s(elem!1))))))))))),
% 2.83/3.07 inference(monotonicity,[status(thm)],[11356])).
% 2.83/3.07 tff(11358,plain,
% 2.83/3.07 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(elem!1)))), s(s(s(s(s(s(elem!1)))))))) | (~b(s(s(s(s(elem!1)))), s(s(s(s(s(s(elem!1)))))))) | (~b(s(z), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(s(s(elem!1)))))), s(z))) | (~b(s(s(s(s(elem!1)))), s(z))) | (~b(s(s(s(s(elem!1)))), s(s(s(s(s(s(elem!1)))))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(elem!1)))), s(z))) | (~b(s(z), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(s(s(elem!1)))))), s(z))) | (~b(s(s(s(s(elem!1)))), s(s(s(s(s(s(elem!1)))))))))),
% 2.83/3.07 inference(transitivity,[status(thm)],[11357, 11355])).
% 2.83/3.07 tff(11359,plain,
% 2.83/3.07 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(elem!1)))), s(s(s(s(s(s(elem!1)))))))) | (~b(s(s(s(s(elem!1)))), s(s(s(s(s(s(elem!1)))))))) | (~b(s(z), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(s(s(elem!1)))))), s(z))) | (~b(s(s(s(s(elem!1)))), s(z))) | (~b(s(s(s(s(elem!1)))), s(s(s(s(s(s(elem!1)))))))))),
% 2.83/3.08 inference(quant_inst,[status(thm)],[])).
% 2.83/3.08 tff(11360,plain,
% 2.83/3.08 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(elem!1)))), s(z))) | (~b(s(z), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(s(s(elem!1)))))), s(z))) | (~b(s(s(s(s(elem!1)))), s(s(s(s(s(s(elem!1))))))))),
% 2.83/3.08 inference(modus_ponens,[status(thm)],[11359, 11358])).
% 2.83/3.08 tff(11361,plain,
% 2.83/3.08 ($false),
% 2.83/3.08 inference(unit_resolution,[status(thm)],[11360, 166, 1402, 11354, 11199, 11352])).
% 2.83/3.08 tff(11362,plain,((~r(s(s(s(s(s(s(elem!1)))))), elem!1)) | (~b(s(s(s(s(elem!1)))), s(z))) | (s(s(s(s(elem!1)))) = s(s(s(s(s(s(elem!1))))))) | (~r(elem!1, s(z))) | (~r(s(s(s(s(elem!1)))), elem!1)) | (~r(s(z), elem!1))), inference(lemma,lemma(discharge,[]))).
% 2.83/3.08 tff(11363,plain,
% 2.83/3.08 (~r(s(s(s(s(elem!1)))), elem!1)),
% 2.83/3.08 inference(unit_resolution,[status(thm)],[11362, 11343, 11315, 11128, 11310, 11119])).
% 2.83/3.08 tff(11364,plain,
% 2.83/3.08 (b(s(s(s(s(elem!1)))), elem!1)),
% 2.83/3.08 inference(unit_resolution,[status(thm)],[717, 79, 11363, 11117])).
% 2.83/3.08 tff(11365,plain,
% 2.83/3.08 (~(s(s(s(elem!1))) = s(s(s(s(elem!1)))))),
% 2.83/3.08 inference(unit_resolution,[status(thm)],[357, 11143])).
% 2.83/3.08 tff(11366,plain,
% 2.83/3.08 (~(s(s(s(s(elem!1)))) = s(s(s(elem!1))))),
% 2.83/3.08 inference(unit_resolution,[status(thm)],[363, 11365])).
% 2.83/3.08 tff(11367,plain,
% 2.83/3.08 (~b(s(s(s(s(elem!1)))), s(s(s(elem!1))))),
% 2.83/3.08 inference(unit_resolution,[status(thm)],[11236, 166, 11164, 11140, 11310])).
% 2.83/3.08 tff(11368,plain,
% 2.83/3.08 (r(s(s(s(s(elem!1)))), s(s(s(elem!1))))),
% 2.83/3.08 inference(unit_resolution,[status(thm)],[1063, 79, 11367, 11366])).
% 2.83/3.08 tff(11369,plain,
% 2.83/3.08 (~b(s(s(elem!1)), s(s(s(elem!1))))),
% 2.83/3.08 inference(unit_resolution,[status(thm)],[3593, 11285, 11102, 11100])).
% 2.83/3.08 tff(11370,plain,
% 2.83/3.08 (r(s(s(elem!1)), s(s(s(elem!1))))),
% 2.83/3.08 inference(unit_resolution,[status(thm)],[461, 11369, 11143])).
% 2.83/3.08 tff(11371,plain,
% 2.83/3.08 (~r(s(s(elem!1)), s(s(s(s(elem!1)))))),
% 2.83/3.08 inference(unit_resolution,[status(thm)],[9172, 197, 11370, 11326, 11368])).
% 2.83/3.08 tff(11372,plain,
% 2.83/3.08 (b(s(s(elem!1)), s(s(s(s(elem!1)))))),
% 2.83/3.08 inference(unit_resolution,[status(thm)],[827, 11371, 11314])).
% 2.83/3.08 tff(11373,plain,
% 2.83/3.08 ($false),
% 2.83/3.08 inference(unit_resolution,[status(thm)],[11192, 166, 11130, 11372, 11127, 11364])).
% 2.83/3.08 tff(11374,plain,((~r(s(z), s(s(z)))) | (~r(s(z), z)) | r(s(s(z)), s(s(elem!1))) | (~b(z, s(s(z)))) | b(s(s(elem!1)), s(z))), inference(lemma,lemma(discharge,[]))).
% 2.83/3.08 tff(11375,plain,
% 2.83/3.08 (~r(s(z), s(s(z)))),
% 2.83/3.08 inference(unit_resolution,[status(thm)],[11374, 97, 2288, 10451, 4568])).
% 2.83/3.08 tff(11376,plain,
% 2.83/3.08 (b(s(z), s(s(z)))),
% 2.83/3.08 inference(unit_resolution,[status(thm)],[427, 11375])).
% 2.83/3.08 tff(11377,plain,
% 2.83/3.08 (~b(s(s(z)), z)),
% 2.83/3.08 inference(unit_resolution,[status(thm)],[10947, 1790, 10451, 97, 4577, 2288])).
% 2.83/3.08 tff(11378,plain,
% 2.83/3.08 (r(s(s(z)), z)),
% 2.83/3.08 inference(unit_resolution,[status(thm)],[186, 11377])).
% 2.83/3.08 tff(11379,plain,
% 2.83/3.08 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(elem!1)))) | (~r(s(z), z)) | (~r(s(s(z)), s(z))) | (~r(s(s(z)), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, s(s(elem!1)))) | (~r(s(z), z)) | (~r(s(s(z)), s(z))) | (~r(s(s(z)), z)))),
% 2.83/3.08 inference(rewrite,[status(thm)],[])).
% 2.83/3.08 tff(11380,plain,
% 2.83/3.08 (((~r(z, s(s(elem!1)))) | (~r(s(z), z)) | (~r(s(s(z)), z)) | (~r(s(s(z)), s(z)))) <=> ((~r(z, s(s(elem!1)))) | (~r(s(z), z)) | (~r(s(s(z)), s(z))) | (~r(s(s(z)), z)))),
% 2.83/3.08 inference(rewrite,[status(thm)],[])).
% 2.83/3.08 tff(11381,plain,
% 2.83/3.08 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(elem!1)))) | (~r(s(z), z)) | (~r(s(s(z)), z)) | (~r(s(s(z)), s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(elem!1)))) | (~r(s(z), z)) | (~r(s(s(z)), s(z))) | (~r(s(s(z)), z))))),
% 2.83/3.08 inference(monotonicity,[status(thm)],[11380])).
% 2.83/3.08 tff(11382,plain,
% 2.83/3.08 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(elem!1)))) | (~r(s(z), z)) | (~r(s(s(z)), z)) | (~r(s(s(z)), s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, s(s(elem!1)))) | (~r(s(z), z)) | (~r(s(s(z)), s(z))) | (~r(s(s(z)), z)))),
% 2.83/3.08 inference(transitivity,[status(thm)],[11381, 11379])).
% 2.83/3.08 tff(11383,plain,
% 2.83/3.08 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(elem!1)))) | (~r(s(z), z)) | (~r(s(s(z)), z)) | (~r(s(s(z)), s(z))))),
% 2.83/3.08 inference(quant_inst,[status(thm)],[])).
% 2.83/3.08 tff(11384,plain,
% 2.83/3.08 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, s(s(elem!1)))) | (~r(s(z), z)) | (~r(s(s(z)), s(z))) | (~r(s(s(z)), z))),
% 2.83/3.08 inference(modus_ponens,[status(thm)],[11383, 11382])).
% 2.83/3.08 tff(11385,plain,
% 2.83/3.08 (~r(s(s(z)), s(z))),
% 2.83/3.08 inference(unit_resolution,[status(thm)],[11384, 197, 97, 4458, 11378])).
% 2.83/3.08 tff(11386,plain,
% 2.83/3.08 (b(s(s(z)), s(z))),
% 2.83/3.08 inference(unit_resolution,[status(thm)],[308, 11385])).
% 2.83/3.08 tff(11387,plain,
% 2.83/3.08 (~r(z, s(z))),
% 2.83/3.08 inference(unit_resolution,[status(thm)],[8426, 4458, 4577, 97])).
% 2.83/3.08 tff(11388,plain,
% 2.83/3.08 (b(z, s(z))),
% 2.83/3.08 inference(unit_resolution,[status(thm)],[321, 11387])).
% 2.83/3.08 tff(11389,plain,
% 2.83/3.08 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(z)))) | (~b(z, s(z))) | (~b(s(z), s(s(z)))) | (~b(s(s(z)), s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(s(z)))) | (~b(z, s(z))) | (~b(s(z), s(s(z)))) | (~b(s(s(z)), s(z))))),
% 2.83/3.08 inference(rewrite,[status(thm)],[])).
% 2.83/3.08 tff(11390,plain,
% 2.83/3.08 (((~b(s(s(z)), s(z))) | (~b(z, s(z))) | (~b(s(z), s(s(z)))) | (~b(s(s(z)), s(z))) | (~b(z, s(z))) | (~b(z, s(s(z))))) <=> ((~b(z, s(s(z)))) | (~b(z, s(z))) | (~b(s(z), s(s(z)))) | (~b(s(s(z)), s(z))))),
% 2.83/3.08 inference(rewrite,[status(thm)],[])).
% 2.83/3.08 tff(11391,plain,
% 2.83/3.08 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), s(z))) | (~b(z, s(z))) | (~b(s(z), s(s(z)))) | (~b(s(s(z)), s(z))) | (~b(z, s(z))) | (~b(z, s(s(z)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(z)))) | (~b(z, s(z))) | (~b(s(z), s(s(z)))) | (~b(s(s(z)), s(z)))))),
% 2.83/3.08 inference(monotonicity,[status(thm)],[11390])).
% 2.83/3.08 tff(11392,plain,
% 2.83/3.08 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), s(z))) | (~b(z, s(z))) | (~b(s(z), s(s(z)))) | (~b(s(s(z)), s(z))) | (~b(z, s(z))) | (~b(z, s(s(z)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(s(z)))) | (~b(z, s(z))) | (~b(s(z), s(s(z)))) | (~b(s(s(z)), s(z))))),
% 2.83/3.08 inference(transitivity,[status(thm)],[11391, 11389])).
% 2.83/3.08 tff(11393,plain,
% 2.83/3.08 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), s(z))) | (~b(z, s(z))) | (~b(s(z), s(s(z)))) | (~b(s(s(z)), s(z))) | (~b(z, s(z))) | (~b(z, s(s(z)))))),
% 2.83/3.08 inference(quant_inst,[status(thm)],[])).
% 2.83/3.08 tff(11394,plain,
% 2.83/3.08 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(s(z)))) | (~b(z, s(z))) | (~b(s(z), s(s(z)))) | (~b(s(s(z)), s(z)))),
% 2.83/3.08 inference(modus_ponens,[status(thm)],[11393, 11392])).
% 2.83/3.08 tff(11395,plain,
% 2.83/3.08 ($false),
% 2.83/3.08 inference(unit_resolution,[status(thm)],[11394, 166, 556, 10451, 11388, 11386])).
% 2.83/3.08 tff(11396,plain,(b(z, s(s(elem!1))) | (~b(s(z), s(s(z)))) | (~b(z, s(s(z)))) | (~r(s(z), z)) | (~r(s(s(elem!1)), s(z))) | r(s(s(z)), s(s(elem!1)))), inference(lemma,lemma(discharge,[]))).
% 2.83/3.08 tff(11397,plain,
% 2.83/3.08 (b(z, s(s(elem!1)))),
% 2.83/3.08 inference(unit_resolution,[status(thm)],[11396, 11376, 10451, 97, 10521, 2288])).
% 2.83/3.08 tff(11398,plain,
% 2.83/3.08 ((s(s(z)) = s(s(s(elem!1)))) <=> (s(s(z)) = s(s(elem!1)))),
% 2.83/3.08 inference(monotonicity,[status(thm)],[47])).
% 2.83/3.08 tff(11399,plain,
% 2.83/3.08 ((s(s(z)) = s(s(s(elem!1)))) <=> (s(s(elem!1)) = s(s(z)))),
% 2.83/3.08 inference(transitivity,[status(thm)],[11398, 126])).
% 2.83/3.08 tff(11400,plain,
% 2.83/3.08 ((~(s(s(z)) = s(s(s(elem!1))))) <=> (~(s(s(elem!1)) = s(s(z))))),
% 2.83/3.08 inference(monotonicity,[status(thm)],[11399])).
% 2.83/3.08 tff(11401,plain,
% 2.83/3.08 (~(s(s(elem!1)) = s(s(z)))),
% 2.83/3.08 inference(modus_ponens,[status(thm)],[209, 11400])).
% 2.83/3.08 tff(11402,plain,
% 2.83/3.08 (b(z, s(s(elem!1)))),
% 2.83/3.08 inference(unit_resolution,[status(thm)],[11396, 556, 10451, 97, 4577, 2288])).
% 2.83/3.08 tff(11403,plain,
% 2.83/3.08 ((s(s(z)) = s(s(s(elem!1)))) <=> (s(s(z)) = s(s(elem!1)))),
% 2.83/3.08 inference(transitivity,[status(thm)],[11399, 127])).
% 2.83/3.08 tff(11404,plain,
% 2.83/3.08 ((~(s(s(z)) = s(s(s(elem!1))))) <=> (~(s(s(z)) = s(s(elem!1))))),
% 2.83/3.08 inference(monotonicity,[status(thm)],[11403])).
% 2.83/3.08 tff(11405,plain,
% 2.83/3.08 (~(s(s(z)) = s(s(elem!1)))),
% 2.83/3.08 inference(modus_ponens,[status(thm)],[209, 11404])).
% 2.83/3.08 tff(11406,plain,
% 2.83/3.08 (b(s(s(z)), s(s(elem!1)))),
% 2.83/3.08 inference(unit_resolution,[status(thm)],[390, 11405, 2288])).
% 2.83/3.08 tff(11407,plain,
% 2.83/3.08 (~b(s(s(elem!1)), s(s(z)))),
% 2.83/3.08 inference(unit_resolution,[status(thm)],[10727, 11406, 10451, 11402])).
% 2.83/3.08 tff(11408,plain,
% 2.83/3.08 (r(s(s(elem!1)), s(s(z)))),
% 2.83/3.08 inference(unit_resolution,[status(thm)],[441, 11407, 11401])).
% 2.83/3.08 tff(11409,plain,
% 2.83/3.08 (~r(s(s(z)), s(z))),
% 2.83/3.08 inference(unit_resolution,[status(thm)],[5331, 11408, 4577, 97])).
% 2.83/3.08 tff(11410,plain,
% 2.83/3.08 (b(s(s(z)), s(z))),
% 2.83/3.08 inference(unit_resolution,[status(thm)],[308, 11409])).
% 2.83/3.08 tff(11411,plain,
% 2.83/3.08 (~b(s(s(elem!1)), z)),
% 2.83/3.08 inference(unit_resolution,[status(thm)],[11110, 11406, 10451, 11402])).
% 2.83/3.08 tff(11412,plain,
% 2.83/3.08 (r(s(s(elem!1)), z)),
% 2.83/3.08 inference(unit_resolution,[status(thm)],[608, 11411])).
% 2.83/3.08 tff(11413,plain,
% 2.83/3.08 (~r(z, s(z))),
% 2.83/3.08 inference(unit_resolution,[status(thm)],[8490, 11412, 97, 4577])).
% 2.83/3.08 tff(11414,plain,
% 2.83/3.08 (b(z, s(z))),
% 2.83/3.08 inference(unit_resolution,[status(thm)],[321, 11413])).
% 2.83/3.08 tff(11415,plain,
% 2.83/3.08 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(z)))) | (~b(z, s(s(elem!1)))) | (~b(z, s(z))) | (~b(s(z), s(s(z)))) | (~b(s(s(z)), s(s(elem!1)))) | (~b(s(s(z)), s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(s(z)))) | (~b(z, s(s(elem!1)))) | (~b(z, s(z))) | (~b(s(z), s(s(z)))) | (~b(s(s(z)), s(s(elem!1)))) | (~b(s(s(z)), s(z))))),
% 2.83/3.08 inference(rewrite,[status(thm)],[])).
% 2.83/3.08 tff(11416,plain,
% 2.83/3.08 (((~b(s(s(z)), s(s(elem!1)))) | (~b(z, s(s(elem!1)))) | (~b(s(z), s(s(z)))) | (~b(s(s(z)), s(z))) | (~b(z, s(z))) | (~b(z, s(s(z))))) <=> ((~b(z, s(s(z)))) | (~b(z, s(s(elem!1)))) | (~b(z, s(z))) | (~b(s(z), s(s(z)))) | (~b(s(s(z)), s(s(elem!1)))) | (~b(s(s(z)), s(z))))),
% 2.83/3.08 inference(rewrite,[status(thm)],[])).
% 2.83/3.08 tff(11417,plain,
% 2.83/3.08 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), s(s(elem!1)))) | (~b(z, s(s(elem!1)))) | (~b(s(z), s(s(z)))) | (~b(s(s(z)), s(z))) | (~b(z, s(z))) | (~b(z, s(s(z)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(z)))) | (~b(z, s(s(elem!1)))) | (~b(z, s(z))) | (~b(s(z), s(s(z)))) | (~b(s(s(z)), s(s(elem!1)))) | (~b(s(s(z)), s(z)))))),
% 2.83/3.08 inference(monotonicity,[status(thm)],[11416])).
% 2.83/3.08 tff(11418,plain,
% 2.83/3.08 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), s(s(elem!1)))) | (~b(z, s(s(elem!1)))) | (~b(s(z), s(s(z)))) | (~b(s(s(z)), s(z))) | (~b(z, s(z))) | (~b(z, s(s(z)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(s(z)))) | (~b(z, s(s(elem!1)))) | (~b(z, s(z))) | (~b(s(z), s(s(z)))) | (~b(s(s(z)), s(s(elem!1)))) | (~b(s(s(z)), s(z))))),
% 2.83/3.08 inference(transitivity,[status(thm)],[11417, 11415])).
% 2.83/3.08 tff(11419,plain,
% 2.83/3.08 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), s(s(elem!1)))) | (~b(z, s(s(elem!1)))) | (~b(s(z), s(s(z)))) | (~b(s(s(z)), s(z))) | (~b(z, s(z))) | (~b(z, s(s(z)))))),
% 2.83/3.08 inference(quant_inst,[status(thm)],[])).
% 2.83/3.08 tff(11420,plain,
% 2.83/3.08 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(s(z)))) | (~b(z, s(s(elem!1)))) | (~b(z, s(z))) | (~b(s(z), s(s(z)))) | (~b(s(s(z)), s(s(elem!1)))) | (~b(s(s(z)), s(z)))),
% 2.83/3.08 inference(modus_ponens,[status(thm)],[11419, 11418])).
% 2.83/3.08 tff(11421,plain,
% 2.83/3.08 ($false),
% 2.83/3.08 inference(unit_resolution,[status(thm)],[11420, 166, 11402, 556, 10451, 11414, 11406, 11410])).
% 2.83/3.08 tff(11422,plain,((~(s(s(s(elem!1))) = s(s(elem!1)))) | (~b(s(z), s(s(z)))) | (~b(z, s(s(z)))) | (~r(s(s(elem!1)), s(z))) | (~r(s(z), z)) | r(s(s(z)), s(s(elem!1)))), inference(lemma,lemma(discharge,[]))).
% 2.83/3.08 tff(11423,plain,
% 2.83/3.08 (~(s(s(s(elem!1))) = s(s(elem!1)))),
% 2.83/3.08 inference(unit_resolution,[status(thm)],[11422, 11376, 10451, 10521, 97, 2288])).
% 2.83/3.08 tff(11424,plain,
% 2.83/3.08 (b(s(s(s(elem!1))), s(s(elem!1)))),
% 2.83/3.08 inference(unit_resolution,[status(thm)],[889, 7424, 1863])).
% 2.83/3.08 tff(11425,plain,
% 2.83/3.08 (~(s(s(elem!1)) = s(s(s(elem!1))))),
% 2.83/3.08 inference(modus_ponens,[status(thm)],[1863, 10907])).
% 2.83/3.08 tff(11426,plain,
% 2.83/3.08 (b(s(s(elem!1)), s(s(s(elem!1))))),
% 2.83/3.08 inference(unit_resolution,[status(thm)],[461, 7420, 11425])).
% 2.83/3.08 tff(11427,plain,
% 2.83/3.08 (~b(s(s(s(elem!1))), z)),
% 2.83/3.08 inference(unit_resolution,[status(thm)],[2339, 166, 11426, 11424, 1820])).
% 2.83/3.08 tff(11428,plain,
% 2.83/3.08 (r(s(s(s(elem!1))), z)),
% 2.83/3.08 inference(unit_resolution,[status(thm)],[94, 11427])).
% 2.83/3.08 tff(11429,plain,
% 2.83/3.08 (~(s(s(z)) = s(s(elem!1)))),
% 2.83/3.08 inference(unit_resolution,[status(thm)],[10769, 11428, 350, 7420, 97, 7424])).
% 2.83/3.08 tff(11430,plain,
% 2.83/3.08 (b(s(s(z)), s(s(elem!1)))),
% 2.83/3.08 inference(unit_resolution,[status(thm)],[390, 11429, 2288])).
% 2.83/3.08 tff(11431,plain,
% 2.83/3.08 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(z, s(s(z)))) | (~b(z, s(s(elem!1)))) | (~b(s(s(z)), s(s(elem!1)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(z, s(s(z)))) | (~b(z, s(s(elem!1)))) | (~b(s(s(z)), s(s(elem!1)))))),
% 2.83/3.08 inference(rewrite,[status(thm)],[])).
% 2.83/3.08 tff(11432,plain,
% 2.83/3.08 (((~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(z, s(s(elem!1)))) | (~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(s(s(z)), s(s(elem!1)))) | (~b(z, s(s(elem!1)))) | (~b(z, s(s(z))))) <=> ((~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(z, s(s(z)))) | (~b(z, s(s(elem!1)))) | (~b(s(s(z)), s(s(elem!1)))))),
% 2.83/3.08 inference(rewrite,[status(thm)],[])).
% 2.83/3.08 tff(11433,plain,
% 2.83/3.08 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(z, s(s(elem!1)))) | (~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(s(s(z)), s(s(elem!1)))) | (~b(z, s(s(elem!1)))) | (~b(z, s(s(z)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(z, s(s(z)))) | (~b(z, s(s(elem!1)))) | (~b(s(s(z)), s(s(elem!1))))))),
% 2.83/3.08 inference(monotonicity,[status(thm)],[11432])).
% 2.83/3.08 tff(11434,plain,
% 2.83/3.08 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(z, s(s(elem!1)))) | (~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(s(s(z)), s(s(elem!1)))) | (~b(z, s(s(elem!1)))) | (~b(z, s(s(z)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(z, s(s(z)))) | (~b(z, s(s(elem!1)))) | (~b(s(s(z)), s(s(elem!1)))))),
% 2.83/3.08 inference(transitivity,[status(thm)],[11433, 11431])).
% 2.83/3.08 tff(11435,plain,
% 2.83/3.08 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(z, s(s(elem!1)))) | (~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(s(s(z)), s(s(elem!1)))) | (~b(z, s(s(elem!1)))) | (~b(z, s(s(z)))))),
% 2.83/3.08 inference(quant_inst,[status(thm)],[])).
% 2.83/3.08 tff(11436,plain,
% 2.83/3.08 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(z, s(s(z)))) | (~b(z, s(s(elem!1)))) | (~b(s(s(z)), s(s(elem!1))))),
% 2.83/3.08 inference(modus_ponens,[status(thm)],[11435, 11434])).
% 2.83/3.08 tff(11437,plain,
% 2.83/3.08 ($false),
% 2.83/3.08 inference(unit_resolution,[status(thm)],[11436, 166, 11426, 11424, 1820, 10451, 11430])).
% 2.83/3.08 tff(11438,plain,((~r(s(s(s(elem!1))), s(z))) | (~b(z, s(s(elem!1)))) | (~b(z, s(s(z)))) | r(s(s(z)), s(s(elem!1))) | (~r(s(z), z)) | (s(s(s(elem!1))) = s(s(elem!1))) | (~r(s(s(elem!1)), s(z)))), inference(lemma,lemma(discharge,[]))).
% 2.83/3.08 tff(11439,plain,
% 2.83/3.08 (~r(s(s(s(elem!1))), s(z))),
% 2.83/3.08 inference(unit_resolution,[status(thm)],[11438, 11397, 10451, 2288, 97, 11423, 10521])).
% 2.83/3.08 tff(11440,plain,
% 2.83/3.08 (b(s(s(s(elem!1))), s(z))),
% 2.83/3.08 inference(unit_resolution,[status(thm)],[1849, 11439])).
% 2.83/3.08 tff(11441,plain,
% 2.83/3.08 (~r(z, s(s(s(elem!1))))),
% 2.83/3.08 inference(unit_resolution,[status(thm)],[3872, 350, 97, 117])).
% 2.83/3.08 tff(11442,plain,
% 2.83/3.08 (b(z, s(s(s(elem!1))))),
% 2.83/3.08 inference(unit_resolution,[status(thm)],[261, 11441])).
% 2.83/3.08 tff(11443,plain,
% 2.83/3.08 (b(z, s(s(elem!1)))),
% 2.83/3.08 inference(unit_resolution,[status(thm)],[7965, 11442, 350, 97, 4577])).
% 2.83/3.08 tff(11444,plain,
% 2.83/3.08 (s(s(elem!1)) = s(s(s(elem!1)))),
% 2.83/3.08 inference(unit_resolution,[status(thm)],[1834, 11443, 7420, 7424, 11442])).
% 2.83/3.08 tff(11445,plain,
% 2.83/3.08 (~b(s(z), s(s(elem!1)))),
% 2.83/3.08 inference(unit_resolution,[status(thm)],[5500, 11444, 98])).
% 2.83/3.08 tff(11446,plain,
% 2.83/3.08 (r(s(z), s(s(elem!1)))),
% 2.83/3.08 inference(unit_resolution,[status(thm)],[84, 11445])).
% 2.83/3.08 tff(11447,plain,
% 2.83/3.08 (r(s(s(elem!1)), s(s(z))) <=> r(s(s(s(elem!1))), s(s(z)))),
% 2.83/3.08 inference(monotonicity,[status(thm)],[11444])).
% 2.83/3.08 tff(11448,plain,
% 2.83/3.08 ((s(s(elem!1)) = s(s(z))) <=> (s(s(s(elem!1))) = s(s(z)))),
% 2.83/3.08 inference(monotonicity,[status(thm)],[11444])).
% 2.83/3.08 tff(11449,plain,
% 2.83/3.08 ((s(s(elem!1)) = s(s(z))) <=> (s(s(z)) = s(s(s(elem!1))))),
% 2.83/3.08 inference(transitivity,[status(thm)],[11448, 487])).
% 2.83/3.08 tff(11450,plain,
% 2.83/3.08 ((s(s(z)) = s(s(s(elem!1)))) <=> (s(s(elem!1)) = s(s(z)))),
% 2.83/3.08 inference(symmetry,[status(thm)],[11449])).
% 2.83/3.08 tff(11451,plain,
% 2.83/3.08 ((~(s(s(z)) = s(s(s(elem!1))))) <=> (~(s(s(elem!1)) = s(s(z))))),
% 2.83/3.08 inference(monotonicity,[status(thm)],[11450])).
% 2.83/3.08 tff(11452,plain,
% 2.83/3.08 (~(s(s(elem!1)) = s(s(z)))),
% 2.83/3.08 inference(modus_ponens,[status(thm)],[209, 11451])).
% 2.83/3.08 tff(11453,plain,
% 2.83/3.08 ((s(s(z)) = s(s(s(elem!1)))) <=> (s(s(z)) = s(s(elem!1)))),
% 2.83/3.08 inference(transitivity,[status(thm)],[11450, 127])).
% 2.83/3.08 tff(11454,plain,
% 2.83/3.08 ((~(s(s(z)) = s(s(s(elem!1))))) <=> (~(s(s(z)) = s(s(elem!1))))),
% 2.83/3.08 inference(monotonicity,[status(thm)],[11453])).
% 2.83/3.08 tff(11455,plain,
% 2.83/3.08 (~(s(s(z)) = s(s(elem!1)))),
% 2.83/3.08 inference(modus_ponens,[status(thm)],[209, 11454])).
% 2.83/3.08 tff(11456,plain,
% 2.83/3.08 (b(s(s(z)), s(s(elem!1)))),
% 2.83/3.08 inference(unit_resolution,[status(thm)],[390, 11455, 2288])).
% 2.83/3.08 tff(11457,plain,
% 2.83/3.08 (~b(s(s(elem!1)), s(s(z)))),
% 2.83/3.08 inference(unit_resolution,[status(thm)],[10727, 11456, 10451, 11443])).
% 2.83/3.08 tff(11458,plain,
% 2.83/3.08 (r(s(s(elem!1)), s(s(z)))),
% 2.83/3.08 inference(unit_resolution,[status(thm)],[441, 11457, 11452])).
% 2.83/3.08 tff(11459,plain,
% 2.83/3.08 (r(s(s(s(elem!1))), s(s(z)))),
% 2.83/3.08 inference(modus_ponens,[status(thm)],[11458, 11447])).
% 2.83/3.08 tff(11460,plain,
% 2.83/3.08 (~r(s(s(z)), s(z))),
% 2.83/3.08 inference(unit_resolution,[status(thm)],[854, 11459, 350, 11446])).
% 2.83/3.08 tff(11461,plain,
% 2.83/3.08 (b(s(s(z)), s(z))),
% 2.83/3.08 inference(unit_resolution,[status(thm)],[308, 11460])).
% 2.83/3.08 tff(11462,plain,
% 2.83/3.08 (s(s(s(elem!1))) = s(elem!1)),
% 2.83/3.08 inference(unit_resolution,[status(thm)],[2594, 11444])).
% 2.83/3.08 tff(11463,plain,
% 2.83/3.08 (s(elem!1) = s(s(s(elem!1)))),
% 2.83/3.08 inference(symmetry,[status(thm)],[11462])).
% 2.83/3.08 tff(11464,plain,
% 2.83/3.08 (inj_0(s(elem!1)) = inj_0(s(s(s(elem!1))))),
% 2.83/3.08 inference(monotonicity,[status(thm)],[11463])).
% 2.83/3.08 tff(11465,plain,
% 2.83/3.08 (elem!1 = s(s(s(elem!1)))),
% 2.83/3.08 inference(transitivity,[status(thm)],[1170, 11464, 104, 11444])).
% 2.83/3.08 tff(11466,plain,
% 2.83/3.08 ((z = elem!1) <=> (z = s(s(s(elem!1))))),
% 2.83/3.08 inference(monotonicity,[status(thm)],[11465])).
% 2.83/3.08 tff(11467,plain,
% 2.83/3.08 ((z = elem!1) <=> (s(s(s(elem!1))) = z)),
% 2.83/3.08 inference(transitivity,[status(thm)],[11466, 7746])).
% 2.83/3.08 tff(11468,plain,
% 2.83/3.08 ((s(s(s(elem!1))) = z) <=> (z = elem!1)),
% 2.83/3.08 inference(symmetry,[status(thm)],[11467])).
% 2.83/3.08 tff(11469,plain,
% 2.83/3.08 ((~(s(s(s(elem!1))) = z)) <=> (~(z = elem!1))),
% 2.83/3.08 inference(monotonicity,[status(thm)],[11468])).
% 2.83/3.08 tff(11470,plain,
% 2.83/3.08 (~(z = elem!1)),
% 2.83/3.08 inference(modus_ponens,[status(thm)],[89, 11469])).
% 2.83/3.08 tff(11471,plain,
% 2.83/3.08 (b(s(s(z)), s(s(s(elem!1))))),
% 2.83/3.08 inference(unit_resolution,[status(thm)],[6647, 334, 446])).
% 2.83/3.08 tff(11472,plain,
% 2.83/3.08 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(z)))) | (~b(z, s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), z)) | (~b(s(s(z)), s(s(s(elem!1))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(s(z)))) | (~b(z, s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), z)) | (~b(s(s(z)), s(s(s(elem!1))))))),
% 2.83/3.08 inference(rewrite,[status(thm)],[])).
% 2.83/3.08 tff(11473,plain,
% 2.83/3.08 (((~b(z, s(s(z)))) | (~b(z, s(s(z)))) | (~b(s(s(s(elem!1))), z)) | (~b(s(s(z)), s(s(s(elem!1))))) | (~b(z, s(s(s(elem!1))))) | (~b(z, s(s(z))))) <=> ((~b(z, s(s(z)))) | (~b(z, s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), z)) | (~b(s(s(z)), s(s(s(elem!1))))))),
% 2.83/3.08 inference(rewrite,[status(thm)],[])).
% 2.83/3.08 tff(11474,plain,
% 2.83/3.08 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(z)))) | (~b(z, s(s(z)))) | (~b(s(s(s(elem!1))), z)) | (~b(s(s(z)), s(s(s(elem!1))))) | (~b(z, s(s(s(elem!1))))) | (~b(z, s(s(z)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(z)))) | (~b(z, s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), z)) | (~b(s(s(z)), s(s(s(elem!1)))))))),
% 2.83/3.08 inference(monotonicity,[status(thm)],[11473])).
% 2.83/3.08 tff(11475,plain,
% 2.83/3.08 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(z)))) | (~b(z, s(s(z)))) | (~b(s(s(s(elem!1))), z)) | (~b(s(s(z)), s(s(s(elem!1))))) | (~b(z, s(s(s(elem!1))))) | (~b(z, s(s(z)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(s(z)))) | (~b(z, s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), z)) | (~b(s(s(z)), s(s(s(elem!1))))))),
% 2.83/3.08 inference(transitivity,[status(thm)],[11474, 11472])).
% 2.83/3.08 tff(11476,plain,
% 2.83/3.08 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(z)))) | (~b(z, s(s(z)))) | (~b(s(s(s(elem!1))), z)) | (~b(s(s(z)), s(s(s(elem!1))))) | (~b(z, s(s(s(elem!1))))) | (~b(z, s(s(z)))))),
% 2.83/3.09 inference(quant_inst,[status(thm)],[])).
% 2.83/3.09 tff(11477,plain,
% 2.83/3.09 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(s(z)))) | (~b(z, s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), z)) | (~b(s(s(z)), s(s(s(elem!1)))))),
% 2.83/3.09 inference(modus_ponens,[status(thm)],[11476, 11475])).
% 2.83/3.09 tff(11478,plain,
% 2.83/3.09 (~b(z, s(s(s(elem!1))))),
% 2.83/3.09 inference(unit_resolution,[status(thm)],[11477, 166, 10451, 121, 11471])).
% 2.83/3.09 tff(11479,plain,
% 2.83/3.09 ((s(s(elem!1)) = elem!1) <=> (s(s(s(elem!1))) = elem!1)),
% 2.83/3.09 inference(monotonicity,[status(thm)],[334])).
% 2.83/3.09 tff(11480,plain,
% 2.83/3.09 ((s(s(elem!1)) = elem!1) <=> (elem!1 = s(s(s(elem!1))))),
% 2.83/3.09 inference(transitivity,[status(thm)],[11479, 5406])).
% 2.83/3.09 tff(11481,plain,
% 2.83/3.09 (elem!1 = s(s(s(elem!1)))),
% 2.83/3.09 inference(modus_ponens,[status(thm)],[10150, 11480])).
% 2.83/3.09 tff(11482,assumption,(elem!1 = s(s(s(elem!1)))), introduced(assumption)).
% 2.83/3.09 tff(11483,plain,
% 2.83/3.09 (b(z, elem!1) <=> b(z, s(s(s(elem!1))))),
% 2.83/3.09 inference(monotonicity,[status(thm)],[11482])).
% 2.83/3.09 tff(11484,plain,
% 2.83/3.09 (b(z, s(s(s(elem!1)))) <=> b(z, elem!1)),
% 2.83/3.09 inference(symmetry,[status(thm)],[11483])).
% 2.83/3.09 tff(11485,plain,
% 2.83/3.09 ((~b(z, s(s(s(elem!1))))) <=> (~b(z, elem!1))),
% 2.83/3.09 inference(monotonicity,[status(thm)],[11484])).
% 2.83/3.09 tff(11486,plain,
% 2.83/3.09 (~b(z, elem!1)),
% 2.83/3.09 inference(modus_ponens,[status(thm)],[256, 11485])).
% 2.83/3.09 tff(11487,plain,
% 2.83/3.09 ($false),
% 2.83/3.09 inference(unit_resolution,[status(thm)],[2517, 11486])).
% 2.83/3.09 tff(11488,plain,((~(elem!1 = s(s(s(elem!1))))) | (~b(z, elem!1)) | b(z, s(s(s(elem!1))))), inference(lemma,lemma(discharge,[]))).
% 2.83/3.09 tff(11489,plain,
% 2.83/3.09 (~b(z, elem!1)),
% 2.83/3.09 inference(unit_resolution,[status(thm)],[11488, 11481, 11478])).
% 2.83/3.09 tff(11490,plain,
% 2.83/3.09 (r(elem!1, s(z)) <=> r(s(s(s(elem!1))), s(z))),
% 2.83/3.09 inference(monotonicity,[status(thm)],[6548])).
% 2.83/3.09 tff(11491,plain,
% 2.83/3.09 (r(s(s(s(elem!1))), s(z)) <=> r(elem!1, s(z))),
% 2.83/3.09 inference(symmetry,[status(thm)],[11490])).
% 2.83/3.09 tff(11492,plain,
% 2.83/3.09 (r(elem!1, s(z))),
% 2.83/3.09 inference(modus_ponens,[status(thm)],[350, 11491])).
% 2.83/3.09 tff(11493,plain,
% 2.83/3.09 (r(s(z), elem!1) <=> r(s(z), s(s(s(elem!1))))),
% 2.83/3.09 inference(monotonicity,[status(thm)],[6548])).
% 2.83/3.09 tff(11494,plain,
% 2.83/3.09 (r(s(z), s(s(s(elem!1)))) <=> r(s(z), elem!1)),
% 2.83/3.09 inference(symmetry,[status(thm)],[11493])).
% 2.83/3.09 tff(11495,plain,
% 2.83/3.09 (r(s(z), elem!1)),
% 2.83/3.09 inference(modus_ponens,[status(thm)],[119, 11494])).
% 2.83/3.09 tff(11496,plain,
% 2.83/3.09 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, elem!1)) | (~r(s(z), elem!1)) | (~r(s(z), z)) | (~r(elem!1, s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, elem!1)) | (~r(s(z), elem!1)) | (~r(s(z), z)) | (~r(elem!1, s(z))))),
% 2.83/3.09 inference(rewrite,[status(thm)],[])).
% 2.83/3.09 tff(11497,plain,
% 2.83/3.09 (((~r(elem!1, s(z))) | (~r(z, elem!1)) | (~r(s(z), elem!1)) | (~r(s(z), z))) <=> ((~r(z, elem!1)) | (~r(s(z), elem!1)) | (~r(s(z), z)) | (~r(elem!1, s(z))))),
% 2.83/3.09 inference(rewrite,[status(thm)],[])).
% 2.83/3.09 tff(11498,plain,
% 2.83/3.09 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(z))) | (~r(z, elem!1)) | (~r(s(z), elem!1)) | (~r(s(z), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, elem!1)) | (~r(s(z), elem!1)) | (~r(s(z), z)) | (~r(elem!1, s(z)))))),
% 2.83/3.09 inference(monotonicity,[status(thm)],[11497])).
% 2.83/3.09 tff(11499,plain,
% 2.83/3.09 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(z))) | (~r(z, elem!1)) | (~r(s(z), elem!1)) | (~r(s(z), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, elem!1)) | (~r(s(z), elem!1)) | (~r(s(z), z)) | (~r(elem!1, s(z))))),
% 2.83/3.09 inference(transitivity,[status(thm)],[11498, 11496])).
% 2.83/3.09 tff(11500,plain,
% 2.83/3.09 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(z))) | (~r(z, elem!1)) | (~r(s(z), elem!1)) | (~r(s(z), z)))),
% 2.83/3.09 inference(quant_inst,[status(thm)],[])).
% 2.83/3.09 tff(11501,plain,
% 2.83/3.09 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, elem!1)) | (~r(s(z), elem!1)) | (~r(s(z), z)) | (~r(elem!1, s(z)))),
% 2.83/3.09 inference(modus_ponens,[status(thm)],[11500, 11499])).
% 2.83/3.09 tff(11502,plain,
% 2.83/3.09 ((~r(z, elem!1)) | (~r(s(z), elem!1)) | (~r(s(z), z)) | (~r(elem!1, s(z)))),
% 2.83/3.09 inference(unit_resolution,[status(thm)],[11501, 197])).
% 2.83/3.09 tff(11503,plain,
% 2.83/3.09 (~r(z, elem!1)),
% 2.83/3.09 inference(unit_resolution,[status(thm)],[11502, 11495, 97, 11492])).
% 2.83/3.09 tff(11504,plain,
% 2.83/3.09 ($false),
% 2.83/3.09 inference(unit_resolution,[status(thm)],[2514, 11503, 11489, 28])).
% 2.83/3.09 tff(11505,plain,((~(s(s(elem!1)) = s(s(s(elem!1))))) | (z = elem!1) | (~r(s(z), z)) | (~b(z, s(s(z)))) | (~b(s(s(s(elem!1))), z)) | (~r(s(z), s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), s(z))) | (~b(s(s(z)), s(s(elem!1))))), inference(lemma,lemma(discharge,[]))).
% 2.83/3.09 tff(11506,plain,
% 2.83/3.09 (~b(s(s(s(elem!1))), z)),
% 2.83/3.09 inference(unit_resolution,[status(thm)],[11505, 11470, 97, 10451, 117, 350, 11444, 11456])).
% 2.83/3.09 tff(11507,plain,
% 2.83/3.09 (r(s(s(s(elem!1))), z)),
% 2.83/3.09 inference(unit_resolution,[status(thm)],[94, 11506])).
% 2.83/3.09 tff(11508,plain,
% 2.83/3.09 (~r(z, s(z))),
% 2.83/3.09 inference(unit_resolution,[status(thm)],[373, 11507, 350, 11446])).
% 2.83/3.09 tff(11509,plain,
% 2.83/3.09 (b(z, s(z))),
% 2.83/3.09 inference(unit_resolution,[status(thm)],[321, 11508])).
% 2.83/3.09 tff(11510,plain,
% 2.83/3.09 ($false),
% 2.83/3.09 inference(unit_resolution,[status(thm)],[11394, 166, 556, 10451, 11509, 11461])).
% 2.83/3.09 tff(11511,plain,((~r(s(s(s(elem!1))), s(z))) | (~b(s(z), s(s(z)))) | (~b(z, s(s(z)))) | (~r(s(z), z)) | r(s(s(z)), s(s(elem!1))) | b(s(z), s(s(s(elem!1)))) | (~r(s(s(elem!1)), s(z)))), inference(lemma,lemma(discharge,[]))).
% 2.83/3.09 tff(11512,plain,
% 2.83/3.09 (~r(s(s(s(elem!1))), s(z))),
% 2.83/3.09 inference(unit_resolution,[status(thm)],[11511, 98, 10451, 97, 2288, 11376, 10521])).
% 2.83/3.09 tff(11513,plain,
% 2.83/3.09 (b(s(s(s(elem!1))), s(z))),
% 2.83/3.09 inference(unit_resolution,[status(thm)],[1849, 11512])).
% 2.83/3.09 tff(11514,plain,
% 2.83/3.09 (~(s(s(elem!1)) = s(s(s(elem!1))))),
% 2.83/3.09 inference(unit_resolution,[status(thm)],[4570, 11513, 4568])).
% 2.83/3.09 tff(11515,plain,
% 2.83/3.09 (~(s(s(s(elem!1))) = s(s(s(s(elem!1)))))),
% 2.83/3.09 inference(unit_resolution,[status(thm)],[357, 11514])).
% 2.83/3.09 tff(11516,plain,
% 2.83/3.09 (~(s(s(s(elem!1))) = s(s(elem!1)))),
% 2.83/3.09 inference(unit_resolution,[status(thm)],[50, 11514])).
% 2.83/3.09 tff(11517,plain,
% 2.83/3.09 (~r(s(z), s(s(elem!1)))),
% 2.83/3.09 inference(unit_resolution,[status(thm)],[8455, 463, 4577, 1820, 97, 119, 1863])).
% 2.83/3.09 tff(11518,plain,
% 2.83/3.09 (b(s(z), s(s(elem!1)))),
% 2.83/3.09 inference(unit_resolution,[status(thm)],[84, 11517])).
% 2.83/3.09 tff(11519,plain,
% 2.83/3.09 (~b(z, s(s(s(elem!1))))),
% 2.83/3.09 inference(unit_resolution,[status(thm)],[7353, 166, 11518, 463, 1820, 96])).
% 2.83/3.09 tff(11520,plain,
% 2.83/3.09 (r(z, s(s(s(elem!1))))),
% 2.83/3.09 inference(unit_resolution,[status(thm)],[261, 11519])).
% 2.83/3.09 tff(11521,plain,
% 2.83/3.09 (~b(s(s(s(elem!1))), s(s(elem!1)))),
% 2.83/3.09 inference(unit_resolution,[status(thm)],[2349, 463, 97, 1820, 119])).
% 2.83/3.09 tff(11522,plain,
% 2.83/3.09 (r(s(s(s(elem!1))), s(s(elem!1)))),
% 2.83/3.09 inference(unit_resolution,[status(thm)],[889, 11521, 1863])).
% 2.83/3.09 tff(11523,plain,
% 2.83/3.09 ($false),
% 2.83/3.09 inference(unit_resolution,[status(thm)],[7363, 197, 97, 11522, 119, 11520])).
% 2.83/3.09 tff(11524,plain,((~b(s(s(elem!1)), s(s(s(elem!1))))) | (~r(s(z), z)) | (~r(s(z), s(s(s(elem!1))))) | (~b(z, s(s(elem!1)))) | (~b(s(s(s(elem!1))), s(z))) | (s(s(s(elem!1))) = s(s(elem!1))) | (~r(s(s(elem!1)), s(z)))), inference(lemma,lemma(discharge,[]))).
% 2.83/3.09 tff(11525,plain,
% 2.83/3.09 (~b(s(s(elem!1)), s(s(s(elem!1))))),
% 2.83/3.09 inference(unit_resolution,[status(thm)],[11524, 117, 97, 11397, 11513, 11516, 10521])).
% 2.83/3.09 tff(11526,plain,
% 2.83/3.09 (r(s(s(elem!1)), s(s(s(elem!1))))),
% 2.83/3.09 inference(unit_resolution,[status(thm)],[461, 11525, 11514])).
% 2.83/3.09 tff(11527,plain,
% 2.83/3.09 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(s(s(elem!1))))) | (~r(s(s(elem!1)), s(s(s(elem!1))))) | (~r(s(s(elem!1)), s(z))) | (~r(s(s(s(elem!1))), s(s(s(s(elem!1)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(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(s(s(elem!1))), s(s(s(s(elem!1)))))))),
% 2.83/3.09 inference(rewrite,[status(thm)],[])).
% 2.83/3.09 tff(11528,plain,
% 2.83/3.09 (((~r(s(s(s(elem!1))), s(s(s(s(elem!1)))))) | (~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(s(s(elem!1))))) | (~r(s(s(elem!1)), s(z))) | (~r(s(s(s(elem!1))), s(s(s(s(elem!1)))))))),
% 2.83/3.09 inference(rewrite,[status(thm)],[])).
% 2.83/3.09 tff(11529,plain,
% 2.83/3.09 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), s(s(s(s(elem!1)))))) | (~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, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(s(s(elem!1))))) | (~r(s(s(elem!1)), s(s(s(elem!1))))) | (~r(s(s(elem!1)), s(z))) | (~r(s(s(s(elem!1))), s(s(s(s(elem!1))))))))),
% 2.83/3.09 inference(monotonicity,[status(thm)],[11528])).
% 2.83/3.09 tff(11530,plain,
% 2.83/3.09 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), s(s(s(s(elem!1)))))) | (~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, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(z), s(s(s(elem!1))))) | (~r(s(s(elem!1)), s(s(s(elem!1))))) | (~r(s(s(elem!1)), s(z))) | (~r(s(s(s(elem!1))), s(s(s(s(elem!1)))))))),
% 2.83/3.09 inference(transitivity,[status(thm)],[11529, 11527])).
% 2.83/3.09 tff(11531,plain,
% 2.83/3.09 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), s(s(s(s(elem!1)))))) | (~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))))),
% 2.83/3.09 inference(quant_inst,[status(thm)],[])).
% 2.83/3.09 tff(11532,plain,
% 2.83/3.09 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(z), s(s(s(elem!1))))) | (~r(s(s(elem!1)), s(s(s(elem!1))))) | (~r(s(s(elem!1)), s(z))) | (~r(s(s(s(elem!1))), s(s(s(s(elem!1))))))),
% 2.83/3.09 inference(modus_ponens,[status(thm)],[11531, 11530])).
% 2.83/3.09 tff(11533,plain,
% 2.83/3.09 ($false),
% 2.83/3.09 inference(unit_resolution,[status(thm)],[11532, 197, 4577, 377, 119, 698])).
% 2.83/3.09 tff(11534,plain,((~r(s(s(s(elem!1))), s(s(s(s(elem!1)))))) | (~r(s(s(elem!1)), s(z))) | (~r(s(s(elem!1)), s(s(s(elem!1))))) | (~r(s(z), s(s(s(elem!1)))))), inference(lemma,lemma(discharge,[]))).
% 2.83/3.09 tff(11535,plain,
% 2.83/3.09 (~r(s(s(s(elem!1))), s(s(s(s(elem!1)))))),
% 2.83/3.09 inference(unit_resolution,[status(thm)],[11534, 11526, 10521, 117])).
% 2.83/3.09 tff(11536,plain,
% 2.83/3.09 (b(s(s(s(elem!1))), s(s(s(s(elem!1)))))),
% 2.83/3.09 inference(unit_resolution,[status(thm)],[696, 11535, 11515])).
% 2.83/3.09 tff(11537,plain,
% 2.83/3.09 (~r(s(s(s(elem!1))), z)),
% 2.83/3.09 inference(unit_resolution,[status(thm)],[5310, 11526, 10521, 117])).
% 2.83/3.09 tff(11538,plain,
% 2.83/3.09 (b(s(s(s(elem!1))), z)),
% 2.83/3.09 inference(unit_resolution,[status(thm)],[94, 11537])).
% 2.83/3.09 tff(11539,plain,
% 2.83/3.09 (~r(s(s(s(elem!1))), s(s(elem!1)))),
% 2.83/3.09 inference(unit_resolution,[status(thm)],[7376, 11526, 10521, 117])).
% 2.83/3.09 tff(11540,plain,
% 2.83/3.09 (b(s(s(s(elem!1))), s(s(elem!1)))),
% 2.83/3.09 inference(unit_resolution,[status(thm)],[889, 11539, 11516])).
% 2.83/3.09 tff(11541,plain,
% 2.83/3.09 (~b(s(s(z)), s(s(elem!1)))),
% 2.83/3.09 inference(unit_resolution,[status(thm)],[11110, 592, 10451, 1820])).
% 2.83/3.09 tff(11542,plain,
% 2.83/3.09 (s(s(z)) = s(s(elem!1))),
% 2.83/3.09 inference(unit_resolution,[status(thm)],[390, 11541, 2288])).
% 2.83/3.09 tff(11543,plain,
% 2.83/3.09 (s(elem!1) = s(z)),
% 2.83/3.09 inference(unit_resolution,[status(thm)],[43, 11542])).
% 2.83/3.09 tff(11544,plain,
% 2.83/3.09 (z = elem!1),
% 2.83/3.09 inference(unit_resolution,[status(thm)],[30, 11543])).
% 2.83/3.09 tff(11545,plain,
% 2.83/3.09 (b(s(s(s(elem!1))), elem!1)),
% 2.83/3.09 inference(unit_resolution,[status(thm)],[634, 11544, 121])).
% 2.83/3.09 tff(11546,plain,
% 2.83/3.09 (elem!1 = z),
% 2.83/3.09 inference(symmetry,[status(thm)],[11544])).
% 2.83/3.09 tff(11547,plain,
% 2.83/3.09 (b(elem!1, s(s(elem!1))) <=> b(z, s(s(elem!1)))),
% 2.83/3.09 inference(monotonicity,[status(thm)],[11546])).
% 2.83/3.09 tff(11548,plain,
% 2.83/3.09 (b(z, s(s(elem!1))) <=> b(elem!1, s(s(elem!1)))),
% 2.83/3.09 inference(symmetry,[status(thm)],[11547])).
% 2.83/3.09 tff(11549,plain,
% 2.83/3.09 (b(elem!1, s(s(elem!1)))),
% 2.83/3.09 inference(modus_ponens,[status(thm)],[1820, 11548])).
% 2.83/3.09 tff(11550,plain,
% 2.83/3.09 (b(s(s(elem!1)), z) <=> b(s(s(elem!1)), elem!1)),
% 2.83/3.09 inference(monotonicity,[status(thm)],[11544])).
% 2.83/3.09 tff(11551,plain,
% 2.83/3.09 (b(s(s(elem!1)), elem!1)),
% 2.83/3.09 inference(modus_ponens,[status(thm)],[592, 11550])).
% 2.83/3.09 tff(11552,plain,
% 2.83/3.09 ($false),
% 2.83/3.09 inference(unit_resolution,[status(thm)],[11324, 166, 11551, 839, 11549, 11545])).
% 2.83/3.09 tff(11553,plain,((~b(s(s(elem!1)), z)) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(z, s(s(elem!1)))) | (~b(s(s(s(elem!1))), z)) | r(s(s(z)), s(s(elem!1))) | (~b(z, s(s(z))))), inference(lemma,lemma(discharge,[]))).
% 2.83/3.09 tff(11554,plain,
% 2.83/3.09 (~b(s(s(elem!1)), z)),
% 2.83/3.09 inference(unit_resolution,[status(thm)],[11553, 11540, 11397, 11538, 2288, 10451])).
% 2.83/3.09 tff(11555,plain,
% 2.83/3.09 (r(s(s(elem!1)), z)),
% 2.83/3.09 inference(unit_resolution,[status(thm)],[608, 11554])).
% 2.83/3.09 tff(11556,plain,
% 2.83/3.09 (~r(z, s(z))),
% 2.83/3.09 inference(unit_resolution,[status(thm)],[8490, 11555, 97, 10521])).
% 2.83/3.09 tff(11557,plain,
% 2.83/3.09 (b(z, s(z))),
% 2.83/3.09 inference(unit_resolution,[status(thm)],[321, 11556])).
% 2.83/3.09 tff(11558,plain,
% 2.83/3.09 (~r(s(s(s(elem!1))), z)),
% 2.83/3.09 inference(unit_resolution,[status(thm)],[5310, 377, 4577, 119])).
% 2.83/3.09 tff(11559,plain,
% 2.83/3.09 (b(s(s(s(elem!1))), z)),
% 2.83/3.09 inference(unit_resolution,[status(thm)],[94, 11558])).
% 2.83/3.09 tff(11560,plain,
% 2.83/3.09 (~r(s(s(s(elem!1))), s(s(elem!1)))),
% 2.83/3.09 inference(unit_resolution,[status(thm)],[7376, 377, 4577, 119])).
% 2.83/3.09 tff(11561,plain,
% 2.83/3.09 (b(s(s(s(elem!1))), s(s(elem!1)))),
% 2.83/3.09 inference(unit_resolution,[status(thm)],[889, 11560, 1863])).
% 2.83/3.09 tff(11562,plain,
% 2.83/3.09 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(s(s(elem!1))), z)) | (~b(s(s(s(elem!1))), s(z))) | (~b(z, s(z))) | (~b(s(z), s(s(z)))) | (~b(s(s(z)), s(s(elem!1)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(s(s(elem!1))), z)) | (~b(s(s(s(elem!1))), s(z))) | (~b(z, s(z))) | (~b(s(z), s(s(z)))) | (~b(s(s(z)), s(s(elem!1)))))),
% 2.83/3.09 inference(rewrite,[status(thm)],[])).
% 2.83/3.09 tff(11563,plain,
% 2.83/3.09 (((~b(s(s(z)), s(s(elem!1)))) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(z), s(s(z)))) | (~b(z, s(z))) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(s(s(elem!1))), z))) <=> ((~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(s(s(elem!1))), z)) | (~b(s(s(s(elem!1))), s(z))) | (~b(z, s(z))) | (~b(s(z), s(s(z)))) | (~b(s(s(z)), s(s(elem!1)))))),
% 2.83/3.09 inference(rewrite,[status(thm)],[])).
% 2.83/3.09 tff(11564,plain,
% 2.83/3.09 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), s(s(elem!1)))) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(z), s(s(z)))) | (~b(z, s(z))) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(s(s(elem!1))), z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(s(s(elem!1))), z)) | (~b(s(s(s(elem!1))), s(z))) | (~b(z, s(z))) | (~b(s(z), s(s(z)))) | (~b(s(s(z)), s(s(elem!1))))))),
% 2.83/3.09 inference(monotonicity,[status(thm)],[11563])).
% 2.83/3.09 tff(11565,plain,
% 2.83/3.09 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), s(s(elem!1)))) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(z), s(s(z)))) | (~b(z, s(z))) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(s(s(elem!1))), z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(s(s(elem!1))), z)) | (~b(s(s(s(elem!1))), s(z))) | (~b(z, s(z))) | (~b(s(z), s(s(z)))) | (~b(s(s(z)), s(s(elem!1)))))),
% 2.83/3.09 inference(transitivity,[status(thm)],[11564, 11562])).
% 2.83/3.09 tff(11566,plain,
% 2.83/3.09 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), s(s(elem!1)))) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(z), s(s(z)))) | (~b(z, s(z))) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(s(s(elem!1))), z)))),
% 2.83/3.09 inference(quant_inst,[status(thm)],[])).
% 2.83/3.09 tff(11567,plain,
% 2.83/3.09 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(s(s(elem!1))), z)) | (~b(s(s(s(elem!1))), s(z))) | (~b(z, s(z))) | (~b(s(z), s(s(z)))) | (~b(s(s(z)), s(s(elem!1))))),
% 2.83/3.09 inference(modus_ponens,[status(thm)],[11566, 11565])).
% 2.83/3.09 tff(11568,plain,
% 2.83/3.09 ($false),
% 2.83/3.09 inference(unit_resolution,[status(thm)],[11567, 166, 11561, 556, 96, 118, 11559, 446])).
% 2.83/3.09 tff(11569,plain,((~r(s(s(elem!1)), s(s(s(elem!1))))) | (~b(s(z), s(s(z)))) | (~b(s(s(s(elem!1))), s(z))) | (~b(z, s(z))) | (~b(s(s(z)), s(s(elem!1)))) | (s(s(s(elem!1))) = s(s(elem!1))) | (~r(s(s(elem!1)), s(z))) | (~r(s(z), s(s(s(elem!1)))))), inference(lemma,lemma(discharge,[]))).
% 2.83/3.09 tff(11570,plain,
% 2.83/3.09 (~b(s(s(z)), s(s(elem!1)))),
% 2.83/3.09 inference(unit_resolution,[status(thm)],[11569, 11557, 11513, 11376, 11526, 11516, 10521, 117])).
% 2.83/3.09 tff(11571,plain,
% 2.83/3.09 (s(s(z)) = s(s(elem!1))),
% 2.83/3.09 inference(unit_resolution,[status(thm)],[390, 11570, 2288])).
% 2.83/3.09 tff(11572,plain,
% 2.83/3.09 (s(elem!1) = s(z)),
% 2.83/3.09 inference(unit_resolution,[status(thm)],[43, 11571])).
% 2.83/3.09 tff(11573,plain,
% 2.83/3.09 (z = elem!1),
% 2.83/3.09 inference(unit_resolution,[status(thm)],[30, 11572])).
% 2.83/3.09 tff(11574,plain,
% 2.83/3.09 (b(s(s(s(elem!1))), elem!1)),
% 2.83/3.09 inference(unit_resolution,[status(thm)],[634, 11573, 11538])).
% 2.83/3.09 tff(11575,plain,
% 2.83/3.09 ((s(s(s(s(elem!1)))) = s(s(z))) <=> (s(s(s(s(elem!1)))) = s(s(elem!1)))),
% 2.83/3.09 inference(monotonicity,[status(thm)],[11571])).
% 2.83/3.09 tff(11576,plain,
% 2.83/3.09 ((s(s(s(s(elem!1)))) = s(s(z))) <=> (s(s(elem!1)) = s(s(s(s(elem!1)))))),
% 2.83/3.09 inference(transitivity,[status(thm)],[11575, 123])).
% 2.83/3.09 tff(11577,plain,
% 2.83/3.09 ((~(s(s(s(s(elem!1)))) = s(s(z)))) <=> (~(s(s(elem!1)) = s(s(s(s(elem!1))))))),
% 2.83/3.09 inference(monotonicity,[status(thm)],[11576])).
% 2.83/3.09 tff(11578,plain,
% 2.83/3.09 (~(s(s(elem!1)) = s(s(s(s(elem!1)))))),
% 2.83/3.09 inference(modus_ponens,[status(thm)],[733, 11577])).
% 2.83/3.09 tff(11579,plain,
% 2.83/3.09 (b(z, s(z)) <=> b(elem!1, s(z))),
% 2.83/3.09 inference(monotonicity,[status(thm)],[11573])).
% 2.83/3.09 tff(11580,plain,
% 2.83/3.09 (b(elem!1, s(z))),
% 2.83/3.09 inference(modus_ponens,[status(thm)],[11557, 11579])).
% 2.83/3.09 tff(11581,plain,
% 2.83/3.09 ((s(s(s(s(elem!1)))) = z) <=> (s(s(s(s(elem!1)))) = elem!1)),
% 2.83/3.09 inference(monotonicity,[status(thm)],[11573])).
% 2.83/3.09 tff(11582,plain,
% 2.83/3.09 ((~(s(s(s(s(elem!1)))) = z)) <=> (~(s(s(s(s(elem!1)))) = elem!1))),
% 2.83/3.09 inference(monotonicity,[status(thm)],[11581])).
% 2.83/3.09 tff(11583,plain,
% 2.83/3.09 (~(s(s(s(s(elem!1)))) = elem!1)),
% 2.83/3.09 inference(modus_ponens,[status(thm)],[626, 11582])).
% 2.83/3.09 tff(11584,plain,
% 2.83/3.09 (s(s(s(z))) = s(s(s(elem!1)))),
% 2.83/3.09 inference(monotonicity,[status(thm)],[11571])).
% 2.83/3.09 tff(11585,plain,
% 2.83/3.09 (b(elem!1, s(s(s(z)))) <=> b(elem!1, s(s(s(elem!1))))),
% 2.83/3.09 inference(monotonicity,[status(thm)],[11584])).
% 2.83/3.09 tff(11586,plain,
% 2.83/3.09 (b(z, s(s(s(z)))) <=> b(elem!1, s(s(s(z))))),
% 2.83/3.09 inference(monotonicity,[status(thm)],[11573])).
% 2.83/3.09 tff(11587,plain,
% 2.83/3.09 (~r(z, s(s(s(z))))),
% 2.83/3.09 inference(unit_resolution,[status(thm)],[10804, 11555, 97, 10521])).
% 2.83/3.09 tff(11588,plain,
% 2.83/3.09 (b(z, s(s(s(z))))),
% 2.83/3.09 inference(unit_resolution,[status(thm)],[1696, 11587, 1692])).
% 2.83/3.09 tff(11589,plain,
% 2.83/3.09 (b(elem!1, s(s(s(z))))),
% 2.83/3.09 inference(modus_ponens,[status(thm)],[11588, 11586])).
% 2.83/3.09 tff(11590,plain,
% 2.83/3.09 (b(elem!1, s(s(s(elem!1))))),
% 2.83/3.09 inference(modus_ponens,[status(thm)],[11589, 11585])).
% 2.83/3.09 tff(11591,plain,
% 2.83/3.09 (~b(s(s(s(s(elem!1)))), elem!1)),
% 2.83/3.09 inference(unit_resolution,[status(thm)],[10668, 11590, 11540, 11536, 11574])).
% 2.83/3.09 tff(11592,plain,
% 2.83/3.09 (r(s(s(s(s(elem!1)))), elem!1)),
% 2.83/3.09 inference(unit_resolution,[status(thm)],[719, 11591, 11583])).
% 2.83/3.09 tff(11593,plain,
% 2.83/3.09 (r(s(z), z) <=> r(s(z), elem!1)),
% 2.83/3.09 inference(monotonicity,[status(thm)],[11573])).
% 2.83/3.09 tff(11594,plain,
% 2.83/3.09 (r(s(z), elem!1)),
% 2.83/3.09 inference(modus_ponens,[status(thm)],[97, 11593])).
% 2.83/3.09 tff(11595,plain,
% 2.83/3.09 (elem!1 = z),
% 2.83/3.09 inference(symmetry,[status(thm)],[11573])).
% 2.83/3.09 tff(11596,plain,
% 2.83/3.09 (b(elem!1, s(s(elem!1))) <=> b(z, s(s(elem!1)))),
% 2.83/3.09 inference(monotonicity,[status(thm)],[11595])).
% 2.83/3.09 tff(11597,plain,
% 2.83/3.09 (b(z, s(s(elem!1))) <=> b(elem!1, s(s(elem!1)))),
% 2.83/3.09 inference(symmetry,[status(thm)],[11596])).
% 2.83/3.09 tff(11598,plain,
% 2.83/3.09 (b(elem!1, s(s(elem!1)))),
% 2.83/3.09 inference(modus_ponens,[status(thm)],[11397, 11597])).
% 2.83/3.09 tff(11599,plain,
% 2.83/3.09 (b(s(z), s(s(z))) <=> b(s(z), s(s(elem!1)))),
% 2.83/3.09 inference(monotonicity,[status(thm)],[11571])).
% 2.83/3.09 tff(11600,plain,
% 2.83/3.09 (b(s(z), s(s(elem!1)))),
% 2.83/3.09 inference(modus_ponens,[status(thm)],[11376, 11599])).
% 2.83/3.09 tff(11601,assumption,(elem!1 = s(s(s(s(elem!1))))), introduced(assumption)).
% 2.83/3.10 tff(11602,plain,
% 2.83/3.10 (s(s(s(s(elem!1)))) = elem!1),
% 2.83/3.10 inference(symmetry,[status(thm)],[11601])).
% 2.83/3.10 tff(11603,plain,
% 2.83/3.10 ($false),
% 2.83/3.10 inference(unit_resolution,[status(thm)],[712, 11602])).
% 2.83/3.10 tff(11604,plain,((~(elem!1 = s(s(s(s(elem!1)))))) | (s(s(s(s(elem!1)))) = elem!1)), inference(lemma,lemma(discharge,[]))).
% 2.83/3.10 tff(11605,plain,
% 2.83/3.10 (~(elem!1 = s(s(s(s(elem!1)))))),
% 2.83/3.10 inference(unit_resolution,[status(thm)],[11604, 11583])).
% 2.83/3.10 tff(11606,plain,
% 2.83/3.10 (~b(s(z), s(s(s(s(elem!1)))))),
% 2.83/3.10 inference(unit_resolution,[status(thm)],[3794, 1402, 641, 96, 1212])).
% 2.83/3.10 tff(11607,plain,
% 2.83/3.10 (r(s(z), s(s(s(s(elem!1)))))),
% 2.83/3.10 inference(unit_resolution,[status(thm)],[681, 11606])).
% 2.83/3.10 tff(11608,plain,
% 2.83/3.10 (~r(elem!1, s(s(s(s(elem!1)))))),
% 2.83/3.10 inference(unit_resolution,[status(thm)],[10678, 11607, 2381, 743])).
% 2.83/3.10 tff(11609,plain,
% 2.83/3.10 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(s(s(elem!1))))) | (~b(elem!1, s(s(elem!1)))) | (~b(s(z), s(s(elem!1)))) | (~b(s(s(s(elem!1))), s(s(s(s(elem!1)))))) | (~b(elem!1, s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(s(s(elem!1))))) | (~b(elem!1, s(s(elem!1)))) | (~b(s(z), s(s(elem!1)))) | (~b(s(s(s(elem!1))), s(s(s(s(elem!1)))))) | (~b(elem!1, s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), s(z))))),
% 2.83/3.10 inference(rewrite,[status(thm)],[])).
% 2.83/3.10 tff(11610,plain,
% 2.83/3.10 (((~b(s(z), s(s(elem!1)))) | (~b(elem!1, s(s(elem!1)))) | (~b(s(s(s(s(elem!1)))), s(z))) | (~b(s(s(s(elem!1))), s(s(s(s(elem!1)))))) | (~b(elem!1, s(s(s(s(elem!1)))))) | (~b(elem!1, s(s(s(elem!1)))))) <=> ((~b(elem!1, s(s(s(elem!1))))) | (~b(elem!1, s(s(elem!1)))) | (~b(s(z), s(s(elem!1)))) | (~b(s(s(s(elem!1))), s(s(s(s(elem!1)))))) | (~b(elem!1, s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), s(z))))),
% 2.83/3.10 inference(rewrite,[status(thm)],[])).
% 2.83/3.10 tff(11611,plain,
% 2.83/3.10 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(elem!1)))) | (~b(elem!1, s(s(elem!1)))) | (~b(s(s(s(s(elem!1)))), s(z))) | (~b(s(s(s(elem!1))), s(s(s(s(elem!1)))))) | (~b(elem!1, s(s(s(s(elem!1)))))) | (~b(elem!1, s(s(s(elem!1))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(s(s(elem!1))))) | (~b(elem!1, s(s(elem!1)))) | (~b(s(z), s(s(elem!1)))) | (~b(s(s(s(elem!1))), s(s(s(s(elem!1)))))) | (~b(elem!1, s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), s(z)))))),
% 2.83/3.10 inference(monotonicity,[status(thm)],[11610])).
% 2.83/3.10 tff(11612,plain,
% 2.83/3.10 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(elem!1)))) | (~b(elem!1, s(s(elem!1)))) | (~b(s(s(s(s(elem!1)))), s(z))) | (~b(s(s(s(elem!1))), s(s(s(s(elem!1)))))) | (~b(elem!1, s(s(s(s(elem!1)))))) | (~b(elem!1, s(s(s(elem!1))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(s(s(elem!1))))) | (~b(elem!1, s(s(elem!1)))) | (~b(s(z), s(s(elem!1)))) | (~b(s(s(s(elem!1))), s(s(s(s(elem!1)))))) | (~b(elem!1, s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), s(z))))),
% 2.83/3.10 inference(transitivity,[status(thm)],[11611, 11609])).
% 2.83/3.10 tff(11613,plain,
% 2.83/3.10 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(elem!1)))) | (~b(elem!1, s(s(elem!1)))) | (~b(s(s(s(s(elem!1)))), s(z))) | (~b(s(s(s(elem!1))), s(s(s(s(elem!1)))))) | (~b(elem!1, s(s(s(s(elem!1)))))) | (~b(elem!1, s(s(s(elem!1))))))),
% 2.83/3.10 inference(quant_inst,[status(thm)],[])).
% 2.83/3.10 tff(11614,plain,
% 2.83/3.10 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(s(s(elem!1))))) | (~b(elem!1, s(s(elem!1)))) | (~b(s(z), s(s(elem!1)))) | (~b(s(s(s(elem!1))), s(s(s(s(elem!1)))))) | (~b(elem!1, s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), s(z)))),
% 2.83/3.10 inference(modus_ponens,[status(thm)],[11613, 11612])).
% 2.83/3.10 tff(11615,plain,
% 2.83/3.10 (~b(elem!1, s(s(s(s(elem!1)))))),
% 2.83/3.10 inference(unit_resolution,[status(thm)],[11614, 166, 376, 643, 1402, 10960, 1311])).
% 2.83/3.10 tff(11616,plain,
% 2.83/3.10 ($false),
% 2.83/3.10 inference(unit_resolution,[status(thm)],[2425, 79, 11615, 11608, 2422])).
% 2.83/3.10 tff(11617,plain,((~b(s(s(s(s(elem!1)))), s(z))) | (elem!1 = s(s(s(s(elem!1))))) | (~b(s(z), s(s(elem!1)))) | (~b(elem!1, s(s(s(elem!1))))) | (~b(elem!1, s(s(elem!1)))) | (~b(s(s(s(elem!1))), s(s(s(s(elem!1)))))) | (~r(s(z), elem!1)) | (~r(s(s(s(s(elem!1)))), elem!1)) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(s(s(elem!1))), s(z))) | (~b(elem!1, s(z)))), inference(lemma,lemma(discharge,[]))).
% 2.83/3.10 tff(11618,plain,
% 2.83/3.10 (~b(s(s(s(s(elem!1)))), s(z))),
% 2.83/3.10 inference(unit_resolution,[status(thm)],[11617, 11605, 11600, 11590, 11598, 11536, 11594, 11592, 11574, 11513, 11580])).
% 2.83/3.10 tff(11619,plain,
% 2.83/3.10 (r(s(s(s(s(elem!1)))), s(z))),
% 2.83/3.10 inference(unit_resolution,[status(thm)],[661, 11618])).
% 2.83/3.10 tff(11620,plain,
% 2.83/3.10 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), elem!1)) | (~r(s(s(elem!1)), s(z))) | (~r(s(s(s(s(elem!1)))), s(z))) | (~r(s(s(elem!1)), s(s(s(s(elem!1)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(z), elem!1)) | (~r(s(s(elem!1)), s(z))) | (~r(s(s(s(s(elem!1)))), s(z))) | (~r(s(s(elem!1)), s(s(s(s(elem!1)))))))),
% 2.83/3.10 inference(rewrite,[status(thm)],[])).
% 2.83/3.10 tff(11621,plain,
% 2.83/3.10 (((~r(s(z), elem!1)) | (~r(s(s(s(s(elem!1)))), s(z))) | (~r(s(s(elem!1)), s(z))) | (~r(s(s(elem!1)), s(s(s(s(elem!1))))))) <=> ((~r(s(z), elem!1)) | (~r(s(s(elem!1)), s(z))) | (~r(s(s(s(s(elem!1)))), s(z))) | (~r(s(s(elem!1)), s(s(s(s(elem!1)))))))),
% 2.83/3.10 inference(rewrite,[status(thm)],[])).
% 2.83/3.10 tff(11622,plain,
% 2.83/3.10 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), elem!1)) | (~r(s(s(s(s(elem!1)))), s(z))) | (~r(s(s(elem!1)), s(z))) | (~r(s(s(elem!1)), s(s(s(s(elem!1)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), elem!1)) | (~r(s(s(elem!1)), s(z))) | (~r(s(s(s(s(elem!1)))), s(z))) | (~r(s(s(elem!1)), s(s(s(s(elem!1))))))))),
% 2.83/3.10 inference(monotonicity,[status(thm)],[11621])).
% 2.83/3.10 tff(11623,plain,
% 2.83/3.10 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), elem!1)) | (~r(s(s(s(s(elem!1)))), s(z))) | (~r(s(s(elem!1)), s(z))) | (~r(s(s(elem!1)), s(s(s(s(elem!1)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(z), elem!1)) | (~r(s(s(elem!1)), s(z))) | (~r(s(s(s(s(elem!1)))), s(z))) | (~r(s(s(elem!1)), s(s(s(s(elem!1)))))))),
% 2.83/3.10 inference(transitivity,[status(thm)],[11622, 11620])).
% 2.83/3.10 tff(11624,plain,
% 2.83/3.10 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), elem!1)) | (~r(s(s(s(s(elem!1)))), s(z))) | (~r(s(s(elem!1)), s(z))) | (~r(s(s(elem!1)), s(s(s(s(elem!1)))))))),
% 2.83/3.10 inference(quant_inst,[status(thm)],[])).
% 2.83/3.10 tff(11625,plain,
% 2.83/3.10 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(z), elem!1)) | (~r(s(s(elem!1)), s(z))) | (~r(s(s(s(s(elem!1)))), s(z))) | (~r(s(s(elem!1)), s(s(s(s(elem!1))))))),
% 2.83/3.10 inference(modus_ponens,[status(thm)],[11624, 11623])).
% 2.83/3.10 tff(11626,plain,
% 2.83/3.10 (~r(s(s(elem!1)), s(s(s(s(elem!1)))))),
% 2.83/3.10 inference(unit_resolution,[status(thm)],[11625, 197, 10521, 11594, 11619])).
% 2.83/3.10 tff(11627,plain,
% 2.83/3.10 (b(s(s(elem!1)), s(s(s(s(elem!1)))))),
% 2.83/3.10 inference(unit_resolution,[status(thm)],[827, 11626, 11578])).
% 2.83/3.10 tff(11628,plain,
% 2.83/3.10 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(z))) | (~b(s(z), s(s(elem!1)))) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(s(elem!1)), s(s(s(s(elem!1)))))) | (~b(s(s(s(elem!1))), s(s(s(s(elem!1)))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(z))) | (~b(s(z), s(s(elem!1)))) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(s(elem!1)), s(s(s(s(elem!1)))))) | (~b(s(s(s(elem!1))), s(s(s(s(elem!1)))))))),
% 2.83/3.10 inference(rewrite,[status(thm)],[])).
% 2.83/3.10 tff(11629,plain,
% 2.83/3.10 (((~b(s(s(elem!1)), s(s(s(s(elem!1)))))) | (~b(s(s(s(elem!1))), s(s(s(s(elem!1)))))) | (~b(s(z), s(s(elem!1)))) | (~b(elem!1, s(z))) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(s(s(elem!1))), elem!1))) <=> ((~b(elem!1, s(z))) | (~b(s(z), s(s(elem!1)))) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(s(elem!1)), s(s(s(s(elem!1)))))) | (~b(s(s(s(elem!1))), s(s(s(s(elem!1)))))))),
% 2.83/3.10 inference(rewrite,[status(thm)],[])).
% 2.83/3.10 tff(11630,plain,
% 2.83/3.10 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), s(s(s(s(elem!1)))))) | (~b(s(s(s(elem!1))), s(s(s(s(elem!1)))))) | (~b(s(z), s(s(elem!1)))) | (~b(elem!1, s(z))) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(s(s(elem!1))), elem!1)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(z))) | (~b(s(z), s(s(elem!1)))) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(s(elem!1)), s(s(s(s(elem!1)))))) | (~b(s(s(s(elem!1))), s(s(s(s(elem!1))))))))),
% 2.83/3.10 inference(monotonicity,[status(thm)],[11629])).
% 2.83/3.10 tff(11631,plain,
% 2.83/3.10 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), s(s(s(s(elem!1)))))) | (~b(s(s(s(elem!1))), s(s(s(s(elem!1)))))) | (~b(s(z), s(s(elem!1)))) | (~b(elem!1, s(z))) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(s(s(elem!1))), elem!1)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(z))) | (~b(s(z), s(s(elem!1)))) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(s(elem!1)), s(s(s(s(elem!1)))))) | (~b(s(s(s(elem!1))), s(s(s(s(elem!1)))))))),
% 2.83/3.10 inference(transitivity,[status(thm)],[11630, 11628])).
% 2.83/3.10 tff(11632,plain,
% 2.83/3.10 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), s(s(s(s(elem!1)))))) | (~b(s(s(s(elem!1))), s(s(s(s(elem!1)))))) | (~b(s(z), s(s(elem!1)))) | (~b(elem!1, s(z))) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(s(s(elem!1))), elem!1)))),
% 2.83/3.10 inference(quant_inst,[status(thm)],[])).
% 2.83/3.10 tff(11633,plain,
% 2.83/3.10 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(z))) | (~b(s(z), s(s(elem!1)))) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(s(elem!1)), s(s(s(s(elem!1)))))) | (~b(s(s(s(elem!1))), s(s(s(s(elem!1))))))),
% 2.83/3.10 inference(modus_ponens,[status(thm)],[11632, 11631])).
% 2.83/3.10 tff(11634,plain,
% 2.83/3.10 ($false),
% 2.83/3.10 inference(unit_resolution,[status(thm)],[11633, 166, 11600, 11513, 11580, 11627, 11574, 11536])).
% 2.83/3.10 tff(11635,plain,(b(s(z), s(s(s(elem!1)))) | (~r(s(z), z)) | r(s(s(z)), s(s(elem!1))) | (~b(z, s(s(z)))) | b(s(s(elem!1)), s(z))), inference(lemma,lemma(discharge,[]))).
% 2.83/3.10 tff(11636,plain,
% 2.83/3.10 (b(s(z), s(s(s(elem!1))))),
% 2.83/3.10 inference(unit_resolution,[status(thm)],[11635, 97, 2288, 10451, 4568])).
% 2.83/3.10 tff(11637,plain,
% 2.83/3.10 (~b(s(s(elem!1)), z)),
% 2.83/3.10 inference(unit_resolution,[status(thm)],[11110, 2516, 10451, 1820])).
% 2.83/3.10 tff(11638,plain,
% 2.83/3.10 (r(s(s(elem!1)), z)),
% 2.83/3.10 inference(unit_resolution,[status(thm)],[608, 11637])).
% 2.83/3.10 tff(11639,plain,
% 2.83/3.10 (~r(z, s(z))),
% 2.83/3.10 inference(unit_resolution,[status(thm)],[8490, 11638, 97, 4577])).
% 2.83/3.10 tff(11640,plain,
% 2.83/3.10 (b(z, s(z))),
% 2.83/3.10 inference(unit_resolution,[status(thm)],[321, 11639])).
% 2.83/3.10 tff(11641,plain,
% 2.83/3.10 (~b(s(s(elem!1)), s(s(z)))),
% 2.83/3.10 inference(unit_resolution,[status(thm)],[10727, 2516, 10451, 1820])).
% 2.83/3.10 tff(11642,plain,
% 2.83/3.10 (r(s(s(elem!1)), s(s(z)))),
% 2.83/3.10 inference(unit_resolution,[status(thm)],[441, 11641, 132])).
% 2.83/3.10 tff(11643,plain,
% 2.83/3.10 (~r(s(s(z)), s(z))),
% 2.83/3.10 inference(unit_resolution,[status(thm)],[5331, 11642, 4577, 97])).
% 2.83/3.10 tff(11644,plain,
% 2.83/3.10 (b(s(s(z)), s(z))),
% 2.83/3.10 inference(unit_resolution,[status(thm)],[308, 11643])).
% 2.83/3.10 tff(11645,plain,
% 2.83/3.10 ($false),
% 2.83/3.10 inference(unit_resolution,[status(thm)],[11081, 11644, 11640, 10451, 241, 96])).
% 2.83/3.10 tff(11646,plain,((s(s(z)) = s(s(elem!1))) | (~b(z, s(s(z)))) | (~b(s(z), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(z))) | (~r(s(s(elem!1)), s(z))) | (~r(s(z), z)) | (~b(z, s(s(elem!1)))) | r(s(s(z)), s(s(elem!1)))), inference(lemma,lemma(discharge,[]))).
% 2.83/3.10 tff(11647,plain,
% 2.83/3.10 (s(s(z)) = s(s(elem!1))),
% 2.83/3.10 inference(unit_resolution,[status(thm)],[11646, 11636, 10451, 11440, 10521, 97, 11397, 2288])).
% 2.83/3.10 tff(11648,plain,
% 2.83/3.10 (s(elem!1) = s(z)),
% 2.83/3.10 inference(unit_resolution,[status(thm)],[43, 11647])).
% 2.83/3.10 tff(11649,plain,
% 2.83/3.10 (z = elem!1),
% 2.83/3.10 inference(unit_resolution,[status(thm)],[30, 11648])).
% 2.83/3.10 tff(11650,plain,
% 2.83/3.10 (b(z, s(s(s(elem!1)))) <=> b(elem!1, s(s(s(elem!1))))),
% 2.83/3.10 inference(monotonicity,[status(thm)],[11649])).
% 2.83/3.10 tff(11651,plain,
% 2.83/3.10 (b(elem!1, s(s(s(elem!1)))) <=> b(z, s(s(s(elem!1))))),
% 2.83/3.10 inference(symmetry,[status(thm)],[11650])).
% 2.83/3.10 tff(11652,plain,
% 2.83/3.10 (s(s(s(z))) = s(s(s(elem!1)))),
% 2.83/3.10 inference(monotonicity,[status(thm)],[11647])).
% 2.83/3.10 tff(11653,plain,
% 2.83/3.10 (b(elem!1, s(s(s(z)))) <=> b(elem!1, s(s(s(elem!1))))),
% 2.83/3.10 inference(monotonicity,[status(thm)],[11652])).
% 2.83/3.10 tff(11654,plain,
% 2.83/3.10 (b(z, s(s(s(z)))) <=> b(elem!1, s(s(s(z))))),
% 2.83/3.10 inference(monotonicity,[status(thm)],[11649])).
% 2.83/3.10 tff(11655,plain,
% 2.83/3.10 (b(z, s(s(s(z)))) <=> b(z, s(s(s(elem!1))))),
% 2.83/3.10 inference(transitivity,[status(thm)],[11654, 11653, 11651])).
% 2.83/3.10 tff(11656,plain,
% 2.83/3.10 (b(s(s(elem!1)), z) <=> b(s(s(elem!1)), elem!1)),
% 2.83/3.10 inference(monotonicity,[status(thm)],[11649])).
% 2.83/3.10 tff(11657,plain,
% 2.83/3.10 (b(s(s(elem!1)), elem!1) <=> b(s(s(elem!1)), z)),
% 2.83/3.10 inference(symmetry,[status(thm)],[11656])).
% 2.83/3.10 tff(11658,plain,
% 2.83/3.10 ((~b(s(s(elem!1)), elem!1)) <=> (~b(s(s(elem!1)), z))),
% 2.83/3.10 inference(monotonicity,[status(thm)],[11657])).
% 2.83/3.10 tff(11659,plain,
% 2.83/3.10 ((s(s(s(s(elem!1)))) = z) <=> (s(s(s(s(elem!1)))) = elem!1)),
% 2.83/3.10 inference(monotonicity,[status(thm)],[11649])).
% 2.83/3.10 tff(11660,plain,
% 2.83/3.10 ((s(s(s(s(elem!1)))) = z) <=> (elem!1 = s(s(s(s(elem!1)))))),
% 2.83/3.10 inference(transitivity,[status(thm)],[11659, 2287])).
% 2.83/3.10 tff(11661,plain,
% 2.83/3.10 ((~(s(s(s(s(elem!1)))) = z)) <=> (~(elem!1 = s(s(s(s(elem!1))))))),
% 2.83/3.10 inference(monotonicity,[status(thm)],[11660])).
% 2.83/3.10 tff(11662,plain,
% 2.83/3.10 (~(elem!1 = s(s(s(s(elem!1)))))),
% 2.83/3.10 inference(modus_ponens,[status(thm)],[626, 11661])).
% 2.83/3.10 tff(11663,plain,
% 2.83/3.10 ((~(s(s(s(s(elem!1)))) = z)) <=> (~(s(s(s(s(elem!1)))) = elem!1))),
% 2.83/3.10 inference(monotonicity,[status(thm)],[11659])).
% 2.83/3.10 tff(11664,plain,
% 2.83/3.10 (~(s(s(s(s(elem!1)))) = elem!1)),
% 2.83/3.10 inference(modus_ponens,[status(thm)],[626, 11663])).
% 2.83/3.10 tff(11665,plain,
% 2.83/3.10 ((s(s(s(s(elem!1)))) = s(s(z))) <=> (s(s(s(s(elem!1)))) = s(s(elem!1)))),
% 2.83/3.10 inference(monotonicity,[status(thm)],[11647])).
% 2.83/3.10 tff(11666,plain,
% 2.83/3.10 ((s(s(s(s(elem!1)))) = s(s(z))) <=> (s(s(elem!1)) = s(s(s(s(elem!1)))))),
% 2.83/3.10 inference(transitivity,[status(thm)],[11665, 123])).
% 2.83/3.10 tff(11667,plain,
% 2.83/3.10 ((s(s(s(s(elem!1)))) = s(s(z))) <=> (s(s(s(s(elem!1)))) = s(s(elem!1)))),
% 2.83/3.10 inference(transitivity,[status(thm)],[11666, 124])).
% 2.83/3.10 tff(11668,plain,
% 2.83/3.10 ((~(s(s(s(s(elem!1)))) = s(s(z)))) <=> (~(s(s(s(s(elem!1)))) = s(s(elem!1))))),
% 2.83/3.10 inference(monotonicity,[status(thm)],[11667])).
% 2.83/3.10 tff(11669,plain,
% 2.83/3.10 (~(s(s(s(s(elem!1)))) = s(s(elem!1)))),
% 2.83/3.10 inference(modus_ponens,[status(thm)],[733, 11668])).
% 2.83/3.10 tff(11670,plain,
% 2.83/3.10 (r(s(z), z) <=> r(s(z), elem!1)),
% 2.83/3.10 inference(monotonicity,[status(thm)],[11649])).
% 2.83/3.10 tff(11671,plain,
% 2.83/3.10 (r(s(z), elem!1)),
% 2.83/3.10 inference(modus_ponens,[status(thm)],[97, 11670])).
% 2.83/3.10 tff(11672,plain,
% 2.83/3.10 (elem!1 = z),
% 2.83/3.10 inference(symmetry,[status(thm)],[11649])).
% 2.83/3.10 tff(11673,plain,
% 2.83/3.10 (b(elem!1, s(s(elem!1))) <=> b(z, s(s(elem!1)))),
% 2.83/3.10 inference(monotonicity,[status(thm)],[11672])).
% 2.83/3.10 tff(11674,plain,
% 2.83/3.10 (b(z, s(s(elem!1))) <=> b(elem!1, s(s(elem!1)))),
% 2.83/3.10 inference(symmetry,[status(thm)],[11673])).
% 2.83/3.10 tff(11675,plain,
% 2.83/3.10 (b(elem!1, s(s(elem!1)))),
% 2.83/3.10 inference(modus_ponens,[status(thm)],[11397, 11674])).
% 2.83/3.10 tff(11676,plain,
% 2.83/3.10 (b(s(z), s(s(z))) <=> b(s(z), s(s(elem!1)))),
% 2.83/3.10 inference(monotonicity,[status(thm)],[11647])).
% 2.83/3.10 tff(11677,plain,
% 2.83/3.10 (b(s(z), s(s(elem!1)))),
% 2.83/3.10 inference(modus_ponens,[status(thm)],[11376, 11676])).
% 2.83/3.10 tff(11678,plain,
% 2.83/3.10 (~(s(s(s(elem!1))) = s(s(s(s(elem!1)))))),
% 2.83/3.10 inference(unit_resolution,[status(thm)],[357, 11425])).
% 2.83/3.10 tff(11679,plain,
% 2.83/3.10 (~b(s(s(s(s(elem!1)))), elem!1)),
% 2.83/3.10 inference(unit_resolution,[status(thm)],[10982, 166, 786, 10960, 3457])).
% 2.83/3.10 tff(11680,plain,
% 2.83/3.10 (r(s(s(s(s(elem!1)))), elem!1)),
% 2.83/3.10 inference(unit_resolution,[status(thm)],[719, 11679, 712])).
% 2.83/3.10 tff(11681,plain,
% 2.83/3.10 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), elem!1)) | (~b(s(s(s(s(elem!1)))), s(s(elem!1)))) | (~b(elem!1, s(s(elem!1)))) | (~b(s(z), s(s(elem!1)))) | (~b(s(z), s(s(s(s(elem!1)))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(elem!1)), elem!1)) | (~b(s(s(s(s(elem!1)))), s(s(elem!1)))) | (~b(elem!1, s(s(elem!1)))) | (~b(s(z), s(s(elem!1)))) | (~b(s(z), s(s(s(s(elem!1)))))))),
% 2.83/3.10 inference(rewrite,[status(thm)],[])).
% 2.83/3.10 tff(11682,plain,
% 2.83/3.10 (((~b(elem!1, s(s(elem!1)))) | (~b(s(z), s(s(elem!1)))) | (~b(s(s(elem!1)), elem!1)) | (~b(s(s(s(s(elem!1)))), s(s(elem!1)))) | (~b(s(z), s(s(elem!1)))) | (~b(s(z), s(s(s(s(elem!1))))))) <=> ((~b(s(s(elem!1)), elem!1)) | (~b(s(s(s(s(elem!1)))), s(s(elem!1)))) | (~b(elem!1, s(s(elem!1)))) | (~b(s(z), s(s(elem!1)))) | (~b(s(z), s(s(s(s(elem!1)))))))),
% 2.83/3.10 inference(rewrite,[status(thm)],[])).
% 2.83/3.10 tff(11683,plain,
% 2.83/3.10 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(s(elem!1)))) | (~b(s(z), s(s(elem!1)))) | (~b(s(s(elem!1)), elem!1)) | (~b(s(s(s(s(elem!1)))), s(s(elem!1)))) | (~b(s(z), s(s(elem!1)))) | (~b(s(z), s(s(s(s(elem!1)))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), elem!1)) | (~b(s(s(s(s(elem!1)))), s(s(elem!1)))) | (~b(elem!1, s(s(elem!1)))) | (~b(s(z), s(s(elem!1)))) | (~b(s(z), s(s(s(s(elem!1))))))))),
% 2.83/3.10 inference(monotonicity,[status(thm)],[11682])).
% 2.83/3.10 tff(11684,plain,
% 2.83/3.10 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(s(elem!1)))) | (~b(s(z), s(s(elem!1)))) | (~b(s(s(elem!1)), elem!1)) | (~b(s(s(s(s(elem!1)))), s(s(elem!1)))) | (~b(s(z), s(s(elem!1)))) | (~b(s(z), s(s(s(s(elem!1)))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(elem!1)), elem!1)) | (~b(s(s(s(s(elem!1)))), s(s(elem!1)))) | (~b(elem!1, s(s(elem!1)))) | (~b(s(z), s(s(elem!1)))) | (~b(s(z), s(s(s(s(elem!1)))))))),
% 2.83/3.10 inference(transitivity,[status(thm)],[11683, 11681])).
% 2.83/3.10 tff(11685,plain,
% 2.83/3.10 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(s(elem!1)))) | (~b(s(z), s(s(elem!1)))) | (~b(s(s(elem!1)), elem!1)) | (~b(s(s(s(s(elem!1)))), s(s(elem!1)))) | (~b(s(z), s(s(elem!1)))) | (~b(s(z), s(s(s(s(elem!1)))))))),
% 2.83/3.10 inference(quant_inst,[status(thm)],[])).
% 2.83/3.10 tff(11686,plain,
% 2.83/3.10 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(elem!1)), elem!1)) | (~b(s(s(s(s(elem!1)))), s(s(elem!1)))) | (~b(elem!1, s(s(elem!1)))) | (~b(s(z), s(s(elem!1)))) | (~b(s(z), s(s(s(s(elem!1))))))),
% 2.83/3.10 inference(modus_ponens,[status(thm)],[11685, 11684])).
% 2.83/3.10 tff(11687,plain,
% 2.83/3.10 (~b(s(z), s(s(s(s(elem!1)))))),
% 2.83/3.10 inference(unit_resolution,[status(thm)],[11686, 166, 376, 786, 10960, 3457])).
% 2.83/3.10 tff(11688,plain,
% 2.83/3.10 (r(s(z), s(s(s(s(elem!1)))))),
% 2.83/3.10 inference(unit_resolution,[status(thm)],[681, 11687])).
% 2.83/3.10 tff(11689,plain,
% 2.83/3.10 (~r(elem!1, s(s(s(s(elem!1)))))),
% 2.83/3.10 inference(unit_resolution,[status(thm)],[10678, 11688, 2381, 11680])).
% 2.83/3.10 tff(11690,plain,
% 2.83/3.10 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), elem!1)) | (~b(s(s(s(s(elem!1)))), s(s(elem!1)))) | (~b(elem!1, s(s(elem!1)))) | (~b(elem!1, s(s(s(s(elem!1)))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(elem!1)), elem!1)) | (~b(s(s(s(s(elem!1)))), s(s(elem!1)))) | (~b(elem!1, s(s(elem!1)))) | (~b(elem!1, s(s(s(s(elem!1)))))))),
% 2.83/3.10 inference(rewrite,[status(thm)],[])).
% 2.83/3.10 tff(11691,plain,
% 2.83/3.10 (((~b(elem!1, s(s(elem!1)))) | (~b(elem!1, s(s(elem!1)))) | (~b(s(s(elem!1)), elem!1)) | (~b(s(s(s(s(elem!1)))), s(s(elem!1)))) | (~b(elem!1, s(s(elem!1)))) | (~b(elem!1, s(s(s(s(elem!1))))))) <=> ((~b(s(s(elem!1)), elem!1)) | (~b(s(s(s(s(elem!1)))), s(s(elem!1)))) | (~b(elem!1, s(s(elem!1)))) | (~b(elem!1, s(s(s(s(elem!1)))))))),
% 2.83/3.10 inference(rewrite,[status(thm)],[])).
% 2.83/3.10 tff(11692,plain,
% 2.83/3.10 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(s(elem!1)))) | (~b(elem!1, s(s(elem!1)))) | (~b(s(s(elem!1)), elem!1)) | (~b(s(s(s(s(elem!1)))), s(s(elem!1)))) | (~b(elem!1, s(s(elem!1)))) | (~b(elem!1, s(s(s(s(elem!1)))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), elem!1)) | (~b(s(s(s(s(elem!1)))), s(s(elem!1)))) | (~b(elem!1, s(s(elem!1)))) | (~b(elem!1, s(s(s(s(elem!1))))))))),
% 2.83/3.10 inference(monotonicity,[status(thm)],[11691])).
% 2.83/3.10 tff(11693,plain,
% 2.83/3.10 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(s(elem!1)))) | (~b(elem!1, s(s(elem!1)))) | (~b(s(s(elem!1)), elem!1)) | (~b(s(s(s(s(elem!1)))), s(s(elem!1)))) | (~b(elem!1, s(s(elem!1)))) | (~b(elem!1, s(s(s(s(elem!1)))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(elem!1)), elem!1)) | (~b(s(s(s(s(elem!1)))), s(s(elem!1)))) | (~b(elem!1, s(s(elem!1)))) | (~b(elem!1, s(s(s(s(elem!1)))))))),
% 2.83/3.10 inference(transitivity,[status(thm)],[11692, 11690])).
% 2.83/3.11 tff(11694,plain,
% 2.83/3.11 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(s(elem!1)))) | (~b(elem!1, s(s(elem!1)))) | (~b(s(s(elem!1)), elem!1)) | (~b(s(s(s(s(elem!1)))), s(s(elem!1)))) | (~b(elem!1, s(s(elem!1)))) | (~b(elem!1, s(s(s(s(elem!1)))))))),
% 2.83/3.11 inference(quant_inst,[status(thm)],[])).
% 2.83/3.11 tff(11695,plain,
% 2.83/3.11 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(elem!1)), elem!1)) | (~b(s(s(s(s(elem!1)))), s(s(elem!1)))) | (~b(elem!1, s(s(elem!1)))) | (~b(elem!1, s(s(s(s(elem!1))))))),
% 2.83/3.11 inference(modus_ponens,[status(thm)],[11694, 11693])).
% 2.83/3.11 tff(11696,plain,
% 2.83/3.11 (~b(elem!1, s(s(s(s(elem!1)))))),
% 2.83/3.11 inference(unit_resolution,[status(thm)],[11695, 166, 786, 10960, 3457])).
% 2.83/3.11 tff(11697,plain,
% 2.83/3.11 ($false),
% 2.83/3.11 inference(unit_resolution,[status(thm)],[2425, 79, 11696, 11689, 2422])).
% 2.83/3.11 tff(11698,plain,((~b(s(s(s(s(elem!1)))), s(s(elem!1)))) | (elem!1 = s(s(s(s(elem!1))))) | (~r(s(z), elem!1)) | (s(s(s(s(elem!1)))) = elem!1) | (~b(s(s(elem!1)), elem!1)) | (~b(elem!1, s(s(elem!1)))) | (~b(s(z), s(s(elem!1))))), inference(lemma,lemma(discharge,[]))).
% 2.83/3.11 tff(11699,plain,
% 2.83/3.11 (~b(s(s(s(s(elem!1)))), s(s(elem!1)))),
% 2.83/3.11 inference(unit_resolution,[status(thm)],[11698, 786, 2381, 712, 2422, 10960, 376])).
% 2.83/3.11 tff(11700,plain,
% 2.83/3.11 (r(s(s(s(s(elem!1)))), s(s(elem!1)))),
% 2.83/3.11 inference(unit_resolution,[status(thm)],[813, 11699, 806])).
% 2.83/3.11 tff(11701,plain,
% 2.83/3.11 (~r(s(s(s(elem!1))), s(s(s(s(elem!1)))))),
% 2.83/3.11 inference(unit_resolution,[status(thm)],[5158, 197, 4577, 905, 3408])).
% 2.83/3.11 tff(11702,plain,
% 2.83/3.11 (b(s(s(s(elem!1))), s(s(s(s(elem!1)))))),
% 2.83/3.11 inference(unit_resolution,[status(thm)],[696, 11701, 361])).
% 2.83/3.11 tff(11703,plain,
% 2.83/3.11 (~b(s(s(s(s(elem!1)))), s(z))),
% 2.83/3.11 inference(unit_resolution,[status(thm)],[5130, 11702, 241, 96])).
% 2.83/3.11 tff(11704,plain,
% 2.83/3.11 (r(s(s(s(s(elem!1)))), s(z))),
% 2.83/3.11 inference(unit_resolution,[status(thm)],[661, 11703])).
% 2.83/3.11 tff(11705,plain,
% 2.83/3.11 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), elem!1)) | (~r(s(s(elem!1)), s(z))) | (~r(s(s(s(s(elem!1)))), s(z))) | (~r(s(s(s(s(elem!1)))), s(s(elem!1)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(z), elem!1)) | (~r(s(s(elem!1)), s(z))) | (~r(s(s(s(s(elem!1)))), s(z))) | (~r(s(s(s(s(elem!1)))), s(s(elem!1)))))),
% 2.83/3.11 inference(rewrite,[status(thm)],[])).
% 2.83/3.11 tff(11706,plain,
% 2.83/3.11 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), elem!1)) | (~r(s(s(elem!1)), s(z))) | (~r(s(s(s(s(elem!1)))), s(z))) | (~r(s(s(s(s(elem!1)))), s(s(elem!1)))))),
% 2.83/3.11 inference(quant_inst,[status(thm)],[])).
% 2.83/3.11 tff(11707,plain,
% 2.83/3.11 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(z), elem!1)) | (~r(s(s(elem!1)), s(z))) | (~r(s(s(s(s(elem!1)))), s(z))) | (~r(s(s(s(s(elem!1)))), s(s(elem!1))))),
% 2.83/3.11 inference(modus_ponens,[status(thm)],[11706, 11705])).
% 2.83/3.11 tff(11708,plain,
% 2.83/3.11 ($false),
% 2.83/3.11 inference(unit_resolution,[status(thm)],[11707, 197, 4577, 2381, 11704, 3408])).
% 2.83/3.11 tff(11709,plain,((~r(s(s(s(s(elem!1)))), s(s(elem!1)))) | (~r(s(s(elem!1)), s(z))) | (~r(s(z), elem!1)) | (~b(s(z), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(z))) | (s(s(s(elem!1))) = s(s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), s(s(elem!1))))), inference(lemma,lemma(discharge,[]))).
% 2.83/3.11 tff(11710,plain,
% 2.83/3.11 (~r(s(s(s(elem!1))), s(s(elem!1)))),
% 2.83/3.11 inference(unit_resolution,[status(thm)],[11709, 11700, 2381, 241, 96, 11678, 4577])).
% 2.83/3.11 tff(11711,plain,
% 2.83/3.11 (b(s(s(s(elem!1))), s(s(elem!1)))),
% 2.83/3.11 inference(unit_resolution,[status(thm)],[889, 11710, 1863])).
% 2.83/3.11 tff(11712,plain,
% 2.83/3.11 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), elem!1)) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(z), s(s(s(elem!1))))) | (~b(elem!1, s(s(elem!1)))) | (~b(s(z), s(s(elem!1)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(elem!1)), elem!1)) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(z), s(s(s(elem!1))))) | (~b(elem!1, s(s(elem!1)))) | (~b(s(z), s(s(elem!1)))))),
% 2.83/3.11 inference(rewrite,[status(thm)],[])).
% 2.83/3.11 tff(11713,plain,
% 2.83/3.11 (((~b(elem!1, s(s(elem!1)))) | (~b(s(z), s(s(elem!1)))) | (~b(s(s(elem!1)), elem!1)) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(z), s(s(elem!1)))) | (~b(s(z), s(s(s(elem!1)))))) <=> ((~b(s(s(elem!1)), elem!1)) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(z), s(s(s(elem!1))))) | (~b(elem!1, s(s(elem!1)))) | (~b(s(z), s(s(elem!1)))))),
% 2.83/3.11 inference(rewrite,[status(thm)],[])).
% 2.83/3.11 tff(11714,plain,
% 2.83/3.11 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(s(elem!1)))) | (~b(s(z), s(s(elem!1)))) | (~b(s(s(elem!1)), elem!1)) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(z), s(s(elem!1)))) | (~b(s(z), s(s(s(elem!1))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), elem!1)) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(z), s(s(s(elem!1))))) | (~b(elem!1, s(s(elem!1)))) | (~b(s(z), s(s(elem!1))))))),
% 2.83/3.11 inference(monotonicity,[status(thm)],[11713])).
% 2.83/3.11 tff(11715,plain,
% 2.83/3.11 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(s(elem!1)))) | (~b(s(z), s(s(elem!1)))) | (~b(s(s(elem!1)), elem!1)) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(z), s(s(elem!1)))) | (~b(s(z), s(s(s(elem!1))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(elem!1)), elem!1)) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(z), s(s(s(elem!1))))) | (~b(elem!1, s(s(elem!1)))) | (~b(s(z), s(s(elem!1)))))),
% 2.83/3.11 inference(transitivity,[status(thm)],[11714, 11712])).
% 2.83/3.11 tff(11716,plain,
% 2.83/3.11 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(s(elem!1)))) | (~b(s(z), s(s(elem!1)))) | (~b(s(s(elem!1)), elem!1)) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(z), s(s(elem!1)))) | (~b(s(z), s(s(s(elem!1))))))),
% 2.83/3.11 inference(quant_inst,[status(thm)],[])).
% 2.83/3.11 tff(11717,plain,
% 2.83/3.11 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(elem!1)), elem!1)) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(z), s(s(s(elem!1))))) | (~b(elem!1, s(s(elem!1)))) | (~b(s(z), s(s(elem!1))))),
% 2.83/3.11 inference(modus_ponens,[status(thm)],[11716, 11715])).
% 2.83/3.11 tff(11718,plain,
% 2.83/3.11 ($false),
% 2.83/3.11 inference(unit_resolution,[status(thm)],[11717, 166, 376, 786, 11711, 241, 10960])).
% 2.83/3.11 tff(11719,plain,((~b(s(s(elem!1)), elem!1)) | (~b(s(z), s(s(elem!1)))) | (~b(s(z), s(s(s(elem!1))))) | (~b(elem!1, s(s(elem!1)))) | (s(s(s(elem!1))) = s(s(elem!1))) | (~r(s(z), elem!1)) | (~b(s(s(s(elem!1))), s(z))) | (~r(s(s(elem!1)), s(z))) | (s(s(s(s(elem!1)))) = s(s(elem!1))) | (s(s(s(s(elem!1)))) = elem!1) | (elem!1 = s(s(s(s(elem!1)))))), inference(lemma,lemma(discharge,[]))).
% 2.83/3.11 tff(11720,plain,
% 2.83/3.11 (~b(s(s(elem!1)), elem!1)),
% 2.83/3.11 inference(unit_resolution,[status(thm)],[11719, 11677, 11636, 11675, 11423, 11671, 11440, 10521, 11669, 11664, 11662])).
% 2.83/3.11 tff(11721,plain,
% 2.83/3.11 (~b(s(s(elem!1)), z)),
% 2.83/3.11 inference(modus_ponens,[status(thm)],[11720, 11658])).
% 2.83/3.11 tff(11722,plain,
% 2.83/3.11 (r(s(s(elem!1)), z)),
% 2.83/3.11 inference(unit_resolution,[status(thm)],[608, 11721])).
% 2.83/3.11 tff(11723,plain,
% 2.83/3.11 (~r(z, s(s(s(z))))),
% 2.83/3.11 inference(unit_resolution,[status(thm)],[10804, 11722, 97, 10521])).
% 2.83/3.11 tff(11724,plain,
% 2.83/3.11 (b(z, s(s(s(z))))),
% 2.83/3.11 inference(unit_resolution,[status(thm)],[1696, 11723, 1692])).
% 2.83/3.11 tff(11725,plain,
% 2.83/3.11 (b(z, s(s(s(elem!1))))),
% 2.95/3.11 inference(modus_ponens,[status(thm)],[11724, 11655])).
% 2.95/3.11 tff(11726,plain,
% 2.95/3.11 (~r(z, s(z))),
% 2.95/3.11 inference(unit_resolution,[status(thm)],[8490, 11722, 97, 10521])).
% 2.95/3.11 tff(11727,plain,
% 2.95/3.11 (b(z, s(z))),
% 2.95/3.11 inference(unit_resolution,[status(thm)],[321, 11726])).
% 2.95/3.11 tff(11728,plain,
% 2.95/3.11 (~b(z, s(s(s(elem!1))))),
% 2.95/3.11 inference(unit_resolution,[status(thm)],[249, 11727, 11636, 11440])).
% 2.95/3.11 tff(11729,plain,
% 2.95/3.11 ($false),
% 2.95/3.11 inference(unit_resolution,[status(thm)],[11728, 11725])).
% 2.95/3.11 tff(11730,plain,((~r(s(z), z)) | (~b(z, s(s(z)))) | r(s(s(z)), s(s(elem!1))) | b(s(s(elem!1)), s(z))), inference(lemma,lemma(discharge,[]))).
% 2.95/3.11 tff(11731,plain,
% 2.95/3.11 ((~r(s(z), z)) | r(s(s(z)), s(s(elem!1))) | b(s(s(elem!1)), s(z))),
% 2.95/3.11 inference(unit_resolution,[status(thm)],[11730, 10450])).
% 2.95/3.11 tff(11732,plain,
% 2.95/3.11 (b(s(s(elem!1)), s(z))),
% 2.95/3.11 inference(unit_resolution,[status(thm)],[11731, 10520, 97])).
% 2.95/3.11 tff(11733,plain,
% 2.95/3.11 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(z)))) | (~b(s(s(s(elem!1))), s(s(z)))) | (~b(s(s(s(elem!1))), z)) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(s(elem!1)), s(z))) | (~b(s(s(z)), s(s(elem!1)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(s(z)))) | (~b(s(s(s(elem!1))), s(s(z)))) | (~b(s(s(s(elem!1))), z)) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(s(elem!1)), s(z))) | (~b(s(s(z)), s(s(elem!1)))))),
% 2.95/3.11 inference(rewrite,[status(thm)],[])).
% 2.95/3.11 tff(11734,plain,
% 2.95/3.11 (((~b(s(s(elem!1)), s(z))) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(s(z)), s(s(elem!1)))) | (~b(z, s(s(z)))) | (~b(s(s(s(elem!1))), s(s(z)))) | (~b(s(s(s(elem!1))), z))) <=> ((~b(z, s(s(z)))) | (~b(s(s(s(elem!1))), s(s(z)))) | (~b(s(s(s(elem!1))), z)) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(s(elem!1)), s(z))) | (~b(s(s(z)), s(s(elem!1)))))),
% 2.95/3.11 inference(rewrite,[status(thm)],[])).
% 2.95/3.11 tff(11735,plain,
% 2.95/3.11 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), s(z))) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(s(z)), s(s(elem!1)))) | (~b(z, s(s(z)))) | (~b(s(s(s(elem!1))), s(s(z)))) | (~b(s(s(s(elem!1))), z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(z)))) | (~b(s(s(s(elem!1))), s(s(z)))) | (~b(s(s(s(elem!1))), z)) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(s(elem!1)), s(z))) | (~b(s(s(z)), s(s(elem!1))))))),
% 2.95/3.11 inference(monotonicity,[status(thm)],[11734])).
% 2.95/3.11 tff(11736,plain,
% 2.95/3.11 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), s(z))) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(s(z)), s(s(elem!1)))) | (~b(z, s(s(z)))) | (~b(s(s(s(elem!1))), s(s(z)))) | (~b(s(s(s(elem!1))), z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(s(z)))) | (~b(s(s(s(elem!1))), s(s(z)))) | (~b(s(s(s(elem!1))), z)) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(s(elem!1)), s(z))) | (~b(s(s(z)), s(s(elem!1)))))),
% 2.95/3.11 inference(transitivity,[status(thm)],[11735, 11733])).
% 2.95/3.11 tff(11737,plain,
% 2.95/3.11 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), s(z))) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(s(z)), s(s(elem!1)))) | (~b(z, s(s(z)))) | (~b(s(s(s(elem!1))), s(s(z)))) | (~b(s(s(s(elem!1))), z)))),
% 2.95/3.11 inference(quant_inst,[status(thm)],[])).
% 2.95/3.11 tff(11738,plain,
% 2.95/3.11 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(s(z)))) | (~b(s(s(s(elem!1))), s(s(z)))) | (~b(s(s(s(elem!1))), z)) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(s(elem!1)), s(z))) | (~b(s(s(z)), s(s(elem!1))))),
% 2.95/3.11 inference(modus_ponens,[status(thm)],[11737, 11736])).
% 2.95/3.11 tff(11739,plain,
% 2.95/3.11 ($false),
% 2.95/3.11 inference(unit_resolution,[status(thm)],[11738, 166, 10450, 96, 310, 121, 446, 2060])).
% 2.95/3.11 tff(11740,plain,((~b(s(s(z)), s(s(elem!1)))) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(s(elem!1)), s(z))) | (~b(s(s(s(elem!1))), z)) | (~b(s(s(s(elem!1))), s(s(z))))), inference(lemma,lemma(discharge,[]))).
% 2.95/3.11 tff(11741,plain,
% 2.95/3.11 (~b(s(s(z)), s(s(elem!1)))),
% 2.95/3.11 inference(unit_resolution,[status(thm)],[11740, 11732, 96, 121, 10519])).
% 2.95/3.11 tff(11742,plain,
% 2.95/3.11 (s(s(z)) = s(s(elem!1))),
% 2.95/3.11 inference(unit_resolution,[status(thm)],[390, 11741, 10520])).
% 2.95/3.11 tff(11743,plain,
% 2.95/3.11 (s(elem!1) = s(z)),
% 2.95/3.11 inference(unit_resolution,[status(thm)],[43, 11742])).
% 2.95/3.11 tff(11744,plain,
% 2.95/3.11 (z = elem!1),
% 2.95/3.11 inference(unit_resolution,[status(thm)],[30, 11743])).
% 2.95/3.11 tff(11745,plain,
% 2.95/3.11 ((s(s(s(s(elem!1)))) = z) <=> (s(s(s(s(elem!1)))) = elem!1)),
% 2.95/3.11 inference(monotonicity,[status(thm)],[11744])).
% 2.95/3.11 tff(11746,plain,
% 2.95/3.11 ((s(s(s(s(elem!1)))) = z) <=> (elem!1 = s(s(s(s(elem!1)))))),
% 2.95/3.11 inference(transitivity,[status(thm)],[11745, 2287])).
% 2.95/3.11 tff(11747,plain,
% 2.95/3.11 ((~(s(s(s(s(elem!1)))) = z)) <=> (~(elem!1 = s(s(s(s(elem!1))))))),
% 2.95/3.11 inference(monotonicity,[status(thm)],[11746])).
% 2.95/3.11 tff(11748,plain,
% 2.95/3.11 (~(elem!1 = s(s(s(s(elem!1)))))),
% 2.95/3.11 inference(modus_ponens,[status(thm)],[626, 11747])).
% 2.95/3.11 tff(11749,plain,
% 2.95/3.11 (b(s(s(s(elem!1))), s(s(elem!1)))),
% 2.95/3.11 inference(unit_resolution,[status(thm)],[889, 10516, 51])).
% 2.95/3.11 tff(11750,plain,
% 2.95/3.11 ((s(s(s(s(elem!1)))) = s(s(z))) <=> (s(s(s(s(elem!1)))) = s(s(elem!1)))),
% 2.95/3.11 inference(monotonicity,[status(thm)],[11742])).
% 2.95/3.11 tff(11751,plain,
% 2.95/3.11 ((s(s(s(s(elem!1)))) = s(s(z))) <=> (s(s(elem!1)) = s(s(s(s(elem!1)))))),
% 2.95/3.11 inference(transitivity,[status(thm)],[11750, 123])).
% 2.95/3.11 tff(11752,plain,
% 2.95/3.11 ((s(s(s(s(elem!1)))) = s(s(z))) <=> (s(s(s(s(elem!1)))) = s(s(elem!1)))),
% 2.95/3.11 inference(transitivity,[status(thm)],[11751, 124])).
% 2.95/3.11 tff(11753,plain,
% 2.95/3.11 ((~(s(s(s(s(elem!1)))) = s(s(z)))) <=> (~(s(s(s(s(elem!1)))) = s(s(elem!1))))),
% 2.95/3.11 inference(monotonicity,[status(thm)],[11752])).
% 2.95/3.11 tff(11754,plain,
% 2.95/3.11 (~(s(s(s(s(elem!1)))) = s(s(elem!1)))),
% 2.95/3.11 inference(modus_ponens,[status(thm)],[733, 11753])).
% 2.95/3.11 tff(11755,plain,
% 2.95/3.11 ((~b(s(s(elem!1)), z)) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(z, s(s(elem!1)))) | (~b(s(s(s(elem!1))), z)) | r(s(s(z)), s(s(elem!1)))),
% 2.95/3.11 inference(unit_resolution,[status(thm)],[11553, 10450])).
% 2.95/3.11 tff(11756,plain,
% 2.95/3.11 (~b(s(s(elem!1)), z)),
% 2.95/3.11 inference(unit_resolution,[status(thm)],[11755, 10520, 121, 11749, 1820])).
% 2.95/3.11 tff(11757,plain,
% 2.95/3.11 (r(s(s(elem!1)), z)),
% 2.95/3.11 inference(unit_resolution,[status(thm)],[608, 11756])).
% 2.95/3.11 tff(11758,plain,
% 2.95/3.11 (r(s(s(elem!1)), elem!1)),
% 2.95/3.11 inference(unit_resolution,[status(thm)],[3398, 11744, 11757])).
% 2.95/3.11 tff(11759,plain,
% 2.95/3.11 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(s(elem!1)))) | (~r(s(s(elem!1)), elem!1)) | (~r(s(z), s(s(s(s(elem!1)))))) | (~r(s(s(s(s(elem!1)))), s(s(elem!1)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(z), s(s(elem!1)))) | (~r(s(s(elem!1)), elem!1)) | (~r(s(z), s(s(s(s(elem!1)))))) | (~r(s(s(s(s(elem!1)))), s(s(elem!1)))))),
% 2.95/3.11 inference(rewrite,[status(thm)],[])).
% 2.95/3.11 tff(11760,plain,
% 2.95/3.11 (((~r(s(s(elem!1)), elem!1)) | (~r(s(s(s(s(elem!1)))), s(s(elem!1)))) | (~r(s(z), s(s(elem!1)))) | (~r(s(z), s(s(s(s(elem!1))))))) <=> ((~r(s(z), s(s(elem!1)))) | (~r(s(s(elem!1)), elem!1)) | (~r(s(z), s(s(s(s(elem!1)))))) | (~r(s(s(s(s(elem!1)))), s(s(elem!1)))))),
% 2.95/3.11 inference(rewrite,[status(thm)],[])).
% 2.95/3.11 tff(11761,plain,
% 2.95/3.11 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(elem!1)), elem!1)) | (~r(s(s(s(s(elem!1)))), s(s(elem!1)))) | (~r(s(z), s(s(elem!1)))) | (~r(s(z), s(s(s(s(elem!1)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(s(elem!1)))) | (~r(s(s(elem!1)), elem!1)) | (~r(s(z), s(s(s(s(elem!1)))))) | (~r(s(s(s(s(elem!1)))), s(s(elem!1))))))),
% 2.95/3.11 inference(monotonicity,[status(thm)],[11760])).
% 2.95/3.11 tff(11762,plain,
% 2.95/3.11 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(elem!1)), elem!1)) | (~r(s(s(s(s(elem!1)))), s(s(elem!1)))) | (~r(s(z), s(s(elem!1)))) | (~r(s(z), s(s(s(s(elem!1)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(z), s(s(elem!1)))) | (~r(s(s(elem!1)), elem!1)) | (~r(s(z), s(s(s(s(elem!1)))))) | (~r(s(s(s(s(elem!1)))), s(s(elem!1)))))),
% 2.95/3.11 inference(transitivity,[status(thm)],[11761, 11759])).
% 2.95/3.11 tff(11763,plain,
% 2.95/3.11 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(elem!1)), elem!1)) | (~r(s(s(s(s(elem!1)))), s(s(elem!1)))) | (~r(s(z), s(s(elem!1)))) | (~r(s(z), s(s(s(s(elem!1)))))))),
% 2.95/3.11 inference(quant_inst,[status(thm)],[])).
% 2.95/3.11 tff(11764,plain,
% 2.95/3.11 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(z), s(s(elem!1)))) | (~r(s(s(elem!1)), elem!1)) | (~r(s(z), s(s(s(s(elem!1)))))) | (~r(s(s(s(s(elem!1)))), s(s(elem!1))))),
% 2.95/3.11 inference(modus_ponens,[status(thm)],[11763, 11762])).
% 2.95/3.11 tff(11765,plain,
% 2.95/3.11 (~r(s(z), s(s(s(s(elem!1)))))),
% 2.95/3.11 inference(unit_resolution,[status(thm)],[11764, 197, 311, 768, 3408])).
% 2.95/3.11 tff(11766,plain,
% 2.95/3.11 (b(s(z), s(s(s(s(elem!1)))))),
% 2.95/3.11 inference(unit_resolution,[status(thm)],[681, 11765])).
% 2.95/3.11 tff(11767,plain,
% 2.95/3.11 ($false),
% 2.95/3.11 inference(unit_resolution,[status(thm)],[2014, 11766, 3424, 96, 839, 310])).
% 2.95/3.11 tff(11768,plain,((~r(s(s(s(s(elem!1)))), s(s(elem!1)))) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(s(elem!1)), s(z))) | (~r(s(z), s(s(elem!1)))) | (~r(s(s(elem!1)), elem!1))), inference(lemma,lemma(discharge,[]))).
% 2.95/3.11 tff(11769,plain,
% 2.95/3.11 (~r(s(s(s(s(elem!1)))), s(s(elem!1)))),
% 2.95/3.11 inference(unit_resolution,[status(thm)],[11768, 11749, 96, 11732, 311, 11758])).
% 2.95/3.11 tff(11770,plain,
% 2.95/3.11 (b(s(s(s(s(elem!1)))), s(s(elem!1)))),
% 2.95/3.11 inference(unit_resolution,[status(thm)],[813, 11769, 11754])).
% 2.95/3.11 tff(11771,plain,
% 2.95/3.11 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(s(s(s(elem!1)))), s(s(elem!1)))) | (~b(s(s(s(elem!1))), z)) | (~b(s(s(s(elem!1))), s(z))) | (~b(z, s(z))) | (~b(s(z), s(s(s(s(elem!1)))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(s(s(s(elem!1)))), s(s(elem!1)))) | (~b(s(s(s(elem!1))), z)) | (~b(s(s(s(elem!1))), s(z))) | (~b(z, s(z))) | (~b(s(z), s(s(s(s(elem!1)))))))),
% 2.95/3.11 inference(rewrite,[status(thm)],[])).
% 2.95/3.11 tff(11772,plain,
% 2.95/3.11 (((~b(s(s(s(s(elem!1)))), s(s(elem!1)))) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(z), s(s(s(s(elem!1)))))) | (~b(z, s(z))) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(s(s(elem!1))), z))) <=> ((~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(s(s(s(elem!1)))), s(s(elem!1)))) | (~b(s(s(s(elem!1))), z)) | (~b(s(s(s(elem!1))), s(z))) | (~b(z, s(z))) | (~b(s(z), s(s(s(s(elem!1)))))))),
% 2.95/3.11 inference(rewrite,[status(thm)],[])).
% 2.95/3.11 tff(11773,plain,
% 2.95/3.11 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(elem!1)))), s(s(elem!1)))) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(z), s(s(s(s(elem!1)))))) | (~b(z, s(z))) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(s(s(elem!1))), z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(s(s(s(elem!1)))), s(s(elem!1)))) | (~b(s(s(s(elem!1))), z)) | (~b(s(s(s(elem!1))), s(z))) | (~b(z, s(z))) | (~b(s(z), s(s(s(s(elem!1))))))))),
% 2.95/3.11 inference(monotonicity,[status(thm)],[11772])).
% 2.95/3.11 tff(11774,plain,
% 2.95/3.11 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(elem!1)))), s(s(elem!1)))) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(z), s(s(s(s(elem!1)))))) | (~b(z, s(z))) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(s(s(elem!1))), z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(s(s(s(elem!1)))), s(s(elem!1)))) | (~b(s(s(s(elem!1))), z)) | (~b(s(s(s(elem!1))), s(z))) | (~b(z, s(z))) | (~b(s(z), s(s(s(s(elem!1)))))))),
% 2.95/3.12 inference(transitivity,[status(thm)],[11773, 11771])).
% 2.95/3.12 tff(11775,plain,
% 2.95/3.12 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(elem!1)))), s(s(elem!1)))) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(z), s(s(s(s(elem!1)))))) | (~b(z, s(z))) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(s(s(elem!1))), z)))),
% 2.95/3.12 inference(quant_inst,[status(thm)],[])).
% 2.95/3.12 tff(11776,plain,
% 2.95/3.12 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(s(s(s(elem!1)))), s(s(elem!1)))) | (~b(s(s(s(elem!1))), z)) | (~b(s(s(s(elem!1))), s(z))) | (~b(z, s(z))) | (~b(s(z), s(s(s(s(elem!1))))))),
% 2.95/3.12 inference(modus_ponens,[status(thm)],[11775, 11774])).
% 2.95/3.12 tff(11777,plain,
% 2.95/3.12 ($false),
% 2.95/3.12 inference(unit_resolution,[status(thm)],[11776, 166, 839, 96, 118, 121, 1327, 3457])).
% 2.95/3.12 tff(11778,plain,((~b(s(s(s(s(elem!1)))), s(s(elem!1)))) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(s(s(elem!1))), s(z))) | (~b(z, s(z))) | (~b(s(s(s(elem!1))), z)) | (~b(s(z), s(s(s(s(elem!1))))))), inference(lemma,lemma(discharge,[]))).
% 2.95/3.12 tff(11779,plain,
% 2.95/3.12 (~b(s(z), s(s(s(s(elem!1)))))),
% 2.95/3.12 inference(unit_resolution,[status(thm)],[11778, 11770, 96, 121, 118, 11749])).
% 2.95/3.12 tff(11780,plain,
% 2.95/3.12 (r(s(z), s(s(s(s(elem!1)))))),
% 2.95/3.12 inference(unit_resolution,[status(thm)],[681, 11779])).
% 2.95/3.12 tff(11781,plain,
% 2.95/3.12 (r(s(z), z) <=> r(s(z), elem!1)),
% 2.95/3.12 inference(monotonicity,[status(thm)],[11744])).
% 2.95/3.12 tff(11782,plain,
% 2.95/3.12 (r(s(z), elem!1)),
% 2.95/3.12 inference(modus_ponens,[status(thm)],[97, 11781])).
% 2.95/3.12 tff(11783,plain,
% 2.95/3.12 ((~(s(s(s(s(elem!1)))) = z)) <=> (~(s(s(s(s(elem!1)))) = elem!1))),
% 2.95/3.12 inference(monotonicity,[status(thm)],[11745])).
% 2.95/3.12 tff(11784,plain,
% 2.95/3.12 (~(s(s(s(s(elem!1)))) = elem!1)),
% 2.95/3.12 inference(modus_ponens,[status(thm)],[626, 11783])).
% 2.95/3.12 tff(11785,plain,
% 2.95/3.12 (b(s(s(s(elem!1))), elem!1)),
% 2.95/3.12 inference(unit_resolution,[status(thm)],[634, 11744, 121])).
% 2.95/3.12 tff(11786,plain,
% 2.95/3.12 (b(z, s(s(s(elem!1)))) <=> b(elem!1, s(s(s(elem!1))))),
% 2.95/3.12 inference(monotonicity,[status(thm)],[11744])).
% 2.95/3.12 tff(11787,plain,
% 2.95/3.12 (b(elem!1, s(s(s(elem!1))))),
% 2.95/3.12 inference(modus_ponens,[status(thm)],[240, 11786])).
% 2.95/3.12 tff(11788,plain,
% 2.95/3.12 ((~(s(s(s(s(elem!1)))) = s(s(z)))) <=> (~(s(s(elem!1)) = s(s(s(s(elem!1))))))),
% 2.95/3.12 inference(monotonicity,[status(thm)],[11751])).
% 2.95/3.12 tff(11789,plain,
% 2.95/3.12 (~(s(s(elem!1)) = s(s(s(s(elem!1)))))),
% 2.95/3.12 inference(modus_ponens,[status(thm)],[733, 11788])).
% 2.95/3.12 tff(11790,plain,
% 2.95/3.12 (elem!1 = z),
% 2.95/3.12 inference(symmetry,[status(thm)],[11744])).
% 2.95/3.12 tff(11791,plain,
% 2.95/3.12 (b(elem!1, s(s(elem!1))) <=> b(z, s(s(elem!1)))),
% 2.95/3.12 inference(monotonicity,[status(thm)],[11790])).
% 2.95/3.12 tff(11792,plain,
% 2.95/3.12 (b(z, s(s(elem!1))) <=> b(elem!1, s(s(elem!1)))),
% 2.95/3.12 inference(symmetry,[status(thm)],[11791])).
% 2.95/3.12 tff(11793,plain,
% 2.95/3.12 (b(elem!1, s(s(elem!1)))),
% 2.95/3.12 inference(modus_ponens,[status(thm)],[1820, 11792])).
% 2.95/3.12 tff(11794,plain,
% 2.95/3.12 ($false),
% 2.95/3.12 inference(unit_resolution,[status(thm)],[10714, 166, 839, 1046, 10960, 3457, 641])).
% 2.95/3.12 tff(11795,plain,((~b(s(s(s(s(elem!1)))), s(s(elem!1)))) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(s(elem!1)), s(s(s(s(elem!1)))))) | (~b(elem!1, s(s(elem!1)))) | (~b(s(s(s(elem!1))), elem!1))), inference(lemma,lemma(discharge,[]))).
% 2.95/3.12 tff(11796,plain,
% 2.95/3.12 (~b(s(s(elem!1)), s(s(s(s(elem!1)))))),
% 2.95/3.12 inference(unit_resolution,[status(thm)],[11795, 11770, 11749, 11793, 11785])).
% 2.95/3.12 tff(11797,plain,
% 2.95/3.12 (r(s(s(elem!1)), s(s(s(s(elem!1)))))),
% 2.95/3.12 inference(unit_resolution,[status(thm)],[827, 11796, 11789])).
% 2.95/3.12 tff(11798,plain,
% 2.95/3.12 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(s(elem!1)))) | (~r(s(z), s(s(s(s(elem!1)))))) | (~r(s(s(s(s(elem!1)))), s(z))) | (~r(s(s(elem!1)), s(s(s(s(elem!1)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(z), s(s(elem!1)))) | (~r(s(z), s(s(s(s(elem!1)))))) | (~r(s(s(s(s(elem!1)))), s(z))) | (~r(s(s(elem!1)), s(s(s(s(elem!1)))))))),
% 2.95/3.12 inference(rewrite,[status(thm)],[])).
% 2.95/3.12 tff(11799,plain,
% 2.95/3.12 (((~r(s(s(s(s(elem!1)))), s(z))) | (~r(s(s(elem!1)), s(s(s(s(elem!1)))))) | (~r(s(z), s(s(s(s(elem!1)))))) | (~r(s(z), s(s(elem!1))))) <=> ((~r(s(z), s(s(elem!1)))) | (~r(s(z), s(s(s(s(elem!1)))))) | (~r(s(s(s(s(elem!1)))), s(z))) | (~r(s(s(elem!1)), s(s(s(s(elem!1)))))))),
% 2.95/3.12 inference(rewrite,[status(thm)],[])).
% 2.95/3.12 tff(11800,plain,
% 2.95/3.12 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(elem!1)))), s(z))) | (~r(s(s(elem!1)), s(s(s(s(elem!1)))))) | (~r(s(z), s(s(s(s(elem!1)))))) | (~r(s(z), s(s(elem!1)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(s(elem!1)))) | (~r(s(z), s(s(s(s(elem!1)))))) | (~r(s(s(s(s(elem!1)))), s(z))) | (~r(s(s(elem!1)), s(s(s(s(elem!1))))))))),
% 2.95/3.12 inference(monotonicity,[status(thm)],[11799])).
% 2.95/3.12 tff(11801,plain,
% 2.95/3.12 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(elem!1)))), s(z))) | (~r(s(s(elem!1)), s(s(s(s(elem!1)))))) | (~r(s(z), s(s(s(s(elem!1)))))) | (~r(s(z), s(s(elem!1)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(z), s(s(elem!1)))) | (~r(s(z), s(s(s(s(elem!1)))))) | (~r(s(s(s(s(elem!1)))), s(z))) | (~r(s(s(elem!1)), s(s(s(s(elem!1)))))))),
% 2.95/3.12 inference(transitivity,[status(thm)],[11800, 11798])).
% 2.95/3.12 tff(11802,plain,
% 2.95/3.12 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(elem!1)))), s(z))) | (~r(s(s(elem!1)), s(s(s(s(elem!1)))))) | (~r(s(z), s(s(s(s(elem!1)))))) | (~r(s(z), s(s(elem!1)))))),
% 2.95/3.12 inference(quant_inst,[status(thm)],[])).
% 2.95/3.12 tff(11803,plain,
% 2.95/3.12 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(z), s(s(elem!1)))) | (~r(s(z), s(s(s(s(elem!1)))))) | (~r(s(s(s(s(elem!1)))), s(z))) | (~r(s(s(elem!1)), s(s(s(s(elem!1))))))),
% 2.95/3.12 inference(modus_ponens,[status(thm)],[11802, 11801])).
% 2.95/3.12 tff(11804,plain,
% 2.95/3.12 ($false),
% 2.95/3.12 inference(unit_resolution,[status(thm)],[11803, 197, 311, 561, 700, 699])).
% 2.95/3.12 tff(11805,plain,((~r(s(s(s(s(elem!1)))), s(z))) | (~r(s(z), s(s(elem!1)))) | (~r(s(s(elem!1)), s(s(s(s(elem!1)))))) | (~r(s(z), s(s(s(s(elem!1))))))), inference(lemma,lemma(discharge,[]))).
% 2.95/3.12 tff(11806,plain,
% 2.95/3.12 (~r(s(s(s(s(elem!1)))), s(z))),
% 2.95/3.12 inference(unit_resolution,[status(thm)],[11805, 11797, 311, 11780])).
% 2.95/3.12 tff(11807,plain,
% 2.95/3.12 (b(s(s(s(s(elem!1)))), s(z))),
% 2.95/3.12 inference(unit_resolution,[status(thm)],[661, 11806])).
% 2.95/3.12 tff(11808,plain,
% 2.95/3.12 (~b(s(s(s(s(elem!1)))), s(s(s(elem!1))))),
% 2.95/3.12 inference(unit_resolution,[status(thm)],[10656, 11807, 96, 11742, 11787, 11782, 11780, 11785])).
% 2.95/3.12 tff(11809,plain,
% 2.95/3.12 (r(s(s(s(s(elem!1)))), s(s(s(elem!1))))),
% 2.95/3.12 inference(unit_resolution,[status(thm)],[1065, 11808, 364])).
% 2.95/3.12 tff(11810,plain,
% 2.95/3.12 (~r(s(s(s(elem!1))), s(s(s(s(elem!1)))))),
% 2.95/3.12 inference(unit_resolution,[status(thm)],[2125, 11809, 119, 11780])).
% 2.95/3.12 tff(11811,plain,
% 2.95/3.12 (b(s(s(s(elem!1))), s(s(s(s(elem!1)))))),
% 2.95/3.12 inference(unit_resolution,[status(thm)],[696, 11810, 358])).
% 2.95/3.12 tff(11812,plain,
% 2.95/3.12 (~b(s(s(s(s(elem!1)))), elem!1)),
% 2.95/3.12 inference(unit_resolution,[status(thm)],[10668, 11811, 11749, 11787, 11785])).
% 2.95/3.12 tff(11813,plain,
% 2.95/3.12 (r(s(s(s(s(elem!1)))), elem!1)),
% 2.95/3.12 inference(unit_resolution,[status(thm)],[719, 11812, 11784])).
% 2.95/3.12 tff(11814,plain,
% 2.95/3.12 (~r(elem!1, s(s(s(s(elem!1)))))),
% 2.95/3.12 inference(unit_resolution,[status(thm)],[10678, 11813, 11782, 11780])).
% 2.95/3.12 tff(11815,plain,
% 2.95/3.12 (b(elem!1, s(s(s(s(elem!1)))))),
% 2.95/3.12 inference(unit_resolution,[status(thm)],[2427, 11814, 11748])).
% 2.95/3.12 tff(11816,plain,
% 2.95/3.12 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(elem!1)))), s(s(elem!1)))) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(s(elem!1)), s(z))) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(s(s(elem!1))), s(s(s(s(elem!1)))))) | (~b(elem!1, s(s(s(s(elem!1)))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(elem!1)))), s(s(elem!1)))) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(s(elem!1)), s(z))) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(s(s(elem!1))), s(s(s(s(elem!1)))))) | (~b(elem!1, s(s(s(s(elem!1)))))))),
% 2.95/3.12 inference(rewrite,[status(thm)],[])).
% 2.95/3.12 tff(11817,plain,
% 2.95/3.12 (((~b(s(s(elem!1)), s(z))) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(s(s(s(elem!1)))), s(s(elem!1)))) | (~b(elem!1, s(s(s(s(elem!1)))))) | (~b(s(s(s(elem!1))), s(s(s(s(elem!1)))))) | (~b(s(s(s(elem!1))), elem!1))) <=> ((~b(s(s(s(s(elem!1)))), s(s(elem!1)))) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(s(elem!1)), s(z))) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(s(s(elem!1))), s(s(s(s(elem!1)))))) | (~b(elem!1, s(s(s(s(elem!1)))))))),
% 2.95/3.12 inference(rewrite,[status(thm)],[])).
% 2.95/3.12 tff(11818,plain,
% 2.95/3.12 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), s(z))) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(s(s(s(elem!1)))), s(s(elem!1)))) | (~b(elem!1, s(s(s(s(elem!1)))))) | (~b(s(s(s(elem!1))), s(s(s(s(elem!1)))))) | (~b(s(s(s(elem!1))), elem!1)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(elem!1)))), s(s(elem!1)))) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(s(elem!1)), s(z))) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(s(s(elem!1))), s(s(s(s(elem!1)))))) | (~b(elem!1, s(s(s(s(elem!1))))))))),
% 2.95/3.12 inference(monotonicity,[status(thm)],[11817])).
% 2.95/3.12 tff(11819,plain,
% 2.95/3.12 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), s(z))) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(s(s(s(elem!1)))), s(s(elem!1)))) | (~b(elem!1, s(s(s(s(elem!1)))))) | (~b(s(s(s(elem!1))), s(s(s(s(elem!1)))))) | (~b(s(s(s(elem!1))), elem!1)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(elem!1)))), s(s(elem!1)))) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(s(elem!1)), s(z))) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(s(s(elem!1))), s(s(s(s(elem!1)))))) | (~b(elem!1, s(s(s(s(elem!1)))))))),
% 2.95/3.12 inference(transitivity,[status(thm)],[11818, 11816])).
% 2.95/3.12 tff(11820,plain,
% 2.95/3.12 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), s(z))) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(s(s(s(elem!1)))), s(s(elem!1)))) | (~b(elem!1, s(s(s(s(elem!1)))))) | (~b(s(s(s(elem!1))), s(s(s(s(elem!1)))))) | (~b(s(s(s(elem!1))), elem!1)))),
% 2.95/3.12 inference(quant_inst,[status(thm)],[])).
% 2.95/3.12 tff(11821,plain,
% 2.95/3.12 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(elem!1)))), s(s(elem!1)))) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(s(elem!1)), s(z))) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(s(s(elem!1))), s(s(s(s(elem!1)))))) | (~b(elem!1, s(s(s(s(elem!1))))))),
% 2.95/3.12 inference(modus_ponens,[status(thm)],[11820, 11819])).
% 2.95/3.12 tff(11822,plain,
% 2.95/3.12 ($false),
% 2.95/3.12 inference(unit_resolution,[status(thm)],[11821, 166, 96, 11732, 11770, 11785, 11811, 11815])).
% 2.95/3.12 tff(11823,plain,((s(s(elem!1)) = s(s(s(elem!1)))) | (~b(s(s(s(elem!1))), s(z))) | (~r(s(z), s(s(s(elem!1))))) | (~r(s(z), s(s(elem!1)))) | (~b(s(s(s(elem!1))), z)) | (~b(z, s(z))) | (~r(s(z), z)) | (~b(z, s(s(elem!1)))) | (~b(z, s(s(s(elem!1))))) | r(z, elem!1)), inference(lemma,lemma(discharge,[]))).
% 2.95/3.12 tff(11824,plain,
% 2.95/3.12 (s(s(elem!1)) = s(s(s(elem!1)))),
% 2.95/3.12 inference(unit_resolution,[status(thm)],[11823, 10500, 119, 311, 95, 118, 97, 96, 10498, 10488])).
% 2.95/3.12 tff(11825,plain,
% 2.95/3.12 (s(s(s(elem!1))) = s(s(elem!1))),
% 2.95/3.12 inference(symmetry,[status(thm)],[11824])).
% 2.95/3.12 tff(11826,plain,
% 2.95/3.12 (s(s(s(s(elem!1)))) = s(s(s(elem!1)))),
% 2.95/3.12 inference(monotonicity,[status(thm)],[11825])).
% 2.95/3.12 tff(11827,plain,
% 2.95/3.12 (b(s(s(s(s(elem!1)))), s(s(z))) <=> b(s(s(s(elem!1))), s(s(z)))),
% 2.95/3.12 inference(monotonicity,[status(thm)],[11826])).
% 2.95/3.12 tff(11828,plain,
% 2.95/3.12 (r(s(z), s(s(s(s(elem!1))))) <=> r(s(z), s(s(s(elem!1))))),
% 2.95/3.12 inference(monotonicity,[status(thm)],[11826])).
% 2.95/3.12 tff(11829,plain,
% 2.95/3.12 (r(s(z), s(s(s(elem!1)))) <=> r(s(z), s(s(s(s(elem!1)))))),
% 2.95/3.12 inference(symmetry,[status(thm)],[11828])).
% 2.95/3.12 tff(11830,plain,
% 2.95/3.12 (r(s(z), s(s(s(s(elem!1)))))),
% 2.95/3.12 inference(modus_ponens,[status(thm)],[119, 11829])).
% 2.95/3.12 tff(11831,plain,
% 2.95/3.12 (r(s(s(z)), s(s(s(s(elem!1))))) <=> r(s(s(z)), s(s(s(elem!1))))),
% 2.95/3.12 inference(monotonicity,[status(thm)],[11826])).
% 2.95/3.12 tff(11832,plain,
% 2.95/3.12 (r(s(s(z)), s(s(s(elem!1)))) <=> r(s(s(z)), s(s(s(s(elem!1)))))),
% 2.95/3.12 inference(symmetry,[status(thm)],[11831])).
% 2.95/3.12 tff(11833,plain,
% 2.95/3.12 (b(s(s(z)), s(s(elem!1))) <=> b(s(s(z)), s(s(s(elem!1))))),
% 2.95/3.12 inference(monotonicity,[status(thm)],[11824])).
% 2.95/3.12 tff(11834,plain,
% 2.95/3.12 ((~b(s(s(z)), s(s(elem!1)))) <=> (~b(s(s(z)), s(s(s(elem!1)))))),
% 2.95/3.12 inference(monotonicity,[status(thm)],[11833])).
% 2.95/3.12 tff(11835,plain,
% 2.95/3.12 (~r(s(s(elem!1)), z)),
% 2.95/3.12 inference(unit_resolution,[status(thm)],[2974, 11824, 86])).
% 2.95/3.12 tff(11836,plain,
% 2.95/3.12 (b(s(s(elem!1)), z)),
% 2.95/3.12 inference(unit_resolution,[status(thm)],[608, 11835])).
% 2.95/3.12 tff(11837,plain,
% 2.95/3.12 ((~b(s(s(z)), s(s(elem!1)))) | (~b(z, s(s(elem!1)))) | (~b(s(s(elem!1)), z))),
% 2.95/3.12 inference(unit_resolution,[status(thm)],[11110, 10450])).
% 2.95/3.12 tff(11838,plain,
% 2.95/3.12 (~b(s(s(z)), s(s(elem!1)))),
% 2.95/3.12 inference(unit_resolution,[status(thm)],[11837, 11836, 10500])).
% 2.95/3.12 tff(11839,plain,
% 2.95/3.12 (~b(s(s(z)), s(s(s(elem!1))))),
% 2.95/3.12 inference(modus_ponens,[status(thm)],[11838, 11834])).
% 2.95/3.12 tff(11840,plain,
% 2.95/3.12 (r(s(s(z)), s(s(s(elem!1))))),
% 2.95/3.12 inference(unit_resolution,[status(thm)],[279, 11839])).
% 2.95/3.12 tff(11841,plain,
% 2.95/3.12 (r(s(s(z)), s(s(s(s(elem!1)))))),
% 2.95/3.12 inference(modus_ponens,[status(thm)],[11840, 11832])).
% 2.95/3.12 tff(11842,assumption,(r(s(s(z)), s(s(s(s(elem!1)))))), introduced(assumption)).
% 2.95/3.12 tff(11843,plain,
% 2.95/3.12 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(s(z)))) | (~r(s(z), s(s(s(s(elem!1)))))) | (~r(s(s(s(s(elem!1)))), s(s(z)))) | (~r(s(s(z)), s(s(s(s(elem!1)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(z), s(s(z)))) | (~r(s(z), s(s(s(s(elem!1)))))) | (~r(s(s(s(s(elem!1)))), s(s(z)))) | (~r(s(s(z)), s(s(s(s(elem!1)))))))),
% 2.95/3.12 inference(rewrite,[status(thm)],[])).
% 2.95/3.12 tff(11844,plain,
% 2.95/3.12 (((~r(s(s(s(s(elem!1)))), s(s(z)))) | (~r(s(s(z)), s(s(s(s(elem!1)))))) | (~r(s(z), s(s(s(s(elem!1)))))) | (~r(s(z), s(s(z))))) <=> ((~r(s(z), s(s(z)))) | (~r(s(z), s(s(s(s(elem!1)))))) | (~r(s(s(s(s(elem!1)))), s(s(z)))) | (~r(s(s(z)), s(s(s(s(elem!1)))))))),
% 2.95/3.12 inference(rewrite,[status(thm)],[])).
% 2.95/3.12 tff(11845,plain,
% 2.95/3.12 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(elem!1)))), s(s(z)))) | (~r(s(s(z)), s(s(s(s(elem!1)))))) | (~r(s(z), s(s(s(s(elem!1)))))) | (~r(s(z), s(s(z)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(s(z)))) | (~r(s(z), s(s(s(s(elem!1)))))) | (~r(s(s(s(s(elem!1)))), s(s(z)))) | (~r(s(s(z)), s(s(s(s(elem!1))))))))),
% 2.95/3.12 inference(monotonicity,[status(thm)],[11844])).
% 2.95/3.12 tff(11846,plain,
% 2.95/3.12 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(elem!1)))), s(s(z)))) | (~r(s(s(z)), s(s(s(s(elem!1)))))) | (~r(s(z), s(s(s(s(elem!1)))))) | (~r(s(z), s(s(z)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(z), s(s(z)))) | (~r(s(z), s(s(s(s(elem!1)))))) | (~r(s(s(s(s(elem!1)))), s(s(z)))) | (~r(s(s(z)), s(s(s(s(elem!1)))))))),
% 2.95/3.12 inference(transitivity,[status(thm)],[11845, 11843])).
% 2.95/3.12 tff(11847,plain,
% 2.95/3.12 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(elem!1)))), s(s(z)))) | (~r(s(s(z)), s(s(s(s(elem!1)))))) | (~r(s(z), s(s(s(s(elem!1)))))) | (~r(s(z), s(s(z)))))),
% 2.95/3.12 inference(quant_inst,[status(thm)],[])).
% 2.95/3.12 tff(11848,plain,
% 2.95/3.12 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(z), s(s(z)))) | (~r(s(z), s(s(s(s(elem!1)))))) | (~r(s(s(s(s(elem!1)))), s(s(z)))) | (~r(s(s(z)), s(s(s(s(elem!1))))))),
% 2.95/3.12 inference(modus_ponens,[status(thm)],[11847, 11846])).
% 2.95/3.12 tff(11849,plain,
% 2.95/3.12 ($false),
% 2.95/3.12 inference(unit_resolution,[status(thm)],[11848, 197, 2168, 120, 699, 11842])).
% 2.95/3.12 tff(11850,plain,((~r(s(s(z)), s(s(s(s(elem!1)))))) | (~r(s(s(s(s(elem!1)))), s(s(z)))) | (~r(s(z), s(s(z)))) | (~r(s(z), s(s(s(s(elem!1))))))), inference(lemma,lemma(discharge,[]))).
% 2.95/3.12 tff(11851,plain,
% 2.95/3.12 (~r(s(s(s(s(elem!1)))), s(s(z)))),
% 2.95/3.12 inference(unit_resolution,[status(thm)],[11850, 11841, 120, 11830])).
% 2.95/3.12 tff(11852,plain,
% 2.95/3.12 (b(s(s(s(s(elem!1)))), s(s(z)))),
% 2.95/3.12 inference(unit_resolution,[status(thm)],[1299, 11851])).
% 2.95/3.12 tff(11853,plain,
% 2.95/3.12 (b(s(s(s(elem!1))), s(s(z)))),
% 2.95/3.12 inference(modus_ponens,[status(thm)],[11852, 11827])).
% 2.95/3.12 tff(11854,plain,
% 2.95/3.12 ((s(s(s(s(elem!1)))) = s(s(s(z)))) <=> (s(s(s(elem!1))) = s(s(s(z))))),
% 2.95/3.12 inference(monotonicity,[status(thm)],[11826])).
% 2.95/3.12 tff(11855,plain,
% 2.95/3.12 ((~(s(s(s(s(elem!1)))) = s(s(s(z))))) <=> (~(s(s(s(elem!1))) = s(s(s(z)))))),
% 2.95/3.12 inference(monotonicity,[status(thm)],[11854])).
% 2.95/3.12 tff(11856,plain,
% 2.95/3.12 (~(s(s(s(elem!1))) = s(s(s(z))))),
% 2.95/3.12 inference(modus_ponens,[status(thm)],[5112, 11855])).
% 2.95/3.12 tff(11857,plain,
% 2.95/3.12 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), s(s(s(z))))) | (~r(s(z), s(s(s(elem!1))))) | (~r(s(z), s(s(z)))) | (~r(s(s(z)), s(s(s(elem!1))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(elem!1))), s(s(s(z))))) | (~r(s(z), s(s(s(elem!1))))) | (~r(s(z), s(s(z)))) | (~r(s(s(z)), s(s(s(elem!1))))))),
% 2.95/3.12 inference(rewrite,[status(thm)],[])).
% 2.95/3.12 tff(11858,plain,
% 2.95/3.12 (((~r(s(s(s(elem!1))), s(s(s(z))))) | (~r(s(s(z)), s(s(s(elem!1))))) | (~r(s(z), s(s(s(elem!1))))) | (~r(s(z), s(s(z))))) <=> ((~r(s(s(s(elem!1))), s(s(s(z))))) | (~r(s(z), s(s(s(elem!1))))) | (~r(s(z), s(s(z)))) | (~r(s(s(z)), s(s(s(elem!1))))))),
% 2.95/3.12 inference(rewrite,[status(thm)],[])).
% 2.95/3.12 tff(11859,plain,
% 2.95/3.12 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), s(s(s(z))))) | (~r(s(s(z)), s(s(s(elem!1))))) | (~r(s(z), s(s(s(elem!1))))) | (~r(s(z), s(s(z)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), s(s(s(z))))) | (~r(s(z), s(s(s(elem!1))))) | (~r(s(z), s(s(z)))) | (~r(s(s(z)), s(s(s(elem!1)))))))),
% 2.95/3.12 inference(monotonicity,[status(thm)],[11858])).
% 2.95/3.12 tff(11860,plain,
% 2.95/3.12 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), s(s(s(z))))) | (~r(s(s(z)), s(s(s(elem!1))))) | (~r(s(z), s(s(s(elem!1))))) | (~r(s(z), s(s(z)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(elem!1))), s(s(s(z))))) | (~r(s(z), s(s(s(elem!1))))) | (~r(s(z), s(s(z)))) | (~r(s(s(z)), s(s(s(elem!1))))))),
% 2.95/3.12 inference(transitivity,[status(thm)],[11859, 11857])).
% 2.95/3.12 tff(11861,plain,
% 2.95/3.12 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), s(s(s(z))))) | (~r(s(s(z)), s(s(s(elem!1))))) | (~r(s(z), s(s(s(elem!1))))) | (~r(s(z), s(s(z)))))),
% 2.95/3.13 inference(quant_inst,[status(thm)],[])).
% 2.95/3.13 tff(11862,plain,
% 2.95/3.13 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(elem!1))), s(s(s(z))))) | (~r(s(z), s(s(s(elem!1))))) | (~r(s(z), s(s(z)))) | (~r(s(s(z)), s(s(s(elem!1)))))),
% 2.95/3.13 inference(modus_ponens,[status(thm)],[11861, 11860])).
% 2.95/3.13 tff(11863,plain,
% 2.95/3.13 ($false),
% 2.95/3.13 inference(unit_resolution,[status(thm)],[11862, 197, 120, 119, 281, 3183])).
% 2.95/3.13 tff(11864,plain,((~r(s(s(s(elem!1))), s(s(s(z))))) | (~r(s(z), s(s(z)))) | (~r(s(z), s(s(s(elem!1))))) | (~r(s(s(z)), s(s(s(elem!1)))))), inference(lemma,lemma(discharge,[]))).
% 2.95/3.13 tff(11865,plain,
% 2.95/3.13 (~r(s(s(s(elem!1))), s(s(s(z))))),
% 2.95/3.13 inference(unit_resolution,[status(thm)],[11864, 120, 119, 11840])).
% 2.95/3.13 tff(11866,plain,
% 2.95/3.13 (b(s(s(s(elem!1))), s(s(s(z))))),
% 2.95/3.13 inference(unit_resolution,[status(thm)],[3574, 11865, 11856])).
% 2.95/3.13 tff(11867,plain,
% 2.95/3.13 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), z)) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(s(s(z))), z)) | (~b(s(s(s(elem!1))), s(s(s(z))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), z)) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(s(s(z))), z)) | (~b(s(s(s(elem!1))), s(s(s(z))))))),
% 2.95/3.13 inference(rewrite,[status(thm)],[])).
% 2.95/3.13 tff(11868,plain,
% 2.95/3.13 (((~b(s(s(s(elem!1))), s(z))) | (~b(s(s(s(elem!1))), s(z))) | (~b(z, s(s(s(elem!1))))) | (~b(s(s(s(z))), z)) | (~b(s(s(s(elem!1))), z)) | (~b(s(s(s(elem!1))), s(s(s(z)))))) <=> ((~b(z, s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), z)) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(s(s(z))), z)) | (~b(s(s(s(elem!1))), s(s(s(z))))))),
% 2.95/3.13 inference(rewrite,[status(thm)],[])).
% 2.95/3.13 tff(11869,plain,
% 2.95/3.13 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), s(z))) | (~b(s(s(s(elem!1))), s(z))) | (~b(z, s(s(s(elem!1))))) | (~b(s(s(s(z))), z)) | (~b(s(s(s(elem!1))), z)) | (~b(s(s(s(elem!1))), s(s(s(z))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), z)) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(s(s(z))), z)) | (~b(s(s(s(elem!1))), s(s(s(z)))))))),
% 2.95/3.13 inference(monotonicity,[status(thm)],[11868])).
% 2.95/3.13 tff(11870,plain,
% 2.95/3.13 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), s(z))) | (~b(s(s(s(elem!1))), s(z))) | (~b(z, s(s(s(elem!1))))) | (~b(s(s(s(z))), z)) | (~b(s(s(s(elem!1))), z)) | (~b(s(s(s(elem!1))), s(s(s(z))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), z)) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(s(s(z))), z)) | (~b(s(s(s(elem!1))), s(s(s(z))))))),
% 2.95/3.13 inference(transitivity,[status(thm)],[11869, 11867])).
% 2.95/3.13 tff(11871,plain,
% 2.95/3.13 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), s(z))) | (~b(s(s(s(elem!1))), s(z))) | (~b(z, s(s(s(elem!1))))) | (~b(s(s(s(z))), z)) | (~b(s(s(s(elem!1))), z)) | (~b(s(s(s(elem!1))), s(s(s(z))))))),
% 2.95/3.13 inference(quant_inst,[status(thm)],[])).
% 2.95/3.13 tff(11872,plain,
% 2.95/3.13 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), z)) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(s(s(z))), z)) | (~b(s(s(s(elem!1))), s(s(s(z)))))),
% 2.95/3.13 inference(modus_ponens,[status(thm)],[11871, 11870])).
% 2.95/3.13 tff(11873,plain,
% 2.95/3.13 ($false),
% 2.95/3.13 inference(unit_resolution,[status(thm)],[11872, 166, 240, 96, 121, 1699, 3251])).
% 2.95/3.13 tff(11874,plain,((~b(s(s(s(z))), z)) | (~b(z, s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(s(s(elem!1))), z)) | (~b(s(s(s(elem!1))), s(s(s(z)))))), inference(lemma,lemma(discharge,[]))).
% 2.95/3.13 tff(11875,plain,
% 2.95/3.13 (~b(s(s(s(z))), z)),
% 2.95/3.13 inference(unit_resolution,[status(thm)],[11874, 10498, 96, 95, 11866])).
% 2.95/3.13 tff(11876,plain,
% 2.95/3.13 (r(s(s(s(z))), z)),
% 2.95/3.13 inference(unit_resolution,[status(thm)],[1713, 11875])).
% 2.95/3.13 tff(11877,plain,
% 2.95/3.13 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(s(z)))) | (~r(s(s(z)), s(s(s(z))))) | (~r(s(s(s(z))), z)) | (~r(s(z), s(s(s(z))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(z), s(s(z)))) | (~r(s(s(z)), s(s(s(z))))) | (~r(s(s(s(z))), z)) | (~r(s(z), s(s(s(z))))))),
% 2.95/3.13 inference(rewrite,[status(thm)],[])).
% 2.95/3.13 tff(11878,plain,
% 2.95/3.13 (((~r(s(s(s(z))), z)) | (~r(s(s(z)), s(s(s(z))))) | (~r(s(z), s(s(s(z))))) | (~r(s(z), s(s(z))))) <=> ((~r(s(z), s(s(z)))) | (~r(s(s(z)), s(s(s(z))))) | (~r(s(s(s(z))), z)) | (~r(s(z), s(s(s(z))))))),
% 2.95/3.13 inference(rewrite,[status(thm)],[])).
% 2.95/3.13 tff(11879,plain,
% 2.95/3.13 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(z))), z)) | (~r(s(s(z)), s(s(s(z))))) | (~r(s(z), s(s(s(z))))) | (~r(s(z), s(s(z)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(s(z)))) | (~r(s(s(z)), s(s(s(z))))) | (~r(s(s(s(z))), z)) | (~r(s(z), s(s(s(z)))))))),
% 2.95/3.13 inference(monotonicity,[status(thm)],[11878])).
% 2.95/3.13 tff(11880,plain,
% 2.95/3.13 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(z))), z)) | (~r(s(s(z)), s(s(s(z))))) | (~r(s(z), s(s(s(z))))) | (~r(s(z), s(s(z)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(z), s(s(z)))) | (~r(s(s(z)), s(s(s(z))))) | (~r(s(s(s(z))), z)) | (~r(s(z), s(s(s(z))))))),
% 2.95/3.13 inference(transitivity,[status(thm)],[11879, 11877])).
% 2.95/3.13 tff(11881,plain,
% 2.95/3.13 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(z))), z)) | (~r(s(s(z)), s(s(s(z))))) | (~r(s(z), s(s(s(z))))) | (~r(s(z), s(s(z)))))),
% 2.95/3.13 inference(quant_inst,[status(thm)],[])).
% 2.95/3.13 tff(11882,plain,
% 2.95/3.13 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(z), s(s(z)))) | (~r(s(s(z)), s(s(s(z))))) | (~r(s(s(s(z))), z)) | (~r(s(z), s(s(s(z)))))),
% 2.95/3.13 inference(modus_ponens,[status(thm)],[11881, 11880])).
% 2.95/3.13 tff(11883,plain,
% 2.95/3.13 ($false),
% 2.95/3.13 inference(unit_resolution,[status(thm)],[11882, 197, 120, 1733, 1653, 1732])).
% 2.95/3.13 tff(11884,plain,((~r(s(s(z)), s(s(s(z))))) | (~r(s(z), s(s(z)))) | (~r(s(s(s(z))), z)) | (~r(s(z), s(s(s(z)))))), inference(lemma,lemma(discharge,[]))).
% 2.95/3.13 tff(11885,plain,
% 2.95/3.13 (~r(s(s(z)), s(s(s(z))))),
% 2.95/3.13 inference(unit_resolution,[status(thm)],[11884, 1653, 1733, 120])).
% 2.95/3.13 tff(11886,plain,
% 2.95/3.13 (b(s(s(z)), s(s(s(z))))),
% 2.95/3.13 inference(unit_resolution,[status(thm)],[1730, 11885])).
% 2.95/3.13 tff(11887,plain,
% 2.95/3.13 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(z)))) | (~b(s(s(s(elem!1))), s(s(z)))) | (~b(s(s(s(elem!1))), z)) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(z)), s(s(s(z))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(s(z)))) | (~b(s(s(s(elem!1))), s(s(z)))) | (~b(s(s(s(elem!1))), z)) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(z)), s(s(s(z))))))),
% 2.95/3.13 inference(rewrite,[status(thm)],[])).
% 2.95/3.13 tff(11888,plain,
% 2.95/3.13 (((~b(s(s(s(z))), s(z))) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(s(z)), s(s(s(z))))) | (~b(z, s(s(z)))) | (~b(s(s(s(elem!1))), s(s(z)))) | (~b(s(s(s(elem!1))), z))) <=> ((~b(z, s(s(z)))) | (~b(s(s(s(elem!1))), s(s(z)))) | (~b(s(s(s(elem!1))), z)) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(z)), s(s(s(z))))))),
% 2.95/3.13 inference(rewrite,[status(thm)],[])).
% 2.95/3.13 tff(11889,plain,
% 2.95/3.13 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), s(z))) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(s(z)), s(s(s(z))))) | (~b(z, s(s(z)))) | (~b(s(s(s(elem!1))), s(s(z)))) | (~b(s(s(s(elem!1))), z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(z)))) | (~b(s(s(s(elem!1))), s(s(z)))) | (~b(s(s(s(elem!1))), z)) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(z)), s(s(s(z)))))))),
% 2.95/3.13 inference(monotonicity,[status(thm)],[11888])).
% 2.95/3.13 tff(11890,plain,
% 2.95/3.13 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), s(z))) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(s(z)), s(s(s(z))))) | (~b(z, s(s(z)))) | (~b(s(s(s(elem!1))), s(s(z)))) | (~b(s(s(s(elem!1))), z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(s(z)))) | (~b(s(s(s(elem!1))), s(s(z)))) | (~b(s(s(s(elem!1))), z)) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(z)), s(s(s(z))))))),
% 2.95/3.13 inference(transitivity,[status(thm)],[11889, 11887])).
% 2.95/3.13 tff(11891,plain,
% 2.95/3.13 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), s(z))) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(s(z)), s(s(s(z))))) | (~b(z, s(s(z)))) | (~b(s(s(s(elem!1))), s(s(z)))) | (~b(s(s(s(elem!1))), z)))),
% 2.95/3.13 inference(quant_inst,[status(thm)],[])).
% 2.95/3.13 tff(11892,plain,
% 2.95/3.13 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(s(z)))) | (~b(s(s(s(elem!1))), s(s(z)))) | (~b(s(s(s(elem!1))), z)) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(z)), s(s(s(z)))))),
% 2.95/3.13 inference(modus_ponens,[status(thm)],[11891, 11890])).
% 2.95/3.13 tff(11893,plain,
% 2.95/3.13 ($false),
% 2.95/3.13 inference(unit_resolution,[status(thm)],[11892, 166, 10450, 96, 121, 986, 2060, 3240])).
% 2.95/3.13 tff(11894,plain,((~b(s(s(s(z))), s(z))) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(s(s(elem!1))), z)) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(s(elem!1))), s(s(z))))), inference(lemma,lemma(discharge,[]))).
% 2.95/3.13 tff(11895,plain,
% 2.95/3.13 (~b(s(s(s(z))), s(z))),
% 2.95/3.13 inference(unit_resolution,[status(thm)],[11894, 11886, 121, 96, 2060])).
% 2.95/3.13 tff(11896,plain,
% 2.95/3.13 (r(s(s(s(z))), s(z))),
% 2.95/3.13 inference(unit_resolution,[status(thm)],[1763, 11895])).
% 2.95/3.13 tff(11897,plain,
% 2.95/3.13 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(s(z))))) | (~r(s(z), z)) | (~r(s(z), s(s(s(z))))) | (~r(s(s(s(z))), s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, s(s(s(z))))) | (~r(s(z), z)) | (~r(s(z), s(s(s(z))))) | (~r(s(s(s(z))), s(z))))),
% 2.95/3.13 inference(rewrite,[status(thm)],[])).
% 2.95/3.13 tff(11898,plain,
% 2.95/3.13 (((~r(s(s(s(z))), s(z))) | (~r(z, s(s(s(z))))) | (~r(s(z), s(s(s(z))))) | (~r(s(z), z))) <=> ((~r(z, s(s(s(z))))) | (~r(s(z), z)) | (~r(s(z), s(s(s(z))))) | (~r(s(s(s(z))), s(z))))),
% 2.95/3.13 inference(rewrite,[status(thm)],[])).
% 2.95/3.13 tff(11899,plain,
% 2.95/3.13 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(z))), s(z))) | (~r(z, s(s(s(z))))) | (~r(s(z), s(s(s(z))))) | (~r(s(z), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(s(z))))) | (~r(s(z), z)) | (~r(s(z), s(s(s(z))))) | (~r(s(s(s(z))), s(z)))))),
% 2.95/3.13 inference(monotonicity,[status(thm)],[11898])).
% 2.95/3.13 tff(11900,plain,
% 2.95/3.13 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(z))), s(z))) | (~r(z, s(s(s(z))))) | (~r(s(z), s(s(s(z))))) | (~r(s(z), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, s(s(s(z))))) | (~r(s(z), z)) | (~r(s(z), s(s(s(z))))) | (~r(s(s(s(z))), s(z))))),
% 2.95/3.13 inference(transitivity,[status(thm)],[11899, 11897])).
% 2.95/3.13 tff(11901,plain,
% 2.95/3.13 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(z))), s(z))) | (~r(z, s(s(s(z))))) | (~r(s(z), s(s(s(z))))) | (~r(s(z), z)))),
% 2.95/3.13 inference(quant_inst,[status(thm)],[])).
% 2.95/3.13 tff(11902,plain,
% 2.95/3.13 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, s(s(s(z))))) | (~r(s(z), z)) | (~r(s(z), s(s(s(z))))) | (~r(s(s(s(z))), s(z)))),
% 2.95/3.13 inference(modus_ponens,[status(thm)],[11901, 11900])).
% 2.95/3.13 tff(11903,plain,
% 2.95/3.13 ($false),
% 2.95/3.13 inference(unit_resolution,[status(thm)],[11902, 197, 97, 1677, 1746, 1653])).
% 2.95/3.13 tff(11904,plain,((~r(z, s(s(s(z))))) | (~r(s(z), z)) | (~r(s(s(s(z))), s(z))) | (~r(s(z), s(s(s(z)))))), inference(lemma,lemma(discharge,[]))).
% 2.95/3.13 tff(11905,plain,
% 2.95/3.13 (~r(z, s(s(s(z))))),
% 2.95/3.13 inference(unit_resolution,[status(thm)],[11904, 11896, 97, 1653])).
% 2.95/3.13 tff(11906,plain,
% 2.95/3.13 (b(z, s(s(s(z))))),
% 2.95/3.13 inference(unit_resolution,[status(thm)],[1697, 11905])).
% 2.95/3.13 tff(11907,plain,
% 2.95/3.13 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(z)))) | (~b(s(s(s(z))), s(s(z)))) | (~b(z, s(s(s(z))))) | (~b(s(s(z)), s(s(s(z))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(s(z)))) | (~b(s(s(s(z))), s(s(z)))) | (~b(z, s(s(s(z))))) | (~b(s(s(z)), s(s(s(z))))))),
% 2.95/3.13 inference(rewrite,[status(thm)],[])).
% 2.95/3.13 tff(11908,plain,
% 2.95/3.13 (((~b(s(s(s(z))), s(s(z)))) | (~b(z, s(s(z)))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(s(z))), s(s(z)))) | (~b(z, s(s(z)))) | (~b(z, s(s(s(z)))))) <=> ((~b(z, s(s(z)))) | (~b(s(s(s(z))), s(s(z)))) | (~b(z, s(s(s(z))))) | (~b(s(s(z)), s(s(s(z))))))),
% 2.95/3.13 inference(rewrite,[status(thm)],[])).
% 2.95/3.13 tff(11909,plain,
% 2.95/3.13 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), s(s(z)))) | (~b(z, s(s(z)))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(s(z))), s(s(z)))) | (~b(z, s(s(z)))) | (~b(z, s(s(s(z))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(z)))) | (~b(s(s(s(z))), s(s(z)))) | (~b(z, s(s(s(z))))) | (~b(s(s(z)), s(s(s(z)))))))),
% 2.95/3.13 inference(monotonicity,[status(thm)],[11908])).
% 2.95/3.13 tff(11910,plain,
% 2.95/3.13 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), s(s(z)))) | (~b(z, s(s(z)))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(s(z))), s(s(z)))) | (~b(z, s(s(z)))) | (~b(z, s(s(s(z))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(s(z)))) | (~b(s(s(s(z))), s(s(z)))) | (~b(z, s(s(s(z))))) | (~b(s(s(z)), s(s(s(z))))))),
% 2.95/3.13 inference(transitivity,[status(thm)],[11909, 11907])).
% 2.95/3.13 tff(11911,plain,
% 2.95/3.13 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), s(s(z)))) | (~b(z, s(s(z)))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(s(z))), s(s(z)))) | (~b(z, s(s(z)))) | (~b(z, s(s(s(z))))))),
% 2.95/3.13 inference(quant_inst,[status(thm)],[])).
% 2.95/3.13 tff(11912,plain,
% 2.95/3.13 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(s(z)))) | (~b(s(s(s(z))), s(s(z)))) | (~b(z, s(s(s(z))))) | (~b(s(s(z)), s(s(s(z)))))),
% 2.95/3.13 inference(modus_ponens,[status(thm)],[11911, 11910])).
% 2.95/3.13 tff(11913,plain,
% 2.95/3.13 ($false),
% 2.95/3.13 inference(unit_resolution,[status(thm)],[11912, 166, 10450, 986, 987, 1700])).
% 2.95/3.13 tff(11914,plain,((~b(s(s(s(z))), s(s(z)))) | (~b(s(s(z)), s(s(s(z))))) | (~b(z, s(s(s(z)))))), inference(lemma,lemma(discharge,[]))).
% 2.95/3.13 tff(11915,plain,
% 2.95/3.13 (~b(s(s(s(z))), s(s(z)))),
% 2.95/3.13 inference(unit_resolution,[status(thm)],[11914, 11886, 11906])).
% 2.95/3.13 tff(11916,plain,
% 2.95/3.13 (r(s(s(s(z))), s(s(z)))),
% 2.95/3.13 inference(unit_resolution,[status(thm)],[1010, 11915])).
% 2.95/3.13 tff(11917,plain,
% 2.95/3.13 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(s(z)))) | (~r(s(s(z)), s(s(s(elem!1))))) | (~r(s(s(s(z))), s(s(z)))) | (~r(s(s(s(z))), s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(z), s(s(z)))) | (~r(s(s(z)), s(s(s(elem!1))))) | (~r(s(s(s(z))), s(s(z)))) | (~r(s(s(s(z))), s(z))))),
% 2.95/3.13 inference(rewrite,[status(thm)],[])).
% 2.95/3.13 tff(11918,plain,
% 2.95/3.13 (((~r(s(s(z)), s(s(s(elem!1))))) | (~r(s(z), s(s(z)))) | (~r(s(s(s(z))), s(s(z)))) | (~r(s(s(s(z))), s(z)))) <=> ((~r(s(z), s(s(z)))) | (~r(s(s(z)), s(s(s(elem!1))))) | (~r(s(s(s(z))), s(s(z)))) | (~r(s(s(s(z))), s(z))))),
% 2.95/3.13 inference(rewrite,[status(thm)],[])).
% 2.95/3.13 tff(11919,plain,
% 2.95/3.13 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(z)), s(s(s(elem!1))))) | (~r(s(z), s(s(z)))) | (~r(s(s(s(z))), s(s(z)))) | (~r(s(s(s(z))), s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(s(z)))) | (~r(s(s(z)), s(s(s(elem!1))))) | (~r(s(s(s(z))), s(s(z)))) | (~r(s(s(s(z))), s(z)))))),
% 2.95/3.13 inference(monotonicity,[status(thm)],[11918])).
% 2.95/3.13 tff(11920,plain,
% 2.95/3.13 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(z)), s(s(s(elem!1))))) | (~r(s(z), s(s(z)))) | (~r(s(s(s(z))), s(s(z)))) | (~r(s(s(s(z))), s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(z), s(s(z)))) | (~r(s(s(z)), s(s(s(elem!1))))) | (~r(s(s(s(z))), s(s(z)))) | (~r(s(s(s(z))), s(z))))),
% 2.95/3.13 inference(transitivity,[status(thm)],[11919, 11917])).
% 2.95/3.13 tff(11921,plain,
% 2.95/3.13 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(z)), s(s(s(elem!1))))) | (~r(s(z), s(s(z)))) | (~r(s(s(s(z))), s(s(z)))) | (~r(s(s(s(z))), s(z))))),
% 2.95/3.13 inference(quant_inst,[status(thm)],[])).
% 2.95/3.13 tff(11922,plain,
% 2.95/3.13 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(z), s(s(z)))) | (~r(s(s(z)), s(s(s(elem!1))))) | (~r(s(s(s(z))), s(s(z)))) | (~r(s(s(s(z))), s(z)))),
% 2.95/3.13 inference(modus_ponens,[status(thm)],[11921, 11920])).
% 2.95/3.13 tff(11923,plain,
% 2.95/3.13 ($false),
% 2.95/3.13 inference(unit_resolution,[status(thm)],[11922, 197, 120, 281, 11916, 11896])).
% 2.95/3.13 tff(11924,plain,((~r(s(z), s(s(s(z))))) | (~r(s(z), s(s(z)))) | (~r(s(s(z)), s(s(s(elem!1))))) | (~r(s(z), z)) | (~b(s(s(s(elem!1))), z)) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(s(s(elem!1))), s(s(z)))) | (~r(s(s(s(z))), z))), inference(lemma,lemma(discharge,[]))).
% 2.95/3.13 tff(11925,plain,
% 2.95/3.13 (~r(s(z), s(s(s(z))))),
% 2.95/3.13 inference(unit_resolution,[status(thm)],[11924, 120, 11840, 97, 95, 96, 11853, 11876])).
% 2.95/3.13 tff(11926,plain,
% 2.95/3.13 (b(s(z), s(s(s(z))))),
% 2.95/3.13 inference(unit_resolution,[status(thm)],[1674, 11925])).
% 2.95/3.13 tff(11927,plain,
% 2.95/3.13 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), s(z))) | (~b(s(s(s(z))), s(z))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(elem!1))), s(s(s(z))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(s(s(z))), s(z))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(elem!1))), s(s(s(z))))))),
% 2.95/3.13 inference(rewrite,[status(thm)],[])).
% 2.95/3.14 tff(11928,plain,
% 2.95/3.14 (((~b(s(s(s(z))), s(z))) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(s(s(elem!1))), s(s(s(z)))))) <=> ((~b(s(s(s(elem!1))), s(z))) | (~b(s(s(s(z))), s(z))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(elem!1))), s(s(s(z))))))),
% 2.95/3.14 inference(rewrite,[status(thm)],[])).
% 2.95/3.14 tff(11929,plain,
% 2.95/3.14 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), s(z))) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(s(s(elem!1))), s(s(s(z))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), s(z))) | (~b(s(s(s(z))), s(z))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(elem!1))), s(s(s(z)))))))),
% 2.95/3.14 inference(monotonicity,[status(thm)],[11928])).
% 2.95/3.14 tff(11930,plain,
% 2.95/3.14 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), s(z))) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(s(s(elem!1))), s(s(s(z))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(s(s(z))), s(z))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(elem!1))), s(s(s(z))))))),
% 2.95/3.14 inference(transitivity,[status(thm)],[11929, 11927])).
% 2.95/3.14 tff(11931,plain,
% 2.95/3.14 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), s(z))) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(s(s(elem!1))), s(s(s(z))))))),
% 2.95/3.14 inference(quant_inst,[status(thm)],[])).
% 2.95/3.14 tff(11932,plain,
% 2.95/3.14 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(s(s(z))), s(z))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(elem!1))), s(s(s(z)))))),
% 2.95/3.14 inference(modus_ponens,[status(thm)],[11931, 11930])).
% 2.95/3.14 tff(11933,plain,
% 2.95/3.14 ($false),
% 2.95/3.14 inference(unit_resolution,[status(thm)],[11932, 166, 96, 988, 3240, 3251])).
% 2.95/3.14 tff(11934,plain,((~b(s(s(s(z))), s(z))) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(elem!1))), s(s(s(z)))))), inference(lemma,lemma(discharge,[]))).
% 2.95/3.14 tff(11935,plain,
% 2.95/3.14 (~b(s(s(s(z))), s(z))),
% 2.95/3.14 inference(unit_resolution,[status(thm)],[11934, 11926, 96, 11866])).
% 2.95/3.14 tff(11936,plain,
% 2.95/3.14 (r(s(s(s(z))), s(z))),
% 2.95/3.14 inference(unit_resolution,[status(thm)],[1763, 11935])).
% 2.95/3.14 tff(11937,plain,
% 2.95/3.14 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(s(z))))) | (~r(s(z), z)) | (~r(s(s(s(z))), z)) | (~r(s(s(s(z))), s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, s(s(s(z))))) | (~r(s(z), z)) | (~r(s(s(s(z))), z)) | (~r(s(s(s(z))), s(z))))),
% 2.95/3.14 inference(rewrite,[status(thm)],[])).
% 2.95/3.14 tff(11938,plain,
% 2.95/3.14 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(s(z))))) | (~r(s(z), z)) | (~r(s(s(s(z))), z)) | (~r(s(s(s(z))), s(z))))),
% 2.95/3.14 inference(quant_inst,[status(thm)],[])).
% 2.95/3.14 tff(11939,plain,
% 2.95/3.14 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, s(s(s(z))))) | (~r(s(z), z)) | (~r(s(s(s(z))), z)) | (~r(s(s(s(z))), s(z)))),
% 2.95/3.14 inference(modus_ponens,[status(thm)],[11938, 11937])).
% 2.95/3.14 tff(11940,plain,
% 2.95/3.14 ($false),
% 2.95/3.14 inference(unit_resolution,[status(thm)],[11939, 197, 97, 1677, 1746, 1733])).
% 2.95/3.14 tff(11941,plain,((~r(z, s(s(s(z))))) | (~r(s(z), z)) | (~r(s(s(s(z))), s(z))) | (~r(s(s(s(z))), z))), inference(lemma,lemma(discharge,[]))).
% 2.95/3.14 tff(11942,plain,
% 2.95/3.14 (~r(z, s(s(s(z))))),
% 2.95/3.14 inference(unit_resolution,[status(thm)],[11941, 11936, 97, 11876])).
% 2.95/3.14 tff(11943,plain,
% 2.95/3.14 (b(z, s(s(s(z))))),
% 2.95/3.14 inference(unit_resolution,[status(thm)],[1697, 11942])).
% 2.95/3.14 tff(11944,plain,
% 2.95/3.14 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(z)))) | (~b(z, s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(s(z)))) | (~b(s(s(z)), s(z))) | (~b(s(z), s(s(s(z))))) | (~b(z, s(s(s(z))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(s(z)))) | (~b(z, s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(s(z)))) | (~b(s(s(z)), s(z))) | (~b(s(z), s(s(s(z))))) | (~b(z, s(s(s(z))))))),
% 2.95/3.14 inference(rewrite,[status(thm)],[])).
% 2.95/3.14 tff(11945,plain,
% 2.95/3.14 (((~b(s(z), s(s(s(z))))) | (~b(z, s(s(s(z))))) | (~b(s(s(z)), s(z))) | (~b(s(s(s(elem!1))), s(s(z)))) | (~b(z, s(s(z)))) | (~b(z, s(s(s(elem!1)))))) <=> ((~b(z, s(s(z)))) | (~b(z, s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(s(z)))) | (~b(s(s(z)), s(z))) | (~b(s(z), s(s(s(z))))) | (~b(z, s(s(s(z))))))),
% 2.95/3.14 inference(rewrite,[status(thm)],[])).
% 2.95/3.14 tff(11946,plain,
% 2.95/3.14 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(s(z))))) | (~b(z, s(s(s(z))))) | (~b(s(s(z)), s(z))) | (~b(s(s(s(elem!1))), s(s(z)))) | (~b(z, s(s(z)))) | (~b(z, s(s(s(elem!1))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(z)))) | (~b(z, s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(s(z)))) | (~b(s(s(z)), s(z))) | (~b(s(z), s(s(s(z))))) | (~b(z, s(s(s(z)))))))),
% 2.95/3.14 inference(monotonicity,[status(thm)],[11945])).
% 2.95/3.14 tff(11947,plain,
% 2.95/3.14 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(s(z))))) | (~b(z, s(s(s(z))))) | (~b(s(s(z)), s(z))) | (~b(s(s(s(elem!1))), s(s(z)))) | (~b(z, s(s(z)))) | (~b(z, s(s(s(elem!1))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(s(z)))) | (~b(z, s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(s(z)))) | (~b(s(s(z)), s(z))) | (~b(s(z), s(s(s(z))))) | (~b(z, s(s(s(z))))))),
% 2.95/3.14 inference(transitivity,[status(thm)],[11946, 11944])).
% 2.95/3.14 tff(11948,plain,
% 2.95/3.14 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(s(z))))) | (~b(z, s(s(s(z))))) | (~b(s(s(z)), s(z))) | (~b(s(s(s(elem!1))), s(s(z)))) | (~b(z, s(s(z)))) | (~b(z, s(s(s(elem!1))))))),
% 2.95/3.14 inference(quant_inst,[status(thm)],[])).
% 2.95/3.14 tff(11949,plain,
% 2.95/3.14 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(s(z)))) | (~b(z, s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(s(z)))) | (~b(s(s(z)), s(z))) | (~b(s(z), s(s(s(z))))) | (~b(z, s(s(s(z)))))),
% 2.95/3.14 inference(modus_ponens,[status(thm)],[11948, 11947])).
% 2.95/3.14 tff(11950,plain,
% 2.95/3.14 ($false),
% 2.95/3.14 inference(unit_resolution,[status(thm)],[11949, 166, 240, 10450, 156, 988, 1700, 2060])).
% 2.95/3.14 tff(11951,plain,((~b(s(s(z)), s(z))) | (~b(z, s(s(s(elem!1))))) | (~b(s(z), s(s(s(z))))) | (~b(z, s(s(s(z))))) | (~b(s(s(s(elem!1))), s(s(z))))), inference(lemma,lemma(discharge,[]))).
% 2.95/3.14 tff(11952,plain,
% 2.95/3.14 (~b(s(s(z)), s(z))),
% 2.95/3.14 inference(unit_resolution,[status(thm)],[11951, 11943, 11926, 10498, 11853])).
% 2.95/3.14 tff(11953,plain,
% 2.95/3.14 (r(s(s(z)), s(z))),
% 2.95/3.14 inference(unit_resolution,[status(thm)],[308, 11952])).
% 2.95/3.14 tff(11954,plain,
% 2.95/3.14 (~b(s(s(s(z))), s(z))),
% 2.95/3.14 inference(unit_resolution,[status(thm)],[11894, 986, 121, 96, 2060])).
% 2.95/3.14 tff(11955,plain,
% 2.95/3.14 (r(s(s(s(z))), s(z))),
% 2.95/3.14 inference(unit_resolution,[status(thm)],[1763, 11954])).
% 2.95/3.14 tff(11956,plain,
% 2.95/3.14 (~r(s(s(s(z))), s(s(z)))),
% 2.95/3.14 inference(unit_resolution,[status(thm)],[5076, 197, 120, 392, 11955])).
% 2.95/3.14 tff(11957,plain,
% 2.95/3.14 (b(s(s(s(z))), s(s(z)))),
% 2.95/3.14 inference(unit_resolution,[status(thm)],[1010, 11956])).
% 2.95/3.14 tff(11958,plain,
% 2.95/3.14 ($false),
% 2.95/3.14 inference(unit_resolution,[status(thm)],[11912, 166, 10450, 986, 11957, 1700])).
% 2.95/3.14 tff(11959,plain,((~b(s(s(z)), s(s(s(z))))) | (~b(z, s(s(s(z))))) | (~r(s(z), s(s(z)))) | (~r(s(s(z)), s(z))) | (~b(s(s(s(elem!1))), z)) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(s(s(elem!1))), s(s(z))))), inference(lemma,lemma(discharge,[]))).
% 2.95/3.14 tff(11960,plain,
% 2.95/3.14 (~b(s(s(z)), s(s(s(z))))),
% 2.95/3.14 inference(unit_resolution,[status(thm)],[11959, 11953, 120, 11943, 95, 96, 11853])).
% 2.95/3.14 tff(11961,plain,
% 2.95/3.14 (r(s(s(z)), s(s(s(z))))),
% 2.95/3.14 inference(unit_resolution,[status(thm)],[1730, 11960])).
% 2.95/3.14 tff(11962,plain,
% 2.95/3.14 ($false),
% 2.95/3.14 inference(unit_resolution,[status(thm)],[5590, 197, 120, 11953, 11936, 11961])).
% 2.95/3.14 tff(11963,plain,((~r(s(z), s(s(z)))) | (~b(s(s(s(elem!1))), s(z))) | (~r(s(z), z)) | (~r(s(z), s(s(s(elem!1))))) | r(s(s(s(elem!1))), z) | (~r(s(z), s(s(elem!1)))) | (~b(z, s(z)))), inference(lemma,lemma(discharge,[]))).
% 2.95/3.14 tff(11964,plain,
% 2.95/3.14 (~r(s(z), s(s(z)))),
% 2.95/3.14 inference(unit_resolution,[status(thm)],[11963, 118, 97, 119, 86, 85, 96])).
% 2.95/3.14 tff(11965,plain,
% 2.95/3.14 (b(s(z), s(s(z)))),
% 2.95/3.14 inference(unit_resolution,[status(thm)],[427, 11964])).
% 2.95/3.14 tff(11966,plain,
% 2.95/3.14 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(z)))) | (~b(z, s(z))) | (~b(s(z), s(s(z)))) | (~b(s(s(z)), z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(s(z)))) | (~b(z, s(z))) | (~b(s(z), s(s(z)))) | (~b(s(s(z)), z)))),
% 2.95/3.14 inference(rewrite,[status(thm)],[])).
% 2.95/3.14 tff(11967,plain,
% 2.95/3.14 (((~b(z, s(s(z)))) | (~b(z, s(s(z)))) | (~b(s(s(z)), z)) | (~b(s(z), s(s(z)))) | (~b(z, s(s(z)))) | (~b(z, s(z)))) <=> ((~b(z, s(s(z)))) | (~b(z, s(z))) | (~b(s(z), s(s(z)))) | (~b(s(s(z)), z)))),
% 2.95/3.14 inference(rewrite,[status(thm)],[])).
% 2.95/3.14 tff(11968,plain,
% 2.95/3.14 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(z)))) | (~b(z, s(s(z)))) | (~b(s(s(z)), z)) | (~b(s(z), s(s(z)))) | (~b(z, s(s(z)))) | (~b(z, s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(z)))) | (~b(z, s(z))) | (~b(s(z), s(s(z)))) | (~b(s(s(z)), z))))),
% 2.95/3.14 inference(monotonicity,[status(thm)],[11967])).
% 2.95/3.14 tff(11969,plain,
% 2.95/3.14 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(z)))) | (~b(z, s(s(z)))) | (~b(s(s(z)), z)) | (~b(s(z), s(s(z)))) | (~b(z, s(s(z)))) | (~b(z, s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(s(z)))) | (~b(z, s(z))) | (~b(s(z), s(s(z)))) | (~b(s(s(z)), z)))),
% 2.95/3.14 inference(transitivity,[status(thm)],[11968, 11966])).
% 2.95/3.14 tff(11970,plain,
% 2.95/3.14 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(z)))) | (~b(z, s(s(z)))) | (~b(s(s(z)), z)) | (~b(s(z), s(s(z)))) | (~b(z, s(s(z)))) | (~b(z, s(z))))),
% 2.95/3.14 inference(quant_inst,[status(thm)],[])).
% 2.95/3.14 tff(11971,plain,
% 2.95/3.14 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(s(z)))) | (~b(z, s(z))) | (~b(s(z), s(s(z)))) | (~b(s(s(z)), z))),
% 2.95/3.14 inference(modus_ponens,[status(thm)],[11970, 11969])).
% 2.95/3.14 tff(11972,plain,
% 2.95/3.14 ($false),
% 2.95/3.14 inference(unit_resolution,[status(thm)],[11971, 166, 556, 10451, 118, 122])).
% 2.95/3.14 tff(11973,plain,((~b(s(s(z)), z)) | (~b(s(z), s(s(z)))) | (~b(z, s(s(z)))) | (~b(z, s(z)))), inference(lemma,lemma(discharge,[]))).
% 2.95/3.14 tff(11974,plain,
% 2.95/3.14 ((~b(s(s(z)), z)) | (~b(s(z), s(s(z)))) | (~b(z, s(z)))),
% 2.95/3.14 inference(unit_resolution,[status(thm)],[11973, 10450])).
% 2.95/3.14 tff(11975,plain,
% 2.95/3.14 (~b(s(s(z)), z)),
% 2.95/3.14 inference(unit_resolution,[status(thm)],[11974, 11965, 118])).
% 2.95/3.14 tff(11976,plain,
% 2.95/3.14 (r(s(s(z)), z)),
% 2.95/3.14 inference(unit_resolution,[status(thm)],[186, 11975])).
% 2.95/3.14 tff(11977,plain,
% 2.95/3.14 (~b(s(s(z)), s(z))),
% 2.95/3.14 inference(unit_resolution,[status(thm)],[6807, 11965, 96, 118, 95])).
% 2.95/3.14 tff(11978,plain,
% 2.95/3.14 (r(s(s(z)), s(z))),
% 2.95/3.14 inference(unit_resolution,[status(thm)],[308, 11977])).
% 2.95/3.14 tff(11979,plain,
% 2.95/3.14 ($false),
% 2.95/3.14 inference(unit_resolution,[status(thm)],[11384, 197, 97, 392, 365, 866])).
% 2.95/3.14 tff(11980,plain,((~r(s(s(z)), z)) | (~r(s(z), z)) | (~r(s(s(z)), s(z))) | (~r(z, s(s(elem!1))))), inference(lemma,lemma(discharge,[]))).
% 2.95/3.14 tff(11981,plain,
% 2.95/3.14 (~r(z, s(s(elem!1)))),
% 2.95/3.14 inference(unit_resolution,[status(thm)],[11980, 11978, 97, 11976])).
% 2.95/3.14 tff(11982,plain,
% 2.95/3.14 (b(z, s(s(elem!1)))),
% 2.95/3.14 inference(unit_resolution,[status(thm)],[1795, 11981])).
% 2.95/3.14 tff(11983,plain,
% 2.95/3.14 (~(s(s(z)) = s(s(elem!1)))),
% 2.95/3.14 inference(unit_resolution,[status(thm)],[4398, 11965, 54])).
% 2.95/3.14 tff(11984,plain,
% 2.95/3.14 (r(s(s(z)), s(s(elem!1)))),
% 2.95/3.14 inference(unit_resolution,[status(thm)],[11730, 97, 10451, 4568])).
% 2.95/3.14 tff(11985,plain,
% 2.95/3.14 ($false),
% 2.95/3.14 inference(unit_resolution,[status(thm)],[6771, 11984, 97, 10521, 392])).
% 2.95/3.14 tff(11986,plain,((~r(s(z), z)) | (~r(s(s(z)), s(z))) | (~b(z, s(s(z)))) | b(s(s(elem!1)), s(z))), inference(lemma,lemma(discharge,[]))).
% 2.95/3.14 tff(11987,plain,
% 2.95/3.14 ((~r(s(z), z)) | (~r(s(s(z)), s(z))) | b(s(s(elem!1)), s(z))),
% 2.95/3.14 inference(unit_resolution,[status(thm)],[11986, 10450])).
% 2.95/3.14 tff(11988,plain,
% 2.95/3.14 (b(s(s(elem!1)), s(z))),
% 2.95/3.14 inference(unit_resolution,[status(thm)],[11987, 11978, 97])).
% 2.95/3.14 tff(11989,plain,
% 2.95/3.14 (~r(s(s(elem!1)), s(s(s(elem!1))))),
% 2.95/3.14 inference(unit_resolution,[status(thm)],[4264, 11988, 96, 85, 119, 11965, 11983])).
% 2.95/3.14 tff(11990,plain,
% 2.95/3.14 (~b(s(s(z)), s(z))),
% 2.95/3.14 inference(unit_resolution,[status(thm)],[6807, 556, 96, 118, 95])).
% 2.95/3.14 tff(11991,plain,
% 2.95/3.14 (r(s(s(z)), s(z))),
% 2.95/3.14 inference(unit_resolution,[status(thm)],[308, 11990])).
% 2.95/3.14 tff(11992,plain,
% 2.95/3.14 (~r(s(s(z)), s(s(s(elem!1))))),
% 2.95/3.14 inference(unit_resolution,[status(thm)],[913, 905, 119, 392])).
% 2.95/3.14 tff(11993,plain,
% 2.95/3.14 (b(s(s(z)), s(s(s(elem!1))))),
% 2.95/3.14 inference(unit_resolution,[status(thm)],[279, 11992])).
% 2.95/3.14 tff(11994,plain,
% 2.95/3.14 (~r(s(s(elem!1)), s(s(z)))),
% 2.95/3.14 inference(unit_resolution,[status(thm)],[4313, 905, 392, 464])).
% 2.95/3.14 tff(11995,plain,
% 2.95/3.14 (b(s(s(elem!1)), s(s(z)))),
% 2.95/3.14 inference(unit_resolution,[status(thm)],[441, 11994, 11])).
% 2.95/3.14 tff(11996,plain,
% 2.95/3.14 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(z)))) | (~b(z, s(s(elem!1)))) | (~b(s(s(elem!1)), s(s(z)))) | (~b(s(s(s(elem!1))), s(z))) | (~b(z, s(z))) | (~b(s(s(z)), s(s(s(elem!1))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(s(z)))) | (~b(z, s(s(elem!1)))) | (~b(s(s(elem!1)), s(s(z)))) | (~b(s(s(s(elem!1))), s(z))) | (~b(z, s(z))) | (~b(s(s(z)), s(s(s(elem!1))))))),
% 2.95/3.14 inference(rewrite,[status(thm)],[])).
% 2.95/3.14 tff(11997,plain,
% 2.95/3.14 (((~b(s(s(s(elem!1))), s(z))) | (~b(z, s(z))) | (~b(s(s(z)), s(s(s(elem!1))))) | (~b(s(s(elem!1)), s(s(z)))) | (~b(z, s(s(z)))) | (~b(z, s(s(elem!1))))) <=> ((~b(z, s(s(z)))) | (~b(z, s(s(elem!1)))) | (~b(s(s(elem!1)), s(s(z)))) | (~b(s(s(s(elem!1))), s(z))) | (~b(z, s(z))) | (~b(s(s(z)), s(s(s(elem!1))))))),
% 2.95/3.14 inference(rewrite,[status(thm)],[])).
% 2.95/3.14 tff(11998,plain,
% 2.95/3.14 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), s(z))) | (~b(z, s(z))) | (~b(s(s(z)), s(s(s(elem!1))))) | (~b(s(s(elem!1)), s(s(z)))) | (~b(z, s(s(z)))) | (~b(z, s(s(elem!1)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(z)))) | (~b(z, s(s(elem!1)))) | (~b(s(s(elem!1)), s(s(z)))) | (~b(s(s(s(elem!1))), s(z))) | (~b(z, s(z))) | (~b(s(s(z)), s(s(s(elem!1)))))))),
% 2.95/3.15 inference(monotonicity,[status(thm)],[11997])).
% 2.95/3.15 tff(11999,plain,
% 2.95/3.15 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), s(z))) | (~b(z, s(z))) | (~b(s(s(z)), s(s(s(elem!1))))) | (~b(s(s(elem!1)), s(s(z)))) | (~b(z, s(s(z)))) | (~b(z, s(s(elem!1)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(s(z)))) | (~b(z, s(s(elem!1)))) | (~b(s(s(elem!1)), s(s(z)))) | (~b(s(s(s(elem!1))), s(z))) | (~b(z, s(z))) | (~b(s(s(z)), s(s(s(elem!1))))))),
% 2.95/3.15 inference(transitivity,[status(thm)],[11998, 11996])).
% 2.95/3.15 tff(12000,plain,
% 2.95/3.15 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), s(z))) | (~b(z, s(z))) | (~b(s(s(z)), s(s(s(elem!1))))) | (~b(s(s(elem!1)), s(s(z)))) | (~b(z, s(s(z)))) | (~b(z, s(s(elem!1)))))),
% 2.95/3.15 inference(quant_inst,[status(thm)],[])).
% 2.95/3.15 tff(12001,plain,
% 2.95/3.15 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(s(z)))) | (~b(z, s(s(elem!1)))) | (~b(s(s(elem!1)), s(s(z)))) | (~b(s(s(s(elem!1))), s(z))) | (~b(z, s(z))) | (~b(s(s(z)), s(s(s(elem!1)))))),
% 2.95/3.15 inference(modus_ponens,[status(thm)],[12000, 11999])).
% 2.95/3.15 tff(12002,plain,
% 2.95/3.15 ($false),
% 2.95/3.15 inference(unit_resolution,[status(thm)],[12001, 166, 1820, 405, 10451, 96, 118, 263])).
% 2.95/3.15 tff(12003,plain,((~b(s(s(z)), s(s(s(elem!1))))) | (~b(z, s(s(elem!1)))) | (~b(s(s(elem!1)), s(s(z)))) | (~b(z, s(s(z)))) | (~b(s(s(s(elem!1))), s(z))) | (~b(z, s(z)))), inference(lemma,lemma(discharge,[]))).
% 2.95/3.15 tff(12004,plain,
% 2.95/3.15 ((~b(s(s(z)), s(s(s(elem!1))))) | (~b(z, s(s(elem!1)))) | (~b(s(s(elem!1)), s(s(z)))) | (~b(s(s(s(elem!1))), s(z))) | (~b(z, s(z)))),
% 2.95/3.15 inference(unit_resolution,[status(thm)],[12003, 10450])).
% 2.95/3.15 tff(12005,plain,
% 2.95/3.15 ($false),
% 2.95/3.15 inference(unit_resolution,[status(thm)],[12004, 11995, 11993, 118, 96, 1820])).
% 2.95/3.15 tff(12006,plain,((~r(s(s(s(elem!1))), s(s(elem!1)))) | (~b(z, s(z))) | (~b(s(s(s(elem!1))), s(z))) | (~b(z, s(s(elem!1)))) | (s(s(elem!1)) = s(s(z))) | (~r(s(s(z)), s(z))) | (~r(s(s(s(elem!1))), s(s(z)))) | (~r(s(z), s(s(s(elem!1)))))), inference(lemma,lemma(discharge,[]))).
% 2.95/3.15 tff(12007,plain,
% 2.95/3.15 (~r(s(s(s(elem!1))), s(s(elem!1)))),
% 2.95/3.15 inference(unit_resolution,[status(thm)],[12006, 464, 96, 1820, 132, 11991, 118, 119])).
% 2.95/3.15 tff(12008,plain,
% 2.95/3.15 (b(s(s(z)), s(s(s(elem!1))))),
% 2.95/3.15 inference(unit_resolution,[status(thm)],[279, 273])).
% 2.95/3.15 tff(12009,plain,
% 2.95/3.15 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(z, s(s(z)))) | (~b(z, s(s(elem!1)))) | (~b(z, s(z))) | (~b(s(z), s(s(z)))) | (~b(s(s(z)), s(s(s(elem!1))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(z, s(s(z)))) | (~b(z, s(s(elem!1)))) | (~b(z, s(z))) | (~b(s(z), s(s(z)))) | (~b(s(s(z)), s(s(s(elem!1))))))),
% 2.95/3.15 inference(rewrite,[status(thm)],[])).
% 2.95/3.15 tff(12010,plain,
% 2.95/3.15 (((~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(z, s(s(elem!1)))) | (~b(s(s(z)), s(s(s(elem!1))))) | (~b(s(z), s(s(z)))) | (~b(z, s(s(z)))) | (~b(z, s(z)))) <=> ((~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(z, s(s(z)))) | (~b(z, s(s(elem!1)))) | (~b(z, s(z))) | (~b(s(z), s(s(z)))) | (~b(s(s(z)), s(s(s(elem!1))))))),
% 2.95/3.15 inference(rewrite,[status(thm)],[])).
% 2.95/3.15 tff(12011,plain,
% 2.95/3.15 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(z, s(s(elem!1)))) | (~b(s(s(z)), s(s(s(elem!1))))) | (~b(s(z), s(s(z)))) | (~b(z, s(s(z)))) | (~b(z, s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(z, s(s(z)))) | (~b(z, s(s(elem!1)))) | (~b(z, s(z))) | (~b(s(z), s(s(z)))) | (~b(s(s(z)), s(s(s(elem!1)))))))),
% 2.95/3.15 inference(monotonicity,[status(thm)],[12010])).
% 2.95/3.15 tff(12012,plain,
% 2.95/3.15 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(z, s(s(elem!1)))) | (~b(s(s(z)), s(s(s(elem!1))))) | (~b(s(z), s(s(z)))) | (~b(z, s(s(z)))) | (~b(z, s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(z, s(s(z)))) | (~b(z, s(s(elem!1)))) | (~b(z, s(z))) | (~b(s(z), s(s(z)))) | (~b(s(s(z)), s(s(s(elem!1))))))),
% 2.95/3.15 inference(transitivity,[status(thm)],[12011, 12009])).
% 2.95/3.15 tff(12013,plain,
% 2.95/3.15 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(z, s(s(elem!1)))) | (~b(s(s(z)), s(s(s(elem!1))))) | (~b(s(z), s(s(z)))) | (~b(z, s(s(z)))) | (~b(z, s(z))))),
% 2.95/3.15 inference(quant_inst,[status(thm)],[])).
% 2.95/3.15 tff(12014,plain,
% 2.95/3.15 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(z, s(s(z)))) | (~b(z, s(s(elem!1)))) | (~b(z, s(z))) | (~b(s(z), s(s(z)))) | (~b(s(s(z)), s(s(s(elem!1)))))),
% 2.95/3.15 inference(modus_ponens,[status(thm)],[12013, 12012])).
% 2.95/3.15 tff(12015,plain,
% 2.95/3.15 ($false),
% 2.95/3.15 inference(unit_resolution,[status(thm)],[12014, 166, 839, 1820, 556, 10451, 118, 263])).
% 2.95/3.15 tff(12016,plain,((~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(z, s(s(elem!1)))) | (~b(s(z), s(s(z)))) | (~b(z, s(s(z)))) | (~b(z, s(z))) | (~b(s(s(z)), s(s(s(elem!1)))))), inference(lemma,lemma(discharge,[]))).
% 2.95/3.15 tff(12017,plain,
% 2.95/3.15 ((~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(z, s(s(elem!1)))) | (~b(s(z), s(s(z)))) | (~b(z, s(z))) | (~b(s(s(z)), s(s(s(elem!1)))))),
% 2.95/3.15 inference(unit_resolution,[status(thm)],[12016, 10450])).
% 2.95/3.15 tff(12018,plain,
% 2.95/3.15 (~b(s(s(s(elem!1))), s(s(elem!1)))),
% 2.95/3.15 inference(unit_resolution,[status(thm)],[12017, 12008, 118, 556, 1820])).
% 2.95/3.15 tff(12019,plain,
% 2.95/3.15 (s(s(s(elem!1))) = s(s(elem!1))),
% 2.95/3.15 inference(unit_resolution,[status(thm)],[889, 12018, 1823])).
% 2.95/3.15 tff(12020,plain,
% 2.95/3.15 (s(s(elem!1)) = s(s(s(elem!1)))),
% 2.95/3.15 inference(unit_resolution,[status(thm)],[50, 12019])).
% 2.95/3.15 tff(12021,plain,
% 2.95/3.15 (~r(s(s(elem!1)), z)),
% 2.95/3.15 inference(unit_resolution,[status(thm)],[2974, 12020, 86])).
% 2.95/3.15 tff(12022,plain,
% 2.95/3.15 (b(s(s(elem!1)), z)),
% 2.95/3.15 inference(unit_resolution,[status(thm)],[608, 12021])).
% 2.95/3.15 tff(12023,plain,
% 2.95/3.15 (~r(s(s(z)), s(s(elem!1)))),
% 2.95/3.15 inference(unit_resolution,[status(thm)],[338, 12020, 273])).
% 2.95/3.15 tff(12024,plain,
% 2.95/3.15 (b(s(s(z)), s(s(elem!1)))),
% 2.95/3.15 inference(unit_resolution,[status(thm)],[390, 12023, 52])).
% 2.95/3.15 tff(12025,plain,
% 2.95/3.15 ($false),
% 2.95/3.15 inference(unit_resolution,[status(thm)],[11837, 12024, 12022, 1820])).
% 2.95/3.15 tff(12026,plain,(r(s(s(z)), s(s(s(elem!1)))) | (~b(z, s(s(elem!1)))) | (s(s(z)) = s(s(elem!1))) | r(s(s(s(elem!1))), z) | r(s(s(s(elem!1))), s(s(elem!1))) | (~b(z, s(z))) | (~b(s(z), s(s(z))))), inference(lemma,lemma(discharge,[]))).
% 2.95/3.15 tff(12027,plain,
% 2.95/3.15 (r(s(s(z)), s(s(s(elem!1))))),
% 2.95/3.15 inference(unit_resolution,[status(thm)],[12026, 12007, 52, 86, 1820, 118, 556])).
% 2.95/3.15 tff(12028,plain,
% 2.95/3.15 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(s(s(elem!1))))) | (~r(s(s(z)), s(z))) | (~r(s(s(z)), s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), s(s(z)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(z), s(s(s(elem!1))))) | (~r(s(s(z)), s(z))) | (~r(s(s(z)), s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), s(s(z)))))),
% 2.95/3.15 inference(rewrite,[status(thm)],[])).
% 2.95/3.15 tff(12029,plain,
% 2.95/3.15 (((~r(s(s(s(elem!1))), s(s(z)))) | (~r(s(z), s(s(s(elem!1))))) | (~r(s(s(z)), s(s(s(elem!1))))) | (~r(s(s(z)), s(z)))) <=> ((~r(s(z), s(s(s(elem!1))))) | (~r(s(s(z)), s(z))) | (~r(s(s(z)), s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), s(s(z)))))),
% 2.95/3.15 inference(rewrite,[status(thm)],[])).
% 2.95/3.15 tff(12030,plain,
% 2.95/3.15 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), s(s(z)))) | (~r(s(z), s(s(s(elem!1))))) | (~r(s(s(z)), s(s(s(elem!1))))) | (~r(s(s(z)), s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(s(s(elem!1))))) | (~r(s(s(z)), s(z))) | (~r(s(s(z)), s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), s(s(z))))))),
% 2.95/3.15 inference(monotonicity,[status(thm)],[12029])).
% 2.95/3.15 tff(12031,plain,
% 2.95/3.15 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), s(s(z)))) | (~r(s(z), s(s(s(elem!1))))) | (~r(s(s(z)), s(s(s(elem!1))))) | (~r(s(s(z)), s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(z), s(s(s(elem!1))))) | (~r(s(s(z)), s(z))) | (~r(s(s(z)), s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), s(s(z)))))),
% 2.95/3.15 inference(transitivity,[status(thm)],[12030, 12028])).
% 2.95/3.15 tff(12032,plain,
% 2.95/3.15 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), s(s(z)))) | (~r(s(z), s(s(s(elem!1))))) | (~r(s(s(z)), s(s(s(elem!1))))) | (~r(s(s(z)), s(z))))),
% 2.95/3.15 inference(quant_inst,[status(thm)],[])).
% 2.95/3.15 tff(12033,plain,
% 2.95/3.15 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(z), s(s(s(elem!1))))) | (~r(s(s(z)), s(z))) | (~r(s(s(z)), s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), s(s(z))))),
% 2.95/3.15 inference(modus_ponens,[status(thm)],[12032, 12031])).
% 2.95/3.15 tff(12034,plain,
% 2.95/3.15 ($false),
% 2.95/3.15 inference(unit_resolution,[status(thm)],[12033, 197, 11991, 119, 12027, 464])).
% 2.95/3.15 tff(12035,plain,((~r(s(s(s(elem!1))), s(s(z)))) | (~r(s(z), s(s(s(elem!1))))) | (s(s(z)) = s(s(elem!1))) | r(s(s(s(elem!1))), z) | (~b(z, s(s(elem!1)))) | (~b(z, s(z))) | (~b(s(z), s(s(z)))) | (~b(s(s(s(elem!1))), s(z)))), inference(lemma,lemma(discharge,[]))).
% 2.95/3.15 tff(12036,plain,
% 2.95/3.15 (~r(s(s(s(elem!1))), s(s(z)))),
% 2.95/3.15 inference(unit_resolution,[status(thm)],[12035, 11983, 119, 86, 11982, 118, 11965, 96])).
% 2.95/3.15 tff(12037,plain,
% 2.95/3.15 (b(s(s(s(elem!1))), s(s(z)))),
% 2.95/3.15 inference(unit_resolution,[status(thm)],[218, 12036])).
% 2.95/3.15 tff(12038,plain,
% 2.95/3.15 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(z)))) | (~b(s(s(s(elem!1))), s(s(z)))) | (~b(z, s(z))) | (~b(s(z), s(s(z)))) | (~b(s(s(z)), s(s(s(elem!1))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(s(z)))) | (~b(s(s(s(elem!1))), s(s(z)))) | (~b(z, s(z))) | (~b(s(z), s(s(z)))) | (~b(s(s(z)), s(s(s(elem!1))))))),
% 2.95/3.15 inference(rewrite,[status(thm)],[])).
% 2.95/3.15 tff(12039,plain,
% 2.95/3.15 (((~b(s(s(s(elem!1))), s(s(z)))) | (~b(z, s(s(z)))) | (~b(s(s(z)), s(s(s(elem!1))))) | (~b(s(z), s(s(z)))) | (~b(z, s(s(z)))) | (~b(z, s(z)))) <=> ((~b(z, s(s(z)))) | (~b(s(s(s(elem!1))), s(s(z)))) | (~b(z, s(z))) | (~b(s(z), s(s(z)))) | (~b(s(s(z)), s(s(s(elem!1))))))),
% 2.95/3.15 inference(rewrite,[status(thm)],[])).
% 2.95/3.15 tff(12040,plain,
% 2.95/3.15 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), s(s(z)))) | (~b(z, s(s(z)))) | (~b(s(s(z)), s(s(s(elem!1))))) | (~b(s(z), s(s(z)))) | (~b(z, s(s(z)))) | (~b(z, s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(z)))) | (~b(s(s(s(elem!1))), s(s(z)))) | (~b(z, s(z))) | (~b(s(z), s(s(z)))) | (~b(s(s(z)), s(s(s(elem!1)))))))),
% 2.95/3.15 inference(monotonicity,[status(thm)],[12039])).
% 2.95/3.15 tff(12041,plain,
% 2.95/3.15 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), s(s(z)))) | (~b(z, s(s(z)))) | (~b(s(s(z)), s(s(s(elem!1))))) | (~b(s(z), s(s(z)))) | (~b(z, s(s(z)))) | (~b(z, s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(s(z)))) | (~b(s(s(s(elem!1))), s(s(z)))) | (~b(z, s(z))) | (~b(s(z), s(s(z)))) | (~b(s(s(z)), s(s(s(elem!1))))))),
% 2.95/3.15 inference(transitivity,[status(thm)],[12040, 12038])).
% 2.95/3.15 tff(12042,plain,
% 2.95/3.15 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), s(s(z)))) | (~b(z, s(s(z)))) | (~b(s(s(z)), s(s(s(elem!1))))) | (~b(s(z), s(s(z)))) | (~b(z, s(s(z)))) | (~b(z, s(z))))),
% 2.95/3.15 inference(quant_inst,[status(thm)],[])).
% 2.95/3.15 tff(12043,plain,
% 2.95/3.15 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(s(z)))) | (~b(s(s(s(elem!1))), s(s(z)))) | (~b(z, s(z))) | (~b(s(z), s(s(z)))) | (~b(s(s(z)), s(s(s(elem!1)))))),
% 2.95/3.15 inference(modus_ponens,[status(thm)],[12042, 12041])).
% 2.95/3.15 tff(12044,plain,
% 2.95/3.15 ($false),
% 2.95/3.15 inference(unit_resolution,[status(thm)],[12043, 166, 556, 10451, 118, 263, 2060])).
% 2.95/3.15 tff(12045,plain,((~b(s(z), s(s(z)))) | (~b(z, s(s(z)))) | (~b(z, s(z))) | (~b(s(s(z)), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(s(z))))), inference(lemma,lemma(discharge,[]))).
% 2.95/3.15 tff(12046,plain,
% 2.95/3.15 ((~b(s(z), s(s(z)))) | (~b(z, s(z))) | (~b(s(s(z)), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(s(z))))),
% 2.95/3.15 inference(unit_resolution,[status(thm)],[12045, 10450])).
% 2.95/3.15 tff(12047,plain,
% 2.95/3.15 (~b(s(s(z)), s(s(s(elem!1))))),
% 2.95/3.15 inference(unit_resolution,[status(thm)],[12046, 12037, 118, 11965])).
% 2.95/3.15 tff(12048,plain,
% 2.95/3.15 (r(s(s(z)), s(s(s(elem!1))))),
% 2.95/3.15 inference(unit_resolution,[status(thm)],[279, 12047])).
% 2.95/3.15 tff(12049,plain,
% 2.95/3.15 (~r(s(s(s(elem!1))), s(s(elem!1)))),
% 2.95/3.15 inference(unit_resolution,[status(thm)],[913, 12048, 119, 11978])).
% 2.95/3.15 tff(12050,plain,
% 2.95/3.15 ($false),
% 2.95/3.15 inference(unit_resolution,[status(thm)],[2349, 1824, 1822, 97, 119, 1820])).
% 2.95/3.15 tff(12051,plain,((s(s(elem!1)) = s(s(s(elem!1)))) | (~r(s(z), z)) | (~r(s(z), s(s(s(elem!1))))) | (~b(z, s(s(elem!1)))) | r(s(s(s(elem!1))), s(s(elem!1))) | r(s(s(elem!1)), s(s(s(elem!1))))), inference(lemma,lemma(discharge,[]))).
% 2.95/3.15 tff(12052,plain,
% 2.95/3.15 (s(s(elem!1)) = s(s(s(elem!1)))),
% 2.95/3.15 inference(unit_resolution,[status(thm)],[12051, 12049, 119, 11982, 97, 11989])).
% 2.95/3.15 tff(12053,plain,
% 2.95/3.15 (s(s(s(elem!1))) = s(s(elem!1))),
% 2.95/3.15 inference(unit_resolution,[status(thm)],[4030, 12052])).
% 2.95/3.15 tff(12054,plain,
% 2.95/3.15 (b(z, s(s(s(elem!1))))),
% 2.95/3.15 inference(unit_resolution,[status(thm)],[8327, 12053, 11982])).
% 2.95/3.15 tff(12055,plain,
% 2.95/3.15 (~(s(s(elem!1)) = s(s(z)))),
% 2.95/3.15 inference(unit_resolution,[status(thm)],[131, 11983])).
% 2.95/3.15 tff(12056,plain,
% 2.95/3.15 (~(s(s(s(elem!1))) = s(s(s(z))))),
% 2.95/3.15 inference(unit_resolution,[status(thm)],[139, 12055])).
% 2.95/3.15 tff(12057,plain,
% 2.95/3.15 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), s(s(s(z))))) | (~r(s(z), s(s(s(elem!1))))) | (~r(s(s(z)), s(z))) | (~r(s(s(z)), s(s(s(elem!1))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(elem!1))), s(s(s(z))))) | (~r(s(z), s(s(s(elem!1))))) | (~r(s(s(z)), s(z))) | (~r(s(s(z)), s(s(s(elem!1))))))),
% 2.95/3.15 inference(rewrite,[status(thm)],[])).
% 2.95/3.15 tff(12058,plain,
% 2.95/3.15 (((~r(s(s(s(elem!1))), s(s(s(z))))) | (~r(s(z), s(s(s(elem!1))))) | (~r(s(s(z)), s(s(s(elem!1))))) | (~r(s(s(z)), s(z)))) <=> ((~r(s(s(s(elem!1))), s(s(s(z))))) | (~r(s(z), s(s(s(elem!1))))) | (~r(s(s(z)), s(z))) | (~r(s(s(z)), s(s(s(elem!1))))))),
% 2.95/3.15 inference(rewrite,[status(thm)],[])).
% 2.95/3.15 tff(12059,plain,
% 2.95/3.15 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), s(s(s(z))))) | (~r(s(z), s(s(s(elem!1))))) | (~r(s(s(z)), s(s(s(elem!1))))) | (~r(s(s(z)), s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), s(s(s(z))))) | (~r(s(z), s(s(s(elem!1))))) | (~r(s(s(z)), s(z))) | (~r(s(s(z)), s(s(s(elem!1)))))))),
% 2.95/3.15 inference(monotonicity,[status(thm)],[12058])).
% 2.95/3.15 tff(12060,plain,
% 2.95/3.15 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), s(s(s(z))))) | (~r(s(z), s(s(s(elem!1))))) | (~r(s(s(z)), s(s(s(elem!1))))) | (~r(s(s(z)), s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(elem!1))), s(s(s(z))))) | (~r(s(z), s(s(s(elem!1))))) | (~r(s(s(z)), s(z))) | (~r(s(s(z)), s(s(s(elem!1))))))),
% 2.95/3.15 inference(transitivity,[status(thm)],[12059, 12057])).
% 2.95/3.15 tff(12061,plain,
% 2.95/3.15 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), s(s(s(z))))) | (~r(s(z), s(s(s(elem!1))))) | (~r(s(s(z)), s(s(s(elem!1))))) | (~r(s(s(z)), s(z))))),
% 2.95/3.15 inference(quant_inst,[status(thm)],[])).
% 2.95/3.15 tff(12062,plain,
% 2.95/3.15 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(elem!1))), s(s(s(z))))) | (~r(s(z), s(s(s(elem!1))))) | (~r(s(s(z)), s(z))) | (~r(s(s(z)), s(s(s(elem!1)))))),
% 2.95/3.15 inference(modus_ponens,[status(thm)],[12061, 12060])).
% 2.95/3.15 tff(12063,plain,
% 2.95/3.15 ($false),
% 2.95/3.15 inference(unit_resolution,[status(thm)],[12062, 197, 392, 119, 281, 3183])).
% 2.95/3.15 tff(12064,plain,((~r(s(s(s(elem!1))), s(s(s(z))))) | (~r(s(s(z)), s(z))) | (~r(s(z), s(s(s(elem!1))))) | (~r(s(s(z)), s(s(s(elem!1)))))), inference(lemma,lemma(discharge,[]))).
% 2.95/3.15 tff(12065,plain,
% 2.95/3.15 (~r(s(s(s(elem!1))), s(s(s(z))))),
% 2.95/3.15 inference(unit_resolution,[status(thm)],[12064, 11978, 119, 12048])).
% 2.95/3.15 tff(12066,plain,
% 2.95/3.15 (b(s(s(s(elem!1))), s(s(s(z))))),
% 2.95/3.15 inference(unit_resolution,[status(thm)],[3574, 12065, 12056])).
% 2.95/3.15 tff(12067,plain,
% 2.95/3.15 (~b(s(s(s(z))), z)),
% 2.95/3.15 inference(unit_resolution,[status(thm)],[11874, 12066, 96, 95, 12054])).
% 2.95/3.15 tff(12068,plain,
% 2.95/3.15 (r(s(s(s(z))), z)),
% 2.95/3.15 inference(unit_resolution,[status(thm)],[1713, 12067])).
% 2.95/3.15 tff(12069,plain,
% 2.95/3.15 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(s(z))))) | (~r(s(s(z)), z)) | (~r(s(s(z)), s(s(s(z))))) | (~r(s(s(s(z))), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, s(s(s(z))))) | (~r(s(s(z)), z)) | (~r(s(s(z)), s(s(s(z))))) | (~r(s(s(s(z))), z)))),
% 2.95/3.15 inference(rewrite,[status(thm)],[])).
% 2.95/3.15 tff(12070,plain,
% 2.95/3.15 (((~r(s(s(s(z))), z)) | (~r(z, s(s(s(z))))) | (~r(s(s(z)), s(s(s(z))))) | (~r(s(s(z)), z))) <=> ((~r(z, s(s(s(z))))) | (~r(s(s(z)), z)) | (~r(s(s(z)), s(s(s(z))))) | (~r(s(s(s(z))), z)))),
% 2.95/3.15 inference(rewrite,[status(thm)],[])).
% 2.95/3.15 tff(12071,plain,
% 2.95/3.15 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(z))), z)) | (~r(z, s(s(s(z))))) | (~r(s(s(z)), s(s(s(z))))) | (~r(s(s(z)), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(s(z))))) | (~r(s(s(z)), z)) | (~r(s(s(z)), s(s(s(z))))) | (~r(s(s(s(z))), z))))),
% 2.95/3.15 inference(monotonicity,[status(thm)],[12070])).
% 2.95/3.15 tff(12072,plain,
% 2.95/3.15 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(z))), z)) | (~r(z, s(s(s(z))))) | (~r(s(s(z)), s(s(s(z))))) | (~r(s(s(z)), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, s(s(s(z))))) | (~r(s(s(z)), z)) | (~r(s(s(z)), s(s(s(z))))) | (~r(s(s(s(z))), z)))),
% 2.95/3.15 inference(transitivity,[status(thm)],[12071, 12069])).
% 2.95/3.15 tff(12073,plain,
% 2.95/3.15 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(z))), z)) | (~r(z, s(s(s(z))))) | (~r(s(s(z)), s(s(s(z))))) | (~r(s(s(z)), z)))),
% 2.95/3.16 inference(quant_inst,[status(thm)],[])).
% 2.95/3.16 tff(12074,plain,
% 2.95/3.16 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, s(s(s(z))))) | (~r(s(s(z)), z)) | (~r(s(s(z)), s(s(s(z))))) | (~r(s(s(s(z))), z))),
% 2.95/3.16 inference(modus_ponens,[status(thm)],[12073, 12072])).
% 2.95/3.16 tff(12075,plain,
% 2.95/3.16 ($false),
% 2.95/3.16 inference(unit_resolution,[status(thm)],[12074, 197, 866, 1677, 1733, 1732])).
% 2.95/3.16 tff(12076,plain,((~r(z, s(s(s(z))))) | (~r(s(s(z)), z)) | (~r(s(s(s(z))), z)) | (~r(s(s(z)), s(s(s(z)))))), inference(lemma,lemma(discharge,[]))).
% 2.95/3.16 tff(12077,plain,
% 2.95/3.16 (~r(s(s(z)), s(s(s(z))))),
% 2.95/3.16 inference(unit_resolution,[status(thm)],[12076, 1677, 866, 1733])).
% 2.95/3.16 tff(12078,plain,
% 2.95/3.16 (b(s(s(z)), s(s(s(z))))),
% 2.95/3.16 inference(unit_resolution,[status(thm)],[1730, 12077])).
% 2.95/3.16 tff(12079,plain,
% 2.95/3.16 (~r(s(s(s(z))), s(z))),
% 2.95/3.16 inference(unit_resolution,[status(thm)],[11941, 1677, 97, 1733])).
% 2.95/3.16 tff(12080,plain,
% 2.95/3.16 (b(s(s(s(z))), s(z))),
% 2.95/3.16 inference(unit_resolution,[status(thm)],[1763, 12079])).
% 2.95/3.16 tff(12081,plain,
% 2.95/3.16 ($false),
% 2.95/3.16 inference(unit_resolution,[status(thm)],[11894, 12080, 12078, 121, 96, 2060])).
% 2.95/3.16 tff(12082,plain,((~r(z, s(s(s(z))))) | (~b(s(s(s(elem!1))), z)) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(s(s(elem!1))), s(s(z)))) | (~r(s(z), z)) | (~r(s(s(s(z))), z)) | (~r(s(s(z)), z))), inference(lemma,lemma(discharge,[]))).
% 2.95/3.16 tff(12083,plain,
% 2.95/3.16 (~r(z, s(s(s(z))))),
% 2.95/3.16 inference(unit_resolution,[status(thm)],[12082, 12037, 96, 95, 97, 12068, 11976])).
% 2.95/3.16 tff(12084,plain,
% 2.95/3.16 (b(z, s(s(s(z))))),
% 2.95/3.16 inference(unit_resolution,[status(thm)],[1697, 12083])).
% 2.95/3.16 tff(12085,plain,
% 2.95/3.16 (~b(s(s(z)), s(s(s(z))))),
% 2.95/3.16 inference(unit_resolution,[status(thm)],[11894, 3240, 121, 96, 2060])).
% 2.95/3.16 tff(12086,plain,
% 2.95/3.16 (r(s(s(z)), s(s(s(z))))),
% 2.95/3.16 inference(unit_resolution,[status(thm)],[1730, 12085])).
% 2.95/3.16 tff(12087,plain,
% 2.95/3.16 (~b(s(z), s(s(s(z))))),
% 2.95/3.16 inference(unit_resolution,[status(thm)],[11934, 3240, 96, 3251])).
% 2.95/3.16 tff(12088,plain,
% 2.95/3.16 (r(s(z), s(s(s(z))))),
% 2.95/3.16 inference(unit_resolution,[status(thm)],[1674, 12087])).
% 2.95/3.16 tff(12089,plain,
% 2.95/3.16 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(z)), s(z))) | (~r(s(s(z)), s(s(s(z))))) | (~r(s(s(s(z))), z)) | (~r(s(z), s(s(s(z))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(z)), s(z))) | (~r(s(s(z)), s(s(s(z))))) | (~r(s(s(s(z))), z)) | (~r(s(z), s(s(s(z))))))),
% 2.95/3.16 inference(rewrite,[status(thm)],[])).
% 2.95/3.16 tff(12090,plain,
% 2.95/3.16 (((~r(s(s(s(z))), z)) | (~r(s(z), s(s(s(z))))) | (~r(s(s(z)), s(s(s(z))))) | (~r(s(s(z)), s(z)))) <=> ((~r(s(s(z)), s(z))) | (~r(s(s(z)), s(s(s(z))))) | (~r(s(s(s(z))), z)) | (~r(s(z), s(s(s(z))))))),
% 2.95/3.16 inference(rewrite,[status(thm)],[])).
% 2.95/3.16 tff(12091,plain,
% 2.95/3.16 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(z))), z)) | (~r(s(z), s(s(s(z))))) | (~r(s(s(z)), s(s(s(z))))) | (~r(s(s(z)), s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(z)), s(z))) | (~r(s(s(z)), s(s(s(z))))) | (~r(s(s(s(z))), z)) | (~r(s(z), s(s(s(z)))))))),
% 2.95/3.16 inference(monotonicity,[status(thm)],[12090])).
% 2.95/3.16 tff(12092,plain,
% 2.95/3.16 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(z))), z)) | (~r(s(z), s(s(s(z))))) | (~r(s(s(z)), s(s(s(z))))) | (~r(s(s(z)), s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(z)), s(z))) | (~r(s(s(z)), s(s(s(z))))) | (~r(s(s(s(z))), z)) | (~r(s(z), s(s(s(z))))))),
% 2.95/3.16 inference(transitivity,[status(thm)],[12091, 12089])).
% 2.95/3.16 tff(12093,plain,
% 2.95/3.16 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(z))), z)) | (~r(s(z), s(s(s(z))))) | (~r(s(s(z)), s(s(s(z))))) | (~r(s(s(z)), s(z))))),
% 2.95/3.16 inference(quant_inst,[status(thm)],[])).
% 2.95/3.16 tff(12094,plain,
% 2.95/3.16 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(z)), s(z))) | (~r(s(s(z)), s(s(s(z))))) | (~r(s(s(s(z))), z)) | (~r(s(z), s(s(s(z)))))),
% 2.95/3.16 inference(modus_ponens,[status(thm)],[12093, 12092])).
% 2.95/3.16 tff(12095,plain,
% 2.95/3.16 ($false),
% 2.95/3.16 inference(unit_resolution,[status(thm)],[12094, 197, 392, 1733, 1653, 1732])).
% 2.95/3.16 tff(12096,plain,((~r(s(s(z)), s(s(s(z))))) | (~r(s(s(z)), s(z))) | (~r(s(s(s(z))), z)) | (~r(s(z), s(s(s(z)))))), inference(lemma,lemma(discharge,[]))).
% 2.95/3.16 tff(12097,plain,
% 2.95/3.16 ($false),
% 2.95/3.16 inference(unit_resolution,[status(thm)],[12096, 12088, 12086, 392, 1733])).
% 2.95/3.16 tff(12098,plain,((~b(s(s(s(z))), s(z))) | (~r(s(s(z)), s(z))) | (~r(s(s(s(z))), z)) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(s(s(elem!1))), s(s(s(z))))) | (~b(s(s(s(elem!1))), z)) | (~b(s(s(s(elem!1))), s(s(z))))), inference(lemma,lemma(discharge,[]))).
% 2.95/3.16 tff(12099,plain,
% 2.95/3.16 (~b(s(s(s(z))), s(z))),
% 2.95/3.16 inference(unit_resolution,[status(thm)],[12098, 11978, 12068, 96, 12066, 95, 12037])).
% 2.95/3.16 tff(12100,plain,
% 2.95/3.16 (r(s(s(s(z))), s(z))),
% 2.95/3.16 inference(unit_resolution,[status(thm)],[1763, 12099])).
% 2.95/3.16 tff(12101,plain,
% 2.95/3.16 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), z)) | (~r(s(s(z)), s(z))) | (~r(s(s(s(z))), s(z))) | (~r(s(s(s(z))), s(s(z)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(z), z)) | (~r(s(s(z)), s(z))) | (~r(s(s(s(z))), s(z))) | (~r(s(s(s(z))), s(s(z)))))),
% 2.95/3.16 inference(rewrite,[status(thm)],[])).
% 2.95/3.16 tff(12102,plain,
% 2.95/3.16 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), z)) | (~r(s(s(z)), s(z))) | (~r(s(s(s(z))), s(z))) | (~r(s(s(s(z))), s(s(z)))))),
% 2.95/3.16 inference(quant_inst,[status(thm)],[])).
% 2.95/3.16 tff(12103,plain,
% 2.95/3.16 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(z), z)) | (~r(s(s(z)), s(z))) | (~r(s(s(s(z))), s(z))) | (~r(s(s(s(z))), s(s(z))))),
% 2.95/3.16 inference(modus_ponens,[status(thm)],[12102, 12101])).
% 2.95/3.16 tff(12104,plain,
% 2.95/3.16 (~r(s(s(s(z))), s(s(z)))),
% 2.95/3.16 inference(unit_resolution,[status(thm)],[12103, 197, 97, 11978, 12100])).
% 2.95/3.16 tff(12105,plain,
% 2.95/3.16 (b(s(s(s(z))), s(s(z)))),
% 2.95/3.16 inference(unit_resolution,[status(thm)],[1010, 12104])).
% 2.95/3.16 tff(12106,plain,
% 2.95/3.16 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), z)) | (~r(s(s(z)), s(z))) | (~r(s(s(z)), s(s(s(z))))) | (~r(s(s(s(z))), s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(z), z)) | (~r(s(s(z)), s(z))) | (~r(s(s(z)), s(s(s(z))))) | (~r(s(s(s(z))), s(z))))),
% 2.95/3.16 inference(rewrite,[status(thm)],[])).
% 2.95/3.16 tff(12107,plain,
% 2.95/3.16 (((~r(s(z), z)) | (~r(s(s(s(z))), s(z))) | (~r(s(s(z)), s(z))) | (~r(s(s(z)), s(s(s(z)))))) <=> ((~r(s(z), z)) | (~r(s(s(z)), s(z))) | (~r(s(s(z)), s(s(s(z))))) | (~r(s(s(s(z))), s(z))))),
% 2.95/3.16 inference(rewrite,[status(thm)],[])).
% 2.95/3.16 tff(12108,plain,
% 2.95/3.16 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), z)) | (~r(s(s(s(z))), s(z))) | (~r(s(s(z)), s(z))) | (~r(s(s(z)), s(s(s(z))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), z)) | (~r(s(s(z)), s(z))) | (~r(s(s(z)), s(s(s(z))))) | (~r(s(s(s(z))), s(z)))))),
% 2.95/3.16 inference(monotonicity,[status(thm)],[12107])).
% 2.95/3.16 tff(12109,plain,
% 2.95/3.16 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), z)) | (~r(s(s(s(z))), s(z))) | (~r(s(s(z)), s(z))) | (~r(s(s(z)), s(s(s(z))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(z), z)) | (~r(s(s(z)), s(z))) | (~r(s(s(z)), s(s(s(z))))) | (~r(s(s(s(z))), s(z))))),
% 2.95/3.16 inference(transitivity,[status(thm)],[12108, 12106])).
% 2.95/3.16 tff(12110,plain,
% 2.95/3.16 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), z)) | (~r(s(s(s(z))), s(z))) | (~r(s(s(z)), s(z))) | (~r(s(s(z)), s(s(s(z))))))),
% 2.95/3.16 inference(quant_inst,[status(thm)],[])).
% 2.95/3.16 tff(12111,plain,
% 2.95/3.16 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(z), z)) | (~r(s(s(z)), s(z))) | (~r(s(s(z)), s(s(s(z))))) | (~r(s(s(s(z))), s(z)))),
% 2.95/3.16 inference(modus_ponens,[status(thm)],[12110, 12109])).
% 2.95/3.16 tff(12112,plain,
% 2.95/3.16 (~r(s(s(z)), s(s(s(z))))),
% 2.95/3.16 inference(unit_resolution,[status(thm)],[12111, 197, 97, 11978, 12100])).
% 2.95/3.16 tff(12113,plain,
% 2.95/3.16 (b(s(s(z)), s(s(s(z))))),
% 2.95/3.16 inference(unit_resolution,[status(thm)],[1730, 12112])).
% 2.95/3.16 tff(12114,plain,
% 2.95/3.16 ($false),
% 2.95/3.16 inference(unit_resolution,[status(thm)],[11914, 12113, 12105, 12084])).
% 2.95/3.16 tff(12115,plain,((~b(z, s(z))) | (~r(s(z), z)) | (~b(s(s(s(elem!1))), s(z))) | (~r(s(z), s(s(s(elem!1))))) | r(s(s(s(elem!1))), z) | b(s(z), s(s(elem!1)))), inference(lemma,lemma(discharge,[]))).
% 2.95/3.16 tff(12116,plain,
% 2.95/3.16 (~b(z, s(z))),
% 2.95/3.16 inference(unit_resolution,[status(thm)],[12115, 117, 96, 97, 86, 54])).
% 2.95/3.16 tff(12117,plain,
% 2.95/3.16 (r(z, s(z))),
% 2.95/3.16 inference(unit_resolution,[status(thm)],[321, 12116])).
% 2.95/3.16 tff(12118,plain,
% 2.95/3.16 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(z)))) | (~b(s(s(s(elem!1))), z)) | (~b(s(s(z)), z)) | (~b(s(s(z)), s(z))) | (~b(s(s(z)), s(s(s(elem!1))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(s(z)))) | (~b(s(s(s(elem!1))), z)) | (~b(s(s(z)), z)) | (~b(s(s(z)), s(z))) | (~b(s(s(z)), s(s(s(elem!1))))))),
% 2.95/3.16 inference(rewrite,[status(thm)],[])).
% 2.95/3.16 tff(12119,plain,
% 2.95/3.16 (((~b(s(s(z)), s(z))) | (~b(s(s(z)), s(z))) | (~b(z, s(s(z)))) | (~b(s(s(s(elem!1))), z)) | (~b(s(s(z)), z)) | (~b(s(s(z)), s(s(s(elem!1)))))) <=> ((~b(z, s(s(z)))) | (~b(s(s(s(elem!1))), z)) | (~b(s(s(z)), z)) | (~b(s(s(z)), s(z))) | (~b(s(s(z)), s(s(s(elem!1))))))),
% 2.95/3.16 inference(rewrite,[status(thm)],[])).
% 2.95/3.16 tff(12120,plain,
% 2.95/3.16 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), s(z))) | (~b(s(s(z)), s(z))) | (~b(z, s(s(z)))) | (~b(s(s(s(elem!1))), z)) | (~b(s(s(z)), z)) | (~b(s(s(z)), s(s(s(elem!1))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(z)))) | (~b(s(s(s(elem!1))), z)) | (~b(s(s(z)), z)) | (~b(s(s(z)), s(z))) | (~b(s(s(z)), s(s(s(elem!1)))))))),
% 2.95/3.16 inference(monotonicity,[status(thm)],[12119])).
% 2.95/3.16 tff(12121,plain,
% 2.95/3.16 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), s(z))) | (~b(s(s(z)), s(z))) | (~b(z, s(s(z)))) | (~b(s(s(s(elem!1))), z)) | (~b(s(s(z)), z)) | (~b(s(s(z)), s(s(s(elem!1))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(s(z)))) | (~b(s(s(s(elem!1))), z)) | (~b(s(s(z)), z)) | (~b(s(s(z)), s(z))) | (~b(s(s(z)), s(s(s(elem!1))))))),
% 2.95/3.16 inference(transitivity,[status(thm)],[12120, 12118])).
% 2.95/3.16 tff(12122,plain,
% 2.95/3.16 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), s(z))) | (~b(s(s(z)), s(z))) | (~b(z, s(s(z)))) | (~b(s(s(s(elem!1))), z)) | (~b(s(s(z)), z)) | (~b(s(s(z)), s(s(s(elem!1))))))),
% 2.95/3.16 inference(quant_inst,[status(thm)],[])).
% 2.95/3.16 tff(12123,plain,
% 2.95/3.16 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(s(z)))) | (~b(s(s(s(elem!1))), z)) | (~b(s(s(z)), z)) | (~b(s(s(z)), s(z))) | (~b(s(s(z)), s(s(s(elem!1)))))),
% 2.95/3.16 inference(modus_ponens,[status(thm)],[12122, 12121])).
% 2.95/3.16 tff(12124,plain,
% 2.95/3.16 ((~b(s(s(z)), z)) | (~b(s(s(z)), s(s(s(elem!1)))))),
% 2.95/3.16 inference(unit_resolution,[status(thm)],[12123, 166, 10450, 121, 156])).
% 2.95/3.16 tff(12125,plain,
% 2.95/3.16 (~b(s(s(z)), z)),
% 2.95/3.16 inference(unit_resolution,[status(thm)],[12124, 263])).
% 2.95/3.16 tff(12126,plain,
% 2.95/3.16 (r(s(s(z)), z)),
% 2.95/3.16 inference(unit_resolution,[status(thm)],[186, 12125])).
% 2.95/3.16 tff(12127,plain,
% 2.95/3.16 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(z))) | (~r(s(z), z)) | (~r(s(z), s(s(z)))) | (~r(s(s(z)), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, s(z))) | (~r(s(z), z)) | (~r(s(z), s(s(z)))) | (~r(s(s(z)), z)))),
% 2.95/3.16 inference(rewrite,[status(thm)],[])).
% 2.95/3.16 tff(12128,plain,
% 2.95/3.16 (((~r(z, s(z))) | (~r(s(s(z)), z)) | (~r(s(z), z)) | (~r(s(z), s(s(z))))) <=> ((~r(z, s(z))) | (~r(s(z), z)) | (~r(s(z), s(s(z)))) | (~r(s(s(z)), z)))),
% 2.95/3.16 inference(rewrite,[status(thm)],[])).
% 2.95/3.16 tff(12129,plain,
% 2.95/3.16 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(z))) | (~r(s(s(z)), z)) | (~r(s(z), z)) | (~r(s(z), s(s(z)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(z))) | (~r(s(z), z)) | (~r(s(z), s(s(z)))) | (~r(s(s(z)), z))))),
% 2.95/3.16 inference(monotonicity,[status(thm)],[12128])).
% 2.95/3.16 tff(12130,plain,
% 2.95/3.16 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(z))) | (~r(s(s(z)), z)) | (~r(s(z), z)) | (~r(s(z), s(s(z)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, s(z))) | (~r(s(z), z)) | (~r(s(z), s(s(z)))) | (~r(s(s(z)), z)))),
% 2.95/3.16 inference(transitivity,[status(thm)],[12129, 12127])).
% 2.95/3.16 tff(12131,plain,
% 2.95/3.16 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(z))) | (~r(s(s(z)), z)) | (~r(s(z), z)) | (~r(s(z), s(s(z)))))),
% 2.95/3.16 inference(quant_inst,[status(thm)],[])).
% 2.95/3.16 tff(12132,plain,
% 2.95/3.16 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, s(z))) | (~r(s(z), z)) | (~r(s(z), s(s(z)))) | (~r(s(s(z)), z))),
% 2.95/3.16 inference(modus_ponens,[status(thm)],[12131, 12130])).
% 2.95/3.16 tff(12133,plain,
% 2.95/3.16 (~r(s(z), s(s(z)))),
% 2.95/3.16 inference(unit_resolution,[status(thm)],[12132, 197, 323, 97, 12126])).
% 2.95/3.16 tff(12134,plain,
% 2.95/3.16 (b(s(z), s(s(z)))),
% 2.95/3.16 inference(unit_resolution,[status(thm)],[427, 12133])).
% 2.95/3.16 tff(12135,plain,
% 2.95/3.16 ($false),
% 2.95/3.16 inference(unit_resolution,[status(thm)],[4503, 166, 12134, 96, 156, 263])).
% 2.95/3.16 tff(12136,plain,((~b(s(s(z)), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(s(z)), s(z))) | (~r(z, s(z))) | (~r(s(z), z)) | (~b(s(s(s(elem!1))), z))), inference(lemma,lemma(discharge,[]))).
% 2.95/3.16 tff(12137,plain,
% 2.95/3.16 (~b(s(s(z)), s(s(s(elem!1))))),
% 2.95/3.16 inference(unit_resolution,[status(thm)],[12136, 156, 96, 323, 97, 121])).
% 2.95/3.16 tff(12138,plain,
% 2.95/3.16 (r(s(s(z)), s(s(s(elem!1))))),
% 2.95/3.16 inference(unit_resolution,[status(thm)],[279, 12137])).
% 2.95/3.16 tff(12139,plain,
% 2.95/3.16 (~r(s(s(elem!1)), s(s(s(elem!1))))),
% 2.95/3.16 inference(unit_resolution,[status(thm)],[2939, 464, 311, 117])).
% 2.95/3.16 tff(12140,plain,
% 2.95/3.16 (~r(z, s(s(s(elem!1))))),
% 2.95/3.16 inference(unit_resolution,[status(thm)],[2057, 464, 117, 323])).
% 2.95/3.16 tff(12141,plain,
% 2.95/3.16 (b(z, s(s(s(elem!1))))),
% 2.95/3.16 inference(unit_resolution,[status(thm)],[261, 12140])).
% 2.95/3.16 tff(12142,plain,
% 2.95/3.16 (~r(s(s(elem!1)), z)),
% 2.95/3.16 inference(unit_resolution,[status(thm)],[4478, 4458, 311, 97])).
% 2.95/3.16 tff(12143,plain,
% 2.95/3.16 (b(s(s(elem!1)), z)),
% 2.95/3.16 inference(unit_resolution,[status(thm)],[608, 12142])).
% 2.95/3.16 tff(12144,plain,
% 2.95/3.16 ($false),
% 2.95/3.16 inference(unit_resolution,[status(thm)],[600, 12143, 4470, 121, 240])).
% 2.95/3.16 tff(12145,plain,(b(z, s(s(elem!1))) | (~b(s(s(s(elem!1))), z)) | (~b(z, s(s(s(elem!1))))) | r(s(s(elem!1)), s(s(s(elem!1)))) | (~r(s(z), s(s(elem!1)))) | (~r(s(z), z))), inference(lemma,lemma(discharge,[]))).
% 2.95/3.16 tff(12146,plain,
% 2.95/3.16 (b(z, s(s(elem!1)))),
% 2.95/3.16 inference(unit_resolution,[status(thm)],[12145, 240, 121, 1821, 311, 97])).
% 2.95/3.16 tff(12147,plain,
% 2.95/3.16 (r(s(s(s(elem!1))), s(s(elem!1)))),
% 2.95/3.16 inference(unit_resolution,[status(thm)],[1834, 45, 240, 12146, 1821])).
% 2.95/3.16 tff(12148,plain,
% 2.95/3.16 (~r(s(s(s(elem!1))), z)),
% 2.95/3.16 inference(unit_resolution,[status(thm)],[2489, 2481, 98, 97])).
% 2.95/3.16 tff(12149,plain,
% 2.95/3.16 (b(s(s(s(elem!1))), z)),
% 2.95/3.16 inference(unit_resolution,[status(thm)],[94, 12148])).
% 2.95/3.16 tff(12150,plain,
% 2.95/3.16 (~b(s(s(elem!1)), z)),
% 2.95/3.16 inference(unit_resolution,[status(thm)],[3593, 12149, 1820, 463])).
% 2.95/3.16 tff(12151,plain,
% 2.95/3.16 (r(s(s(elem!1)), z)),
% 2.95/3.16 inference(unit_resolution,[status(thm)],[608, 12150])).
% 2.95/3.16 tff(12152,plain,
% 2.95/3.16 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, elem!1)) | (~r(s(z), s(s(elem!1)))) | (~r(s(s(elem!1)), z)) | (~r(s(z), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, elem!1)) | (~r(s(z), s(s(elem!1)))) | (~r(s(s(elem!1)), z)) | (~r(s(z), z)))),
% 2.95/3.16 inference(rewrite,[status(thm)],[])).
% 2.95/3.16 tff(12153,plain,
% 2.95/3.16 (((~r(z, elem!1)) | (~r(s(s(elem!1)), z)) | (~r(s(z), z)) | (~r(s(z), s(s(elem!1))))) <=> ((~r(z, elem!1)) | (~r(s(z), s(s(elem!1)))) | (~r(s(s(elem!1)), z)) | (~r(s(z), z)))),
% 2.95/3.16 inference(rewrite,[status(thm)],[])).
% 2.95/3.16 tff(12154,plain,
% 2.95/3.16 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, elem!1)) | (~r(s(s(elem!1)), z)) | (~r(s(z), z)) | (~r(s(z), s(s(elem!1)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, elem!1)) | (~r(s(z), s(s(elem!1)))) | (~r(s(s(elem!1)), z)) | (~r(s(z), z))))),
% 2.95/3.16 inference(monotonicity,[status(thm)],[12153])).
% 2.95/3.16 tff(12155,plain,
% 2.95/3.16 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, elem!1)) | (~r(s(s(elem!1)), z)) | (~r(s(z), z)) | (~r(s(z), s(s(elem!1)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, elem!1)) | (~r(s(z), s(s(elem!1)))) | (~r(s(s(elem!1)), z)) | (~r(s(z), z)))),
% 2.95/3.16 inference(transitivity,[status(thm)],[12154, 12152])).
% 2.95/3.16 tff(12156,plain,
% 2.95/3.16 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, elem!1)) | (~r(s(s(elem!1)), z)) | (~r(s(z), z)) | (~r(s(z), s(s(elem!1)))))),
% 2.95/3.16 inference(quant_inst,[status(thm)],[])).
% 2.95/3.16 tff(12157,plain,
% 2.95/3.16 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, elem!1)) | (~r(s(z), s(s(elem!1)))) | (~r(s(s(elem!1)), z)) | (~r(s(z), z))),
% 2.95/3.16 inference(modus_ponens,[status(thm)],[12156, 12155])).
% 2.95/3.16 tff(12158,plain,
% 2.95/3.16 ($false),
% 2.95/3.16 inference(unit_resolution,[status(thm)],[12157, 197, 2481, 311, 97, 12151])).
% 2.95/3.16 tff(12159,plain,((~r(z, elem!1)) | (~r(s(z), s(s(elem!1)))) | (~r(s(z), z)) | (~b(z, s(s(elem!1)))) | (~b(s(s(elem!1)), s(s(s(elem!1))))) | b(s(z), s(s(s(elem!1))))), inference(lemma,lemma(discharge,[]))).
% 2.95/3.16 tff(12160,plain,
% 2.95/3.16 (~r(z, elem!1)),
% 2.95/3.16 inference(unit_resolution,[status(thm)],[12159, 1822, 97, 311, 98, 12146])).
% 2.95/3.16 tff(12161,plain,
% 2.95/3.16 ($false),
% 2.95/3.16 inference(unit_resolution,[status(thm)],[10515, 12160, 12147, 240, 121, 12146, 45, 311, 117])).
% 2.95/3.16 tff(12162,plain,((s(s(elem!1)) = s(s(s(elem!1)))) | (~b(z, s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), z)) | (~r(s(z), s(s(elem!1)))) | (~r(s(z), z)) | b(s(z), s(s(s(elem!1)))) | r(s(s(elem!1)), s(s(s(elem!1))))), inference(lemma,lemma(discharge,[]))).
% 2.95/3.16 tff(12163,plain,
% 2.95/3.16 (s(s(elem!1)) = s(s(s(elem!1)))),
% 2.95/3.16 inference(unit_resolution,[status(thm)],[12162, 12141, 121, 311, 97, 98, 12139])).
% 2.95/3.16 tff(12164,plain,
% 2.95/3.16 (s(s(s(elem!1))) = s(elem!1)),
% 2.95/3.16 inference(unit_resolution,[status(thm)],[2594, 12163])).
% 2.95/3.16 tff(12165,plain,
% 2.95/3.16 (s(elem!1) = s(s(s(elem!1)))),
% 2.95/3.16 inference(symmetry,[status(thm)],[12164])).
% 2.95/3.16 tff(12166,plain,
% 2.95/3.16 (inj_0(s(elem!1)) = inj_0(s(s(s(elem!1))))),
% 2.95/3.16 inference(monotonicity,[status(thm)],[12165])).
% 2.95/3.16 tff(12167,plain,
% 2.95/3.16 (elem!1 = s(s(elem!1))),
% 2.95/3.17 inference(transitivity,[status(thm)],[1170, 12166, 104])).
% 2.95/3.17 tff(12168,plain,
% 2.95/3.17 (r(s(s(s(z))), elem!1) <=> r(s(s(s(z))), s(s(elem!1)))),
% 2.95/3.17 inference(monotonicity,[status(thm)],[12167])).
% 2.95/3.17 tff(12169,plain,
% 2.95/3.17 (~(s(s(s(z))) = elem!1)),
% 2.95/3.17 inference(unit_resolution,[status(thm)],[3122, 12163])).
% 2.95/3.17 tff(12170,plain,
% 2.95/3.17 (s(s(s(elem!1))) = s(s(elem!1))),
% 2.95/3.17 inference(unit_resolution,[status(thm)],[4030, 12163])).
% 2.95/3.17 tff(12171,plain,
% 2.95/3.17 (((~b(s(s(s(elem!1))), z)) | (~b(s(s(s(z))), z)) | (~b(z, s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), z)) | (~b(s(s(s(z))), z)) | (~b(s(s(s(z))), s(s(s(elem!1)))))) <=> ((~b(z, s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), z)) | (~b(s(s(s(z))), z)) | (~b(s(s(s(z))), s(s(s(elem!1))))))),
% 2.95/3.17 inference(rewrite,[status(thm)],[])).
% 2.95/3.17 tff(12172,plain,
% 2.95/3.17 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), z)) | (~b(s(s(s(z))), z)) | (~b(z, s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), z)) | (~b(s(s(s(z))), z)) | (~b(s(s(s(z))), s(s(s(elem!1))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), z)) | (~b(s(s(s(z))), z)) | (~b(s(s(s(z))), s(s(s(elem!1)))))))),
% 2.95/3.17 inference(monotonicity,[status(thm)],[12171])).
% 2.95/3.17 tff(12173,plain,
% 2.95/3.17 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), z)) | (~b(s(s(s(z))), z)) | (~b(z, s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), z)) | (~b(s(s(s(z))), z)) | (~b(s(s(s(z))), s(s(s(elem!1))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), z)) | (~b(s(s(s(z))), z)) | (~b(s(s(s(z))), s(s(s(elem!1))))))),
% 2.95/3.17 inference(transitivity,[status(thm)],[12172, 8088])).
% 2.95/3.17 tff(12174,plain,
% 2.95/3.17 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), z)) | (~b(s(s(s(z))), z)) | (~b(z, s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), z)) | (~b(s(s(s(z))), z)) | (~b(s(s(s(z))), s(s(s(elem!1))))))),
% 2.95/3.17 inference(quant_inst,[status(thm)],[])).
% 2.95/3.17 tff(12175,plain,
% 2.95/3.17 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), z)) | (~b(s(s(s(z))), z)) | (~b(s(s(s(z))), s(s(s(elem!1)))))),
% 2.95/3.17 inference(modus_ponens,[status(thm)],[12174, 12173])).
% 2.95/3.17 tff(12176,plain,
% 2.95/3.17 (~b(s(s(s(z))), s(s(s(elem!1))))),
% 2.95/3.17 inference(unit_resolution,[status(thm)],[12175, 166, 12141, 121, 1699])).
% 2.95/3.17 tff(12177,plain,
% 2.95/3.17 (~b(s(s(s(z))), elem!1)),
% 2.95/3.17 inference(unit_resolution,[status(thm)],[4078, 12176, 12170])).
% 2.95/3.17 tff(12178,plain,
% 2.95/3.17 (r(s(s(s(z))), elem!1)),
% 2.95/3.17 inference(unit_resolution,[status(thm)],[2826, 12177, 12169])).
% 2.95/3.17 tff(12179,plain,
% 2.95/3.17 (r(s(s(s(z))), s(s(elem!1)))),
% 2.95/3.17 inference(modus_ponens,[status(thm)],[12178, 12168])).
% 2.95/3.17 tff(12180,plain,
% 2.95/3.17 (r(s(s(z)), s(s(elem!1))) <=> r(s(s(z)), s(s(s(elem!1))))),
% 2.95/3.17 inference(monotonicity,[status(thm)],[12163])).
% 2.95/3.17 tff(12181,plain,
% 2.95/3.17 (r(s(s(z)), s(s(s(elem!1)))) <=> r(s(s(z)), s(s(elem!1)))),
% 2.95/3.17 inference(symmetry,[status(thm)],[12180])).
% 2.95/3.17 tff(12182,plain,
% 2.95/3.17 (r(s(s(z)), s(s(elem!1)))),
% 2.95/3.17 inference(modus_ponens,[status(thm)],[281, 12181])).
% 2.95/3.17 tff(12183,plain,
% 2.95/3.17 (r(s(s(elem!1)), s(s(z))) <=> r(s(s(s(elem!1))), s(s(z)))),
% 2.95/3.17 inference(monotonicity,[status(thm)],[12163])).
% 2.95/3.17 tff(12184,plain,
% 2.95/3.17 (r(s(s(s(elem!1))), s(s(z))) <=> r(s(s(elem!1)), s(s(z)))),
% 2.95/3.17 inference(symmetry,[status(thm)],[12183])).
% 2.95/3.17 tff(12185,plain,
% 2.95/3.17 (r(s(s(elem!1)), s(s(z)))),
% 2.95/3.17 inference(modus_ponens,[status(thm)],[464, 12184])).
% 2.95/3.17 tff(12186,plain,
% 2.95/3.17 (~r(s(s(s(z))), s(s(elem!1)))),
% 2.95/3.17 inference(unit_resolution,[status(thm)],[4435, 12185, 311, 156, 12182])).
% 2.95/3.17 tff(12187,plain,
% 2.95/3.17 ($false),
% 2.95/3.17 inference(unit_resolution,[status(thm)],[12186, 12179])).
% 2.95/3.17 tff(12188,plain,((~r(s(s(s(elem!1))), s(s(z)))) | (~b(s(s(s(elem!1))), z)) | (~b(s(s(s(z))), z)) | (~r(s(z), s(s(elem!1)))) | (~b(s(s(z)), s(z))) | (~r(s(s(z)), s(s(s(elem!1))))) | (~r(s(z), z)) | b(s(z), s(s(s(elem!1)))) | (~r(z, s(z)))), inference(lemma,lemma(discharge,[]))).
% 2.95/3.17 tff(12189,plain,
% 2.95/3.17 (~r(s(s(s(elem!1))), s(s(z)))),
% 2.95/3.17 inference(unit_resolution,[status(thm)],[12188, 1699, 121, 85, 156, 12138, 97, 98, 323])).
% 2.95/3.17 tff(12190,plain,
% 2.95/3.17 (b(s(s(s(elem!1))), s(s(z)))),
% 2.95/3.17 inference(unit_resolution,[status(thm)],[218, 12189])).
% 2.95/3.17 tff(12191,plain,
% 2.95/3.17 (~b(s(s(z)), z)),
% 2.95/3.17 inference(unit_resolution,[status(thm)],[10460, 12190, 121])).
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% 2.95/3.17 (r(s(s(z)), z)),
% 2.95/3.17 inference(unit_resolution,[status(thm)],[186, 12191])).
% 2.95/3.17 tff(12193,plain,
% 2.95/3.17 (~r(s(z), s(s(z)))),
% 2.95/3.17 inference(unit_resolution,[status(thm)],[12132, 197, 323, 97, 12192])).
% 2.95/3.17 tff(12194,plain,
% 2.95/3.17 (b(s(z), s(s(z)))),
% 2.95/3.17 inference(unit_resolution,[status(thm)],[427, 12193])).
% 2.95/3.17 tff(12195,plain,
% 2.95/3.17 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(z)))) | (~b(s(s(s(elem!1))), z)) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(s(z)), s(z))) | (~b(s(s(s(z))), z)) | (~b(s(s(s(elem!1))), s(s(s(z))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(s(z)))) | (~b(s(s(s(elem!1))), z)) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(s(z)), s(z))) | (~b(s(s(s(z))), z)) | (~b(s(s(s(elem!1))), s(s(s(z))))))),
% 2.95/3.17 inference(rewrite,[status(thm)],[])).
% 2.95/3.17 tff(12196,plain,
% 2.95/3.17 (((~b(s(s(z)), s(z))) | (~b(s(s(s(elem!1))), s(z))) | (~b(z, s(s(z)))) | (~b(s(s(s(z))), z)) | (~b(s(s(s(elem!1))), z)) | (~b(s(s(s(elem!1))), s(s(s(z)))))) <=> ((~b(z, s(s(z)))) | (~b(s(s(s(elem!1))), z)) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(s(z)), s(z))) | (~b(s(s(s(z))), z)) | (~b(s(s(s(elem!1))), s(s(s(z))))))),
% 2.95/3.17 inference(rewrite,[status(thm)],[])).
% 2.95/3.17 tff(12197,plain,
% 2.95/3.17 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), s(z))) | (~b(s(s(s(elem!1))), s(z))) | (~b(z, s(s(z)))) | (~b(s(s(s(z))), z)) | (~b(s(s(s(elem!1))), z)) | (~b(s(s(s(elem!1))), s(s(s(z))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(z)))) | (~b(s(s(s(elem!1))), z)) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(s(z)), s(z))) | (~b(s(s(s(z))), z)) | (~b(s(s(s(elem!1))), s(s(s(z)))))))),
% 2.95/3.17 inference(monotonicity,[status(thm)],[12196])).
% 2.95/3.17 tff(12198,plain,
% 2.95/3.17 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), s(z))) | (~b(s(s(s(elem!1))), s(z))) | (~b(z, s(s(z)))) | (~b(s(s(s(z))), z)) | (~b(s(s(s(elem!1))), z)) | (~b(s(s(s(elem!1))), s(s(s(z))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(s(z)))) | (~b(s(s(s(elem!1))), z)) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(s(z)), s(z))) | (~b(s(s(s(z))), z)) | (~b(s(s(s(elem!1))), s(s(s(z))))))),
% 2.95/3.17 inference(transitivity,[status(thm)],[12197, 12195])).
% 2.95/3.17 tff(12199,plain,
% 2.95/3.17 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), s(z))) | (~b(s(s(s(elem!1))), s(z))) | (~b(z, s(s(z)))) | (~b(s(s(s(z))), z)) | (~b(s(s(s(elem!1))), z)) | (~b(s(s(s(elem!1))), s(s(s(z))))))),
% 2.95/3.17 inference(quant_inst,[status(thm)],[])).
% 2.95/3.17 tff(12200,plain,
% 2.95/3.17 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(s(z)))) | (~b(s(s(s(elem!1))), z)) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(s(z)), s(z))) | (~b(s(s(s(z))), z)) | (~b(s(s(s(elem!1))), s(s(s(z)))))),
% 2.95/3.17 inference(modus_ponens,[status(thm)],[12199, 12198])).
% 2.95/3.17 tff(12201,plain,
% 2.95/3.17 (~b(s(s(s(elem!1))), s(s(s(z))))),
% 2.95/3.17 inference(unit_resolution,[status(thm)],[12200, 166, 10450, 96, 121, 156, 1699])).
% 2.95/3.17 tff(12202,plain,
% 2.95/3.17 (~(s(s(z)) = s(s(elem!1)))),
% 2.95/3.17 inference(unit_resolution,[status(thm)],[4398, 12194, 54])).
% 2.95/3.17 tff(12203,plain,
% 2.95/3.17 (~(s(s(elem!1)) = s(s(z)))),
% 2.95/3.17 inference(unit_resolution,[status(thm)],[131, 12202])).
% 2.95/3.17 tff(12204,plain,
% 2.95/3.17 (~(s(s(s(elem!1))) = s(s(s(z))))),
% 2.95/3.17 inference(unit_resolution,[status(thm)],[139, 12203])).
% 2.95/3.17 tff(12205,plain,
% 2.95/3.17 (r(s(s(s(elem!1))), s(s(s(z))))),
% 2.95/3.17 inference(unit_resolution,[status(thm)],[3574, 12204, 12201])).
% 2.95/3.17 tff(12206,plain,
% 2.95/3.17 (~r(z, s(s(s(elem!1))))),
% 2.95/3.17 inference(unit_resolution,[status(thm)],[3191, 12205, 117, 323])).
% 2.95/3.17 tff(12207,plain,
% 2.95/3.17 (b(z, s(s(s(elem!1))))),
% 2.95/3.17 inference(unit_resolution,[status(thm)],[261, 12206])).
% 2.95/3.17 tff(12208,plain,
% 2.95/3.17 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(z)))) | (~b(z, s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(s(z)))) | (~b(s(z), s(s(z)))) | (~b(s(s(z)), s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(s(z)))) | (~b(z, s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(s(z)))) | (~b(s(z), s(s(z)))) | (~b(s(s(z)), s(z))))),
% 2.95/3.17 inference(rewrite,[status(thm)],[])).
% 2.95/3.17 tff(12209,plain,
% 2.95/3.17 (((~b(s(z), s(s(z)))) | (~b(z, s(s(z)))) | (~b(s(s(z)), s(z))) | (~b(s(s(s(elem!1))), s(s(z)))) | (~b(z, s(s(z)))) | (~b(z, s(s(s(elem!1)))))) <=> ((~b(z, s(s(z)))) | (~b(z, s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(s(z)))) | (~b(s(z), s(s(z)))) | (~b(s(s(z)), s(z))))),
% 2.95/3.17 inference(rewrite,[status(thm)],[])).
% 2.95/3.17 tff(12210,plain,
% 2.95/3.17 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(z)))) | (~b(z, s(s(z)))) | (~b(s(s(z)), s(z))) | (~b(s(s(s(elem!1))), s(s(z)))) | (~b(z, s(s(z)))) | (~b(z, s(s(s(elem!1))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(z)))) | (~b(z, s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(s(z)))) | (~b(s(z), s(s(z)))) | (~b(s(s(z)), s(z)))))),
% 2.95/3.17 inference(monotonicity,[status(thm)],[12209])).
% 2.95/3.17 tff(12211,plain,
% 2.95/3.17 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(z)))) | (~b(z, s(s(z)))) | (~b(s(s(z)), s(z))) | (~b(s(s(s(elem!1))), s(s(z)))) | (~b(z, s(s(z)))) | (~b(z, s(s(s(elem!1))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(s(z)))) | (~b(z, s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(s(z)))) | (~b(s(z), s(s(z)))) | (~b(s(s(z)), s(z))))),
% 2.95/3.17 inference(transitivity,[status(thm)],[12210, 12208])).
% 2.95/3.17 tff(12212,plain,
% 2.95/3.17 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(z)))) | (~b(z, s(s(z)))) | (~b(s(s(z)), s(z))) | (~b(s(s(s(elem!1))), s(s(z)))) | (~b(z, s(s(z)))) | (~b(z, s(s(s(elem!1))))))),
% 2.95/3.17 inference(quant_inst,[status(thm)],[])).
% 2.95/3.17 tff(12213,plain,
% 2.95/3.17 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(s(z)))) | (~b(z, s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(s(z)))) | (~b(s(z), s(s(z)))) | (~b(s(s(z)), s(z)))),
% 2.95/3.17 inference(modus_ponens,[status(thm)],[12212, 12211])).
% 2.95/3.17 tff(12214,plain,
% 2.95/3.17 ($false),
% 2.95/3.17 inference(unit_resolution,[status(thm)],[12213, 166, 12207, 12194, 10450, 156, 12190])).
% 2.95/3.17 tff(12215,plain,((~b(s(s(s(z))), z)) | (~b(s(s(z)), s(z))) | (~r(z, s(z))) | b(s(z), s(s(elem!1))) | (~r(s(z), z)) | (~b(s(s(s(elem!1))), z)) | b(s(z), s(s(s(elem!1)))) | (~b(s(s(s(elem!1))), s(z)))), inference(lemma,lemma(discharge,[]))).
% 2.95/3.17 tff(12216,plain,
% 2.95/3.17 (~b(s(s(s(z))), z)),
% 2.95/3.17 inference(unit_resolution,[status(thm)],[12215, 156, 323, 54, 97, 121, 98, 96])).
% 2.95/3.17 tff(12217,plain,
% 2.95/3.17 (r(s(s(s(z))), z)),
% 2.95/3.17 inference(unit_resolution,[status(thm)],[1713, 12216])).
% 2.95/3.17 tff(12218,plain,
% 2.95/3.17 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(z))) | (~r(s(z), z)) | (~r(s(s(s(z))), z)) | (~r(s(s(s(z))), s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, s(z))) | (~r(s(z), z)) | (~r(s(s(s(z))), z)) | (~r(s(s(s(z))), s(z))))),
% 2.95/3.17 inference(rewrite,[status(thm)],[])).
% 2.95/3.17 tff(12219,plain,
% 2.95/3.17 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(z))) | (~r(s(z), z)) | (~r(s(s(s(z))), z)) | (~r(s(s(s(z))), s(z))))),
% 2.95/3.17 inference(quant_inst,[status(thm)],[])).
% 2.95/3.17 tff(12220,plain,
% 2.95/3.17 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, s(z))) | (~r(s(z), z)) | (~r(s(s(s(z))), z)) | (~r(s(s(s(z))), s(z)))),
% 2.95/3.17 inference(modus_ponens,[status(thm)],[12219, 12218])).
% 2.95/3.17 tff(12221,plain,
% 2.95/3.17 (~r(s(s(s(z))), s(z))),
% 2.95/3.17 inference(unit_resolution,[status(thm)],[12220, 197, 323, 97, 12217])).
% 2.95/3.17 tff(12222,plain,
% 2.95/3.17 (b(s(s(s(z))), s(z))),
% 2.95/3.17 inference(unit_resolution,[status(thm)],[1763, 12221])).
% 2.95/3.17 tff(12223,plain,
% 2.95/3.17 (~r(s(z), s(s(s(z))))),
% 2.95/3.17 inference(unit_resolution,[status(thm)],[8876, 12217, 323, 97])).
% 2.95/3.17 tff(12224,plain,
% 2.95/3.17 (b(s(z), s(s(s(z))))),
% 2.95/3.17 inference(unit_resolution,[status(thm)],[1674, 12223])).
% 2.95/3.17 tff(12225,plain,
% 2.95/3.17 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), s(s(z)))) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(z)), s(z))) | (~b(s(z), s(s(s(z))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(elem!1))), s(s(z)))) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(z)), s(z))) | (~b(s(z), s(s(s(z))))))),
% 2.95/3.17 inference(rewrite,[status(thm)],[])).
% 2.95/3.17 tff(12226,plain,
% 2.95/3.17 (((~b(s(s(s(z))), s(z))) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(z)), s(z))) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(s(s(elem!1))), s(s(z))))) <=> ((~b(s(s(s(elem!1))), s(s(z)))) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(z)), s(z))) | (~b(s(z), s(s(s(z))))))),
% 2.95/3.17 inference(rewrite,[status(thm)],[])).
% 2.95/3.17 tff(12227,plain,
% 2.95/3.17 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), s(z))) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(z)), s(z))) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(s(s(elem!1))), s(s(z)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), s(s(z)))) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(z)), s(z))) | (~b(s(z), s(s(s(z)))))))),
% 2.95/3.17 inference(monotonicity,[status(thm)],[12226])).
% 2.95/3.17 tff(12228,plain,
% 2.95/3.17 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), s(z))) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(z)), s(z))) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(s(s(elem!1))), s(s(z)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(elem!1))), s(s(z)))) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(z)), s(z))) | (~b(s(z), s(s(s(z))))))),
% 2.95/3.17 inference(transitivity,[status(thm)],[12227, 12225])).
% 2.95/3.17 tff(12229,plain,
% 2.95/3.17 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), s(z))) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(z)), s(z))) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(s(s(elem!1))), s(s(z)))))),
% 2.95/3.17 inference(quant_inst,[status(thm)],[])).
% 2.95/3.17 tff(12230,plain,
% 2.95/3.17 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(elem!1))), s(s(z)))) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(z)), s(z))) | (~b(s(z), s(s(s(z)))))),
% 2.95/3.17 inference(modus_ponens,[status(thm)],[12229, 12228])).
% 2.95/3.17 tff(12231,plain,
% 2.95/3.17 (~b(s(s(s(elem!1))), s(s(z)))),
% 2.95/3.17 inference(unit_resolution,[status(thm)],[12230, 166, 96, 156, 12224, 12222])).
% 2.95/3.17 tff(12232,plain,
% 2.95/3.17 (r(s(s(s(elem!1))), s(s(z)))),
% 2.95/3.17 inference(unit_resolution,[status(thm)],[218, 12231])).
% 2.95/3.17 tff(12233,plain,
% 2.95/3.17 (~r(s(s(elem!1)), s(s(s(elem!1))))),
% 2.95/3.17 inference(unit_resolution,[status(thm)],[2939, 12232, 85, 117])).
% 2.95/3.17 tff(12234,plain,
% 2.95/3.17 (~r(z, s(s(s(elem!1))))),
% 2.95/3.17 inference(unit_resolution,[status(thm)],[2057, 12232, 117, 323])).
% 2.95/3.17 tff(12235,plain,
% 2.95/3.17 (b(z, s(s(s(elem!1))))),
% 2.95/3.17 inference(unit_resolution,[status(thm)],[261, 12234])).
% 2.95/3.17 tff(12236,plain,
% 2.95/3.17 (s(s(elem!1)) = s(s(s(elem!1)))),
% 2.95/3.17 inference(unit_resolution,[status(thm)],[12162, 12235, 121, 85, 97, 98, 12233])).
% 2.95/3.17 tff(12237,plain,
% 2.95/3.17 (r(s(s(z)), s(s(elem!1))) <=> r(s(s(z)), s(s(s(elem!1))))),
% 2.95/3.17 inference(monotonicity,[status(thm)],[12236])).
% 2.95/3.17 tff(12238,plain,
% 2.95/3.17 (r(s(s(z)), s(s(s(elem!1)))) <=> r(s(s(z)), s(s(elem!1)))),
% 2.95/3.17 inference(symmetry,[status(thm)],[12237])).
% 2.95/3.17 tff(12239,plain,
% 2.95/3.17 (r(s(s(z)), s(s(elem!1)))),
% 2.95/3.17 inference(modus_ponens,[status(thm)],[12138, 12238])).
% 2.95/3.17 tff(12240,plain,
% 2.95/3.17 (r(s(s(elem!1)), s(s(z))) <=> r(s(s(s(elem!1))), s(s(z)))),
% 2.95/3.17 inference(monotonicity,[status(thm)],[12236])).
% 2.95/3.17 tff(12241,plain,
% 2.95/3.17 (r(s(s(s(elem!1))), s(s(z))) <=> r(s(s(elem!1)), s(s(z)))),
% 2.95/3.17 inference(symmetry,[status(thm)],[12240])).
% 2.95/3.17 tff(12242,plain,
% 2.95/3.17 (r(s(s(elem!1)), s(s(z)))),
% 2.95/3.17 inference(modus_ponens,[status(thm)],[12232, 12241])).
% 2.95/3.17 tff(12243,plain,
% 2.95/3.17 (s(s(s(elem!1))) = s(elem!1)),
% 2.95/3.17 inference(unit_resolution,[status(thm)],[2594, 12236])).
% 2.95/3.17 tff(12244,plain,
% 2.95/3.17 (s(elem!1) = s(s(s(elem!1)))),
% 2.95/3.17 inference(symmetry,[status(thm)],[12243])).
% 2.95/3.17 tff(12245,plain,
% 2.95/3.17 (inj_0(s(elem!1)) = inj_0(s(s(s(elem!1))))),
% 2.95/3.17 inference(monotonicity,[status(thm)],[12244])).
% 2.95/3.17 tff(12246,plain,
% 2.95/3.17 (elem!1 = s(s(elem!1))),
% 2.95/3.17 inference(transitivity,[status(thm)],[1170, 12245, 104])).
% 2.95/3.17 tff(12247,plain,
% 2.95/3.17 (r(s(s(s(z))), elem!1) <=> r(s(s(s(z))), s(s(elem!1)))),
% 2.95/3.17 inference(monotonicity,[status(thm)],[12246])).
% 2.95/3.17 tff(12248,plain,
% 2.95/3.17 (~(s(s(s(z))) = elem!1)),
% 2.95/3.17 inference(unit_resolution,[status(thm)],[3122, 12236])).
% 2.95/3.17 tff(12249,plain,
% 2.95/3.17 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), s(z))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(z))), s(s(s(elem!1))))) | (~b(s(z), s(s(s(z))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(z))), s(s(s(elem!1))))) | (~b(s(z), s(s(s(z))))))),
% 2.95/3.17 inference(rewrite,[status(thm)],[])).
% 2.95/3.17 tff(12250,plain,
% 2.95/3.17 (((~b(s(s(s(z))), s(z))) | (~b(s(s(s(z))), s(z))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(z))), s(s(s(elem!1)))))) <=> ((~b(s(s(s(elem!1))), s(z))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(z))), s(s(s(elem!1))))) | (~b(s(z), s(s(s(z))))))),
% 2.95/3.17 inference(rewrite,[status(thm)],[])).
% 2.95/3.17 tff(12251,plain,
% 2.95/3.17 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), s(z))) | (~b(s(s(s(z))), s(z))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(z))), s(s(s(elem!1))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), s(z))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(z))), s(s(s(elem!1))))) | (~b(s(z), s(s(s(z)))))))),
% 2.95/3.18 inference(monotonicity,[status(thm)],[12250])).
% 2.95/3.18 tff(12252,plain,
% 2.95/3.18 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), s(z))) | (~b(s(s(s(z))), s(z))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(z))), s(s(s(elem!1))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(z))), s(s(s(elem!1))))) | (~b(s(z), s(s(s(z))))))),
% 2.95/3.18 inference(transitivity,[status(thm)],[12251, 12249])).
% 2.95/3.18 tff(12253,plain,
% 2.95/3.18 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), s(z))) | (~b(s(s(s(z))), s(z))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(z))), s(s(s(elem!1))))))),
% 2.95/3.18 inference(quant_inst,[status(thm)],[])).
% 2.95/3.18 tff(12254,plain,
% 2.95/3.18 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(z))), s(s(s(elem!1))))) | (~b(s(z), s(s(s(z)))))),
% 2.95/3.18 inference(modus_ponens,[status(thm)],[12253, 12252])).
% 2.95/3.18 tff(12255,plain,
% 2.95/3.18 (~b(s(s(s(z))), s(s(s(elem!1))))),
% 2.95/3.18 inference(unit_resolution,[status(thm)],[12254, 166, 96, 12224, 12222])).
% 2.95/3.18 tff(12256,plain,
% 2.95/3.18 (s(s(s(elem!1))) = s(s(elem!1))),
% 2.95/3.18 inference(unit_resolution,[status(thm)],[4030, 12236])).
% 2.95/3.18 tff(12257,plain,
% 2.95/3.18 (~b(s(s(s(z))), elem!1)),
% 2.95/3.18 inference(unit_resolution,[status(thm)],[4078, 12256, 12255])).
% 2.95/3.18 tff(12258,plain,
% 2.95/3.18 (r(s(s(s(z))), elem!1)),
% 2.95/3.18 inference(unit_resolution,[status(thm)],[2826, 12257, 12248])).
% 2.95/3.18 tff(12259,plain,
% 2.95/3.18 (r(s(s(s(z))), s(s(elem!1)))),
% 2.95/3.18 inference(modus_ponens,[status(thm)],[12258, 12247])).
% 2.95/3.18 tff(12260,plain,
% 2.95/3.18 ($false),
% 2.95/3.18 inference(unit_resolution,[status(thm)],[4435, 12259, 12242, 85, 156, 12239])).
% 2.95/3.18 tff(12261,plain,((~b(s(s(z)), s(z))) | (~b(s(s(s(elem!1))), z)) | (~r(s(z), z)) | b(s(z), s(s(s(elem!1)))) | (~r(z, s(z))) | (~b(s(s(s(elem!1))), s(z))) | b(s(z), s(s(elem!1)))), inference(lemma,lemma(discharge,[]))).
% 2.95/3.18 tff(12262,plain,
% 2.95/3.18 (~b(s(s(z)), s(z))),
% 2.95/3.18 inference(unit_resolution,[status(thm)],[12261, 98, 97, 95, 12117, 96, 54])).
% 2.95/3.18 tff(12263,plain,
% 2.95/3.18 (r(s(s(z)), s(z))),
% 2.95/3.18 inference(unit_resolution,[status(thm)],[308, 12262])).
% 2.95/3.18 tff(12264,plain,
% 2.95/3.18 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(z))) | (~r(s(z), s(s(s(elem!1))))) | (~r(s(s(z)), s(z))) | (~r(s(s(z)), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, s(z))) | (~r(s(z), s(s(s(elem!1))))) | (~r(s(s(z)), s(z))) | (~r(s(s(z)), z)))),
% 2.95/3.18 inference(rewrite,[status(thm)],[])).
% 2.95/3.18 tff(12265,plain,
% 2.95/3.18 (((~r(s(z), s(s(s(elem!1))))) | (~r(z, s(z))) | (~r(s(s(z)), s(z))) | (~r(s(s(z)), z))) <=> ((~r(z, s(z))) | (~r(s(z), s(s(s(elem!1))))) | (~r(s(s(z)), s(z))) | (~r(s(s(z)), z)))),
% 2.95/3.18 inference(rewrite,[status(thm)],[])).
% 2.95/3.18 tff(12266,plain,
% 2.95/3.18 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(s(s(elem!1))))) | (~r(z, s(z))) | (~r(s(s(z)), s(z))) | (~r(s(s(z)), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(z))) | (~r(s(z), s(s(s(elem!1))))) | (~r(s(s(z)), s(z))) | (~r(s(s(z)), z))))),
% 2.95/3.18 inference(monotonicity,[status(thm)],[12265])).
% 2.95/3.18 tff(12267,plain,
% 2.95/3.18 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(s(s(elem!1))))) | (~r(z, s(z))) | (~r(s(s(z)), s(z))) | (~r(s(s(z)), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, s(z))) | (~r(s(z), s(s(s(elem!1))))) | (~r(s(s(z)), s(z))) | (~r(s(s(z)), z)))),
% 2.95/3.18 inference(transitivity,[status(thm)],[12266, 12264])).
% 2.95/3.18 tff(12268,plain,
% 2.95/3.18 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(s(s(elem!1))))) | (~r(z, s(z))) | (~r(s(s(z)), s(z))) | (~r(s(s(z)), z)))),
% 2.95/3.18 inference(quant_inst,[status(thm)],[])).
% 2.95/3.18 tff(12269,plain,
% 2.95/3.18 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, s(z))) | (~r(s(z), s(s(s(elem!1))))) | (~r(s(s(z)), s(z))) | (~r(s(s(z)), z))),
% 2.95/3.18 inference(modus_ponens,[status(thm)],[12268, 12267])).
% 2.95/3.18 tff(12270,plain,
% 2.95/3.18 ($false),
% 2.95/3.18 inference(unit_resolution,[status(thm)],[12269, 197, 323, 392, 119, 866])).
% 2.95/3.18 tff(12271,plain,((~r(s(z), s(s(s(elem!1))))) | (~r(z, s(z))) | (~r(s(s(z)), s(z))) | (~r(s(s(z)), z))), inference(lemma,lemma(discharge,[]))).
% 2.95/3.18 tff(12272,plain,
% 2.95/3.18 (~r(s(s(z)), z)),
% 2.95/3.18 inference(unit_resolution,[status(thm)],[12271, 12263, 117, 12117])).
% 2.95/3.18 tff(12273,plain,
% 2.95/3.18 (b(s(s(z)), z)),
% 2.95/3.18 inference(unit_resolution,[status(thm)],[186, 12272])).
% 2.95/3.18 tff(12274,plain,
% 2.95/3.18 (~b(s(s(s(elem!1))), s(s(z)))),
% 2.95/3.18 inference(unit_resolution,[status(thm)],[10460, 12273, 95])).
% 2.95/3.18 tff(12275,plain,
% 2.95/3.18 (r(s(s(s(elem!1))), s(s(z)))),
% 2.95/3.18 inference(unit_resolution,[status(thm)],[218, 12274])).
% 2.95/3.18 tff(12276,plain,
% 2.95/3.18 (~r(s(s(elem!1)), s(s(s(elem!1))))),
% 2.95/3.18 inference(unit_resolution,[status(thm)],[2939, 12275, 85, 117])).
% 2.95/3.18 tff(12277,plain,
% 2.95/3.18 (~r(z, s(s(s(elem!1))))),
% 2.95/3.18 inference(unit_resolution,[status(thm)],[2057, 12275, 117, 12117])).
% 2.95/3.18 tff(12278,plain,
% 2.95/3.18 (b(z, s(s(s(elem!1))))),
% 2.95/3.18 inference(unit_resolution,[status(thm)],[261, 12277])).
% 2.95/3.18 tff(12279,plain,
% 2.95/3.18 (s(s(elem!1)) = s(s(s(elem!1)))),
% 2.95/3.18 inference(unit_resolution,[status(thm)],[12162, 12278, 95, 85, 97, 98, 12276])).
% 2.95/3.18 tff(12280,plain,
% 2.95/3.18 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(z)))) | (~b(s(s(s(elem!1))), z)) | (~b(s(s(z)), z)) | (~b(s(s(s(z))), z)) | (~b(s(s(s(z))), s(s(s(elem!1))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(s(z)))) | (~b(s(s(s(elem!1))), z)) | (~b(s(s(z)), z)) | (~b(s(s(s(z))), z)) | (~b(s(s(s(z))), s(s(s(elem!1))))))),
% 2.95/3.18 inference(rewrite,[status(thm)],[])).
% 2.95/3.18 tff(12281,plain,
% 2.95/3.18 (((~b(s(s(z)), z)) | (~b(s(s(s(z))), z)) | (~b(z, s(s(z)))) | (~b(s(s(s(elem!1))), z)) | (~b(s(s(s(z))), z)) | (~b(s(s(s(z))), s(s(s(elem!1)))))) <=> ((~b(z, s(s(z)))) | (~b(s(s(s(elem!1))), z)) | (~b(s(s(z)), z)) | (~b(s(s(s(z))), z)) | (~b(s(s(s(z))), s(s(s(elem!1))))))),
% 2.95/3.18 inference(rewrite,[status(thm)],[])).
% 2.95/3.18 tff(12282,plain,
% 2.95/3.18 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), z)) | (~b(s(s(s(z))), z)) | (~b(z, s(s(z)))) | (~b(s(s(s(elem!1))), z)) | (~b(s(s(s(z))), z)) | (~b(s(s(s(z))), s(s(s(elem!1))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(z)))) | (~b(s(s(s(elem!1))), z)) | (~b(s(s(z)), z)) | (~b(s(s(s(z))), z)) | (~b(s(s(s(z))), s(s(s(elem!1)))))))),
% 2.95/3.18 inference(monotonicity,[status(thm)],[12281])).
% 2.95/3.18 tff(12283,plain,
% 2.95/3.18 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), z)) | (~b(s(s(s(z))), z)) | (~b(z, s(s(z)))) | (~b(s(s(s(elem!1))), z)) | (~b(s(s(s(z))), z)) | (~b(s(s(s(z))), s(s(s(elem!1))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(s(z)))) | (~b(s(s(s(elem!1))), z)) | (~b(s(s(z)), z)) | (~b(s(s(s(z))), z)) | (~b(s(s(s(z))), s(s(s(elem!1))))))),
% 2.95/3.18 inference(transitivity,[status(thm)],[12282, 12280])).
% 2.95/3.18 tff(12284,plain,
% 2.95/3.18 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), z)) | (~b(s(s(s(z))), z)) | (~b(z, s(s(z)))) | (~b(s(s(s(elem!1))), z)) | (~b(s(s(s(z))), z)) | (~b(s(s(s(z))), s(s(s(elem!1))))))),
% 2.95/3.18 inference(quant_inst,[status(thm)],[])).
% 2.95/3.18 tff(12285,plain,
% 2.95/3.18 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(s(z)))) | (~b(s(s(s(elem!1))), z)) | (~b(s(s(z)), z)) | (~b(s(s(s(z))), z)) | (~b(s(s(s(z))), s(s(s(elem!1)))))),
% 2.95/3.18 inference(modus_ponens,[status(thm)],[12284, 12283])).
% 2.95/3.18 tff(12286,plain,
% 2.95/3.18 (~b(s(s(s(z))), s(s(s(elem!1))))),
% 2.95/3.18 inference(unit_resolution,[status(thm)],[12285, 166, 10451, 121, 122, 1699])).
% 2.95/3.18 tff(12287,plain,
% 2.95/3.18 (~b(s(s(s(z))), elem!1)),
% 2.95/3.18 inference(unit_resolution,[status(thm)],[4078, 12286, 4031])).
% 2.95/3.18 tff(12288,plain,
% 2.95/3.18 (r(s(s(s(z))), elem!1)),
% 2.95/3.18 inference(unit_resolution,[status(thm)],[2826, 12287, 4027])).
% 2.95/3.18 tff(12289,plain,
% 2.95/3.18 (r(s(s(s(z))), s(s(elem!1)))),
% 2.95/3.18 inference(modus_ponens,[status(thm)],[12288, 4026])).
% 2.95/3.18 tff(12290,plain,
% 2.95/3.18 (r(s(s(s(z))), s(s(s(elem!1))))),
% 2.95/3.18 inference(modus_ponens,[status(thm)],[12289, 4024])).
% 2.95/3.18 tff(12291,plain,
% 2.95/3.18 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(z)))) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(s(z)), z)) | (~b(s(s(s(z))), z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(s(z)))) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(s(z)), z)) | (~b(s(s(s(z))), z)))),
% 2.95/3.18 inference(rewrite,[status(thm)],[])).
% 2.95/3.18 tff(12292,plain,
% 2.95/3.18 (((~b(s(s(z)), z)) | (~b(s(s(s(z))), z)) | (~b(z, s(s(z)))) | (~b(s(s(z)), z)) | (~b(s(s(s(z))), z)) | (~b(s(s(s(z))), s(s(z))))) <=> ((~b(z, s(s(z)))) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(s(z)), z)) | (~b(s(s(s(z))), z)))),
% 2.95/3.18 inference(rewrite,[status(thm)],[])).
% 2.95/3.18 tff(12293,plain,
% 2.95/3.18 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), z)) | (~b(s(s(s(z))), z)) | (~b(z, s(s(z)))) | (~b(s(s(z)), z)) | (~b(s(s(s(z))), z)) | (~b(s(s(s(z))), s(s(z)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(z)))) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(s(z)), z)) | (~b(s(s(s(z))), z))))),
% 2.95/3.18 inference(monotonicity,[status(thm)],[12292])).
% 2.95/3.18 tff(12294,plain,
% 2.95/3.18 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), z)) | (~b(s(s(s(z))), z)) | (~b(z, s(s(z)))) | (~b(s(s(z)), z)) | (~b(s(s(s(z))), z)) | (~b(s(s(s(z))), s(s(z)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(s(z)))) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(s(z)), z)) | (~b(s(s(s(z))), z)))),
% 2.95/3.18 inference(transitivity,[status(thm)],[12293, 12291])).
% 2.95/3.18 tff(12295,plain,
% 2.95/3.18 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), z)) | (~b(s(s(s(z))), z)) | (~b(z, s(s(z)))) | (~b(s(s(z)), z)) | (~b(s(s(s(z))), z)) | (~b(s(s(s(z))), s(s(z)))))),
% 2.95/3.18 inference(quant_inst,[status(thm)],[])).
% 2.95/3.18 tff(12296,plain,
% 2.95/3.18 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(s(z)))) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(s(z)), z)) | (~b(s(s(s(z))), z))),
% 2.95/3.18 inference(modus_ponens,[status(thm)],[12295, 12294])).
% 2.95/3.18 tff(12297,plain,
% 2.95/3.18 (~b(s(s(s(z))), s(s(z)))),
% 2.95/3.18 inference(unit_resolution,[status(thm)],[12296, 166, 10451, 122, 1699])).
% 2.95/3.18 tff(12298,plain,
% 2.95/3.18 (r(s(s(s(z))), s(s(z)))),
% 2.95/3.18 inference(unit_resolution,[status(thm)],[1010, 12297])).
% 2.95/3.18 tff(12299,plain,
% 2.95/3.18 (~b(s(s(s(elem!1))), s(s(z)))),
% 2.95/3.18 inference(unit_resolution,[status(thm)],[10459, 121, 10451, 122])).
% 2.95/3.18 tff(12300,plain,
% 2.95/3.18 (r(s(s(s(elem!1))), s(s(z)))),
% 2.95/3.18 inference(unit_resolution,[status(thm)],[218, 12299])).
% 2.95/3.18 tff(12301,plain,
% 2.95/3.18 (r(s(s(z)), s(s(s(elem!1))))),
% 2.95/3.18 inference(unit_resolution,[status(thm)],[279, 10742])).
% 2.95/3.18 tff(12302,plain,
% 2.95/3.18 (~r(s(s(s(z))), s(s(s(elem!1))))),
% 2.95/3.18 inference(unit_resolution,[status(thm)],[8852, 197, 12301, 12300, 12298])).
% 2.95/3.18 tff(12303,plain,
% 2.95/3.18 ($false),
% 2.95/3.18 inference(unit_resolution,[status(thm)],[12302, 12290])).
% 2.95/3.18 tff(12304,plain,((~b(s(s(s(z))), z)) | (~(s(s(elem!1)) = s(s(s(elem!1))))) | (~b(z, s(s(z)))) | (~b(s(s(z)), z)) | (~b(s(s(s(elem!1))), z))), inference(lemma,lemma(discharge,[]))).
% 2.95/3.18 tff(12305,plain,
% 2.95/3.18 ((~b(s(s(s(z))), z)) | (~(s(s(elem!1)) = s(s(s(elem!1))))) | (~b(s(s(z)), z)) | (~b(s(s(s(elem!1))), z))),
% 2.95/3.18 inference(unit_resolution,[status(thm)],[12304, 10450])).
% 2.95/3.18 tff(12306,plain,
% 2.95/3.18 (~b(s(s(s(z))), z)),
% 2.95/3.18 inference(unit_resolution,[status(thm)],[12305, 12279, 95, 12273])).
% 2.95/3.18 tff(12307,plain,
% 2.95/3.18 (r(s(s(s(z))), z)),
% 2.95/3.18 inference(unit_resolution,[status(thm)],[1713, 12306])).
% 2.95/3.18 tff(12308,plain,
% 2.95/3.18 (~r(s(z), s(s(s(z))))),
% 2.95/3.18 inference(unit_resolution,[status(thm)],[8876, 12307, 12117, 97])).
% 2.95/3.18 tff(12309,plain,
% 2.95/3.18 (b(s(z), s(s(s(z))))),
% 2.95/3.18 inference(unit_resolution,[status(thm)],[1674, 12308])).
% 2.95/3.18 tff(12310,plain,
% 2.95/3.18 (b(s(s(elem!1)), s(z))),
% 2.95/3.18 inference(unit_resolution,[status(thm)],[11987, 12263, 97])).
% 2.95/3.18 tff(12311,plain,
% 2.95/3.18 (~(s(s(z)) = s(s(elem!1)))),
% 2.95/3.18 inference(unit_resolution,[status(thm)],[3938, 12310, 12262])).
% 2.95/3.18 tff(12312,plain,
% 2.95/3.18 (~(s(s(elem!1)) = s(s(z)))),
% 2.95/3.18 inference(unit_resolution,[status(thm)],[131, 12311])).
% 2.95/3.18 tff(12313,plain,
% 2.95/3.18 (~(s(s(s(elem!1))) = s(s(s(z))))),
% 2.95/3.18 inference(unit_resolution,[status(thm)],[139, 12312])).
% 2.95/3.18 tff(12314,plain,
% 2.95/3.18 (b(z, s(s(elem!1)))),
% 2.95/3.18 inference(unit_resolution,[status(thm)],[12145, 12278, 95, 12276, 85, 97])).
% 2.95/3.18 tff(12315,plain,
% 2.95/3.18 (~r(s(s(elem!1)), z)),
% 2.95/3.18 inference(unit_resolution,[status(thm)],[2974, 12279, 86])).
% 2.95/3.18 tff(12316,plain,
% 2.95/3.18 (b(s(s(elem!1)), z)),
% 2.95/3.18 inference(unit_resolution,[status(thm)],[608, 12315])).
% 2.95/3.18 tff(12317,plain,
% 2.95/3.18 (~b(s(s(z)), s(s(elem!1)))),
% 2.95/3.18 inference(unit_resolution,[status(thm)],[11837, 12316, 12314])).
% 2.95/3.18 tff(12318,plain,
% 2.95/3.18 (r(s(s(z)), s(s(elem!1)))),
% 2.95/3.18 inference(unit_resolution,[status(thm)],[390, 12317, 12311])).
% 2.95/3.18 tff(12319,plain,
% 2.95/3.18 (r(s(s(z)), s(s(s(elem!1))))),
% 2.95/3.18 inference(unit_resolution,[status(thm)],[338, 12318, 12279])).
% 2.95/3.18 tff(12320,plain,
% 2.95/3.18 (~r(s(s(s(elem!1))), s(s(s(z))))),
% 2.95/3.18 inference(unit_resolution,[status(thm)],[12064, 12319, 117, 12263])).
% 2.95/3.18 tff(12321,plain,
% 2.95/3.18 (b(s(s(s(elem!1))), s(s(s(z))))),
% 2.95/3.18 inference(unit_resolution,[status(thm)],[3574, 12320, 12313])).
% 2.95/3.18 tff(12322,plain,
% 2.95/3.18 (~b(s(s(s(z))), s(z))),
% 2.95/3.18 inference(unit_resolution,[status(thm)],[11934, 12321, 96, 12309])).
% 2.95/3.18 tff(12323,plain,
% 2.95/3.18 (r(s(s(s(z))), s(z))),
% 2.95/3.18 inference(unit_resolution,[status(thm)],[1763, 12322])).
% 2.95/3.18 tff(12324,plain,
% 2.95/3.18 ($false),
% 2.95/3.18 inference(unit_resolution,[status(thm)],[12220, 197, 12117, 97, 12323, 12307])).
% 2.95/3.18 tff(12325,plain,(b(s(z), s(s(s(elem!1)))) | (~r(s(z), z)) | (~b(s(s(s(elem!1))), s(z))) | r(s(s(s(elem!1))), z) | b(s(z), s(s(elem!1)))), inference(lemma,lemma(discharge,[]))).
% 2.95/3.18 tff(12326,plain,
% 2.95/3.18 (b(s(z), s(s(s(elem!1))))),
% 2.95/3.18 inference(unit_resolution,[status(thm)],[12325, 97, 96, 86, 54])).
% 2.95/3.18 tff(12327,plain,
% 2.95/3.18 (b(s(z), s(s(elem!1)))),
% 2.95/3.18 inference(modus_ponens,[status(thm)],[241, 5496])).
% 2.95/3.18 tff(12328,plain,
% 2.95/3.18 ($false),
% 2.95/3.18 inference(unit_resolution,[status(thm)],[54, 12327])).
% 2.95/3.18 tff(12329,plain,((~(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,[]))).
% 2.95/3.18 tff(12330,plain,
% 2.95/3.18 (~(s(s(elem!1)) = s(s(s(elem!1))))),
% 2.95/3.18 inference(unit_resolution,[status(thm)],[12329, 12326, 54])).
% 2.95/3.18 tff(12331,plain,
% 2.95/3.18 (~(s(s(s(elem!1))) = s(s(s(s(elem!1)))))),
% 2.95/3.18 inference(unit_resolution,[status(thm)],[357, 12330])).
% 2.95/3.18 tff(12332,plain,
% 2.95/3.18 (~(s(s(s(s(elem!1)))) = s(s(s(elem!1))))),
% 2.95/3.18 inference(unit_resolution,[status(thm)],[363, 12331])).
% 2.95/3.18 tff(12333,plain,
% 2.95/3.18 (~b(s(s(s(elem!1))), s(s(z)))),
% 2.95/3.18 inference(unit_resolution,[status(thm)],[9072, 166, 241, 96, 156])).
% 2.95/3.18 tff(12334,plain,
% 2.95/3.18 (r(s(s(s(elem!1))), s(s(z)))),
% 2.95/3.18 inference(unit_resolution,[status(thm)],[218, 12333])).
% 2.95/3.18 tff(12335,plain,
% 2.95/3.18 (~b(s(s(z)), s(z))),
% 2.95/3.18 inference(unit_resolution,[status(thm)],[271, 263, 96, 241])).
% 2.95/3.18 tff(12336,plain,
% 2.95/3.18 (r(s(s(z)), s(z))),
% 2.95/3.18 inference(unit_resolution,[status(thm)],[308, 12335])).
% 2.95/3.18 tff(12337,plain,
% 2.95/3.18 (b(s(s(elem!1)), s(z))),
% 2.95/3.18 inference(unit_resolution,[status(thm)],[11987, 12336, 97])).
% 2.95/3.18 tff(12338,plain,
% 2.95/3.18 (~b(s(s(elem!1)), s(s(s(elem!1))))),
% 2.95/3.18 inference(unit_resolution,[status(thm)],[1994, 12337, 96, 241])).
% 2.95/3.18 tff(12339,plain,
% 2.95/3.18 (~(s(s(z)) = s(s(elem!1)))),
% 2.95/3.18 inference(unit_resolution,[status(thm)],[3938, 12337, 12335])).
% 2.95/3.18 tff(12340,plain,
% 2.95/3.18 (~(s(s(elem!1)) = s(s(s(elem!1))))),
% 2.95/3.18 inference(unit_resolution,[status(thm)],[12329, 241, 54])).
% 2.95/3.18 tff(12341,plain,
% 2.95/3.18 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(z), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(s(elem!1)), s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(z), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(s(elem!1)), s(z))))),
% 2.95/3.18 inference(rewrite,[status(thm)],[])).
% 2.95/3.18 tff(12342,plain,
% 2.95/3.18 (((~b(s(s(s(elem!1))), s(z))) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(z), s(s(s(elem!1))))) | (~b(s(s(elem!1)), s(z))) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(s(s(elem!1))), s(s(elem!1))))) <=> ((~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(z), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(s(elem!1)), s(z))))),
% 2.95/3.18 inference(rewrite,[status(thm)],[])).
% 2.95/3.18 tff(12343,plain,
% 2.95/3.18 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), s(z))) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(z), s(s(s(elem!1))))) | (~b(s(s(elem!1)), s(z))) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(s(s(elem!1))), s(s(elem!1)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(z), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(s(elem!1)), s(z)))))),
% 2.95/3.18 inference(monotonicity,[status(thm)],[12342])).
% 2.95/3.18 tff(12344,plain,
% 2.95/3.18 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), s(z))) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(z), s(s(s(elem!1))))) | (~b(s(s(elem!1)), s(z))) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(s(s(elem!1))), s(s(elem!1)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(z), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(s(elem!1)), s(z))))),
% 2.95/3.18 inference(transitivity,[status(thm)],[12343, 12341])).
% 2.95/3.18 tff(12345,plain,
% 2.95/3.18 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), s(z))) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(z), s(s(s(elem!1))))) | (~b(s(s(elem!1)), s(z))) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(s(s(elem!1))), s(s(elem!1)))))),
% 2.95/3.18 inference(quant_inst,[status(thm)],[])).
% 2.95/3.18 tff(12346,plain,
% 2.95/3.18 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(z), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(s(elem!1)), s(z)))),
% 2.95/3.19 inference(modus_ponens,[status(thm)],[12345, 12344])).
% 2.95/3.19 tff(12347,plain,
% 2.95/3.19 (~b(s(s(s(elem!1))), s(s(elem!1)))),
% 2.95/3.19 inference(unit_resolution,[status(thm)],[12346, 166, 241, 96, 12337])).
% 2.95/3.19 tff(12348,assumption,(~b(s(s(s(elem!1))), s(s(elem!1)))), introduced(assumption)).
% 2.95/3.19 tff(12349,plain,
% 2.95/3.19 (r(s(s(s(elem!1))), s(s(elem!1)))),
% 2.95/3.19 inference(unit_resolution,[status(thm)],[889, 51, 12348])).
% 2.95/3.19 tff(12350,assumption,(~b(s(s(elem!1)), s(s(s(elem!1))))), introduced(assumption)).
% 2.95/3.19 tff(12351,plain,
% 2.95/3.19 (r(s(s(elem!1)), s(s(s(elem!1))))),
% 2.95/3.19 inference(unit_resolution,[status(thm)],[461, 45, 12350])).
% 2.95/3.19 tff(12352,plain,
% 2.95/3.19 (~r(z, s(s(elem!1)))),
% 2.95/3.19 inference(unit_resolution,[status(thm)],[1956, 12351, 12349, 282])).
% 2.95/3.19 tff(12353,plain,
% 2.95/3.19 (b(z, s(s(elem!1)))),
% 2.95/3.19 inference(unit_resolution,[status(thm)],[1795, 12352])).
% 2.95/3.19 tff(12354,plain,
% 2.95/3.19 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), s(s(elem!1)))) | (~r(s(s(elem!1)), z)) | (~r(s(s(elem!1)), s(s(s(elem!1))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), s(s(elem!1)))) | (~r(s(s(elem!1)), z)) | (~r(s(s(elem!1)), s(s(s(elem!1))))))),
% 2.95/3.19 inference(rewrite,[status(thm)],[])).
% 2.95/3.19 tff(12355,plain,
% 2.95/3.19 (((~r(s(s(s(elem!1))), s(s(elem!1)))) | (~r(z, s(s(s(elem!1))))) | (~r(s(s(elem!1)), s(s(s(elem!1))))) | (~r(s(s(elem!1)), z))) <=> ((~r(z, s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), s(s(elem!1)))) | (~r(s(s(elem!1)), z)) | (~r(s(s(elem!1)), s(s(s(elem!1))))))),
% 2.95/3.19 inference(rewrite,[status(thm)],[])).
% 2.95/3.19 tff(12356,plain,
% 2.95/3.19 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), s(s(elem!1)))) | (~r(z, s(s(s(elem!1))))) | (~r(s(s(elem!1)), s(s(s(elem!1))))) | (~r(s(s(elem!1)), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), s(s(elem!1)))) | (~r(s(s(elem!1)), z)) | (~r(s(s(elem!1)), s(s(s(elem!1)))))))),
% 2.95/3.19 inference(monotonicity,[status(thm)],[12355])).
% 2.95/3.19 tff(12357,plain,
% 2.95/3.19 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), s(s(elem!1)))) | (~r(z, s(s(s(elem!1))))) | (~r(s(s(elem!1)), s(s(s(elem!1))))) | (~r(s(s(elem!1)), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), s(s(elem!1)))) | (~r(s(s(elem!1)), z)) | (~r(s(s(elem!1)), s(s(s(elem!1))))))),
% 2.95/3.19 inference(transitivity,[status(thm)],[12356, 12354])).
% 2.95/3.19 tff(12358,plain,
% 2.95/3.19 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), s(s(elem!1)))) | (~r(z, s(s(s(elem!1))))) | (~r(s(s(elem!1)), s(s(s(elem!1))))) | (~r(s(s(elem!1)), z)))),
% 2.95/3.19 inference(quant_inst,[status(thm)],[])).
% 2.95/3.19 tff(12359,plain,
% 2.95/3.19 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), s(s(elem!1)))) | (~r(s(s(elem!1)), z)) | (~r(s(s(elem!1)), s(s(s(elem!1)))))),
% 2.95/3.19 inference(modus_ponens,[status(thm)],[12358, 12357])).
% 2.95/3.19 tff(12360,plain,
% 2.95/3.19 (~r(s(s(elem!1)), z)),
% 2.95/3.19 inference(unit_resolution,[status(thm)],[12359, 197, 12351, 12349, 282])).
% 2.95/3.19 tff(12361,plain,
% 2.95/3.19 (b(s(s(elem!1)), z)),
% 2.95/3.19 inference(unit_resolution,[status(thm)],[608, 12360])).
% 2.95/3.19 tff(12362,plain,
% 2.95/3.19 (~b(s(s(z)), s(s(elem!1)))),
% 2.95/3.19 inference(unit_resolution,[status(thm)],[11837, 12361, 12353])).
% 2.95/3.19 tff(12363,plain,
% 2.95/3.19 (r(s(s(z)), s(s(elem!1)))),
% 2.95/3.19 inference(unit_resolution,[status(thm)],[390, 12362, 52])).
% 2.95/3.19 tff(12364,plain,
% 2.95/3.19 ($false),
% 2.95/3.19 inference(unit_resolution,[status(thm)],[4235, 197, 311, 12351, 12363, 392])).
% 2.95/3.19 tff(12365,plain,((s(s(elem!1)) = s(s(s(elem!1)))) | (~r(s(z), s(s(elem!1)))) | (~r(s(s(z)), s(z))) | (s(s(z)) = s(s(elem!1))) | (~r(z, s(s(s(elem!1))))) | b(s(s(s(elem!1))), s(s(elem!1))) | b(s(s(elem!1)), s(s(s(elem!1))))), inference(lemma,lemma(discharge,[]))).
% 2.95/3.19 tff(12366,plain,
% 2.95/3.19 (~r(z, s(s(s(elem!1))))),
% 2.95/3.19 inference(unit_resolution,[status(thm)],[12365, 12347, 12340, 12336, 85, 12339, 12338])).
% 2.95/3.19 tff(12367,plain,
% 2.95/3.19 (b(z, s(s(s(elem!1))))),
% 2.95/3.19 inference(unit_resolution,[status(thm)],[261, 12366])).
% 2.95/3.19 tff(12368,plain,
% 2.95/3.19 (~b(z, s(z))),
% 2.95/3.19 inference(unit_resolution,[status(thm)],[249, 12367, 96, 241])).
% 2.95/3.19 tff(12369,plain,
% 2.95/3.19 (r(z, s(z))),
% 2.95/3.19 inference(unit_resolution,[status(thm)],[321, 12368])).
% 2.95/3.19 tff(12370,plain,
% 2.95/3.19 (~(s(s(elem!1)) = s(s(z)))),
% 2.95/3.19 inference(unit_resolution,[status(thm)],[131, 12339])).
% 2.95/3.19 tff(12371,plain,
% 2.95/3.19 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(z))) | (~r(s(z), z)) | (~r(s(s(z)), s(z))) | (~r(s(s(z)), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, s(z))) | (~r(s(z), z)) | (~r(s(s(z)), s(z))) | (~r(s(s(z)), z)))),
% 2.95/3.19 inference(rewrite,[status(thm)],[])).
% 2.95/3.19 tff(12372,plain,
% 2.95/3.19 (((~r(s(z), z)) | (~r(z, s(z))) | (~r(s(s(z)), s(z))) | (~r(s(s(z)), z))) <=> ((~r(z, s(z))) | (~r(s(z), z)) | (~r(s(s(z)), s(z))) | (~r(s(s(z)), z)))),
% 2.95/3.19 inference(rewrite,[status(thm)],[])).
% 2.95/3.19 tff(12373,plain,
% 2.95/3.19 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), z)) | (~r(z, s(z))) | (~r(s(s(z)), s(z))) | (~r(s(s(z)), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(z))) | (~r(s(z), z)) | (~r(s(s(z)), s(z))) | (~r(s(s(z)), z))))),
% 2.95/3.19 inference(monotonicity,[status(thm)],[12372])).
% 2.95/3.19 tff(12374,plain,
% 2.95/3.19 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), z)) | (~r(z, s(z))) | (~r(s(s(z)), s(z))) | (~r(s(s(z)), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, s(z))) | (~r(s(z), z)) | (~r(s(s(z)), s(z))) | (~r(s(s(z)), z)))),
% 2.95/3.19 inference(transitivity,[status(thm)],[12373, 12371])).
% 2.95/3.19 tff(12375,plain,
% 2.95/3.19 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), z)) | (~r(z, s(z))) | (~r(s(s(z)), s(z))) | (~r(s(s(z)), z)))),
% 2.95/3.19 inference(quant_inst,[status(thm)],[])).
% 2.95/3.19 tff(12376,plain,
% 2.95/3.19 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, s(z))) | (~r(s(z), z)) | (~r(s(s(z)), s(z))) | (~r(s(s(z)), z))),
% 2.95/3.19 inference(modus_ponens,[status(thm)],[12375, 12374])).
% 2.95/3.19 tff(12377,plain,
% 2.95/3.19 (~r(s(s(z)), z)),
% 2.95/3.19 inference(unit_resolution,[status(thm)],[12376, 197, 323, 97, 392])).
% 2.95/3.19 tff(12378,plain,
% 2.95/3.19 (b(s(s(z)), z)),
% 2.95/3.19 inference(unit_resolution,[status(thm)],[186, 12377])).
% 2.95/3.19 tff(12379,plain,
% 2.95/3.19 (~b(s(s(s(elem!1))), s(s(z)))),
% 2.95/3.19 inference(unit_resolution,[status(thm)],[10459, 121, 10451, 12378])).
% 2.95/3.19 tff(12380,plain,
% 2.95/3.19 (r(s(s(s(elem!1))), s(s(z)))),
% 2.95/3.19 inference(unit_resolution,[status(thm)],[218, 12379])).
% 2.95/3.19 tff(12381,plain,
% 2.95/3.19 (~r(s(s(elem!1)), s(s(z)))),
% 2.95/3.19 inference(unit_resolution,[status(thm)],[4313, 12349, 392, 12380])).
% 2.95/3.19 tff(12382,plain,
% 2.95/3.19 (b(s(s(elem!1)), s(s(z)))),
% 2.95/3.19 inference(unit_resolution,[status(thm)],[441, 12381, 11])).
% 2.95/3.19 tff(12383,plain,
% 2.95/3.19 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(z)))) | (~b(z, s(s(elem!1)))) | (~b(s(s(elem!1)), s(s(z)))) | (~b(s(s(z)), z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(s(z)))) | (~b(z, s(s(elem!1)))) | (~b(s(s(elem!1)), s(s(z)))) | (~b(s(s(z)), z)))),
% 2.95/3.19 inference(rewrite,[status(thm)],[])).
% 2.95/3.19 tff(12384,plain,
% 2.95/3.19 (((~b(z, s(s(z)))) | (~b(z, s(s(z)))) | (~b(s(s(z)), z)) | (~b(s(s(elem!1)), s(s(z)))) | (~b(z, s(s(z)))) | (~b(z, s(s(elem!1))))) <=> ((~b(z, s(s(z)))) | (~b(z, s(s(elem!1)))) | (~b(s(s(elem!1)), s(s(z)))) | (~b(s(s(z)), z)))),
% 2.95/3.19 inference(rewrite,[status(thm)],[])).
% 2.95/3.19 tff(12385,plain,
% 2.95/3.19 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(z)))) | (~b(z, s(s(z)))) | (~b(s(s(z)), z)) | (~b(s(s(elem!1)), s(s(z)))) | (~b(z, s(s(z)))) | (~b(z, s(s(elem!1)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(z)))) | (~b(z, s(s(elem!1)))) | (~b(s(s(elem!1)), s(s(z)))) | (~b(s(s(z)), z))))),
% 2.95/3.19 inference(monotonicity,[status(thm)],[12384])).
% 2.95/3.19 tff(12386,plain,
% 2.95/3.19 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(z)))) | (~b(z, s(s(z)))) | (~b(s(s(z)), z)) | (~b(s(s(elem!1)), s(s(z)))) | (~b(z, s(s(z)))) | (~b(z, s(s(elem!1)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(s(z)))) | (~b(z, s(s(elem!1)))) | (~b(s(s(elem!1)), s(s(z)))) | (~b(s(s(z)), z)))),
% 2.95/3.19 inference(transitivity,[status(thm)],[12385, 12383])).
% 2.95/3.19 tff(12387,plain,
% 2.95/3.19 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(z)))) | (~b(z, s(s(z)))) | (~b(s(s(z)), z)) | (~b(s(s(elem!1)), s(s(z)))) | (~b(z, s(s(z)))) | (~b(z, s(s(elem!1)))))),
% 2.95/3.19 inference(quant_inst,[status(thm)],[])).
% 2.95/3.19 tff(12388,plain,
% 2.95/3.19 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(s(z)))) | (~b(z, s(s(elem!1)))) | (~b(s(s(elem!1)), s(s(z)))) | (~b(s(s(z)), z))),
% 2.95/3.19 inference(modus_ponens,[status(thm)],[12387, 12386])).
% 2.95/3.19 tff(12389,plain,
% 2.95/3.19 (~b(z, s(s(elem!1)))),
% 2.95/3.19 inference(unit_resolution,[status(thm)],[12388, 166, 12382, 10451, 12378])).
% 2.95/3.19 tff(12390,plain,
% 2.95/3.19 (~b(s(s(z)), s(s(s(elem!1))))),
% 2.95/3.19 inference(unit_resolution,[status(thm)],[10468, 166, 10451, 121, 12378])).
% 2.95/3.19 tff(12391,plain,
% 2.95/3.19 (r(s(s(z)), s(s(s(elem!1))))),
% 2.95/3.19 inference(unit_resolution,[status(thm)],[279, 12390])).
% 2.95/3.19 tff(12392,plain,
% 2.95/3.19 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), s(s(elem!1)))) | (~r(s(s(elem!1)), s(s(s(elem!1))))) | (~r(s(s(z)), s(s(elem!1)))) | (~r(s(s(z)), s(s(s(elem!1))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(elem!1))), s(s(elem!1)))) | (~r(s(s(elem!1)), s(s(s(elem!1))))) | (~r(s(s(z)), s(s(elem!1)))) | (~r(s(s(z)), s(s(s(elem!1))))))),
% 2.95/3.19 inference(rewrite,[status(thm)],[])).
% 2.95/3.19 tff(12393,plain,
% 2.95/3.19 (((~r(s(s(s(elem!1))), s(s(elem!1)))) | (~r(s(s(elem!1)), s(s(s(elem!1))))) | (~r(s(s(z)), s(s(s(elem!1))))) | (~r(s(s(z)), s(s(elem!1))))) <=> ((~r(s(s(s(elem!1))), s(s(elem!1)))) | (~r(s(s(elem!1)), s(s(s(elem!1))))) | (~r(s(s(z)), s(s(elem!1)))) | (~r(s(s(z)), s(s(s(elem!1))))))),
% 2.95/3.19 inference(rewrite,[status(thm)],[])).
% 2.95/3.19 tff(12394,plain,
% 2.95/3.19 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), s(s(elem!1)))) | (~r(s(s(elem!1)), s(s(s(elem!1))))) | (~r(s(s(z)), s(s(s(elem!1))))) | (~r(s(s(z)), s(s(elem!1)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), s(s(elem!1)))) | (~r(s(s(elem!1)), s(s(s(elem!1))))) | (~r(s(s(z)), s(s(elem!1)))) | (~r(s(s(z)), s(s(s(elem!1)))))))),
% 2.95/3.19 inference(monotonicity,[status(thm)],[12393])).
% 2.95/3.19 tff(12395,plain,
% 2.95/3.19 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), s(s(elem!1)))) | (~r(s(s(elem!1)), s(s(s(elem!1))))) | (~r(s(s(z)), s(s(s(elem!1))))) | (~r(s(s(z)), s(s(elem!1)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(elem!1))), s(s(elem!1)))) | (~r(s(s(elem!1)), s(s(s(elem!1))))) | (~r(s(s(z)), s(s(elem!1)))) | (~r(s(s(z)), s(s(s(elem!1))))))),
% 2.95/3.19 inference(transitivity,[status(thm)],[12394, 12392])).
% 2.95/3.19 tff(12396,plain,
% 2.95/3.19 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), s(s(elem!1)))) | (~r(s(s(elem!1)), s(s(s(elem!1))))) | (~r(s(s(z)), s(s(s(elem!1))))) | (~r(s(s(z)), s(s(elem!1)))))),
% 2.95/3.19 inference(quant_inst,[status(thm)],[])).
% 2.95/3.19 tff(12397,plain,
% 2.95/3.19 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(elem!1))), s(s(elem!1)))) | (~r(s(s(elem!1)), s(s(s(elem!1))))) | (~r(s(s(z)), s(s(elem!1)))) | (~r(s(s(z)), s(s(s(elem!1)))))),
% 2.95/3.19 inference(modus_ponens,[status(thm)],[12396, 12395])).
% 2.95/3.19 tff(12398,plain,
% 2.95/3.19 (~r(s(s(z)), s(s(elem!1)))),
% 2.95/3.19 inference(unit_resolution,[status(thm)],[12397, 197, 12351, 12349, 12391])).
% 2.95/3.19 tff(12399,plain,
% 2.95/3.19 (r(s(z), s(s(z)))),
% 2.95/3.19 inference(unit_resolution,[status(thm)],[427, 5433])).
% 2.95/3.19 tff(12400,plain,
% 2.95/3.19 (b(s(s(z)), s(s(elem!1)))),
% 2.95/3.19 inference(unit_resolution,[status(thm)],[390, 44, 2288])).
% 2.95/3.19 tff(12401,plain,
% 2.95/3.19 (~r(s(z), s(s(s(elem!1))))),
% 2.95/3.19 inference(unit_resolution,[status(thm)],[10475, 197, 120, 10743, 10741])).
% 2.95/3.19 tff(12402,plain,
% 2.95/3.19 (b(s(z), s(s(s(elem!1))))),
% 2.95/3.19 inference(unit_resolution,[status(thm)],[116, 12401])).
% 2.95/3.19 tff(12403,plain,
% 2.95/3.19 (~r(s(s(s(elem!1))), s(z))),
% 2.95/3.19 inference(unit_resolution,[status(thm)],[3174, 197, 120, 10743, 10741])).
% 2.95/3.19 tff(12404,plain,
% 2.95/3.19 (b(s(s(s(elem!1))), s(z))),
% 2.95/3.19 inference(unit_resolution,[status(thm)],[1849, 12403])).
% 2.95/3.19 tff(12405,plain,
% 2.95/3.19 (~r(s(s(elem!1)), s(z))),
% 2.95/3.19 inference(unit_resolution,[status(thm)],[8426, 365, 97, 323])).
% 2.95/3.19 tff(12406,plain,
% 2.95/3.19 (b(s(s(elem!1)), s(z))),
% 2.95/3.19 inference(unit_resolution,[status(thm)],[1912, 12405])).
% 2.95/3.19 tff(12407,plain,
% 2.95/3.19 (~b(s(s(elem!1)), s(s(s(elem!1))))),
% 2.95/3.19 inference(unit_resolution,[status(thm)],[1994, 12406, 12402, 12404])).
% 2.95/3.19 tff(12408,plain,
% 2.95/3.19 (~(s(s(elem!1)) = s(s(s(elem!1))))),
% 2.95/3.19 inference(unit_resolution,[status(thm)],[6647, 12400, 10742])).
% 2.95/3.19 tff(12409,plain,
% 2.95/3.19 (r(s(s(elem!1)), s(s(s(elem!1))))),
% 2.95/3.19 inference(unit_resolution,[status(thm)],[461, 12408, 12407])).
% 2.95/3.19 tff(12410,plain,
% 2.95/3.19 (~r(s(s(elem!1)), s(s(s(elem!1))))),
% 2.95/3.19 inference(unit_resolution,[status(thm)],[413, 85, 365, 323])).
% 2.95/3.19 tff(12411,plain,
% 2.95/3.19 (s(s(elem!1)) = s(s(s(elem!1)))),
% 2.95/3.19 inference(unit_resolution,[status(thm)],[461, 12410, 12350])).
% 2.95/3.19 tff(12412,plain,
% 2.95/3.19 (b(s(z), s(s(elem!1))) <=> b(s(z), s(s(s(elem!1))))),
% 2.95/3.19 inference(monotonicity,[status(thm)],[12411])).
% 2.95/3.19 tff(12413,plain,
% 2.95/3.19 (b(s(z), s(s(s(elem!1)))) <=> b(s(z), s(s(elem!1)))),
% 2.95/3.19 inference(symmetry,[status(thm)],[12412])).
% 2.95/3.19 tff(12414,plain,
% 2.95/3.19 (b(s(z), s(s(elem!1)))),
% 2.95/3.19 inference(modus_ponens,[status(thm)],[241, 12413])).
% 2.95/3.19 tff(12415,plain,
% 2.95/3.19 ($false),
% 2.95/3.19 inference(unit_resolution,[status(thm)],[54, 12414])).
% 2.95/3.19 tff(12416,plain,(b(s(z), s(s(elem!1))) | (~b(s(z), s(s(s(elem!1))))) | b(s(s(elem!1)), s(s(s(elem!1)))) | (~r(z, s(s(elem!1)))) | (~r(z, s(z)))), inference(lemma,lemma(discharge,[]))).
% 2.95/3.19 tff(12417,plain,
% 2.95/3.19 (b(s(z), s(s(elem!1)))),
% 2.95/3.19 inference(unit_resolution,[status(thm)],[12416, 12407, 323, 365, 12402])).
% 2.95/3.19 tff(12418,plain,
% 2.95/3.19 (~b(s(s(z)), s(z))),
% 2.95/3.19 inference(unit_resolution,[status(thm)],[454, 12400, 12406, 12417])).
% 2.95/3.19 tff(12419,plain,
% 2.95/3.19 (r(s(s(z)), s(z))),
% 2.95/3.19 inference(unit_resolution,[status(thm)],[308, 12418])).
% 2.95/3.19 tff(12420,plain,
% 2.95/3.19 (~r(z, s(s(z)))),
% 2.95/3.19 inference(unit_resolution,[status(thm)],[401, 393, 392, 365])).
% 2.95/3.19 tff(12421,plain,
% 2.95/3.19 (b(z, s(s(z)))),
% 2.95/3.19 inference(unit_resolution,[status(thm)],[151, 12420])).
% 2.95/3.19 tff(12422,plain,
% 2.95/3.19 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(z)))) | (~b(s(z), z)) | (~b(s(z), s(s(s(elem!1))))) | (~b(s(z), s(s(elem!1)))) | (~b(s(s(s(elem!1))), z)) | (~b(s(s(z)), s(s(elem!1)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(s(z)))) | (~b(s(z), z)) | (~b(s(z), s(s(s(elem!1))))) | (~b(s(z), s(s(elem!1)))) | (~b(s(s(s(elem!1))), z)) | (~b(s(s(z)), s(s(elem!1)))))),
% 2.95/3.19 inference(rewrite,[status(thm)],[])).
% 2.95/3.19 tff(12423,plain,
% 2.95/3.19 (((~b(s(s(z)), s(s(elem!1)))) | (~b(s(z), s(s(elem!1)))) | (~b(z, s(s(z)))) | (~b(s(s(s(elem!1))), z)) | (~b(s(z), z)) | (~b(s(z), s(s(s(elem!1)))))) <=> ((~b(z, s(s(z)))) | (~b(s(z), z)) | (~b(s(z), s(s(s(elem!1))))) | (~b(s(z), s(s(elem!1)))) | (~b(s(s(s(elem!1))), z)) | (~b(s(s(z)), s(s(elem!1)))))),
% 2.95/3.19 inference(rewrite,[status(thm)],[])).
% 2.95/3.19 tff(12424,plain,
% 2.95/3.19 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), s(s(elem!1)))) | (~b(s(z), s(s(elem!1)))) | (~b(z, s(s(z)))) | (~b(s(s(s(elem!1))), z)) | (~b(s(z), z)) | (~b(s(z), s(s(s(elem!1))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(z)))) | (~b(s(z), z)) | (~b(s(z), s(s(s(elem!1))))) | (~b(s(z), s(s(elem!1)))) | (~b(s(s(s(elem!1))), z)) | (~b(s(s(z)), s(s(elem!1))))))),
% 2.95/3.19 inference(monotonicity,[status(thm)],[12423])).
% 2.95/3.19 tff(12425,plain,
% 2.95/3.19 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), s(s(elem!1)))) | (~b(s(z), s(s(elem!1)))) | (~b(z, s(s(z)))) | (~b(s(s(s(elem!1))), z)) | (~b(s(z), z)) | (~b(s(z), s(s(s(elem!1))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(s(z)))) | (~b(s(z), z)) | (~b(s(z), s(s(s(elem!1))))) | (~b(s(z), s(s(elem!1)))) | (~b(s(s(s(elem!1))), z)) | (~b(s(s(z)), s(s(elem!1)))))),
% 2.95/3.19 inference(transitivity,[status(thm)],[12424, 12422])).
% 2.95/3.19 tff(12426,plain,
% 2.95/3.19 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), s(s(elem!1)))) | (~b(s(z), s(s(elem!1)))) | (~b(z, s(s(z)))) | (~b(s(s(s(elem!1))), z)) | (~b(s(z), z)) | (~b(s(z), s(s(s(elem!1))))))),
% 2.95/3.19 inference(quant_inst,[status(thm)],[])).
% 2.95/3.19 tff(12427,plain,
% 2.95/3.19 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(s(z)))) | (~b(s(z), z)) | (~b(s(z), s(s(s(elem!1))))) | (~b(s(z), s(s(elem!1)))) | (~b(s(s(s(elem!1))), z)) | (~b(s(s(z)), s(s(elem!1))))),
% 2.95/3.19 inference(modus_ponens,[status(thm)],[12426, 12425])).
% 2.95/3.19 tff(12428,plain,
% 2.95/3.19 ($false),
% 2.95/3.19 inference(unit_resolution,[status(thm)],[12427, 166, 376, 241, 53, 10451, 121, 446])).
% 2.95/3.19 tff(12429,plain,((~b(z, s(s(z)))) | (~b(s(z), s(s(elem!1)))) | (~b(s(z), s(s(s(elem!1))))) | (~b(s(z), z)) | (~b(s(s(s(elem!1))), z)) | (~b(s(s(z)), s(s(elem!1))))), inference(lemma,lemma(discharge,[]))).
% 2.95/3.19 tff(12430,plain,
% 2.95/3.19 (~b(s(s(z)), s(s(elem!1)))),
% 2.95/3.19 inference(unit_resolution,[status(thm)],[12429, 53, 241, 10451, 121, 376])).
% 2.95/3.19 tff(12431,plain,
% 2.95/3.19 (r(s(s(z)), s(s(elem!1)))),
% 2.95/3.19 inference(unit_resolution,[status(thm)],[390, 12430, 52])).
% 2.95/3.19 tff(12432,plain,
% 2.95/3.19 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(elem!1)))) | (~r(s(s(z)), s(s(elem!1)))) | (~r(s(s(z)), z)) | (~r(s(s(elem!1)), s(s(z)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, s(s(elem!1)))) | (~r(s(s(z)), s(s(elem!1)))) | (~r(s(s(z)), z)) | (~r(s(s(elem!1)), s(s(z)))))),
% 2.95/3.19 inference(rewrite,[status(thm)],[])).
% 2.95/3.19 tff(12433,plain,
% 2.95/3.19 (((~r(s(s(elem!1)), s(s(z)))) | (~r(z, s(s(elem!1)))) | (~r(s(s(z)), s(s(elem!1)))) | (~r(s(s(z)), z))) <=> ((~r(z, s(s(elem!1)))) | (~r(s(s(z)), s(s(elem!1)))) | (~r(s(s(z)), z)) | (~r(s(s(elem!1)), s(s(z)))))),
% 2.95/3.19 inference(rewrite,[status(thm)],[])).
% 2.95/3.19 tff(12434,plain,
% 2.95/3.19 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(elem!1)), s(s(z)))) | (~r(z, s(s(elem!1)))) | (~r(s(s(z)), s(s(elem!1)))) | (~r(s(s(z)), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(elem!1)))) | (~r(s(s(z)), s(s(elem!1)))) | (~r(s(s(z)), z)) | (~r(s(s(elem!1)), s(s(z))))))),
% 3.03/3.20 inference(monotonicity,[status(thm)],[12433])).
% 3.03/3.20 tff(12435,plain,
% 3.03/3.20 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(elem!1)), s(s(z)))) | (~r(z, s(s(elem!1)))) | (~r(s(s(z)), s(s(elem!1)))) | (~r(s(s(z)), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, s(s(elem!1)))) | (~r(s(s(z)), s(s(elem!1)))) | (~r(s(s(z)), z)) | (~r(s(s(elem!1)), s(s(z)))))),
% 3.03/3.20 inference(transitivity,[status(thm)],[12434, 12432])).
% 3.03/3.20 tff(12436,plain,
% 3.03/3.20 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(elem!1)), s(s(z)))) | (~r(z, s(s(elem!1)))) | (~r(s(s(z)), s(s(elem!1)))) | (~r(s(s(z)), z)))),
% 3.03/3.20 inference(quant_inst,[status(thm)],[])).
% 3.03/3.20 tff(12437,plain,
% 3.03/3.20 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, s(s(elem!1)))) | (~r(s(s(z)), s(s(elem!1)))) | (~r(s(s(z)), z)) | (~r(s(s(elem!1)), s(s(z))))),
% 3.03/3.20 inference(modus_ponens,[status(thm)],[12436, 12435])).
% 3.03/3.20 tff(12438,plain,
% 3.03/3.20 (~r(s(s(z)), z)),
% 3.03/3.20 inference(unit_resolution,[status(thm)],[12437, 197, 393, 12431, 365])).
% 3.03/3.20 tff(12439,plain,
% 3.03/3.20 (b(s(s(z)), z)),
% 3.03/3.20 inference(unit_resolution,[status(thm)],[186, 12438])).
% 3.03/3.20 tff(12440,plain,
% 3.03/3.20 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(z)))) | (~b(s(z), z)) | (~b(s(z), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), z)) | (~b(s(s(z)), z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(s(z)))) | (~b(s(z), z)) | (~b(s(z), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), z)) | (~b(s(s(z)), z)))),
% 3.03/3.20 inference(rewrite,[status(thm)],[])).
% 3.03/3.20 tff(12441,plain,
% 3.03/3.20 (((~b(s(s(z)), z)) | (~b(s(z), z)) | (~b(z, s(s(z)))) | (~b(s(s(s(elem!1))), z)) | (~b(s(z), z)) | (~b(s(z), s(s(s(elem!1)))))) <=> ((~b(z, s(s(z)))) | (~b(s(z), z)) | (~b(s(z), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), z)) | (~b(s(s(z)), z)))),
% 3.03/3.20 inference(rewrite,[status(thm)],[])).
% 3.03/3.20 tff(12442,plain,
% 3.03/3.20 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), z)) | (~b(s(z), z)) | (~b(z, s(s(z)))) | (~b(s(s(s(elem!1))), z)) | (~b(s(z), z)) | (~b(s(z), s(s(s(elem!1))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(z)))) | (~b(s(z), z)) | (~b(s(z), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), z)) | (~b(s(s(z)), z))))),
% 3.03/3.20 inference(monotonicity,[status(thm)],[12441])).
% 3.03/3.20 tff(12443,plain,
% 3.03/3.20 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), z)) | (~b(s(z), z)) | (~b(z, s(s(z)))) | (~b(s(s(s(elem!1))), z)) | (~b(s(z), z)) | (~b(s(z), s(s(s(elem!1))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(s(z)))) | (~b(s(z), z)) | (~b(s(z), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), z)) | (~b(s(s(z)), z)))),
% 3.03/3.20 inference(transitivity,[status(thm)],[12442, 12440])).
% 3.03/3.20 tff(12444,plain,
% 3.03/3.20 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), z)) | (~b(s(z), z)) | (~b(z, s(s(z)))) | (~b(s(s(s(elem!1))), z)) | (~b(s(z), z)) | (~b(s(z), s(s(s(elem!1))))))),
% 3.03/3.20 inference(quant_inst,[status(thm)],[])).
% 3.03/3.20 tff(12445,plain,
% 3.03/3.20 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(s(z)))) | (~b(s(z), z)) | (~b(s(z), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), z)) | (~b(s(s(z)), z))),
% 3.03/3.20 inference(modus_ponens,[status(thm)],[12444, 12443])).
% 3.03/3.20 tff(12446,plain,
% 3.03/3.20 ($false),
% 3.03/3.20 inference(unit_resolution,[status(thm)],[12445, 166, 241, 53, 10451, 121, 12439])).
% 3.03/3.20 tff(12447,plain,((~b(s(z), z)) | (~b(s(z), s(s(s(elem!1))))) | (~b(z, s(s(z)))) | (~b(s(s(s(elem!1))), z)) | (~r(s(s(elem!1)), s(s(z)))) | (~r(z, s(s(elem!1)))) | (s(s(z)) = s(s(elem!1))) | (~b(s(z), s(s(elem!1))))), inference(lemma,lemma(discharge,[]))).
% 3.03/3.20 tff(12448,plain,
% 3.03/3.20 (~b(s(z), z)),
% 3.03/3.20 inference(unit_resolution,[status(thm)],[12447, 12421, 241, 121, 393, 365, 52, 415])).
% 3.03/3.20 tff(12449,plain,
% 3.03/3.20 (r(s(z), z)),
% 3.03/3.20 inference(unit_resolution,[status(thm)],[230, 12448])).
% 3.03/3.20 tff(12450,plain,
% 3.03/3.20 (~r(s(s(z)), z)),
% 3.03/3.20 inference(unit_resolution,[status(thm)],[12376, 197, 323, 12449, 392])).
% 3.03/3.20 tff(12451,plain,
% 3.03/3.20 (b(s(s(z)), z)),
% 3.03/3.20 inference(unit_resolution,[status(thm)],[186, 12450])).
% 3.03/3.20 tff(12452,plain,
% 3.03/3.20 (~b(s(s(s(elem!1))), s(s(z)))),
% 3.03/3.20 inference(unit_resolution,[status(thm)],[10457, 166, 12421, 121, 12451])).
% 3.03/3.20 tff(12453,plain,
% 3.03/3.20 ((s(s(s(elem!1))) = s(s(z))) | r(s(s(s(elem!1))), s(s(z)))),
% 3.03/3.20 inference(unit_resolution,[status(thm)],[216, 79, 12452])).
% 3.03/3.20 tff(12454,plain,
% 3.03/3.20 (r(s(s(s(elem!1))), s(s(z)))),
% 3.03/3.20 inference(unit_resolution,[status(thm)],[12453, 490])).
% 3.03/3.20 tff(12455,plain,
% 3.03/3.20 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(elem!1)), s(s(s(elem!1))))) | (~r(s(s(z)), s(z))) | (~r(s(s(elem!1)), s(s(z)))) | (~r(s(s(s(elem!1))), s(s(z)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(elem!1)), s(s(s(elem!1))))) | (~r(s(s(z)), s(z))) | (~r(s(s(elem!1)), s(s(z)))) | (~r(s(s(s(elem!1))), s(s(z)))))),
% 3.03/3.20 inference(rewrite,[status(thm)],[])).
% 3.03/3.20 tff(12456,plain,
% 3.03/3.20 (((~r(s(s(z)), s(z))) | (~r(s(s(s(elem!1))), s(s(z)))) | (~r(s(s(elem!1)), s(s(z)))) | (~r(s(s(elem!1)), s(s(s(elem!1)))))) <=> ((~r(s(s(elem!1)), s(s(s(elem!1))))) | (~r(s(s(z)), s(z))) | (~r(s(s(elem!1)), s(s(z)))) | (~r(s(s(s(elem!1))), s(s(z)))))),
% 3.03/3.20 inference(rewrite,[status(thm)],[])).
% 3.03/3.20 tff(12457,plain,
% 3.03/3.20 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(z)), s(z))) | (~r(s(s(s(elem!1))), s(s(z)))) | (~r(s(s(elem!1)), s(s(z)))) | (~r(s(s(elem!1)), s(s(s(elem!1))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(elem!1)), s(s(s(elem!1))))) | (~r(s(s(z)), s(z))) | (~r(s(s(elem!1)), s(s(z)))) | (~r(s(s(s(elem!1))), s(s(z))))))),
% 3.03/3.20 inference(monotonicity,[status(thm)],[12456])).
% 3.03/3.20 tff(12458,plain,
% 3.03/3.20 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(z)), s(z))) | (~r(s(s(s(elem!1))), s(s(z)))) | (~r(s(s(elem!1)), s(s(z)))) | (~r(s(s(elem!1)), s(s(s(elem!1))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(elem!1)), s(s(s(elem!1))))) | (~r(s(s(z)), s(z))) | (~r(s(s(elem!1)), s(s(z)))) | (~r(s(s(s(elem!1))), s(s(z)))))),
% 3.03/3.20 inference(transitivity,[status(thm)],[12457, 12455])).
% 3.03/3.20 tff(12459,plain,
% 3.03/3.20 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(z)), s(z))) | (~r(s(s(s(elem!1))), s(s(z)))) | (~r(s(s(elem!1)), s(s(z)))) | (~r(s(s(elem!1)), s(s(s(elem!1))))))),
% 3.03/3.20 inference(quant_inst,[status(thm)],[])).
% 3.03/3.20 tff(12460,plain,
% 3.03/3.20 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(elem!1)), s(s(s(elem!1))))) | (~r(s(s(z)), s(z))) | (~r(s(s(elem!1)), s(s(z)))) | (~r(s(s(s(elem!1))), s(s(z))))),
% 3.03/3.20 inference(modus_ponens,[status(thm)],[12459, 12458])).
% 3.03/3.20 tff(12461,plain,
% 3.03/3.20 ($false),
% 3.03/3.20 inference(unit_resolution,[status(thm)],[12460, 197, 393, 377, 392, 12454])).
% 3.03/3.20 tff(12462,plain,((~r(s(s(elem!1)), s(s(z)))) | (~r(s(s(elem!1)), s(s(s(elem!1))))) | (~r(s(s(z)), s(z))) | (~b(s(s(s(elem!1))), z)) | (~r(z, s(z))) | (~b(s(z), s(s(s(elem!1))))) | (~r(z, s(s(elem!1)))) | (s(s(z)) = s(s(elem!1)))), inference(lemma,lemma(discharge,[]))).
% 3.03/3.20 tff(12463,plain,
% 3.03/3.20 (~r(s(s(elem!1)), s(s(z)))),
% 3.03/3.20 inference(unit_resolution,[status(thm)],[12462, 12419, 121, 12409, 323, 12402, 365, 44])).
% 3.03/3.20 tff(12464,plain,
% 3.03/3.20 (b(s(s(elem!1)), s(s(z)))),
% 3.03/3.20 inference(unit_resolution,[status(thm)],[441, 12463, 11])).
% 3.03/3.20 tff(12465,plain,
% 3.03/3.20 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(z)))) | (~b(s(s(elem!1)), z)) | (~b(s(s(elem!1)), s(s(z)))) | (~b(s(s(z)), s(s(elem!1)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(s(z)))) | (~b(s(s(elem!1)), z)) | (~b(s(s(elem!1)), s(s(z)))) | (~b(s(s(z)), s(s(elem!1)))))),
% 3.03/3.20 inference(rewrite,[status(thm)],[])).
% 3.03/3.20 tff(12466,plain,
% 3.03/3.20 (((~b(s(s(elem!1)), s(s(z)))) | (~b(s(s(elem!1)), s(s(z)))) | (~b(s(s(z)), s(s(elem!1)))) | (~b(z, s(s(z)))) | (~b(s(s(elem!1)), s(s(z)))) | (~b(s(s(elem!1)), z))) <=> ((~b(z, s(s(z)))) | (~b(s(s(elem!1)), z)) | (~b(s(s(elem!1)), s(s(z)))) | (~b(s(s(z)), s(s(elem!1)))))),
% 3.03/3.20 inference(rewrite,[status(thm)],[])).
% 3.03/3.20 tff(12467,plain,
% 3.03/3.20 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), s(s(z)))) | (~b(s(s(elem!1)), s(s(z)))) | (~b(s(s(z)), s(s(elem!1)))) | (~b(z, s(s(z)))) | (~b(s(s(elem!1)), s(s(z)))) | (~b(s(s(elem!1)), z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(z)))) | (~b(s(s(elem!1)), z)) | (~b(s(s(elem!1)), s(s(z)))) | (~b(s(s(z)), s(s(elem!1))))))),
% 3.03/3.20 inference(monotonicity,[status(thm)],[12466])).
% 3.03/3.20 tff(12468,plain,
% 3.03/3.20 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), s(s(z)))) | (~b(s(s(elem!1)), s(s(z)))) | (~b(s(s(z)), s(s(elem!1)))) | (~b(z, s(s(z)))) | (~b(s(s(elem!1)), s(s(z)))) | (~b(s(s(elem!1)), z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(s(z)))) | (~b(s(s(elem!1)), z)) | (~b(s(s(elem!1)), s(s(z)))) | (~b(s(s(z)), s(s(elem!1)))))),
% 3.03/3.20 inference(transitivity,[status(thm)],[12467, 12465])).
% 3.03/3.20 tff(12469,plain,
% 3.03/3.20 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), s(s(z)))) | (~b(s(s(elem!1)), s(s(z)))) | (~b(s(s(z)), s(s(elem!1)))) | (~b(z, s(s(z)))) | (~b(s(s(elem!1)), s(s(z)))) | (~b(s(s(elem!1)), z)))),
% 3.03/3.20 inference(quant_inst,[status(thm)],[])).
% 3.03/3.20 tff(12470,plain,
% 3.03/3.20 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(s(z)))) | (~b(s(s(elem!1)), z)) | (~b(s(s(elem!1)), s(s(z)))) | (~b(s(s(z)), s(s(elem!1))))),
% 3.03/3.20 inference(modus_ponens,[status(thm)],[12469, 12468])).
% 3.03/3.20 tff(12471,plain,
% 3.03/3.20 (~b(s(s(elem!1)), z)),
% 3.03/3.20 inference(unit_resolution,[status(thm)],[12470, 166, 12464, 10451, 12400])).
% 3.03/3.20 tff(12472,plain,
% 3.03/3.20 (r(s(s(elem!1)), z)),
% 3.03/3.20 inference(unit_resolution,[status(thm)],[608, 12471])).
% 3.03/3.20 tff(12473,plain,
% 3.03/3.20 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(z))) | (~r(s(z), s(s(z)))) | (~r(s(s(s(s(elem!1)))), s(z))) | (~r(s(s(s(s(elem!1)))), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, s(z))) | (~r(s(z), s(s(z)))) | (~r(s(s(s(s(elem!1)))), s(z))) | (~r(s(s(s(s(elem!1)))), z)))),
% 3.03/3.20 inference(rewrite,[status(thm)],[])).
% 3.03/3.20 tff(12474,plain,
% 3.03/3.20 (((~r(s(z), s(s(z)))) | (~r(z, s(z))) | (~r(s(s(s(s(elem!1)))), s(z))) | (~r(s(s(s(s(elem!1)))), z))) <=> ((~r(z, s(z))) | (~r(s(z), s(s(z)))) | (~r(s(s(s(s(elem!1)))), s(z))) | (~r(s(s(s(s(elem!1)))), z)))),
% 3.03/3.20 inference(rewrite,[status(thm)],[])).
% 3.03/3.20 tff(12475,plain,
% 3.03/3.20 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(s(z)))) | (~r(z, s(z))) | (~r(s(s(s(s(elem!1)))), s(z))) | (~r(s(s(s(s(elem!1)))), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(z))) | (~r(s(z), s(s(z)))) | (~r(s(s(s(s(elem!1)))), s(z))) | (~r(s(s(s(s(elem!1)))), z))))),
% 3.03/3.20 inference(monotonicity,[status(thm)],[12474])).
% 3.03/3.20 tff(12476,plain,
% 3.03/3.20 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(s(z)))) | (~r(z, s(z))) | (~r(s(s(s(s(elem!1)))), s(z))) | (~r(s(s(s(s(elem!1)))), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, s(z))) | (~r(s(z), s(s(z)))) | (~r(s(s(s(s(elem!1)))), s(z))) | (~r(s(s(s(s(elem!1)))), z)))),
% 3.03/3.20 inference(transitivity,[status(thm)],[12475, 12473])).
% 3.03/3.20 tff(12477,plain,
% 3.03/3.20 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(s(z)))) | (~r(z, s(z))) | (~r(s(s(s(s(elem!1)))), s(z))) | (~r(s(s(s(s(elem!1)))), z)))),
% 3.03/3.20 inference(quant_inst,[status(thm)],[])).
% 3.03/3.20 tff(12478,plain,
% 3.03/3.20 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, s(z))) | (~r(s(z), s(s(z)))) | (~r(s(s(s(s(elem!1)))), s(z))) | (~r(s(s(s(s(elem!1)))), z))),
% 3.03/3.20 inference(modus_ponens,[status(thm)],[12477, 12476])).
% 3.03/3.20 tff(12479,plain,
% 3.03/3.20 (~r(s(s(s(s(elem!1)))), z)),
% 3.03/3.20 inference(unit_resolution,[status(thm)],[12478, 197, 120, 323, 700])).
% 3.03/3.20 tff(12480,plain,
% 3.03/3.20 (b(s(s(s(s(elem!1)))), z)),
% 3.03/3.20 inference(unit_resolution,[status(thm)],[1339, 79, 626, 12479])).
% 3.03/3.20 tff(12481,plain,
% 3.03/3.20 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(s(z)))) | (~r(s(s(z)), s(z))) | (~r(s(s(s(s(elem!1)))), s(z))) | (~r(s(s(s(s(elem!1)))), s(s(z)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(z), s(s(z)))) | (~r(s(s(z)), s(z))) | (~r(s(s(s(s(elem!1)))), s(z))) | (~r(s(s(s(s(elem!1)))), s(s(z)))))),
% 3.03/3.20 inference(rewrite,[status(thm)],[])).
% 3.03/3.20 tff(12482,plain,
% 3.03/3.20 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(s(z)))) | (~r(s(s(z)), s(z))) | (~r(s(s(s(s(elem!1)))), s(z))) | (~r(s(s(s(s(elem!1)))), s(s(z)))))),
% 3.03/3.20 inference(quant_inst,[status(thm)],[])).
% 3.03/3.20 tff(12483,plain,
% 3.03/3.20 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(z), s(s(z)))) | (~r(s(s(z)), s(z))) | (~r(s(s(s(s(elem!1)))), s(z))) | (~r(s(s(s(s(elem!1)))), s(s(z))))),
% 3.03/3.20 inference(modus_ponens,[status(thm)],[12482, 12481])).
% 3.03/3.20 tff(12484,plain,
% 3.03/3.20 (~r(s(s(s(s(elem!1)))), s(s(z)))),
% 3.03/3.20 inference(unit_resolution,[status(thm)],[12483, 197, 120, 392, 700])).
% 3.03/3.20 tff(12485,plain,
% 3.03/3.20 (b(s(s(s(s(elem!1)))), s(s(z)))),
% 3.03/3.20 inference(unit_resolution,[status(thm)],[1299, 12484])).
% 3.03/3.20 tff(12486,plain,
% 3.03/3.20 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(z)))) | (~b(s(s(elem!1)), s(s(z)))) | (~b(s(s(z)), s(s(elem!1)))) | (~b(s(s(s(s(elem!1)))), s(s(z)))) | (~b(s(s(s(s(elem!1)))), z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(s(z)))) | (~b(s(s(elem!1)), s(s(z)))) | (~b(s(s(z)), s(s(elem!1)))) | (~b(s(s(s(s(elem!1)))), s(s(z)))) | (~b(s(s(s(s(elem!1)))), z)))),
% 3.03/3.20 inference(rewrite,[status(thm)],[])).
% 3.03/3.20 tff(12487,plain,
% 3.03/3.20 (((~b(s(s(elem!1)), s(s(z)))) | (~b(s(s(s(s(elem!1)))), s(s(z)))) | (~b(s(s(z)), s(s(elem!1)))) | (~b(z, s(s(z)))) | (~b(s(s(s(s(elem!1)))), s(s(z)))) | (~b(s(s(s(s(elem!1)))), z))) <=> ((~b(z, s(s(z)))) | (~b(s(s(elem!1)), s(s(z)))) | (~b(s(s(z)), s(s(elem!1)))) | (~b(s(s(s(s(elem!1)))), s(s(z)))) | (~b(s(s(s(s(elem!1)))), z)))),
% 3.03/3.21 inference(rewrite,[status(thm)],[])).
% 3.03/3.21 tff(12488,plain,
% 3.03/3.21 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), s(s(z)))) | (~b(s(s(s(s(elem!1)))), s(s(z)))) | (~b(s(s(z)), s(s(elem!1)))) | (~b(z, s(s(z)))) | (~b(s(s(s(s(elem!1)))), s(s(z)))) | (~b(s(s(s(s(elem!1)))), z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(z)))) | (~b(s(s(elem!1)), s(s(z)))) | (~b(s(s(z)), s(s(elem!1)))) | (~b(s(s(s(s(elem!1)))), s(s(z)))) | (~b(s(s(s(s(elem!1)))), z))))),
% 3.03/3.21 inference(monotonicity,[status(thm)],[12487])).
% 3.03/3.21 tff(12489,plain,
% 3.03/3.21 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), s(s(z)))) | (~b(s(s(s(s(elem!1)))), s(s(z)))) | (~b(s(s(z)), s(s(elem!1)))) | (~b(z, s(s(z)))) | (~b(s(s(s(s(elem!1)))), s(s(z)))) | (~b(s(s(s(s(elem!1)))), z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(s(z)))) | (~b(s(s(elem!1)), s(s(z)))) | (~b(s(s(z)), s(s(elem!1)))) | (~b(s(s(s(s(elem!1)))), s(s(z)))) | (~b(s(s(s(s(elem!1)))), z)))),
% 3.03/3.21 inference(transitivity,[status(thm)],[12488, 12486])).
% 3.03/3.21 tff(12490,plain,
% 3.03/3.21 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), s(s(z)))) | (~b(s(s(s(s(elem!1)))), s(s(z)))) | (~b(s(s(z)), s(s(elem!1)))) | (~b(z, s(s(z)))) | (~b(s(s(s(s(elem!1)))), s(s(z)))) | (~b(s(s(s(s(elem!1)))), z)))),
% 3.03/3.21 inference(quant_inst,[status(thm)],[])).
% 3.03/3.21 tff(12491,plain,
% 3.03/3.21 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(s(z)))) | (~b(s(s(elem!1)), s(s(z)))) | (~b(s(s(z)), s(s(elem!1)))) | (~b(s(s(s(s(elem!1)))), s(s(z)))) | (~b(s(s(s(s(elem!1)))), z))),
% 3.03/3.21 inference(modus_ponens,[status(thm)],[12490, 12489])).
% 3.03/3.21 tff(12492,plain,
% 3.03/3.21 ($false),
% 3.03/3.21 inference(unit_resolution,[status(thm)],[12491, 166, 12485, 405, 10451, 446, 12480])).
% 3.03/3.21 tff(12493,plain,((~r(s(s(s(s(elem!1)))), s(z))) | (~b(s(s(elem!1)), s(s(z)))) | (~b(z, s(s(z)))) | (~b(s(s(z)), s(s(elem!1)))) | (~r(s(z), s(s(z)))) | (~r(s(s(z)), s(z))) | (~r(z, s(z)))), inference(lemma,lemma(discharge,[]))).
% 3.03/3.21 tff(12494,plain,
% 3.03/3.21 (~r(s(s(s(s(elem!1)))), s(z))),
% 3.03/3.21 inference(unit_resolution,[status(thm)],[12493, 12464, 10451, 12400, 120, 12419, 323])).
% 3.03/3.21 tff(12495,plain,
% 3.03/3.21 (b(s(s(s(s(elem!1)))), s(z))),
% 3.03/3.21 inference(unit_resolution,[status(thm)],[661, 12494])).
% 3.03/3.21 tff(12496,plain,
% 3.03/3.21 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(s(elem!1))))) | (~b(s(s(s(s(elem!1)))), s(s(elem!1)))) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(s(elem!1)), s(z))) | (~b(s(s(s(s(elem!1)))), s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), s(s(s(elem!1))))) | (~b(s(s(s(s(elem!1)))), s(s(elem!1)))) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(s(elem!1)), s(z))) | (~b(s(s(s(s(elem!1)))), s(z))))),
% 3.03/3.21 inference(rewrite,[status(thm)],[])).
% 3.03/3.21 tff(12497,plain,
% 3.03/3.21 (((~b(s(s(s(elem!1))), s(z))) | (~b(s(s(s(s(elem!1)))), s(z))) | (~b(s(z), s(s(s(elem!1))))) | (~b(s(s(elem!1)), s(z))) | (~b(s(s(s(s(elem!1)))), s(z))) | (~b(s(s(s(s(elem!1)))), s(s(elem!1))))) <=> ((~b(s(z), s(s(s(elem!1))))) | (~b(s(s(s(s(elem!1)))), s(s(elem!1)))) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(s(elem!1)), s(z))) | (~b(s(s(s(s(elem!1)))), s(z))))),
% 3.03/3.21 inference(rewrite,[status(thm)],[])).
% 3.03/3.21 tff(12498,plain,
% 3.03/3.21 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), s(z))) | (~b(s(s(s(s(elem!1)))), s(z))) | (~b(s(z), s(s(s(elem!1))))) | (~b(s(s(elem!1)), s(z))) | (~b(s(s(s(s(elem!1)))), s(z))) | (~b(s(s(s(s(elem!1)))), s(s(elem!1)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(s(elem!1))))) | (~b(s(s(s(s(elem!1)))), s(s(elem!1)))) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(s(elem!1)), s(z))) | (~b(s(s(s(s(elem!1)))), s(z)))))),
% 3.03/3.21 inference(monotonicity,[status(thm)],[12497])).
% 3.03/3.21 tff(12499,plain,
% 3.03/3.21 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), s(z))) | (~b(s(s(s(s(elem!1)))), s(z))) | (~b(s(z), s(s(s(elem!1))))) | (~b(s(s(elem!1)), s(z))) | (~b(s(s(s(s(elem!1)))), s(z))) | (~b(s(s(s(s(elem!1)))), s(s(elem!1)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), s(s(s(elem!1))))) | (~b(s(s(s(s(elem!1)))), s(s(elem!1)))) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(s(elem!1)), s(z))) | (~b(s(s(s(s(elem!1)))), s(z))))),
% 3.03/3.21 inference(transitivity,[status(thm)],[12498, 12496])).
% 3.03/3.21 tff(12500,plain,
% 3.03/3.21 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), s(z))) | (~b(s(s(s(s(elem!1)))), s(z))) | (~b(s(z), s(s(s(elem!1))))) | (~b(s(s(elem!1)), s(z))) | (~b(s(s(s(s(elem!1)))), s(z))) | (~b(s(s(s(s(elem!1)))), s(s(elem!1)))))),
% 3.03/3.21 inference(quant_inst,[status(thm)],[])).
% 3.03/3.21 tff(12501,plain,
% 3.03/3.21 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), s(s(s(elem!1))))) | (~b(s(s(s(s(elem!1)))), s(s(elem!1)))) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(s(elem!1)), s(z))) | (~b(s(s(s(s(elem!1)))), s(z)))),
% 3.03/3.21 inference(modus_ponens,[status(thm)],[12500, 12499])).
% 3.03/3.21 tff(12502,plain,
% 3.03/3.21 (~b(s(s(s(s(elem!1)))), s(s(elem!1)))),
% 3.03/3.21 inference(unit_resolution,[status(thm)],[12501, 166, 12402, 12404, 12406, 12495])).
% 3.03/3.21 tff(12503,plain,
% 3.03/3.21 (~b(s(s(s(elem!1))), s(s(s(s(elem!1)))))),
% 3.03/3.21 inference(unit_resolution,[status(thm)],[9110, 166, 12417, 12404, 12406, 12495])).
% 3.03/3.21 tff(12504,plain,
% 3.03/3.21 (~(s(s(s(elem!1))) = s(s(s(s(elem!1)))))),
% 3.03/3.21 inference(unit_resolution,[status(thm)],[357, 12408])).
% 3.03/3.21 tff(12505,plain,
% 3.03/3.21 (r(s(s(s(elem!1))), s(s(s(s(elem!1)))))),
% 3.03/3.21 inference(unit_resolution,[status(thm)],[694, 79, 12504, 12503])).
% 3.03/3.21 tff(12506,plain,
% 3.03/3.21 (~(s(s(s(s(elem!1)))) = s(s(s(elem!1))))),
% 3.03/3.21 inference(unit_resolution,[status(thm)],[363, 12504])).
% 3.03/3.21 tff(12507,plain,
% 3.03/3.21 (~b(s(s(s(s(elem!1)))), s(s(s(elem!1))))),
% 3.03/3.21 inference(unit_resolution,[status(thm)],[11236, 166, 12402, 12404, 12495])).
% 3.03/3.21 tff(12508,plain,
% 3.03/3.21 (r(s(s(s(s(elem!1)))), s(s(s(elem!1))))),
% 3.03/3.21 inference(unit_resolution,[status(thm)],[1063, 79, 12507, 12506])).
% 3.03/3.21 tff(12509,plain,
% 3.03/3.21 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(elem!1)), s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), s(s(s(s(elem!1)))))) | (~r(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~r(s(s(s(s(elem!1)))), s(s(elem!1)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(elem!1)), s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), s(s(s(s(elem!1)))))) | (~r(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~r(s(s(s(s(elem!1)))), s(s(elem!1)))))),
% 3.03/3.21 inference(rewrite,[status(thm)],[])).
% 3.03/3.21 tff(12510,plain,
% 3.03/3.21 (((~r(s(s(s(elem!1))), s(s(s(s(elem!1)))))) | (~r(s(s(elem!1)), s(s(s(elem!1))))) | (~r(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~r(s(s(s(s(elem!1)))), s(s(elem!1))))) <=> ((~r(s(s(elem!1)), s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), s(s(s(s(elem!1)))))) | (~r(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~r(s(s(s(s(elem!1)))), s(s(elem!1)))))),
% 3.03/3.21 inference(rewrite,[status(thm)],[])).
% 3.03/3.21 tff(12511,plain,
% 3.03/3.21 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), s(s(s(s(elem!1)))))) | (~r(s(s(elem!1)), s(s(s(elem!1))))) | (~r(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~r(s(s(s(s(elem!1)))), s(s(elem!1)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(elem!1)), s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), s(s(s(s(elem!1)))))) | (~r(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~r(s(s(s(s(elem!1)))), s(s(elem!1))))))),
% 3.03/3.21 inference(monotonicity,[status(thm)],[12510])).
% 3.03/3.21 tff(12512,plain,
% 3.03/3.21 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), s(s(s(s(elem!1)))))) | (~r(s(s(elem!1)), s(s(s(elem!1))))) | (~r(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~r(s(s(s(s(elem!1)))), s(s(elem!1)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(elem!1)), s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), s(s(s(s(elem!1)))))) | (~r(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~r(s(s(s(s(elem!1)))), s(s(elem!1)))))),
% 3.03/3.21 inference(transitivity,[status(thm)],[12511, 12509])).
% 3.03/3.21 tff(12513,plain,
% 3.03/3.21 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), s(s(s(s(elem!1)))))) | (~r(s(s(elem!1)), s(s(s(elem!1))))) | (~r(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~r(s(s(s(s(elem!1)))), s(s(elem!1)))))),
% 3.03/3.21 inference(quant_inst,[status(thm)],[])).
% 3.03/3.21 tff(12514,plain,
% 3.03/3.21 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(elem!1)), s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), s(s(s(s(elem!1)))))) | (~r(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~r(s(s(s(s(elem!1)))), s(s(elem!1))))),
% 3.03/3.21 inference(modus_ponens,[status(thm)],[12513, 12512])).
% 3.03/3.21 tff(12515,plain,
% 3.03/3.21 (~r(s(s(s(s(elem!1)))), s(s(elem!1)))),
% 3.03/3.21 inference(unit_resolution,[status(thm)],[12514, 197, 12409, 12508, 12505])).
% 3.03/3.21 tff(12516,plain,
% 3.03/3.21 (s(s(s(s(elem!1)))) = s(s(elem!1))),
% 3.03/3.21 inference(unit_resolution,[status(thm)],[813, 12515, 12502])).
% 3.03/3.21 tff(12517,plain,
% 3.03/3.21 (s(s(s(elem!1))) = s(elem!1)),
% 3.03/3.21 inference(unit_resolution,[status(thm)],[1166, 12516])).
% 3.03/3.21 tff(12518,plain,
% 3.03/3.21 (b(s(z), s(s(s(elem!1)))) <=> b(s(z), s(elem!1))),
% 3.03/3.21 inference(monotonicity,[status(thm)],[12517])).
% 3.03/3.21 tff(12519,plain,
% 3.03/3.21 (b(s(z), s(elem!1))),
% 3.03/3.21 inference(modus_ponens,[status(thm)],[12402, 12518])).
% 3.03/3.21 tff(12520,plain,
% 3.03/3.21 (b(s(s(s(elem!1))), s(z)) <=> b(s(elem!1), s(z))),
% 3.03/3.21 inference(monotonicity,[status(thm)],[12517])).
% 3.03/3.21 tff(12521,plain,
% 3.03/3.21 (b(s(elem!1), s(z))),
% 3.03/3.21 inference(modus_ponens,[status(thm)],[12404, 12520])).
% 3.03/3.21 tff(12522,plain,
% 3.03/3.21 (~(s(s(s(z))) = elem!1)),
% 3.03/3.21 inference(unit_resolution,[status(thm)],[1556, 12517])).
% 3.03/3.21 tff(12523,plain,
% 3.03/3.21 (s(s(elem!1)) = elem!1),
% 3.03/3.21 inference(unit_resolution,[status(thm)],[10139, 12517])).
% 3.03/3.21 tff(12524,plain,
% 3.03/3.21 (b(s(s(s(z))), s(s(elem!1))) <=> b(s(s(s(z))), elem!1)),
% 3.03/3.21 inference(monotonicity,[status(thm)],[2559])).
% 3.03/3.21 tff(12525,plain,
% 3.03/3.21 (b(s(s(s(z))), elem!1) <=> b(s(s(s(z))), s(s(elem!1)))),
% 3.03/3.21 inference(symmetry,[status(thm)],[12524])).
% 3.03/3.21 tff(12526,plain,
% 3.03/3.21 (r(s(s(s(z))), s(s(elem!1))) <=> r(s(s(s(z))), elem!1)),
% 3.03/3.21 inference(monotonicity,[status(thm)],[2559])).
% 3.03/3.21 tff(12527,plain,
% 3.03/3.21 ((~r(s(s(s(z))), s(s(elem!1)))) <=> (~r(s(s(s(z))), elem!1))),
% 3.03/3.21 inference(monotonicity,[status(thm)],[12526])).
% 3.03/3.21 tff(12528,plain,
% 3.03/3.21 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(z))) | (~r(s(s(elem!1)), z)) | (~r(s(s(s(z))), z)) | (~r(s(s(s(z))), s(s(elem!1)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, s(z))) | (~r(s(s(elem!1)), z)) | (~r(s(s(s(z))), z)) | (~r(s(s(s(z))), s(s(elem!1)))))),
% 3.03/3.21 inference(rewrite,[status(thm)],[])).
% 3.03/3.21 tff(12529,plain,
% 3.03/3.21 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(z))) | (~r(s(s(elem!1)), z)) | (~r(s(s(s(z))), z)) | (~r(s(s(s(z))), s(s(elem!1)))))),
% 3.03/3.21 inference(quant_inst,[status(thm)],[])).
% 3.03/3.21 tff(12530,plain,
% 3.03/3.21 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, s(z))) | (~r(s(s(elem!1)), z)) | (~r(s(s(s(z))), z)) | (~r(s(s(s(z))), s(s(elem!1))))),
% 3.03/3.21 inference(modus_ponens,[status(thm)],[12529, 12528])).
% 3.03/3.21 tff(12531,plain,
% 3.03/3.21 (~r(s(s(s(z))), s(s(elem!1)))),
% 3.03/3.21 inference(unit_resolution,[status(thm)],[12530, 197, 323, 1970, 1733])).
% 3.03/3.21 tff(12532,plain,
% 3.03/3.21 (~r(s(s(s(z))), elem!1)),
% 3.03/3.21 inference(modus_ponens,[status(thm)],[12531, 12527])).
% 3.03/3.21 tff(12533,plain,
% 3.03/3.21 (b(s(s(s(z))), elem!1)),
% 3.03/3.21 inference(unit_resolution,[status(thm)],[2826, 12532, 1562])).
% 3.03/3.21 tff(12534,plain,
% 3.03/3.21 (b(s(s(s(z))), s(s(elem!1)))),
% 3.03/3.21 inference(modus_ponens,[status(thm)],[12533, 12525])).
% 3.03/3.21 tff(12535,plain,
% 3.03/3.21 (~r(s(s(s(z))), s(z))),
% 3.03/3.21 inference(unit_resolution,[status(thm)],[12220, 197, 323, 97, 1733])).
% 3.03/3.21 tff(12536,plain,
% 3.03/3.21 (b(s(s(s(z))), s(z))),
% 3.03/3.21 inference(unit_resolution,[status(thm)],[1762, 12535, 1758])).
% 3.03/3.21 tff(12537,plain,
% 3.03/3.21 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), s(z))) | (~b(s(z), s(elem!1))) | (~b(s(s(elem!1)), s(z))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(z))), s(s(elem!1)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(elem!1), s(z))) | (~b(s(z), s(elem!1))) | (~b(s(s(elem!1)), s(z))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(z))), s(s(elem!1)))))),
% 3.03/3.21 inference(rewrite,[status(thm)],[])).
% 3.03/3.21 tff(12538,plain,
% 3.03/3.21 (((~b(s(elem!1), s(z))) | (~b(s(s(s(z))), s(z))) | (~b(s(z), s(elem!1))) | (~b(s(s(elem!1)), s(z))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(z))), s(s(elem!1))))) <=> ((~b(s(elem!1), s(z))) | (~b(s(z), s(elem!1))) | (~b(s(s(elem!1)), s(z))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(z))), s(s(elem!1)))))),
% 3.03/3.21 inference(rewrite,[status(thm)],[])).
% 3.03/3.21 tff(12539,plain,
% 3.03/3.21 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), s(z))) | (~b(s(s(s(z))), s(z))) | (~b(s(z), s(elem!1))) | (~b(s(s(elem!1)), s(z))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(z))), s(s(elem!1)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), s(z))) | (~b(s(z), s(elem!1))) | (~b(s(s(elem!1)), s(z))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(z))), s(s(elem!1))))))),
% 3.03/3.21 inference(monotonicity,[status(thm)],[12538])).
% 3.03/3.21 tff(12540,plain,
% 3.03/3.21 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), s(z))) | (~b(s(s(s(z))), s(z))) | (~b(s(z), s(elem!1))) | (~b(s(s(elem!1)), s(z))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(z))), s(s(elem!1)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(elem!1), s(z))) | (~b(s(z), s(elem!1))) | (~b(s(s(elem!1)), s(z))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(z))), s(s(elem!1)))))),
% 3.03/3.21 inference(transitivity,[status(thm)],[12539, 12537])).
% 3.03/3.21 tff(12541,plain,
% 3.03/3.21 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), s(z))) | (~b(s(s(s(z))), s(z))) | (~b(s(z), s(elem!1))) | (~b(s(s(elem!1)), s(z))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(z))), s(s(elem!1)))))),
% 3.03/3.21 inference(quant_inst,[status(thm)],[])).
% 3.03/3.21 tff(12542,plain,
% 3.03/3.21 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(elem!1), s(z))) | (~b(s(z), s(elem!1))) | (~b(s(s(elem!1)), s(z))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(z))), s(s(elem!1))))),
% 3.03/3.21 inference(modus_ponens,[status(thm)],[12541, 12540])).
% 3.03/3.21 tff(12543,plain,
% 3.03/3.21 (~b(s(s(s(z))), s(s(elem!1)))),
% 3.03/3.21 inference(unit_resolution,[status(thm)],[12542, 166, 4330, 310, 1211, 12536])).
% 3.03/3.21 tff(12544,plain,
% 3.03/3.21 ($false),
% 3.03/3.21 inference(unit_resolution,[status(thm)],[12543, 12534])).
% 3.03/3.21 tff(12545,plain,((~r(s(s(s(z))), z)) | (~(s(s(elem!1)) = elem!1)) | (s(s(s(z))) = elem!1) | (~b(s(elem!1), s(z))) | (~b(s(s(elem!1)), s(z))) | (~b(s(z), s(elem!1))) | (~r(z, s(z))) | (~r(s(s(elem!1)), z)) | (~r(s(z), z))), inference(lemma,lemma(discharge,[]))).
% 3.03/3.21 tff(12546,plain,
% 3.03/3.21 (~r(s(s(s(z))), z)),
% 3.03/3.21 inference(unit_resolution,[status(thm)],[12545, 12523, 12522, 12521, 12406, 12519, 323, 12472, 97])).
% 3.03/3.21 tff(12547,plain,
% 3.03/3.21 (b(s(s(s(z))), z)),
% 3.03/3.21 inference(unit_resolution,[status(thm)],[1713, 12546])).
% 3.03/3.21 tff(12548,plain,
% 3.03/3.21 (b(z, s(s(s(elem!1)))) <=> b(z, s(elem!1))),
% 3.03/3.21 inference(monotonicity,[status(thm)],[12517])).
% 3.03/3.21 tff(12549,plain,
% 3.03/3.21 (~b(s(s(s(elem!1))), s(s(elem!1)))),
% 3.03/3.21 inference(unit_resolution,[status(thm)],[1858, 12417, 12404, 12406])).
% 3.03/3.21 tff(12550,plain,
% 3.03/3.21 (~(s(s(s(elem!1))) = s(s(elem!1)))),
% 3.03/3.21 inference(unit_resolution,[status(thm)],[50, 12408])).
% 3.03/3.21 tff(12551,plain,
% 3.03/3.21 (r(s(s(s(elem!1))), s(s(elem!1)))),
% 3.03/3.21 inference(unit_resolution,[status(thm)],[889, 12550, 12549])).
% 3.03/3.21 tff(12552,plain,
% 3.03/3.21 (~r(z, s(s(s(elem!1))))),
% 3.03/3.21 inference(unit_resolution,[status(thm)],[1956, 12551, 365, 12409])).
% 3.03/3.21 tff(12553,plain,
% 3.03/3.21 (b(z, s(s(s(elem!1))))),
% 3.03/3.21 inference(unit_resolution,[status(thm)],[261, 12552])).
% 3.03/3.21 tff(12554,plain,
% 3.03/3.21 (b(z, s(elem!1))),
% 3.03/3.21 inference(modus_ponens,[status(thm)],[12553, 12548])).
% 3.03/3.21 tff(12555,plain,
% 3.03/3.21 (b(s(s(s(elem!1))), z) <=> b(s(elem!1), z)),
% 3.03/3.21 inference(monotonicity,[status(thm)],[12517])).
% 3.03/3.21 tff(12556,plain,
% 3.03/3.21 (b(s(elem!1), z)),
% 3.03/3.21 inference(modus_ponens,[status(thm)],[121, 12555])).
% 3.03/3.21 tff(12557,plain,
% 3.03/3.21 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), z)) | (~b(s(s(s(z))), s(s(z)))) | (~b(z, s(elem!1))) | (~b(s(s(z)), z)) | (~b(s(s(s(z))), z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(elem!1), z)) | (~b(s(s(s(z))), s(s(z)))) | (~b(z, s(elem!1))) | (~b(s(s(z)), z)) | (~b(s(s(s(z))), z)))),
% 3.03/3.21 inference(rewrite,[status(thm)],[])).
% 3.03/3.21 tff(12558,plain,
% 3.03/3.21 (((~b(s(elem!1), z)) | (~b(s(s(s(z))), z)) | (~b(z, s(elem!1))) | (~b(s(s(z)), z)) | (~b(s(s(s(z))), z)) | (~b(s(s(s(z))), s(s(z))))) <=> ((~b(s(elem!1), z)) | (~b(s(s(s(z))), s(s(z)))) | (~b(z, s(elem!1))) | (~b(s(s(z)), z)) | (~b(s(s(s(z))), z)))),
% 3.03/3.21 inference(rewrite,[status(thm)],[])).
% 3.03/3.21 tff(12559,plain,
% 3.03/3.21 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), z)) | (~b(s(s(s(z))), z)) | (~b(z, s(elem!1))) | (~b(s(s(z)), z)) | (~b(s(s(s(z))), z)) | (~b(s(s(s(z))), s(s(z)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), z)) | (~b(s(s(s(z))), s(s(z)))) | (~b(z, s(elem!1))) | (~b(s(s(z)), z)) | (~b(s(s(s(z))), z))))),
% 3.03/3.21 inference(monotonicity,[status(thm)],[12558])).
% 3.03/3.21 tff(12560,plain,
% 3.03/3.21 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), z)) | (~b(s(s(s(z))), z)) | (~b(z, s(elem!1))) | (~b(s(s(z)), z)) | (~b(s(s(s(z))), z)) | (~b(s(s(s(z))), s(s(z)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(elem!1), z)) | (~b(s(s(s(z))), s(s(z)))) | (~b(z, s(elem!1))) | (~b(s(s(z)), z)) | (~b(s(s(s(z))), z)))),
% 3.03/3.21 inference(transitivity,[status(thm)],[12559, 12557])).
% 3.03/3.21 tff(12561,plain,
% 3.03/3.22 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), z)) | (~b(s(s(s(z))), z)) | (~b(z, s(elem!1))) | (~b(s(s(z)), z)) | (~b(s(s(s(z))), z)) | (~b(s(s(s(z))), s(s(z)))))),
% 3.03/3.22 inference(quant_inst,[status(thm)],[])).
% 3.03/3.22 tff(12562,plain,
% 3.03/3.22 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(elem!1), z)) | (~b(s(s(s(z))), s(s(z)))) | (~b(z, s(elem!1))) | (~b(s(s(z)), z)) | (~b(s(s(s(z))), z))),
% 3.03/3.22 inference(modus_ponens,[status(thm)],[12561, 12560])).
% 3.03/3.22 tff(12563,plain,
% 3.03/3.22 (~b(s(s(s(z))), s(s(z)))),
% 3.03/3.22 inference(unit_resolution,[status(thm)],[12562, 166, 12556, 12554, 122, 12547])).
% 3.03/3.22 tff(12564,plain,
% 3.03/3.22 (r(s(s(s(z))), s(s(z)))),
% 3.03/3.22 inference(unit_resolution,[status(thm)],[1008, 79, 12563, 1003])).
% 3.03/3.22 tff(12565,plain,
% 3.03/3.22 (r(s(s(z)), s(s(s(elem!1)))) <=> r(s(s(z)), s(elem!1))),
% 3.03/3.22 inference(monotonicity,[status(thm)],[12517])).
% 3.03/3.22 tff(12566,plain,
% 3.03/3.22 (r(s(s(z)), s(elem!1))),
% 3.03/3.22 inference(modus_ponens,[status(thm)],[10743, 12565])).
% 3.03/3.22 tff(12567,plain,
% 3.03/3.22 (r(s(s(s(elem!1))), s(s(z))) <=> r(s(elem!1), s(s(z)))),
% 3.03/3.22 inference(monotonicity,[status(thm)],[12517])).
% 3.03/3.22 tff(12568,plain,
% 3.03/3.22 (r(s(elem!1), s(s(z)))),
% 3.03/3.22 inference(modus_ponens,[status(thm)],[10741, 12567])).
% 3.03/3.22 tff(12569,plain,
% 3.03/3.22 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(z)), s(elem!1))) | (~r(s(elem!1), s(s(z)))) | (~r(s(s(s(z))), s(s(z)))) | (~r(s(s(s(z))), s(elem!1))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(z)), s(elem!1))) | (~r(s(elem!1), s(s(z)))) | (~r(s(s(s(z))), s(s(z)))) | (~r(s(s(s(z))), s(elem!1))))),
% 3.03/3.22 inference(rewrite,[status(thm)],[])).
% 3.03/3.22 tff(12570,plain,
% 3.03/3.22 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(z)), s(elem!1))) | (~r(s(elem!1), s(s(z)))) | (~r(s(s(s(z))), s(s(z)))) | (~r(s(s(s(z))), s(elem!1))))),
% 3.03/3.22 inference(quant_inst,[status(thm)],[])).
% 3.03/3.22 tff(12571,plain,
% 3.03/3.22 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(z)), s(elem!1))) | (~r(s(elem!1), s(s(z)))) | (~r(s(s(s(z))), s(s(z)))) | (~r(s(s(s(z))), s(elem!1)))),
% 3.03/3.22 inference(modus_ponens,[status(thm)],[12570, 12569])).
% 3.03/3.22 tff(12572,plain,
% 3.03/3.22 (~r(s(s(s(z))), s(elem!1))),
% 3.03/3.22 inference(unit_resolution,[status(thm)],[12571, 197, 12568, 12566, 12564])).
% 3.03/3.22 tff(12573,plain,
% 3.03/3.22 (~b(s(s(s(z))), s(elem!1))),
% 3.03/3.22 inference(unit_resolution,[status(thm)],[2834, 166, 12556, 12554, 12547])).
% 3.03/3.22 tff(12574,plain,
% 3.03/3.22 ((s(s(s(z))) = s(elem!1)) | r(s(s(s(z))), s(elem!1))),
% 3.03/3.22 inference(unit_resolution,[status(thm)],[2845, 79, 12573])).
% 3.03/3.22 tff(12575,plain,
% 3.03/3.22 (s(s(s(z))) = s(elem!1)),
% 3.03/3.22 inference(unit_resolution,[status(thm)],[12574, 12572])).
% 3.03/3.22 tff(12576,plain,
% 3.03/3.22 (inj_0(s(s(s(z)))) = inj_0(s(elem!1))),
% 3.03/3.22 inference(monotonicity,[status(thm)],[12575])).
% 3.03/3.22 tff(12577,plain,
% 3.03/3.22 (inj_0(s(elem!1)) = inj_0(s(s(s(z))))),
% 3.03/3.22 inference(symmetry,[status(thm)],[12576])).
% 3.03/3.22 tff(12578,plain,
% 3.03/3.22 (s(s(elem!1)) = s(s(z))),
% 3.03/3.22 inference(transitivity,[status(thm)],[12523, 1170, 12577, 134])).
% 3.03/3.22 tff(12579,plain,
% 3.03/3.22 ($false),
% 3.03/3.22 inference(unit_resolution,[status(thm)],[11, 12578])).
% 3.03/3.22 tff(12580,plain,((s(s(elem!1)) = s(s(z))) | (~b(s(s(z)), z)) | (~r(z, s(z))) | (~r(s(z), z)) | (~b(s(s(s(elem!1))), z)) | (~b(z, s(s(z)))) | (~r(s(z), s(s(z)))) | (~r(z, s(s(elem!1)))) | r(s(s(z)), s(s(elem!1)))), inference(lemma,lemma(discharge,[]))).
% 3.03/3.22 tff(12581,plain,
% 3.03/3.22 (s(s(elem!1)) = s(s(z))),
% 3.03/3.22 inference(unit_resolution,[status(thm)],[12580, 365, 323, 97, 121, 10451, 12399, 122, 2288])).
% 3.03/3.22 tff(12582,plain,
% 3.03/3.22 (b(s(z), s(s(elem!1))) <=> b(s(z), s(s(z)))),
% 3.03/3.22 inference(monotonicity,[status(thm)],[12581])).
% 3.03/3.22 tff(12583,plain,
% 3.03/3.22 (b(s(z), s(s(z))) <=> b(s(z), s(s(elem!1)))),
% 3.03/3.22 inference(symmetry,[status(thm)],[12582])).
% 3.03/3.22 tff(12584,plain,
% 3.03/3.22 ((~b(s(z), s(s(z)))) <=> (~b(s(z), s(s(elem!1))))),
% 3.03/3.22 inference(monotonicity,[status(thm)],[12583])).
% 3.03/3.22 tff(12585,plain,
% 3.03/3.22 (~b(s(z), s(s(elem!1)))),
% 3.03/3.22 inference(modus_ponens,[status(thm)],[5433, 12584])).
% 3.03/3.22 tff(12586,plain,
% 3.03/3.22 (~r(s(z), s(s(s(elem!1))))),
% 3.03/3.22 inference(unit_resolution,[status(thm)],[10475, 197, 12399, 10743, 10741])).
% 3.03/3.22 tff(12587,plain,
% 3.03/3.22 (b(s(z), s(s(s(elem!1))))),
% 3.03/3.22 inference(unit_resolution,[status(thm)],[116, 12586])).
% 3.03/3.22 tff(12588,plain,
% 3.03/3.22 (~r(s(s(s(elem!1))), s(z))),
% 3.03/3.22 inference(unit_resolution,[status(thm)],[3174, 197, 12399, 10743, 10741])).
% 3.03/3.22 tff(12589,plain,
% 3.03/3.22 (b(s(s(s(elem!1))), s(z))),
% 3.03/3.22 inference(unit_resolution,[status(thm)],[1849, 12588])).
% 3.03/3.22 tff(12590,plain,
% 3.03/3.22 (~b(s(s(elem!1)), s(s(s(elem!1))))),
% 3.03/3.22 inference(unit_resolution,[status(thm)],[1994, 12406, 12587, 12589])).
% 3.03/3.22 tff(12591,plain,
% 3.03/3.22 (b(s(z), s(s(elem!1)))),
% 3.03/3.22 inference(unit_resolution,[status(thm)],[12416, 12590, 323, 365, 12587])).
% 3.03/3.22 tff(12592,plain,
% 3.03/3.22 ($false),
% 3.03/3.22 inference(unit_resolution,[status(thm)],[12591, 12585])).
% 3.03/3.22 tff(12593,plain,((~r(z, s(s(elem!1)))) | b(s(z), s(s(z))) | (~r(z, s(z))) | (~r(s(z), z)) | (~b(s(s(s(elem!1))), z)) | (~b(z, s(s(z)))) | (~b(s(s(z)), z)) | r(s(s(z)), s(s(elem!1)))), inference(lemma,lemma(discharge,[]))).
% 3.03/3.22 tff(12594,plain,
% 3.03/3.22 (~r(z, s(s(elem!1)))),
% 3.03/3.22 inference(unit_resolution,[status(thm)],[12593, 12398, 10451, 97, 323, 12378, 121, 5433])).
% 3.03/3.22 tff(12595,plain,
% 3.03/3.22 ($false),
% 3.03/3.22 inference(unit_resolution,[status(thm)],[1795, 12594, 12389])).
% 3.03/3.22 tff(12596,plain,((s(s(elem!1)) = s(s(s(elem!1)))) | (~b(z, s(s(z)))) | (~r(s(z), z)) | (~r(z, s(z))) | (~b(s(s(s(elem!1))), z)) | b(s(z), s(s(z))) | (s(s(elem!1)) = s(s(z))) | (~r(s(s(z)), s(z))) | b(s(s(s(elem!1))), s(s(elem!1))) | b(s(s(elem!1)), s(s(s(elem!1))))), inference(lemma,lemma(discharge,[]))).
% 3.03/3.22 tff(12597,plain,
% 3.03/3.22 ((s(s(elem!1)) = s(s(s(elem!1)))) | (~r(s(z), z)) | (~r(z, s(z))) | (~b(s(s(s(elem!1))), z)) | b(s(z), s(s(z))) | (s(s(elem!1)) = s(s(z))) | (~r(s(s(z)), s(z))) | b(s(s(s(elem!1))), s(s(elem!1))) | b(s(s(elem!1)), s(s(s(elem!1))))),
% 3.03/3.22 inference(unit_resolution,[status(thm)],[12596, 10450])).
% 3.03/3.22 tff(12598,plain,
% 3.03/3.22 (b(s(z), s(s(z)))),
% 3.03/3.22 inference(unit_resolution,[status(thm)],[12597, 12369, 97, 12340, 121, 12336, 12370, 12347, 12338])).
% 3.03/3.22 tff(12599,plain,
% 3.03/3.22 (~b(s(z), s(s(s(z))))),
% 3.03/3.22 inference(unit_resolution,[status(thm)],[8665, 12598, 96, 241, 263])).
% 3.03/3.22 tff(12600,plain,
% 3.03/3.22 (r(s(z), s(s(s(z))))),
% 3.03/3.22 inference(unit_resolution,[status(thm)],[1674, 12599])).
% 3.03/3.22 tff(12601,plain,
% 3.03/3.22 (~r(s(s(z)), z)),
% 3.03/3.22 inference(unit_resolution,[status(thm)],[1661, 12600, 12369, 12336])).
% 3.03/3.22 tff(12602,plain,
% 3.03/3.22 (b(s(s(z)), z)),
% 3.03/3.22 inference(unit_resolution,[status(thm)],[186, 12601])).
% 3.03/3.22 tff(12603,plain,
% 3.03/3.22 (~b(s(s(s(elem!1))), s(s(z)))),
% 3.03/3.22 inference(unit_resolution,[status(thm)],[10460, 12602, 121])).
% 3.03/3.22 tff(12604,plain,
% 3.03/3.22 (r(s(s(s(elem!1))), s(s(z)))),
% 3.03/3.22 inference(unit_resolution,[status(thm)],[218, 12603])).
% 3.03/3.22 tff(12605,plain,
% 3.03/3.22 (~(s(s(s(elem!1))) = s(s(elem!1)))),
% 3.03/3.22 inference(unit_resolution,[status(thm)],[50, 12340])).
% 3.03/3.22 tff(12606,plain,
% 3.03/3.22 (r(s(s(s(elem!1))), s(s(elem!1)))),
% 3.03/3.22 inference(unit_resolution,[status(thm)],[889, 12347, 12605])).
% 3.03/3.22 tff(12607,plain,
% 3.03/3.22 (~r(z, s(s(elem!1)))),
% 3.03/3.22 inference(unit_resolution,[status(thm)],[12416, 12369, 54, 241, 12338])).
% 3.03/3.22 tff(12608,plain,
% 3.03/3.22 (b(z, s(s(elem!1)))),
% 3.03/3.22 inference(unit_resolution,[status(thm)],[1795, 12607])).
% 3.03/3.22 tff(12609,plain,
% 3.03/3.22 (~r(s(s(elem!1)), s(s(z)))),
% 3.03/3.22 inference(unit_resolution,[status(thm)],[4313, 12604, 12336, 12606])).
% 3.03/3.22 tff(12610,plain,
% 3.03/3.22 (b(s(s(elem!1)), s(s(z)))),
% 3.03/3.22 inference(unit_resolution,[status(thm)],[441, 12609, 12370])).
% 3.03/3.22 tff(12611,plain,
% 3.03/3.22 ((~b(s(s(elem!1)), s(s(z)))) | (~b(z, s(s(elem!1)))) | (~b(s(s(z)), s(s(elem!1))))),
% 3.03/3.22 inference(unit_resolution,[status(thm)],[10727, 10450])).
% 3.03/3.22 tff(12612,plain,
% 3.03/3.22 (~b(s(s(z)), s(s(elem!1)))),
% 3.03/3.22 inference(unit_resolution,[status(thm)],[12611, 12610, 12608])).
% 3.03/3.22 tff(12613,plain,
% 3.03/3.22 (r(s(s(z)), s(s(elem!1)))),
% 3.03/3.22 inference(unit_resolution,[status(thm)],[390, 12612, 12339])).
% 3.03/3.22 tff(12614,plain,
% 3.03/3.22 (r(s(s(elem!1)), s(s(s(elem!1))))),
% 3.03/3.22 inference(unit_resolution,[status(thm)],[461, 12338, 12340])).
% 3.03/3.22 tff(12615,plain,
% 3.03/3.22 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), s(s(elem!1)))) | (~r(s(s(elem!1)), s(s(s(elem!1))))) | (~r(s(s(z)), s(s(elem!1)))) | (~r(s(s(s(elem!1))), s(s(z)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(elem!1))), s(s(elem!1)))) | (~r(s(s(elem!1)), s(s(s(elem!1))))) | (~r(s(s(z)), s(s(elem!1)))) | (~r(s(s(s(elem!1))), s(s(z)))))),
% 3.03/3.22 inference(rewrite,[status(thm)],[])).
% 3.03/3.22 tff(12616,plain,
% 3.03/3.22 (((~r(s(s(elem!1)), s(s(s(elem!1))))) | (~r(s(s(z)), s(s(elem!1)))) | (~r(s(s(s(elem!1))), s(s(elem!1)))) | (~r(s(s(s(elem!1))), s(s(z))))) <=> ((~r(s(s(s(elem!1))), s(s(elem!1)))) | (~r(s(s(elem!1)), s(s(s(elem!1))))) | (~r(s(s(z)), s(s(elem!1)))) | (~r(s(s(s(elem!1))), s(s(z)))))),
% 3.03/3.22 inference(rewrite,[status(thm)],[])).
% 3.03/3.22 tff(12617,plain,
% 3.03/3.22 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(elem!1)), s(s(s(elem!1))))) | (~r(s(s(z)), s(s(elem!1)))) | (~r(s(s(s(elem!1))), s(s(elem!1)))) | (~r(s(s(s(elem!1))), s(s(z)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), s(s(elem!1)))) | (~r(s(s(elem!1)), s(s(s(elem!1))))) | (~r(s(s(z)), s(s(elem!1)))) | (~r(s(s(s(elem!1))), s(s(z))))))),
% 3.03/3.22 inference(monotonicity,[status(thm)],[12616])).
% 3.03/3.22 tff(12618,plain,
% 3.03/3.22 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(elem!1)), s(s(s(elem!1))))) | (~r(s(s(z)), s(s(elem!1)))) | (~r(s(s(s(elem!1))), s(s(elem!1)))) | (~r(s(s(s(elem!1))), s(s(z)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(elem!1))), s(s(elem!1)))) | (~r(s(s(elem!1)), s(s(s(elem!1))))) | (~r(s(s(z)), s(s(elem!1)))) | (~r(s(s(s(elem!1))), s(s(z)))))),
% 3.03/3.22 inference(transitivity,[status(thm)],[12617, 12615])).
% 3.03/3.22 tff(12619,plain,
% 3.03/3.22 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(elem!1)), s(s(s(elem!1))))) | (~r(s(s(z)), s(s(elem!1)))) | (~r(s(s(s(elem!1))), s(s(elem!1)))) | (~r(s(s(s(elem!1))), s(s(z)))))),
% 3.03/3.22 inference(quant_inst,[status(thm)],[])).
% 3.03/3.22 tff(12620,plain,
% 3.03/3.22 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(elem!1))), s(s(elem!1)))) | (~r(s(s(elem!1)), s(s(s(elem!1))))) | (~r(s(s(z)), s(s(elem!1)))) | (~r(s(s(s(elem!1))), s(s(z))))),
% 3.03/3.22 inference(modus_ponens,[status(thm)],[12619, 12618])).
% 3.03/3.22 tff(12621,plain,
% 3.03/3.22 ($false),
% 3.03/3.22 inference(unit_resolution,[status(thm)],[12620, 197, 12614, 12613, 12606, 12604])).
% 3.03/3.22 tff(12622,plain,((~b(s(s(z)), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), z)) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(z), s(s(s(elem!1))))) | (~r(s(z), z)) | b(s(z), s(s(elem!1)))), inference(lemma,lemma(discharge,[]))).
% 3.03/3.22 tff(12623,plain,
% 3.03/3.22 (~b(s(s(z)), s(s(s(elem!1))))),
% 3.03/3.22 inference(unit_resolution,[status(thm)],[12622, 241, 96, 121, 97, 54])).
% 3.03/3.22 tff(12624,plain,
% 3.03/3.22 (r(s(s(z)), s(s(s(elem!1))))),
% 3.03/3.22 inference(unit_resolution,[status(thm)],[279, 12623])).
% 3.03/3.22 tff(12625,plain,
% 3.03/3.22 (~b(s(s(elem!1)), s(z))),
% 3.03/3.22 inference(unit_resolution,[status(thm)],[1994, 463, 96, 241])).
% 3.03/3.22 tff(12626,plain,
% 3.03/3.22 (r(s(s(elem!1)), s(z))),
% 3.03/3.22 inference(unit_resolution,[status(thm)],[1912, 12625])).
% 3.03/3.22 tff(12627,plain,
% 3.03/3.22 (~r(s(s(z)), s(z))),
% 3.03/3.22 inference(unit_resolution,[status(thm)],[11987, 12625, 97])).
% 3.03/3.22 tff(12628,plain,
% 3.03/3.22 (b(s(s(z)), s(z))),
% 3.03/3.22 inference(unit_resolution,[status(thm)],[308, 12627])).
% 3.03/3.22 tff(12629,plain,
% 3.03/3.22 ((~b(s(z), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(z))) | (~b(z, s(z))) | (~b(s(s(z)), s(z)))),
% 3.03/3.22 inference(unit_resolution,[status(thm)],[11081, 10450])).
% 3.03/3.22 tff(12630,plain,
% 3.03/3.22 (~b(z, s(z))),
% 3.03/3.22 inference(unit_resolution,[status(thm)],[12629, 12628, 96, 241])).
% 3.03/3.22 tff(12631,plain,
% 3.03/3.22 (r(z, s(z))),
% 3.03/3.22 inference(unit_resolution,[status(thm)],[321, 12630])).
% 3.03/3.22 tff(12632,plain,
% 3.03/3.22 (~r(z, s(s(elem!1)))),
% 3.03/3.22 inference(unit_resolution,[status(thm)],[8426, 12631, 97, 12626])).
% 3.03/3.22 tff(12633,plain,
% 3.03/3.22 (b(z, s(s(elem!1)))),
% 3.03/3.22 inference(unit_resolution,[status(thm)],[1795, 12632])).
% 3.03/3.22 tff(12634,plain,
% 3.03/3.22 (~r(s(s(elem!1)), z)),
% 3.03/3.22 inference(unit_resolution,[status(thm)],[8590, 12631, 311, 12626])).
% 3.03/3.22 tff(12635,plain,
% 3.03/3.22 (b(s(s(elem!1)), z)),
% 3.03/3.22 inference(unit_resolution,[status(thm)],[608, 12634])).
% 3.03/3.22 tff(12636,plain,
% 3.03/3.22 ($false),
% 3.03/3.22 inference(unit_resolution,[status(thm)],[3593, 12635, 12633, 463, 121])).
% 3.03/3.22 tff(12637,plain,((~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), z)) | (~r(s(z), s(s(elem!1)))) | (~r(s(z), z)) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(z), s(s(s(elem!1)))))), inference(lemma,lemma(discharge,[]))).
% 3.03/3.22 tff(12638,plain,
% 3.03/3.22 (~b(s(s(elem!1)), s(s(s(elem!1))))),
% 3.03/3.22 inference(unit_resolution,[status(thm)],[12637, 97, 85, 121, 96, 241])).
% 3.03/3.22 tff(12639,plain,
% 3.03/3.22 (r(s(s(elem!1)), s(s(s(elem!1))))),
% 3.03/3.22 inference(unit_resolution,[status(thm)],[461, 12638, 12340])).
% 3.03/3.22 tff(12640,plain,
% 3.03/3.22 (~r(s(s(z)), s(s(elem!1)))),
% 3.03/3.22 inference(unit_resolution,[status(thm)],[9490, 197, 12639, 12624, 12334])).
% 3.03/3.22 tff(12641,plain,
% 3.03/3.22 (b(s(s(elem!1)), s(z))),
% 3.03/3.22 inference(unit_resolution,[status(thm)],[11731, 12640, 97])).
% 3.03/3.22 tff(12642,plain,
% 3.03/3.22 (~b(s(s(z)), s(s(elem!1)))),
% 3.03/3.22 inference(unit_resolution,[status(thm)],[2929, 12641, 241, 156, 96])).
% 3.03/3.22 tff(12643,plain,
% 3.03/3.22 (s(s(z)) = s(s(elem!1))),
% 3.03/3.22 inference(unit_resolution,[status(thm)],[390, 12642, 12640])).
% 3.03/3.22 tff(12644,plain,
% 3.03/3.22 (s(s(s(z))) = s(s(s(elem!1)))),
% 3.03/3.22 inference(monotonicity,[status(thm)],[12643])).
% 3.03/3.22 tff(12645,plain,
% 3.03/3.22 (s(s(s(s(z)))) = s(s(s(s(elem!1))))),
% 3.03/3.22 inference(monotonicity,[status(thm)],[12644])).
% 3.03/3.22 tff(12646,plain,
% 3.03/3.22 (r(s(s(s(s(z)))), s(s(s(z)))) <=> r(s(s(s(s(elem!1)))), s(s(s(elem!1))))),
% 3.03/3.22 inference(monotonicity,[status(thm)],[12645, 12644])).
% 3.03/3.22 tff(12647,plain,
% 3.03/3.22 (s(elem!1) = s(z)),
% 3.03/3.22 inference(unit_resolution,[status(thm)],[43, 12643])).
% 3.03/3.22 tff(12648,plain,
% 3.03/3.22 (z = elem!1),
% 3.03/3.22 inference(unit_resolution,[status(thm)],[30, 12647])).
% 3.03/3.22 tff(12649,plain,
% 3.03/3.22 (b(s(s(s(z))), z) <=> b(s(s(s(z))), elem!1)),
% 3.03/3.22 inference(monotonicity,[status(thm)],[12648])).
% 3.03/3.22 tff(12650,plain,
% 3.03/3.22 (b(s(s(s(z))), elem!1) <=> b(s(s(s(z))), z)),
% 3.03/3.22 inference(symmetry,[status(thm)],[12649])).
% 3.03/3.22 tff(12651,plain,
% 3.03/3.22 (b(s(s(s(z))), elem!1) <=> b(s(s(s(elem!1))), elem!1)),
% 3.03/3.22 inference(monotonicity,[status(thm)],[12644])).
% 3.03/3.22 tff(12652,plain,
% 3.03/3.22 (b(s(s(s(elem!1))), elem!1) <=> b(s(s(s(z))), elem!1)),
% 3.03/3.22 inference(symmetry,[status(thm)],[12651])).
% 3.03/3.22 tff(12653,plain,
% 3.03/3.22 (b(s(s(s(elem!1))), elem!1) <=> b(s(s(s(z))), z)),
% 3.03/3.22 inference(transitivity,[status(thm)],[12652, 12650])).
% 3.03/3.22 tff(12654,plain,
% 3.03/3.22 (b(s(s(s(elem!1))), elem!1)),
% 3.03/3.22 inference(unit_resolution,[status(thm)],[634, 12648, 121])).
% 3.03/3.22 tff(12655,plain,
% 3.03/3.22 (b(s(s(s(z))), z)),
% 3.03/3.22 inference(modus_ponens,[status(thm)],[12654, 12653])).
% 3.03/3.22 tff(12656,plain,
% 3.03/3.22 (~b(s(z), s(s(z)))),
% 3.03/3.22 inference(unit_resolution,[status(thm)],[4398, 12643, 54])).
% 3.03/3.22 tff(12657,plain,
% 3.03/3.22 (r(s(z), s(s(z)))),
% 3.03/3.22 inference(unit_resolution,[status(thm)],[427, 12656])).
% 3.03/3.22 tff(12658,plain,
% 3.03/3.22 (~b(z, s(z))),
% 3.03/3.22 inference(unit_resolution,[status(thm)],[12629, 156, 96, 241])).
% 3.03/3.22 tff(12659,plain,
% 3.03/3.22 (r(z, s(z))),
% 3.03/3.22 inference(unit_resolution,[status(thm)],[321, 12658])).
% 3.03/3.22 tff(12660,plain,
% 3.03/3.22 (r(s(s(s(s(z)))), s(z)) <=> r(s(s(s(s(elem!1)))), s(z))),
% 3.03/3.22 inference(monotonicity,[status(thm)],[12645])).
% 3.03/3.22 tff(12661,plain,
% 3.03/3.22 (r(s(s(s(s(elem!1)))), s(z)) <=> r(s(s(s(s(z)))), s(z))),
% 3.03/3.22 inference(symmetry,[status(thm)],[12660])).
% 3.03/3.22 tff(12662,plain,
% 3.03/3.22 (~(s(s(s(elem!1))) = s(s(s(s(elem!1)))))),
% 3.03/3.22 inference(unit_resolution,[status(thm)],[357, 12340])).
% 3.03/3.22 tff(12663,plain,
% 3.03/3.22 (~(s(s(s(s(elem!1)))) = s(s(s(elem!1))))),
% 3.03/3.22 inference(unit_resolution,[status(thm)],[363, 12662])).
% 3.03/3.22 tff(12664,plain,
% 3.03/3.22 ((s(s(s(s(elem!1)))) = s(s(z))) <=> (s(s(s(s(elem!1)))) = s(s(elem!1)))),
% 3.03/3.22 inference(monotonicity,[status(thm)],[12643])).
% 3.03/3.22 tff(12665,plain,
% 3.03/3.22 ((s(s(s(s(elem!1)))) = s(s(z))) <=> (s(s(elem!1)) = s(s(s(s(elem!1)))))),
% 3.03/3.22 inference(transitivity,[status(thm)],[12664, 123])).
% 3.03/3.22 tff(12666,plain,
% 3.03/3.22 ((s(s(s(s(elem!1)))) = s(s(z))) <=> (s(s(s(s(elem!1)))) = s(s(elem!1)))),
% 3.03/3.22 inference(transitivity,[status(thm)],[12665, 124])).
% 3.03/3.22 tff(12667,plain,
% 3.03/3.22 ((~(s(s(s(s(elem!1)))) = s(s(z)))) <=> (~(s(s(s(s(elem!1)))) = s(s(elem!1))))),
% 3.03/3.22 inference(monotonicity,[status(thm)],[12666])).
% 3.03/3.22 tff(12668,plain,
% 3.03/3.22 (~(s(s(s(s(elem!1)))) = s(s(elem!1)))),
% 3.03/3.22 inference(modus_ponens,[status(thm)],[733, 12667])).
% 3.03/3.22 tff(12669,plain,
% 3.03/3.22 (~r(z, s(z))),
% 3.03/3.22 inference(unit_resolution,[status(thm)],[12416, 4458, 54, 241, 12350])).
% 3.03/3.22 tff(12670,plain,
% 3.03/3.22 (b(z, s(z))),
% 3.03/3.22 inference(unit_resolution,[status(thm)],[321, 12669])).
% 3.03/3.22 tff(12671,plain,
% 3.03/3.22 ((~(s(s(z)) = s(s(elem!1)))) | b(z, s(s(elem!1)))),
% 3.03/3.22 inference(unit_resolution,[status(thm)],[10937, 10450])).
% 3.03/3.22 tff(12672,plain,
% 3.03/3.22 (~(s(s(z)) = s(s(elem!1)))),
% 3.03/3.22 inference(unit_resolution,[status(thm)],[12671, 1790])).
% 3.03/3.22 tff(12673,plain,
% 3.03/3.22 (~b(z, s(s(s(elem!1))))),
% 3.03/3.22 inference(unit_resolution,[status(thm)],[249, 12670, 96, 241])).
% 3.03/3.22 tff(12674,plain,
% 3.03/3.22 (r(z, s(s(s(elem!1))))),
% 3.03/3.22 inference(unit_resolution,[status(thm)],[261, 12673])).
% 3.03/3.22 tff(12675,plain,
% 3.03/3.22 (~b(s(s(z)), s(z))),
% 3.03/3.22 inference(unit_resolution,[status(thm)],[12629, 12670, 96, 241])).
% 3.03/3.22 tff(12676,plain,
% 3.03/3.22 (r(s(s(z)), s(z))),
% 3.03/3.22 inference(unit_resolution,[status(thm)],[308, 12675])).
% 3.03/3.22 tff(12677,plain,
% 3.03/3.22 (b(s(s(s(elem!1))), s(s(elem!1)))),
% 3.03/3.22 inference(unit_resolution,[status(thm)],[12365, 12676, 12340, 12674, 85, 12672, 12350])).
% 3.03/3.22 tff(12678,plain,
% 3.03/3.22 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(z), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), z)) | (~b(s(s(s(elem!1))), s(z))) | (~b(z, s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(z), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), z)) | (~b(s(s(s(elem!1))), s(z))) | (~b(z, s(z))))),
% 3.03/3.22 inference(rewrite,[status(thm)],[])).
% 3.03/3.22 tff(12679,plain,
% 3.03/3.22 (((~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(z), s(s(s(elem!1))))) | (~b(z, s(z))) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(s(s(elem!1))), z))) <=> ((~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(z), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), z)) | (~b(s(s(s(elem!1))), s(z))) | (~b(z, s(z))))),
% 3.03/3.22 inference(rewrite,[status(thm)],[])).
% 3.03/3.22 tff(12680,plain,
% 3.03/3.22 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(z), s(s(s(elem!1))))) | (~b(z, s(z))) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(s(s(elem!1))), z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(z), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), z)) | (~b(s(s(s(elem!1))), s(z))) | (~b(z, s(z)))))),
% 3.03/3.22 inference(monotonicity,[status(thm)],[12679])).
% 3.03/3.22 tff(12681,plain,
% 3.03/3.22 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(z), s(s(s(elem!1))))) | (~b(z, s(z))) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(s(s(elem!1))), z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(z), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), z)) | (~b(s(s(s(elem!1))), s(z))) | (~b(z, s(z))))),
% 3.03/3.22 inference(transitivity,[status(thm)],[12680, 12678])).
% 3.03/3.22 tff(12682,plain,
% 3.03/3.22 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(z), s(s(s(elem!1))))) | (~b(z, s(z))) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(s(s(elem!1))), z)))),
% 3.03/3.22 inference(quant_inst,[status(thm)],[])).
% 3.03/3.22 tff(12683,plain,
% 3.03/3.22 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(z), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), z)) | (~b(s(s(s(elem!1))), s(z))) | (~b(z, s(z)))),
% 3.03/3.22 inference(modus_ponens,[status(thm)],[12682, 12681])).
% 3.03/3.22 tff(12684,plain,
% 3.03/3.22 ($false),
% 3.03/3.22 inference(unit_resolution,[status(thm)],[12683, 166, 12677, 241, 96, 12670, 121])).
% 3.03/3.22 tff(12685,plain,(b(z, s(s(elem!1))) | (~b(s(z), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(s(s(elem!1))), z)) | b(s(s(elem!1)), s(s(s(elem!1)))) | b(s(z), s(s(elem!1)))), inference(lemma,lemma(discharge,[]))).
% 3.03/3.22 tff(12686,plain,
% 3.03/3.22 (b(z, s(s(elem!1)))),
% 3.03/3.22 inference(unit_resolution,[status(thm)],[12685, 241, 96, 121, 12638, 54])).
% 3.03/3.22 tff(12687,plain,
% 3.03/3.22 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(s(elem!1))))) | (~r(s(s(elem!1)), z)) | (~r(s(s(elem!1)), s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), s(s(z)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, s(s(s(elem!1))))) | (~r(s(s(elem!1)), z)) | (~r(s(s(elem!1)), s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), s(s(z)))))),
% 3.03/3.22 inference(rewrite,[status(thm)],[])).
% 3.03/3.22 tff(12688,plain,
% 3.03/3.22 (((~r(s(s(s(elem!1))), s(s(z)))) | (~r(z, s(s(s(elem!1))))) | (~r(s(s(elem!1)), s(s(s(elem!1))))) | (~r(s(s(elem!1)), z))) <=> ((~r(z, s(s(s(elem!1))))) | (~r(s(s(elem!1)), z)) | (~r(s(s(elem!1)), s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), s(s(z)))))),
% 3.03/3.22 inference(rewrite,[status(thm)],[])).
% 3.03/3.22 tff(12689,plain,
% 3.03/3.22 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), s(s(z)))) | (~r(z, s(s(s(elem!1))))) | (~r(s(s(elem!1)), s(s(s(elem!1))))) | (~r(s(s(elem!1)), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(s(elem!1))))) | (~r(s(s(elem!1)), z)) | (~r(s(s(elem!1)), s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), s(s(z))))))),
% 3.03/3.22 inference(monotonicity,[status(thm)],[12688])).
% 3.03/3.22 tff(12690,plain,
% 3.03/3.22 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), s(s(z)))) | (~r(z, s(s(s(elem!1))))) | (~r(s(s(elem!1)), s(s(s(elem!1))))) | (~r(s(s(elem!1)), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, s(s(s(elem!1))))) | (~r(s(s(elem!1)), z)) | (~r(s(s(elem!1)), s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), s(s(z)))))),
% 3.03/3.22 inference(transitivity,[status(thm)],[12689, 12687])).
% 3.03/3.22 tff(12691,plain,
% 3.03/3.22 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), s(s(z)))) | (~r(z, s(s(s(elem!1))))) | (~r(s(s(elem!1)), s(s(s(elem!1))))) | (~r(s(s(elem!1)), z)))),
% 3.03/3.22 inference(quant_inst,[status(thm)],[])).
% 3.03/3.22 tff(12692,plain,
% 3.03/3.22 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, s(s(s(elem!1))))) | (~r(s(s(elem!1)), z)) | (~r(s(s(elem!1)), s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), s(s(z))))),
% 3.03/3.22 inference(modus_ponens,[status(thm)],[12691, 12690])).
% 3.03/3.22 tff(12693,plain,
% 3.03/3.22 (~r(s(s(elem!1)), z)),
% 3.03/3.22 inference(unit_resolution,[status(thm)],[12692, 197, 12639, 282, 12334])).
% 3.03/3.22 tff(12694,plain,
% 3.03/3.22 (b(s(s(elem!1)), z)),
% 3.03/3.22 inference(unit_resolution,[status(thm)],[608, 12693])).
% 3.03/3.22 tff(12695,plain,
% 3.03/3.22 (~b(s(s(s(elem!1))), s(s(elem!1)))),
% 3.03/3.22 inference(unit_resolution,[status(thm)],[11755, 12694, 121, 12686, 12640])).
% 3.03/3.22 tff(12696,plain,
% 3.03/3.22 (r(s(s(s(elem!1))), s(s(elem!1)))),
% 3.03/3.22 inference(unit_resolution,[status(thm)],[889, 12695, 12605])).
% 3.03/3.22 tff(12697,plain,
% 3.03/3.22 (~b(s(s(s(s(elem!1)))), s(s(s(elem!1))))),
% 3.03/3.22 inference(unit_resolution,[status(thm)],[11236, 166, 241, 96, 1402])).
% 3.03/3.23 tff(12698,plain,
% 3.03/3.23 (r(s(s(s(s(elem!1)))), s(s(s(elem!1))))),
% 3.03/3.23 inference(unit_resolution,[status(thm)],[1065, 12697, 1058])).
% 3.03/3.23 tff(12699,plain,
% 3.03/3.23 (~b(s(s(s(s(elem!1)))), s(s(elem!1)))),
% 3.03/3.23 inference(unit_resolution,[status(thm)],[12501, 166, 241, 96, 310, 1402])).
% 3.03/3.23 tff(12700,plain,
% 3.03/3.23 (r(s(s(s(s(elem!1)))), s(s(elem!1)))),
% 3.03/3.23 inference(unit_resolution,[status(thm)],[813, 12699, 806])).
% 3.03/3.23 tff(12701,plain,
% 3.03/3.23 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), s(s(elem!1)))) | (~r(s(s(elem!1)), s(s(s(elem!1))))) | (~r(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~r(s(s(s(s(elem!1)))), s(s(elem!1)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(elem!1))), s(s(elem!1)))) | (~r(s(s(elem!1)), s(s(s(elem!1))))) | (~r(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~r(s(s(s(s(elem!1)))), s(s(elem!1)))))),
% 3.03/3.23 inference(rewrite,[status(thm)],[])).
% 3.03/3.23 tff(12702,plain,
% 3.03/3.23 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), s(s(elem!1)))) | (~r(s(s(elem!1)), s(s(s(elem!1))))) | (~r(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~r(s(s(s(s(elem!1)))), s(s(elem!1)))))),
% 3.03/3.23 inference(quant_inst,[status(thm)],[])).
% 3.03/3.23 tff(12703,plain,
% 3.03/3.23 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(elem!1))), s(s(elem!1)))) | (~r(s(s(elem!1)), s(s(s(elem!1))))) | (~r(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~r(s(s(s(s(elem!1)))), s(s(elem!1))))),
% 3.03/3.23 inference(modus_ponens,[status(thm)],[12702, 12701])).
% 3.03/3.23 tff(12704,plain,
% 3.03/3.23 ($false),
% 3.03/3.23 inference(unit_resolution,[status(thm)],[12703, 197, 377, 905, 12700, 12698])).
% 3.03/3.23 tff(12705,plain,((~b(s(s(s(s(elem!1)))), s(z))) | (~r(s(s(elem!1)), s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), s(s(elem!1)))) | (s(s(s(s(elem!1)))) = s(s(elem!1))) | (s(s(s(s(elem!1)))) = s(s(s(elem!1)))) | (~b(s(z), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(s(elem!1)), s(z)))), inference(lemma,lemma(discharge,[]))).
% 3.03/3.23 tff(12706,plain,
% 3.03/3.23 (~b(s(s(s(s(elem!1)))), s(z))),
% 3.03/3.23 inference(unit_resolution,[status(thm)],[12705, 12696, 12639, 12668, 12663, 241, 96, 12641])).
% 3.03/3.23 tff(12707,plain,
% 3.03/3.23 (r(s(s(s(s(elem!1)))), s(z))),
% 3.03/3.23 inference(unit_resolution,[status(thm)],[661, 12706])).
% 3.03/3.23 tff(12708,plain,
% 3.03/3.23 (r(s(s(s(s(z)))), s(z))),
% 3.03/3.23 inference(modus_ponens,[status(thm)],[12707, 12661])).
% 3.03/3.23 tff(12709,plain,
% 3.03/3.23 ((z = s(s(s(s(z))))) <=> (s(s(s(s(z)))) = z)),
% 3.03/3.23 inference(commutativity,[status(thm)],[])).
% 3.03/3.23 tff(12710,plain,
% 3.03/3.23 ((s(s(s(s(z)))) = z) <=> (z = s(s(s(s(z)))))),
% 3.03/3.23 inference(symmetry,[status(thm)],[12709])).
% 3.03/3.23 tff(12711,plain,
% 3.03/3.23 ((~(s(s(s(s(z)))) = z)) <=> (~(z = s(s(s(s(z))))))),
% 3.03/3.23 inference(monotonicity,[status(thm)],[12710])).
% 3.03/3.23 tff(12712,plain,
% 3.03/3.23 (~(z = s(s(s(s(z)))))),
% 3.03/3.23 inference(modus_ponens,[status(thm)],[1044, 12711])).
% 3.03/3.23 tff(12713,plain,
% 3.03/3.23 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(z))) | (~r(s(z), s(s(z)))) | (~r(s(s(s(s(z)))), s(z))) | (~r(z, s(s(s(s(z)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, s(z))) | (~r(s(z), s(s(z)))) | (~r(s(s(s(s(z)))), s(z))) | (~r(z, s(s(s(s(z)))))))),
% 3.03/3.23 inference(rewrite,[status(thm)],[])).
% 3.03/3.23 tff(12714,plain,
% 3.03/3.23 (((~r(s(z), s(s(z)))) | (~r(s(s(s(s(z)))), s(z))) | (~r(z, s(z))) | (~r(z, s(s(s(s(z))))))) <=> ((~r(z, s(z))) | (~r(s(z), s(s(z)))) | (~r(s(s(s(s(z)))), s(z))) | (~r(z, s(s(s(s(z)))))))),
% 3.03/3.23 inference(rewrite,[status(thm)],[])).
% 3.03/3.23 tff(12715,plain,
% 3.03/3.23 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(s(z)))) | (~r(s(s(s(s(z)))), s(z))) | (~r(z, s(z))) | (~r(z, s(s(s(s(z)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(z))) | (~r(s(z), s(s(z)))) | (~r(s(s(s(s(z)))), s(z))) | (~r(z, s(s(s(s(z))))))))),
% 3.03/3.23 inference(monotonicity,[status(thm)],[12714])).
% 3.03/3.23 tff(12716,plain,
% 3.03/3.23 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(s(z)))) | (~r(s(s(s(s(z)))), s(z))) | (~r(z, s(z))) | (~r(z, s(s(s(s(z)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, s(z))) | (~r(s(z), s(s(z)))) | (~r(s(s(s(s(z)))), s(z))) | (~r(z, s(s(s(s(z)))))))),
% 3.03/3.23 inference(transitivity,[status(thm)],[12715, 12713])).
% 3.03/3.23 tff(12717,plain,
% 3.03/3.23 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(s(z)))) | (~r(s(s(s(s(z)))), s(z))) | (~r(z, s(z))) | (~r(z, s(s(s(s(z)))))))),
% 3.03/3.23 inference(quant_inst,[status(thm)],[])).
% 3.03/3.23 tff(12718,plain,
% 3.03/3.23 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, s(z))) | (~r(s(z), s(s(z)))) | (~r(s(s(s(s(z)))), s(z))) | (~r(z, s(s(s(s(z))))))),
% 3.03/3.23 inference(modus_ponens,[status(thm)],[12717, 12716])).
% 3.03/3.23 tff(12719,plain,
% 3.03/3.23 (~r(z, s(s(s(s(z)))))),
% 3.03/3.23 inference(unit_resolution,[status(thm)],[12718, 197, 120, 323, 7222])).
% 3.03/3.23 tff(12720,plain,
% 3.03/3.23 (((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((z = s(s(s(s(z))))) | b(z, s(s(s(s(z))))) | r(z, s(s(s(s(z))))))) <=> ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (z = s(s(s(s(z))))) | b(z, s(s(s(s(z))))) | r(z, s(s(s(s(z))))))),
% 3.03/3.23 inference(rewrite,[status(thm)],[])).
% 3.03/3.23 tff(12721,plain,
% 3.03/3.23 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((z = s(s(s(s(z))))) | b(z, s(s(s(s(z))))) | r(z, s(s(s(s(z))))))),
% 3.03/3.23 inference(quant_inst,[status(thm)],[])).
% 3.03/3.23 tff(12722,plain,
% 3.03/3.23 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (z = s(s(s(s(z))))) | b(z, s(s(s(s(z))))) | r(z, s(s(s(s(z)))))),
% 3.03/3.23 inference(modus_ponens,[status(thm)],[12721, 12720])).
% 3.03/3.23 tff(12723,plain,
% 3.03/3.23 ((z = s(s(s(s(z))))) | b(z, s(s(s(s(z)))))),
% 3.03/3.23 inference(unit_resolution,[status(thm)],[12722, 79, 12719])).
% 3.03/3.23 tff(12724,plain,
% 3.03/3.23 (b(z, s(s(s(s(z)))))),
% 3.03/3.23 inference(unit_resolution,[status(thm)],[12723, 12712])).
% 3.03/3.23 tff(12725,plain,
% 3.03/3.23 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(z))) | (~r(s(z), s(s(z)))) | (~r(s(s(s(s(z)))), z)) | (~r(s(s(s(s(z)))), s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, s(z))) | (~r(s(z), s(s(z)))) | (~r(s(s(s(s(z)))), z)) | (~r(s(s(s(s(z)))), s(z))))),
% 3.03/3.23 inference(rewrite,[status(thm)],[])).
% 3.03/3.23 tff(12726,plain,
% 3.03/3.23 (((~r(s(z), s(s(z)))) | (~r(z, s(z))) | (~r(s(s(s(s(z)))), s(z))) | (~r(s(s(s(s(z)))), z))) <=> ((~r(z, s(z))) | (~r(s(z), s(s(z)))) | (~r(s(s(s(s(z)))), z)) | (~r(s(s(s(s(z)))), s(z))))),
% 3.03/3.23 inference(rewrite,[status(thm)],[])).
% 3.03/3.23 tff(12727,plain,
% 3.03/3.23 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(s(z)))) | (~r(z, s(z))) | (~r(s(s(s(s(z)))), s(z))) | (~r(s(s(s(s(z)))), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(z))) | (~r(s(z), s(s(z)))) | (~r(s(s(s(s(z)))), z)) | (~r(s(s(s(s(z)))), s(z)))))),
% 3.03/3.23 inference(monotonicity,[status(thm)],[12726])).
% 3.03/3.23 tff(12728,plain,
% 3.03/3.23 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(s(z)))) | (~r(z, s(z))) | (~r(s(s(s(s(z)))), s(z))) | (~r(s(s(s(s(z)))), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, s(z))) | (~r(s(z), s(s(z)))) | (~r(s(s(s(s(z)))), z)) | (~r(s(s(s(s(z)))), s(z))))),
% 3.03/3.23 inference(transitivity,[status(thm)],[12727, 12725])).
% 3.03/3.23 tff(12729,plain,
% 3.03/3.23 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(s(z)))) | (~r(z, s(z))) | (~r(s(s(s(s(z)))), s(z))) | (~r(s(s(s(s(z)))), z)))),
% 3.03/3.23 inference(quant_inst,[status(thm)],[])).
% 3.03/3.23 tff(12730,plain,
% 3.03/3.23 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, s(z))) | (~r(s(z), s(s(z)))) | (~r(s(s(s(s(z)))), z)) | (~r(s(s(s(s(z)))), s(z)))),
% 3.03/3.23 inference(modus_ponens,[status(thm)],[12729, 12728])).
% 3.03/3.23 tff(12731,plain,
% 3.03/3.23 (~r(s(s(s(s(z)))), z)),
% 3.03/3.23 inference(unit_resolution,[status(thm)],[12730, 197, 120, 323, 7222])).
% 3.03/3.23 tff(12732,plain,
% 3.03/3.23 (b(s(s(s(s(z)))), z)),
% 3.03/3.23 inference(unit_resolution,[status(thm)],[3266, 12731])).
% 3.03/3.23 tff(12733,plain,
% 3.03/3.23 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), z)) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(s(z)))), z)) | (~b(z, s(s(s(s(z)))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(z))), z)) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(s(z)))), z)) | (~b(z, s(s(s(s(z)))))))),
% 3.03/3.23 inference(rewrite,[status(thm)],[])).
% 3.03/3.23 tff(12734,plain,
% 3.03/3.23 (((~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(z, s(s(s(s(z)))))) | (~b(s(s(s(z))), z)) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(s(z)))), s(s(s(z)))))) <=> ((~b(s(s(s(z))), z)) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(s(z)))), z)) | (~b(z, s(s(s(s(z)))))))),
% 3.03/3.23 inference(rewrite,[status(thm)],[])).
% 3.03/3.23 tff(12735,plain,
% 3.03/3.23 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(z, s(s(s(s(z)))))) | (~b(s(s(s(z))), z)) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(s(z)))), s(s(s(z))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), z)) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(s(z)))), z)) | (~b(z, s(s(s(s(z))))))))),
% 3.03/3.23 inference(monotonicity,[status(thm)],[12734])).
% 3.03/3.23 tff(12736,plain,
% 3.03/3.23 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(z, s(s(s(s(z)))))) | (~b(s(s(s(z))), z)) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(s(z)))), s(s(s(z))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(z))), z)) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(s(z)))), z)) | (~b(z, s(s(s(s(z)))))))),
% 3.03/3.23 inference(transitivity,[status(thm)],[12735, 12733])).
% 3.03/3.23 tff(12737,plain,
% 3.03/3.23 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(z, s(s(s(s(z)))))) | (~b(s(s(s(z))), z)) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(s(z)))), s(s(s(z))))))),
% 3.03/3.23 inference(quant_inst,[status(thm)],[])).
% 3.03/3.23 tff(12738,plain,
% 3.03/3.23 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(z))), z)) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(s(z)))), z)) | (~b(z, s(s(s(s(z))))))),
% 3.03/3.23 inference(modus_ponens,[status(thm)],[12737, 12736])).
% 3.03/3.23 tff(12739,plain,
% 3.03/3.23 ($false),
% 3.03/3.23 inference(unit_resolution,[status(thm)],[12738, 166, 1699, 4732, 12732, 12724])).
% 3.03/3.23 tff(12740,plain,((~r(s(s(s(s(z)))), s(z))) | (~b(s(s(s(z))), z)) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~r(s(z), s(s(z)))) | (~r(z, s(z)))), inference(lemma,lemma(discharge,[]))).
% 3.03/3.23 tff(12741,plain,
% 3.03/3.23 (~b(s(s(s(s(z)))), s(s(s(z))))),
% 3.03/3.23 inference(unit_resolution,[status(thm)],[12740, 12708, 12659, 12657, 12655])).
% 3.03/3.23 tff(12742,plain,
% 3.03/3.23 (r(s(s(s(s(z)))), s(s(s(z))))),
% 3.03/3.23 inference(unit_resolution,[status(thm)],[4662, 12741])).
% 3.03/3.23 tff(12743,plain,
% 3.03/3.23 (r(s(s(s(s(elem!1)))), s(s(s(elem!1))))),
% 3.03/3.23 inference(modus_ponens,[status(thm)],[12742, 12646])).
% 3.03/3.23 tff(12744,plain,
% 3.03/3.23 (r(s(s(elem!1)), s(s(s(s(elem!1)))))),
% 3.03/3.23 inference(unit_resolution,[status(thm)],[3081, 12706, 85, 12659, 12686, 12641])).
% 3.03/3.23 tff(12745,plain,
% 3.03/3.23 ($false),
% 3.03/3.23 inference(unit_resolution,[status(thm)],[9172, 197, 12639, 12696, 12744, 12743])).
% 3.03/3.23 tff(12746,plain,((~b(s(s(z)), s(z))) | (~b(s(z), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(s(s(elem!1))), z)) | b(s(z), s(s(elem!1))) | (~r(s(z), z)) | (~r(z, s(s(s(elem!1)))))), inference(lemma,lemma(discharge,[]))).
% 3.03/3.23 tff(12747,plain,
% 3.03/3.23 (~b(s(s(z)), s(z))),
% 3.03/3.23 inference(unit_resolution,[status(thm)],[12746, 282, 96, 121, 54, 97, 241])).
% 3.03/3.23 tff(12748,plain,
% 3.03/3.23 (r(s(s(z)), s(z))),
% 3.03/3.23 inference(unit_resolution,[status(thm)],[308, 12747])).
% 3.03/3.23 tff(12749,plain,
% 3.03/3.23 (b(s(s(elem!1)), s(z))),
% 3.03/3.23 inference(unit_resolution,[status(thm)],[11987, 12748, 97])).
% 3.03/3.23 tff(12750,plain,
% 3.03/3.23 (~(s(s(z)) = s(s(elem!1)))),
% 3.03/3.23 inference(unit_resolution,[status(thm)],[3938, 12749, 12747])).
% 3.03/3.23 tff(12751,plain,
% 3.03/3.23 (b(s(s(s(elem!1))), s(s(elem!1)))),
% 3.03/3.23 inference(unit_resolution,[status(thm)],[12365, 12750, 12340, 282, 85, 12748, 12638])).
% 3.03/3.23 tff(12752,plain,
% 3.03/3.23 (((~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(z), s(s(s(elem!1))))) | (~b(s(s(elem!1)), s(z))) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(s(s(elem!1))), s(s(elem!1))))) <=> ((~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(z), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(s(elem!1)), s(z))))),
% 3.03/3.23 inference(rewrite,[status(thm)],[])).
% 3.03/3.23 tff(12753,plain,
% 3.03/3.23 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(z), s(s(s(elem!1))))) | (~b(s(s(elem!1)), s(z))) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(s(s(elem!1))), s(s(elem!1)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(z), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(s(elem!1)), s(z)))))),
% 3.03/3.23 inference(monotonicity,[status(thm)],[12752])).
% 3.03/3.23 tff(12754,plain,
% 3.03/3.23 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(z), s(s(s(elem!1))))) | (~b(s(s(elem!1)), s(z))) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(s(s(elem!1))), s(s(elem!1)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(z), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(s(elem!1)), s(z))))),
% 3.03/3.23 inference(transitivity,[status(thm)],[12753, 12341])).
% 3.03/3.23 tff(12755,plain,
% 3.03/3.23 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(z), s(s(s(elem!1))))) | (~b(s(s(elem!1)), s(z))) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(s(s(elem!1))), s(s(elem!1)))))),
% 3.03/3.23 inference(quant_inst,[status(thm)],[])).
% 3.03/3.23 tff(12756,plain,
% 3.03/3.23 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(z), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(s(elem!1)), s(z)))),
% 3.03/3.23 inference(modus_ponens,[status(thm)],[12755, 12754])).
% 3.03/3.23 tff(12757,plain,
% 3.03/3.23 ($false),
% 3.03/3.23 inference(unit_resolution,[status(thm)],[12756, 166, 12751, 241, 96, 12749])).
% 3.03/3.23 tff(12758,plain,((~r(z, s(s(s(elem!1))))) | (~b(s(z), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(z))) | (~r(s(z), z)) | (~b(s(s(s(elem!1))), z)) | b(s(z), s(s(elem!1)))), inference(lemma,lemma(discharge,[]))).
% 3.03/3.23 tff(12759,plain,
% 3.03/3.23 (~r(z, s(s(s(elem!1))))),
% 3.03/3.23 inference(unit_resolution,[status(thm)],[12758, 12326, 96, 97, 95, 54])).
% 3.03/3.23 tff(12760,plain,
% 3.03/3.23 (b(z, s(s(s(elem!1))))),
% 3.03/3.23 inference(unit_resolution,[status(thm)],[261, 12759])).
% 3.03/3.23 tff(12761,plain,
% 3.03/3.23 (~b(z, s(z))),
% 3.03/3.23 inference(unit_resolution,[status(thm)],[249, 12760, 96, 12326])).
% 3.03/3.23 tff(12762,plain,
% 3.03/3.23 (r(z, s(z))),
% 3.03/3.23 inference(unit_resolution,[status(thm)],[321, 12761])).
% 3.03/3.23 tff(12763,plain,
% 3.03/3.23 (~(s(s(s(elem!1))) = s(s(elem!1)))),
% 3.03/3.23 inference(unit_resolution,[status(thm)],[50, 12330])).
% 3.03/3.23 tff(12764,plain,
% 3.03/3.23 (~b(s(s(elem!1)), s(s(s(elem!1))))),
% 3.03/3.23 inference(unit_resolution,[status(thm)],[12637, 97, 85, 95, 96, 12326])).
% 3.03/3.23 tff(12765,plain,
% 3.03/3.23 (b(z, s(s(elem!1)))),
% 3.03/3.23 inference(unit_resolution,[status(thm)],[12685, 12326, 96, 95, 12764, 54])).
% 3.03/3.23 tff(12766,plain,
% 3.03/3.23 (r(s(s(elem!1)), s(s(s(elem!1))))),
% 3.03/3.23 inference(unit_resolution,[status(thm)],[461, 12764, 12330])).
% 3.03/3.23 tff(12767,plain,
% 3.03/3.23 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(s(elem!1)))) | (~r(z, s(z))) | (~r(s(s(z)), s(z))) | (~r(s(s(z)), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(z), s(s(elem!1)))) | (~r(z, s(z))) | (~r(s(s(z)), s(z))) | (~r(s(s(z)), z)))),
% 3.03/3.23 inference(rewrite,[status(thm)],[])).
% 3.03/3.23 tff(12768,plain,
% 3.03/3.23 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(s(elem!1)))) | (~r(z, s(z))) | (~r(s(s(z)), s(z))) | (~r(s(s(z)), z)))),
% 3.03/3.23 inference(quant_inst,[status(thm)],[])).
% 3.03/3.23 tff(12769,plain,
% 3.03/3.23 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(z), s(s(elem!1)))) | (~r(z, s(z))) | (~r(s(s(z)), s(z))) | (~r(s(s(z)), z))),
% 3.03/3.23 inference(modus_ponens,[status(thm)],[12768, 12767])).
% 3.03/3.23 tff(12770,plain,
% 3.03/3.23 (~r(s(s(z)), z)),
% 3.03/3.23 inference(unit_resolution,[status(thm)],[12769, 197, 311, 323, 4143])).
% 3.03/3.23 tff(12771,plain,
% 3.03/3.23 (b(s(s(z)), z)),
% 3.03/3.23 inference(unit_resolution,[status(thm)],[186, 12770])).
% 3.03/3.23 tff(12772,plain,
% 3.03/3.23 (~b(s(s(s(elem!1))), s(s(z)))),
% 3.03/3.23 inference(unit_resolution,[status(thm)],[10460, 12771, 121])).
% 3.03/3.23 tff(12773,plain,
% 3.03/3.23 (r(s(s(s(elem!1))), s(s(z)))),
% 3.03/3.23 inference(unit_resolution,[status(thm)],[218, 12772])).
% 3.03/3.23 tff(12774,plain,
% 3.03/3.23 (b(s(s(elem!1)), s(z))),
% 3.03/3.23 inference(unit_resolution,[status(thm)],[11987, 4143, 97])).
% 3.03/3.23 tff(12775,plain,
% 3.03/3.23 (~b(s(s(s(elem!1))), s(s(elem!1)))),
% 3.03/3.23 inference(unit_resolution,[status(thm)],[12346, 166, 241, 96, 12774])).
% 3.03/3.23 tff(12776,plain,
% 3.03/3.23 (r(s(s(s(elem!1))), s(s(elem!1)))),
% 3.03/3.23 inference(unit_resolution,[status(thm)],[889, 12775, 1863])).
% 3.03/3.23 tff(12777,plain,
% 3.03/3.23 (~(s(s(z)) = s(s(elem!1)))),
% 3.03/3.23 inference(unit_resolution,[status(thm)],[3938, 12774, 3936])).
% 3.03/3.23 tff(12778,plain,
% 3.03/3.23 (~(s(s(elem!1)) = s(s(z)))),
% 3.03/3.23 inference(unit_resolution,[status(thm)],[131, 12777])).
% 3.03/3.23 tff(12779,plain,
% 3.03/3.23 (~r(s(s(elem!1)), s(s(z)))),
% 3.03/3.23 inference(unit_resolution,[status(thm)],[4313, 12773, 4143, 12776])).
% 3.03/3.23 tff(12780,plain,
% 3.03/3.23 (b(s(s(elem!1)), s(s(z)))),
% 3.03/3.23 inference(unit_resolution,[status(thm)],[441, 12779, 12778])).
% 3.03/3.23 tff(12781,plain,
% 3.03/3.23 (~b(s(s(z)), s(s(elem!1)))),
% 3.03/3.23 inference(unit_resolution,[status(thm)],[12611, 12780, 1820])).
% 3.03/3.23 tff(12782,plain,
% 3.03/3.23 (r(s(s(z)), s(s(elem!1)))),
% 3.03/3.23 inference(unit_resolution,[status(thm)],[390, 12781, 12777])).
% 3.03/3.23 tff(12783,plain,
% 3.03/3.23 ($false),
% 3.03/3.23 inference(unit_resolution,[status(thm)],[12620, 197, 377, 12782, 12776, 12773])).
% 3.03/3.23 tff(12784,plain,(b(s(s(z)), s(z)) | (~r(s(s(elem!1)), s(s(s(elem!1))))) | (~b(z, s(s(elem!1)))) | (~b(s(s(s(elem!1))), z)) | (s(s(s(elem!1))) = s(s(elem!1))) | (~b(s(z), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(z))) | (~r(s(z), s(s(elem!1)))) | (~r(z, s(z))) | (~r(s(z), z))), inference(lemma,lemma(discharge,[]))).
% 3.03/3.23 tff(12785,plain,
% 3.03/3.23 (b(s(s(z)), s(z))),
% 3.03/3.23 inference(unit_resolution,[status(thm)],[12784, 12766, 12765, 95, 12763, 12326, 96, 85, 12762, 97])).
% 3.03/3.23 tff(12786,plain,
% 3.03/3.23 (~b(s(s(s(elem!1))), s(s(z)))),
% 3.03/3.23 inference(unit_resolution,[status(thm)],[9072, 166, 12326, 96, 12785])).
% 3.03/3.23 tff(12787,plain,
% 3.03/3.23 (r(s(s(s(elem!1))), s(s(z)))),
% 3.03/3.23 inference(unit_resolution,[status(thm)],[218, 12786])).
% 3.03/3.23 tff(12788,plain,
% 3.03/3.23 (~b(s(s(z)), s(s(s(elem!1))))),
% 3.03/3.23 inference(unit_resolution,[status(thm)],[12622, 12326, 96, 95, 97, 54])).
% 3.03/3.23 tff(12789,plain,
% 3.03/3.23 (r(s(s(z)), s(s(s(elem!1))))),
% 3.03/3.23 inference(unit_resolution,[status(thm)],[279, 12788])).
% 3.03/3.23 tff(12790,plain,
% 3.03/3.23 (~r(s(s(z)), s(s(elem!1)))),
% 3.03/3.23 inference(unit_resolution,[status(thm)],[9490, 197, 12766, 12789, 12787])).
% 3.03/3.23 tff(12791,plain,
% 3.03/3.23 (b(s(s(elem!1)), s(z))),
% 3.03/3.23 inference(unit_resolution,[status(thm)],[11731, 12790, 97])).
% 3.03/3.23 tff(12792,plain,
% 3.03/3.23 (~b(s(s(z)), s(s(elem!1)))),
% 3.03/3.23 inference(unit_resolution,[status(thm)],[2929, 12791, 12326, 12785, 96])).
% 3.03/3.23 tff(12793,plain,
% 3.03/3.23 (s(s(z)) = s(s(elem!1))),
% 3.03/3.23 inference(unit_resolution,[status(thm)],[390, 12792, 12790])).
% 3.03/3.23 tff(12794,plain,
% 3.03/3.23 (s(elem!1) = s(z)),
% 3.03/3.23 inference(unit_resolution,[status(thm)],[43, 12793])).
% 3.03/3.23 tff(12795,plain,
% 3.03/3.23 (z = elem!1),
% 3.03/3.23 inference(unit_resolution,[status(thm)],[30, 12794])).
% 3.03/3.23 tff(12796,plain,
% 3.03/3.23 (b(z, s(s(s(elem!1)))) <=> b(elem!1, s(s(s(elem!1))))),
% 3.03/3.23 inference(monotonicity,[status(thm)],[12795])).
% 3.03/3.23 tff(12797,plain,
% 3.03/3.23 (b(elem!1, s(s(s(elem!1))))),
% 3.03/3.23 inference(modus_ponens,[status(thm)],[12760, 12796])).
% 3.03/3.23 tff(12798,plain,
% 3.03/3.23 (b(s(s(s(elem!1))), elem!1)),
% 3.03/3.23 inference(unit_resolution,[status(thm)],[634, 12795, 95])).
% 3.03/3.23 tff(12799,plain,
% 3.03/3.23 ((s(s(s(s(elem!1)))) = z) <=> (s(s(s(s(elem!1)))) = elem!1)),
% 3.03/3.23 inference(monotonicity,[status(thm)],[12795])).
% 3.03/3.23 tff(12800,plain,
% 3.03/3.23 ((s(s(s(s(elem!1)))) = z) <=> (elem!1 = s(s(s(s(elem!1)))))),
% 3.03/3.23 inference(transitivity,[status(thm)],[12799, 2287])).
% 3.03/3.23 tff(12801,plain,
% 3.03/3.23 ((~(s(s(s(s(elem!1)))) = z)) <=> (~(elem!1 = s(s(s(s(elem!1))))))),
% 3.03/3.23 inference(monotonicity,[status(thm)],[12800])).
% 3.03/3.23 tff(12802,plain,
% 3.03/3.23 (~(elem!1 = s(s(s(s(elem!1)))))),
% 3.03/3.23 inference(modus_ponens,[status(thm)],[626, 12801])).
% 3.03/3.23 tff(12803,plain,
% 3.03/3.23 (r(s(s(s(elem!1))), s(s(z))) <=> r(s(s(s(elem!1))), s(s(elem!1)))),
% 3.03/3.23 inference(monotonicity,[status(thm)],[12793])).
% 3.03/3.23 tff(12804,plain,
% 3.03/3.23 (r(s(s(s(elem!1))), s(s(elem!1)))),
% 3.03/3.23 inference(modus_ponens,[status(thm)],[12787, 12803])).
% 3.03/3.23 tff(12805,plain,
% 3.03/3.23 ((s(s(s(s(elem!1)))) = s(s(z))) <=> (s(s(s(s(elem!1)))) = s(s(elem!1)))),
% 3.03/3.23 inference(monotonicity,[status(thm)],[12793])).
% 3.03/3.23 tff(12806,plain,
% 3.03/3.23 ((s(s(s(s(elem!1)))) = s(s(z))) <=> (s(s(elem!1)) = s(s(s(s(elem!1)))))),
% 3.03/3.23 inference(transitivity,[status(thm)],[12805, 123])).
% 3.03/3.23 tff(12807,plain,
% 3.03/3.23 ((s(s(s(s(elem!1)))) = s(s(z))) <=> (s(s(s(s(elem!1)))) = s(s(elem!1)))),
% 3.03/3.23 inference(transitivity,[status(thm)],[12806, 124])).
% 3.03/3.23 tff(12808,plain,
% 3.03/3.23 ((~(s(s(s(s(elem!1)))) = s(s(z)))) <=> (~(s(s(s(s(elem!1)))) = s(s(elem!1))))),
% 3.03/3.23 inference(monotonicity,[status(thm)],[12807])).
% 3.03/3.23 tff(12809,plain,
% 3.03/3.23 (~(s(s(s(s(elem!1)))) = s(s(elem!1)))),
% 3.03/3.23 inference(modus_ponens,[status(thm)],[733, 12808])).
% 3.03/3.23 tff(12810,plain,
% 3.03/3.23 (~b(s(s(s(s(elem!1)))), s(z))),
% 3.03/3.23 inference(unit_resolution,[status(thm)],[12705, 12809, 12766, 12804, 12332, 12326, 96, 12791])).
% 3.03/3.23 tff(12811,plain,
% 3.03/3.23 (r(s(s(s(s(elem!1)))), s(z))),
% 3.03/3.23 inference(unit_resolution,[status(thm)],[661, 12810])).
% 3.03/3.23 tff(12812,plain,
% 3.03/3.23 (r(elem!1, s(z))),
% 3.03/3.23 inference(unit_resolution,[status(thm)],[741, 12795, 12762])).
% 3.03/3.23 tff(12813,plain,
% 3.03/3.23 (~r(elem!1, s(s(s(s(elem!1)))))),
% 3.03/3.23 inference(unit_resolution,[status(thm)],[2470, 197, 85, 12812, 12811])).
% 3.03/3.23 tff(12814,plain,
% 3.03/3.23 (b(elem!1, s(s(s(s(elem!1)))))),
% 3.03/3.23 inference(unit_resolution,[status(thm)],[2427, 12813, 12802])).
% 3.03/3.23 tff(12815,plain,
% 3.03/3.23 (~b(s(s(s(s(elem!1)))), s(s(s(elem!1))))),
% 3.03/3.23 inference(unit_resolution,[status(thm)],[2912, 12814, 12798, 12797])).
% 3.03/3.23 tff(12816,plain,
% 3.03/3.23 (r(s(s(s(s(elem!1)))), s(s(s(elem!1))))),
% 3.03/3.23 inference(unit_resolution,[status(thm)],[1065, 12815, 12332])).
% 3.03/3.23 tff(12817,plain,
% 3.03/3.23 (r(s(s(elem!1)), s(s(s(s(elem!1)))))),
% 3.03/3.23 inference(unit_resolution,[status(thm)],[3081, 12810, 85, 12762, 12765, 12791])).
% 3.03/3.23 tff(12818,plain,
% 3.03/3.23 ($false),
% 3.03/3.23 inference(unit_resolution,[status(thm)],[9172, 197, 12766, 12804, 12817, 12816])).
% 3.03/3.23 tff(12819,plain,((~r(s(z), z)) | (~b(s(s(s(elem!1))), s(z))) | b(s(z), s(s(elem!1))) | r(s(s(s(elem!1))), z)), inference(lemma,lemma(discharge,[]))).
% 3.03/3.23 tff(12820,plain,
% 3.03/3.23 (~r(s(z), z)),
% 3.03/3.23 inference(unit_resolution,[status(thm)],[12819, 96, 54, 86])).
% 3.03/3.24 tff(12821,plain,
% 3.03/3.24 (b(s(z), z)),
% 3.03/3.24 inference(unit_resolution,[status(thm)],[230, 12820])).
% 3.03/3.24 tff(12822,plain,
% 3.03/3.24 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(z)))) | (~b(s(z), z)) | (~b(s(s(s(elem!1))), z)) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(s(z)), s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(s(z)))) | (~b(s(z), z)) | (~b(s(s(s(elem!1))), z)) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(s(z)), s(z))))),
% 3.03/3.24 inference(rewrite,[status(thm)],[])).
% 3.03/3.24 tff(12823,plain,
% 3.03/3.24 (((~b(s(s(z)), s(z))) | (~b(s(s(s(elem!1))), s(z))) | (~b(z, s(s(z)))) | (~b(s(z), z)) | (~b(s(s(s(elem!1))), z)) | (~b(s(s(s(elem!1))), s(z)))) <=> ((~b(z, s(s(z)))) | (~b(s(z), z)) | (~b(s(s(s(elem!1))), z)) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(s(z)), s(z))))),
% 3.03/3.24 inference(rewrite,[status(thm)],[])).
% 3.03/3.24 tff(12824,plain,
% 3.03/3.24 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), s(z))) | (~b(s(s(s(elem!1))), s(z))) | (~b(z, s(s(z)))) | (~b(s(z), z)) | (~b(s(s(s(elem!1))), z)) | (~b(s(s(s(elem!1))), s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(z)))) | (~b(s(z), z)) | (~b(s(s(s(elem!1))), z)) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(s(z)), s(z)))))),
% 3.03/3.24 inference(monotonicity,[status(thm)],[12823])).
% 3.03/3.24 tff(12825,plain,
% 3.03/3.24 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), s(z))) | (~b(s(s(s(elem!1))), s(z))) | (~b(z, s(s(z)))) | (~b(s(z), z)) | (~b(s(s(s(elem!1))), z)) | (~b(s(s(s(elem!1))), s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(s(z)))) | (~b(s(z), z)) | (~b(s(s(s(elem!1))), z)) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(s(z)), s(z))))),
% 3.03/3.24 inference(transitivity,[status(thm)],[12824, 12822])).
% 3.03/3.24 tff(12826,plain,
% 3.03/3.24 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), s(z))) | (~b(s(s(s(elem!1))), s(z))) | (~b(z, s(s(z)))) | (~b(s(z), z)) | (~b(s(s(s(elem!1))), z)) | (~b(s(s(s(elem!1))), s(z))))),
% 3.03/3.24 inference(quant_inst,[status(thm)],[])).
% 3.03/3.24 tff(12827,plain,
% 3.03/3.24 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(s(z)))) | (~b(s(z), z)) | (~b(s(s(s(elem!1))), z)) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(s(z)), s(z)))),
% 3.03/3.24 inference(modus_ponens,[status(thm)],[12826, 12825])).
% 3.03/3.24 tff(12828,plain,
% 3.03/3.24 ($false),
% 3.03/3.24 inference(unit_resolution,[status(thm)],[12827, 166, 53, 10451, 96, 121, 156])).
% 3.03/3.24 tff(12829,plain,((~b(z, s(s(z)))) | (~b(s(z), z)) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(s(s(elem!1))), z)) | (~b(s(s(z)), s(z)))), inference(lemma,lemma(discharge,[]))).
% 3.03/3.24 tff(12830,plain,
% 3.03/3.24 ((~b(s(z), z)) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(s(s(elem!1))), z)) | (~b(s(s(z)), s(z)))),
% 3.03/3.24 inference(unit_resolution,[status(thm)],[12829, 10450])).
% 3.03/3.24 tff(12831,plain,
% 3.03/3.24 (~b(s(s(z)), s(z))),
% 3.03/3.24 inference(unit_resolution,[status(thm)],[12830, 12821, 96, 95])).
% 3.03/3.24 tff(12832,plain,
% 3.03/3.24 (r(s(s(z)), s(z))),
% 3.03/3.24 inference(unit_resolution,[status(thm)],[308, 12831])).
% 3.03/3.24 tff(12833,plain,
% 3.03/3.24 ($false),
% 3.03/3.24 inference(unit_resolution,[status(thm)],[3997, 166, 53, 96, 118, 121])).
% 3.03/3.24 tff(12834,plain,((~b(z, s(z))) | (~b(s(z), z)) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(s(s(elem!1))), z))), inference(lemma,lemma(discharge,[]))).
% 3.03/3.24 tff(12835,plain,
% 3.03/3.24 (~b(z, s(z))),
% 3.03/3.24 inference(unit_resolution,[status(thm)],[12834, 12821, 96, 95])).
% 3.03/3.24 tff(12836,plain,
% 3.03/3.24 (r(z, s(z))),
% 3.03/3.24 inference(unit_resolution,[status(thm)],[321, 12835])).
% 3.03/3.24 tff(12837,plain,
% 3.03/3.24 (~r(s(s(z)), z)),
% 3.03/3.24 inference(unit_resolution,[status(thm)],[12769, 197, 85, 12836, 12832])).
% 3.03/3.24 tff(12838,plain,
% 3.03/3.24 (b(s(s(z)), z)),
% 3.03/3.24 inference(unit_resolution,[status(thm)],[186, 12837])).
% 3.03/3.24 tff(12839,plain,
% 3.03/3.24 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(z)))) | (~b(s(z), z)) | (~b(s(z), s(s(z)))) | (~b(s(s(z)), z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(s(z)))) | (~b(s(z), z)) | (~b(s(z), s(s(z)))) | (~b(s(s(z)), z)))),
% 3.03/3.24 inference(rewrite,[status(thm)],[])).
% 3.03/3.24 tff(12840,plain,
% 3.03/3.24 (((~b(s(s(z)), z)) | (~b(s(z), z)) | (~b(z, s(s(z)))) | (~b(s(s(z)), z)) | (~b(s(z), z)) | (~b(s(z), s(s(z))))) <=> ((~b(z, s(s(z)))) | (~b(s(z), z)) | (~b(s(z), s(s(z)))) | (~b(s(s(z)), z)))),
% 3.03/3.24 inference(rewrite,[status(thm)],[])).
% 3.03/3.24 tff(12841,plain,
% 3.03/3.24 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), z)) | (~b(s(z), z)) | (~b(z, s(s(z)))) | (~b(s(s(z)), z)) | (~b(s(z), z)) | (~b(s(z), s(s(z)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(z)))) | (~b(s(z), z)) | (~b(s(z), s(s(z)))) | (~b(s(s(z)), z))))),
% 3.03/3.24 inference(monotonicity,[status(thm)],[12840])).
% 3.03/3.24 tff(12842,plain,
% 3.03/3.24 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), z)) | (~b(s(z), z)) | (~b(z, s(s(z)))) | (~b(s(s(z)), z)) | (~b(s(z), z)) | (~b(s(z), s(s(z)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(s(z)))) | (~b(s(z), z)) | (~b(s(z), s(s(z)))) | (~b(s(s(z)), z)))),
% 3.03/3.24 inference(transitivity,[status(thm)],[12841, 12839])).
% 3.03/3.24 tff(12843,plain,
% 3.03/3.24 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), z)) | (~b(s(z), z)) | (~b(z, s(s(z)))) | (~b(s(s(z)), z)) | (~b(s(z), z)) | (~b(s(z), s(s(z)))))),
% 3.03/3.24 inference(quant_inst,[status(thm)],[])).
% 3.03/3.24 tff(12844,plain,
% 3.03/3.24 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(s(z)))) | (~b(s(z), z)) | (~b(s(z), s(s(z)))) | (~b(s(s(z)), z))),
% 3.03/3.24 inference(modus_ponens,[status(thm)],[12843, 12842])).
% 3.03/3.24 tff(12845,plain,
% 3.03/3.24 ($false),
% 3.03/3.24 inference(unit_resolution,[status(thm)],[12844, 166, 53, 556, 10451, 122])).
% 3.03/3.24 tff(12846,plain,((~b(s(s(z)), z)) | (~b(s(z), z)) | (~b(s(z), s(s(z)))) | (~b(z, s(s(z))))), inference(lemma,lemma(discharge,[]))).
% 3.03/3.24 tff(12847,plain,
% 3.03/3.24 ((~b(s(s(z)), z)) | (~b(s(z), z)) | (~b(s(z), s(s(z))))),
% 3.03/3.24 inference(unit_resolution,[status(thm)],[12846, 10450])).
% 3.03/3.24 tff(12848,plain,
% 3.03/3.24 (~b(s(z), s(s(z)))),
% 3.03/3.24 inference(unit_resolution,[status(thm)],[12847, 12838, 12821])).
% 3.03/3.24 tff(12849,plain,
% 3.03/3.24 (r(s(z), s(s(z)))),
% 3.03/3.24 inference(unit_resolution,[status(thm)],[427, 12848])).
% 3.03/3.24 tff(12850,plain,
% 3.03/3.24 (~r(s(z), s(s(s(elem!1))))),
% 3.03/3.24 inference(unit_resolution,[status(thm)],[10477, 12849, 12838, 95])).
% 3.03/3.24 tff(12851,plain,
% 3.03/3.24 (b(s(z), s(s(s(elem!1))))),
% 3.03/3.24 inference(unit_resolution,[status(thm)],[116, 12850])).
% 3.03/3.24 tff(12852,plain,
% 3.03/3.24 ($false),
% 3.03/3.24 inference(unit_resolution,[status(thm)],[12445, 166, 12851, 12821, 10450, 95, 12838])).
% 3.03/3.24 tff(12853,plain,((~b(s(s(s(elem!1))), s(z))) | b(s(z), s(s(elem!1))) | r(s(s(s(elem!1))), z)), inference(lemma,lemma(discharge,[]))).
% 3.03/3.24 tff(12854,plain,
% 3.03/3.24 (~b(s(s(s(elem!1))), s(z))),
% 3.03/3.24 inference(unit_resolution,[status(thm)],[12853, 86, 54])).
% 3.03/3.24 tff(12855,plain,
% 3.03/3.24 (~r(s(s(elem!1)), s(s(s(elem!1))))),
% 3.03/3.24 inference(unit_resolution,[status(thm)],[764, 117, 85, 3953])).
% 3.03/3.24 tff(12856,plain,
% 3.03/3.24 (~r(s(s(z)), s(s(s(elem!1))))),
% 3.03/3.24 inference(unit_resolution,[status(thm)],[3958, 392, 311, 350])).
% 3.03/3.24 tff(12857,plain,
% 3.03/3.24 (b(s(s(z)), s(s(s(elem!1))))),
% 3.03/3.24 inference(unit_resolution,[status(thm)],[279, 12856])).
% 3.03/3.24 tff(12858,plain,
% 3.03/3.24 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(z)))) | (~b(s(s(s(elem!1))), s(s(z)))) | (~b(s(s(s(elem!1))), z)) | (~b(s(s(z)), s(s(s(elem!1))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(s(z)))) | (~b(s(s(s(elem!1))), s(s(z)))) | (~b(s(s(s(elem!1))), z)) | (~b(s(s(z)), s(s(s(elem!1))))))),
% 3.03/3.24 inference(rewrite,[status(thm)],[])).
% 3.03/3.24 tff(12859,plain,
% 3.03/3.24 (((~b(s(s(s(elem!1))), z)) | (~b(s(s(s(elem!1))), z)) | (~b(s(s(z)), s(s(s(elem!1))))) | (~b(z, s(s(z)))) | (~b(s(s(s(elem!1))), s(s(z)))) | (~b(s(s(s(elem!1))), z))) <=> ((~b(z, s(s(z)))) | (~b(s(s(s(elem!1))), s(s(z)))) | (~b(s(s(s(elem!1))), z)) | (~b(s(s(z)), s(s(s(elem!1))))))),
% 3.03/3.24 inference(rewrite,[status(thm)],[])).
% 3.03/3.24 tff(12860,plain,
% 3.03/3.24 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), z)) | (~b(s(s(s(elem!1))), z)) | (~b(s(s(z)), s(s(s(elem!1))))) | (~b(z, s(s(z)))) | (~b(s(s(s(elem!1))), s(s(z)))) | (~b(s(s(s(elem!1))), z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(z)))) | (~b(s(s(s(elem!1))), s(s(z)))) | (~b(s(s(s(elem!1))), z)) | (~b(s(s(z)), s(s(s(elem!1)))))))),
% 3.03/3.24 inference(monotonicity,[status(thm)],[12859])).
% 3.03/3.24 tff(12861,plain,
% 3.03/3.24 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), z)) | (~b(s(s(s(elem!1))), z)) | (~b(s(s(z)), s(s(s(elem!1))))) | (~b(z, s(s(z)))) | (~b(s(s(s(elem!1))), s(s(z)))) | (~b(s(s(s(elem!1))), z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(s(z)))) | (~b(s(s(s(elem!1))), s(s(z)))) | (~b(s(s(s(elem!1))), z)) | (~b(s(s(z)), s(s(s(elem!1))))))),
% 3.03/3.24 inference(transitivity,[status(thm)],[12860, 12858])).
% 3.03/3.24 tff(12862,plain,
% 3.03/3.24 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), z)) | (~b(s(s(s(elem!1))), z)) | (~b(s(s(z)), s(s(s(elem!1))))) | (~b(z, s(s(z)))) | (~b(s(s(s(elem!1))), s(s(z)))) | (~b(s(s(s(elem!1))), z)))),
% 3.03/3.24 inference(quant_inst,[status(thm)],[])).
% 3.03/3.24 tff(12863,plain,
% 3.03/3.24 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(s(z)))) | (~b(s(s(s(elem!1))), s(s(z)))) | (~b(s(s(s(elem!1))), z)) | (~b(s(s(z)), s(s(s(elem!1)))))),
% 3.03/3.24 inference(modus_ponens,[status(thm)],[12862, 12861])).
% 3.03/3.24 tff(12864,plain,
% 3.03/3.24 ($false),
% 3.03/3.24 inference(unit_resolution,[status(thm)],[12863, 166, 10450, 121, 12857, 8195])).
% 3.03/3.24 tff(12865,plain,((~r(s(s(z)), s(z))) | (~b(s(s(s(elem!1))), z)) | (~r(s(z), s(s(elem!1)))) | (~r(s(s(s(elem!1))), s(z)))), inference(lemma,lemma(discharge,[]))).
% 3.03/3.24 tff(12866,plain,
% 3.03/3.24 (~r(s(s(z)), s(z))),
% 3.03/3.24 inference(unit_resolution,[status(thm)],[12865, 121, 85, 3953])).
% 3.03/3.24 tff(12867,plain,
% 3.03/3.24 (b(s(s(z)), s(z))),
% 3.03/3.24 inference(unit_resolution,[status(thm)],[308, 12866])).
% 3.03/3.24 tff(12868,plain,
% 3.03/3.24 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(z)))) | (~b(s(z), z)) | (~b(s(s(s(elem!1))), s(s(z)))) | (~b(s(s(s(elem!1))), z)) | (~b(s(s(z)), s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(s(z)))) | (~b(s(z), z)) | (~b(s(s(s(elem!1))), s(s(z)))) | (~b(s(s(s(elem!1))), z)) | (~b(s(s(z)), s(z))))),
% 3.03/3.24 inference(rewrite,[status(thm)],[])).
% 3.03/3.24 tff(12869,plain,
% 3.03/3.24 (((~b(s(z), z)) | (~b(s(s(s(elem!1))), z)) | (~b(s(s(z)), s(z))) | (~b(z, s(s(z)))) | (~b(s(s(s(elem!1))), s(s(z)))) | (~b(s(s(s(elem!1))), z))) <=> ((~b(z, s(s(z)))) | (~b(s(z), z)) | (~b(s(s(s(elem!1))), s(s(z)))) | (~b(s(s(s(elem!1))), z)) | (~b(s(s(z)), s(z))))),
% 3.03/3.24 inference(rewrite,[status(thm)],[])).
% 3.03/3.24 tff(12870,plain,
% 3.03/3.24 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), z)) | (~b(s(s(s(elem!1))), z)) | (~b(s(s(z)), s(z))) | (~b(z, s(s(z)))) | (~b(s(s(s(elem!1))), s(s(z)))) | (~b(s(s(s(elem!1))), z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(z)))) | (~b(s(z), z)) | (~b(s(s(s(elem!1))), s(s(z)))) | (~b(s(s(s(elem!1))), z)) | (~b(s(s(z)), s(z)))))),
% 3.03/3.24 inference(monotonicity,[status(thm)],[12869])).
% 3.03/3.24 tff(12871,plain,
% 3.03/3.24 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), z)) | (~b(s(s(s(elem!1))), z)) | (~b(s(s(z)), s(z))) | (~b(z, s(s(z)))) | (~b(s(s(s(elem!1))), s(s(z)))) | (~b(s(s(s(elem!1))), z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(s(z)))) | (~b(s(z), z)) | (~b(s(s(s(elem!1))), s(s(z)))) | (~b(s(s(s(elem!1))), z)) | (~b(s(s(z)), s(z))))),
% 3.03/3.24 inference(transitivity,[status(thm)],[12870, 12868])).
% 3.03/3.24 tff(12872,plain,
% 3.03/3.24 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), z)) | (~b(s(s(s(elem!1))), z)) | (~b(s(s(z)), s(z))) | (~b(z, s(s(z)))) | (~b(s(s(s(elem!1))), s(s(z)))) | (~b(s(s(s(elem!1))), z)))),
% 3.03/3.24 inference(quant_inst,[status(thm)],[])).
% 3.03/3.24 tff(12873,plain,
% 3.03/3.24 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(s(z)))) | (~b(s(z), z)) | (~b(s(s(s(elem!1))), s(s(z)))) | (~b(s(s(s(elem!1))), z)) | (~b(s(s(z)), s(z)))),
% 3.03/3.24 inference(modus_ponens,[status(thm)],[12872, 12871])).
% 3.03/3.24 tff(12874,plain,
% 3.03/3.24 ($false),
% 3.03/3.24 inference(unit_resolution,[status(thm)],[12873, 166, 53, 10451, 121, 156, 2060])).
% 3.03/3.24 tff(12875,plain,((~b(s(z), z)) | (~b(z, s(s(z)))) | (~b(s(s(s(elem!1))), z)) | (~b(s(s(z)), s(z))) | (~b(s(s(s(elem!1))), s(s(z))))), inference(lemma,lemma(discharge,[]))).
% 3.03/3.24 tff(12876,plain,
% 3.03/3.24 ((~b(s(z), z)) | (~b(s(s(s(elem!1))), z)) | (~b(s(s(z)), s(z))) | (~b(s(s(s(elem!1))), s(s(z))))),
% 3.03/3.24 inference(unit_resolution,[status(thm)],[12875, 10450])).
% 3.03/3.24 tff(12877,plain,
% 3.03/3.24 (~b(s(s(s(elem!1))), s(s(z)))),
% 3.03/3.24 inference(unit_resolution,[status(thm)],[12876, 53, 156, 121])).
% 3.03/3.24 tff(12878,plain,
% 3.03/3.24 (r(s(s(s(elem!1))), s(s(z)))),
% 3.03/3.24 inference(unit_resolution,[status(thm)],[218, 12877])).
% 3.03/3.24 tff(12879,plain,
% 3.03/3.24 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(z)))) | (~b(s(z), z)) | (~b(s(s(z)), z)) | (~b(s(s(z)), s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(s(z)))) | (~b(s(z), z)) | (~b(s(s(z)), z)) | (~b(s(s(z)), s(z))))),
% 3.03/3.24 inference(rewrite,[status(thm)],[])).
% 3.03/3.24 tff(12880,plain,
% 3.03/3.24 (((~b(s(s(z)), s(z))) | (~b(s(s(z)), s(z))) | (~b(z, s(s(z)))) | (~b(s(z), z)) | (~b(s(s(z)), z)) | (~b(s(s(z)), s(z)))) <=> ((~b(z, s(s(z)))) | (~b(s(z), z)) | (~b(s(s(z)), z)) | (~b(s(s(z)), s(z))))),
% 3.03/3.24 inference(rewrite,[status(thm)],[])).
% 3.03/3.24 tff(12881,plain,
% 3.03/3.24 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), s(z))) | (~b(s(s(z)), s(z))) | (~b(z, s(s(z)))) | (~b(s(z), z)) | (~b(s(s(z)), z)) | (~b(s(s(z)), s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(z)))) | (~b(s(z), z)) | (~b(s(s(z)), z)) | (~b(s(s(z)), s(z)))))),
% 3.03/3.25 inference(monotonicity,[status(thm)],[12880])).
% 3.03/3.25 tff(12882,plain,
% 3.03/3.25 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), s(z))) | (~b(s(s(z)), s(z))) | (~b(z, s(s(z)))) | (~b(s(z), z)) | (~b(s(s(z)), z)) | (~b(s(s(z)), s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(s(z)))) | (~b(s(z), z)) | (~b(s(s(z)), z)) | (~b(s(s(z)), s(z))))),
% 3.03/3.25 inference(transitivity,[status(thm)],[12881, 12879])).
% 3.03/3.25 tff(12883,plain,
% 3.03/3.25 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), s(z))) | (~b(s(s(z)), s(z))) | (~b(z, s(s(z)))) | (~b(s(z), z)) | (~b(s(s(z)), z)) | (~b(s(s(z)), s(z))))),
% 3.03/3.25 inference(quant_inst,[status(thm)],[])).
% 3.03/3.25 tff(12884,plain,
% 3.03/3.25 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(s(z)))) | (~b(s(z), z)) | (~b(s(s(z)), z)) | (~b(s(s(z)), s(z)))),
% 3.03/3.25 inference(modus_ponens,[status(thm)],[12883, 12882])).
% 3.03/3.25 tff(12885,plain,
% 3.03/3.25 (~b(s(s(z)), z)),
% 3.03/3.25 inference(unit_resolution,[status(thm)],[12884, 166, 53, 10450, 156])).
% 3.03/3.25 tff(12886,plain,
% 3.03/3.25 (r(s(s(z)), z)),
% 3.03/3.25 inference(unit_resolution,[status(thm)],[186, 12885])).
% 3.03/3.25 tff(12887,plain,
% 3.03/3.25 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(z)))) | (~b(s(z), z)) | (~b(s(z), s(s(z)))) | (~b(s(s(z)), s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(s(z)))) | (~b(s(z), z)) | (~b(s(z), s(s(z)))) | (~b(s(s(z)), s(z))))),
% 3.03/3.25 inference(rewrite,[status(thm)],[])).
% 3.03/3.25 tff(12888,plain,
% 3.03/3.25 (((~b(s(z), z)) | (~b(s(z), z)) | (~b(s(s(z)), s(z))) | (~b(z, s(s(z)))) | (~b(s(z), s(s(z)))) | (~b(s(z), z))) <=> ((~b(z, s(s(z)))) | (~b(s(z), z)) | (~b(s(z), s(s(z)))) | (~b(s(s(z)), s(z))))),
% 3.03/3.25 inference(rewrite,[status(thm)],[])).
% 3.03/3.25 tff(12889,plain,
% 3.03/3.25 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), z)) | (~b(s(z), z)) | (~b(s(s(z)), s(z))) | (~b(z, s(s(z)))) | (~b(s(z), s(s(z)))) | (~b(s(z), z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(z)))) | (~b(s(z), z)) | (~b(s(z), s(s(z)))) | (~b(s(s(z)), s(z)))))),
% 3.03/3.25 inference(monotonicity,[status(thm)],[12888])).
% 3.03/3.25 tff(12890,plain,
% 3.03/3.25 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), z)) | (~b(s(z), z)) | (~b(s(s(z)), s(z))) | (~b(z, s(s(z)))) | (~b(s(z), s(s(z)))) | (~b(s(z), z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(s(z)))) | (~b(s(z), z)) | (~b(s(z), s(s(z)))) | (~b(s(s(z)), s(z))))),
% 3.03/3.25 inference(transitivity,[status(thm)],[12889, 12887])).
% 3.03/3.25 tff(12891,plain,
% 3.03/3.25 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), z)) | (~b(s(z), z)) | (~b(s(s(z)), s(z))) | (~b(z, s(s(z)))) | (~b(s(z), s(s(z)))) | (~b(s(z), z)))),
% 3.03/3.25 inference(quant_inst,[status(thm)],[])).
% 3.03/3.25 tff(12892,plain,
% 3.03/3.25 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(s(z)))) | (~b(s(z), z)) | (~b(s(z), s(s(z)))) | (~b(s(s(z)), s(z)))),
% 3.03/3.25 inference(modus_ponens,[status(thm)],[12891, 12890])).
% 3.03/3.25 tff(12893,plain,
% 3.03/3.25 (~b(s(z), s(s(z)))),
% 3.03/3.25 inference(unit_resolution,[status(thm)],[12892, 166, 53, 10450, 156])).
% 3.03/3.25 tff(12894,plain,
% 3.03/3.25 (r(s(z), s(s(z)))),
% 3.03/3.25 inference(unit_resolution,[status(thm)],[427, 12893])).
% 3.03/3.25 tff(12895,plain,
% 3.03/3.25 ($false),
% 3.03/3.25 inference(unit_resolution,[status(thm)],[874, 12894, 12886, 350, 12878])).
% 3.03/3.25 tff(12896,plain,((~b(s(z), z)) | (~r(s(s(s(elem!1))), s(z))) | (~b(s(s(z)), s(z))) | (~b(s(s(s(elem!1))), z))), inference(lemma,lemma(discharge,[]))).
% 3.03/3.25 tff(12897,plain,
% 3.03/3.25 (~b(s(z), z)),
% 3.03/3.25 inference(unit_resolution,[status(thm)],[12896, 3953, 12867, 121])).
% 3.03/3.25 tff(12898,plain,
% 3.03/3.25 (r(s(z), z)),
% 3.03/3.25 inference(unit_resolution,[status(thm)],[230, 12897])).
% 3.03/3.25 tff(12899,plain,
% 3.03/3.25 (~r(z, s(s(s(elem!1))))),
% 3.03/3.25 inference(unit_resolution,[status(thm)],[3872, 117, 3953, 12898])).
% 3.03/3.25 tff(12900,plain,
% 3.03/3.25 (b(z, s(s(s(elem!1))))),
% 3.03/3.25 inference(unit_resolution,[status(thm)],[261, 12899])).
% 3.03/3.25 tff(12901,plain,
% 3.03/3.25 (s(s(elem!1)) = s(s(s(elem!1)))),
% 3.03/3.25 inference(unit_resolution,[status(thm)],[12162, 12900, 121, 85, 12898, 98, 12855])).
% 3.03/3.25 tff(12902,plain,
% 3.03/3.25 (~b(s(s(elem!1)), s(z))),
% 3.03/3.25 inference(unit_resolution,[status(thm)],[3849, 12901, 3846])).
% 3.03/3.25 tff(12903,plain,
% 3.03/3.25 (r(s(s(elem!1)), s(z))),
% 3.03/3.25 inference(unit_resolution,[status(thm)],[1912, 12902])).
% 3.03/3.25 tff(12904,plain,
% 3.03/3.25 (r(s(s(z)), s(s(elem!1)))),
% 3.03/3.25 inference(unit_resolution,[status(thm)],[11731, 12902, 12898])).
% 3.03/3.25 tff(12905,plain,
% 3.03/3.25 (~r(s(z), s(s(z)))),
% 3.03/3.25 inference(unit_resolution,[status(thm)],[6744, 12904, 85, 12903])).
% 3.03/3.25 tff(12906,plain,
% 3.03/3.25 (b(s(z), s(s(z)))),
% 3.03/3.25 inference(unit_resolution,[status(thm)],[427, 12905])).
% 3.03/3.25 tff(12907,plain,
% 3.03/3.25 (r(s(s(z)), s(s(s(elem!1))))),
% 3.03/3.25 inference(unit_resolution,[status(thm)],[338, 12904, 12901])).
% 3.03/3.25 tff(12908,plain,
% 3.03/3.25 (~(s(s(z)) = s(s(elem!1)))),
% 3.03/3.25 inference(unit_resolution,[status(thm)],[4398, 12906, 54])).
% 3.03/3.25 tff(12909,plain,
% 3.03/3.25 (~(s(s(elem!1)) = s(s(z)))),
% 3.03/3.25 inference(unit_resolution,[status(thm)],[131, 12908])).
% 3.03/3.25 tff(12910,plain,
% 3.03/3.25 (~(s(s(s(elem!1))) = s(s(s(z))))),
% 3.03/3.25 inference(unit_resolution,[status(thm)],[139, 12909])).
% 3.03/3.25 tff(12911,plain,
% 3.03/3.25 (~r(s(s(z)), s(z))),
% 3.03/3.25 inference(unit_resolution,[status(thm)],[12865, 121, 311, 350])).
% 3.03/3.25 tff(12912,plain,
% 3.03/3.25 (b(s(s(z)), s(z))),
% 3.03/3.25 inference(unit_resolution,[status(thm)],[308, 12911])).
% 3.03/3.25 tff(12913,plain,
% 3.03/3.25 (~b(s(z), z)),
% 3.03/3.25 inference(unit_resolution,[status(thm)],[12896, 350, 12912, 121])).
% 3.03/3.25 tff(12914,plain,
% 3.03/3.25 (r(s(z), z)),
% 3.03/3.25 inference(unit_resolution,[status(thm)],[230, 12913])).
% 3.03/3.25 tff(12915,plain,
% 3.03/3.25 (((~b(s(z), s(s(z)))) | (~b(z, s(s(z)))) | (~b(s(s(z)), s(z))) | (~b(s(z), s(s(z)))) | (~b(z, s(s(z)))) | (~b(z, s(z)))) <=> ((~b(z, s(s(z)))) | (~b(z, s(z))) | (~b(s(z), s(s(z)))) | (~b(s(s(z)), s(z))))),
% 3.03/3.25 inference(rewrite,[status(thm)],[])).
% 3.03/3.25 tff(12916,plain,
% 3.03/3.25 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(z)))) | (~b(z, s(s(z)))) | (~b(s(s(z)), s(z))) | (~b(s(z), s(s(z)))) | (~b(z, s(s(z)))) | (~b(z, s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(z)))) | (~b(z, s(z))) | (~b(s(z), s(s(z)))) | (~b(s(s(z)), s(z)))))),
% 3.03/3.25 inference(monotonicity,[status(thm)],[12915])).
% 3.03/3.25 tff(12917,plain,
% 3.03/3.25 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(z)))) | (~b(z, s(s(z)))) | (~b(s(s(z)), s(z))) | (~b(s(z), s(s(z)))) | (~b(z, s(s(z)))) | (~b(z, s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(s(z)))) | (~b(z, s(z))) | (~b(s(z), s(s(z)))) | (~b(s(s(z)), s(z))))),
% 3.03/3.25 inference(transitivity,[status(thm)],[12916, 11389])).
% 3.03/3.25 tff(12918,plain,
% 3.03/3.25 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(z)))) | (~b(z, s(s(z)))) | (~b(s(s(z)), s(z))) | (~b(s(z), s(s(z)))) | (~b(z, s(s(z)))) | (~b(z, s(z))))),
% 3.03/3.25 inference(quant_inst,[status(thm)],[])).
% 3.03/3.25 tff(12919,plain,
% 3.03/3.25 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(s(z)))) | (~b(z, s(z))) | (~b(s(z), s(s(z)))) | (~b(s(s(z)), s(z)))),
% 3.03/3.25 inference(modus_ponens,[status(thm)],[12918, 12917])).
% 3.03/3.25 tff(12920,plain,
% 3.03/3.25 (~b(z, s(z))),
% 3.03/3.25 inference(unit_resolution,[status(thm)],[12919, 166, 556, 10450, 12912])).
% 3.03/3.25 tff(12921,plain,
% 3.03/3.25 (r(z, s(z))),
% 3.03/3.25 inference(unit_resolution,[status(thm)],[321, 12920])).
% 3.03/3.25 tff(12922,plain,
% 3.03/3.25 (~b(s(s(s(z))), z)),
% 3.03/3.25 inference(unit_resolution,[status(thm)],[12188, 464, 121, 311, 12912, 98, 12914, 281, 12921])).
% 3.03/3.25 tff(12923,plain,
% 3.03/3.25 (r(s(s(s(z))), z)),
% 3.03/3.25 inference(unit_resolution,[status(thm)],[1713, 12922])).
% 3.03/3.25 tff(12924,plain,
% 3.03/3.25 (~r(s(z), s(s(s(z))))),
% 3.03/3.25 inference(unit_resolution,[status(thm)],[8876, 12923, 12921, 12914])).
% 3.03/3.25 tff(12925,plain,
% 3.03/3.25 (b(s(z), s(s(s(z))))),
% 3.03/3.25 inference(unit_resolution,[status(thm)],[1674, 12924])).
% 3.03/3.25 tff(12926,plain,
% 3.03/3.25 (~r(s(s(s(z))), s(z))),
% 3.03/3.25 inference(unit_resolution,[status(thm)],[12220, 197, 12921, 12914, 12923])).
% 3.03/3.25 tff(12927,plain,
% 3.03/3.25 (b(s(s(s(z))), s(z))),
% 3.03/3.25 inference(unit_resolution,[status(thm)],[1763, 12926])).
% 3.03/3.25 tff(12928,plain,
% 3.03/3.25 (~b(s(s(z)), s(s(s(z))))),
% 3.03/3.25 inference(unit_resolution,[status(thm)],[3248, 12927, 12912, 12925])).
% 3.03/3.25 tff(12929,plain,
% 3.03/3.25 (r(s(s(z)), s(s(s(z))))),
% 3.03/3.25 inference(unit_resolution,[status(thm)],[1730, 12928])).
% 3.03/3.25 tff(12930,plain,
% 3.03/3.25 (~b(s(s(s(z))), s(s(z)))),
% 3.03/3.25 inference(unit_resolution,[status(thm)],[8144, 166, 556, 12912, 12927])).
% 3.03/3.25 tff(12931,plain,
% 3.03/3.25 (r(s(s(s(z))), s(s(z)))),
% 3.03/3.25 inference(unit_resolution,[status(thm)],[1010, 12930])).
% 3.03/3.25 tff(12932,plain,
% 3.03/3.25 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), s(s(s(z))))) | (~r(s(s(z)), s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), s(s(z)))) | (~r(s(s(s(z))), s(s(z)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(elem!1))), s(s(s(z))))) | (~r(s(s(z)), s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), s(s(z)))) | (~r(s(s(s(z))), s(s(z)))))),
% 3.03/3.25 inference(rewrite,[status(thm)],[])).
% 3.03/3.25 tff(12933,plain,
% 3.03/3.25 (((~r(s(s(z)), s(s(s(elem!1))))) | (~r(s(s(s(z))), s(s(z)))) | (~r(s(s(s(elem!1))), s(s(z)))) | (~r(s(s(s(elem!1))), s(s(s(z)))))) <=> ((~r(s(s(s(elem!1))), s(s(s(z))))) | (~r(s(s(z)), s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), s(s(z)))) | (~r(s(s(s(z))), s(s(z)))))),
% 3.03/3.25 inference(rewrite,[status(thm)],[])).
% 3.03/3.25 tff(12934,plain,
% 3.03/3.25 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(z)), s(s(s(elem!1))))) | (~r(s(s(s(z))), s(s(z)))) | (~r(s(s(s(elem!1))), s(s(z)))) | (~r(s(s(s(elem!1))), s(s(s(z))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), s(s(s(z))))) | (~r(s(s(z)), s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), s(s(z)))) | (~r(s(s(s(z))), s(s(z))))))),
% 3.03/3.25 inference(monotonicity,[status(thm)],[12933])).
% 3.03/3.25 tff(12935,plain,
% 3.03/3.25 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(z)), s(s(s(elem!1))))) | (~r(s(s(s(z))), s(s(z)))) | (~r(s(s(s(elem!1))), s(s(z)))) | (~r(s(s(s(elem!1))), s(s(s(z))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(elem!1))), s(s(s(z))))) | (~r(s(s(z)), s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), s(s(z)))) | (~r(s(s(s(z))), s(s(z)))))),
% 3.03/3.25 inference(transitivity,[status(thm)],[12934, 12932])).
% 3.03/3.25 tff(12936,plain,
% 3.03/3.25 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(z)), s(s(s(elem!1))))) | (~r(s(s(s(z))), s(s(z)))) | (~r(s(s(s(elem!1))), s(s(z)))) | (~r(s(s(s(elem!1))), s(s(s(z))))))),
% 3.03/3.25 inference(quant_inst,[status(thm)],[])).
% 3.03/3.25 tff(12937,plain,
% 3.03/3.25 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(elem!1))), s(s(s(z))))) | (~r(s(s(z)), s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), s(s(z)))) | (~r(s(s(s(z))), s(s(z))))),
% 3.03/3.25 inference(modus_ponens,[status(thm)],[12936, 12935])).
% 3.03/3.25 tff(12938,plain,
% 3.03/3.25 (~r(s(s(s(elem!1))), s(s(s(z))))),
% 3.03/3.25 inference(unit_resolution,[status(thm)],[12937, 197, 281, 464, 12931])).
% 3.03/3.25 tff(12939,plain,
% 3.03/3.25 (b(s(s(s(elem!1))), s(s(s(z))))),
% 3.03/3.25 inference(unit_resolution,[status(thm)],[3574, 12938, 3567])).
% 3.03/3.25 tff(12940,plain,
% 3.03/3.25 (~r(s(s(elem!1)), s(s(s(elem!1))))),
% 3.03/3.25 inference(unit_resolution,[status(thm)],[764, 117, 311, 350])).
% 3.03/3.25 tff(12941,plain,
% 3.03/3.25 (~r(z, s(s(s(elem!1))))),
% 3.03/3.25 inference(unit_resolution,[status(thm)],[3872, 117, 350, 12914])).
% 3.03/3.25 tff(12942,plain,
% 3.03/3.25 (b(z, s(s(s(elem!1))))),
% 3.03/3.25 inference(unit_resolution,[status(thm)],[261, 12941])).
% 3.03/3.25 tff(12943,plain,
% 3.03/3.25 (s(s(elem!1)) = s(s(s(elem!1)))),
% 3.03/3.25 inference(unit_resolution,[status(thm)],[12162, 12942, 121, 311, 12914, 98, 12940])).
% 3.03/3.25 tff(12944,plain,
% 3.03/3.25 (s(s(s(elem!1))) = s(s(elem!1))),
% 3.03/3.25 inference(unit_resolution,[status(thm)],[4030, 12943])).
% 3.03/3.25 tff(12945,plain,
% 3.03/3.25 (~(s(s(s(z))) = elem!1)),
% 3.03/3.25 inference(unit_resolution,[status(thm)],[3122, 12943])).
% 3.03/3.25 tff(12946,plain,
% 3.03/3.25 (~r(s(s(s(z))), elem!1)),
% 3.03/3.25 inference(unit_resolution,[status(thm)],[8084, 12929, 350, 281, 12943])).
% 3.03/3.25 tff(12947,plain,
% 3.03/3.25 (b(s(s(s(z))), elem!1)),
% 3.03/3.25 inference(unit_resolution,[status(thm)],[2826, 12946, 12945])).
% 3.03/3.25 tff(12948,plain,
% 3.03/3.25 (b(s(s(s(z))), s(s(s(elem!1))))),
% 3.03/3.25 inference(unit_resolution,[status(thm)],[4078, 12947, 12944])).
% 3.03/3.25 tff(12949,plain,
% 3.03/3.25 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), z)) | (~b(s(s(s(z))), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(elem!1))), s(s(s(s(z)))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(elem!1))), z)) | (~b(s(s(s(z))), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(elem!1))), s(s(s(s(z)))))))),
% 3.03/3.25 inference(rewrite,[status(thm)],[])).
% 3.03/3.25 tff(12950,plain,
% 3.03/3.25 (((~b(s(s(s(elem!1))), z)) | (~b(s(s(s(elem!1))), z)) | (~b(s(s(s(z))), s(s(s(elem!1))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(elem!1))), s(s(s(z))))) | (~b(s(s(s(elem!1))), s(s(s(s(z))))))) <=> ((~b(s(s(s(elem!1))), z)) | (~b(s(s(s(z))), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(elem!1))), s(s(s(s(z)))))))),
% 3.03/3.25 inference(rewrite,[status(thm)],[])).
% 3.03/3.25 tff(12951,plain,
% 3.03/3.25 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), z)) | (~b(s(s(s(elem!1))), z)) | (~b(s(s(s(z))), s(s(s(elem!1))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(elem!1))), s(s(s(z))))) | (~b(s(s(s(elem!1))), s(s(s(s(z)))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), z)) | (~b(s(s(s(z))), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(elem!1))), s(s(s(s(z))))))))),
% 3.03/3.25 inference(monotonicity,[status(thm)],[12950])).
% 3.03/3.25 tff(12952,plain,
% 3.03/3.25 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), z)) | (~b(s(s(s(elem!1))), z)) | (~b(s(s(s(z))), s(s(s(elem!1))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(elem!1))), s(s(s(z))))) | (~b(s(s(s(elem!1))), s(s(s(s(z)))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(elem!1))), z)) | (~b(s(s(s(z))), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(elem!1))), s(s(s(s(z)))))))),
% 3.03/3.25 inference(transitivity,[status(thm)],[12951, 12949])).
% 3.03/3.25 tff(12953,plain,
% 3.03/3.25 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), z)) | (~b(s(s(s(elem!1))), z)) | (~b(s(s(s(z))), s(s(s(elem!1))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(elem!1))), s(s(s(z))))) | (~b(s(s(s(elem!1))), s(s(s(s(z)))))))),
% 3.03/3.25 inference(quant_inst,[status(thm)],[])).
% 3.03/3.25 tff(12954,plain,
% 3.03/3.25 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(elem!1))), z)) | (~b(s(s(s(z))), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(elem!1))), s(s(s(s(z))))))),
% 3.03/3.25 inference(modus_ponens,[status(thm)],[12953, 12952])).
% 3.03/3.25 tff(12955,plain,
% 3.03/3.25 (~b(s(s(s(elem!1))), s(s(s(s(z)))))),
% 3.03/3.25 inference(unit_resolution,[status(thm)],[12954, 166, 121, 6552, 4732, 3251])).
% 3.03/3.25 tff(12956,plain,
% 3.03/3.25 (b(s(s(s(elem!1))), s(s(s(s(z))))) <=> b(s(s(s(s(elem!1)))), s(s(s(s(z)))))),
% 3.03/3.25 inference(monotonicity,[status(thm)],[6566])).
% 3.03/3.25 tff(12957,plain,
% 3.03/3.25 (b(s(s(s(s(elem!1)))), s(s(s(s(z))))) <=> b(s(s(s(elem!1))), s(s(s(s(z)))))),
% 3.03/3.25 inference(symmetry,[status(thm)],[12956])).
% 3.03/3.25 tff(12958,assumption,(b(s(s(s(s(elem!1)))), s(s(s(s(z)))))), introduced(assumption)).
% 3.03/3.25 tff(12959,plain,
% 3.03/3.25 (b(s(s(s(elem!1))), s(s(s(s(z)))))),
% 3.03/3.25 inference(modus_ponens,[status(thm)],[12958, 12957])).
% 3.03/3.25 tff(12960,assumption,(~b(s(s(s(elem!1))), s(s(s(s(z)))))), introduced(assumption)).
% 3.03/3.25 tff(12961,plain,
% 3.03/3.25 ($false),
% 3.03/3.25 inference(unit_resolution,[status(thm)],[12960, 12959])).
% 3.03/3.25 tff(12962,plain,(b(s(s(s(elem!1))), s(s(s(s(z))))) | (~b(s(s(s(s(elem!1)))), s(s(s(s(z)))))) | (~(s(s(elem!1)) = s(s(s(elem!1)))))), inference(lemma,lemma(discharge,[]))).
% 3.03/3.25 tff(12963,plain,
% 3.03/3.25 (~b(s(s(s(s(elem!1)))), s(s(s(s(z)))))),
% 3.03/3.25 inference(unit_resolution,[status(thm)],[12962, 12955, 334])).
% 3.03/3.25 tff(12964,plain,
% 3.03/3.25 (b(s(s(s(s(elem!1)))), s(s(s(s(z))))) <=> b(s(s(s(elem!1))), s(s(s(s(z)))))),
% 3.03/3.25 inference(monotonicity,[status(thm)],[6471])).
% 3.03/3.25 tff(12965,plain,
% 3.03/3.25 (b(s(s(s(elem!1))), s(s(s(s(z))))) <=> b(s(s(s(s(elem!1)))), s(s(s(s(z)))))),
% 3.03/3.25 inference(symmetry,[status(thm)],[12964])).
% 3.03/3.25 tff(12966,plain,
% 3.03/3.25 (b(elem!1, s(s(s(s(z))))) <=> b(s(s(s(s(elem!1)))), s(s(s(s(z)))))),
% 3.03/3.25 inference(transitivity,[status(thm)],[6549, 12965])).
% 3.03/3.25 tff(12967,plain,
% 3.03/3.25 (b(s(s(s(s(elem!1)))), s(s(s(s(z)))))),
% 3.03/3.25 inference(modus_ponens,[status(thm)],[1101, 12966])).
% 3.03/3.25 tff(12968,assumption,(~b(s(s(s(s(elem!1)))), s(s(s(s(z)))))), introduced(assumption)).
% 3.03/3.25 tff(12969,plain,
% 3.03/3.25 ($false),
% 3.03/3.25 inference(unit_resolution,[status(thm)],[12968, 12967])).
% 3.03/3.25 tff(12970,plain,((~b(elem!1, s(s(s(s(z)))))) | b(s(s(s(s(elem!1)))), s(s(s(s(z))))) | (~(s(s(elem!1)) = s(s(s(elem!1)))))), inference(lemma,lemma(discharge,[]))).
% 3.03/3.25 tff(12971,plain,
% 3.03/3.25 (~b(elem!1, s(s(s(s(z)))))),
% 3.03/3.25 inference(unit_resolution,[status(thm)],[12970, 12963, 334])).
% 3.03/3.25 tff(12972,plain,
% 3.03/3.25 (r(elem!1, s(s(s(s(z)))))),
% 3.03/3.25 inference(unit_resolution,[status(thm)],[1098, 12971, 6568])).
% 3.03/3.25 tff(12973,plain,
% 3.03/3.25 (r(s(s(s(elem!1))), s(s(s(s(z)))))),
% 3.03/3.25 inference(unit_resolution,[status(thm)],[5665, 12972, 334])).
% 3.03/3.25 tff(12974,plain,
% 3.03/3.25 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), s(s(s(elem!1))))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(elem!1))), s(s(s(z))))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(s(z))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(z))), s(s(s(elem!1))))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(elem!1))), s(s(s(z))))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(s(z))))))),
% 3.03/3.25 inference(rewrite,[status(thm)],[])).
% 3.03/3.25 tff(12975,plain,
% 3.03/3.25 (((~b(s(s(s(elem!1))), s(s(s(z))))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(z))), s(s(s(elem!1))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(z), s(s(s(z))))) | (~b(s(z), s(s(s(s(z))))))) <=> ((~b(s(s(s(z))), s(s(s(elem!1))))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(elem!1))), s(s(s(z))))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(s(z))))))),
% 3.03/3.26 inference(rewrite,[status(thm)],[])).
% 3.03/3.26 tff(12976,plain,
% 3.03/3.26 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), s(s(s(z))))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(z))), s(s(s(elem!1))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(z), s(s(s(z))))) | (~b(s(z), s(s(s(s(z)))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), s(s(s(elem!1))))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(elem!1))), s(s(s(z))))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(s(z)))))))),
% 3.03/3.26 inference(monotonicity,[status(thm)],[12975])).
% 3.03/3.26 tff(12977,plain,
% 3.03/3.26 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), s(s(s(z))))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(z))), s(s(s(elem!1))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(z), s(s(s(z))))) | (~b(s(z), s(s(s(s(z)))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(z))), s(s(s(elem!1))))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(elem!1))), s(s(s(z))))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(s(z))))))),
% 3.03/3.26 inference(transitivity,[status(thm)],[12976, 12974])).
% 3.03/3.26 tff(12978,plain,
% 3.03/3.26 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), s(s(s(z))))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(z))), s(s(s(elem!1))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(z), s(s(s(z))))) | (~b(s(z), s(s(s(s(z)))))))),
% 3.03/3.26 inference(quant_inst,[status(thm)],[])).
% 3.03/3.26 tff(12979,plain,
% 3.03/3.26 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(z))), s(s(s(elem!1))))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(elem!1))), s(s(s(z))))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(s(z)))))),
% 3.03/3.26 inference(modus_ponens,[status(thm)],[12978, 12977])).
% 3.03/3.26 tff(12980,plain,
% 3.03/3.26 (~b(s(z), s(s(s(s(z)))))),
% 3.03/3.26 inference(unit_resolution,[status(thm)],[12979, 166, 6552, 988, 4732, 3251])).
% 3.03/3.26 tff(12981,plain,
% 3.03/3.26 (r(s(z), s(s(s(s(z)))))),
% 3.03/3.26 inference(unit_resolution,[status(thm)],[3302, 12980])).
% 3.03/3.26 tff(12982,plain,
% 3.03/3.26 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(s(s(elem!1))))) | (~r(s(z), s(s(s(s(z)))))) | (~r(s(s(s(s(z)))), s(z))) | (~r(s(s(s(elem!1))), s(s(s(s(z)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(z), s(s(s(elem!1))))) | (~r(s(z), s(s(s(s(z)))))) | (~r(s(s(s(s(z)))), s(z))) | (~r(s(s(s(elem!1))), s(s(s(s(z)))))))),
% 3.03/3.26 inference(rewrite,[status(thm)],[])).
% 3.03/3.26 tff(12983,plain,
% 3.03/3.26 (((~r(s(s(s(s(z)))), s(z))) | (~r(s(s(s(elem!1))), s(s(s(s(z)))))) | (~r(s(z), s(s(s(s(z)))))) | (~r(s(z), s(s(s(elem!1)))))) <=> ((~r(s(z), s(s(s(elem!1))))) | (~r(s(z), s(s(s(s(z)))))) | (~r(s(s(s(s(z)))), s(z))) | (~r(s(s(s(elem!1))), s(s(s(s(z)))))))),
% 3.03/3.26 inference(rewrite,[status(thm)],[])).
% 3.03/3.26 tff(12984,plain,
% 3.03/3.26 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(z)))), s(z))) | (~r(s(s(s(elem!1))), s(s(s(s(z)))))) | (~r(s(z), s(s(s(s(z)))))) | (~r(s(z), s(s(s(elem!1))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(s(s(elem!1))))) | (~r(s(z), s(s(s(s(z)))))) | (~r(s(s(s(s(z)))), s(z))) | (~r(s(s(s(elem!1))), s(s(s(s(z))))))))),
% 3.03/3.26 inference(monotonicity,[status(thm)],[12983])).
% 3.03/3.26 tff(12985,plain,
% 3.03/3.26 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(z)))), s(z))) | (~r(s(s(s(elem!1))), s(s(s(s(z)))))) | (~r(s(z), s(s(s(s(z)))))) | (~r(s(z), s(s(s(elem!1))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(z), s(s(s(elem!1))))) | (~r(s(z), s(s(s(s(z)))))) | (~r(s(s(s(s(z)))), s(z))) | (~r(s(s(s(elem!1))), s(s(s(s(z)))))))),
% 3.03/3.26 inference(transitivity,[status(thm)],[12984, 12982])).
% 3.03/3.26 tff(12986,plain,
% 3.03/3.26 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(z)))), s(z))) | (~r(s(s(s(elem!1))), s(s(s(s(z)))))) | (~r(s(z), s(s(s(s(z)))))) | (~r(s(z), s(s(s(elem!1))))))),
% 3.03/3.26 inference(quant_inst,[status(thm)],[])).
% 3.03/3.26 tff(12987,plain,
% 3.03/3.26 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(z), s(s(s(elem!1))))) | (~r(s(z), s(s(s(s(z)))))) | (~r(s(s(s(s(z)))), s(z))) | (~r(s(s(s(elem!1))), s(s(s(s(z))))))),
% 3.03/3.26 inference(modus_ponens,[status(thm)],[12986, 12985])).
% 3.03/3.26 tff(12988,plain,
% 3.03/3.26 ($false),
% 3.03/3.26 inference(unit_resolution,[status(thm)],[12987, 197, 119, 4770, 12981, 12973])).
% 3.03/3.26 tff(12989,plain,((~b(s(s(s(s(z)))), s(s(s(z))))) | (~r(s(z), s(s(s(elem!1))))) | (~(s(s(elem!1)) = s(s(s(elem!1))))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(z))), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(s(s(z))))) | (~b(s(s(s(elem!1))), z))), inference(lemma,lemma(discharge,[]))).
% 3.03/3.26 tff(12990,plain,
% 3.03/3.26 (~b(s(s(s(s(z)))), s(s(s(z))))),
% 3.03/3.26 inference(unit_resolution,[status(thm)],[12989, 12925, 12943, 117, 12927, 12948, 12939, 121])).
% 3.03/3.26 tff(12991,plain,
% 3.03/3.26 (r(s(s(s(s(z)))), s(s(s(z))))),
% 3.03/3.26 inference(unit_resolution,[status(thm)],[4662, 12990])).
% 3.03/3.26 tff(12992,plain,
% 3.03/3.26 (~r(s(s(z)), s(s(s(s(z)))))),
% 3.03/3.26 inference(unit_resolution,[status(thm)],[6600, 197, 12931, 12991, 12929])).
% 3.03/3.26 tff(12993,plain,
% 3.03/3.26 (b(s(s(z)), s(s(s(s(z)))))),
% 3.03/3.26 inference(unit_resolution,[status(thm)],[4753, 12992])).
% 3.03/3.26 tff(12994,plain,
% 3.03/3.26 (~b(z, s(s(s(z))))),
% 3.03/3.26 inference(unit_resolution,[status(thm)],[8101, 166, 12942, 121, 12948])).
% 3.03/3.26 tff(12995,plain,
% 3.03/3.26 (r(z, s(s(s(z))))),
% 3.03/3.26 inference(unit_resolution,[status(thm)],[1697, 12994])).
% 3.03/3.26 tff(12996,plain,
% 3.03/3.26 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(s(z))))) | (~r(s(s(s(z))), s(s(z)))) | (~r(s(s(s(s(z)))), z)) | (~r(s(s(s(s(z)))), s(s(s(z))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, s(s(s(z))))) | (~r(s(s(s(z))), s(s(z)))) | (~r(s(s(s(s(z)))), z)) | (~r(s(s(s(s(z)))), s(s(s(z))))))),
% 3.03/3.26 inference(rewrite,[status(thm)],[])).
% 3.03/3.26 tff(12997,plain,
% 3.03/3.26 (((~r(s(s(s(z))), s(s(z)))) | (~r(z, s(s(s(z))))) | (~r(s(s(s(s(z)))), s(s(s(z))))) | (~r(s(s(s(s(z)))), z))) <=> ((~r(z, s(s(s(z))))) | (~r(s(s(s(z))), s(s(z)))) | (~r(s(s(s(s(z)))), z)) | (~r(s(s(s(s(z)))), s(s(s(z))))))),
% 3.03/3.26 inference(rewrite,[status(thm)],[])).
% 3.03/3.26 tff(12998,plain,
% 3.03/3.26 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(z))), s(s(z)))) | (~r(z, s(s(s(z))))) | (~r(s(s(s(s(z)))), s(s(s(z))))) | (~r(s(s(s(s(z)))), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(s(z))))) | (~r(s(s(s(z))), s(s(z)))) | (~r(s(s(s(s(z)))), z)) | (~r(s(s(s(s(z)))), s(s(s(z)))))))),
% 3.03/3.26 inference(monotonicity,[status(thm)],[12997])).
% 3.03/3.26 tff(12999,plain,
% 3.03/3.26 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(z))), s(s(z)))) | (~r(z, s(s(s(z))))) | (~r(s(s(s(s(z)))), s(s(s(z))))) | (~r(s(s(s(s(z)))), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, s(s(s(z))))) | (~r(s(s(s(z))), s(s(z)))) | (~r(s(s(s(s(z)))), z)) | (~r(s(s(s(s(z)))), s(s(s(z))))))),
% 3.03/3.26 inference(transitivity,[status(thm)],[12998, 12996])).
% 3.03/3.26 tff(13000,plain,
% 3.03/3.26 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(z))), s(s(z)))) | (~r(z, s(s(s(z))))) | (~r(s(s(s(s(z)))), s(s(s(z))))) | (~r(s(s(s(s(z)))), z)))),
% 3.03/3.26 inference(quant_inst,[status(thm)],[])).
% 3.03/3.26 tff(13001,plain,
% 3.03/3.26 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, s(s(s(z))))) | (~r(s(s(s(z))), s(s(z)))) | (~r(s(s(s(s(z)))), z)) | (~r(s(s(s(s(z)))), s(s(s(z)))))),
% 3.03/3.26 inference(modus_ponens,[status(thm)],[13000, 12999])).
% 3.03/3.26 tff(13002,plain,
% 3.03/3.26 (~r(s(s(s(s(z)))), z)),
% 3.03/3.26 inference(unit_resolution,[status(thm)],[13001, 197, 12995, 12931, 12991])).
% 3.03/3.26 tff(13003,plain,
% 3.03/3.26 (b(s(s(s(s(z)))), z)),
% 3.03/3.26 inference(unit_resolution,[status(thm)],[3266, 13002])).
% 3.03/3.26 tff(13004,plain,
% 3.03/3.26 (~r(s(z), s(s(s(z))))),
% 3.03/3.26 inference(unit_resolution,[status(thm)],[8876, 1733, 97, 323])).
% 3.03/3.26 tff(13005,plain,
% 3.03/3.26 (~b(s(z), s(s(s(z))))),
% 3.03/3.26 inference(unit_resolution,[status(thm)],[8748, 1733, 866, 323, 556])).
% 3.03/3.26 tff(13006,plain,
% 3.03/3.26 ($false),
% 3.03/3.26 inference(unit_resolution,[status(thm)],[1674, 13005, 13004])).
% 3.03/3.26 tff(13007,plain,((~r(s(s(s(z))), z)) | (~r(s(s(z)), z)) | (~r(z, s(z))) | (~b(s(z), s(s(z)))) | (~r(s(z), z))), inference(lemma,lemma(discharge,[]))).
% 3.03/3.26 tff(13008,plain,
% 3.03/3.26 (~r(s(s(z)), z)),
% 3.03/3.26 inference(unit_resolution,[status(thm)],[13007, 12923, 12914, 12921, 556])).
% 3.03/3.26 tff(13009,plain,
% 3.03/3.26 (b(s(s(z)), z)),
% 3.03/3.26 inference(unit_resolution,[status(thm)],[186, 13008])).
% 3.03/3.26 tff(13010,plain,
% 3.03/3.26 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), z)) | (~b(s(s(z)), z)) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), z)) | (~b(s(s(z)), z)) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), z)))),
% 3.03/3.26 inference(rewrite,[status(thm)],[])).
% 3.03/3.26 tff(13011,plain,
% 3.03/3.26 (((~b(s(s(s(elem!1))), z)) | (~b(s(s(z)), z)) | (~b(z, s(s(s(elem!1))))) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(z)), z)) | (~b(s(s(z)), s(s(s(s(z))))))) <=> ((~b(z, s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), z)) | (~b(s(s(z)), z)) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), z)))),
% 3.03/3.26 inference(rewrite,[status(thm)],[])).
% 3.03/3.26 tff(13012,plain,
% 3.03/3.26 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), z)) | (~b(s(s(z)), z)) | (~b(z, s(s(s(elem!1))))) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(z)), z)) | (~b(s(s(z)), s(s(s(s(z)))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), z)) | (~b(s(s(z)), z)) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), z))))),
% 3.03/3.26 inference(monotonicity,[status(thm)],[13011])).
% 3.03/3.26 tff(13013,plain,
% 3.03/3.26 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), z)) | (~b(s(s(z)), z)) | (~b(z, s(s(s(elem!1))))) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(z)), z)) | (~b(s(s(z)), s(s(s(s(z)))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), z)) | (~b(s(s(z)), z)) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), z)))),
% 3.03/3.26 inference(transitivity,[status(thm)],[13012, 13010])).
% 3.03/3.26 tff(13014,plain,
% 3.03/3.26 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), z)) | (~b(s(s(z)), z)) | (~b(z, s(s(s(elem!1))))) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(z)), z)) | (~b(s(s(z)), s(s(s(s(z)))))))),
% 3.03/3.26 inference(quant_inst,[status(thm)],[])).
% 3.03/3.26 tff(13015,plain,
% 3.03/3.26 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), z)) | (~b(s(s(z)), z)) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), z))),
% 3.03/3.26 inference(modus_ponens,[status(thm)],[13014, 13013])).
% 3.03/3.26 tff(13016,plain,
% 3.03/3.26 ($false),
% 3.03/3.26 inference(unit_resolution,[status(thm)],[13015, 166, 12942, 121, 13009, 13003, 12993])).
% 3.03/3.26 tff(13017,plain,((~r(s(s(s(elem!1))), s(s(z)))) | (~b(s(s(s(elem!1))), z)) | (s(s(s(elem!1))) = s(s(s(z)))) | (~r(s(s(z)), s(s(s(elem!1))))) | (~b(s(z), s(s(z)))) | (~r(s(s(s(elem!1))), s(z))) | (~r(s(z), s(s(elem!1)))) | b(s(z), s(s(s(elem!1))))), inference(lemma,lemma(discharge,[]))).
% 3.03/3.26 tff(13018,plain,
% 3.03/3.26 (~r(s(s(s(elem!1))), s(s(z)))),
% 3.03/3.26 inference(unit_resolution,[status(thm)],[13017, 12910, 121, 12907, 12906, 3953, 85, 98])).
% 3.03/3.26 tff(13019,plain,
% 3.03/3.26 (b(s(s(s(elem!1))), s(s(z)))),
% 3.03/3.26 inference(unit_resolution,[status(thm)],[218, 13018])).
% 3.03/3.26 tff(13020,plain,
% 3.03/3.26 ($false),
% 3.03/3.26 inference(unit_resolution,[status(thm)],[12213, 166, 12900, 12906, 10450, 12867, 13019])).
% 3.03/3.26 tff(13021,plain,(b(s(z), s(s(s(elem!1)))) | (~b(s(s(s(elem!1))), z)) | b(s(z), s(s(elem!1))) | b(s(s(s(elem!1))), s(z))), inference(lemma,lemma(discharge,[]))).
% 3.03/3.26 tff(13022,plain,
% 3.03/3.26 (b(s(z), s(s(s(elem!1))))),
% 3.03/3.26 inference(unit_resolution,[status(thm)],[13021, 95, 54, 12854])).
% 3.03/3.26 tff(13023,plain,
% 3.03/3.26 (r(s(s(s(elem!1))), s(z))),
% 3.03/3.26 inference(unit_resolution,[status(thm)],[1849, 12854])).
% 3.03/3.26 tff(13024,plain,
% 3.03/3.26 (~r(s(s(z)), s(z))),
% 3.03/3.26 inference(unit_resolution,[status(thm)],[12865, 95, 85, 13023])).
% 3.03/3.26 tff(13025,plain,
% 3.03/3.26 (b(s(s(z)), s(z))),
% 3.03/3.26 inference(unit_resolution,[status(thm)],[308, 13024])).
% 3.03/3.26 tff(13026,plain,
% 3.03/3.26 (~b(s(z), z)),
% 3.03/3.26 inference(unit_resolution,[status(thm)],[12896, 13023, 13025, 95])).
% 3.03/3.26 tff(13027,plain,
% 3.03/3.26 (r(s(z), z)),
% 3.03/3.26 inference(unit_resolution,[status(thm)],[230, 13026])).
% 3.03/3.26 tff(13028,plain,
% 3.03/3.26 (~(s(s(elem!1)) = s(s(s(elem!1))))),
% 3.03/3.26 inference(unit_resolution,[status(thm)],[12329, 13022, 54])).
% 3.03/3.26 tff(13029,plain,
% 3.03/3.26 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(z)))) | (~b(z, s(s(s(elem!1))))) | (~b(s(z), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), z)) | (~b(z, s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(s(z)))) | (~b(z, s(s(s(elem!1))))) | (~b(s(z), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), z)) | (~b(z, s(z))))),
% 3.03/3.26 inference(rewrite,[status(thm)],[])).
% 3.03/3.26 tff(13030,plain,
% 3.03/3.26 (((~b(z, s(s(z)))) | (~b(z, s(s(z)))) | (~b(s(s(s(elem!1))), z)) | (~b(s(z), s(s(s(elem!1))))) | (~b(z, s(s(s(elem!1))))) | (~b(z, s(z)))) <=> ((~b(z, s(s(z)))) | (~b(z, s(s(s(elem!1))))) | (~b(s(z), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), z)) | (~b(z, s(z))))),
% 3.03/3.26 inference(rewrite,[status(thm)],[])).
% 3.03/3.26 tff(13031,plain,
% 3.03/3.26 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(z)))) | (~b(z, s(s(z)))) | (~b(s(s(s(elem!1))), z)) | (~b(s(z), s(s(s(elem!1))))) | (~b(z, s(s(s(elem!1))))) | (~b(z, s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(z)))) | (~b(z, s(s(s(elem!1))))) | (~b(s(z), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), z)) | (~b(z, s(z)))))),
% 3.03/3.26 inference(monotonicity,[status(thm)],[13030])).
% 3.03/3.26 tff(13032,plain,
% 3.03/3.26 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(z)))) | (~b(z, s(s(z)))) | (~b(s(s(s(elem!1))), z)) | (~b(s(z), s(s(s(elem!1))))) | (~b(z, s(s(s(elem!1))))) | (~b(z, s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(s(z)))) | (~b(z, s(s(s(elem!1))))) | (~b(s(z), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), z)) | (~b(z, s(z))))),
% 3.03/3.26 inference(transitivity,[status(thm)],[13031, 13029])).
% 3.03/3.26 tff(13033,plain,
% 3.03/3.26 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(z)))) | (~b(z, s(s(z)))) | (~b(s(s(s(elem!1))), z)) | (~b(s(z), s(s(s(elem!1))))) | (~b(z, s(s(s(elem!1))))) | (~b(z, s(z))))),
% 3.03/3.26 inference(quant_inst,[status(thm)],[])).
% 3.03/3.26 tff(13034,plain,
% 3.03/3.26 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(s(z)))) | (~b(z, s(s(s(elem!1))))) | (~b(s(z), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), z)) | (~b(z, s(z)))),
% 3.03/3.26 inference(modus_ponens,[status(thm)],[13033, 13032])).
% 3.03/3.26 tff(13035,plain,
% 3.03/3.26 ((~b(z, s(s(s(elem!1))))) | (~b(z, s(z)))),
% 3.03/3.26 inference(unit_resolution,[status(thm)],[13034, 166, 241, 10450, 121])).
% 3.03/3.26 tff(13036,plain,
% 3.03/3.26 (~b(z, s(z))),
% 3.03/3.26 inference(unit_resolution,[status(thm)],[13035, 240])).
% 3.03/3.26 tff(13037,plain,
% 3.03/3.26 (r(z, s(z))),
% 3.03/3.26 inference(unit_resolution,[status(thm)],[321, 13036])).
% 3.03/3.26 tff(13038,plain,
% 3.03/3.26 (~r(s(s(elem!1)), s(z))),
% 3.03/3.26 inference(unit_resolution,[status(thm)],[10127, 13037, 350, 12914, 45, 121, 240])).
% 3.03/3.26 tff(13039,plain,
% 3.03/3.26 (b(s(s(elem!1)), s(z))),
% 3.03/3.26 inference(unit_resolution,[status(thm)],[1912, 13038])).
% 3.03/3.26 tff(13040,plain,
% 3.03/3.26 (~r(s(s(elem!1)), s(s(s(elem!1))))),
% 3.03/3.26 inference(unit_resolution,[status(thm)],[2637, 13039, 311, 350, 51, 13037, 240])).
% 3.03/3.26 tff(13041,plain,
% 3.03/3.26 (b(s(s(elem!1)), s(s(s(elem!1))))),
% 3.03/3.26 inference(unit_resolution,[status(thm)],[461, 13040, 45])).
% 3.03/3.26 tff(13042,plain,
% 3.03/3.26 (~b(s(s(elem!1)), z)),
% 3.03/3.26 inference(unit_resolution,[status(thm)],[2283, 13041, 311, 350, 13037])).
% 3.03/3.26 tff(13043,plain,
% 3.03/3.26 (r(s(s(elem!1)), z)),
% 3.03/3.26 inference(unit_resolution,[status(thm)],[608, 13042])).
% 3.03/3.26 tff(13044,plain,
% 3.03/3.26 (b(z, s(s(elem!1)))),
% 3.03/3.26 inference(unit_resolution,[status(thm)],[12145, 13040, 121, 12914, 311, 240])).
% 3.03/3.26 tff(13045,plain,
% 3.03/3.26 (r(s(s(s(elem!1))), s(s(elem!1)))),
% 3.03/3.26 inference(unit_resolution,[status(thm)],[1834, 13044, 45, 13040, 240])).
% 3.03/3.26 tff(13046,plain,
% 3.03/3.26 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), s(s(elem!1)))) | (~r(s(z), s(s(elem!1)))) | (~r(s(s(s(elem!1))), s(z))) | (~r(s(s(elem!1)), elem!1)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(elem!1))), s(s(elem!1)))) | (~r(s(z), s(s(elem!1)))) | (~r(s(s(s(elem!1))), s(z))) | (~r(s(s(elem!1)), elem!1)))),
% 3.03/3.26 inference(rewrite,[status(thm)],[])).
% 3.03/3.26 tff(13047,plain,
% 3.03/3.26 (((~r(s(s(elem!1)), elem!1)) | (~r(s(z), s(s(elem!1)))) | (~r(s(s(s(elem!1))), s(s(elem!1)))) | (~r(s(s(s(elem!1))), s(z)))) <=> ((~r(s(s(s(elem!1))), s(s(elem!1)))) | (~r(s(z), s(s(elem!1)))) | (~r(s(s(s(elem!1))), s(z))) | (~r(s(s(elem!1)), elem!1)))),
% 3.03/3.26 inference(rewrite,[status(thm)],[])).
% 3.03/3.26 tff(13048,plain,
% 3.03/3.26 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(elem!1)), elem!1)) | (~r(s(z), s(s(elem!1)))) | (~r(s(s(s(elem!1))), s(s(elem!1)))) | (~r(s(s(s(elem!1))), s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), s(s(elem!1)))) | (~r(s(z), s(s(elem!1)))) | (~r(s(s(s(elem!1))), s(z))) | (~r(s(s(elem!1)), elem!1))))),
% 3.03/3.26 inference(monotonicity,[status(thm)],[13047])).
% 3.03/3.26 tff(13049,plain,
% 3.03/3.26 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(elem!1)), elem!1)) | (~r(s(z), s(s(elem!1)))) | (~r(s(s(s(elem!1))), s(s(elem!1)))) | (~r(s(s(s(elem!1))), s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(elem!1))), s(s(elem!1)))) | (~r(s(z), s(s(elem!1)))) | (~r(s(s(s(elem!1))), s(z))) | (~r(s(s(elem!1)), elem!1)))),
% 3.03/3.26 inference(transitivity,[status(thm)],[13048, 13046])).
% 3.03/3.26 tff(13050,plain,
% 3.03/3.26 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(elem!1)), elem!1)) | (~r(s(z), s(s(elem!1)))) | (~r(s(s(s(elem!1))), s(s(elem!1)))) | (~r(s(s(s(elem!1))), s(z))))),
% 3.03/3.27 inference(quant_inst,[status(thm)],[])).
% 3.03/3.27 tff(13051,plain,
% 3.03/3.27 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(elem!1))), s(s(elem!1)))) | (~r(s(z), s(s(elem!1)))) | (~r(s(s(s(elem!1))), s(z))) | (~r(s(s(elem!1)), elem!1))),
% 3.03/3.27 inference(modus_ponens,[status(thm)],[13050, 13049])).
% 3.03/3.27 tff(13052,plain,
% 3.03/3.27 ($false),
% 3.03/3.27 inference(unit_resolution,[status(thm)],[13051, 197, 311, 350, 768, 905])).
% 3.03/3.27 tff(13053,plain,((~r(s(s(elem!1)), elem!1)) | (~r(s(z), s(s(elem!1)))) | (~r(s(s(s(elem!1))), s(z))) | (~r(s(s(s(elem!1))), s(s(elem!1))))), inference(lemma,lemma(discharge,[]))).
% 3.03/3.27 tff(13054,plain,
% 3.03/3.27 (~r(s(s(elem!1)), elem!1)),
% 3.03/3.27 inference(unit_resolution,[status(thm)],[13053, 13045, 311, 350])).
% 3.03/3.27 tff(13055,plain,
% 3.03/3.27 (~(z = elem!1)),
% 3.03/3.27 inference(unit_resolution,[status(thm)],[3398, 13043, 13054])).
% 3.03/3.27 tff(13056,plain,
% 3.03/3.27 (~(s(elem!1) = s(z))),
% 3.03/3.27 inference(unit_resolution,[status(thm)],[30, 13055])).
% 3.03/3.27 tff(13057,plain,
% 3.03/3.27 (~(s(s(z)) = s(s(elem!1)))),
% 3.03/3.27 inference(unit_resolution,[status(thm)],[43, 13056])).
% 3.03/3.27 tff(13058,plain,
% 3.03/3.27 (~r(s(s(elem!1)), s(s(z)))),
% 3.03/3.27 inference(unit_resolution,[status(thm)],[4199, 13045, 311, 350])).
% 3.03/3.27 tff(13059,plain,
% 3.03/3.27 (~(s(s(elem!1)) = s(s(z)))),
% 3.03/3.27 inference(unit_resolution,[status(thm)],[131, 13057])).
% 3.03/3.27 tff(13060,plain,
% 3.03/3.27 (b(s(s(elem!1)), s(s(z)))),
% 3.03/3.27 inference(unit_resolution,[status(thm)],[441, 13059, 13058])).
% 3.03/3.27 tff(13061,plain,
% 3.03/3.27 (~b(s(s(z)), s(s(elem!1)))),
% 3.03/3.27 inference(unit_resolution,[status(thm)],[12611, 13060, 13044])).
% 3.03/3.27 tff(13062,plain,
% 3.03/3.27 (r(s(s(z)), s(s(elem!1)))),
% 3.03/3.27 inference(unit_resolution,[status(thm)],[390, 13061, 13057])).
% 3.03/3.27 tff(13063,plain,
% 3.03/3.27 (~r(s(s(z)), z)),
% 3.03/3.27 inference(unit_resolution,[status(thm)],[9517, 13062, 13037, 13043])).
% 3.03/3.27 tff(13064,plain,
% 3.03/3.27 (b(s(s(z)), z)),
% 3.03/3.27 inference(unit_resolution,[status(thm)],[186, 13063])).
% 3.03/3.27 tff(13065,plain,
% 3.03/3.27 ((~b(s(s(s(elem!1))), z)) | (~r(s(z), s(s(z)))) | (~r(s(s(s(elem!1))), s(z))) | (~b(s(s(z)), z))),
% 3.03/3.27 inference(unit_resolution,[status(thm)],[10745, 10450])).
% 3.03/3.27 tff(13066,plain,
% 3.03/3.27 (~r(s(z), s(s(z)))),
% 3.03/3.27 inference(unit_resolution,[status(thm)],[13065, 13064, 350, 121])).
% 3.03/3.27 tff(13067,plain,
% 3.03/3.27 (b(s(z), s(s(z)))),
% 3.03/3.27 inference(unit_resolution,[status(thm)],[427, 13066])).
% 3.03/3.27 tff(13068,plain,
% 3.03/3.27 ($false),
% 3.03/3.27 inference(unit_resolution,[status(thm)],[4405, 166, 13060, 13067, 13039, 12912])).
% 3.03/3.27 tff(13069,plain,((~b(z, s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), s(z))) | (~b(s(s(s(elem!1))), z)) | (~r(s(z), s(s(elem!1)))) | (s(s(elem!1)) = s(s(s(elem!1)))) | (~b(s(z), s(s(s(elem!1)))))), inference(lemma,lemma(discharge,[]))).
% 3.03/3.27 tff(13070,plain,
% 3.03/3.27 (~b(z, s(s(s(elem!1))))),
% 3.03/3.27 inference(unit_resolution,[status(thm)],[13069, 13023, 95, 85, 13028, 13022])).
% 3.03/3.27 tff(13071,plain,
% 3.03/3.27 (r(z, s(s(s(elem!1))))),
% 3.03/3.27 inference(unit_resolution,[status(thm)],[261, 13070])).
% 3.03/3.27 tff(13072,plain,
% 3.03/3.27 (~r(z, s(z))),
% 3.03/3.27 inference(unit_resolution,[status(thm)],[2613, 13071, 13023, 13027])).
% 3.03/3.27 tff(13073,plain,
% 3.03/3.27 (b(z, s(z))),
% 3.03/3.27 inference(unit_resolution,[status(thm)],[321, 13072])).
% 3.03/3.27 tff(13074,plain,
% 3.03/3.27 (~r(z, s(z))),
% 3.03/3.27 inference(unit_resolution,[status(thm)],[2613, 282, 350, 97])).
% 3.03/3.27 tff(13075,plain,
% 3.03/3.27 (b(z, s(z))),
% 3.03/3.27 inference(unit_resolution,[status(thm)],[321, 13074])).
% 3.03/3.27 tff(13076,plain,
% 3.03/3.27 (~r(s(z), s(s(z)))),
% 3.03/3.27 inference(unit_resolution,[status(thm)],[10496, 282, 97, 866])).
% 3.03/3.27 tff(13077,plain,
% 3.03/3.27 (b(s(z), s(s(z)))),
% 3.03/3.27 inference(unit_resolution,[status(thm)],[427, 13076])).
% 3.03/3.27 tff(13078,plain,
% 3.03/3.27 ($false),
% 3.03/3.27 inference(unit_resolution,[status(thm)],[11394, 166, 13077, 10450, 13075, 156])).
% 3.03/3.27 tff(13079,plain,((~r(z, s(s(s(elem!1))))) | (~b(s(s(z)), s(z))) | (~r(s(z), z)) | (~r(s(s(z)), z)) | (~r(s(s(s(elem!1))), s(z)))), inference(lemma,lemma(discharge,[]))).
% 3.03/3.27 tff(13080,plain,
% 3.03/3.27 (~r(s(s(z)), z)),
% 3.03/3.27 inference(unit_resolution,[status(thm)],[13079, 13071, 13027, 13025, 13023])).
% 3.03/3.27 tff(13081,plain,
% 3.03/3.27 (b(s(s(z)), z)),
% 3.03/3.27 inference(unit_resolution,[status(thm)],[186, 13080])).
% 3.03/3.27 tff(13082,plain,
% 3.03/3.27 ($false),
% 3.03/3.27 inference(unit_resolution,[status(thm)],[3860, 13081, 13073, 13025, 95, 13022])).
% 3.03/3.27 tff(13083,plain,(r(s(s(s(elem!1))), z) | b(s(z), s(s(elem!1)))), inference(lemma,lemma(discharge,[]))).
% 3.03/3.27 tff(13084,plain,
% 3.03/3.27 (r(s(s(s(elem!1))), z)),
% 3.03/3.27 inference(unit_resolution,[status(thm)],[13083, 54])).
% 3.03/3.27 tff(13085,plain,
% 3.03/3.27 ((s(s(s(elem!1))) = s(s(s(s(s(s(s(s(elem!1))))))))) <=> (s(s(s(s(s(s(s(s(elem!1)))))))) = s(s(s(elem!1))))),
% 3.03/3.27 inference(commutativity,[status(thm)],[])).
% 3.03/3.27 tff(13086,plain,
% 3.03/3.27 ((~(s(s(s(elem!1))) = s(s(s(s(s(s(s(s(elem!1)))))))))) <=> (~(s(s(s(s(s(s(s(s(elem!1)))))))) = s(s(s(elem!1)))))),
% 3.03/3.27 inference(monotonicity,[status(thm)],[13085])).
% 3.03/3.27 tff(13087,plain,
% 3.03/3.27 (~r(s(s(s(elem!1))), s(s(z)))),
% 3.03/3.27 inference(unit_resolution,[status(thm)],[854, 350, 311, 4143])).
% 3.03/3.27 tff(13088,plain,
% 3.03/3.27 (b(s(s(s(elem!1))), s(s(z)))),
% 3.03/3.27 inference(unit_resolution,[status(thm)],[218, 13087])).
% 3.03/3.27 tff(13089,plain,
% 3.03/3.27 (~r(s(s(z)), s(s(s(elem!1))))),
% 3.03/3.27 inference(unit_resolution,[status(thm)],[3958, 350, 311, 4143])).
% 3.03/3.27 tff(13090,plain,
% 3.03/3.27 (b(s(s(z)), s(s(s(elem!1))))),
% 3.03/3.27 inference(unit_resolution,[status(thm)],[279, 13089])).
% 3.03/3.27 tff(13091,plain,
% 3.03/3.27 (~r(s(s(elem!1)), s(s(s(elem!1))))),
% 3.03/3.27 inference(unit_resolution,[status(thm)],[764, 350, 311, 119])).
% 3.03/3.27 tff(13092,plain,
% 3.03/3.27 (b(s(s(elem!1)), s(s(s(elem!1))))),
% 3.03/3.27 inference(unit_resolution,[status(thm)],[461, 13091, 45])).
% 3.03/3.27 tff(13093,plain,
% 3.03/3.27 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(s(z)))) | (~b(s(s(z)), s(s(elem!1)))) | (~b(s(s(z)), s(s(s(elem!1))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(s(z)))) | (~b(s(s(z)), s(s(elem!1)))) | (~b(s(s(z)), s(s(s(elem!1))))))),
% 3.03/3.27 inference(rewrite,[status(thm)],[])).
% 3.03/3.27 tff(13094,plain,
% 3.03/3.27 (((~b(s(s(z)), s(s(s(elem!1))))) | (~b(s(s(z)), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(s(z)))) | (~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(s(s(z)), s(s(s(elem!1))))) | (~b(s(s(z)), s(s(elem!1))))) <=> ((~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(s(z)))) | (~b(s(s(z)), s(s(elem!1)))) | (~b(s(s(z)), s(s(s(elem!1))))))),
% 3.03/3.27 inference(rewrite,[status(thm)],[])).
% 3.03/3.27 tff(13095,plain,
% 3.03/3.27 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), s(s(s(elem!1))))) | (~b(s(s(z)), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(s(z)))) | (~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(s(s(z)), s(s(s(elem!1))))) | (~b(s(s(z)), s(s(elem!1)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(s(z)))) | (~b(s(s(z)), s(s(elem!1)))) | (~b(s(s(z)), s(s(s(elem!1)))))))),
% 3.03/3.27 inference(monotonicity,[status(thm)],[13094])).
% 3.03/3.27 tff(13096,plain,
% 3.03/3.27 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), s(s(s(elem!1))))) | (~b(s(s(z)), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(s(z)))) | (~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(s(s(z)), s(s(s(elem!1))))) | (~b(s(s(z)), s(s(elem!1)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(s(z)))) | (~b(s(s(z)), s(s(elem!1)))) | (~b(s(s(z)), s(s(s(elem!1))))))),
% 3.03/3.27 inference(transitivity,[status(thm)],[13095, 13093])).
% 3.03/3.27 tff(13097,plain,
% 3.03/3.27 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), s(s(s(elem!1))))) | (~b(s(s(z)), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(s(z)))) | (~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(s(s(z)), s(s(s(elem!1))))) | (~b(s(s(z)), s(s(elem!1)))))),
% 3.03/3.27 inference(quant_inst,[status(thm)],[])).
% 3.03/3.27 tff(13098,plain,
% 3.03/3.27 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(s(z)))) | (~b(s(s(z)), s(s(elem!1)))) | (~b(s(s(z)), s(s(s(elem!1)))))),
% 3.03/3.27 inference(modus_ponens,[status(thm)],[13097, 13096])).
% 3.03/3.27 tff(13099,plain,
% 3.03/3.27 (~b(s(s(z)), s(s(elem!1)))),
% 3.03/3.27 inference(unit_resolution,[status(thm)],[13098, 166, 13092, 13090, 13088])).
% 3.03/3.27 tff(13100,plain,
% 3.03/3.27 (~b(s(s(elem!1)), s(s(z)))),
% 3.03/3.27 inference(unit_resolution,[status(thm)],[501, 13092, 13089, 13087])).
% 3.03/3.27 tff(13101,plain,
% 3.03/3.27 ($false),
% 3.03/3.27 inference(unit_resolution,[status(thm)],[5759, 197, 311, 2077, 2073, 392])).
% 3.03/3.27 tff(13102,plain,((s(s(z)) = s(s(elem!1))) | (~r(s(z), s(s(elem!1)))) | (~r(s(s(z)), s(z))) | b(s(s(elem!1)), s(s(z))) | b(s(s(z)), s(s(elem!1)))), inference(lemma,lemma(discharge,[]))).
% 3.03/3.27 tff(13103,plain,
% 3.03/3.27 (s(s(z)) = s(s(elem!1))),
% 3.03/3.27 inference(unit_resolution,[status(thm)],[13102, 13100, 4143, 311, 13099])).
% 3.03/3.27 tff(13104,assumption,(s(s(s(elem!1))) = s(s(s(s(s(s(s(s(elem!1))))))))), introduced(assumption)).
% 3.03/3.27 tff(13105,plain,
% 3.03/3.27 (s(s(s(s(s(s(s(s(elem!1)))))))) = s(s(s(elem!1)))),
% 3.03/3.27 inference(symmetry,[status(thm)],[13104])).
% 3.03/3.27 tff(13106,plain,
% 3.03/3.27 (inj_0(s(s(s(s(s(s(s(s(elem!1))))))))) = inj_0(s(s(s(elem!1))))),
% 3.03/3.27 inference(monotonicity,[status(thm)],[13105])).
% 3.03/3.27 tff(13107,plain,
% 3.03/3.27 (inj_0(s(s(s(elem!1)))) = inj_0(s(s(s(s(s(s(s(s(elem!1)))))))))),
% 3.03/3.27 inference(symmetry,[status(thm)],[13106])).
% 3.03/3.27 tff(13108,plain,
% 3.03/3.27 (s(s(z)) = s(s(s(s(s(s(s(elem!1)))))))),
% 3.03/3.27 inference(transitivity,[status(thm)],[34, 105, 13107, 10])).
% 3.03/3.27 tff(13109,plain,
% 3.03/3.27 ($false),
% 3.03/3.27 inference(unit_resolution,[status(thm)],[5016, 13108])).
% 3.03/3.27 tff(13110,plain,((~(s(s(s(elem!1))) = s(s(s(s(s(s(s(s(elem!1)))))))))) | (~(s(s(z)) = s(s(elem!1))))), inference(lemma,lemma(discharge,[]))).
% 3.03/3.27 tff(13111,plain,
% 3.03/3.27 (~(s(s(s(elem!1))) = s(s(s(s(s(s(s(s(elem!1)))))))))),
% 3.03/3.27 inference(unit_resolution,[status(thm)],[13110, 13103])).
% 3.03/3.27 tff(13112,plain,
% 3.03/3.27 (~(s(s(s(s(s(s(s(s(elem!1)))))))) = s(s(s(elem!1))))),
% 3.03/3.27 inference(modus_ponens,[status(thm)],[13111, 13086])).
% 3.03/3.27 tff(13113,plain,
% 3.03/3.27 (s(elem!1) = s(z)),
% 3.03/3.27 inference(unit_resolution,[status(thm)],[43, 13103])).
% 3.03/3.27 tff(13114,plain,
% 3.03/3.27 (z = elem!1),
% 3.03/3.27 inference(unit_resolution,[status(thm)],[30, 13113])).
% 3.03/3.27 tff(13115,plain,
% 3.03/3.27 (r(s(s(s(elem!1))), elem!1)),
% 3.03/3.27 inference(unit_resolution,[status(thm)],[966, 13114, 154])).
% 3.03/3.27 tff(13116,plain,
% 3.03/3.27 ((s(s(s(s(s(s(s(s(elem!1)))))))) = z) <=> (s(s(s(s(s(s(s(s(elem!1)))))))) = elem!1)),
% 3.03/3.27 inference(monotonicity,[status(thm)],[13114])).
% 3.03/3.27 tff(13117,plain,
% 3.03/3.27 ((~(s(s(s(s(s(s(s(s(elem!1)))))))) = z)) <=> (~(s(s(s(s(s(s(s(s(elem!1)))))))) = elem!1))),
% 3.03/3.27 inference(monotonicity,[status(thm)],[13116])).
% 3.03/3.27 tff(13118,plain,
% 3.03/3.27 ((~![X: $i] : (~(s(X) = z))) | (~(s(s(s(s(s(s(s(s(elem!1)))))))) = z))),
% 3.03/3.27 inference(quant_inst,[status(thm)],[])).
% 3.03/3.27 tff(13119,plain,
% 3.03/3.27 (~(s(s(s(s(s(s(s(s(elem!1)))))))) = z)),
% 3.03/3.27 inference(unit_resolution,[status(thm)],[13118, 65])).
% 3.03/3.27 tff(13120,plain,
% 3.03/3.27 (~(s(s(s(s(s(s(s(s(elem!1)))))))) = elem!1)),
% 3.03/3.27 inference(modus_ponens,[status(thm)],[13119, 13117])).
% 3.03/3.27 tff(13121,plain,
% 3.03/3.27 (elem!1 = z),
% 3.03/3.27 inference(symmetry,[status(thm)],[13114])).
% 3.03/3.27 tff(13122,plain,
% 3.03/3.27 (b(elem!1, s(s(elem!1))) <=> b(z, s(s(elem!1)))),
% 3.03/3.27 inference(monotonicity,[status(thm)],[13121])).
% 3.03/3.27 tff(13123,plain,
% 3.03/3.27 (b(z, s(s(elem!1))) <=> b(elem!1, s(s(elem!1)))),
% 3.03/3.27 inference(symmetry,[status(thm)],[13122])).
% 3.03/3.27 tff(13124,plain,
% 3.03/3.27 (b(z, s(s(elem!1)))),
% 3.03/3.27 inference(unit_resolution,[status(thm)],[12671, 13103])).
% 3.03/3.27 tff(13125,plain,
% 3.03/3.27 (b(elem!1, s(s(elem!1)))),
% 3.03/3.27 inference(modus_ponens,[status(thm)],[13124, 13123])).
% 3.03/3.27 tff(13126,plain,
% 3.03/3.27 (b(s(z), z) <=> b(s(z), elem!1)),
% 3.03/3.27 inference(monotonicity,[status(thm)],[13114])).
% 3.03/3.27 tff(13127,plain,
% 3.03/3.27 (b(s(z), elem!1)),
% 3.03/3.27 inference(modus_ponens,[status(thm)],[53, 13126])).
% 3.03/3.27 tff(13128,plain,
% 3.03/3.27 ((s(s(elem!1)) = elem!1) <=> (s(s(elem!1)) = z)),
% 3.03/3.27 inference(monotonicity,[status(thm)],[13121])).
% 3.03/3.27 tff(13129,plain,
% 3.03/3.27 ((s(s(elem!1)) = z) <=> (s(s(elem!1)) = elem!1)),
% 3.03/3.27 inference(symmetry,[status(thm)],[13128])).
% 3.03/3.27 tff(13130,plain,
% 3.03/3.27 ((~(s(s(elem!1)) = z)) <=> (~(s(s(elem!1)) = elem!1))),
% 3.03/3.27 inference(monotonicity,[status(thm)],[13129])).
% 3.03/3.27 tff(13131,plain,
% 3.03/3.27 (~(s(s(elem!1)) = elem!1)),
% 3.03/3.27 inference(modus_ponens,[status(thm)],[108, 13130])).
% 3.03/3.27 tff(13132,plain,
% 3.03/3.27 ((s(s(s(s(elem!1)))) = z) <=> (s(s(s(s(elem!1)))) = elem!1)),
% 3.03/3.27 inference(monotonicity,[status(thm)],[13114])).
% 3.03/3.27 tff(13133,plain,
% 3.03/3.27 ((s(s(s(s(elem!1)))) = z) <=> (elem!1 = s(s(s(s(elem!1)))))),
% 3.03/3.27 inference(transitivity,[status(thm)],[13132, 2287])).
% 3.03/3.27 tff(13134,plain,
% 3.03/3.27 ((~(s(s(s(s(elem!1)))) = z)) <=> (~(elem!1 = s(s(s(s(elem!1))))))),
% 3.03/3.27 inference(monotonicity,[status(thm)],[13133])).
% 3.03/3.27 tff(13135,plain,
% 3.03/3.27 (~(elem!1 = s(s(s(s(elem!1)))))),
% 3.03/3.27 inference(modus_ponens,[status(thm)],[626, 13134])).
% 3.03/3.27 tff(13136,plain,
% 3.03/3.27 (~b(s(s(elem!1)), s(z))),
% 3.03/3.27 inference(unit_resolution,[status(thm)],[3938, 13103, 3936])).
% 3.03/3.27 tff(13137,plain,
% 3.03/3.27 (r(s(s(elem!1)), s(z))),
% 3.03/3.27 inference(unit_resolution,[status(thm)],[1912, 13136])).
% 3.03/3.27 tff(13138,plain,
% 3.03/3.27 ((s(s(s(s(elem!1)))) = s(s(z))) <=> (s(s(s(s(elem!1)))) = s(s(elem!1)))),
% 3.03/3.27 inference(monotonicity,[status(thm)],[13103])).
% 3.03/3.27 tff(13139,plain,
% 3.03/3.27 ((s(s(s(s(elem!1)))) = s(s(z))) <=> (s(s(elem!1)) = s(s(s(s(elem!1)))))),
% 3.03/3.27 inference(transitivity,[status(thm)],[13138, 123])).
% 3.03/3.27 tff(13140,plain,
% 3.03/3.27 ((s(s(s(s(elem!1)))) = s(s(z))) <=> (s(s(s(s(elem!1)))) = s(s(elem!1)))),
% 3.03/3.27 inference(transitivity,[status(thm)],[13139, 124])).
% 3.03/3.27 tff(13141,plain,
% 3.03/3.27 ((~(s(s(s(s(elem!1)))) = s(s(z)))) <=> (~(s(s(s(s(elem!1)))) = s(s(elem!1))))),
% 3.03/3.27 inference(monotonicity,[status(thm)],[13140])).
% 3.03/3.27 tff(13142,plain,
% 3.03/3.27 (~(s(s(s(s(elem!1)))) = s(s(elem!1)))),
% 3.03/3.27 inference(modus_ponens,[status(thm)],[733, 13141])).
% 3.03/3.27 tff(13143,plain,
% 3.03/3.27 (~r(s(s(s(s(elem!1)))), s(z))),
% 3.03/3.27 inference(unit_resolution,[status(thm)],[5809, 13142, 311, 350, 13092, 13137, 358])).
% 3.03/3.27 tff(13144,plain,
% 3.03/3.27 (b(s(s(s(s(elem!1)))), s(z))),
% 3.03/3.27 inference(unit_resolution,[status(thm)],[661, 13143])).
% 3.03/3.27 tff(13145,plain,
% 3.03/3.27 (b(z, s(z)) <=> b(elem!1, s(z))),
% 3.03/3.27 inference(monotonicity,[status(thm)],[13114])).
% 3.03/3.27 tff(13146,plain,
% 3.03/3.27 (b(elem!1, s(z))),
% 3.03/3.27 inference(modus_ponens,[status(thm)],[118, 13145])).
% 3.03/3.27 tff(13147,plain,
% 3.03/3.27 (~b(elem!1, s(s(s(s(elem!1)))))),
% 3.03/3.27 inference(unit_resolution,[status(thm)],[3430, 166, 13146, 13127, 13144])).
% 3.03/3.27 tff(13148,plain,
% 3.03/3.27 (r(elem!1, s(s(s(s(elem!1)))))),
% 3.03/3.27 inference(unit_resolution,[status(thm)],[2427, 13147, 13135])).
% 3.03/3.27 tff(13149,plain,
% 3.03/3.27 ((~(s(s(s(s(elem!1)))) = z)) <=> (~(s(s(s(s(elem!1)))) = elem!1))),
% 3.03/3.27 inference(monotonicity,[status(thm)],[13132])).
% 3.03/3.27 tff(13150,plain,
% 3.03/3.27 (~(s(s(s(s(elem!1)))) = elem!1)),
% 3.03/3.27 inference(modus_ponens,[status(thm)],[626, 13149])).
% 3.03/3.27 tff(13151,plain,
% 3.03/3.27 (~b(s(s(s(s(elem!1)))), elem!1)),
% 3.03/3.27 inference(unit_resolution,[status(thm)],[6168, 166, 13146, 13127, 13144])).
% 3.03/3.27 tff(13152,plain,
% 3.03/3.27 (r(s(s(s(s(elem!1)))), elem!1)),
% 3.03/3.27 inference(unit_resolution,[status(thm)],[719, 13151, 13150])).
% 3.03/3.27 tff(13153,plain,
% 3.03/3.27 (s(s(s(z))) = s(s(s(elem!1)))),
% 3.03/3.27 inference(monotonicity,[status(thm)],[13103])).
% 3.03/3.27 tff(13154,plain,
% 3.03/3.27 (s(s(s(s(z)))) = s(s(s(s(elem!1))))),
% 3.03/3.27 inference(monotonicity,[status(thm)],[13153])).
% 3.03/3.27 tff(13155,plain,
% 3.03/3.27 (r(s(s(z)), s(s(s(s(z))))) <=> r(s(s(elem!1)), s(s(s(s(elem!1)))))),
% 3.03/3.27 inference(monotonicity,[status(thm)],[13103, 13154])).
% 3.03/3.27 tff(13156,plain,
% 3.03/3.27 (~r(s(s(s(z))), s(s(z)))),
% 3.03/3.27 inference(unit_resolution,[status(thm)],[4714, 13103, 13087])).
% 3.03/3.27 tff(13157,plain,
% 3.03/3.27 (b(s(s(s(z))), s(s(z)))),
% 3.03/3.27 inference(unit_resolution,[status(thm)],[1010, 13156])).
% 3.03/3.27 tff(13158,plain,
% 3.03/3.27 (b(s(s(z)), s(s(s(z)))) <=> b(s(s(elem!1)), s(s(s(z))))),
% 3.03/3.27 inference(monotonicity,[status(thm)],[13103])).
% 3.03/3.27 tff(13159,plain,
% 3.03/3.27 (b(s(s(elem!1)), s(s(s(z)))) <=> b(s(s(z)), s(s(s(z))))),
% 3.03/3.27 inference(symmetry,[status(thm)],[13158])).
% 3.03/3.27 tff(13160,plain,
% 3.03/3.27 (b(s(s(elem!1)), s(s(s(z)))) <=> b(s(s(elem!1)), s(s(s(elem!1))))),
% 3.03/3.27 inference(monotonicity,[status(thm)],[13153])).
% 3.03/3.27 tff(13161,plain,
% 3.03/3.27 (b(s(s(elem!1)), s(s(s(elem!1)))) <=> b(s(s(elem!1)), s(s(s(z))))),
% 3.03/3.27 inference(symmetry,[status(thm)],[13160])).
% 3.03/3.27 tff(13162,plain,
% 3.03/3.27 (b(s(s(elem!1)), s(s(s(elem!1)))) <=> b(s(s(z)), s(s(s(z))))),
% 3.03/3.27 inference(transitivity,[status(thm)],[13161, 13159])).
% 3.03/3.27 tff(13163,plain,
% 3.03/3.27 (b(s(s(z)), s(s(s(z))))),
% 3.03/3.27 inference(modus_ponens,[status(thm)],[13092, 13162])).
% 3.03/3.27 tff(13164,plain,
% 3.03/3.27 (r(s(s(s(s(z)))), s(s(s(z)))) <=> r(s(s(s(s(elem!1)))), s(s(s(elem!1))))),
% 3.03/3.27 inference(monotonicity,[status(thm)],[13154, 13153])).
% 3.03/3.27 tff(13165,plain,
% 3.03/3.27 (r(s(s(s(s(elem!1)))), s(s(s(elem!1)))) <=> r(s(s(s(s(z)))), s(s(s(z))))),
% 3.03/3.27 inference(symmetry,[status(thm)],[13164])).
% 3.03/3.27 tff(13166,plain,
% 3.03/3.27 ((~r(s(s(s(s(elem!1)))), s(s(s(elem!1))))) <=> (~r(s(s(s(s(z)))), s(s(s(z)))))),
% 3.03/3.27 inference(monotonicity,[status(thm)],[13165])).
% 3.03/3.27 tff(13167,plain,
% 3.03/3.27 (r(z, s(s(s(elem!1)))) <=> r(elem!1, s(s(s(elem!1))))),
% 3.03/3.27 inference(monotonicity,[status(thm)],[13114])).
% 3.03/3.27 tff(13168,plain,
% 3.03/3.27 (r(elem!1, s(s(s(elem!1))))),
% 3.03/3.27 inference(modus_ponens,[status(thm)],[282, 13167])).
% 3.03/3.27 tff(13169,plain,
% 3.03/3.27 (~r(s(s(s(s(elem!1)))), s(s(s(elem!1))))),
% 3.03/3.27 inference(unit_resolution,[status(thm)],[1056, 13148, 350, 13168])).
% 3.03/3.27 tff(13170,plain,
% 3.03/3.27 (~r(s(s(s(s(z)))), s(s(s(z))))),
% 3.03/3.27 inference(modus_ponens,[status(thm)],[13169, 13166])).
% 3.03/3.27 tff(13171,plain,
% 3.03/3.27 (b(s(s(s(s(z)))), s(s(s(z))))),
% 3.03/3.27 inference(unit_resolution,[status(thm)],[4662, 13170])).
% 3.03/3.27 tff(13172,plain,
% 3.03/3.27 (~b(s(s(z)), s(s(s(s(z)))))),
% 3.03/3.27 inference(unit_resolution,[status(thm)],[4741, 13171, 13163, 13157])).
% 3.03/3.27 tff(13173,plain,
% 3.03/3.27 (r(s(s(z)), s(s(s(s(z)))))),
% 3.03/3.27 inference(unit_resolution,[status(thm)],[4753, 13172])).
% 3.03/3.27 tff(13174,plain,
% 3.03/3.27 (r(s(s(elem!1)), s(s(s(s(elem!1)))))),
% 3.03/3.27 inference(modus_ponens,[status(thm)],[13173, 13155])).
% 3.03/3.27 tff(13175,plain,
% 3.03/3.27 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(s(s(s(elem!1)))))) | (~r(s(s(elem!1)), elem!1)) | (~r(s(s(s(s(elem!1)))), elem!1)) | (~r(s(s(elem!1)), s(s(s(s(elem!1)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(elem!1, s(s(s(s(elem!1)))))) | (~r(s(s(elem!1)), elem!1)) | (~r(s(s(s(s(elem!1)))), elem!1)) | (~r(s(s(elem!1)), s(s(s(s(elem!1)))))))),
% 3.03/3.27 inference(rewrite,[status(thm)],[])).
% 3.03/3.27 tff(13176,plain,
% 3.03/3.27 (((~r(s(s(s(s(elem!1)))), elem!1)) | (~r(elem!1, s(s(s(s(elem!1)))))) | (~r(s(s(elem!1)), s(s(s(s(elem!1)))))) | (~r(s(s(elem!1)), elem!1))) <=> ((~r(elem!1, s(s(s(s(elem!1)))))) | (~r(s(s(elem!1)), elem!1)) | (~r(s(s(s(s(elem!1)))), elem!1)) | (~r(s(s(elem!1)), s(s(s(s(elem!1)))))))),
% 3.03/3.27 inference(rewrite,[status(thm)],[])).
% 3.03/3.27 tff(13177,plain,
% 3.03/3.27 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(elem!1)))), elem!1)) | (~r(elem!1, s(s(s(s(elem!1)))))) | (~r(s(s(elem!1)), s(s(s(s(elem!1)))))) | (~r(s(s(elem!1)), elem!1)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(s(s(s(elem!1)))))) | (~r(s(s(elem!1)), elem!1)) | (~r(s(s(s(s(elem!1)))), elem!1)) | (~r(s(s(elem!1)), s(s(s(s(elem!1))))))))),
% 3.03/3.27 inference(monotonicity,[status(thm)],[13176])).
% 3.03/3.27 tff(13178,plain,
% 3.03/3.27 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(elem!1)))), elem!1)) | (~r(elem!1, s(s(s(s(elem!1)))))) | (~r(s(s(elem!1)), s(s(s(s(elem!1)))))) | (~r(s(s(elem!1)), elem!1)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(elem!1, s(s(s(s(elem!1)))))) | (~r(s(s(elem!1)), elem!1)) | (~r(s(s(s(s(elem!1)))), elem!1)) | (~r(s(s(elem!1)), s(s(s(s(elem!1)))))))),
% 3.03/3.27 inference(transitivity,[status(thm)],[13177, 13175])).
% 3.03/3.27 tff(13179,plain,
% 3.03/3.27 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(elem!1)))), elem!1)) | (~r(elem!1, s(s(s(s(elem!1)))))) | (~r(s(s(elem!1)), s(s(s(s(elem!1)))))) | (~r(s(s(elem!1)), elem!1)))),
% 3.03/3.27 inference(quant_inst,[status(thm)],[])).
% 3.03/3.27 tff(13180,plain,
% 3.03/3.27 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(elem!1, s(s(s(s(elem!1)))))) | (~r(s(s(elem!1)), elem!1)) | (~r(s(s(s(s(elem!1)))), elem!1)) | (~r(s(s(elem!1)), s(s(s(s(elem!1))))))),
% 3.03/3.27 inference(modus_ponens,[status(thm)],[13179, 13178])).
% 3.03/3.27 tff(13181,plain,
% 3.03/3.27 (~r(s(s(elem!1)), elem!1)),
% 3.03/3.27 inference(unit_resolution,[status(thm)],[13180, 197, 13174, 13152, 13148])).
% 3.03/3.27 tff(13182,plain,
% 3.03/3.27 (b(s(s(elem!1)), elem!1)),
% 3.03/3.27 inference(unit_resolution,[status(thm)],[784, 13181, 13131])).
% 3.03/3.27 tff(13183,assumption,(s(s(s(s(s(s(s(s(elem!1)))))))) = s(s(elem!1))), introduced(assumption)).
% 3.03/3.27 tff(13184,plain,
% 3.03/3.27 (inj_0(s(s(s(s(s(s(s(s(elem!1))))))))) = inj_0(s(s(elem!1)))),
% 3.03/3.27 inference(monotonicity,[status(thm)],[13183])).
% 3.03/3.27 tff(13185,plain,
% 3.03/3.27 (s(s(s(s(s(s(s(elem!1))))))) = inj_0(s(s(s(s(s(s(s(s(elem!1)))))))))),
% 3.03/3.27 inference(symmetry,[status(thm)],[10])).
% 3.03/3.27 tff(13186,plain,
% 3.03/3.27 (s(s(s(s(s(s(s(elem!1))))))) = s(z)),
% 3.03/3.27 inference(transitivity,[status(thm)],[13185, 13184, 38, 21])).
% 3.03/3.27 tff(13187,plain,
% 3.03/3.27 (~(s(s(s(s(s(s(s(elem!1))))))) = s(z))),
% 3.03/3.27 inference(unit_resolution,[status(thm)],[4900, 10966])).
% 3.03/3.27 tff(13188,plain,
% 3.03/3.27 ($false),
% 3.03/3.27 inference(unit_resolution,[status(thm)],[13187, 13186])).
% 3.03/3.27 tff(13189,plain,((~(s(s(s(s(s(s(s(s(elem!1)))))))) = s(s(elem!1)))) | (~(s(elem!1) = s(z)))), inference(lemma,lemma(discharge,[]))).
% 3.03/3.27 tff(13190,plain,
% 3.03/3.27 (~(s(s(s(s(s(s(s(s(elem!1)))))))) = s(s(elem!1)))),
% 3.03/3.27 inference(unit_resolution,[status(thm)],[13189, 13113])).
% 3.03/3.27 tff(13191,assumption,(s(s(s(s(s(s(s(s(elem!1)))))))) = s(z)), introduced(assumption)).
% 3.03/3.27 tff(13192,plain,
% 3.03/3.27 (inj_0(s(s(s(s(s(s(s(s(elem!1))))))))) = inj_0(s(z))),
% 3.03/3.27 inference(monotonicity,[status(thm)],[13191])).
% 3.03/3.27 tff(13193,plain,
% 3.03/3.27 (s(s(s(s(s(s(s(elem!1))))))) = elem!1),
% 3.03/3.27 inference(transitivity,[status(thm)],[13185, 13192, 25, 12])).
% 3.03/3.27 tff(13194,plain,
% 3.03/3.27 (~(s(s(s(s(s(s(s(elem!1))))))) = elem!1)),
% 3.03/3.27 inference(unit_resolution,[status(thm)],[6283, 12])).
% 3.03/3.27 tff(13195,plain,
% 3.03/3.27 ($false),
% 3.03/3.27 inference(unit_resolution,[status(thm)],[13194, 13193])).
% 3.03/3.27 tff(13196,plain,((~(s(s(s(s(s(s(s(s(elem!1)))))))) = s(z))) | (~(z = elem!1))), inference(lemma,lemma(discharge,[]))).
% 3.03/3.27 tff(13197,plain,
% 3.03/3.27 (~(s(s(s(s(s(s(s(s(elem!1)))))))) = s(z))),
% 3.03/3.27 inference(unit_resolution,[status(thm)],[13196, 13114])).
% 3.03/3.27 tff(13198,assumption,(b(s(s(s(s(s(s(s(s(elem!1)))))))), elem!1)), introduced(assumption)).
% 3.03/3.27 tff(13199,plain,
% 3.03/3.27 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), elem!1)) | (~b(elem!1, s(s(elem!1)))) | (~b(s(z), elem!1)) | (~b(s(s(s(s(s(s(s(s(elem!1)))))))), elem!1)) | (~b(s(s(s(s(s(s(s(s(elem!1)))))))), s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(elem!1)), elem!1)) | (~b(elem!1, s(s(elem!1)))) | (~b(s(z), elem!1)) | (~b(s(s(s(s(s(s(s(s(elem!1)))))))), elem!1)) | (~b(s(s(s(s(s(s(s(s(elem!1)))))))), s(z))))),
% 3.03/3.27 inference(rewrite,[status(thm)],[])).
% 3.03/3.27 tff(13200,plain,
% 3.03/3.27 (((~b(s(s(elem!1)), elem!1)) | (~b(s(s(s(s(s(s(s(s(elem!1)))))))), elem!1)) | (~b(elem!1, s(s(elem!1)))) | (~b(s(z), elem!1)) | (~b(s(s(s(s(s(s(s(s(elem!1)))))))), elem!1)) | (~b(s(s(s(s(s(s(s(s(elem!1)))))))), s(z)))) <=> ((~b(s(s(elem!1)), elem!1)) | (~b(elem!1, s(s(elem!1)))) | (~b(s(z), elem!1)) | (~b(s(s(s(s(s(s(s(s(elem!1)))))))), elem!1)) | (~b(s(s(s(s(s(s(s(s(elem!1)))))))), s(z))))),
% 3.03/3.27 inference(rewrite,[status(thm)],[])).
% 3.03/3.27 tff(13201,plain,
% 3.03/3.27 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), elem!1)) | (~b(s(s(s(s(s(s(s(s(elem!1)))))))), elem!1)) | (~b(elem!1, s(s(elem!1)))) | (~b(s(z), elem!1)) | (~b(s(s(s(s(s(s(s(s(elem!1)))))))), elem!1)) | (~b(s(s(s(s(s(s(s(s(elem!1)))))))), s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), elem!1)) | (~b(elem!1, s(s(elem!1)))) | (~b(s(z), elem!1)) | (~b(s(s(s(s(s(s(s(s(elem!1)))))))), elem!1)) | (~b(s(s(s(s(s(s(s(s(elem!1)))))))), s(z)))))),
% 3.03/3.28 inference(monotonicity,[status(thm)],[13200])).
% 3.03/3.28 tff(13202,plain,
% 3.03/3.28 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), elem!1)) | (~b(s(s(s(s(s(s(s(s(elem!1)))))))), elem!1)) | (~b(elem!1, s(s(elem!1)))) | (~b(s(z), elem!1)) | (~b(s(s(s(s(s(s(s(s(elem!1)))))))), elem!1)) | (~b(s(s(s(s(s(s(s(s(elem!1)))))))), s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(elem!1)), elem!1)) | (~b(elem!1, s(s(elem!1)))) | (~b(s(z), elem!1)) | (~b(s(s(s(s(s(s(s(s(elem!1)))))))), elem!1)) | (~b(s(s(s(s(s(s(s(s(elem!1)))))))), s(z))))),
% 3.03/3.28 inference(transitivity,[status(thm)],[13201, 13199])).
% 3.03/3.28 tff(13203,plain,
% 3.03/3.28 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), elem!1)) | (~b(s(s(s(s(s(s(s(s(elem!1)))))))), elem!1)) | (~b(elem!1, s(s(elem!1)))) | (~b(s(z), elem!1)) | (~b(s(s(s(s(s(s(s(s(elem!1)))))))), elem!1)) | (~b(s(s(s(s(s(s(s(s(elem!1)))))))), s(z))))),
% 3.03/3.28 inference(quant_inst,[status(thm)],[])).
% 3.03/3.28 tff(13204,plain,
% 3.03/3.28 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(elem!1)), elem!1)) | (~b(elem!1, s(s(elem!1)))) | (~b(s(z), elem!1)) | (~b(s(s(s(s(s(s(s(s(elem!1)))))))), elem!1)) | (~b(s(s(s(s(s(s(s(s(elem!1)))))))), s(z)))),
% 3.03/3.28 inference(modus_ponens,[status(thm)],[13203, 13202])).
% 3.03/3.28 tff(13205,plain,
% 3.03/3.28 (~b(s(s(s(s(s(s(s(s(elem!1)))))))), s(z))),
% 3.03/3.28 inference(unit_resolution,[status(thm)],[13204, 166, 786, 642, 10960, 13198])).
% 3.03/3.28 tff(13206,assumption,(~(s(s(s(s(s(s(s(s(elem!1)))))))) = s(z))), introduced(assumption)).
% 3.03/3.28 tff(13207,plain,
% 3.03/3.28 (((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((s(s(s(s(s(s(s(s(elem!1)))))))) = s(z)) | b(s(s(s(s(s(s(s(s(elem!1)))))))), s(z)) | r(s(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(s(elem!1)))))))) = s(z)) | b(s(s(s(s(s(s(s(s(elem!1)))))))), s(z)) | r(s(s(s(s(s(s(s(s(elem!1)))))))), s(z)))),
% 3.03/3.28 inference(rewrite,[status(thm)],[])).
% 3.03/3.28 tff(13208,plain,
% 3.03/3.28 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((s(s(s(s(s(s(s(s(elem!1)))))))) = s(z)) | b(s(s(s(s(s(s(s(s(elem!1)))))))), s(z)) | r(s(s(s(s(s(s(s(s(elem!1)))))))), s(z)))),
% 3.03/3.28 inference(quant_inst,[status(thm)],[])).
% 3.03/3.28 tff(13209,plain,
% 3.03/3.28 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (s(s(s(s(s(s(s(s(elem!1)))))))) = s(z)) | b(s(s(s(s(s(s(s(s(elem!1)))))))), s(z)) | r(s(s(s(s(s(s(s(s(elem!1)))))))), s(z))),
% 3.03/3.28 inference(modus_ponens,[status(thm)],[13208, 13207])).
% 3.03/3.28 tff(13210,plain,
% 3.03/3.28 (r(s(s(s(s(s(s(s(s(elem!1)))))))), s(z))),
% 3.03/3.28 inference(unit_resolution,[status(thm)],[13209, 79, 13206, 13205])).
% 3.03/3.28 tff(13211,plain,
% 3.03/3.28 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), elem!1)) | (~b(elem!1, s(s(elem!1)))) | (~b(s(s(s(s(s(s(s(s(elem!1)))))))), elem!1)) | (~b(s(s(s(s(s(s(s(s(elem!1)))))))), s(s(elem!1)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(elem!1)), elem!1)) | (~b(elem!1, s(s(elem!1)))) | (~b(s(s(s(s(s(s(s(s(elem!1)))))))), elem!1)) | (~b(s(s(s(s(s(s(s(s(elem!1)))))))), s(s(elem!1)))))),
% 3.03/3.28 inference(rewrite,[status(thm)],[])).
% 3.03/3.28 tff(13212,plain,
% 3.03/3.28 (((~b(s(s(elem!1)), elem!1)) | (~b(s(s(s(s(s(s(s(s(elem!1)))))))), elem!1)) | (~b(elem!1, s(s(elem!1)))) | (~b(s(s(elem!1)), elem!1)) | (~b(s(s(s(s(s(s(s(s(elem!1)))))))), elem!1)) | (~b(s(s(s(s(s(s(s(s(elem!1)))))))), s(s(elem!1))))) <=> ((~b(s(s(elem!1)), elem!1)) | (~b(elem!1, s(s(elem!1)))) | (~b(s(s(s(s(s(s(s(s(elem!1)))))))), elem!1)) | (~b(s(s(s(s(s(s(s(s(elem!1)))))))), s(s(elem!1)))))),
% 3.03/3.28 inference(rewrite,[status(thm)],[])).
% 3.03/3.28 tff(13213,plain,
% 3.03/3.28 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), elem!1)) | (~b(s(s(s(s(s(s(s(s(elem!1)))))))), elem!1)) | (~b(elem!1, s(s(elem!1)))) | (~b(s(s(elem!1)), elem!1)) | (~b(s(s(s(s(s(s(s(s(elem!1)))))))), elem!1)) | (~b(s(s(s(s(s(s(s(s(elem!1)))))))), s(s(elem!1)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), elem!1)) | (~b(elem!1, s(s(elem!1)))) | (~b(s(s(s(s(s(s(s(s(elem!1)))))))), elem!1)) | (~b(s(s(s(s(s(s(s(s(elem!1)))))))), s(s(elem!1))))))),
% 3.03/3.28 inference(monotonicity,[status(thm)],[13212])).
% 3.03/3.28 tff(13214,plain,
% 3.03/3.28 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), elem!1)) | (~b(s(s(s(s(s(s(s(s(elem!1)))))))), elem!1)) | (~b(elem!1, s(s(elem!1)))) | (~b(s(s(elem!1)), elem!1)) | (~b(s(s(s(s(s(s(s(s(elem!1)))))))), elem!1)) | (~b(s(s(s(s(s(s(s(s(elem!1)))))))), s(s(elem!1)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(elem!1)), elem!1)) | (~b(elem!1, s(s(elem!1)))) | (~b(s(s(s(s(s(s(s(s(elem!1)))))))), elem!1)) | (~b(s(s(s(s(s(s(s(s(elem!1)))))))), s(s(elem!1)))))),
% 3.03/3.28 inference(transitivity,[status(thm)],[13213, 13211])).
% 3.03/3.28 tff(13215,plain,
% 3.03/3.28 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), elem!1)) | (~b(s(s(s(s(s(s(s(s(elem!1)))))))), elem!1)) | (~b(elem!1, s(s(elem!1)))) | (~b(s(s(elem!1)), elem!1)) | (~b(s(s(s(s(s(s(s(s(elem!1)))))))), elem!1)) | (~b(s(s(s(s(s(s(s(s(elem!1)))))))), s(s(elem!1)))))),
% 3.03/3.28 inference(quant_inst,[status(thm)],[])).
% 3.03/3.28 tff(13216,plain,
% 3.03/3.28 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(elem!1)), elem!1)) | (~b(elem!1, s(s(elem!1)))) | (~b(s(s(s(s(s(s(s(s(elem!1)))))))), elem!1)) | (~b(s(s(s(s(s(s(s(s(elem!1)))))))), s(s(elem!1))))),
% 3.03/3.28 inference(modus_ponens,[status(thm)],[13215, 13214])).
% 3.03/3.28 tff(13217,plain,
% 3.03/3.28 (~b(s(s(s(s(s(s(s(s(elem!1)))))))), s(s(elem!1)))),
% 3.03/3.28 inference(unit_resolution,[status(thm)],[13216, 166, 786, 10960, 13198])).
% 3.03/3.28 tff(13218,assumption,(~(s(s(s(s(s(s(s(s(elem!1)))))))) = s(s(elem!1)))), introduced(assumption)).
% 3.03/3.28 tff(13219,plain,
% 3.03/3.28 (((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((s(s(s(s(s(s(s(s(elem!1)))))))) = s(s(elem!1))) | b(s(s(s(s(s(s(s(s(elem!1)))))))), s(s(elem!1))) | r(s(s(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(s(s(elem!1)))))))) = s(s(elem!1))) | b(s(s(s(s(s(s(s(s(elem!1)))))))), s(s(elem!1))) | r(s(s(s(s(s(s(s(s(elem!1)))))))), s(s(elem!1))))),
% 3.03/3.28 inference(rewrite,[status(thm)],[])).
% 3.03/3.28 tff(13220,plain,
% 3.03/3.28 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((s(s(s(s(s(s(s(s(elem!1)))))))) = s(s(elem!1))) | b(s(s(s(s(s(s(s(s(elem!1)))))))), s(s(elem!1))) | r(s(s(s(s(s(s(s(s(elem!1)))))))), s(s(elem!1))))),
% 3.03/3.28 inference(quant_inst,[status(thm)],[])).
% 3.03/3.28 tff(13221,plain,
% 3.03/3.28 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (s(s(s(s(s(s(s(s(elem!1)))))))) = s(s(elem!1))) | b(s(s(s(s(s(s(s(s(elem!1)))))))), s(s(elem!1))) | r(s(s(s(s(s(s(s(s(elem!1)))))))), s(s(elem!1)))),
% 3.03/3.28 inference(modus_ponens,[status(thm)],[13220, 13219])).
% 3.03/3.28 tff(13222,plain,
% 3.03/3.28 (r(s(s(s(s(s(s(s(s(elem!1)))))))), s(s(elem!1)))),
% 3.03/3.28 inference(unit_resolution,[status(thm)],[13221, 79, 13218, 13217])).
% 3.03/3.28 tff(13223,plain,
% 3.03/3.28 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(s(elem!1)))) | (~r(s(s(elem!1)), s(z))) | (~r(s(s(s(s(s(s(s(s(elem!1)))))))), s(z))) | (~r(s(s(s(s(s(s(s(s(elem!1)))))))), s(s(elem!1)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(z), s(s(elem!1)))) | (~r(s(s(elem!1)), s(z))) | (~r(s(s(s(s(s(s(s(s(elem!1)))))))), s(z))) | (~r(s(s(s(s(s(s(s(s(elem!1)))))))), s(s(elem!1)))))),
% 3.03/3.28 inference(rewrite,[status(thm)],[])).
% 3.03/3.28 tff(13224,plain,
% 3.03/3.28 (((~r(s(s(elem!1)), s(z))) | (~r(s(z), s(s(elem!1)))) | (~r(s(s(s(s(s(s(s(s(elem!1)))))))), s(s(elem!1)))) | (~r(s(s(s(s(s(s(s(s(elem!1)))))))), s(z)))) <=> ((~r(s(z), s(s(elem!1)))) | (~r(s(s(elem!1)), s(z))) | (~r(s(s(s(s(s(s(s(s(elem!1)))))))), s(z))) | (~r(s(s(s(s(s(s(s(s(elem!1)))))))), s(s(elem!1)))))),
% 3.03/3.28 inference(rewrite,[status(thm)],[])).
% 3.03/3.28 tff(13225,plain,
% 3.03/3.28 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(elem!1)), s(z))) | (~r(s(z), s(s(elem!1)))) | (~r(s(s(s(s(s(s(s(s(elem!1)))))))), s(s(elem!1)))) | (~r(s(s(s(s(s(s(s(s(elem!1)))))))), s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(s(elem!1)))) | (~r(s(s(elem!1)), s(z))) | (~r(s(s(s(s(s(s(s(s(elem!1)))))))), s(z))) | (~r(s(s(s(s(s(s(s(s(elem!1)))))))), s(s(elem!1))))))),
% 3.03/3.28 inference(monotonicity,[status(thm)],[13224])).
% 3.03/3.28 tff(13226,plain,
% 3.03/3.28 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(elem!1)), s(z))) | (~r(s(z), s(s(elem!1)))) | (~r(s(s(s(s(s(s(s(s(elem!1)))))))), s(s(elem!1)))) | (~r(s(s(s(s(s(s(s(s(elem!1)))))))), s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(z), s(s(elem!1)))) | (~r(s(s(elem!1)), s(z))) | (~r(s(s(s(s(s(s(s(s(elem!1)))))))), s(z))) | (~r(s(s(s(s(s(s(s(s(elem!1)))))))), s(s(elem!1)))))),
% 3.03/3.28 inference(transitivity,[status(thm)],[13225, 13223])).
% 3.03/3.28 tff(13227,plain,
% 3.03/3.28 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(elem!1)), s(z))) | (~r(s(z), s(s(elem!1)))) | (~r(s(s(s(s(s(s(s(s(elem!1)))))))), s(s(elem!1)))) | (~r(s(s(s(s(s(s(s(s(elem!1)))))))), s(z))))),
% 3.03/3.28 inference(quant_inst,[status(thm)],[])).
% 3.03/3.28 tff(13228,plain,
% 3.03/3.28 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(z), s(s(elem!1)))) | (~r(s(s(elem!1)), s(z))) | (~r(s(s(s(s(s(s(s(s(elem!1)))))))), s(z))) | (~r(s(s(s(s(s(s(s(s(elem!1)))))))), s(s(elem!1))))),
% 3.03/3.28 inference(modus_ponens,[status(thm)],[13227, 13226])).
% 3.03/3.28 tff(13229,plain,
% 3.03/3.28 ($false),
% 3.03/3.28 inference(unit_resolution,[status(thm)],[13228, 197, 311, 4577, 13222, 13210])).
% 3.03/3.28 tff(13230,plain,((~b(s(s(s(s(s(s(s(s(elem!1)))))))), elem!1)) | (~r(s(z), s(s(elem!1)))) | (~r(s(s(elem!1)), s(z))) | (s(s(s(s(s(s(s(s(elem!1)))))))) = s(z)) | (s(s(s(s(s(s(s(s(elem!1)))))))) = s(s(elem!1))) | (~b(s(s(elem!1)), elem!1)) | (~b(s(z), elem!1)) | (~b(elem!1, s(s(elem!1))))), inference(lemma,lemma(discharge,[]))).
% 3.03/3.28 tff(13231,plain,
% 3.03/3.28 (~b(s(s(s(s(s(s(s(s(elem!1)))))))), elem!1)),
% 3.03/3.28 inference(unit_resolution,[status(thm)],[13230, 13137, 311, 13197, 13190, 13182, 13127, 13125])).
% 3.03/3.28 tff(13232,plain,
% 3.03/3.28 (((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((s(s(s(s(s(s(s(s(elem!1)))))))) = elem!1) | b(s(s(s(s(s(s(s(s(elem!1)))))))), elem!1) | r(s(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(s(elem!1)))))))) = elem!1) | b(s(s(s(s(s(s(s(s(elem!1)))))))), elem!1) | r(s(s(s(s(s(s(s(s(elem!1)))))))), elem!1))),
% 3.03/3.28 inference(rewrite,[status(thm)],[])).
% 3.03/3.28 tff(13233,plain,
% 3.03/3.28 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((s(s(s(s(s(s(s(s(elem!1)))))))) = elem!1) | b(s(s(s(s(s(s(s(s(elem!1)))))))), elem!1) | r(s(s(s(s(s(s(s(s(elem!1)))))))), elem!1))),
% 3.03/3.28 inference(quant_inst,[status(thm)],[])).
% 3.03/3.28 tff(13234,plain,
% 3.03/3.28 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (s(s(s(s(s(s(s(s(elem!1)))))))) = elem!1) | b(s(s(s(s(s(s(s(s(elem!1)))))))), elem!1) | r(s(s(s(s(s(s(s(s(elem!1)))))))), elem!1)),
% 3.03/3.28 inference(modus_ponens,[status(thm)],[13233, 13232])).
% 3.03/3.28 tff(13235,plain,
% 3.03/3.28 ((s(s(s(s(s(s(s(s(elem!1)))))))) = elem!1) | b(s(s(s(s(s(s(s(s(elem!1)))))))), elem!1) | r(s(s(s(s(s(s(s(s(elem!1)))))))), elem!1)),
% 3.03/3.28 inference(unit_resolution,[status(thm)],[13234, 79])).
% 3.03/3.28 tff(13236,plain,
% 3.03/3.28 (r(s(s(s(s(s(s(s(s(elem!1)))))))), elem!1)),
% 3.03/3.28 inference(unit_resolution,[status(thm)],[13235, 13231, 13120])).
% 3.03/3.28 tff(13237,plain,
% 3.03/3.28 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), elem!1)) | (~r(s(s(s(s(s(s(s(s(elem!1)))))))), elem!1)) | (~r(s(s(s(s(s(s(s(s(elem!1)))))))), s(s(s(elem!1))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(elem!1, s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), elem!1)) | (~r(s(s(s(s(s(s(s(s(elem!1)))))))), elem!1)) | (~r(s(s(s(s(s(s(s(s(elem!1)))))))), s(s(s(elem!1))))))),
% 3.03/3.28 inference(rewrite,[status(thm)],[])).
% 3.03/3.28 tff(13238,plain,
% 3.03/3.28 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), elem!1)) | (~r(s(s(s(s(s(s(s(s(elem!1)))))))), elem!1)) | (~r(s(s(s(s(s(s(s(s(elem!1)))))))), s(s(s(elem!1))))))),
% 3.03/3.28 inference(quant_inst,[status(thm)],[])).
% 3.03/3.28 tff(13239,plain,
% 3.03/3.28 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(elem!1, s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), elem!1)) | (~r(s(s(s(s(s(s(s(s(elem!1)))))))), elem!1)) | (~r(s(s(s(s(s(s(s(s(elem!1)))))))), s(s(s(elem!1)))))),
% 3.03/3.28 inference(modus_ponens,[status(thm)],[13238, 13237])).
% 3.03/3.28 tff(13240,plain,
% 3.03/3.28 (~r(s(s(s(s(s(s(s(s(elem!1)))))))), s(s(s(elem!1))))),
% 3.03/3.28 inference(unit_resolution,[status(thm)],[13239, 197, 13168, 13236, 13115])).
% 3.03/3.28 tff(13241,plain,
% 3.03/3.28 (((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((s(s(s(s(s(s(s(s(elem!1)))))))) = s(s(s(elem!1)))) | b(s(s(s(s(s(s(s(s(elem!1)))))))), s(s(s(elem!1)))) | r(s(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(s(elem!1)))))))) = s(s(s(elem!1)))) | b(s(s(s(s(s(s(s(s(elem!1)))))))), s(s(s(elem!1)))) | r(s(s(s(s(s(s(s(s(elem!1)))))))), s(s(s(elem!1)))))),
% 3.03/3.28 inference(rewrite,[status(thm)],[])).
% 3.03/3.28 tff(13242,plain,
% 3.03/3.28 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((s(s(s(s(s(s(s(s(elem!1)))))))) = s(s(s(elem!1)))) | b(s(s(s(s(s(s(s(s(elem!1)))))))), s(s(s(elem!1)))) | r(s(s(s(s(s(s(s(s(elem!1)))))))), s(s(s(elem!1)))))),
% 3.03/3.28 inference(quant_inst,[status(thm)],[])).
% 3.03/3.28 tff(13243,plain,
% 3.03/3.28 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (s(s(s(s(s(s(s(s(elem!1)))))))) = s(s(s(elem!1)))) | b(s(s(s(s(s(s(s(s(elem!1)))))))), s(s(s(elem!1)))) | r(s(s(s(s(s(s(s(s(elem!1)))))))), s(s(s(elem!1))))),
% 3.03/3.28 inference(modus_ponens,[status(thm)],[13242, 13241])).
% 3.03/3.28 tff(13244,plain,
% 3.03/3.28 ((s(s(s(s(s(s(s(s(elem!1)))))))) = s(s(s(elem!1)))) | b(s(s(s(s(s(s(s(s(elem!1)))))))), s(s(s(elem!1))))),
% 3.03/3.28 inference(unit_resolution,[status(thm)],[13243, 79, 13240])).
% 3.03/3.28 tff(13245,plain,
% 3.03/3.28 (b(s(s(s(s(s(s(s(s(elem!1)))))))), s(s(s(elem!1))))),
% 3.03/3.28 inference(unit_resolution,[status(thm)],[13244, 13112])).
% 3.03/3.28 tff(13246,plain,
% 3.03/3.28 (b(s(s(s(s(elem!1)))), s(s(s(elem!1))))),
% 3.03/3.28 inference(unit_resolution,[status(thm)],[1065, 13169, 364])).
% 3.03/3.28 tff(13247,plain,
% 3.03/3.28 (~r(s(s(s(elem!1))), s(s(elem!1)))),
% 3.03/3.28 inference(unit_resolution,[status(thm)],[3454, 13103, 13087])).
% 3.03/3.28 tff(13248,plain,
% 3.03/3.28 (b(s(s(s(elem!1))), s(s(elem!1)))),
% 3.03/3.28 inference(unit_resolution,[status(thm)],[889, 13247, 51])).
% 3.03/3.28 tff(13249,plain,
% 3.03/3.28 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~b(s(s(s(s(s(s(s(s(elem!1)))))))), s(s(s(elem!1))))) | (~b(s(s(s(s(elem!1)))), s(s(s(s(s(s(s(s(elem!1)))))))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~b(s(s(s(s(s(s(s(s(elem!1)))))))), s(s(s(elem!1))))) | (~b(s(s(s(s(elem!1)))), s(s(s(s(s(s(s(s(elem!1)))))))))))),
% 3.03/3.28 inference(rewrite,[status(thm)],[])).
% 3.03/3.28 tff(13250,plain,
% 3.03/3.28 (((~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(s(s(s(s(s(s(s(elem!1)))))))), s(s(s(elem!1))))) | (~b(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~b(s(s(s(s(elem!1)))), s(s(s(s(s(s(s(s(elem!1))))))))))) <=> ((~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~b(s(s(s(s(s(s(s(s(elem!1)))))))), s(s(s(elem!1))))) | (~b(s(s(s(s(elem!1)))), s(s(s(s(s(s(s(s(elem!1)))))))))))),
% 3.03/3.28 inference(rewrite,[status(thm)],[])).
% 3.03/3.28 tff(13251,plain,
% 3.03/3.28 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(s(s(s(s(s(s(s(elem!1)))))))), s(s(s(elem!1))))) | (~b(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~b(s(s(s(s(elem!1)))), s(s(s(s(s(s(s(s(elem!1)))))))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~b(s(s(s(s(s(s(s(s(elem!1)))))))), s(s(s(elem!1))))) | (~b(s(s(s(s(elem!1)))), s(s(s(s(s(s(s(s(elem!1))))))))))))),
% 3.03/3.28 inference(monotonicity,[status(thm)],[13250])).
% 3.03/3.28 tff(13252,plain,
% 3.03/3.28 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(s(s(s(s(s(s(s(elem!1)))))))), s(s(s(elem!1))))) | (~b(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~b(s(s(s(s(elem!1)))), s(s(s(s(s(s(s(s(elem!1)))))))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~b(s(s(s(s(s(s(s(s(elem!1)))))))), s(s(s(elem!1))))) | (~b(s(s(s(s(elem!1)))), s(s(s(s(s(s(s(s(elem!1)))))))))))),
% 3.03/3.28 inference(transitivity,[status(thm)],[13251, 13249])).
% 3.03/3.28 tff(13253,plain,
% 3.03/3.28 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(s(s(s(s(s(s(s(elem!1)))))))), s(s(s(elem!1))))) | (~b(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~b(s(s(s(s(elem!1)))), s(s(s(s(s(s(s(s(elem!1)))))))))))),
% 3.03/3.28 inference(quant_inst,[status(thm)],[])).
% 3.03/3.28 tff(13254,plain,
% 3.03/3.28 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~b(s(s(s(s(s(s(s(s(elem!1)))))))), s(s(s(elem!1))))) | (~b(s(s(s(s(elem!1)))), s(s(s(s(s(s(s(s(elem!1))))))))))),
% 3.03/3.28 inference(modus_ponens,[status(thm)],[13253, 13252])).
% 3.03/3.28 tff(13255,plain,
% 3.03/3.28 (~b(s(s(s(s(elem!1)))), s(s(s(s(s(s(s(s(elem!1)))))))))),
% 3.03/3.28 inference(unit_resolution,[status(thm)],[13254, 166, 13092, 13248, 13246, 13245])).
% 3.03/3.28 tff(13256,plain,
% 3.03/3.28 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(s(s(elem!1))))) | (~r(s(s(s(s(elem!1)))), elem!1)) | (~r(s(s(s(s(s(s(s(s(elem!1)))))))), elem!1)) | (~r(s(s(s(s(elem!1)))), s(s(s(s(s(s(s(s(elem!1)))))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(elem!1, s(s(s(elem!1))))) | (~r(s(s(s(s(elem!1)))), elem!1)) | (~r(s(s(s(s(s(s(s(s(elem!1)))))))), elem!1)) | (~r(s(s(s(s(elem!1)))), s(s(s(s(s(s(s(s(elem!1)))))))))))),
% 3.03/3.29 inference(rewrite,[status(thm)],[])).
% 3.03/3.29 tff(13257,plain,
% 3.03/3.29 (((~r(elem!1, s(s(s(elem!1))))) | (~r(s(s(s(s(s(s(s(s(elem!1)))))))), elem!1)) | (~r(s(s(s(s(elem!1)))), elem!1)) | (~r(s(s(s(s(elem!1)))), s(s(s(s(s(s(s(s(elem!1))))))))))) <=> ((~r(elem!1, s(s(s(elem!1))))) | (~r(s(s(s(s(elem!1)))), elem!1)) | (~r(s(s(s(s(s(s(s(s(elem!1)))))))), elem!1)) | (~r(s(s(s(s(elem!1)))), s(s(s(s(s(s(s(s(elem!1)))))))))))),
% 3.03/3.29 inference(rewrite,[status(thm)],[])).
% 3.03/3.29 tff(13258,plain,
% 3.03/3.29 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(s(s(elem!1))))) | (~r(s(s(s(s(s(s(s(s(elem!1)))))))), elem!1)) | (~r(s(s(s(s(elem!1)))), elem!1)) | (~r(s(s(s(s(elem!1)))), s(s(s(s(s(s(s(s(elem!1)))))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(s(s(elem!1))))) | (~r(s(s(s(s(elem!1)))), elem!1)) | (~r(s(s(s(s(s(s(s(s(elem!1)))))))), elem!1)) | (~r(s(s(s(s(elem!1)))), s(s(s(s(s(s(s(s(elem!1))))))))))))),
% 3.03/3.29 inference(monotonicity,[status(thm)],[13257])).
% 3.03/3.29 tff(13259,plain,
% 3.03/3.29 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(s(s(elem!1))))) | (~r(s(s(s(s(s(s(s(s(elem!1)))))))), elem!1)) | (~r(s(s(s(s(elem!1)))), elem!1)) | (~r(s(s(s(s(elem!1)))), s(s(s(s(s(s(s(s(elem!1)))))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(elem!1, s(s(s(elem!1))))) | (~r(s(s(s(s(elem!1)))), elem!1)) | (~r(s(s(s(s(s(s(s(s(elem!1)))))))), elem!1)) | (~r(s(s(s(s(elem!1)))), s(s(s(s(s(s(s(s(elem!1)))))))))))),
% 3.03/3.29 inference(transitivity,[status(thm)],[13258, 13256])).
% 3.03/3.29 tff(13260,plain,
% 3.03/3.29 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(s(s(elem!1))))) | (~r(s(s(s(s(s(s(s(s(elem!1)))))))), elem!1)) | (~r(s(s(s(s(elem!1)))), elem!1)) | (~r(s(s(s(s(elem!1)))), s(s(s(s(s(s(s(s(elem!1)))))))))))),
% 3.03/3.29 inference(quant_inst,[status(thm)],[])).
% 3.03/3.29 tff(13261,plain,
% 3.03/3.29 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(elem!1, s(s(s(elem!1))))) | (~r(s(s(s(s(elem!1)))), elem!1)) | (~r(s(s(s(s(s(s(s(s(elem!1)))))))), elem!1)) | (~r(s(s(s(s(elem!1)))), s(s(s(s(s(s(s(s(elem!1))))))))))),
% 3.03/3.29 inference(modus_ponens,[status(thm)],[13260, 13259])).
% 3.03/3.29 tff(13262,plain,
% 3.03/3.29 (~r(s(s(s(s(elem!1)))), s(s(s(s(s(s(s(s(elem!1)))))))))),
% 3.03/3.29 inference(unit_resolution,[status(thm)],[13261, 197, 13168, 13236, 13152])).
% 3.03/3.29 tff(13263,plain,
% 3.03/3.29 (((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((s(s(s(s(elem!1)))) = s(s(s(s(s(s(s(s(elem!1))))))))) | b(s(s(s(s(elem!1)))), s(s(s(s(s(s(s(s(elem!1))))))))) | r(s(s(s(s(elem!1)))), s(s(s(s(s(s(s(s(elem!1))))))))))) <=> ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (s(s(s(s(elem!1)))) = s(s(s(s(s(s(s(s(elem!1))))))))) | b(s(s(s(s(elem!1)))), s(s(s(s(s(s(s(s(elem!1))))))))) | r(s(s(s(s(elem!1)))), s(s(s(s(s(s(s(s(elem!1))))))))))),
% 3.03/3.29 inference(rewrite,[status(thm)],[])).
% 3.03/3.29 tff(13264,plain,
% 3.03/3.29 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((s(s(s(s(elem!1)))) = s(s(s(s(s(s(s(s(elem!1))))))))) | b(s(s(s(s(elem!1)))), s(s(s(s(s(s(s(s(elem!1))))))))) | r(s(s(s(s(elem!1)))), s(s(s(s(s(s(s(s(elem!1))))))))))),
% 3.03/3.29 inference(quant_inst,[status(thm)],[])).
% 3.03/3.29 tff(13265,plain,
% 3.03/3.29 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (s(s(s(s(elem!1)))) = s(s(s(s(s(s(s(s(elem!1))))))))) | b(s(s(s(s(elem!1)))), s(s(s(s(s(s(s(s(elem!1))))))))) | r(s(s(s(s(elem!1)))), s(s(s(s(s(s(s(s(elem!1)))))))))),
% 3.03/3.29 inference(modus_ponens,[status(thm)],[13264, 13263])).
% 3.03/3.29 tff(13266,plain,
% 3.03/3.29 ((s(s(s(s(elem!1)))) = s(s(s(s(s(s(s(s(elem!1))))))))) | b(s(s(s(s(elem!1)))), s(s(s(s(s(s(s(s(elem!1)))))))))),
% 3.03/3.29 inference(unit_resolution,[status(thm)],[13265, 79, 13262])).
% 3.03/3.29 tff(13267,plain,
% 3.03/3.29 (s(s(s(s(elem!1)))) = s(s(s(s(s(s(s(s(elem!1))))))))),
% 3.03/3.29 inference(unit_resolution,[status(thm)],[13266, 13255])).
% 3.03/3.29 tff(13268,plain,
% 3.03/3.29 (s(s(s(s(s(s(s(s(elem!1)))))))) = s(s(s(s(elem!1))))),
% 3.03/3.29 inference(symmetry,[status(thm)],[13267])).
% 3.03/3.29 tff(13269,plain,
% 3.03/3.29 (inj_0(s(s(s(s(s(s(s(s(elem!1))))))))) = inj_0(s(s(s(s(elem!1)))))),
% 3.03/3.29 inference(monotonicity,[status(thm)],[13268])).
% 3.03/3.29 tff(13270,plain,
% 3.03/3.29 (inj_0(s(s(s(s(elem!1))))) = inj_0(s(s(s(s(s(s(s(s(elem!1)))))))))),
% 3.03/3.29 inference(symmetry,[status(thm)],[13269])).
% 3.03/3.29 tff(13271,plain,
% 3.03/3.29 (s(s(s(z))) = s(s(s(s(s(s(s(elem!1)))))))),
% 3.03/3.29 inference(transitivity,[status(thm)],[13153, 653, 13270, 10])).
% 3.03/3.29 tff(13272,plain,
% 3.03/3.29 (s(s(elem!1)) = s(s(z))),
% 3.03/3.29 inference(unit_resolution,[status(thm)],[17, 13114])).
% 3.03/3.29 tff(13273,plain,
% 3.03/3.29 (~(s(s(s(s(s(s(elem!1)))))) = s(s(elem!1)))),
% 3.03/3.29 inference(unit_resolution,[status(thm)],[4986, 13113])).
% 3.03/3.29 tff(13274,plain,
% 3.03/3.29 (~(s(s(s(z))) = s(s(s(s(s(s(s(elem!1))))))))),
% 3.03/3.29 inference(unit_resolution,[status(thm)],[4995, 13273, 13272])).
% 3.03/3.29 tff(13275,plain,
% 3.03/3.29 ($false),
% 3.03/3.29 inference(unit_resolution,[status(thm)],[13274, 13271])).
% 3.03/3.29 tff(13276,plain,((~r(s(s(s(elem!1))), s(z))) | (~r(s(z), s(s(elem!1)))) | (~r(z, s(s(s(elem!1))))) | (~b(z, s(z))) | (~b(s(z), z)) | (~r(s(s(s(elem!1))), z)) | b(s(s(z)), s(z)) | (s(s(elem!1)) = s(s(s(elem!1)))) | (~r(s(z), s(s(s(elem!1)))))), inference(lemma,lemma(discharge,[]))).
% 3.03/3.29 tff(13277,plain,
% 3.03/3.29 (~r(s(s(s(elem!1))), s(z))),
% 3.03/3.29 inference(unit_resolution,[status(thm)],[13276, 282, 311, 118, 53, 154, 3936, 45, 119])).
% 3.03/3.29 tff(13278,plain,
% 3.03/3.29 (b(s(s(s(elem!1))), s(z))),
% 3.03/3.29 inference(unit_resolution,[status(thm)],[1849, 13277])).
% 3.03/3.29 tff(13279,plain,
% 3.03/3.29 (~b(s(s(elem!1)), s(z))),
% 3.03/3.29 inference(unit_resolution,[status(thm)],[4277, 13278, 118, 53, 45])).
% 3.03/3.29 tff(13280,plain,
% 3.03/3.29 (r(s(s(elem!1)), s(z))),
% 3.03/3.29 inference(unit_resolution,[status(thm)],[1912, 13279])).
% 3.03/3.29 tff(13281,plain,
% 3.03/3.29 (~r(s(s(z)), s(s(elem!1)))),
% 3.03/3.29 inference(unit_resolution,[status(thm)],[6892, 13280, 4143, 119])).
% 3.03/3.29 tff(13282,plain,
% 3.03/3.29 (~r(s(s(elem!1)), s(s(z)))),
% 3.03/3.29 inference(unit_resolution,[status(thm)],[4565, 197, 311, 13280, 4143])).
% 3.03/3.29 tff(13283,plain,
% 3.03/3.29 ($false),
% 3.03/3.29 inference(unit_resolution,[status(thm)],[5242, 197, 154, 282, 281, 866])).
% 3.03/3.29 tff(13284,plain,((~r(z, s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), z)) | (~r(s(s(z)), s(s(s(elem!1))))) | (~r(s(s(z)), z))), inference(lemma,lemma(discharge,[]))).
% 3.03/3.29 tff(13285,plain,
% 3.03/3.29 (~r(s(s(z)), z)),
% 3.03/3.29 inference(unit_resolution,[status(thm)],[13284, 281, 154, 282])).
% 3.03/3.29 tff(13286,plain,
% 3.03/3.29 (b(s(s(z)), z)),
% 3.03/3.29 inference(unit_resolution,[status(thm)],[186, 13285])).
% 3.03/3.29 tff(13287,plain,
% 3.03/3.29 (~r(s(z), s(s(z)))),
% 3.03/3.29 inference(unit_resolution,[status(thm)],[2304, 281, 154, 119])).
% 3.03/3.29 tff(13288,plain,
% 3.03/3.29 (b(s(z), s(s(z)))),
% 3.03/3.29 inference(unit_resolution,[status(thm)],[427, 13287])).
% 3.03/3.29 tff(13289,plain,
% 3.03/3.29 ($false),
% 3.03/3.29 inference(unit_resolution,[status(thm)],[12847, 13288, 13286, 53])).
% 3.03/3.29 tff(13290,plain,((~r(s(s(z)), s(s(s(elem!1))))) | (~b(s(z), z)) | (~r(s(s(s(elem!1))), z)) | (~r(s(z), s(s(s(elem!1))))) | (~r(z, s(s(s(elem!1)))))), inference(lemma,lemma(discharge,[]))).
% 3.03/3.29 tff(13291,plain,
% 3.03/3.29 (~r(s(s(z)), s(s(s(elem!1))))),
% 3.03/3.29 inference(unit_resolution,[status(thm)],[13290, 282, 154, 119, 53])).
% 3.03/3.29 tff(13292,plain,
% 3.03/3.29 (b(s(s(z)), s(s(s(elem!1))))),
% 3.03/3.29 inference(unit_resolution,[status(thm)],[279, 13291])).
% 3.03/3.29 tff(13293,plain,
% 3.03/3.29 (~r(s(s(elem!1)), s(s(s(elem!1))))),
% 3.03/3.29 inference(unit_resolution,[status(thm)],[5310, 13280, 154, 119])).
% 3.03/3.29 tff(13294,plain,
% 3.03/3.29 (b(s(s(elem!1)), s(s(s(elem!1))))),
% 3.03/3.29 inference(unit_resolution,[status(thm)],[461, 13293, 45])).
% 3.03/3.29 tff(13295,plain,
% 3.03/3.29 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(s(z), z)) | (~b(s(s(elem!1)), z)) | (~b(s(s(elem!1)), s(s(z)))) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(s(z)), s(s(s(elem!1))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(s(z), z)) | (~b(s(s(elem!1)), z)) | (~b(s(s(elem!1)), s(s(z)))) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(s(z)), s(s(s(elem!1))))))),
% 3.03/3.29 inference(rewrite,[status(thm)],[])).
% 3.03/3.29 tff(13296,plain,
% 3.03/3.29 (((~b(s(z), z)) | (~b(s(s(elem!1)), z)) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(s(z)), s(s(s(elem!1))))) | (~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(s(s(elem!1)), s(s(z))))) <=> ((~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(s(z), z)) | (~b(s(s(elem!1)), z)) | (~b(s(s(elem!1)), s(s(z)))) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(s(z)), s(s(s(elem!1))))))),
% 3.03/3.29 inference(rewrite,[status(thm)],[])).
% 3.03/3.29 tff(13297,plain,
% 3.03/3.29 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), z)) | (~b(s(s(elem!1)), z)) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(s(z)), s(s(s(elem!1))))) | (~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(s(s(elem!1)), s(s(z)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(s(z), z)) | (~b(s(s(elem!1)), z)) | (~b(s(s(elem!1)), s(s(z)))) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(s(z)), s(s(s(elem!1)))))))),
% 3.03/3.29 inference(monotonicity,[status(thm)],[13296])).
% 3.03/3.29 tff(13298,plain,
% 3.03/3.29 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), z)) | (~b(s(s(elem!1)), z)) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(s(z)), s(s(s(elem!1))))) | (~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(s(s(elem!1)), s(s(z)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(s(z), z)) | (~b(s(s(elem!1)), z)) | (~b(s(s(elem!1)), s(s(z)))) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(s(z)), s(s(s(elem!1))))))),
% 3.03/3.29 inference(transitivity,[status(thm)],[13297, 13295])).
% 3.03/3.29 tff(13299,plain,
% 3.03/3.29 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), z)) | (~b(s(s(elem!1)), z)) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(s(z)), s(s(s(elem!1))))) | (~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(s(s(elem!1)), s(s(z)))))),
% 3.03/3.29 inference(quant_inst,[status(thm)],[])).
% 3.03/3.29 tff(13300,plain,
% 3.03/3.29 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(s(z), z)) | (~b(s(s(elem!1)), z)) | (~b(s(s(elem!1)), s(s(z)))) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(s(z)), s(s(s(elem!1)))))),
% 3.03/3.29 inference(modus_ponens,[status(thm)],[13299, 13298])).
% 3.03/3.29 tff(13301,plain,
% 3.03/3.29 ($false),
% 3.03/3.29 inference(unit_resolution,[status(thm)],[13300, 166, 463, 53, 405, 96, 592, 263])).
% 3.03/3.29 tff(13302,plain,((~b(s(s(s(elem!1))), s(z))) | (~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(s(z), z)) | (~b(s(s(elem!1)), s(s(z)))) | (~b(s(s(elem!1)), z)) | (~b(s(s(z)), s(s(s(elem!1)))))), inference(lemma,lemma(discharge,[]))).
% 3.03/3.29 tff(13303,plain,
% 3.03/3.29 (~b(s(s(elem!1)), z)),
% 3.03/3.29 inference(unit_resolution,[status(thm)],[13302, 3964, 96, 53, 463, 263])).
% 3.03/3.29 tff(13304,plain,
% 3.03/3.29 (r(s(s(elem!1)), z)),
% 3.03/3.29 inference(unit_resolution,[status(thm)],[608, 13303])).
% 3.03/3.29 tff(13305,plain,
% 3.03/3.29 ((~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(z, s(s(elem!1)))) | (~b(s(s(s(elem!1))), s(z))) | (~b(z, s(z))) | (~b(s(s(z)), s(s(elem!1))))),
% 3.03/3.29 inference(unit_resolution,[status(thm)],[10592, 10450])).
% 3.03/3.29 tff(13306,plain,
% 3.03/3.29 (~b(z, s(s(elem!1)))),
% 3.03/3.29 inference(unit_resolution,[status(thm)],[13305, 2516, 96, 118, 463])).
% 3.03/3.29 tff(13307,plain,
% 3.03/3.29 (r(z, s(s(elem!1)))),
% 3.03/3.29 inference(unit_resolution,[status(thm)],[1795, 13306])).
% 3.03/3.29 tff(13308,plain,
% 3.03/3.29 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(elem!1)))) | (~r(s(s(elem!1)), z)) | (~r(s(s(s(elem!1))), z)) | (~r(s(s(s(elem!1))), s(s(elem!1)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, s(s(elem!1)))) | (~r(s(s(elem!1)), z)) | (~r(s(s(s(elem!1))), z)) | (~r(s(s(s(elem!1))), s(s(elem!1)))))),
% 3.03/3.29 inference(rewrite,[status(thm)],[])).
% 3.03/3.29 tff(13309,plain,
% 3.03/3.29 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(elem!1)))) | (~r(s(s(elem!1)), z)) | (~r(s(s(s(elem!1))), z)) | (~r(s(s(s(elem!1))), s(s(elem!1)))))),
% 3.03/3.29 inference(quant_inst,[status(thm)],[])).
% 3.03/3.29 tff(13310,plain,
% 3.03/3.29 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, s(s(elem!1)))) | (~r(s(s(elem!1)), z)) | (~r(s(s(s(elem!1))), z)) | (~r(s(s(s(elem!1))), s(s(elem!1))))),
% 3.03/3.29 inference(modus_ponens,[status(thm)],[13309, 13308])).
% 3.03/3.29 tff(13311,plain,
% 3.03/3.29 (~r(s(s(s(elem!1))), s(s(elem!1)))),
% 3.03/3.29 inference(unit_resolution,[status(thm)],[13310, 197, 154, 13307, 13304])).
% 3.03/3.29 tff(13312,plain,
% 3.03/3.29 (b(s(s(s(elem!1))), s(s(elem!1)))),
% 3.03/3.29 inference(unit_resolution,[status(thm)],[889, 13311, 1863])).
% 3.03/3.29 tff(13313,plain,
% 3.03/3.29 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(s(z)), s(s(elem!1)))) | (~b(s(s(z)), s(s(s(elem!1))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(s(z)), s(s(elem!1)))) | (~b(s(s(z)), s(s(s(elem!1))))))),
% 3.03/3.29 inference(rewrite,[status(thm)],[])).
% 3.03/3.29 tff(13314,plain,
% 3.03/3.29 (((~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(s(z)), s(s(elem!1)))) | (~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(s(z)), s(s(elem!1)))) | (~b(s(s(z)), s(s(s(elem!1)))))) <=> ((~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(s(z)), s(s(elem!1)))) | (~b(s(s(z)), s(s(s(elem!1))))))),
% 3.03/3.29 inference(rewrite,[status(thm)],[])).
% 3.03/3.29 tff(13315,plain,
% 3.03/3.29 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(s(z)), s(s(elem!1)))) | (~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(s(z)), s(s(elem!1)))) | (~b(s(s(z)), s(s(s(elem!1))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(s(z)), s(s(elem!1)))) | (~b(s(s(z)), s(s(s(elem!1)))))))),
% 3.03/3.29 inference(monotonicity,[status(thm)],[13314])).
% 3.03/3.29 tff(13316,plain,
% 3.03/3.29 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(s(z)), s(s(elem!1)))) | (~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(s(z)), s(s(elem!1)))) | (~b(s(s(z)), s(s(s(elem!1))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(s(z)), s(s(elem!1)))) | (~b(s(s(z)), s(s(s(elem!1))))))),
% 3.03/3.29 inference(transitivity,[status(thm)],[13315, 13313])).
% 3.03/3.29 tff(13317,plain,
% 3.03/3.29 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(s(z)), s(s(elem!1)))) | (~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(s(z)), s(s(elem!1)))) | (~b(s(s(z)), s(s(s(elem!1))))))),
% 3.03/3.29 inference(quant_inst,[status(thm)],[])).
% 3.03/3.29 tff(13318,plain,
% 3.03/3.29 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(s(z)), s(s(elem!1)))) | (~b(s(s(z)), s(s(s(elem!1)))))),
% 3.03/3.29 inference(modus_ponens,[status(thm)],[13317, 13316])).
% 3.03/3.29 tff(13319,plain,
% 3.03/3.29 ($false),
% 3.03/3.29 inference(unit_resolution,[status(thm)],[13318, 166, 463, 13312, 2516, 263])).
% 3.03/3.29 tff(13320,plain,((s(s(z)) = s(s(elem!1))) | (~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(s(s(z)), s(s(s(elem!1))))) | (s(s(s(elem!1))) = s(s(elem!1))) | (~r(s(s(s(elem!1))), z)) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(z), z)) | (~b(z, s(z))) | r(s(s(elem!1)), s(s(z))) | r(s(s(z)), s(s(elem!1)))), inference(lemma,lemma(discharge,[]))).
% 3.03/3.29 tff(13321,plain,
% 3.03/3.29 (s(s(z)) = s(s(elem!1))),
% 3.03/3.29 inference(unit_resolution,[status(thm)],[13320, 13294, 13292, 51, 154, 13278, 53, 118, 13282, 13281])).
% 3.03/3.29 tff(13322,plain,
% 3.03/3.29 (s(elem!1) = s(z)),
% 3.03/3.29 inference(unit_resolution,[status(thm)],[43, 13321])).
% 3.03/3.29 tff(13323,plain,
% 3.03/3.29 (z = elem!1),
% 3.03/3.29 inference(unit_resolution,[status(thm)],[30, 13322])).
% 3.03/3.29 tff(13324,plain,
% 3.03/3.29 (~(s(s(s(s(s(s(s(elem!1))))))) = elem!1)),
% 3.03/3.29 inference(unit_resolution,[status(thm)],[6283, 13323])).
% 3.03/3.29 tff(13325,plain,
% 3.03/3.29 (r(z, s(s(s(elem!1)))) <=> r(elem!1, s(s(s(elem!1))))),
% 3.03/3.29 inference(monotonicity,[status(thm)],[13323])).
% 3.03/3.29 tff(13326,plain,
% 3.03/3.29 (r(elem!1, s(s(s(elem!1))))),
% 3.03/3.29 inference(modus_ponens,[status(thm)],[282, 13325])).
% 3.03/3.29 tff(13327,plain,
% 3.03/3.29 (r(s(s(s(elem!1))), elem!1)),
% 3.03/3.29 inference(unit_resolution,[status(thm)],[966, 13323, 154])).
% 3.03/3.29 tff(13328,plain,
% 3.03/3.29 (elem!1 = z),
% 3.03/3.29 inference(symmetry,[status(thm)],[13323])).
% 3.03/3.29 tff(13329,plain,
% 3.03/3.29 ((s(s(elem!1)) = elem!1) <=> (s(s(elem!1)) = z)),
% 3.03/3.29 inference(monotonicity,[status(thm)],[13328])).
% 3.03/3.29 tff(13330,plain,
% 3.03/3.29 ((s(s(elem!1)) = z) <=> (s(s(elem!1)) = elem!1)),
% 3.03/3.29 inference(symmetry,[status(thm)],[13329])).
% 3.03/3.29 tff(13331,plain,
% 3.03/3.29 ((~(s(s(elem!1)) = z)) <=> (~(s(s(elem!1)) = elem!1))),
% 3.03/3.29 inference(monotonicity,[status(thm)],[13330])).
% 3.03/3.29 tff(13332,plain,
% 3.03/3.29 (~(s(s(elem!1)) = elem!1)),
% 3.03/3.29 inference(modus_ponens,[status(thm)],[108, 13331])).
% 3.03/3.29 tff(13333,plain,
% 3.03/3.29 (b(s(z), z) <=> b(s(z), elem!1)),
% 3.03/3.29 inference(monotonicity,[status(thm)],[13323])).
% 3.03/3.29 tff(13334,plain,
% 3.03/3.29 (b(s(z), elem!1)),
% 3.03/3.29 inference(modus_ponens,[status(thm)],[53, 13333])).
% 3.03/3.29 tff(13335,plain,
% 3.03/3.29 (b(elem!1, s(s(elem!1))) <=> b(z, s(s(elem!1)))),
% 3.03/3.29 inference(monotonicity,[status(thm)],[13328])).
% 3.03/3.29 tff(13336,plain,
% 3.03/3.29 (b(z, s(s(elem!1))) <=> b(elem!1, s(s(elem!1)))),
% 3.03/3.29 inference(symmetry,[status(thm)],[13335])).
% 3.03/3.29 tff(13337,plain,
% 3.03/3.29 (b(z, s(s(elem!1)))),
% 3.03/3.29 inference(unit_resolution,[status(thm)],[12671, 13321])).
% 3.03/3.29 tff(13338,plain,
% 3.03/3.29 (b(elem!1, s(s(elem!1)))),
% 3.03/3.29 inference(modus_ponens,[status(thm)],[13337, 13336])).
% 3.03/3.29 tff(13339,plain,
% 3.03/3.29 (~(s(s(s(s(s(s(s(s(elem!1)))))))) = s(s(elem!1)))),
% 3.03/3.29 inference(unit_resolution,[status(thm)],[13189, 13322])).
% 3.03/3.29 tff(13340,plain,
% 3.03/3.29 (~(s(s(s(s(s(s(s(s(elem!1)))))))) = s(z))),
% 3.03/3.29 inference(unit_resolution,[status(thm)],[13196, 13323])).
% 3.03/3.29 tff(13341,plain,
% 3.03/3.29 ((s(s(s(s(s(s(s(s(elem!1)))))))) = z) <=> (s(s(s(s(s(s(s(s(elem!1)))))))) = elem!1)),
% 3.03/3.29 inference(monotonicity,[status(thm)],[13323])).
% 3.03/3.29 tff(13342,plain,
% 3.03/3.29 ((~(s(s(s(s(s(s(s(s(elem!1)))))))) = z)) <=> (~(s(s(s(s(s(s(s(s(elem!1)))))))) = elem!1))),
% 3.03/3.29 inference(monotonicity,[status(thm)],[13341])).
% 3.03/3.29 tff(13343,plain,
% 3.03/3.29 (~(s(s(s(s(s(s(s(s(elem!1)))))))) = elem!1)),
% 3.03/3.29 inference(modus_ponens,[status(thm)],[13119, 13342])).
% 3.03/3.29 tff(13344,plain,
% 3.03/3.29 (~(s(s(s(elem!1))) = s(s(s(s(s(s(s(s(elem!1)))))))))),
% 3.03/3.29 inference(unit_resolution,[status(thm)],[13110, 13321])).
% 3.03/3.29 tff(13345,plain,
% 3.03/3.29 (b(z, s(z)) <=> b(elem!1, s(z))),
% 3.03/3.29 inference(monotonicity,[status(thm)],[13323])).
% 3.03/3.29 tff(13346,plain,
% 3.03/3.29 (b(elem!1, s(z))),
% 3.03/3.29 inference(modus_ponens,[status(thm)],[118, 13345])).
% 3.03/3.29 tff(13347,assumption,(r(s(s(s(s(s(s(s(s(elem!1)))))))), elem!1)), introduced(assumption)).
% 3.03/3.30 tff(13348,plain,
% 3.03/3.30 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), elem!1)) | (~r(s(s(s(s(s(s(s(s(elem!1)))))))), elem!1)) | (~r(s(s(s(elem!1))), s(s(s(s(s(s(s(s(elem!1)))))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(elem!1, s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), elem!1)) | (~r(s(s(s(s(s(s(s(s(elem!1)))))))), elem!1)) | (~r(s(s(s(elem!1))), s(s(s(s(s(s(s(s(elem!1)))))))))))),
% 3.03/3.30 inference(rewrite,[status(thm)],[])).
% 3.03/3.30 tff(13349,plain,
% 3.03/3.30 (((~r(elem!1, s(s(s(elem!1))))) | (~r(s(s(s(s(s(s(s(s(elem!1)))))))), elem!1)) | (~r(s(s(s(elem!1))), elem!1)) | (~r(s(s(s(elem!1))), s(s(s(s(s(s(s(s(elem!1))))))))))) <=> ((~r(elem!1, s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), elem!1)) | (~r(s(s(s(s(s(s(s(s(elem!1)))))))), elem!1)) | (~r(s(s(s(elem!1))), s(s(s(s(s(s(s(s(elem!1)))))))))))),
% 3.03/3.30 inference(rewrite,[status(thm)],[])).
% 3.03/3.30 tff(13350,plain,
% 3.03/3.30 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(s(s(elem!1))))) | (~r(s(s(s(s(s(s(s(s(elem!1)))))))), elem!1)) | (~r(s(s(s(elem!1))), elem!1)) | (~r(s(s(s(elem!1))), s(s(s(s(s(s(s(s(elem!1)))))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), elem!1)) | (~r(s(s(s(s(s(s(s(s(elem!1)))))))), elem!1)) | (~r(s(s(s(elem!1))), s(s(s(s(s(s(s(s(elem!1))))))))))))),
% 3.03/3.30 inference(monotonicity,[status(thm)],[13349])).
% 3.03/3.30 tff(13351,plain,
% 3.03/3.30 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(s(s(elem!1))))) | (~r(s(s(s(s(s(s(s(s(elem!1)))))))), elem!1)) | (~r(s(s(s(elem!1))), elem!1)) | (~r(s(s(s(elem!1))), s(s(s(s(s(s(s(s(elem!1)))))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(elem!1, s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), elem!1)) | (~r(s(s(s(s(s(s(s(s(elem!1)))))))), elem!1)) | (~r(s(s(s(elem!1))), s(s(s(s(s(s(s(s(elem!1)))))))))))),
% 3.03/3.30 inference(transitivity,[status(thm)],[13350, 13348])).
% 3.03/3.30 tff(13352,plain,
% 3.03/3.30 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(s(s(elem!1))))) | (~r(s(s(s(s(s(s(s(s(elem!1)))))))), elem!1)) | (~r(s(s(s(elem!1))), elem!1)) | (~r(s(s(s(elem!1))), s(s(s(s(s(s(s(s(elem!1)))))))))))),
% 3.03/3.30 inference(quant_inst,[status(thm)],[])).
% 3.03/3.30 tff(13353,plain,
% 3.03/3.30 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(elem!1, s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), elem!1)) | (~r(s(s(s(s(s(s(s(s(elem!1)))))))), elem!1)) | (~r(s(s(s(elem!1))), s(s(s(s(s(s(s(s(elem!1))))))))))),
% 3.03/3.30 inference(modus_ponens,[status(thm)],[13352, 13351])).
% 3.03/3.30 tff(13354,plain,
% 3.03/3.30 (~r(s(s(s(elem!1))), s(s(s(s(s(s(s(s(elem!1)))))))))),
% 3.03/3.30 inference(unit_resolution,[status(thm)],[13353, 197, 942, 13347, 1013])).
% 3.03/3.30 tff(13355,assumption,(~(s(s(s(elem!1))) = s(s(s(s(s(s(s(s(elem!1)))))))))), introduced(assumption)).
% 3.03/3.30 tff(13356,plain,
% 3.03/3.30 (((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((s(s(s(elem!1))) = s(s(s(s(s(s(s(s(elem!1))))))))) | b(s(s(s(elem!1))), s(s(s(s(s(s(s(s(elem!1))))))))) | r(s(s(s(elem!1))), s(s(s(s(s(s(s(s(elem!1))))))))))) <=> ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (s(s(s(elem!1))) = s(s(s(s(s(s(s(s(elem!1))))))))) | b(s(s(s(elem!1))), s(s(s(s(s(s(s(s(elem!1))))))))) | r(s(s(s(elem!1))), s(s(s(s(s(s(s(s(elem!1))))))))))),
% 3.03/3.30 inference(rewrite,[status(thm)],[])).
% 3.03/3.30 tff(13357,plain,
% 3.03/3.30 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((s(s(s(elem!1))) = s(s(s(s(s(s(s(s(elem!1))))))))) | b(s(s(s(elem!1))), s(s(s(s(s(s(s(s(elem!1))))))))) | r(s(s(s(elem!1))), s(s(s(s(s(s(s(s(elem!1))))))))))),
% 3.03/3.30 inference(quant_inst,[status(thm)],[])).
% 3.03/3.30 tff(13358,plain,
% 3.03/3.30 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (s(s(s(elem!1))) = s(s(s(s(s(s(s(s(elem!1))))))))) | b(s(s(s(elem!1))), s(s(s(s(s(s(s(s(elem!1))))))))) | r(s(s(s(elem!1))), s(s(s(s(s(s(s(s(elem!1)))))))))),
% 3.13/3.30 inference(modus_ponens,[status(thm)],[13357, 13356])).
% 3.13/3.30 tff(13359,plain,
% 3.13/3.30 (b(s(s(s(elem!1))), s(s(s(s(s(s(s(s(elem!1)))))))))),
% 3.13/3.30 inference(unit_resolution,[status(thm)],[13358, 79, 13355, 13354])).
% 3.13/3.30 tff(13360,plain,
% 3.13/3.30 ((s(s(s(s(s(s(s(s(elem!1)))))))) = s(s(s(elem!1)))) <=> (s(s(s(elem!1))) = s(s(s(s(s(s(s(s(elem!1)))))))))),
% 3.13/3.30 inference(commutativity,[status(thm)],[])).
% 3.13/3.30 tff(13361,plain,
% 3.13/3.30 ((s(s(s(elem!1))) = s(s(s(s(s(s(s(s(elem!1))))))))) <=> (s(s(s(s(s(s(s(s(elem!1)))))))) = s(s(s(elem!1))))),
% 3.13/3.30 inference(symmetry,[status(thm)],[13360])).
% 3.13/3.30 tff(13362,plain,
% 3.13/3.30 ((~(s(s(s(elem!1))) = s(s(s(s(s(s(s(s(elem!1)))))))))) <=> (~(s(s(s(s(s(s(s(s(elem!1)))))))) = s(s(s(elem!1)))))),
% 3.13/3.30 inference(monotonicity,[status(thm)],[13361])).
% 3.13/3.30 tff(13363,plain,
% 3.13/3.30 (~(s(s(s(s(s(s(s(s(elem!1)))))))) = s(s(s(elem!1))))),
% 3.13/3.30 inference(modus_ponens,[status(thm)],[13355, 13362])).
% 3.13/3.30 tff(13364,plain,
% 3.13/3.30 (~r(s(s(s(s(s(s(s(s(elem!1)))))))), s(s(s(elem!1))))),
% 3.13/3.30 inference(unit_resolution,[status(thm)],[13239, 197, 942, 13347, 1013])).
% 3.13/3.30 tff(13365,plain,
% 3.13/3.30 ((s(s(s(s(s(s(s(s(elem!1)))))))) = s(s(s(elem!1)))) | b(s(s(s(s(s(s(s(s(elem!1)))))))), s(s(s(elem!1))))),
% 3.13/3.30 inference(unit_resolution,[status(thm)],[13243, 79, 13364])).
% 3.13/3.30 tff(13366,plain,
% 3.13/3.30 (b(s(s(s(s(s(s(s(s(elem!1)))))))), s(s(s(elem!1))))),
% 3.13/3.30 inference(unit_resolution,[status(thm)],[13365, 13363])).
% 3.13/3.30 tff(13367,plain,
% 3.13/3.30 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(s(s(s(s(s(s(s(elem!1)))))))))) | (~b(s(s(s(s(s(s(s(s(elem!1)))))))), s(s(elem!1)))) | (~b(s(s(s(s(s(s(s(s(elem!1)))))))), s(s(s(elem!1))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(s(s(s(s(s(s(s(elem!1)))))))))) | (~b(s(s(s(s(s(s(s(s(elem!1)))))))), s(s(elem!1)))) | (~b(s(s(s(s(s(s(s(s(elem!1)))))))), s(s(s(elem!1))))))),
% 3.13/3.30 inference(rewrite,[status(thm)],[])).
% 3.13/3.30 tff(13368,plain,
% 3.13/3.30 (((~b(s(s(s(s(s(s(s(s(elem!1)))))))), s(s(s(elem!1))))) | (~b(s(s(s(s(s(s(s(s(elem!1)))))))), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(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(s(elem!1)))))))), s(s(s(elem!1))))) | (~b(s(s(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(elem!1))), s(s(s(s(s(s(s(s(elem!1)))))))))) | (~b(s(s(s(s(s(s(s(s(elem!1)))))))), s(s(elem!1)))) | (~b(s(s(s(s(s(s(s(s(elem!1)))))))), s(s(s(elem!1))))))),
% 3.13/3.30 inference(rewrite,[status(thm)],[])).
% 3.13/3.30 tff(13369,plain,
% 3.13/3.30 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(s(s(s(elem!1)))))))), s(s(s(elem!1))))) | (~b(s(s(s(s(s(s(s(s(elem!1)))))))), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(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(s(elem!1)))))))), s(s(s(elem!1))))) | (~b(s(s(s(s(s(s(s(s(elem!1)))))))), s(s(elem!1)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(s(s(s(s(s(s(s(elem!1)))))))))) | (~b(s(s(s(s(s(s(s(s(elem!1)))))))), s(s(elem!1)))) | (~b(s(s(s(s(s(s(s(s(elem!1)))))))), s(s(s(elem!1)))))))),
% 3.13/3.30 inference(monotonicity,[status(thm)],[13368])).
% 3.13/3.30 tff(13370,plain,
% 3.13/3.30 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(s(s(s(elem!1)))))))), s(s(s(elem!1))))) | (~b(s(s(s(s(s(s(s(s(elem!1)))))))), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(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(s(elem!1)))))))), s(s(s(elem!1))))) | (~b(s(s(s(s(s(s(s(s(elem!1)))))))), s(s(elem!1)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(s(s(s(s(s(s(s(elem!1)))))))))) | (~b(s(s(s(s(s(s(s(s(elem!1)))))))), s(s(elem!1)))) | (~b(s(s(s(s(s(s(s(s(elem!1)))))))), s(s(s(elem!1))))))),
% 3.13/3.30 inference(transitivity,[status(thm)],[13369, 13367])).
% 3.13/3.30 tff(13371,plain,
% 3.13/3.30 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(s(s(s(elem!1)))))))), s(s(s(elem!1))))) | (~b(s(s(s(s(s(s(s(s(elem!1)))))))), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(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(s(elem!1)))))))), s(s(s(elem!1))))) | (~b(s(s(s(s(s(s(s(s(elem!1)))))))), s(s(elem!1)))))),
% 3.13/3.30 inference(quant_inst,[status(thm)],[])).
% 3.13/3.30 tff(13372,plain,
% 3.13/3.30 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(s(s(s(s(s(s(s(elem!1)))))))))) | (~b(s(s(s(s(s(s(s(s(elem!1)))))))), s(s(elem!1)))) | (~b(s(s(s(s(s(s(s(s(elem!1)))))))), s(s(s(elem!1)))))),
% 3.13/3.30 inference(modus_ponens,[status(thm)],[13371, 13370])).
% 3.13/3.30 tff(13373,plain,
% 3.13/3.30 (~b(s(s(s(s(s(s(s(s(elem!1)))))))), s(s(elem!1)))),
% 3.13/3.30 inference(unit_resolution,[status(thm)],[13372, 166, 463, 13366, 13359])).
% 3.13/3.30 tff(13374,plain,
% 3.13/3.30 (r(s(s(s(s(s(s(s(s(elem!1)))))))), s(s(elem!1)))),
% 3.13/3.30 inference(unit_resolution,[status(thm)],[13221, 79, 13218, 13373])).
% 3.13/3.30 tff(13375,plain,
% 3.13/3.30 (~r(s(s(s(s(s(s(s(s(elem!1)))))))), s(z))),
% 3.13/3.30 inference(unit_resolution,[status(thm)],[13228, 197, 311, 4577, 13374])).
% 3.13/3.30 tff(13376,plain,
% 3.13/3.30 (b(s(s(s(s(s(s(s(s(elem!1)))))))), s(z))),
% 3.13/3.30 inference(unit_resolution,[status(thm)],[13209, 79, 13206, 13375])).
% 3.13/3.30 tff(13377,plain,
% 3.13/3.30 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(z))) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(z), elem!1)) | (~b(s(s(s(elem!1))), s(s(s(s(s(s(s(s(elem!1)))))))))) | (~b(s(s(s(s(s(s(s(s(elem!1)))))))), s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(z))) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(z), elem!1)) | (~b(s(s(s(elem!1))), s(s(s(s(s(s(s(s(elem!1)))))))))) | (~b(s(s(s(s(s(s(s(s(elem!1)))))))), s(z))))),
% 3.13/3.30 inference(rewrite,[status(thm)],[])).
% 3.13/3.30 tff(13378,plain,
% 3.13/3.30 (((~b(elem!1, s(z))) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(z), elem!1)) | (~b(s(s(s(s(s(s(s(s(elem!1)))))))), s(z))) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(s(s(elem!1))), s(s(s(s(s(s(s(s(elem!1))))))))))) <=> ((~b(elem!1, s(z))) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(z), elem!1)) | (~b(s(s(s(elem!1))), s(s(s(s(s(s(s(s(elem!1)))))))))) | (~b(s(s(s(s(s(s(s(s(elem!1)))))))), s(z))))),
% 3.13/3.30 inference(rewrite,[status(thm)],[])).
% 3.13/3.30 tff(13379,plain,
% 3.13/3.30 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(z))) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(z), elem!1)) | (~b(s(s(s(s(s(s(s(s(elem!1)))))))), s(z))) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(s(s(elem!1))), s(s(s(s(s(s(s(s(elem!1)))))))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(z))) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(z), elem!1)) | (~b(s(s(s(elem!1))), s(s(s(s(s(s(s(s(elem!1)))))))))) | (~b(s(s(s(s(s(s(s(s(elem!1)))))))), s(z)))))),
% 3.13/3.30 inference(monotonicity,[status(thm)],[13378])).
% 3.13/3.30 tff(13380,plain,
% 3.13/3.30 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(z))) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(z), elem!1)) | (~b(s(s(s(s(s(s(s(s(elem!1)))))))), s(z))) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(s(s(elem!1))), s(s(s(s(s(s(s(s(elem!1)))))))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(z))) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(z), elem!1)) | (~b(s(s(s(elem!1))), s(s(s(s(s(s(s(s(elem!1)))))))))) | (~b(s(s(s(s(s(s(s(s(elem!1)))))))), s(z))))),
% 3.13/3.30 inference(transitivity,[status(thm)],[13379, 13377])).
% 3.13/3.30 tff(13381,plain,
% 3.13/3.30 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(z))) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(z), elem!1)) | (~b(s(s(s(s(s(s(s(s(elem!1)))))))), s(z))) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(s(s(elem!1))), s(s(s(s(s(s(s(s(elem!1)))))))))))),
% 3.13/3.30 inference(quant_inst,[status(thm)],[])).
% 3.13/3.30 tff(13382,plain,
% 3.13/3.30 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(z))) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(z), elem!1)) | (~b(s(s(s(elem!1))), s(s(s(s(s(s(s(s(elem!1)))))))))) | (~b(s(s(s(s(s(s(s(s(elem!1)))))))), s(z)))),
% 3.13/3.30 inference(modus_ponens,[status(thm)],[13381, 13380])).
% 3.13/3.30 tff(13383,plain,
% 3.13/3.30 ($false),
% 3.13/3.30 inference(unit_resolution,[status(thm)],[13382, 166, 96, 1212, 642, 13359, 13376])).
% 3.13/3.30 tff(13384,plain,((~r(s(s(s(s(s(s(s(s(elem!1)))))))), elem!1)) | (~b(s(s(s(elem!1))), s(z))) | (~b(elem!1, s(z))) | (~b(s(z), elem!1)) | (s(s(s(s(s(s(s(s(elem!1)))))))) = s(z)) | (~r(s(z), s(s(elem!1)))) | (~r(s(s(elem!1)), s(z))) | (s(s(s(s(s(s(s(s(elem!1)))))))) = s(s(elem!1))) | (~b(s(s(elem!1)), s(s(s(elem!1))))) | (s(s(s(elem!1))) = s(s(s(s(s(s(s(s(elem!1))))))))) | (~r(elem!1, s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), elem!1))), inference(lemma,lemma(discharge,[]))).
% 3.13/3.30 tff(13385,plain,
% 3.13/3.30 (~r(s(s(s(s(s(s(s(s(elem!1)))))))), elem!1)),
% 3.13/3.30 inference(unit_resolution,[status(thm)],[13384, 13278, 13346, 13334, 13340, 311, 13280, 13339, 13294, 13344, 13326, 13327])).
% 3.13/3.30 tff(13386,plain,
% 3.13/3.30 (b(s(s(s(s(s(s(s(s(elem!1)))))))), elem!1)),
% 3.13/3.30 inference(unit_resolution,[status(thm)],[13235, 13385, 13343])).
% 3.13/3.30 tff(13387,plain,
% 3.13/3.30 (~b(s(s(elem!1)), elem!1)),
% 3.13/3.30 inference(unit_resolution,[status(thm)],[13230, 13386, 13280, 13340, 13339, 13338, 13334, 311])).
% 3.13/3.30 tff(13388,plain,
% 3.13/3.30 (r(s(s(elem!1)), elem!1)),
% 3.13/3.30 inference(unit_resolution,[status(thm)],[784, 13387, 13332])).
% 3.13/3.30 tff(13389,plain,
% 3.13/3.30 (~r(s(s(s(elem!1))), s(s(elem!1)))),
% 3.13/3.30 inference(unit_resolution,[status(thm)],[2508, 13388, 311, 119])).
% 3.13/3.30 tff(13390,plain,
% 3.13/3.30 (b(s(s(s(elem!1))), s(s(elem!1)))),
% 3.13/3.30 inference(unit_resolution,[status(thm)],[889, 13389, 51])).
% 3.13/3.30 tff(13391,plain,
% 3.13/3.30 (~r(s(s(s(s(s(s(s(elem!1))))))), elem!1)),
% 3.13/3.30 inference(unit_resolution,[status(thm)],[6369, 13390, 13388, 13321, 13294, 13327, 13326])).
% 3.13/3.30 tff(13392,plain,
% 3.13/3.30 (b(s(s(s(s(s(s(s(elem!1))))))), elem!1)),
% 3.13/3.30 inference(unit_resolution,[status(thm)],[6375, 13391, 13324])).
% 3.13/3.30 tff(13393,plain,
% 3.13/3.30 (~b(s(s(s(s(s(s(s(elem!1))))))), s(z))),
% 3.13/3.30 inference(unit_resolution,[status(thm)],[4946, 166, 13346, 13334, 13392])).
% 3.13/3.30 tff(13394,plain,
% 3.13/3.30 (~(s(s(s(s(s(s(s(elem!1))))))) = s(z))),
% 3.13/3.30 inference(unit_resolution,[status(thm)],[4900, 13323])).
% 3.13/3.30 tff(13395,plain,
% 3.13/3.30 (r(s(s(s(s(s(s(s(elem!1))))))), s(z))),
% 3.13/3.30 inference(unit_resolution,[status(thm)],[4951, 79, 13394, 13393])).
% 3.13/3.30 tff(13396,plain,
% 3.13/3.30 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(z))) | (~b(s(z), elem!1)) | (~b(s(s(s(s(s(s(s(s(elem!1)))))))), elem!1)) | (~b(s(s(s(s(s(s(s(s(elem!1)))))))), s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(z))) | (~b(s(z), elem!1)) | (~b(s(s(s(s(s(s(s(s(elem!1)))))))), elem!1)) | (~b(s(s(s(s(s(s(s(s(elem!1)))))))), s(z))))),
% 3.13/3.30 inference(rewrite,[status(thm)],[])).
% 3.13/3.30 tff(13397,plain,
% 3.13/3.30 (((~b(s(z), elem!1)) | (~b(s(s(s(s(s(s(s(s(elem!1)))))))), elem!1)) | (~b(elem!1, s(z))) | (~b(s(z), elem!1)) | (~b(s(s(s(s(s(s(s(s(elem!1)))))))), elem!1)) | (~b(s(s(s(s(s(s(s(s(elem!1)))))))), s(z)))) <=> ((~b(elem!1, s(z))) | (~b(s(z), elem!1)) | (~b(s(s(s(s(s(s(s(s(elem!1)))))))), elem!1)) | (~b(s(s(s(s(s(s(s(s(elem!1)))))))), s(z))))),
% 3.13/3.30 inference(rewrite,[status(thm)],[])).
% 3.13/3.30 tff(13398,plain,
% 3.13/3.30 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), elem!1)) | (~b(s(s(s(s(s(s(s(s(elem!1)))))))), elem!1)) | (~b(elem!1, s(z))) | (~b(s(z), elem!1)) | (~b(s(s(s(s(s(s(s(s(elem!1)))))))), elem!1)) | (~b(s(s(s(s(s(s(s(s(elem!1)))))))), s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(z))) | (~b(s(z), elem!1)) | (~b(s(s(s(s(s(s(s(s(elem!1)))))))), elem!1)) | (~b(s(s(s(s(s(s(s(s(elem!1)))))))), s(z)))))),
% 3.13/3.30 inference(monotonicity,[status(thm)],[13397])).
% 3.13/3.30 tff(13399,plain,
% 3.13/3.30 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), elem!1)) | (~b(s(s(s(s(s(s(s(s(elem!1)))))))), elem!1)) | (~b(elem!1, s(z))) | (~b(s(z), elem!1)) | (~b(s(s(s(s(s(s(s(s(elem!1)))))))), elem!1)) | (~b(s(s(s(s(s(s(s(s(elem!1)))))))), s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(z))) | (~b(s(z), elem!1)) | (~b(s(s(s(s(s(s(s(s(elem!1)))))))), elem!1)) | (~b(s(s(s(s(s(s(s(s(elem!1)))))))), s(z))))),
% 3.13/3.30 inference(transitivity,[status(thm)],[13398, 13396])).
% 3.13/3.30 tff(13400,plain,
% 3.13/3.30 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), elem!1)) | (~b(s(s(s(s(s(s(s(s(elem!1)))))))), elem!1)) | (~b(elem!1, s(z))) | (~b(s(z), elem!1)) | (~b(s(s(s(s(s(s(s(s(elem!1)))))))), elem!1)) | (~b(s(s(s(s(s(s(s(s(elem!1)))))))), s(z))))),
% 3.13/3.30 inference(quant_inst,[status(thm)],[])).
% 3.13/3.30 tff(13401,plain,
% 3.13/3.30 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(z))) | (~b(s(z), elem!1)) | (~b(s(s(s(s(s(s(s(s(elem!1)))))))), elem!1)) | (~b(s(s(s(s(s(s(s(s(elem!1)))))))), s(z)))),
% 3.13/3.30 inference(modus_ponens,[status(thm)],[13400, 13399])).
% 3.13/3.30 tff(13402,plain,
% 3.13/3.30 (~b(s(s(s(s(s(s(s(s(elem!1)))))))), s(z))),
% 3.13/3.30 inference(unit_resolution,[status(thm)],[13401, 166, 13346, 13334, 13386])).
% 3.13/3.30 tff(13403,plain,
% 3.13/3.30 (r(s(s(s(s(s(s(s(s(elem!1)))))))), s(z))),
% 3.13/3.30 inference(unit_resolution,[status(thm)],[13209, 79, 13340, 13402])).
% 3.13/3.30 tff(13404,plain,
% 3.13/3.30 ((s(z) = s(s(s(s(s(s(s(s(elem!1))))))))) <=> (s(s(s(s(s(s(s(s(elem!1)))))))) = s(z))),
% 3.13/3.30 inference(commutativity,[status(thm)],[])).
% 3.13/3.30 tff(13405,plain,
% 3.13/3.30 ((s(s(s(s(s(s(s(s(elem!1)))))))) = s(z)) <=> (s(z) = s(s(s(s(s(s(s(s(elem!1)))))))))),
% 3.13/3.30 inference(symmetry,[status(thm)],[13404])).
% 3.13/3.30 tff(13406,plain,
% 3.13/3.30 ((~(s(s(s(s(s(s(s(s(elem!1)))))))) = s(z))) <=> (~(s(z) = s(s(s(s(s(s(s(s(elem!1))))))))))),
% 3.13/3.30 inference(monotonicity,[status(thm)],[13405])).
% 3.13/3.30 tff(13407,plain,
% 3.13/3.30 (~(s(z) = s(s(s(s(s(s(s(s(elem!1)))))))))),
% 3.13/3.30 inference(modus_ponens,[status(thm)],[13340, 13406])).
% 3.13/3.30 tff(13408,plain,
% 3.13/3.30 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(z))) | (~b(s(z), elem!1)) | (~b(s(s(s(s(s(s(s(s(elem!1)))))))), elem!1)) | (~b(s(z), s(s(s(s(s(s(s(s(elem!1)))))))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(z))) | (~b(s(z), elem!1)) | (~b(s(s(s(s(s(s(s(s(elem!1)))))))), elem!1)) | (~b(s(z), s(s(s(s(s(s(s(s(elem!1)))))))))))),
% 3.13/3.31 inference(rewrite,[status(thm)],[])).
% 3.13/3.31 tff(13409,plain,
% 3.13/3.31 (((~b(s(z), elem!1)) | (~b(s(z), elem!1)) | (~b(elem!1, s(z))) | (~b(s(s(s(s(s(s(s(s(elem!1)))))))), elem!1)) | (~b(s(z), elem!1)) | (~b(s(z), s(s(s(s(s(s(s(s(elem!1))))))))))) <=> ((~b(elem!1, s(z))) | (~b(s(z), elem!1)) | (~b(s(s(s(s(s(s(s(s(elem!1)))))))), elem!1)) | (~b(s(z), s(s(s(s(s(s(s(s(elem!1)))))))))))),
% 3.13/3.31 inference(rewrite,[status(thm)],[])).
% 3.13/3.31 tff(13410,plain,
% 3.13/3.31 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), elem!1)) | (~b(s(z), elem!1)) | (~b(elem!1, s(z))) | (~b(s(s(s(s(s(s(s(s(elem!1)))))))), elem!1)) | (~b(s(z), elem!1)) | (~b(s(z), s(s(s(s(s(s(s(s(elem!1)))))))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(z))) | (~b(s(z), elem!1)) | (~b(s(s(s(s(s(s(s(s(elem!1)))))))), elem!1)) | (~b(s(z), s(s(s(s(s(s(s(s(elem!1))))))))))))),
% 3.13/3.31 inference(monotonicity,[status(thm)],[13409])).
% 3.13/3.31 tff(13411,plain,
% 3.13/3.31 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), elem!1)) | (~b(s(z), elem!1)) | (~b(elem!1, s(z))) | (~b(s(s(s(s(s(s(s(s(elem!1)))))))), elem!1)) | (~b(s(z), elem!1)) | (~b(s(z), s(s(s(s(s(s(s(s(elem!1)))))))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(z))) | (~b(s(z), elem!1)) | (~b(s(s(s(s(s(s(s(s(elem!1)))))))), elem!1)) | (~b(s(z), s(s(s(s(s(s(s(s(elem!1)))))))))))),
% 3.13/3.31 inference(transitivity,[status(thm)],[13410, 13408])).
% 3.13/3.31 tff(13412,plain,
% 3.13/3.31 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), elem!1)) | (~b(s(z), elem!1)) | (~b(elem!1, s(z))) | (~b(s(s(s(s(s(s(s(s(elem!1)))))))), elem!1)) | (~b(s(z), elem!1)) | (~b(s(z), s(s(s(s(s(s(s(s(elem!1)))))))))))),
% 3.13/3.31 inference(quant_inst,[status(thm)],[])).
% 3.13/3.31 tff(13413,plain,
% 3.13/3.31 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(z))) | (~b(s(z), elem!1)) | (~b(s(s(s(s(s(s(s(s(elem!1)))))))), elem!1)) | (~b(s(z), s(s(s(s(s(s(s(s(elem!1))))))))))),
% 3.13/3.31 inference(modus_ponens,[status(thm)],[13412, 13411])).
% 3.13/3.31 tff(13414,plain,
% 3.13/3.31 (~b(s(z), s(s(s(s(s(s(s(s(elem!1)))))))))),
% 3.13/3.31 inference(unit_resolution,[status(thm)],[13413, 166, 13346, 13334, 13386])).
% 3.13/3.31 tff(13415,plain,
% 3.13/3.31 (((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((s(z) = s(s(s(s(s(s(s(s(elem!1))))))))) | b(s(z), s(s(s(s(s(s(s(s(elem!1))))))))) | r(s(z), s(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(s(elem!1))))))))) | b(s(z), s(s(s(s(s(s(s(s(elem!1))))))))) | r(s(z), s(s(s(s(s(s(s(s(elem!1))))))))))),
% 3.13/3.31 inference(rewrite,[status(thm)],[])).
% 3.13/3.31 tff(13416,plain,
% 3.13/3.31 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((s(z) = s(s(s(s(s(s(s(s(elem!1))))))))) | b(s(z), s(s(s(s(s(s(s(s(elem!1))))))))) | r(s(z), s(s(s(s(s(s(s(s(elem!1))))))))))),
% 3.13/3.31 inference(quant_inst,[status(thm)],[])).
% 3.13/3.31 tff(13417,plain,
% 3.13/3.31 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (s(z) = s(s(s(s(s(s(s(s(elem!1))))))))) | b(s(z), s(s(s(s(s(s(s(s(elem!1))))))))) | r(s(z), s(s(s(s(s(s(s(s(elem!1)))))))))),
% 3.13/3.31 inference(modus_ponens,[status(thm)],[13416, 13415])).
% 3.13/3.31 tff(13418,plain,
% 3.13/3.31 ((s(z) = s(s(s(s(s(s(s(s(elem!1))))))))) | r(s(z), s(s(s(s(s(s(s(s(elem!1)))))))))),
% 3.13/3.31 inference(unit_resolution,[status(thm)],[13417, 79, 13414])).
% 3.13/3.31 tff(13419,plain,
% 3.13/3.31 (r(s(z), s(s(s(s(s(s(s(s(elem!1)))))))))),
% 3.13/3.31 inference(unit_resolution,[status(thm)],[13418, 13407])).
% 3.13/3.31 tff(13420,plain,
% 3.13/3.31 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(s(s(s(elem!1))))))), s(z))) | (~r(s(s(s(s(s(s(s(s(elem!1)))))))), s(z))) | (~r(s(z), s(s(s(s(s(s(s(s(elem!1)))))))))) | (~r(s(s(s(s(s(s(s(s(elem!1)))))))), s(s(s(s(s(s(s(elem!1))))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(s(s(s(s(elem!1))))))), s(z))) | (~r(s(s(s(s(s(s(s(s(elem!1)))))))), s(z))) | (~r(s(z), s(s(s(s(s(s(s(s(elem!1)))))))))) | (~r(s(s(s(s(s(s(s(s(elem!1)))))))), s(s(s(s(s(s(s(elem!1))))))))))),
% 3.13/3.31 inference(rewrite,[status(thm)],[])).
% 3.13/3.31 tff(13421,plain,
% 3.13/3.31 (((~r(s(z), s(s(s(s(s(s(s(s(elem!1)))))))))) | (~r(s(s(s(s(s(s(s(elem!1))))))), s(z))) | (~r(s(s(s(s(s(s(s(s(elem!1)))))))), s(z))) | (~r(s(s(s(s(s(s(s(s(elem!1)))))))), s(s(s(s(s(s(s(elem!1)))))))))) <=> ((~r(s(s(s(s(s(s(s(elem!1))))))), s(z))) | (~r(s(s(s(s(s(s(s(s(elem!1)))))))), s(z))) | (~r(s(z), s(s(s(s(s(s(s(s(elem!1)))))))))) | (~r(s(s(s(s(s(s(s(s(elem!1)))))))), s(s(s(s(s(s(s(elem!1))))))))))),
% 3.13/3.31 inference(rewrite,[status(thm)],[])).
% 3.13/3.31 tff(13422,plain,
% 3.13/3.31 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(s(s(s(s(s(s(s(elem!1)))))))))) | (~r(s(s(s(s(s(s(s(elem!1))))))), s(z))) | (~r(s(s(s(s(s(s(s(s(elem!1)))))))), s(z))) | (~r(s(s(s(s(s(s(s(s(elem!1)))))))), s(s(s(s(s(s(s(elem!1))))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(s(s(s(elem!1))))))), s(z))) | (~r(s(s(s(s(s(s(s(s(elem!1)))))))), s(z))) | (~r(s(z), s(s(s(s(s(s(s(s(elem!1)))))))))) | (~r(s(s(s(s(s(s(s(s(elem!1)))))))), s(s(s(s(s(s(s(elem!1)))))))))))),
% 3.13/3.31 inference(monotonicity,[status(thm)],[13421])).
% 3.13/3.31 tff(13423,plain,
% 3.13/3.31 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(s(s(s(s(s(s(s(elem!1)))))))))) | (~r(s(s(s(s(s(s(s(elem!1))))))), s(z))) | (~r(s(s(s(s(s(s(s(s(elem!1)))))))), s(z))) | (~r(s(s(s(s(s(s(s(s(elem!1)))))))), s(s(s(s(s(s(s(elem!1))))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(s(s(s(s(elem!1))))))), s(z))) | (~r(s(s(s(s(s(s(s(s(elem!1)))))))), s(z))) | (~r(s(z), s(s(s(s(s(s(s(s(elem!1)))))))))) | (~r(s(s(s(s(s(s(s(s(elem!1)))))))), s(s(s(s(s(s(s(elem!1))))))))))),
% 3.13/3.31 inference(transitivity,[status(thm)],[13422, 13420])).
% 3.13/3.31 tff(13424,plain,
% 3.13/3.31 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(s(s(s(s(s(s(s(elem!1)))))))))) | (~r(s(s(s(s(s(s(s(elem!1))))))), s(z))) | (~r(s(s(s(s(s(s(s(s(elem!1)))))))), s(z))) | (~r(s(s(s(s(s(s(s(s(elem!1)))))))), s(s(s(s(s(s(s(elem!1))))))))))),
% 3.13/3.31 inference(quant_inst,[status(thm)],[])).
% 3.13/3.31 tff(13425,plain,
% 3.13/3.31 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(s(s(s(s(elem!1))))))), s(z))) | (~r(s(s(s(s(s(s(s(s(elem!1)))))))), s(z))) | (~r(s(z), s(s(s(s(s(s(s(s(elem!1)))))))))) | (~r(s(s(s(s(s(s(s(s(elem!1)))))))), s(s(s(s(s(s(s(elem!1)))))))))),
% 3.13/3.31 inference(modus_ponens,[status(thm)],[13424, 13423])).
% 3.13/3.31 tff(13426,plain,
% 3.13/3.31 (~r(s(s(s(s(s(s(s(s(elem!1)))))))), s(s(s(s(s(s(s(elem!1))))))))),
% 3.13/3.31 inference(unit_resolution,[status(thm)],[13425, 197, 13419, 13403, 13395])).
% 3.13/3.31 tff(13427,plain,
% 3.13/3.31 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(z))) | (~b(s(z), elem!1)) | (~b(s(s(s(s(s(s(s(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(s(elem!1)))))))), s(s(s(s(s(s(s(elem!1))))))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(z))) | (~b(s(z), elem!1)) | (~b(s(s(s(s(s(s(s(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(s(elem!1)))))))), s(s(s(s(s(s(s(elem!1))))))))))),
% 3.13/3.31 inference(rewrite,[status(thm)],[])).
% 3.13/3.31 tff(13428,plain,
% 3.13/3.31 (((~b(s(z), elem!1)) | (~b(s(s(s(s(s(s(s(s(elem!1)))))))), elem!1)) | (~b(elem!1, s(z))) | (~b(s(s(s(s(s(s(s(elem!1))))))), elem!1)) | (~b(s(s(s(s(s(s(s(s(elem!1)))))))), elem!1)) | (~b(s(s(s(s(s(s(s(s(elem!1)))))))), s(s(s(s(s(s(s(elem!1)))))))))) <=> ((~b(elem!1, s(z))) | (~b(s(z), elem!1)) | (~b(s(s(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(s(elem!1)))))))), s(s(s(s(s(s(s(elem!1))))))))))),
% 3.13/3.31 inference(rewrite,[status(thm)],[])).
% 3.13/3.31 tff(13429,plain,
% 3.13/3.31 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), elem!1)) | (~b(s(s(s(s(s(s(s(s(elem!1)))))))), elem!1)) | (~b(elem!1, s(z))) | (~b(s(s(s(s(s(s(s(elem!1))))))), elem!1)) | (~b(s(s(s(s(s(s(s(s(elem!1)))))))), elem!1)) | (~b(s(s(s(s(s(s(s(s(elem!1)))))))), s(s(s(s(s(s(s(elem!1))))))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(z))) | (~b(s(z), elem!1)) | (~b(s(s(s(s(s(s(s(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(s(elem!1)))))))), s(s(s(s(s(s(s(elem!1)))))))))))),
% 3.13/3.31 inference(monotonicity,[status(thm)],[13428])).
% 3.13/3.31 tff(13430,plain,
% 3.13/3.31 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), elem!1)) | (~b(s(s(s(s(s(s(s(s(elem!1)))))))), elem!1)) | (~b(elem!1, s(z))) | (~b(s(s(s(s(s(s(s(elem!1))))))), elem!1)) | (~b(s(s(s(s(s(s(s(s(elem!1)))))))), elem!1)) | (~b(s(s(s(s(s(s(s(s(elem!1)))))))), s(s(s(s(s(s(s(elem!1))))))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(z))) | (~b(s(z), elem!1)) | (~b(s(s(s(s(s(s(s(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(s(elem!1)))))))), s(s(s(s(s(s(s(elem!1))))))))))),
% 3.13/3.31 inference(transitivity,[status(thm)],[13429, 13427])).
% 3.13/3.31 tff(13431,plain,
% 3.13/3.31 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), elem!1)) | (~b(s(s(s(s(s(s(s(s(elem!1)))))))), elem!1)) | (~b(elem!1, s(z))) | (~b(s(s(s(s(s(s(s(elem!1))))))), elem!1)) | (~b(s(s(s(s(s(s(s(s(elem!1)))))))), elem!1)) | (~b(s(s(s(s(s(s(s(s(elem!1)))))))), s(s(s(s(s(s(s(elem!1))))))))))),
% 3.13/3.31 inference(quant_inst,[status(thm)],[])).
% 3.13/3.31 tff(13432,plain,
% 3.13/3.31 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(z))) | (~b(s(z), elem!1)) | (~b(s(s(s(s(s(s(s(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(s(elem!1)))))))), s(s(s(s(s(s(s(elem!1)))))))))),
% 3.13/3.31 inference(modus_ponens,[status(thm)],[13431, 13430])).
% 3.13/3.31 tff(13433,plain,
% 3.13/3.31 (~b(s(s(s(s(s(s(s(s(elem!1)))))))), s(s(s(s(s(s(s(elem!1))))))))),
% 3.13/3.31 inference(unit_resolution,[status(thm)],[13432, 166, 13346, 13334, 13386, 13392])).
% 3.13/3.31 tff(13434,plain,
% 3.13/3.31 (((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((s(s(s(s(s(s(s(s(elem!1)))))))) = s(s(s(s(s(s(s(elem!1)))))))) | b(s(s(s(s(s(s(s(s(elem!1)))))))), s(s(s(s(s(s(s(elem!1)))))))) | r(s(s(s(s(s(s(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(s(s(s(s(s(s(elem!1)))))))) = s(s(s(s(s(s(s(elem!1)))))))) | b(s(s(s(s(s(s(s(s(elem!1)))))))), s(s(s(s(s(s(s(elem!1)))))))) | r(s(s(s(s(s(s(s(s(elem!1)))))))), s(s(s(s(s(s(s(elem!1)))))))))),
% 3.13/3.31 inference(rewrite,[status(thm)],[])).
% 3.13/3.31 tff(13435,plain,
% 3.13/3.31 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((s(s(s(s(s(s(s(s(elem!1)))))))) = s(s(s(s(s(s(s(elem!1)))))))) | b(s(s(s(s(s(s(s(s(elem!1)))))))), s(s(s(s(s(s(s(elem!1)))))))) | r(s(s(s(s(s(s(s(s(elem!1)))))))), s(s(s(s(s(s(s(elem!1)))))))))),
% 3.13/3.31 inference(quant_inst,[status(thm)],[])).
% 3.13/3.31 tff(13436,plain,
% 3.13/3.31 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (s(s(s(s(s(s(s(s(elem!1)))))))) = s(s(s(s(s(s(s(elem!1)))))))) | b(s(s(s(s(s(s(s(s(elem!1)))))))), s(s(s(s(s(s(s(elem!1)))))))) | r(s(s(s(s(s(s(s(s(elem!1)))))))), s(s(s(s(s(s(s(elem!1))))))))),
% 3.13/3.31 inference(modus_ponens,[status(thm)],[13435, 13434])).
% 3.13/3.31 tff(13437,plain,
% 3.13/3.31 ((s(s(s(s(s(s(s(s(elem!1)))))))) = s(s(s(s(s(s(s(elem!1)))))))) | r(s(s(s(s(s(s(s(s(elem!1)))))))), s(s(s(s(s(s(s(elem!1))))))))),
% 3.13/3.31 inference(unit_resolution,[status(thm)],[13436, 79, 13433])).
% 3.13/3.31 tff(13438,plain,
% 3.13/3.31 (s(s(s(s(s(s(s(s(elem!1)))))))) = s(s(s(s(s(s(s(elem!1)))))))),
% 3.13/3.31 inference(unit_resolution,[status(thm)],[13437, 13426])).
% 3.13/3.31 tff(13439,plain,
% 3.13/3.31 (s(s(s(s(s(s(s(elem!1))))))) = s(s(s(s(s(s(s(s(elem!1))))))))),
% 3.13/3.31 inference(symmetry,[status(thm)],[13438])).
% 3.13/3.31 tff(13440,plain,
% 3.13/3.31 (inj_0(s(s(s(s(s(s(s(elem!1)))))))) = inj_0(s(s(s(s(s(s(s(s(elem!1)))))))))),
% 3.13/3.31 inference(monotonicity,[status(thm)],[13439])).
% 3.13/3.31 tff(13441,plain,
% 3.13/3.31 (inj_0(s(s(s(s(s(s(s(s(elem!1))))))))) = inj_0(s(s(s(s(s(s(s(elem!1))))))))),
% 3.13/3.31 inference(symmetry,[status(thm)],[13440])).
% 3.13/3.31 tff(13442,plain,
% 3.13/3.31 (s(s(s(s(s(s(s(elem!1))))))) = s(s(s(s(s(s(elem!1))))))),
% 3.13/3.31 inference(transitivity,[status(thm)],[13185, 13441, 4888])).
% 3.13/3.31 tff(13443,plain,
% 3.13/3.31 ((s(s(s(s(elem!1)))) = s(s(z))) <=> (s(s(s(s(elem!1)))) = s(s(elem!1)))),
% 3.13/3.31 inference(monotonicity,[status(thm)],[13321])).
% 3.13/3.31 tff(13444,plain,
% 3.13/3.31 ((s(s(s(s(elem!1)))) = s(s(z))) <=> (s(s(elem!1)) = s(s(s(s(elem!1)))))),
% 3.13/3.31 inference(transitivity,[status(thm)],[13443, 123])).
% 3.13/3.31 tff(13445,plain,
% 3.13/3.31 ((~(s(s(s(s(elem!1)))) = s(s(z)))) <=> (~(s(s(elem!1)) = s(s(s(s(elem!1))))))),
% 3.13/3.31 inference(monotonicity,[status(thm)],[13444])).
% 3.13/3.31 tff(13446,plain,
% 3.13/3.31 (~(s(s(elem!1)) = s(s(s(s(elem!1)))))),
% 3.13/3.31 inference(modus_ponens,[status(thm)],[733, 13445])).
% 3.13/3.31 tff(13447,plain,
% 3.13/3.31 (~(s(s(s(s(elem!1)))) = s(s(s(s(s(s(elem!1)))))))),
% 3.13/3.31 inference(unit_resolution,[status(thm)],[9243, 13446])).
% 3.13/3.31 tff(13448,assumption,(s(s(s(s(s(s(s(elem!1))))))) = s(s(s(s(s(s(elem!1))))))), introduced(assumption)).
% 3.13/3.31 tff(13449,plain,
% 3.13/3.31 (s(s(s(s(s(s(elem!1)))))) = s(s(s(s(s(s(s(elem!1)))))))),
% 3.13/3.31 inference(symmetry,[status(thm)],[13448])).
% 3.13/3.31 tff(13450,plain,
% 3.13/3.31 (inj_0(s(s(s(s(s(s(elem!1))))))) = inj_0(s(s(s(s(s(s(s(elem!1))))))))),
% 3.13/3.31 inference(monotonicity,[status(thm)],[13449])).
% 3.13/3.31 tff(13451,plain,
% 3.13/3.31 (s(s(s(s(s(elem!1))))) = s(s(s(s(s(s(elem!1))))))),
% 3.13/3.31 inference(transitivity,[status(thm)],[4981, 13450, 4888])).
% 3.13/3.31 tff(13452,plain,
% 3.13/3.31 (inj_0(s(s(s(s(s(elem!1)))))) = inj_0(s(s(s(s(s(s(elem!1)))))))),
% 3.13/3.31 inference(monotonicity,[status(thm)],[13451])).
% 3.13/3.31 tff(13453,plain,
% 3.13/3.31 (s(s(s(s(elem!1)))) = s(s(s(s(s(s(elem!1))))))),
% 3.13/3.31 inference(transitivity,[status(thm)],[4919, 13452, 13450, 4888])).
% 3.13/3.31 tff(13454,plain,
% 3.13/3.31 ($false),
% 3.13/3.31 inference(unit_resolution,[status(thm)],[11344, 13453])).
% 3.13/3.31 tff(13455,plain,((~(s(s(s(s(s(s(s(elem!1))))))) = s(s(s(s(s(s(elem!1)))))))) | (s(s(s(s(elem!1)))) = s(s(s(s(s(s(elem!1)))))))), inference(lemma,lemma(discharge,[]))).
% 3.13/3.31 tff(13456,plain,
% 3.13/3.31 (~(s(s(s(s(s(s(s(elem!1))))))) = s(s(s(s(s(s(elem!1)))))))),
% 3.13/3.31 inference(unit_resolution,[status(thm)],[13455, 13447])).
% 3.13/3.31 tff(13457,plain,
% 3.13/3.31 ($false),
% 3.13/3.31 inference(unit_resolution,[status(thm)],[13456, 13442])).
% 3.13/3.31 tff(13458,plain,((~r(z, s(s(s(elem!1))))) | (~r(s(z), s(s(elem!1)))) | (~r(s(z), s(s(s(elem!1))))) | (~b(z, s(z))) | (~b(s(z), z)) | (~r(s(s(s(elem!1))), z)) | (s(s(elem!1)) = s(s(s(elem!1)))) | b(s(s(z)), s(z))), inference(lemma,lemma(discharge,[]))).
% 3.13/3.31 tff(13459,plain,
% 3.13/3.31 (~r(z, s(s(s(elem!1))))),
% 3.13/3.31 inference(unit_resolution,[status(thm)],[13458, 118, 119, 311, 53, 154, 45, 3936])).
% 3.13/3.31 tff(13460,plain,
% 3.13/3.31 (b(z, s(s(s(elem!1))))),
% 3.13/3.31 inference(unit_resolution,[status(thm)],[261, 13459])).
% 3.13/3.31 tff(13461,plain,
% 3.13/3.31 (((~b(z, s(s(s(elem!1))))) | (~b(z, s(s(s(elem!1))))) | (~b(s(z), z)) | (~b(s(s(s(elem!1))), s(z))) | (~b(z, s(z))) | (~b(z, s(s(s(elem!1)))))) <=> ((~b(z, s(s(s(elem!1))))) | (~b(s(z), z)) | (~b(s(s(s(elem!1))), s(z))) | (~b(z, s(z))))),
% 3.13/3.31 inference(rewrite,[status(thm)],[])).
% 3.13/3.31 tff(13462,plain,
% 3.13/3.31 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(s(elem!1))))) | (~b(z, s(s(s(elem!1))))) | (~b(s(z), z)) | (~b(s(s(s(elem!1))), s(z))) | (~b(z, s(z))) | (~b(z, s(s(s(elem!1))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(s(elem!1))))) | (~b(s(z), z)) | (~b(s(s(s(elem!1))), s(z))) | (~b(z, s(z)))))),
% 3.13/3.31 inference(monotonicity,[status(thm)],[13461])).
% 3.13/3.31 tff(13463,plain,
% 3.13/3.31 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(s(elem!1))))) | (~b(z, s(s(s(elem!1))))) | (~b(s(z), z)) | (~b(s(s(s(elem!1))), s(z))) | (~b(z, s(z))) | (~b(z, s(s(s(elem!1))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(s(s(elem!1))))) | (~b(s(z), z)) | (~b(s(s(s(elem!1))), s(z))) | (~b(z, s(z))))),
% 3.13/3.31 inference(transitivity,[status(thm)],[13462, 3984])).
% 3.13/3.31 tff(13464,plain,
% 3.13/3.31 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(s(elem!1))))) | (~b(z, s(s(s(elem!1))))) | (~b(s(z), z)) | (~b(s(s(s(elem!1))), s(z))) | (~b(z, s(z))) | (~b(z, s(s(s(elem!1))))))),
% 3.13/3.31 inference(quant_inst,[status(thm)],[])).
% 3.13/3.31 tff(13465,plain,
% 3.13/3.31 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(s(s(elem!1))))) | (~b(s(z), z)) | (~b(s(s(s(elem!1))), s(z))) | (~b(z, s(z)))),
% 3.13/3.31 inference(modus_ponens,[status(thm)],[13464, 13463])).
% 3.13/3.31 tff(13466,plain,
% 3.13/3.31 ($false),
% 3.13/3.31 inference(unit_resolution,[status(thm)],[13465, 166, 240, 53, 96, 118])).
% 3.13/3.31 tff(13467,plain,((~b(s(s(s(elem!1))), s(z))) | (~b(z, s(s(s(elem!1))))) | (~b(s(z), z)) | (~b(z, s(z)))), inference(lemma,lemma(discharge,[]))).
% 3.13/3.31 tff(13468,plain,
% 3.13/3.31 (~b(s(s(s(elem!1))), s(z))),
% 3.13/3.31 inference(unit_resolution,[status(thm)],[13467, 13460, 53, 118])).
% 3.13/3.31 tff(13469,plain,
% 3.13/3.31 (r(s(s(s(elem!1))), s(z))),
% 3.13/3.31 inference(unit_resolution,[status(thm)],[1849, 13468])).
% 3.13/3.31 tff(13470,plain,
% 3.13/3.31 (~r(s(s(elem!1)), s(s(s(elem!1))))),
% 3.13/3.31 inference(unit_resolution,[status(thm)],[764, 13469, 311, 119])).
% 3.13/3.31 tff(13471,plain,
% 3.13/3.31 (~r(s(s(s(elem!1))), s(s(z)))),
% 3.13/3.31 inference(unit_resolution,[status(thm)],[854, 350, 311, 392])).
% 3.13/3.31 tff(13472,plain,
% 3.13/3.31 (b(s(s(s(elem!1))), s(s(z)))),
% 3.13/3.31 inference(unit_resolution,[status(thm)],[218, 13471])).
% 3.13/3.31 tff(13473,plain,
% 3.13/3.31 (~r(s(s(z)), s(s(s(elem!1))))),
% 3.13/3.31 inference(unit_resolution,[status(thm)],[913, 905, 392, 119])).
% 3.13/3.31 tff(13474,plain,
% 3.13/3.31 (~b(s(s(elem!1)), s(s(z)))),
% 3.13/3.31 inference(unit_resolution,[status(thm)],[501, 13473, 463, 213])).
% 3.13/3.31 tff(13475,plain,
% 3.13/3.31 (r(s(s(elem!1)), s(s(z)))),
% 3.13/3.31 inference(unit_resolution,[status(thm)],[441, 13474, 11])).
% 3.13/3.31 tff(13476,plain,
% 3.13/3.31 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), s(s(elem!1)))) | (~r(s(z), s(s(elem!1)))) | (~r(s(z), s(s(s(elem!1))))) | (~r(s(s(elem!1)), s(s(z)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(elem!1))), s(s(elem!1)))) | (~r(s(z), s(s(elem!1)))) | (~r(s(z), s(s(s(elem!1))))) | (~r(s(s(elem!1)), s(s(z)))))),
% 3.13/3.31 inference(rewrite,[status(thm)],[])).
% 3.13/3.31 tff(13477,plain,
% 3.13/3.31 (((~r(s(s(elem!1)), s(s(z)))) | (~r(s(s(s(elem!1))), s(s(elem!1)))) | (~r(s(z), s(s(elem!1)))) | (~r(s(z), s(s(s(elem!1)))))) <=> ((~r(s(s(s(elem!1))), s(s(elem!1)))) | (~r(s(z), s(s(elem!1)))) | (~r(s(z), s(s(s(elem!1))))) | (~r(s(s(elem!1)), s(s(z)))))),
% 3.13/3.31 inference(rewrite,[status(thm)],[])).
% 3.13/3.31 tff(13478,plain,
% 3.13/3.31 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(elem!1)), s(s(z)))) | (~r(s(s(s(elem!1))), s(s(elem!1)))) | (~r(s(z), s(s(elem!1)))) | (~r(s(z), s(s(s(elem!1))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), s(s(elem!1)))) | (~r(s(z), s(s(elem!1)))) | (~r(s(z), s(s(s(elem!1))))) | (~r(s(s(elem!1)), s(s(z))))))),
% 3.13/3.31 inference(monotonicity,[status(thm)],[13477])).
% 3.13/3.31 tff(13479,plain,
% 3.13/3.31 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(elem!1)), s(s(z)))) | (~r(s(s(s(elem!1))), s(s(elem!1)))) | (~r(s(z), s(s(elem!1)))) | (~r(s(z), s(s(s(elem!1))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(elem!1))), s(s(elem!1)))) | (~r(s(z), s(s(elem!1)))) | (~r(s(z), s(s(s(elem!1))))) | (~r(s(s(elem!1)), s(s(z)))))),
% 3.13/3.31 inference(transitivity,[status(thm)],[13478, 13476])).
% 3.13/3.31 tff(13480,plain,
% 3.13/3.31 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(elem!1)), s(s(z)))) | (~r(s(s(s(elem!1))), s(s(elem!1)))) | (~r(s(z), s(s(elem!1)))) | (~r(s(z), s(s(s(elem!1))))))),
% 3.13/3.31 inference(quant_inst,[status(thm)],[])).
% 3.13/3.31 tff(13481,plain,
% 3.13/3.31 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(elem!1))), s(s(elem!1)))) | (~r(s(z), s(s(elem!1)))) | (~r(s(z), s(s(s(elem!1))))) | (~r(s(s(elem!1)), s(s(z))))),
% 3.13/3.31 inference(modus_ponens,[status(thm)],[13480, 13479])).
% 3.13/3.31 tff(13482,plain,
% 3.13/3.31 ($false),
% 3.13/3.31 inference(unit_resolution,[status(thm)],[13481, 197, 311, 13475, 905, 119])).
% 3.13/3.31 tff(13483,plain,((~r(s(s(s(elem!1))), s(s(elem!1)))) | (~r(s(z), s(s(elem!1)))) | (~r(s(z), s(s(s(elem!1))))) | (s(s(elem!1)) = s(s(z))) | (~b(s(s(elem!1)), s(s(s(elem!1))))) | r(s(s(s(elem!1))), s(s(z))) | (~r(s(s(z)), s(z)))), inference(lemma,lemma(discharge,[]))).
% 3.13/3.31 tff(13484,plain,
% 3.13/3.31 (~r(s(s(s(elem!1))), s(s(elem!1)))),
% 3.13/3.31 inference(unit_resolution,[status(thm)],[13483, 13092, 311, 392, 119, 132, 13471])).
% 3.13/3.31 tff(13485,plain,
% 3.13/3.31 (b(s(s(s(elem!1))), s(s(elem!1)))),
% 3.13/3.31 inference(unit_resolution,[status(thm)],[889, 13484, 51])).
% 3.13/3.31 tff(13486,plain,
% 3.13/3.31 (~r(s(s(z)), s(s(s(elem!1))))),
% 3.13/3.31 inference(unit_resolution,[status(thm)],[3958, 350, 311, 392])).
% 3.13/3.31 tff(13487,plain,
% 3.13/3.31 (~b(s(s(elem!1)), s(s(z)))),
% 3.13/3.31 inference(unit_resolution,[status(thm)],[501, 13092, 13471, 13486])).
% 3.13/3.31 tff(13488,plain,
% 3.13/3.31 (b(s(s(z)), s(s(elem!1)))),
% 3.13/3.31 inference(unit_resolution,[status(thm)],[13102, 13487, 392, 311, 52])).
% 3.13/3.31 tff(13489,plain,
% 3.13/3.31 ($false),
% 3.13/3.31 inference(unit_resolution,[status(thm)],[2068, 13488, 13485, 13472, 13092])).
% 3.13/3.31 tff(13490,plain,((~r(s(s(s(elem!1))), s(z))) | (~r(s(s(z)), s(z))) | (~r(s(z), s(s(elem!1)))) | (s(s(z)) = s(s(elem!1))) | (~r(s(z), s(s(s(elem!1))))) | (s(s(elem!1)) = s(s(s(elem!1))))), inference(lemma,lemma(discharge,[]))).
% 3.13/3.31 tff(13491,plain,
% 3.13/3.31 (s(s(z)) = s(s(elem!1))),
% 3.13/3.31 inference(unit_resolution,[status(thm)],[13490, 13469, 311, 4143, 119, 45])).
% 3.13/3.31 tff(13492,plain,
% 3.13/3.31 (b(z, s(s(elem!1)))),
% 3.13/3.31 inference(unit_resolution,[status(thm)],[12671, 13491])).
% 3.13/3.31 tff(13493,plain,
% 3.13/3.31 (~r(s(s(s(elem!1))), s(s(z)))),
% 3.13/3.31 inference(unit_resolution,[status(thm)],[854, 13469, 311, 4143])).
% 3.13/3.31 tff(13494,plain,
% 3.13/3.31 (~r(s(s(s(elem!1))), s(s(elem!1)))),
% 3.13/3.31 inference(unit_resolution,[status(thm)],[3454, 13491, 13493])).
% 3.13/3.31 tff(13495,plain,
% 3.13/3.31 ($false),
% 3.13/3.31 inference(unit_resolution,[status(thm)],[1834, 13494, 13492, 45, 13460, 13470])).
% 3.13/3.31 tff(13496,plain,((~b(z, s(z))) | (s(s(elem!1)) = s(s(s(elem!1)))) | (~r(s(z), s(s(elem!1)))) | (~r(s(z), s(s(s(elem!1))))) | (~b(s(z), z)) | (~r(s(s(s(elem!1))), z)) | b(s(s(z)), s(z))), inference(lemma,lemma(discharge,[]))).
% 3.13/3.31 tff(13497,plain,
% 3.13/3.31 (~b(z, s(z))),
% 3.13/3.31 inference(unit_resolution,[status(thm)],[13496, 45, 311, 119, 53, 154, 3936])).
% 3.13/3.31 tff(13498,plain,
% 3.13/3.31 (r(z, s(z))),
% 3.13/3.31 inference(unit_resolution,[status(thm)],[321, 13497])).
% 3.13/3.31 tff(13499,plain,
% 3.13/3.31 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), z)) | (~r(z, s(s(s(elem!1))))) | (~r(z, s(z))) | (~r(s(z), s(s(s(elem!1))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(elem!1))), z)) | (~r(z, s(s(s(elem!1))))) | (~r(z, s(z))) | (~r(s(z), s(s(s(elem!1))))))),
% 3.13/3.32 inference(rewrite,[status(thm)],[])).
% 3.13/3.32 tff(13500,plain,
% 3.13/3.32 (((~r(s(s(s(elem!1))), z)) | (~r(s(z), s(s(s(elem!1))))) | (~r(z, s(s(s(elem!1))))) | (~r(z, s(z)))) <=> ((~r(s(s(s(elem!1))), z)) | (~r(z, s(s(s(elem!1))))) | (~r(z, s(z))) | (~r(s(z), s(s(s(elem!1))))))),
% 3.13/3.32 inference(rewrite,[status(thm)],[])).
% 3.13/3.32 tff(13501,plain,
% 3.13/3.32 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), z)) | (~r(s(z), s(s(s(elem!1))))) | (~r(z, s(s(s(elem!1))))) | (~r(z, s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), z)) | (~r(z, s(s(s(elem!1))))) | (~r(z, s(z))) | (~r(s(z), s(s(s(elem!1)))))))),
% 3.13/3.32 inference(monotonicity,[status(thm)],[13500])).
% 3.13/3.32 tff(13502,plain,
% 3.13/3.32 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), z)) | (~r(s(z), s(s(s(elem!1))))) | (~r(z, s(s(s(elem!1))))) | (~r(z, s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(elem!1))), z)) | (~r(z, s(s(s(elem!1))))) | (~r(z, s(z))) | (~r(s(z), s(s(s(elem!1))))))),
% 3.13/3.32 inference(transitivity,[status(thm)],[13501, 13499])).
% 3.13/3.32 tff(13503,plain,
% 3.13/3.32 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), z)) | (~r(s(z), s(s(s(elem!1))))) | (~r(z, s(s(s(elem!1))))) | (~r(z, s(z))))),
% 3.13/3.32 inference(quant_inst,[status(thm)],[])).
% 3.13/3.32 tff(13504,plain,
% 3.13/3.32 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(elem!1))), z)) | (~r(z, s(s(s(elem!1))))) | (~r(z, s(z))) | (~r(s(z), s(s(s(elem!1)))))),
% 3.13/3.32 inference(modus_ponens,[status(thm)],[13503, 13502])).
% 3.13/3.32 tff(13505,plain,
% 3.13/3.32 ($false),
% 3.13/3.32 inference(unit_resolution,[status(thm)],[13504, 197, 154, 323, 119, 282])).
% 3.13/3.32 tff(13506,plain,((~r(z, s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), z)) | (~r(z, s(z))) | (~r(s(z), s(s(s(elem!1)))))), inference(lemma,lemma(discharge,[]))).
% 3.13/3.32 tff(13507,plain,
% 3.13/3.32 (~r(z, s(s(s(elem!1))))),
% 3.13/3.32 inference(unit_resolution,[status(thm)],[13506, 13498, 154, 119])).
% 3.13/3.32 tff(13508,plain,
% 3.13/3.32 (b(z, s(s(s(elem!1))))),
% 3.13/3.32 inference(unit_resolution,[status(thm)],[261, 13507])).
% 3.13/3.32 tff(13509,plain,
% 3.13/3.32 (~r(s(s(s(elem!1))), s(z))),
% 3.13/3.32 inference(unit_resolution,[status(thm)],[373, 13498, 311, 154])).
% 3.13/3.32 tff(13510,plain,
% 3.13/3.32 (b(s(s(s(elem!1))), s(z))),
% 3.13/3.32 inference(unit_resolution,[status(thm)],[1849, 13509])).
% 3.13/3.32 tff(13511,plain,
% 3.13/3.32 (~r(s(s(s(elem!1))), s(z))),
% 3.13/3.32 inference(unit_resolution,[status(thm)],[373, 323, 311, 154])).
% 3.13/3.32 tff(13512,plain,
% 3.13/3.32 (b(s(s(s(elem!1))), s(z))),
% 3.13/3.32 inference(unit_resolution,[status(thm)],[1849, 13511])).
% 3.13/3.32 tff(13513,plain,
% 3.13/3.32 (~b(z, s(s(elem!1)))),
% 3.13/3.32 inference(unit_resolution,[status(thm)],[1834, 1821, 45, 240, 1823])).
% 3.13/3.32 tff(13514,plain,
% 3.13/3.32 (r(z, s(s(elem!1)))),
% 3.13/3.32 inference(unit_resolution,[status(thm)],[1795, 13513])).
% 3.13/3.32 tff(13515,plain,
% 3.13/3.32 (b(s(s(elem!1)), s(s(s(elem!1))))),
% 3.13/3.32 inference(unit_resolution,[status(thm)],[461, 1821, 45])).
% 3.13/3.32 tff(13516,plain,
% 3.13/3.32 (~b(s(s(elem!1)), z)),
% 3.13/3.32 inference(unit_resolution,[status(thm)],[1984, 13515, 96, 53, 240])).
% 3.13/3.32 tff(13517,plain,
% 3.13/3.32 (r(s(s(elem!1)), z)),
% 3.13/3.32 inference(unit_resolution,[status(thm)],[608, 13516])).
% 3.13/3.32 tff(13518,plain,
% 3.13/3.32 ($false),
% 3.13/3.32 inference(unit_resolution,[status(thm)],[1972, 13517, 13514, 311, 323])).
% 3.13/3.32 tff(13519,plain,(r(s(s(elem!1)), s(s(s(elem!1)))) | (~r(s(z), s(s(elem!1)))) | (~r(z, s(z))) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(z), z)) | (~b(z, s(s(s(elem!1))))) | (s(s(elem!1)) = s(s(s(elem!1)))) | r(s(s(s(elem!1))), s(s(elem!1)))), inference(lemma,lemma(discharge,[]))).
% 3.13/3.32 tff(13520,plain,
% 3.13/3.32 (r(s(s(elem!1)), s(s(s(elem!1))))),
% 3.13/3.32 inference(unit_resolution,[status(thm)],[13519, 1823, 323, 13512, 53, 240, 45, 311])).
% 3.13/3.32 tff(13521,plain,
% 3.13/3.32 (~r(s(s(elem!1)), s(z))),
% 3.13/3.32 inference(unit_resolution,[status(thm)],[5310, 13520, 154, 119])).
% 3.13/3.32 tff(13522,plain,
% 3.13/3.32 (b(s(s(elem!1)), s(z))),
% 3.13/3.32 inference(unit_resolution,[status(thm)],[1912, 13521])).
% 3.13/3.32 tff(13523,plain,
% 3.13/3.32 (~r(z, s(s(elem!1)))),
% 3.13/3.32 inference(unit_resolution,[status(thm)],[413, 13520, 311, 323])).
% 3.13/3.32 tff(13524,plain,
% 3.13/3.32 (b(z, s(s(elem!1)))),
% 3.13/3.32 inference(unit_resolution,[status(thm)],[1795, 13523])).
% 3.13/3.32 tff(13525,plain,
% 3.13/3.32 ($false),
% 3.13/3.32 inference(unit_resolution,[status(thm)],[1871, 13524, 13522, 13512, 53, 2329])).
% 3.13/3.32 tff(13526,plain,(r(s(s(s(elem!1))), s(s(elem!1))) | (~b(s(z), z)) | (~r(s(z), s(s(elem!1)))) | (~r(z, s(z))) | (~r(s(s(s(elem!1))), z)) | (~r(s(z), s(s(s(elem!1))))) | (~b(z, s(s(s(elem!1))))) | (s(s(elem!1)) = s(s(s(elem!1))))), inference(lemma,lemma(discharge,[]))).
% 3.13/3.32 tff(13527,plain,
% 3.13/3.32 (r(s(s(s(elem!1))), s(s(elem!1)))),
% 3.13/3.32 inference(unit_resolution,[status(thm)],[13526, 13508, 311, 13498, 154, 119, 53, 45])).
% 3.13/3.32 tff(13528,plain,
% 3.13/3.32 (~r(s(s(elem!1)), s(s(s(elem!1))))),
% 3.13/3.32 inference(unit_resolution,[status(thm)],[2949, 13527, 311, 119])).
% 3.13/3.32 tff(13529,plain,
% 3.13/3.32 (b(s(s(elem!1)), s(s(s(elem!1))))),
% 3.13/3.32 inference(unit_resolution,[status(thm)],[461, 13528, 45])).
% 3.13/3.32 tff(13530,plain,
% 3.13/3.32 (~r(s(s(z)), z)),
% 3.13/3.32 inference(unit_resolution,[status(thm)],[12271, 13498, 4143, 119])).
% 3.13/3.32 tff(13531,plain,
% 3.13/3.32 (b(s(s(z)), z)),
% 3.13/3.32 inference(unit_resolution,[status(thm)],[186, 13530])).
% 3.13/3.32 tff(13532,plain,
% 3.13/3.32 (r(s(s(s(elem!1))), s(s(elem!1)))),
% 3.13/3.32 inference(unit_resolution,[status(thm)],[13526, 240, 311, 323, 154, 119, 53, 45])).
% 3.13/3.32 tff(13533,plain,
% 3.13/3.32 (~r(s(s(elem!1)), s(s(s(elem!1))))),
% 3.13/3.32 inference(unit_resolution,[status(thm)],[2949, 13532, 311, 119])).
% 3.13/3.32 tff(13534,plain,
% 3.13/3.32 (b(s(s(elem!1)), s(s(s(elem!1))))),
% 3.13/3.32 inference(unit_resolution,[status(thm)],[461, 13533, 45])).
% 3.13/3.32 tff(13535,plain,
% 3.13/3.32 (r(s(s(s(elem!1))), s(s(z)))),
% 3.13/3.32 inference(unit_resolution,[status(thm)],[13483, 13534, 311, 392, 119, 11, 13532])).
% 3.13/3.32 tff(13536,plain,
% 3.13/3.32 (~r(s(s(elem!1)), s(s(z)))),
% 3.13/3.32 inference(unit_resolution,[status(thm)],[4313, 13535, 392, 13532])).
% 3.13/3.32 tff(13537,plain,
% 3.13/3.32 (b(s(s(elem!1)), s(s(z)))),
% 3.13/3.32 inference(unit_resolution,[status(thm)],[441, 13536, 11])).
% 3.13/3.32 tff(13538,plain,
% 3.13/3.32 (~b(s(s(elem!1)), z)),
% 3.13/3.32 inference(unit_resolution,[status(thm)],[1984, 13534, 13512, 53, 240])).
% 3.13/3.32 tff(13539,plain,
% 3.13/3.32 (r(s(s(elem!1)), z)),
% 3.13/3.32 inference(unit_resolution,[status(thm)],[608, 13538])).
% 3.13/3.32 tff(13540,plain,
% 3.13/3.32 (~r(s(s(elem!1)), s(z))),
% 3.13/3.32 inference(unit_resolution,[status(thm)],[8590, 13539, 311, 323])).
% 3.13/3.32 tff(13541,plain,
% 3.13/3.32 (b(s(s(elem!1)), s(z))),
% 3.13/3.32 inference(unit_resolution,[status(thm)],[1912, 13540])).
% 3.13/3.32 tff(13542,plain,
% 3.13/3.32 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(z, s(s(z)))) | (~b(s(z), z)) | (~b(s(s(elem!1)), s(s(z)))) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(s(elem!1)), s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(z, s(s(z)))) | (~b(s(z), z)) | (~b(s(s(elem!1)), s(s(z)))) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(s(elem!1)), s(z))))),
% 3.13/3.32 inference(rewrite,[status(thm)],[])).
% 3.13/3.32 tff(13543,plain,
% 3.13/3.32 (((~b(z, s(s(z)))) | (~b(s(s(elem!1)), s(s(z)))) | (~b(s(z), z)) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(s(elem!1)), s(z))) | (~b(s(s(elem!1)), s(s(s(elem!1)))))) <=> ((~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(z, s(s(z)))) | (~b(s(z), z)) | (~b(s(s(elem!1)), s(s(z)))) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(s(elem!1)), s(z))))),
% 3.13/3.32 inference(rewrite,[status(thm)],[])).
% 3.13/3.32 tff(13544,plain,
% 3.13/3.32 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(z)))) | (~b(s(s(elem!1)), s(s(z)))) | (~b(s(z), z)) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(s(elem!1)), s(z))) | (~b(s(s(elem!1)), s(s(s(elem!1))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(z, s(s(z)))) | (~b(s(z), z)) | (~b(s(s(elem!1)), s(s(z)))) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(s(elem!1)), s(z)))))),
% 3.13/3.32 inference(monotonicity,[status(thm)],[13543])).
% 3.13/3.32 tff(13545,plain,
% 3.13/3.32 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(z)))) | (~b(s(s(elem!1)), s(s(z)))) | (~b(s(z), z)) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(s(elem!1)), s(z))) | (~b(s(s(elem!1)), s(s(s(elem!1))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(z, s(s(z)))) | (~b(s(z), z)) | (~b(s(s(elem!1)), s(s(z)))) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(s(elem!1)), s(z))))),
% 3.13/3.32 inference(transitivity,[status(thm)],[13544, 13542])).
% 3.13/3.32 tff(13546,plain,
% 3.13/3.32 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(z)))) | (~b(s(s(elem!1)), s(s(z)))) | (~b(s(z), z)) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(s(elem!1)), s(z))) | (~b(s(s(elem!1)), s(s(s(elem!1))))))),
% 3.13/3.32 inference(quant_inst,[status(thm)],[])).
% 3.13/3.32 tff(13547,plain,
% 3.13/3.32 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(z, s(s(z)))) | (~b(s(z), z)) | (~b(s(s(elem!1)), s(s(z)))) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(s(elem!1)), s(z)))),
% 3.13/3.32 inference(modus_ponens,[status(thm)],[13546, 13545])).
% 3.13/3.32 tff(13548,plain,
% 3.13/3.32 ($false),
% 3.13/3.32 inference(unit_resolution,[status(thm)],[13547, 166, 463, 53, 405, 10451, 96, 310])).
% 3.13/3.32 tff(13549,plain,((~b(s(z), z)) | (~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(s(s(elem!1)), s(s(z)))) | (~b(z, s(s(z)))) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(s(elem!1)), s(z)))), inference(lemma,lemma(discharge,[]))).
% 3.13/3.32 tff(13550,plain,
% 3.13/3.32 ((~b(s(z), z)) | (~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(s(s(elem!1)), s(s(z)))) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(s(elem!1)), s(z)))),
% 3.13/3.32 inference(unit_resolution,[status(thm)],[13549, 10450])).
% 3.13/3.32 tff(13551,plain,
% 3.13/3.32 ($false),
% 3.13/3.32 inference(unit_resolution,[status(thm)],[13550, 13541, 13537, 13512, 53, 13534])).
% 3.13/3.32 tff(13552,plain,((~b(z, s(s(s(elem!1))))) | (~b(s(z), z)) | (s(s(elem!1)) = s(s(z))) | (~r(s(z), s(s(elem!1)))) | (~r(z, s(z))) | (~r(s(s(z)), s(z))) | (~r(s(z), s(s(s(elem!1))))) | (s(s(elem!1)) = s(s(s(elem!1)))) | (~r(s(s(s(elem!1))), z))), inference(lemma,lemma(discharge,[]))).
% 3.13/3.32 tff(13553,plain,
% 3.13/3.32 (s(s(elem!1)) = s(s(z))),
% 3.13/3.32 inference(unit_resolution,[status(thm)],[13552, 13508, 53, 311, 13498, 4143, 119, 45, 154])).
% 3.13/3.32 tff(13554,plain,
% 3.13/3.32 (s(s(z)) = s(s(elem!1))),
% 3.13/3.32 inference(unit_resolution,[status(thm)],[131, 13553])).
% 3.13/3.32 tff(13555,plain,
% 3.13/3.32 (b(s(s(elem!1)), z)),
% 3.13/3.32 inference(unit_resolution,[status(thm)],[2965, 13554, 13531])).
% 3.13/3.32 tff(13556,plain,
% 3.13/3.32 ($false),
% 3.13/3.32 inference(unit_resolution,[status(thm)],[1984, 13555, 13529, 13510, 53, 13508])).
% 3.13/3.32 tff(13557,plain,((s(s(elem!1)) = s(s(s(elem!1)))) | (~b(s(z), z)) | (~r(s(z), s(s(elem!1)))) | (~r(s(z), s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), z)) | b(s(s(z)), s(z))), inference(lemma,lemma(discharge,[]))).
% 3.13/3.32 tff(13558,plain,
% 3.13/3.32 (s(s(elem!1)) = s(s(s(elem!1)))),
% 3.13/3.32 inference(unit_resolution,[status(thm)],[13557, 119, 311, 53, 154, 3936])).
% 3.13/3.32 tff(13559,plain,
% 3.13/3.32 (r(s(s(elem!1)), s(s(z))) <=> r(s(s(s(elem!1))), s(s(z)))),
% 3.13/3.32 inference(monotonicity,[status(thm)],[13558])).
% 3.13/3.32 tff(13560,plain,
% 3.13/3.32 ((s(s(elem!1)) = s(s(z))) <=> (s(s(s(elem!1))) = s(s(z)))),
% 3.13/3.32 inference(monotonicity,[status(thm)],[13558])).
% 3.13/3.32 tff(13561,plain,
% 3.13/3.32 ((s(s(elem!1)) = s(s(z))) <=> (s(s(z)) = s(s(s(elem!1))))),
% 3.13/3.32 inference(transitivity,[status(thm)],[13560, 487])).
% 3.13/3.32 tff(13562,plain,
% 3.13/3.32 ((s(s(z)) = s(s(s(elem!1)))) <=> (s(s(elem!1)) = s(s(z)))),
% 3.13/3.32 inference(symmetry,[status(thm)],[13561])).
% 3.13/3.32 tff(13563,plain,
% 3.13/3.32 ((~(s(s(z)) = s(s(s(elem!1))))) <=> (~(s(s(elem!1)) = s(s(z))))),
% 3.13/3.32 inference(monotonicity,[status(thm)],[13562])).
% 3.13/3.32 tff(13564,plain,
% 3.13/3.32 (~(s(s(elem!1)) = s(s(z)))),
% 3.13/3.32 inference(modus_ponens,[status(thm)],[209, 13563])).
% 3.13/3.32 tff(13565,plain,
% 3.13/3.32 (~r(s(s(z)), s(s(s(elem!1))))),
% 3.13/3.32 inference(unit_resolution,[status(thm)],[3958, 3953, 311, 392])).
% 3.13/3.32 tff(13566,plain,
% 3.13/3.32 (~r(s(s(z)), s(s(elem!1)))),
% 3.13/3.32 inference(unit_resolution,[status(thm)],[338, 13565, 334])).
% 3.13/3.32 tff(13567,plain,
% 3.13/3.32 (b(s(s(z)), s(s(elem!1)))),
% 3.13/3.32 inference(unit_resolution,[status(thm)],[390, 13566, 6641])).
% 3.13/3.32 tff(13568,plain,
% 3.13/3.32 ((~(s(s(z)) = s(s(s(elem!1))))) <=> (~(s(s(elem!1)) = s(s(z))))),
% 3.13/3.32 inference(monotonicity,[status(thm)],[6638])).
% 3.13/3.32 tff(13569,plain,
% 3.13/3.32 (~(s(s(elem!1)) = s(s(z)))),
% 3.13/3.32 inference(modus_ponens,[status(thm)],[209, 13568])).
% 3.13/3.32 tff(13570,plain,
% 3.13/3.32 (~b(s(s(elem!1)), s(z))),
% 3.13/3.32 inference(unit_resolution,[status(thm)],[3849, 3846, 334])).
% 3.13/3.32 tff(13571,plain,
% 3.13/3.32 (r(s(s(elem!1)), s(z))),
% 3.13/3.32 inference(unit_resolution,[status(thm)],[1912, 13570])).
% 3.13/3.32 tff(13572,plain,
% 3.13/3.32 (b(s(s(z)), s(s(s(elem!1))))),
% 3.13/3.32 inference(unit_resolution,[status(thm)],[279, 13565])).
% 3.13/3.32 tff(13573,plain,
% 3.13/3.32 (~r(z, s(z))),
% 3.13/3.32 inference(unit_resolution,[status(thm)],[373, 3953, 311, 154])).
% 3.13/3.32 tff(13574,plain,
% 3.13/3.32 (b(z, s(z))),
% 3.13/3.32 inference(unit_resolution,[status(thm)],[321, 13573])).
% 3.13/3.32 tff(13575,plain,
% 3.13/3.32 (~r(s(s(s(elem!1))), s(s(z)))),
% 3.13/3.32 inference(unit_resolution,[status(thm)],[854, 3953, 311, 392])).
% 3.13/3.32 tff(13576,plain,
% 3.13/3.32 (b(s(s(s(elem!1))), s(s(z)))),
% 3.13/3.32 inference(unit_resolution,[status(thm)],[218, 13575])).
% 3.13/3.32 tff(13577,plain,
% 3.13/3.32 (~b(s(z), s(s(z)))),
% 3.13/3.32 inference(unit_resolution,[status(thm)],[12046, 13576, 13574, 13572])).
% 3.13/3.32 tff(13578,plain,
% 3.13/3.32 (r(s(z), s(s(z)))),
% 3.13/3.32 inference(unit_resolution,[status(thm)],[427, 13577])).
% 3.13/3.32 tff(13579,plain,
% 3.13/3.32 (~r(s(s(elem!1)), s(s(z)))),
% 3.13/3.32 inference(unit_resolution,[status(thm)],[5362, 13578, 392, 13571])).
% 3.13/3.32 tff(13580,plain,
% 3.13/3.32 (b(s(s(elem!1)), s(s(z)))),
% 3.13/3.32 inference(unit_resolution,[status(thm)],[441, 13579, 13569])).
% 3.13/3.32 tff(13581,plain,
% 3.13/3.32 (~b(z, s(s(elem!1)))),
% 3.13/3.32 inference(unit_resolution,[status(thm)],[12611, 13580, 13567])).
% 3.13/3.32 tff(13582,plain,
% 3.13/3.32 (~b(z, s(s(s(elem!1))))),
% 3.13/3.32 inference(unit_resolution,[status(thm)],[4345, 13581, 334])).
% 3.13/3.32 tff(13583,plain,
% 3.13/3.32 (r(z, s(s(s(elem!1))))),
% 3.13/3.32 inference(unit_resolution,[status(thm)],[261, 13582])).
% 3.13/3.32 tff(13584,plain,
% 3.13/3.32 (r(s(s(s(elem!1))), s(s(s(z)))) <=> r(elem!1, s(s(s(z))))),
% 3.13/3.32 inference(monotonicity,[status(thm)],[5659])).
% 3.13/3.32 tff(13585,plain,
% 3.13/3.32 (r(elem!1, s(s(s(z)))) <=> r(s(s(s(elem!1))), s(s(s(z))))),
% 3.13/3.32 inference(symmetry,[status(thm)],[13584])).
% 3.13/3.32 tff(13586,plain,
% 3.13/3.32 (b(s(s(s(elem!1))), s(s(s(z)))) <=> b(elem!1, s(s(s(z))))),
% 3.13/3.32 inference(monotonicity,[status(thm)],[5659])).
% 3.13/3.32 tff(13587,plain,
% 3.13/3.32 (b(elem!1, s(s(s(z)))) <=> b(s(s(s(elem!1))), s(s(s(z))))),
% 3.13/3.32 inference(symmetry,[status(thm)],[13586])).
% 3.13/3.32 tff(13588,plain,
% 3.13/3.32 (b(s(s(s(elem!1))), s(s(s(z))))),
% 3.13/3.32 inference(modus_ponens,[status(thm)],[9035, 13587])).
% 3.13/3.32 tff(13589,plain,
% 3.13/3.32 (r(s(z), s(s(s(z))))),
% 3.13/3.32 inference(unit_resolution,[status(thm)],[1673, 4038, 1669])).
% 3.13/3.32 tff(13590,plain,
% 3.13/3.32 (r(s(s(s(z))), s(z))),
% 3.13/3.32 inference(unit_resolution,[status(thm)],[1762, 4046, 1758])).
% 3.13/3.32 tff(13591,plain,
% 3.13/3.32 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(z)))) | (~b(s(z), z)) | (~b(z, s(z))) | (~b(s(s(z)), s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(s(z)))) | (~b(s(z), z)) | (~b(z, s(z))) | (~b(s(s(z)), s(z))))),
% 3.13/3.32 inference(rewrite,[status(thm)],[])).
% 3.13/3.32 tff(13592,plain,
% 3.13/3.32 (((~b(z, s(s(z)))) | (~b(z, s(s(z)))) | (~b(s(z), z)) | (~b(s(s(z)), s(z))) | (~b(z, s(z))) | (~b(z, s(s(z))))) <=> ((~b(z, s(s(z)))) | (~b(s(z), z)) | (~b(z, s(z))) | (~b(s(s(z)), s(z))))),
% 3.13/3.32 inference(rewrite,[status(thm)],[])).
% 3.13/3.32 tff(13593,plain,
% 3.13/3.32 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(z)))) | (~b(z, s(s(z)))) | (~b(s(z), z)) | (~b(s(s(z)), s(z))) | (~b(z, s(z))) | (~b(z, s(s(z)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(z)))) | (~b(s(z), z)) | (~b(z, s(z))) | (~b(s(s(z)), s(z)))))),
% 3.13/3.32 inference(monotonicity,[status(thm)],[13592])).
% 3.13/3.32 tff(13594,plain,
% 3.13/3.32 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(z)))) | (~b(z, s(s(z)))) | (~b(s(z), z)) | (~b(s(s(z)), s(z))) | (~b(z, s(z))) | (~b(z, s(s(z)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(s(z)))) | (~b(s(z), z)) | (~b(z, s(z))) | (~b(s(s(z)), s(z))))),
% 3.13/3.32 inference(transitivity,[status(thm)],[13593, 13591])).
% 3.13/3.32 tff(13595,plain,
% 3.13/3.32 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(z)))) | (~b(z, s(s(z)))) | (~b(s(z), z)) | (~b(s(s(z)), s(z))) | (~b(z, s(z))) | (~b(z, s(s(z)))))),
% 3.13/3.32 inference(quant_inst,[status(thm)],[])).
% 3.13/3.32 tff(13596,plain,
% 3.13/3.32 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(s(z)))) | (~b(s(z), z)) | (~b(z, s(z))) | (~b(s(s(z)), s(z)))),
% 3.13/3.32 inference(modus_ponens,[status(thm)],[13595, 13594])).
% 3.13/3.32 tff(13597,plain,
% 3.13/3.32 ($false),
% 3.13/3.32 inference(unit_resolution,[status(thm)],[13596, 166, 53, 10451, 118, 156])).
% 3.13/3.32 tff(13598,plain,((~b(s(s(z)), s(z))) | (~b(s(z), z)) | (~b(z, s(s(z)))) | (~b(z, s(z)))), inference(lemma,lemma(discharge,[]))).
% 3.13/3.32 tff(13599,plain,
% 3.13/3.32 (~b(s(s(z)), s(z))),
% 3.13/3.32 inference(unit_resolution,[status(thm)],[13598, 118, 10451, 53])).
% 3.13/3.32 tff(13600,plain,
% 3.13/3.32 (r(s(s(z)), s(z))),
% 3.13/3.32 inference(unit_resolution,[status(thm)],[308, 13599])).
% 3.13/3.32 tff(13601,plain,
% 3.13/3.32 (~r(s(s(z)), s(s(s(z))))),
% 3.13/3.32 inference(unit_resolution,[status(thm)],[5052, 197, 13600, 13590, 13589])).
% 3.13/3.32 tff(13602,plain,
% 3.13/3.32 (b(s(s(z)), s(s(s(z))))),
% 3.13/3.32 inference(unit_resolution,[status(thm)],[1729, 13601, 1725])).
% 3.13/3.32 tff(13603,plain,
% 3.13/3.32 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(z)))) | (~b(s(s(s(elem!1))), s(s(z)))) | (~b(s(s(s(z))), z)) | (~b(s(s(s(elem!1))), s(s(s(z))))) | (~b(s(s(z)), s(s(s(z))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(s(z)))) | (~b(s(s(s(elem!1))), s(s(z)))) | (~b(s(s(s(z))), z)) | (~b(s(s(s(elem!1))), s(s(s(z))))) | (~b(s(s(z)), s(s(s(z))))))),
% 3.13/3.32 inference(rewrite,[status(thm)],[])).
% 3.13/3.32 tff(13604,plain,
% 3.13/3.32 (((~b(z, s(s(z)))) | (~b(s(s(s(elem!1))), s(s(z)))) | (~b(s(s(s(z))), z)) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(s(elem!1))), s(s(s(z))))) | (~b(s(s(s(elem!1))), s(s(z))))) <=> ((~b(z, s(s(z)))) | (~b(s(s(s(elem!1))), s(s(z)))) | (~b(s(s(s(z))), z)) | (~b(s(s(s(elem!1))), s(s(s(z))))) | (~b(s(s(z)), s(s(s(z))))))),
% 3.13/3.32 inference(rewrite,[status(thm)],[])).
% 3.13/3.32 tff(13605,plain,
% 3.13/3.32 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(z)))) | (~b(s(s(s(elem!1))), s(s(z)))) | (~b(s(s(s(z))), z)) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(s(elem!1))), s(s(s(z))))) | (~b(s(s(s(elem!1))), s(s(z)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(z)))) | (~b(s(s(s(elem!1))), s(s(z)))) | (~b(s(s(s(z))), z)) | (~b(s(s(s(elem!1))), s(s(s(z))))) | (~b(s(s(z)), s(s(s(z)))))))),
% 3.13/3.32 inference(monotonicity,[status(thm)],[13604])).
% 3.13/3.32 tff(13606,plain,
% 3.13/3.32 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(z)))) | (~b(s(s(s(elem!1))), s(s(z)))) | (~b(s(s(s(z))), z)) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(s(elem!1))), s(s(s(z))))) | (~b(s(s(s(elem!1))), s(s(z)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(s(z)))) | (~b(s(s(s(elem!1))), s(s(z)))) | (~b(s(s(s(z))), z)) | (~b(s(s(s(elem!1))), s(s(s(z))))) | (~b(s(s(z)), s(s(s(z))))))),
% 3.13/3.33 inference(transitivity,[status(thm)],[13605, 13603])).
% 3.13/3.33 tff(13607,plain,
% 3.13/3.33 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(z)))) | (~b(s(s(s(elem!1))), s(s(z)))) | (~b(s(s(s(z))), z)) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(s(elem!1))), s(s(s(z))))) | (~b(s(s(s(elem!1))), s(s(z)))))),
% 3.13/3.33 inference(quant_inst,[status(thm)],[])).
% 3.13/3.33 tff(13608,plain,
% 3.13/3.33 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(s(z)))) | (~b(s(s(s(elem!1))), s(s(z)))) | (~b(s(s(s(z))), z)) | (~b(s(s(s(elem!1))), s(s(s(z))))) | (~b(s(s(z)), s(s(s(z)))))),
% 3.13/3.33 inference(modus_ponens,[status(thm)],[13607, 13606])).
% 3.13/3.33 tff(13609,plain,
% 3.13/3.33 ($false),
% 3.13/3.33 inference(unit_resolution,[status(thm)],[13608, 166, 10451, 13602, 1699, 2060, 13588])).
% 3.13/3.33 tff(13610,plain,((~b(s(s(s(z))), z)) | (~b(z, s(s(z)))) | (~b(s(s(s(elem!1))), s(s(z)))) | (~b(elem!1, s(s(s(z))))) | (~(s(s(elem!1)) = s(s(s(elem!1))))) | (~b(s(z), z)) | (~b(z, s(z)))), inference(lemma,lemma(discharge,[]))).
% 3.13/3.33 tff(13611,plain,
% 3.13/3.33 (~b(elem!1, s(s(s(z))))),
% 3.13/3.33 inference(unit_resolution,[status(thm)],[13610, 1699, 2060, 10451, 334, 53, 118])).
% 3.13/3.33 tff(13612,plain,
% 3.13/3.33 (r(elem!1, s(s(s(z))))),
% 3.13/3.33 inference(unit_resolution,[status(thm)],[1619, 13611, 8222])).
% 3.13/3.33 tff(13613,plain,
% 3.13/3.33 (r(s(s(s(elem!1))), s(s(s(z))))),
% 3.13/3.33 inference(modus_ponens,[status(thm)],[13612, 13585])).
% 3.13/3.33 tff(13614,plain,
% 3.13/3.33 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), s(s(s(z))))) | (~r(s(z), s(s(s(elem!1))))) | (~r(s(z), s(s(s(z))))) | (~r(s(s(s(z))), s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(elem!1))), s(s(s(z))))) | (~r(s(z), s(s(s(elem!1))))) | (~r(s(z), s(s(s(z))))) | (~r(s(s(s(z))), s(z))))),
% 3.13/3.33 inference(rewrite,[status(thm)],[])).
% 3.13/3.33 tff(13615,plain,
% 3.13/3.33 (((~r(s(s(s(z))), s(z))) | (~r(s(s(s(elem!1))), s(s(s(z))))) | (~r(s(z), s(s(s(z))))) | (~r(s(z), s(s(s(elem!1)))))) <=> ((~r(s(s(s(elem!1))), s(s(s(z))))) | (~r(s(z), s(s(s(elem!1))))) | (~r(s(z), s(s(s(z))))) | (~r(s(s(s(z))), s(z))))),
% 3.13/3.33 inference(rewrite,[status(thm)],[])).
% 3.13/3.33 tff(13616,plain,
% 3.13/3.33 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(z))), s(z))) | (~r(s(s(s(elem!1))), s(s(s(z))))) | (~r(s(z), s(s(s(z))))) | (~r(s(z), s(s(s(elem!1))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), s(s(s(z))))) | (~r(s(z), s(s(s(elem!1))))) | (~r(s(z), s(s(s(z))))) | (~r(s(s(s(z))), s(z)))))),
% 3.13/3.33 inference(monotonicity,[status(thm)],[13615])).
% 3.13/3.33 tff(13617,plain,
% 3.13/3.33 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(z))), s(z))) | (~r(s(s(s(elem!1))), s(s(s(z))))) | (~r(s(z), s(s(s(z))))) | (~r(s(z), s(s(s(elem!1))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(elem!1))), s(s(s(z))))) | (~r(s(z), s(s(s(elem!1))))) | (~r(s(z), s(s(s(z))))) | (~r(s(s(s(z))), s(z))))),
% 3.13/3.33 inference(transitivity,[status(thm)],[13616, 13614])).
% 3.13/3.33 tff(13618,plain,
% 3.13/3.33 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(z))), s(z))) | (~r(s(s(s(elem!1))), s(s(s(z))))) | (~r(s(z), s(s(s(z))))) | (~r(s(z), s(s(s(elem!1))))))),
% 3.13/3.33 inference(quant_inst,[status(thm)],[])).
% 3.13/3.33 tff(13619,plain,
% 3.13/3.33 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(elem!1))), s(s(s(z))))) | (~r(s(z), s(s(s(elem!1))))) | (~r(s(z), s(s(s(z))))) | (~r(s(s(s(z))), s(z)))),
% 3.13/3.33 inference(modus_ponens,[status(thm)],[13618, 13617])).
% 3.13/3.33 tff(13620,plain,
% 3.13/3.33 (~r(s(s(s(elem!1))), s(s(s(z))))),
% 3.13/3.33 inference(unit_resolution,[status(thm)],[13619, 197, 119, 13590, 13589])).
% 3.13/3.33 tff(13621,plain,
% 3.13/3.33 ($false),
% 3.13/3.33 inference(unit_resolution,[status(thm)],[13620, 13613])).
% 3.13/3.33 tff(13622,plain,((~b(s(s(s(z))), z)) | (~(s(s(elem!1)) = s(s(s(elem!1))))) | (~r(s(z), s(s(s(elem!1))))) | (~b(s(z), z)) | (~b(z, s(z))) | (~b(s(s(s(elem!1))), s(s(z)))) | (~b(z, s(s(z))))), inference(lemma,lemma(discharge,[]))).
% 3.13/3.33 tff(13623,plain,
% 3.13/3.33 ((~b(s(s(s(z))), z)) | (~(s(s(elem!1)) = s(s(s(elem!1))))) | (~r(s(z), s(s(s(elem!1))))) | (~b(s(z), z)) | (~b(z, s(z))) | (~b(s(s(s(elem!1))), s(s(z))))),
% 3.13/3.33 inference(unit_resolution,[status(thm)],[13622, 10450])).
% 3.13/3.33 tff(13624,plain,
% 3.13/3.33 (~b(s(s(s(z))), z)),
% 3.13/3.33 inference(unit_resolution,[status(thm)],[13623, 13574, 53, 119, 334, 13576])).
% 3.13/3.33 tff(13625,plain,
% 3.13/3.33 (r(s(s(s(z))), z)),
% 3.13/3.33 inference(unit_resolution,[status(thm)],[1713, 13624])).
% 3.13/3.33 tff(13626,plain,
% 3.13/3.33 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), z)) | (~r(s(s(s(z))), z)) | (~r(s(s(s(z))), s(s(s(elem!1))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), z)) | (~r(s(s(s(z))), z)) | (~r(s(s(s(z))), s(s(s(elem!1))))))),
% 3.13/3.33 inference(rewrite,[status(thm)],[])).
% 3.13/3.33 tff(13627,plain,
% 3.13/3.33 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), z)) | (~r(s(s(s(z))), z)) | (~r(s(s(s(z))), s(s(s(elem!1))))))),
% 3.13/3.33 inference(quant_inst,[status(thm)],[])).
% 3.13/3.33 tff(13628,plain,
% 3.13/3.33 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), z)) | (~r(s(s(s(z))), z)) | (~r(s(s(s(z))), s(s(s(elem!1)))))),
% 3.13/3.33 inference(modus_ponens,[status(thm)],[13627, 13626])).
% 3.13/3.33 tff(13629,plain,
% 3.13/3.33 (~r(s(s(s(z))), s(s(s(elem!1))))),
% 3.13/3.33 inference(unit_resolution,[status(thm)],[13628, 197, 154, 13583, 13625])).
% 3.13/3.33 tff(13630,plain,
% 3.13/3.33 (~r(s(s(s(z))), elem!1)),
% 3.13/3.33 inference(modus_ponens,[status(thm)],[13629, 5509])).
% 3.13/3.33 tff(13631,plain,
% 3.13/3.33 (b(s(s(s(z))), elem!1)),
% 3.13/3.33 inference(unit_resolution,[status(thm)],[2826, 13630, 4027])).
% 3.13/3.33 tff(13632,plain,
% 3.13/3.33 (b(s(s(s(z))), s(s(s(elem!1))))),
% 3.13/3.33 inference(unit_resolution,[status(thm)],[4078, 13631, 4031])).
% 3.13/3.33 tff(13633,plain,
% 3.13/3.33 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), z)) | (~r(s(s(s(elem!1))), s(s(s(z))))) | (~r(z, s(s(s(elem!1))))) | (~r(s(s(s(z))), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(elem!1))), z)) | (~r(s(s(s(elem!1))), s(s(s(z))))) | (~r(z, s(s(s(elem!1))))) | (~r(s(s(s(z))), z)))),
% 3.13/3.33 inference(rewrite,[status(thm)],[])).
% 3.13/3.33 tff(13634,plain,
% 3.13/3.33 (((~r(z, s(s(s(elem!1))))) | (~r(s(s(s(z))), z)) | (~r(s(s(s(elem!1))), z)) | (~r(s(s(s(elem!1))), s(s(s(z)))))) <=> ((~r(s(s(s(elem!1))), z)) | (~r(s(s(s(elem!1))), s(s(s(z))))) | (~r(z, s(s(s(elem!1))))) | (~r(s(s(s(z))), z)))),
% 3.13/3.33 inference(rewrite,[status(thm)],[])).
% 3.13/3.33 tff(13635,plain,
% 3.13/3.33 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(s(elem!1))))) | (~r(s(s(s(z))), z)) | (~r(s(s(s(elem!1))), z)) | (~r(s(s(s(elem!1))), s(s(s(z))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), z)) | (~r(s(s(s(elem!1))), s(s(s(z))))) | (~r(z, s(s(s(elem!1))))) | (~r(s(s(s(z))), z))))),
% 3.13/3.33 inference(monotonicity,[status(thm)],[13634])).
% 3.13/3.33 tff(13636,plain,
% 3.13/3.33 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(s(elem!1))))) | (~r(s(s(s(z))), z)) | (~r(s(s(s(elem!1))), z)) | (~r(s(s(s(elem!1))), s(s(s(z))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(elem!1))), z)) | (~r(s(s(s(elem!1))), s(s(s(z))))) | (~r(z, s(s(s(elem!1))))) | (~r(s(s(s(z))), z)))),
% 3.13/3.33 inference(transitivity,[status(thm)],[13635, 13633])).
% 3.13/3.33 tff(13637,plain,
% 3.13/3.33 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(s(elem!1))))) | (~r(s(s(s(z))), z)) | (~r(s(s(s(elem!1))), z)) | (~r(s(s(s(elem!1))), s(s(s(z))))))),
% 3.13/3.33 inference(quant_inst,[status(thm)],[])).
% 3.13/3.33 tff(13638,plain,
% 3.13/3.33 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(elem!1))), z)) | (~r(s(s(s(elem!1))), s(s(s(z))))) | (~r(z, s(s(s(elem!1))))) | (~r(s(s(s(z))), z))),
% 3.13/3.33 inference(modus_ponens,[status(thm)],[13637, 13636])).
% 3.13/3.33 tff(13639,plain,
% 3.13/3.33 (~r(s(s(s(elem!1))), s(s(s(z))))),
% 3.13/3.33 inference(unit_resolution,[status(thm)],[13638, 197, 154, 13583, 13625])).
% 3.13/3.33 tff(13640,plain,
% 3.13/3.33 (b(s(s(s(elem!1))), s(s(s(z))))),
% 3.13/3.33 inference(unit_resolution,[status(thm)],[3574, 13639, 6474])).
% 3.13/3.33 tff(13641,plain,
% 3.13/3.33 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(s(elem!1))))) | (~r(s(s(z)), z)) | (~r(s(s(s(z))), z)) | (~r(s(s(s(z))), s(s(z)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, s(s(s(elem!1))))) | (~r(s(s(z)), z)) | (~r(s(s(s(z))), z)) | (~r(s(s(s(z))), s(s(z)))))),
% 3.13/3.33 inference(rewrite,[status(thm)],[])).
% 3.13/3.33 tff(13642,plain,
% 3.13/3.33 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(s(elem!1))))) | (~r(s(s(z)), z)) | (~r(s(s(s(z))), z)) | (~r(s(s(s(z))), s(s(z)))))),
% 3.13/3.33 inference(quant_inst,[status(thm)],[])).
% 3.13/3.33 tff(13643,plain,
% 3.13/3.33 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, s(s(s(elem!1))))) | (~r(s(s(z)), z)) | (~r(s(s(s(z))), z)) | (~r(s(s(s(z))), s(s(z))))),
% 3.13/3.33 inference(modus_ponens,[status(thm)],[13642, 13641])).
% 3.13/3.33 tff(13644,plain,
% 3.13/3.33 (~r(s(s(s(z))), s(s(z)))),
% 3.13/3.33 inference(unit_resolution,[status(thm)],[13643, 197, 282, 866, 1733])).
% 3.13/3.33 tff(13645,plain,
% 3.13/3.33 (b(s(s(s(z))), s(s(z)))),
% 3.13/3.33 inference(unit_resolution,[status(thm)],[1010, 13644])).
% 3.13/3.33 tff(13646,plain,
% 3.13/3.33 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(s(elem!1))))) | (~r(s(s(z)), z)) | (~r(s(s(z)), s(s(s(z))))) | (~r(s(s(s(z))), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, s(s(s(elem!1))))) | (~r(s(s(z)), z)) | (~r(s(s(z)), s(s(s(z))))) | (~r(s(s(s(z))), z)))),
% 3.13/3.33 inference(rewrite,[status(thm)],[])).
% 3.13/3.33 tff(13647,plain,
% 3.13/3.33 (((~r(z, s(s(s(elem!1))))) | (~r(s(s(s(z))), z)) | (~r(s(s(z)), z)) | (~r(s(s(z)), s(s(s(z)))))) <=> ((~r(z, s(s(s(elem!1))))) | (~r(s(s(z)), z)) | (~r(s(s(z)), s(s(s(z))))) | (~r(s(s(s(z))), z)))),
% 3.13/3.33 inference(rewrite,[status(thm)],[])).
% 3.13/3.33 tff(13648,plain,
% 3.13/3.33 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(s(elem!1))))) | (~r(s(s(s(z))), z)) | (~r(s(s(z)), z)) | (~r(s(s(z)), s(s(s(z))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(s(elem!1))))) | (~r(s(s(z)), z)) | (~r(s(s(z)), s(s(s(z))))) | (~r(s(s(s(z))), z))))),
% 3.13/3.33 inference(monotonicity,[status(thm)],[13647])).
% 3.13/3.33 tff(13649,plain,
% 3.13/3.33 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(s(elem!1))))) | (~r(s(s(s(z))), z)) | (~r(s(s(z)), z)) | (~r(s(s(z)), s(s(s(z))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, s(s(s(elem!1))))) | (~r(s(s(z)), z)) | (~r(s(s(z)), s(s(s(z))))) | (~r(s(s(s(z))), z)))),
% 3.13/3.33 inference(transitivity,[status(thm)],[13648, 13646])).
% 3.13/3.33 tff(13650,plain,
% 3.13/3.33 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(s(elem!1))))) | (~r(s(s(s(z))), z)) | (~r(s(s(z)), z)) | (~r(s(s(z)), s(s(s(z))))))),
% 3.13/3.33 inference(quant_inst,[status(thm)],[])).
% 3.13/3.33 tff(13651,plain,
% 3.13/3.33 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, s(s(s(elem!1))))) | (~r(s(s(z)), z)) | (~r(s(s(z)), s(s(s(z))))) | (~r(s(s(s(z))), z))),
% 3.13/3.33 inference(modus_ponens,[status(thm)],[13650, 13649])).
% 3.13/3.33 tff(13652,plain,
% 3.13/3.33 (~r(s(s(z)), s(s(s(z))))),
% 3.13/3.33 inference(unit_resolution,[status(thm)],[13651, 197, 282, 866, 1733])).
% 3.13/3.33 tff(13653,plain,
% 3.13/3.33 (b(s(s(z)), s(s(s(z))))),
% 3.13/3.33 inference(unit_resolution,[status(thm)],[1729, 13652, 1725])).
% 3.13/3.33 tff(13654,plain,
% 3.13/3.33 ((~r(s(s(s(z))), s(s(s(elem!1))))) <=> (~r(s(s(s(z))), elem!1))),
% 3.13/3.33 inference(monotonicity,[status(thm)],[8072])).
% 3.13/3.33 tff(13655,plain,
% 3.13/3.33 (~r(s(s(s(z))), s(s(s(elem!1))))),
% 3.13/3.33 inference(unit_resolution,[status(thm)],[13628, 197, 154, 282, 1733])).
% 3.13/3.33 tff(13656,plain,
% 3.13/3.33 (~r(s(s(s(z))), elem!1)),
% 3.13/3.33 inference(modus_ponens,[status(thm)],[13655, 13654])).
% 3.13/3.33 tff(13657,plain,
% 3.13/3.33 (b(s(s(s(z))), elem!1)),
% 3.13/3.33 inference(unit_resolution,[status(thm)],[2826, 13656, 4027])).
% 3.13/3.33 tff(13658,plain,
% 3.13/3.33 (b(s(s(s(z))), s(s(s(elem!1))))),
% 3.13/3.33 inference(modus_ponens,[status(thm)],[13657, 8071])).
% 3.13/3.33 tff(13659,plain,
% 3.13/3.33 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), s(s(z)))) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(s(s(z))), s(s(s(elem!1))))) | (~b(s(s(z)), s(s(s(z))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(elem!1))), s(s(z)))) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(s(s(z))), s(s(s(elem!1))))) | (~b(s(s(z)), s(s(s(z))))))),
% 3.13/3.33 inference(rewrite,[status(thm)],[])).
% 3.13/3.33 tff(13660,plain,
% 3.13/3.33 (((~b(s(s(s(z))), s(s(z)))) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(s(elem!1))), s(s(z)))) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(s(s(z))), s(s(s(elem!1)))))) <=> ((~b(s(s(s(elem!1))), s(s(z)))) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(s(s(z))), s(s(s(elem!1))))) | (~b(s(s(z)), s(s(s(z))))))),
% 3.13/3.33 inference(rewrite,[status(thm)],[])).
% 3.13/3.33 tff(13661,plain,
% 3.13/3.33 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), s(s(z)))) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(s(elem!1))), s(s(z)))) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(s(s(z))), s(s(s(elem!1))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), s(s(z)))) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(s(s(z))), s(s(s(elem!1))))) | (~b(s(s(z)), s(s(s(z)))))))),
% 3.13/3.33 inference(monotonicity,[status(thm)],[13660])).
% 3.13/3.33 tff(13662,plain,
% 3.13/3.33 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), s(s(z)))) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(s(elem!1))), s(s(z)))) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(s(s(z))), s(s(s(elem!1))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(elem!1))), s(s(z)))) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(s(s(z))), s(s(s(elem!1))))) | (~b(s(s(z)), s(s(s(z))))))),
% 3.13/3.33 inference(transitivity,[status(thm)],[13661, 13659])).
% 3.13/3.33 tff(13663,plain,
% 3.13/3.33 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), s(s(z)))) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(s(elem!1))), s(s(z)))) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(s(s(z))), s(s(s(elem!1))))))),
% 3.13/3.33 inference(quant_inst,[status(thm)],[])).
% 3.13/3.33 tff(13664,plain,
% 3.13/3.33 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(elem!1))), s(s(z)))) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(s(s(z))), s(s(s(elem!1))))) | (~b(s(s(z)), s(s(s(z)))))),
% 3.13/3.33 inference(modus_ponens,[status(thm)],[13663, 13662])).
% 3.13/3.33 tff(13665,plain,
% 3.13/3.33 ($false),
% 3.13/3.33 inference(unit_resolution,[status(thm)],[13664, 166, 13658, 13653, 13645, 2060])).
% 3.13/3.33 tff(13666,plain,((~r(s(s(s(z))), z)) | (~b(s(s(s(elem!1))), s(s(z)))) | (~(s(s(elem!1)) = s(s(s(elem!1))))) | (~r(z, s(s(s(elem!1))))) | (~r(s(s(z)), z)) | (~r(s(s(s(elem!1))), z))), inference(lemma,lemma(discharge,[]))).
% 3.13/3.33 tff(13667,plain,
% 3.13/3.33 (~r(s(s(z)), z)),
% 3.13/3.33 inference(unit_resolution,[status(thm)],[13666, 13583, 154, 334, 13625, 13576])).
% 3.13/3.33 tff(13668,plain,
% 3.13/3.33 (b(s(s(z)), z)),
% 3.13/3.33 inference(unit_resolution,[status(thm)],[186, 13667])).
% 3.13/3.33 tff(13669,plain,
% 3.13/3.33 (~b(s(s(s(z))), z)),
% 3.13/3.33 inference(unit_resolution,[status(thm)],[10794, 986, 10451, 446, 122])).
% 3.13/3.33 tff(13670,plain,
% 3.13/3.33 (r(s(s(s(z))), z)),
% 3.13/3.33 inference(unit_resolution,[status(thm)],[1713, 13669])).
% 3.13/3.33 tff(13671,plain,
% 3.13/3.33 (~r(s(s(s(z))), s(s(s(elem!1))))),
% 3.13/3.33 inference(unit_resolution,[status(thm)],[13628, 197, 154, 282, 13670])).
% 3.13/3.33 tff(13672,plain,
% 3.13/3.33 (~r(s(s(s(z))), elem!1)),
% 3.13/3.33 inference(modus_ponens,[status(thm)],[13671, 13654])).
% 3.13/3.33 tff(13673,plain,
% 3.13/3.33 (b(s(s(s(z))), elem!1)),
% 3.13/3.33 inference(unit_resolution,[status(thm)],[2826, 13672, 4027])).
% 3.13/3.33 tff(13674,plain,
% 3.13/3.33 (b(s(s(s(z))), s(s(s(elem!1))))),
% 3.13/3.33 inference(unit_resolution,[status(thm)],[4078, 13673, 4031])).
% 3.13/3.33 tff(13675,plain,
% 3.13/3.33 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), s(s(z)))) | (~b(s(s(z)), s(s(s(elem!1))))) | (~b(s(s(s(z))), s(s(s(elem!1))))) | (~b(s(s(z)), s(s(s(z))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(elem!1))), s(s(z)))) | (~b(s(s(z)), s(s(s(elem!1))))) | (~b(s(s(s(z))), s(s(s(elem!1))))) | (~b(s(s(z)), s(s(s(z))))))),
% 3.13/3.33 inference(rewrite,[status(thm)],[])).
% 3.13/3.33 tff(13676,plain,
% 3.13/3.33 (((~b(s(s(z)), s(s(s(elem!1))))) | (~b(s(s(z)), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(s(z)))) | (~b(s(s(s(z))), s(s(s(elem!1))))) | (~b(s(s(z)), s(s(s(elem!1))))) | (~b(s(s(z)), s(s(s(z)))))) <=> ((~b(s(s(s(elem!1))), s(s(z)))) | (~b(s(s(z)), s(s(s(elem!1))))) | (~b(s(s(s(z))), s(s(s(elem!1))))) | (~b(s(s(z)), s(s(s(z))))))),
% 3.13/3.33 inference(rewrite,[status(thm)],[])).
% 3.13/3.33 tff(13677,plain,
% 3.13/3.33 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), s(s(s(elem!1))))) | (~b(s(s(z)), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(s(z)))) | (~b(s(s(s(z))), s(s(s(elem!1))))) | (~b(s(s(z)), s(s(s(elem!1))))) | (~b(s(s(z)), s(s(s(z))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), s(s(z)))) | (~b(s(s(z)), s(s(s(elem!1))))) | (~b(s(s(s(z))), s(s(s(elem!1))))) | (~b(s(s(z)), s(s(s(z)))))))),
% 3.13/3.33 inference(monotonicity,[status(thm)],[13676])).
% 3.13/3.33 tff(13678,plain,
% 3.13/3.33 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), s(s(s(elem!1))))) | (~b(s(s(z)), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(s(z)))) | (~b(s(s(s(z))), s(s(s(elem!1))))) | (~b(s(s(z)), s(s(s(elem!1))))) | (~b(s(s(z)), s(s(s(z))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(elem!1))), s(s(z)))) | (~b(s(s(z)), s(s(s(elem!1))))) | (~b(s(s(s(z))), s(s(s(elem!1))))) | (~b(s(s(z)), s(s(s(z))))))),
% 3.13/3.33 inference(transitivity,[status(thm)],[13677, 13675])).
% 3.13/3.33 tff(13679,plain,
% 3.13/3.33 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), s(s(s(elem!1))))) | (~b(s(s(z)), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(s(z)))) | (~b(s(s(s(z))), s(s(s(elem!1))))) | (~b(s(s(z)), s(s(s(elem!1))))) | (~b(s(s(z)), s(s(s(z))))))),
% 3.13/3.34 inference(quant_inst,[status(thm)],[])).
% 3.13/3.34 tff(13680,plain,
% 3.13/3.34 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(elem!1))), s(s(z)))) | (~b(s(s(z)), s(s(s(elem!1))))) | (~b(s(s(s(z))), s(s(s(elem!1))))) | (~b(s(s(z)), s(s(s(z)))))),
% 3.13/3.34 inference(modus_ponens,[status(thm)],[13679, 13678])).
% 3.13/3.34 tff(13681,plain,
% 3.13/3.34 ($false),
% 3.13/3.34 inference(unit_resolution,[status(thm)],[13680, 166, 11471, 13674, 986, 2060])).
% 3.13/3.34 tff(13682,plain,((~b(s(s(z)), s(s(s(z))))) | (~b(s(s(s(elem!1))), s(s(z)))) | (~(s(s(elem!1)) = s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), z)) | (~r(z, s(s(s(elem!1))))) | (~b(z, s(s(z)))) | (~b(s(s(z)), s(s(elem!1)))) | (~b(s(s(z)), z))), inference(lemma,lemma(discharge,[]))).
% 3.13/3.34 tff(13683,plain,
% 3.13/3.34 (~b(s(s(z)), s(s(s(z))))),
% 3.13/3.34 inference(unit_resolution,[status(thm)],[13682, 122, 334, 154, 282, 10451, 446, 2060])).
% 3.13/3.34 tff(13684,plain,
% 3.13/3.34 (r(s(s(z)), s(s(s(z))))),
% 3.13/3.34 inference(unit_resolution,[status(thm)],[1730, 13683])).
% 3.13/3.34 tff(13685,plain,
% 3.13/3.34 (~b(s(s(s(z))), z)),
% 3.13/3.34 inference(unit_resolution,[status(thm)],[5078, 122, 392, 53, 118, 120])).
% 3.13/3.34 tff(13686,plain,
% 3.13/3.34 (r(s(s(s(z))), z)),
% 3.13/3.34 inference(unit_resolution,[status(thm)],[1713, 13685])).
% 3.13/3.34 tff(13687,plain,
% 3.13/3.34 ($false),
% 3.13/3.34 inference(unit_resolution,[status(thm)],[12094, 197, 392, 13686, 1653, 13684])).
% 3.13/3.34 tff(13688,plain,((~b(s(s(z)), z)) | (~r(s(s(z)), s(z))) | (~r(s(z), s(s(s(z))))) | (~b(s(z), z)) | (~b(z, s(z))) | (~r(s(z), s(s(z)))) | (~(s(s(elem!1)) = s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), z)) | (~r(z, s(s(s(elem!1))))) | (~b(z, s(s(z)))) | (~b(s(s(z)), s(s(elem!1)))) | (~b(s(s(s(elem!1))), s(s(z))))), inference(lemma,lemma(discharge,[]))).
% 3.13/3.34 tff(13689,plain,
% 3.13/3.34 ((~b(s(s(z)), z)) | (~r(s(s(z)), s(z))) | (~r(s(z), s(s(s(z))))) | (~b(s(z), z)) | (~b(z, s(z))) | (~r(s(z), s(s(z)))) | (~(s(s(elem!1)) = s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), z)) | (~r(z, s(s(s(elem!1))))) | (~b(s(s(z)), s(s(elem!1)))) | (~b(s(s(s(elem!1))), s(s(z))))),
% 3.13/3.34 inference(unit_resolution,[status(thm)],[13688, 10450])).
% 3.13/3.34 tff(13690,plain,
% 3.13/3.34 (~r(s(z), s(s(s(z))))),
% 3.13/3.34 inference(unit_resolution,[status(thm)],[13689, 13668, 53, 392, 334, 13574, 154, 13576, 13567, 13578, 13583])).
% 3.13/3.34 tff(13691,plain,
% 3.13/3.34 (b(s(z), s(s(s(z))))),
% 3.13/3.34 inference(unit_resolution,[status(thm)],[1674, 13690])).
% 3.13/3.34 tff(13692,plain,
% 3.13/3.34 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(z)))) | (~b(s(s(s(elem!1))), s(s(z)))) | (~b(z, s(z))) | (~b(s(s(s(z))), s(s(s(elem!1))))) | (~b(s(z), s(s(s(z))))) | (~b(z, s(s(s(z))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(s(z)))) | (~b(s(s(s(elem!1))), s(s(z)))) | (~b(z, s(z))) | (~b(s(s(s(z))), s(s(s(elem!1))))) | (~b(s(z), s(s(s(z))))) | (~b(z, s(s(s(z))))))),
% 3.13/3.34 inference(rewrite,[status(thm)],[])).
% 3.13/3.34 tff(13693,plain,
% 3.13/3.34 (((~b(s(s(s(elem!1))), s(s(z)))) | (~b(z, s(s(z)))) | (~b(s(s(s(z))), s(s(s(elem!1))))) | (~b(s(z), s(s(s(z))))) | (~b(z, s(s(s(z))))) | (~b(z, s(z)))) <=> ((~b(z, s(s(z)))) | (~b(s(s(s(elem!1))), s(s(z)))) | (~b(z, s(z))) | (~b(s(s(s(z))), s(s(s(elem!1))))) | (~b(s(z), s(s(s(z))))) | (~b(z, s(s(s(z))))))),
% 3.13/3.34 inference(rewrite,[status(thm)],[])).
% 3.13/3.34 tff(13694,plain,
% 3.13/3.34 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), s(s(z)))) | (~b(z, s(s(z)))) | (~b(s(s(s(z))), s(s(s(elem!1))))) | (~b(s(z), s(s(s(z))))) | (~b(z, s(s(s(z))))) | (~b(z, s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(z)))) | (~b(s(s(s(elem!1))), s(s(z)))) | (~b(z, s(z))) | (~b(s(s(s(z))), s(s(s(elem!1))))) | (~b(s(z), s(s(s(z))))) | (~b(z, s(s(s(z)))))))),
% 3.13/3.34 inference(monotonicity,[status(thm)],[13693])).
% 3.13/3.34 tff(13695,plain,
% 3.13/3.34 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), s(s(z)))) | (~b(z, s(s(z)))) | (~b(s(s(s(z))), s(s(s(elem!1))))) | (~b(s(z), s(s(s(z))))) | (~b(z, s(s(s(z))))) | (~b(z, s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(s(z)))) | (~b(s(s(s(elem!1))), s(s(z)))) | (~b(z, s(z))) | (~b(s(s(s(z))), s(s(s(elem!1))))) | (~b(s(z), s(s(s(z))))) | (~b(z, s(s(s(z))))))),
% 3.13/3.34 inference(transitivity,[status(thm)],[13694, 13692])).
% 3.13/3.34 tff(13696,plain,
% 3.13/3.34 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), s(s(z)))) | (~b(z, s(s(z)))) | (~b(s(s(s(z))), s(s(s(elem!1))))) | (~b(s(z), s(s(s(z))))) | (~b(z, s(s(s(z))))) | (~b(z, s(z))))),
% 3.13/3.34 inference(quant_inst,[status(thm)],[])).
% 3.13/3.34 tff(13697,plain,
% 3.13/3.34 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(s(z)))) | (~b(s(s(s(elem!1))), s(s(z)))) | (~b(z, s(z))) | (~b(s(s(s(z))), s(s(s(elem!1))))) | (~b(s(z), s(s(s(z))))) | (~b(z, s(s(s(z)))))),
% 3.13/3.34 inference(modus_ponens,[status(thm)],[13696, 13695])).
% 3.13/3.34 tff(13698,plain,
% 3.13/3.34 (~b(z, s(s(s(z))))),
% 3.13/3.34 inference(unit_resolution,[status(thm)],[13697, 166, 10450, 13574, 13632, 13691, 13576])).
% 3.13/3.34 tff(13699,plain,
% 3.13/3.34 (r(z, s(s(s(z))))),
% 3.13/3.34 inference(unit_resolution,[status(thm)],[1697, 13698])).
% 3.13/3.34 tff(13700,plain,
% 3.13/3.34 ((~b(s(s(z)), s(s(s(z))))) | (~b(s(s(s(elem!1))), s(s(z)))) | (~(s(s(elem!1)) = s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), z)) | (~r(z, s(s(s(elem!1))))) | (~b(s(s(z)), s(s(elem!1)))) | (~b(s(s(z)), z))),
% 3.13/3.34 inference(unit_resolution,[status(thm)],[13682, 10450])).
% 3.13/3.34 tff(13701,plain,
% 3.13/3.34 (~b(s(s(z)), s(s(s(z))))),
% 3.13/3.34 inference(unit_resolution,[status(thm)],[13700, 13668, 154, 334, 13576, 13583, 13567])).
% 3.13/3.34 tff(13702,plain,
% 3.13/3.34 (r(s(s(z)), s(s(s(z))))),
% 3.13/3.34 inference(unit_resolution,[status(thm)],[1730, 13701])).
% 3.13/3.34 tff(13703,plain,
% 3.13/3.34 (~b(s(s(s(z))), s(s(z)))),
% 3.13/3.34 inference(unit_resolution,[status(thm)],[4130, 166, 13572, 13632, 13640])).
% 3.13/3.34 tff(13704,plain,
% 3.13/3.34 (r(s(s(s(z))), s(s(z)))),
% 3.13/3.34 inference(unit_resolution,[status(thm)],[1010, 13703])).
% 3.13/3.34 tff(13705,plain,
% 3.13/3.34 (~r(s(s(z)), s(s(s(s(z)))))),
% 3.13/3.34 inference(unit_resolution,[status(thm)],[6600, 197, 1676, 4680, 1732])).
% 3.13/3.34 tff(13706,plain,
% 3.13/3.34 (b(s(s(z)), s(s(s(s(z)))))),
% 3.13/3.34 inference(unit_resolution,[status(thm)],[4753, 13705])).
% 3.13/3.34 tff(13707,plain,
% 3.13/3.34 (~r(s(s(s(s(z)))), z)),
% 3.13/3.34 inference(unit_resolution,[status(thm)],[13001, 197, 1677, 1676, 4680])).
% 3.13/3.34 tff(13708,plain,
% 3.13/3.34 (b(s(s(s(s(z)))), z)),
% 3.13/3.34 inference(unit_resolution,[status(thm)],[3266, 13707])).
% 3.13/3.34 tff(13709,plain,
% 3.13/3.34 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(z)))) | (~b(s(s(z)), z)) | (~b(s(s(z)), s(s(s(elem!1))))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(s(z)))) | (~b(s(s(z)), z)) | (~b(s(s(z)), s(s(s(elem!1))))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), z)))),
% 3.13/3.34 inference(rewrite,[status(thm)],[])).
% 3.13/3.34 tff(13710,plain,
% 3.13/3.34 (((~b(s(s(z)), s(s(s(elem!1))))) | (~b(s(s(z)), s(s(s(elem!1))))) | (~b(z, s(s(z)))) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(z)), z)) | (~b(s(s(z)), s(s(s(s(z))))))) <=> ((~b(z, s(s(z)))) | (~b(s(s(z)), z)) | (~b(s(s(z)), s(s(s(elem!1))))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), z)))),
% 3.13/3.34 inference(rewrite,[status(thm)],[])).
% 3.13/3.34 tff(13711,plain,
% 3.13/3.34 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), s(s(s(elem!1))))) | (~b(s(s(z)), s(s(s(elem!1))))) | (~b(z, s(s(z)))) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(z)), z)) | (~b(s(s(z)), s(s(s(s(z)))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(z)))) | (~b(s(s(z)), z)) | (~b(s(s(z)), s(s(s(elem!1))))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), z))))),
% 3.13/3.34 inference(monotonicity,[status(thm)],[13710])).
% 3.13/3.34 tff(13712,plain,
% 3.13/3.34 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), s(s(s(elem!1))))) | (~b(s(s(z)), s(s(s(elem!1))))) | (~b(z, s(s(z)))) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(z)), z)) | (~b(s(s(z)), s(s(s(s(z)))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(s(z)))) | (~b(s(s(z)), z)) | (~b(s(s(z)), s(s(s(elem!1))))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), z)))),
% 3.13/3.34 inference(transitivity,[status(thm)],[13711, 13709])).
% 3.13/3.34 tff(13713,plain,
% 3.13/3.34 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), s(s(s(elem!1))))) | (~b(s(s(z)), s(s(s(elem!1))))) | (~b(z, s(s(z)))) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(z)), z)) | (~b(s(s(z)), s(s(s(s(z)))))))),
% 3.13/3.34 inference(quant_inst,[status(thm)],[])).
% 3.13/3.34 tff(13714,plain,
% 3.13/3.34 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(s(z)))) | (~b(s(s(z)), z)) | (~b(s(s(z)), s(s(s(elem!1))))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), z))),
% 3.13/3.34 inference(modus_ponens,[status(thm)],[13713, 13712])).
% 3.13/3.34 tff(13715,plain,
% 3.13/3.34 ($false),
% 3.13/3.34 inference(unit_resolution,[status(thm)],[13714, 166, 10450, 263, 122, 13708, 13706])).
% 3.13/3.34 tff(13716,plain,((~r(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(z)), s(s(s(elem!1))))) | (~b(s(s(z)), z)) | (~r(s(s(s(z))), s(s(z)))) | (~r(s(s(z)), s(s(s(z))))) | (~r(z, s(s(s(z)))))), inference(lemma,lemma(discharge,[]))).
% 3.13/3.34 tff(13717,plain,
% 3.13/3.34 (~r(s(s(s(s(z)))), s(s(s(z))))),
% 3.13/3.34 inference(unit_resolution,[status(thm)],[13716, 13572, 13668, 13704, 13702, 13699])).
% 3.13/3.34 tff(13718,plain,
% 3.13/3.34 (b(s(s(s(s(z)))), s(s(s(z))))),
% 3.13/3.34 inference(unit_resolution,[status(thm)],[4662, 13717])).
% 3.13/3.34 tff(13719,plain,
% 3.13/3.34 (~b(s(s(s(elem!1))), s(s(s(s(z)))))),
% 3.13/3.34 inference(unit_resolution,[status(thm)],[6561, 13718, 13576, 13640, 13632])).
% 3.13/3.34 tff(13720,plain,
% 3.13/3.34 (~b(s(s(s(s(elem!1)))), s(s(s(s(z)))))),
% 3.13/3.34 inference(unit_resolution,[status(thm)],[12962, 13719, 334])).
% 3.13/3.34 tff(13721,plain,
% 3.13/3.34 (~b(elem!1, s(s(s(s(z)))))),
% 3.13/3.34 inference(unit_resolution,[status(thm)],[12970, 13720, 334])).
% 3.13/3.34 tff(13722,plain,
% 3.13/3.34 (r(elem!1, s(s(s(s(z)))))),
% 3.13/3.34 inference(unit_resolution,[status(thm)],[1098, 13721, 6568])).
% 3.13/3.34 tff(13723,plain,
% 3.13/3.34 (r(s(s(s(elem!1))), s(s(s(s(z)))))),
% 3.13/3.34 inference(unit_resolution,[status(thm)],[5665, 13722, 334])).
% 3.13/3.34 tff(13724,plain,
% 3.13/3.34 (~r(s(s(s(s(z)))), z)),
% 3.13/3.34 inference(unit_resolution,[status(thm)],[6585, 13723, 154, 13583])).
% 3.13/3.34 tff(13725,plain,
% 3.13/3.34 (b(s(s(s(s(z)))), z)),
% 3.13/3.34 inference(unit_resolution,[status(thm)],[3266, 13724])).
% 3.13/3.34 tff(13726,plain,
% 3.13/3.34 (~b(s(s(z)), s(s(s(s(z)))))),
% 3.13/3.34 inference(unit_resolution,[status(thm)],[13714, 166, 10450, 13572, 13668, 13725])).
% 3.13/3.34 tff(13727,plain,
% 3.13/3.34 (r(s(s(z)), s(s(s(s(z)))))),
% 3.13/3.34 inference(unit_resolution,[status(thm)],[4753, 13726])).
% 3.13/3.34 tff(13728,plain,
% 3.13/3.34 (~b(s(z), s(s(s(s(z)))))),
% 3.13/3.34 inference(unit_resolution,[status(thm)],[12979, 166, 13632, 13691, 13718, 13640])).
% 3.13/3.34 tff(13729,plain,
% 3.13/3.34 (r(s(z), s(s(s(s(z)))))),
% 3.13/3.34 inference(unit_resolution,[status(thm)],[3302, 13728])).
% 3.13/3.34 tff(13730,plain,
% 3.13/3.34 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), z)) | (~b(z, s(z))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(s(z)))), z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), z)) | (~b(z, s(z))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(s(z)))), z)))),
% 3.13/3.34 inference(rewrite,[status(thm)],[])).
% 3.13/3.34 tff(13731,plain,
% 3.13/3.34 (((~b(s(z), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(z, s(z))) | (~b(s(z), z)) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(s(z)))), s(z)))) <=> ((~b(s(z), z)) | (~b(z, s(z))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(s(z)))), z)))),
% 3.13/3.34 inference(rewrite,[status(thm)],[])).
% 3.13/3.34 tff(13732,plain,
% 3.13/3.34 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(z, s(z))) | (~b(s(z), z)) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(s(z)))), s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), z)) | (~b(z, s(z))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(s(z)))), z))))),
% 3.13/3.34 inference(monotonicity,[status(thm)],[13731])).
% 3.13/3.34 tff(13733,plain,
% 3.13/3.34 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(z, s(z))) | (~b(s(z), z)) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(s(z)))), s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), z)) | (~b(z, s(z))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(s(z)))), z)))),
% 3.13/3.34 inference(transitivity,[status(thm)],[13732, 13730])).
% 3.13/3.34 tff(13734,plain,
% 3.13/3.34 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(z, s(z))) | (~b(s(z), z)) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(s(z)))), s(z))))),
% 3.13/3.34 inference(quant_inst,[status(thm)],[])).
% 3.13/3.34 tff(13735,plain,
% 3.13/3.34 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), z)) | (~b(z, s(z))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(s(z)))), z))),
% 3.13/3.34 inference(modus_ponens,[status(thm)],[13734, 13733])).
% 3.13/3.34 tff(13736,plain,
% 3.13/3.34 (~b(s(s(s(s(z)))), s(z))),
% 3.13/3.34 inference(unit_resolution,[status(thm)],[13735, 166, 53, 13574, 13691, 13718, 13725])).
% 3.13/3.34 tff(13737,plain,
% 3.13/3.34 (r(s(s(s(s(z)))), s(z))),
% 3.13/3.34 inference(unit_resolution,[status(thm)],[3285, 13736])).
% 3.13/3.34 tff(13738,plain,
% 3.13/3.34 ($false),
% 3.13/3.34 inference(unit_resolution,[status(thm)],[4776, 197, 13578, 13737, 13729, 13727])).
% 3.13/3.34 tff(13739,plain,(b(s(s(s(elem!1))), s(z)) | (~b(s(z), z)) | (~r(s(s(s(elem!1))), z)) | (~(s(s(elem!1)) = s(s(s(elem!1))))) | (~r(s(s(z)), s(z))) | (~r(s(z), s(s(s(elem!1))))) | (~r(s(z), s(s(elem!1))))), inference(lemma,lemma(discharge,[]))).
% 3.13/3.34 tff(13740,plain,
% 3.13/3.34 (b(s(s(s(elem!1))), s(z))),
% 3.13/3.34 inference(unit_resolution,[status(thm)],[13739, 13558, 154, 53, 4143, 119, 311])).
% 3.13/3.34 tff(13741,plain,
% 3.13/3.34 (~r(z, s(z))),
% 3.13/3.34 inference(unit_resolution,[status(thm)],[13506, 282, 154, 119])).
% 3.13/3.34 tff(13742,plain,
% 3.13/3.34 (b(z, s(z))),
% 3.13/3.34 inference(unit_resolution,[status(thm)],[321, 13741])).
% 3.13/3.34 tff(13743,plain,
% 3.13/3.34 (~b(s(s(s(z))), z)),
% 3.13/3.34 inference(unit_resolution,[status(thm)],[4093, 13292, 334, 53, 119, 96, 392, 13742])).
% 3.13/3.34 tff(13744,plain,
% 3.13/3.34 (r(s(s(s(z))), z)),
% 3.13/3.34 inference(unit_resolution,[status(thm)],[1713, 13743])).
% 3.13/3.34 tff(13745,plain,
% 3.13/3.34 (~r(s(s(s(elem!1))), s(s(s(z))))),
% 3.13/3.34 inference(unit_resolution,[status(thm)],[13638, 197, 154, 282, 13744])).
% 3.13/3.34 tff(13746,plain,
% 3.13/3.34 (b(s(s(s(elem!1))), s(s(s(z))))),
% 3.13/3.34 inference(unit_resolution,[status(thm)],[3574, 13745, 6474])).
% 3.13/3.34 tff(13747,plain,
% 3.13/3.34 (~r(s(s(s(z))), s(s(s(elem!1))))),
% 3.13/3.34 inference(unit_resolution,[status(thm)],[13628, 197, 154, 282, 13744])).
% 3.13/3.34 tff(13748,plain,
% 3.13/3.34 (~r(s(s(s(z))), elem!1)),
% 3.13/3.34 inference(modus_ponens,[status(thm)],[13747, 5509])).
% 3.13/3.34 tff(13749,plain,
% 3.13/3.34 (b(s(s(s(z))), elem!1)),
% 3.13/3.34 inference(unit_resolution,[status(thm)],[2826, 13748, 4027])).
% 3.13/3.34 tff(13750,plain,
% 3.13/3.34 (b(s(s(s(z))), s(s(s(elem!1))))),
% 3.13/3.34 inference(unit_resolution,[status(thm)],[4078, 13749, 4031])).
% 3.13/3.34 tff(13751,plain,
% 3.13/3.34 (~b(s(s(z)), s(s(s(z))))),
% 3.13/3.34 inference(unit_resolution,[status(thm)],[5519, 166, 13292, 13750, 13746])).
% 3.13/3.34 tff(13752,plain,
% 3.13/3.34 (r(s(s(z)), s(s(s(z))))),
% 3.13/3.34 inference(unit_resolution,[status(thm)],[1730, 13751])).
% 3.13/3.34 tff(13753,plain,
% 3.13/3.34 (~r(s(z), s(s(s(z))))),
% 3.13/3.34 inference(unit_resolution,[status(thm)],[12096, 13752, 392, 13744])).
% 3.13/3.34 tff(13754,plain,
% 3.13/3.34 (b(s(z), s(s(s(z))))),
% 3.13/3.34 inference(unit_resolution,[status(thm)],[1674, 13753])).
% 3.13/3.34 tff(13755,plain,
% 3.13/3.34 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), s(z))) | (~b(s(s(s(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, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(s(s(z))), s(s(s(elem!1))))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(elem!1))), s(s(s(z))))))),
% 3.13/3.34 inference(rewrite,[status(thm)],[])).
% 3.13/3.34 tff(13756,plain,
% 3.13/3.34 (((~b(s(s(s(elem!1))), s(z))) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(s(s(z))), s(s(s(elem!1))))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(elem!1))), s(s(s(z))))) | (~b(s(s(s(elem!1))), s(z)))) <=> ((~b(s(s(s(elem!1))), s(z))) | (~b(s(s(s(z))), s(s(s(elem!1))))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(elem!1))), s(s(s(z))))))),
% 3.13/3.34 inference(rewrite,[status(thm)],[])).
% 3.13/3.34 tff(13757,plain,
% 3.13/3.34 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), s(z))) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(s(s(z))), s(s(s(elem!1))))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(elem!1))), s(s(s(z))))) | (~b(s(s(s(elem!1))), s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), s(z))) | (~b(s(s(s(z))), s(s(s(elem!1))))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(elem!1))), s(s(s(z)))))))),
% 3.13/3.34 inference(monotonicity,[status(thm)],[13756])).
% 3.13/3.34 tff(13758,plain,
% 3.13/3.34 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), s(z))) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(s(s(z))), s(s(s(elem!1))))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(elem!1))), s(s(s(z))))) | (~b(s(s(s(elem!1))), s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(s(s(z))), s(s(s(elem!1))))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(elem!1))), s(s(s(z))))))),
% 3.13/3.34 inference(transitivity,[status(thm)],[13757, 13755])).
% 3.13/3.34 tff(13759,plain,
% 3.13/3.34 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), s(z))) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(s(s(z))), s(s(s(elem!1))))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(elem!1))), s(s(s(z))))) | (~b(s(s(s(elem!1))), s(z))))),
% 3.13/3.34 inference(quant_inst,[status(thm)],[])).
% 3.13/3.34 tff(13760,plain,
% 3.13/3.34 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(s(s(z))), s(s(s(elem!1))))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(elem!1))), s(s(s(z)))))),
% 3.13/3.35 inference(modus_ponens,[status(thm)],[13759, 13758])).
% 3.13/3.35 tff(13761,plain,
% 3.13/3.35 ($false),
% 3.13/3.35 inference(unit_resolution,[status(thm)],[13760, 166, 96, 13750, 13754, 13746])).
% 3.13/3.35 tff(13762,plain,((~r(z, s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(z))) | (~r(s(s(z)), s(z))) | (~(s(s(elem!1)) = s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), z)) | (~b(s(z), z)) | (~r(s(z), s(s(s(elem!1)))))), inference(lemma,lemma(discharge,[]))).
% 3.13/3.35 tff(13763,plain,
% 3.13/3.35 (~r(z, s(s(s(elem!1))))),
% 3.13/3.35 inference(unit_resolution,[status(thm)],[13762, 13740, 4143, 13558, 154, 53, 119])).
% 3.13/3.35 tff(13764,plain,
% 3.13/3.35 (b(z, s(s(s(elem!1))))),
% 3.13/3.35 inference(unit_resolution,[status(thm)],[261, 13763])).
% 3.13/3.35 tff(13765,plain,
% 3.13/3.35 (b(z, s(s(elem!1)))),
% 3.13/3.35 inference(unit_resolution,[status(thm)],[4345, 13764, 13558])).
% 3.13/3.35 tff(13766,plain,
% 3.13/3.35 ((s(s(z)) = s(s(s(elem!1)))) <=> (s(s(z)) = s(s(elem!1)))),
% 3.13/3.35 inference(transitivity,[status(thm)],[13562, 127])).
% 3.13/3.35 tff(13767,plain,
% 3.13/3.35 ((~(s(s(z)) = s(s(s(elem!1))))) <=> (~(s(s(z)) = s(s(elem!1))))),
% 3.13/3.35 inference(monotonicity,[status(thm)],[13766])).
% 3.13/3.35 tff(13768,plain,
% 3.13/3.35 (~(s(s(z)) = s(s(elem!1)))),
% 3.13/3.35 inference(modus_ponens,[status(thm)],[209, 13767])).
% 3.13/3.35 tff(13769,plain,
% 3.13/3.35 (~b(z, s(z))),
% 3.13/3.35 inference(unit_resolution,[status(thm)],[13467, 13764, 53, 13740])).
% 3.13/3.35 tff(13770,plain,
% 3.13/3.35 (r(z, s(z))),
% 3.13/3.35 inference(unit_resolution,[status(thm)],[321, 13769])).
% 3.13/3.35 tff(13771,plain,
% 3.13/3.35 (~r(s(s(z)), z)),
% 3.13/3.35 inference(unit_resolution,[status(thm)],[12271, 13770, 4143, 119])).
% 3.13/3.35 tff(13772,plain,
% 3.13/3.35 (b(s(s(z)), z)),
% 3.13/3.35 inference(unit_resolution,[status(thm)],[186, 13771])).
% 3.13/3.35 tff(13773,plain,
% 3.13/3.35 (~b(s(z), s(s(z)))),
% 3.13/3.35 inference(unit_resolution,[status(thm)],[12847, 13772, 53])).
% 3.13/3.35 tff(13774,plain,
% 3.13/3.35 (r(s(z), s(s(z)))),
% 3.13/3.35 inference(unit_resolution,[status(thm)],[427, 13773])).
% 3.13/3.35 tff(13775,plain,
% 3.13/3.35 (~r(s(s(z)), s(s(s(elem!1))))),
% 3.13/3.35 inference(unit_resolution,[status(thm)],[2304, 13774, 154, 119])).
% 3.13/3.35 tff(13776,plain,
% 3.13/3.35 (~r(s(s(z)), s(s(elem!1)))),
% 3.13/3.35 inference(unit_resolution,[status(thm)],[338, 13775, 13558])).
% 3.13/3.35 tff(13777,plain,
% 3.13/3.35 (b(s(s(z)), s(s(elem!1)))),
% 3.13/3.35 inference(unit_resolution,[status(thm)],[390, 13776, 13768])).
% 3.13/3.35 tff(13778,plain,
% 3.13/3.35 (~b(s(s(elem!1)), s(s(z)))),
% 3.13/3.35 inference(unit_resolution,[status(thm)],[12611, 13777, 13765])).
% 3.13/3.35 tff(13779,plain,
% 3.13/3.35 (r(s(s(elem!1)), s(s(z)))),
% 3.13/3.35 inference(unit_resolution,[status(thm)],[441, 13778, 13564])).
% 3.13/3.35 tff(13780,plain,
% 3.13/3.35 (r(s(s(s(elem!1))), s(s(z)))),
% 3.13/3.35 inference(modus_ponens,[status(thm)],[13779, 13559])).
% 3.13/3.35 tff(13781,plain,
% 3.13/3.35 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(s(s(elem!1))))) | (~r(s(s(z)), s(z))) | (~r(s(z), s(s(z)))) | (~r(s(s(s(elem!1))), s(s(z)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(z), s(s(s(elem!1))))) | (~r(s(s(z)), s(z))) | (~r(s(z), s(s(z)))) | (~r(s(s(s(elem!1))), s(s(z)))))),
% 3.13/3.35 inference(rewrite,[status(thm)],[])).
% 3.13/3.35 tff(13782,plain,
% 3.13/3.35 (((~r(s(s(z)), s(z))) | (~r(s(s(s(elem!1))), s(s(z)))) | (~r(s(z), s(s(z)))) | (~r(s(z), s(s(s(elem!1)))))) <=> ((~r(s(z), s(s(s(elem!1))))) | (~r(s(s(z)), s(z))) | (~r(s(z), s(s(z)))) | (~r(s(s(s(elem!1))), s(s(z)))))),
% 3.13/3.35 inference(rewrite,[status(thm)],[])).
% 3.13/3.35 tff(13783,plain,
% 3.13/3.35 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(z)), s(z))) | (~r(s(s(s(elem!1))), s(s(z)))) | (~r(s(z), s(s(z)))) | (~r(s(z), s(s(s(elem!1))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(s(s(elem!1))))) | (~r(s(s(z)), s(z))) | (~r(s(z), s(s(z)))) | (~r(s(s(s(elem!1))), s(s(z))))))),
% 3.13/3.35 inference(monotonicity,[status(thm)],[13782])).
% 3.13/3.35 tff(13784,plain,
% 3.13/3.35 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(z)), s(z))) | (~r(s(s(s(elem!1))), s(s(z)))) | (~r(s(z), s(s(z)))) | (~r(s(z), s(s(s(elem!1))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(z), s(s(s(elem!1))))) | (~r(s(s(z)), s(z))) | (~r(s(z), s(s(z)))) | (~r(s(s(s(elem!1))), s(s(z)))))),
% 3.13/3.35 inference(transitivity,[status(thm)],[13783, 13781])).
% 3.13/3.35 tff(13785,plain,
% 3.13/3.35 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(z)), s(z))) | (~r(s(s(s(elem!1))), s(s(z)))) | (~r(s(z), s(s(z)))) | (~r(s(z), s(s(s(elem!1))))))),
% 3.13/3.35 inference(quant_inst,[status(thm)],[])).
% 3.13/3.35 tff(13786,plain,
% 3.13/3.35 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(z), s(s(s(elem!1))))) | (~r(s(s(z)), s(z))) | (~r(s(z), s(s(z)))) | (~r(s(s(s(elem!1))), s(s(z))))),
% 3.13/3.35 inference(modus_ponens,[status(thm)],[13785, 13784])).
% 3.13/3.35 tff(13787,plain,
% 3.13/3.35 ($false),
% 3.13/3.35 inference(unit_resolution,[status(thm)],[13786, 197, 13774, 4143, 119, 13780])).
% 3.13/3.35 tff(13788,plain,((~r(s(z), s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), z)) | (~b(s(z), z)) | (~r(s(z), s(s(elem!1)))) | b(s(s(z)), s(z))), inference(lemma,lemma(discharge,[]))).
% 3.13/3.35 tff(13789,plain,
% 3.13/3.35 (~r(s(z), s(s(s(elem!1))))),
% 3.13/3.35 inference(unit_resolution,[status(thm)],[13788, 3936, 53, 85, 13084])).
% 3.13/3.35 tff(13790,plain,
% 3.13/3.35 (b(s(z), s(s(s(elem!1))))),
% 3.13/3.35 inference(unit_resolution,[status(thm)],[116, 13789])).
% 3.13/3.35 tff(13791,plain,
% 3.13/3.35 (~(s(s(elem!1)) = s(s(s(elem!1))))),
% 3.13/3.35 inference(unit_resolution,[status(thm)],[12329, 13790, 54])).
% 3.13/3.35 tff(13792,plain,
% 3.13/3.35 (b(s(s(z)), s(s(s(elem!1))))),
% 3.13/3.35 inference(unit_resolution,[status(thm)],[279, 13486])).
% 3.13/3.35 tff(13793,plain,
% 3.13/3.35 (~b(z, s(s(s(elem!1))))),
% 3.13/3.35 inference(unit_resolution,[status(thm)],[10577, 166, 10450, 13792, 13472])).
% 3.13/3.35 tff(13794,plain,
% 3.13/3.35 (r(z, s(s(s(elem!1))))),
% 3.13/3.35 inference(unit_resolution,[status(thm)],[261, 13793])).
% 3.13/3.35 tff(13795,plain,
% 3.13/3.35 (~r(z, s(z))),
% 3.13/3.35 inference(unit_resolution,[status(thm)],[373, 350, 311, 154])).
% 3.13/3.35 tff(13796,plain,
% 3.13/3.35 (b(z, s(z))),
% 3.13/3.35 inference(unit_resolution,[status(thm)],[321, 13795])).
% 3.13/3.35 tff(13797,plain,
% 3.13/3.35 (~b(s(z), s(s(z)))),
% 3.13/3.35 inference(unit_resolution,[status(thm)],[12046, 13472, 13796, 13792])).
% 3.13/3.35 tff(13798,plain,
% 3.13/3.35 (r(s(z), s(s(z)))),
% 3.13/3.35 inference(unit_resolution,[status(thm)],[427, 13797])).
% 3.13/3.35 tff(13799,plain,
% 3.13/3.35 (~r(z, s(s(elem!1)))),
% 3.13/3.35 inference(unit_resolution,[status(thm)],[933, 377, 350, 282])).
% 3.13/3.35 tff(13800,plain,
% 3.13/3.35 (b(z, s(s(elem!1)))),
% 3.13/3.35 inference(unit_resolution,[status(thm)],[1795, 13799])).
% 3.13/3.35 tff(13801,plain,
% 3.13/3.35 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(z)))) | (~b(z, s(s(elem!1)))) | (~b(s(z), z)) | (~b(z, s(z))) | (~b(s(s(elem!1)), s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(s(z)))) | (~b(z, s(s(elem!1)))) | (~b(s(z), z)) | (~b(z, s(z))) | (~b(s(s(elem!1)), s(z))))),
% 3.13/3.35 inference(rewrite,[status(thm)],[])).
% 3.13/3.35 tff(13802,plain,
% 3.13/3.35 (((~b(z, s(s(z)))) | (~b(z, s(s(z)))) | (~b(s(z), z)) | (~b(s(s(elem!1)), s(z))) | (~b(z, s(z))) | (~b(z, s(s(elem!1))))) <=> ((~b(z, s(s(z)))) | (~b(z, s(s(elem!1)))) | (~b(s(z), z)) | (~b(z, s(z))) | (~b(s(s(elem!1)), s(z))))),
% 3.13/3.35 inference(rewrite,[status(thm)],[])).
% 3.13/3.35 tff(13803,plain,
% 3.13/3.35 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(z)))) | (~b(z, s(s(z)))) | (~b(s(z), z)) | (~b(s(s(elem!1)), s(z))) | (~b(z, s(z))) | (~b(z, s(s(elem!1)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(z)))) | (~b(z, s(s(elem!1)))) | (~b(s(z), z)) | (~b(z, s(z))) | (~b(s(s(elem!1)), s(z)))))),
% 3.13/3.35 inference(monotonicity,[status(thm)],[13802])).
% 3.13/3.35 tff(13804,plain,
% 3.13/3.35 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(z)))) | (~b(z, s(s(z)))) | (~b(s(z), z)) | (~b(s(s(elem!1)), s(z))) | (~b(z, s(z))) | (~b(z, s(s(elem!1)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(s(z)))) | (~b(z, s(s(elem!1)))) | (~b(s(z), z)) | (~b(z, s(z))) | (~b(s(s(elem!1)), s(z))))),
% 3.13/3.35 inference(transitivity,[status(thm)],[13803, 13801])).
% 3.13/3.35 tff(13805,plain,
% 3.13/3.35 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(z)))) | (~b(z, s(s(z)))) | (~b(s(z), z)) | (~b(s(s(elem!1)), s(z))) | (~b(z, s(z))) | (~b(z, s(s(elem!1)))))),
% 3.13/3.35 inference(quant_inst,[status(thm)],[])).
% 3.13/3.35 tff(13806,plain,
% 3.13/3.35 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(s(z)))) | (~b(z, s(s(elem!1)))) | (~b(s(z), z)) | (~b(z, s(z))) | (~b(s(s(elem!1)), s(z)))),
% 3.13/3.35 inference(modus_ponens,[status(thm)],[13805, 13804])).
% 3.13/3.35 tff(13807,plain,
% 3.13/3.35 ($false),
% 3.13/3.35 inference(unit_resolution,[status(thm)],[13806, 166, 1820, 53, 10451, 118, 310])).
% 3.13/3.35 tff(13808,plain,((~b(s(z), z)) | (~b(z, s(s(elem!1)))) | (~b(z, s(s(z)))) | (~b(z, s(z))) | (~b(s(s(elem!1)), s(z)))), inference(lemma,lemma(discharge,[]))).
% 3.13/3.35 tff(13809,plain,
% 3.13/3.35 ((~b(s(z), z)) | (~b(z, s(s(elem!1)))) | (~b(z, s(z))) | (~b(s(s(elem!1)), s(z)))),
% 3.13/3.35 inference(unit_resolution,[status(thm)],[13808, 10450])).
% 3.13/3.35 tff(13810,plain,
% 3.13/3.35 (~b(s(s(elem!1)), s(z))),
% 3.13/3.35 inference(unit_resolution,[status(thm)],[13809, 13800, 53, 118])).
% 3.13/3.35 tff(13811,plain,
% 3.13/3.35 (r(s(s(elem!1)), s(z))),
% 3.13/3.35 inference(unit_resolution,[status(thm)],[1912, 13810])).
% 3.13/3.35 tff(13812,plain,
% 3.13/3.35 (~r(s(s(elem!1)), z)),
% 3.13/3.35 inference(unit_resolution,[status(thm)],[4018, 377, 154, 282])).
% 3.13/3.35 tff(13813,plain,
% 3.13/3.35 (b(s(s(elem!1)), z)),
% 3.13/3.35 inference(unit_resolution,[status(thm)],[608, 13812])).
% 3.13/3.35 tff(13814,plain,
% 3.13/3.35 (~b(s(s(z)), s(s(elem!1)))),
% 3.13/3.35 inference(unit_resolution,[status(thm)],[11837, 13800, 13813])).
% 3.13/3.35 tff(13815,plain,
% 3.13/3.35 (r(s(s(z)), s(s(elem!1)))),
% 3.13/3.35 inference(unit_resolution,[status(thm)],[390, 13814, 52])).
% 3.13/3.35 tff(13816,plain,
% 3.13/3.35 ($false),
% 3.13/3.35 inference(unit_resolution,[status(thm)],[5384, 13815, 13811, 392, 120])).
% 3.13/3.35 tff(13817,plain,((~r(s(s(elem!1)), s(s(s(elem!1))))) | (~r(s(s(z)), s(z))) | (~r(s(z), s(s(z)))) | (s(s(z)) = s(s(elem!1))) | (~b(s(z), z)) | (~b(z, s(z))) | (~r(s(s(s(elem!1))), s(z))) | (~r(z, s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), z))), inference(lemma,lemma(discharge,[]))).
% 3.13/3.35 tff(13818,plain,
% 3.13/3.35 (~r(s(s(elem!1)), s(s(s(elem!1))))),
% 3.13/3.35 inference(unit_resolution,[status(thm)],[13817, 52, 13798, 392, 53, 13796, 350, 13794, 154])).
% 3.13/3.35 tff(13819,plain,
% 3.13/3.35 (b(s(s(elem!1)), s(s(s(elem!1))))),
% 3.13/3.35 inference(unit_resolution,[status(thm)],[461, 13818, 45])).
% 3.13/3.35 tff(13820,plain,
% 3.13/3.35 (~b(s(s(elem!1)), s(s(z)))),
% 3.13/3.35 inference(unit_resolution,[status(thm)],[501, 13819, 13471, 13486])).
% 3.13/3.35 tff(13821,plain,
% 3.13/3.35 (r(s(s(elem!1)), s(s(z)))),
% 3.13/3.35 inference(unit_resolution,[status(thm)],[441, 13820, 132])).
% 3.13/3.35 tff(13822,plain,
% 3.13/3.35 (~b(s(s(elem!1)), s(s(z)))),
% 3.13/3.35 inference(unit_resolution,[status(thm)],[501, 463, 213, 273])).
% 3.13/3.35 tff(13823,plain,
% 3.13/3.35 (~b(s(s(z)), s(s(elem!1)))),
% 3.13/3.35 inference(unit_resolution,[status(thm)],[2068, 463, 839, 3962])).
% 3.13/3.35 tff(13824,plain,
% 3.13/3.35 ($false),
% 3.13/3.35 inference(unit_resolution,[status(thm)],[13102, 13823, 13822, 392, 311, 52])).
% 3.13/3.35 tff(13825,plain,((~b(s(s(elem!1)), s(s(s(elem!1))))) | (~r(s(s(z)), s(z))) | (~r(s(z), s(s(elem!1)))) | (s(s(z)) = s(s(elem!1))) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | r(s(s(s(elem!1))), s(s(z))) | r(s(s(z)), s(s(s(elem!1))))), inference(lemma,lemma(discharge,[]))).
% 3.13/3.35 tff(13826,plain,
% 3.13/3.35 (~b(s(s(s(elem!1))), s(s(elem!1)))),
% 3.13/3.35 inference(unit_resolution,[status(thm)],[13825, 13819, 311, 52, 392, 13471, 13486])).
% 3.13/3.35 tff(13827,plain,
% 3.13/3.35 (r(s(s(s(elem!1))), s(s(elem!1)))),
% 3.13/3.35 inference(unit_resolution,[status(thm)],[889, 13826, 51])).
% 3.13/3.35 tff(13828,plain,
% 3.13/3.35 ($false),
% 3.13/3.35 inference(unit_resolution,[status(thm)],[4199, 13827, 13821, 311, 350])).
% 3.13/3.35 tff(13829,plain,((s(s(z)) = s(s(elem!1))) | (~r(s(z), s(s(elem!1)))) | (~r(s(s(s(elem!1))), s(z))) | (~r(s(s(z)), s(z))) | (s(s(elem!1)) = s(s(s(elem!1)))) | (~b(s(z), z)) | (~r(s(s(s(elem!1))), z))), inference(lemma,lemma(discharge,[]))).
% 3.13/3.35 tff(13830,plain,
% 3.13/3.35 (s(s(z)) = s(s(elem!1))),
% 3.13/3.35 inference(unit_resolution,[status(thm)],[13829, 350, 311, 4143, 45, 53, 154])).
% 3.13/3.35 tff(13831,plain,
% 3.13/3.35 (s(elem!1) = s(z)),
% 3.13/3.35 inference(unit_resolution,[status(thm)],[43, 13830])).
% 3.13/3.35 tff(13832,plain,
% 3.13/3.35 (z = elem!1),
% 3.13/3.35 inference(unit_resolution,[status(thm)],[30, 13831])).
% 3.13/3.35 tff(13833,plain,
% 3.13/3.35 (r(z, s(s(s(elem!1)))) <=> r(elem!1, s(s(s(elem!1))))),
% 3.13/3.35 inference(monotonicity,[status(thm)],[13832])).
% 3.13/3.35 tff(13834,plain,
% 3.13/3.35 (~b(z, s(s(s(elem!1))))),
% 3.13/3.35 inference(unit_resolution,[status(thm)],[10577, 166, 10450, 13090, 13088])).
% 3.13/3.35 tff(13835,plain,
% 3.13/3.35 (r(z, s(s(s(elem!1))))),
% 3.13/3.35 inference(unit_resolution,[status(thm)],[261, 13834])).
% 3.13/3.35 tff(13836,plain,
% 3.13/3.35 (r(elem!1, s(s(s(elem!1))))),
% 3.13/3.35 inference(modus_ponens,[status(thm)],[13835, 13833])).
% 3.13/3.35 tff(13837,plain,
% 3.13/3.35 ((s(s(s(s(elem!1)))) = z) <=> (s(s(s(s(elem!1)))) = elem!1)),
% 3.13/3.35 inference(monotonicity,[status(thm)],[13832])).
% 3.13/3.35 tff(13838,plain,
% 3.13/3.35 ((s(s(s(s(elem!1)))) = z) <=> (elem!1 = s(s(s(s(elem!1)))))),
% 3.13/3.35 inference(transitivity,[status(thm)],[13837, 2287])).
% 3.13/3.35 tff(13839,plain,
% 3.13/3.35 ((~(s(s(s(s(elem!1)))) = z)) <=> (~(elem!1 = s(s(s(s(elem!1))))))),
% 3.13/3.35 inference(monotonicity,[status(thm)],[13838])).
% 3.13/3.35 tff(13840,plain,
% 3.13/3.35 (~(elem!1 = s(s(s(s(elem!1)))))),
% 3.13/3.35 inference(modus_ponens,[status(thm)],[626, 13839])).
% 3.13/3.35 tff(13841,plain,
% 3.13/3.35 (elem!1 = z),
% 3.13/3.35 inference(symmetry,[status(thm)],[13832])).
% 3.13/3.35 tff(13842,plain,
% 3.13/3.35 (b(elem!1, s(s(elem!1))) <=> b(z, s(s(elem!1)))),
% 3.13/3.35 inference(monotonicity,[status(thm)],[13841])).
% 3.13/3.35 tff(13843,plain,
% 3.13/3.35 (b(z, s(s(elem!1))) <=> b(elem!1, s(s(elem!1)))),
% 3.13/3.35 inference(symmetry,[status(thm)],[13842])).
% 3.13/3.35 tff(13844,plain,
% 3.13/3.35 (b(z, s(s(elem!1)))),
% 3.13/3.35 inference(unit_resolution,[status(thm)],[12671, 13830])).
% 3.13/3.35 tff(13845,plain,
% 3.13/3.35 (b(elem!1, s(s(elem!1)))),
% 3.13/3.35 inference(modus_ponens,[status(thm)],[13844, 13843])).
% 3.13/3.35 tff(13846,plain,
% 3.13/3.35 (~b(s(s(elem!1)), s(z))),
% 3.13/3.35 inference(unit_resolution,[status(thm)],[3938, 13830, 3936])).
% 3.13/3.35 tff(13847,plain,
% 3.13/3.35 (r(s(s(elem!1)), s(z))),
% 3.13/3.35 inference(unit_resolution,[status(thm)],[1912, 13846])).
% 3.13/3.35 tff(13848,plain,
% 3.13/3.35 (b(s(s(z)), s(s(s(elem!1)))) <=> b(s(s(elem!1)), s(s(s(elem!1))))),
% 3.13/3.35 inference(monotonicity,[status(thm)],[13830])).
% 3.13/3.35 tff(13849,plain,
% 3.13/3.35 (b(s(s(elem!1)), s(s(s(elem!1))))),
% 3.13/3.35 inference(modus_ponens,[status(thm)],[13090, 13848])).
% 3.13/3.35 tff(13850,plain,
% 3.13/3.35 ((s(s(s(s(elem!1)))) = s(s(z))) <=> (s(s(s(s(elem!1)))) = s(s(elem!1)))),
% 3.13/3.35 inference(monotonicity,[status(thm)],[13830])).
% 3.13/3.35 tff(13851,plain,
% 3.13/3.35 ((s(s(s(s(elem!1)))) = s(s(z))) <=> (s(s(elem!1)) = s(s(s(s(elem!1)))))),
% 3.13/3.35 inference(transitivity,[status(thm)],[13850, 123])).
% 3.13/3.35 tff(13852,plain,
% 3.13/3.35 ((s(s(s(s(elem!1)))) = s(s(z))) <=> (s(s(s(s(elem!1)))) = s(s(elem!1)))),
% 3.13/3.35 inference(transitivity,[status(thm)],[13851, 124])).
% 3.13/3.35 tff(13853,plain,
% 3.13/3.35 ((~(s(s(s(s(elem!1)))) = s(s(z)))) <=> (~(s(s(s(s(elem!1)))) = s(s(elem!1))))),
% 3.13/3.35 inference(monotonicity,[status(thm)],[13852])).
% 3.13/3.35 tff(13854,plain,
% 3.13/3.35 (~(s(s(s(s(elem!1)))) = s(s(elem!1)))),
% 3.13/3.35 inference(modus_ponens,[status(thm)],[733, 13853])).
% 3.13/3.35 tff(13855,plain,
% 3.13/3.35 (~r(s(s(s(s(elem!1)))), s(z))),
% 3.13/3.35 inference(unit_resolution,[status(thm)],[5809, 13854, 311, 350, 13849, 13847, 358])).
% 3.13/3.35 tff(13856,plain,
% 3.13/3.35 (b(s(s(s(s(elem!1)))), s(z))),
% 3.13/3.35 inference(unit_resolution,[status(thm)],[661, 13855])).
% 3.13/3.35 tff(13857,plain,
% 3.13/3.35 (b(z, s(z)) <=> b(elem!1, s(z))),
% 3.13/3.35 inference(monotonicity,[status(thm)],[13832])).
% 3.13/3.35 tff(13858,plain,
% 3.13/3.35 (b(elem!1, s(z))),
% 3.13/3.35 inference(modus_ponens,[status(thm)],[13796, 13857])).
% 3.13/3.35 tff(13859,plain,
% 3.13/3.35 (~r(s(z), s(s(s(elem!1))))),
% 3.13/3.35 inference(unit_resolution,[status(thm)],[13788, 3936, 53, 311, 154])).
% 3.13/3.35 tff(13860,plain,
% 3.13/3.35 (b(s(z), s(s(s(elem!1))))),
% 3.13/3.35 inference(unit_resolution,[status(thm)],[116, 13859])).
% 3.13/3.35 tff(13861,plain,
% 3.13/3.35 (~r(s(s(s(elem!1))), s(s(elem!1)))),
% 3.13/3.35 inference(unit_resolution,[status(thm)],[3454, 13830, 13087])).
% 3.13/3.35 tff(13862,plain,
% 3.13/3.35 (b(s(s(s(elem!1))), s(s(elem!1)))),
% 3.13/3.35 inference(unit_resolution,[status(thm)],[889, 13861, 51])).
% 3.13/3.35 tff(13863,plain,
% 3.13/3.35 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(elem!1, s(z))) | (~b(s(z), s(s(s(elem!1))))) | (~b(elem!1, s(s(elem!1)))) | (~b(elem!1, s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(elem!1, s(z))) | (~b(s(z), s(s(s(elem!1))))) | (~b(elem!1, s(s(elem!1)))) | (~b(elem!1, s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), s(z))))),
% 3.13/3.35 inference(rewrite,[status(thm)],[])).
% 3.13/3.35 tff(13864,plain,
% 3.13/3.35 (((~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(elem!1, s(s(elem!1)))) | (~b(s(z), s(s(s(elem!1))))) | (~b(s(s(s(s(elem!1)))), s(z))) | (~b(elem!1, s(z))) | (~b(elem!1, s(s(s(s(elem!1))))))) <=> ((~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(elem!1, s(z))) | (~b(s(z), s(s(s(elem!1))))) | (~b(elem!1, s(s(elem!1)))) | (~b(elem!1, s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), s(z))))),
% 3.13/3.35 inference(rewrite,[status(thm)],[])).
% 3.13/3.35 tff(13865,plain,
% 3.13/3.35 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(elem!1, s(s(elem!1)))) | (~b(s(z), s(s(s(elem!1))))) | (~b(s(s(s(s(elem!1)))), s(z))) | (~b(elem!1, s(z))) | (~b(elem!1, s(s(s(s(elem!1)))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(elem!1, s(z))) | (~b(s(z), s(s(s(elem!1))))) | (~b(elem!1, s(s(elem!1)))) | (~b(elem!1, s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), s(z)))))),
% 3.13/3.35 inference(monotonicity,[status(thm)],[13864])).
% 3.13/3.35 tff(13866,plain,
% 3.13/3.35 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(elem!1, s(s(elem!1)))) | (~b(s(z), s(s(s(elem!1))))) | (~b(s(s(s(s(elem!1)))), s(z))) | (~b(elem!1, s(z))) | (~b(elem!1, s(s(s(s(elem!1)))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(elem!1, s(z))) | (~b(s(z), s(s(s(elem!1))))) | (~b(elem!1, s(s(elem!1)))) | (~b(elem!1, s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), s(z))))),
% 3.13/3.35 inference(transitivity,[status(thm)],[13865, 13863])).
% 3.13/3.35 tff(13867,plain,
% 3.13/3.35 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(elem!1, s(s(elem!1)))) | (~b(s(z), s(s(s(elem!1))))) | (~b(s(s(s(s(elem!1)))), s(z))) | (~b(elem!1, s(z))) | (~b(elem!1, s(s(s(s(elem!1)))))))),
% 3.13/3.35 inference(quant_inst,[status(thm)],[])).
% 3.13/3.35 tff(13868,plain,
% 3.13/3.35 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(elem!1, s(z))) | (~b(s(z), s(s(s(elem!1))))) | (~b(elem!1, s(s(elem!1)))) | (~b(elem!1, s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), s(z)))),
% 3.13/3.35 inference(modus_ponens,[status(thm)],[13867, 13866])).
% 3.13/3.35 tff(13869,plain,
% 3.13/3.35 (~b(elem!1, s(s(s(s(elem!1)))))),
% 3.13/3.35 inference(unit_resolution,[status(thm)],[13868, 166, 13862, 13860, 13858, 13856, 13845])).
% 3.13/3.35 tff(13870,plain,
% 3.13/3.35 (r(elem!1, s(s(s(s(elem!1)))))),
% 3.13/3.35 inference(unit_resolution,[status(thm)],[2427, 13869, 13840])).
% 3.13/3.35 tff(13871,plain,
% 3.13/3.35 (~r(s(s(s(s(elem!1)))), s(s(s(elem!1))))),
% 3.13/3.35 inference(unit_resolution,[status(thm)],[1056, 13870, 350, 13836])).
% 3.13/3.35 tff(13872,plain,
% 3.13/3.35 (b(s(s(s(s(elem!1)))), s(s(s(elem!1))))),
% 3.13/3.35 inference(unit_resolution,[status(thm)],[1065, 13871, 364])).
% 3.13/3.35 tff(13873,plain,
% 3.13/3.35 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(z), s(s(s(elem!1))))) | (~b(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~b(s(s(s(s(elem!1)))), s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(z), s(s(s(elem!1))))) | (~b(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~b(s(s(s(s(elem!1)))), s(z))))),
% 3.13/3.35 inference(rewrite,[status(thm)],[])).
% 3.13/3.35 tff(13874,plain,
% 3.13/3.35 (((~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(z), s(s(s(elem!1))))) | (~b(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~b(s(s(s(s(elem!1)))), s(z)))) <=> ((~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(z), s(s(s(elem!1))))) | (~b(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~b(s(s(s(s(elem!1)))), s(z))))),
% 3.13/3.35 inference(rewrite,[status(thm)],[])).
% 3.13/3.35 tff(13875,plain,
% 3.13/3.35 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(z), s(s(s(elem!1))))) | (~b(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~b(s(s(s(s(elem!1)))), s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(z), s(s(s(elem!1))))) | (~b(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~b(s(s(s(s(elem!1)))), s(z)))))),
% 3.13/3.35 inference(monotonicity,[status(thm)],[13874])).
% 3.13/3.35 tff(13876,plain,
% 3.13/3.35 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(z), s(s(s(elem!1))))) | (~b(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~b(s(s(s(s(elem!1)))), s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(z), s(s(s(elem!1))))) | (~b(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~b(s(s(s(s(elem!1)))), s(z))))),
% 3.13/3.35 inference(transitivity,[status(thm)],[13875, 13873])).
% 3.13/3.35 tff(13877,plain,
% 3.13/3.35 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(z), s(s(s(elem!1))))) | (~b(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~b(s(s(s(s(elem!1)))), s(z))))),
% 3.13/3.35 inference(quant_inst,[status(thm)],[])).
% 3.13/3.35 tff(13878,plain,
% 3.13/3.35 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(z), s(s(s(elem!1))))) | (~b(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~b(s(s(s(s(elem!1)))), s(z)))),
% 3.13/3.35 inference(modus_ponens,[status(thm)],[13877, 13876])).
% 3.13/3.35 tff(13879,plain,
% 3.13/3.35 ($false),
% 3.13/3.35 inference(unit_resolution,[status(thm)],[13878, 166, 13849, 13862, 13860, 13856, 13872])).
% 3.13/3.35 tff(13880,plain,((~r(s(s(s(elem!1))), s(z))) | (~r(s(z), s(s(elem!1)))) | b(s(s(z)), s(z)) | (s(s(elem!1)) = s(s(s(elem!1)))) | (~b(s(z), z)) | (~r(s(s(s(elem!1))), z))), inference(lemma,lemma(discharge,[]))).
% 3.13/3.35 tff(13881,plain,
% 3.13/3.35 (~r(s(s(s(elem!1))), s(z))),
% 3.13/3.35 inference(unit_resolution,[status(thm)],[13880, 3936, 85, 13791, 53, 13084])).
% 3.13/3.35 tff(13882,plain,
% 3.13/3.35 (b(s(s(s(elem!1))), s(z))),
% 3.13/3.35 inference(unit_resolution,[status(thm)],[1849, 13881])).
% 3.13/3.36 tff(13883,plain,
% 3.13/3.36 (~(s(s(s(z))) = s(s(s(elem!1))))),
% 3.13/3.36 inference(modus_ponens,[status(thm)],[140, 10055])).
% 3.13/3.36 tff(13884,plain,
% 3.13/3.36 (~r(s(s(z)), z)),
% 3.13/3.36 inference(unit_resolution,[status(thm)],[12769, 197, 311, 323, 392])).
% 3.13/3.36 tff(13885,plain,
% 3.13/3.36 (b(s(s(z)), z)),
% 3.13/3.36 inference(unit_resolution,[status(thm)],[186, 13884])).
% 3.13/3.36 tff(13886,plain,
% 3.13/3.36 (~b(s(z), s(s(z)))),
% 3.13/3.36 inference(unit_resolution,[status(thm)],[12847, 13885, 53])).
% 3.13/3.36 tff(13887,plain,
% 3.13/3.36 (r(s(z), s(s(z)))),
% 3.13/3.36 inference(unit_resolution,[status(thm)],[427, 13886])).
% 3.13/3.36 tff(13888,plain,
% 3.13/3.36 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), z)) | (~r(s(s(s(elem!1))), s(s(s(z))))) | (~r(z, s(z))) | (~r(s(s(s(z))), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(elem!1))), z)) | (~r(s(s(s(elem!1))), s(s(s(z))))) | (~r(z, s(z))) | (~r(s(s(s(z))), z)))),
% 3.13/3.36 inference(rewrite,[status(thm)],[])).
% 3.13/3.36 tff(13889,plain,
% 3.13/3.36 (((~r(z, s(z))) | (~r(s(s(s(z))), z)) | (~r(s(s(s(elem!1))), z)) | (~r(s(s(s(elem!1))), s(s(s(z)))))) <=> ((~r(s(s(s(elem!1))), z)) | (~r(s(s(s(elem!1))), s(s(s(z))))) | (~r(z, s(z))) | (~r(s(s(s(z))), z)))),
% 3.13/3.36 inference(rewrite,[status(thm)],[])).
% 3.13/3.36 tff(13890,plain,
% 3.13/3.36 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(z))) | (~r(s(s(s(z))), z)) | (~r(s(s(s(elem!1))), z)) | (~r(s(s(s(elem!1))), s(s(s(z))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), z)) | (~r(s(s(s(elem!1))), s(s(s(z))))) | (~r(z, s(z))) | (~r(s(s(s(z))), z))))),
% 3.13/3.36 inference(monotonicity,[status(thm)],[13889])).
% 3.13/3.36 tff(13891,plain,
% 3.13/3.36 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(z))) | (~r(s(s(s(z))), z)) | (~r(s(s(s(elem!1))), z)) | (~r(s(s(s(elem!1))), s(s(s(z))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(elem!1))), z)) | (~r(s(s(s(elem!1))), s(s(s(z))))) | (~r(z, s(z))) | (~r(s(s(s(z))), z)))),
% 3.13/3.36 inference(transitivity,[status(thm)],[13890, 13888])).
% 3.13/3.36 tff(13892,plain,
% 3.13/3.36 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(z))) | (~r(s(s(s(z))), z)) | (~r(s(s(s(elem!1))), z)) | (~r(s(s(s(elem!1))), s(s(s(z))))))),
% 3.13/3.36 inference(quant_inst,[status(thm)],[])).
% 3.13/3.36 tff(13893,plain,
% 3.13/3.36 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(elem!1))), z)) | (~r(s(s(s(elem!1))), s(s(s(z))))) | (~r(z, s(z))) | (~r(s(s(s(z))), z))),
% 3.13/3.36 inference(modus_ponens,[status(thm)],[13892, 13891])).
% 3.13/3.36 tff(13894,plain,
% 3.13/3.36 (~r(s(s(s(elem!1))), s(s(s(z))))),
% 3.13/3.36 inference(unit_resolution,[status(thm)],[13893, 197, 154, 323, 1733])).
% 3.13/3.36 tff(13895,plain,
% 3.13/3.36 (~r(s(s(s(z))), s(z))),
% 3.13/3.36 inference(unit_resolution,[status(thm)],[3213, 1733, 323, 120])).
% 3.13/3.36 tff(13896,plain,
% 3.13/3.36 (b(s(s(s(z))), s(z))),
% 3.13/3.36 inference(unit_resolution,[status(thm)],[1763, 13895])).
% 3.13/3.36 tff(13897,plain,
% 3.13/3.36 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(elem!1))), s(s(s(z))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(elem!1))), s(s(s(z))))))),
% 3.13/3.36 inference(rewrite,[status(thm)],[])).
% 3.13/3.36 tff(13898,plain,
% 3.13/3.36 (((~b(s(s(s(elem!1))), s(z))) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(z), s(s(s(elem!1))))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(s(s(elem!1))), s(s(s(z)))))) <=> ((~b(s(z), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(elem!1))), s(s(s(z))))))),
% 3.13/3.36 inference(rewrite,[status(thm)],[])).
% 3.13/3.36 tff(13899,plain,
% 3.13/3.36 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), s(z))) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(z), s(s(s(elem!1))))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(s(s(elem!1))), s(s(s(z))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(elem!1))), s(s(s(z)))))))),
% 3.13/3.36 inference(monotonicity,[status(thm)],[13898])).
% 3.13/3.36 tff(13900,plain,
% 3.13/3.36 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), s(z))) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(z), s(s(s(elem!1))))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(s(s(elem!1))), s(s(s(z))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(elem!1))), s(s(s(z))))))),
% 3.13/3.36 inference(transitivity,[status(thm)],[13899, 13897])).
% 3.13/3.36 tff(13901,plain,
% 3.13/3.36 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), s(z))) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(z), s(s(s(elem!1))))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(s(s(elem!1))), s(s(s(z))))))),
% 3.13/3.36 inference(quant_inst,[status(thm)],[])).
% 3.13/3.36 tff(13902,plain,
% 3.13/3.36 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(elem!1))), s(s(s(z)))))),
% 3.13/3.36 inference(modus_ponens,[status(thm)],[13901, 13900])).
% 3.13/3.36 tff(13903,plain,
% 3.13/3.36 (~b(s(s(s(elem!1))), s(s(s(z))))),
% 3.13/3.36 inference(unit_resolution,[status(thm)],[13902, 166, 241, 96, 13896])).
% 3.13/3.36 tff(13904,plain,
% 3.13/3.36 ($false),
% 3.13/3.36 inference(unit_resolution,[status(thm)],[3574, 13903, 13894, 3567])).
% 3.13/3.36 tff(13905,plain,((~r(s(s(s(z))), z)) | (s(s(s(elem!1))) = s(s(s(z)))) | (~b(s(z), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(z))) | (~r(s(s(s(elem!1))), z)) | (~r(z, s(z))) | (~r(s(z), s(s(z))))), inference(lemma,lemma(discharge,[]))).
% 3.13/3.36 tff(13906,plain,
% 3.13/3.36 (~r(s(s(s(z))), z)),
% 3.13/3.36 inference(unit_resolution,[status(thm)],[13905, 13887, 154, 241, 96, 3567, 323])).
% 3.13/3.36 tff(13907,plain,
% 3.13/3.36 (b(s(s(s(z))), z)),
% 3.13/3.36 inference(unit_resolution,[status(thm)],[1713, 13906])).
% 3.13/3.36 tff(13908,plain,
% 3.13/3.36 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(z)))) | (~b(s(s(z)), z)) | (~b(s(s(s(z))), z)) | (~b(s(s(z)), s(s(s(z))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(s(z)))) | (~b(s(s(z)), z)) | (~b(s(s(s(z))), z)) | (~b(s(s(z)), s(s(s(z))))))),
% 3.13/3.36 inference(rewrite,[status(thm)],[])).
% 3.13/3.36 tff(13909,plain,
% 3.13/3.36 (((~b(s(s(z)), z)) | (~b(s(s(z)), z)) | (~b(z, s(s(z)))) | (~b(s(s(s(z))), z)) | (~b(s(s(z)), z)) | (~b(s(s(z)), s(s(s(z)))))) <=> ((~b(z, s(s(z)))) | (~b(s(s(z)), z)) | (~b(s(s(s(z))), z)) | (~b(s(s(z)), s(s(s(z))))))),
% 3.13/3.36 inference(rewrite,[status(thm)],[])).
% 3.13/3.36 tff(13910,plain,
% 3.13/3.36 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), z)) | (~b(s(s(z)), z)) | (~b(z, s(s(z)))) | (~b(s(s(s(z))), z)) | (~b(s(s(z)), z)) | (~b(s(s(z)), s(s(s(z))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(z)))) | (~b(s(s(z)), z)) | (~b(s(s(s(z))), z)) | (~b(s(s(z)), s(s(s(z)))))))),
% 3.13/3.36 inference(monotonicity,[status(thm)],[13909])).
% 3.13/3.36 tff(13911,plain,
% 3.13/3.36 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), z)) | (~b(s(s(z)), z)) | (~b(z, s(s(z)))) | (~b(s(s(s(z))), z)) | (~b(s(s(z)), z)) | (~b(s(s(z)), s(s(s(z))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(s(z)))) | (~b(s(s(z)), z)) | (~b(s(s(s(z))), z)) | (~b(s(s(z)), s(s(s(z))))))),
% 3.13/3.36 inference(transitivity,[status(thm)],[13910, 13908])).
% 3.13/3.36 tff(13912,plain,
% 3.13/3.36 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), z)) | (~b(s(s(z)), z)) | (~b(z, s(s(z)))) | (~b(s(s(s(z))), z)) | (~b(s(s(z)), z)) | (~b(s(s(z)), s(s(s(z))))))),
% 3.13/3.36 inference(quant_inst,[status(thm)],[])).
% 3.13/3.36 tff(13913,plain,
% 3.13/3.36 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(s(z)))) | (~b(s(s(z)), z)) | (~b(s(s(s(z))), z)) | (~b(s(s(z)), s(s(s(z)))))),
% 3.13/3.36 inference(modus_ponens,[status(thm)],[13912, 13911])).
% 3.13/3.36 tff(13914,plain,
% 3.13/3.36 (~b(s(s(z)), s(s(s(z))))),
% 3.13/3.36 inference(unit_resolution,[status(thm)],[13913, 166, 10450, 13885, 13907])).
% 3.13/3.36 tff(13915,plain,
% 3.13/3.36 (r(s(s(z)), s(s(s(z))))),
% 3.13/3.36 inference(unit_resolution,[status(thm)],[1730, 13914])).
% 3.13/3.36 tff(13916,plain,
% 3.13/3.36 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(z)))) | (~b(s(z), z)) | (~b(s(s(z)), z)) | (~b(s(s(s(z))), z)) | (~b(s(z), s(s(s(z))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(s(z)))) | (~b(s(z), z)) | (~b(s(s(z)), z)) | (~b(s(s(s(z))), z)) | (~b(s(z), s(s(s(z))))))),
% 3.13/3.36 inference(rewrite,[status(thm)],[])).
% 3.13/3.36 tff(13917,plain,
% 3.13/3.36 (((~b(s(s(z)), z)) | (~b(s(z), z)) | (~b(z, s(s(z)))) | (~b(s(s(s(z))), z)) | (~b(s(z), z)) | (~b(s(z), s(s(s(z)))))) <=> ((~b(z, s(s(z)))) | (~b(s(z), z)) | (~b(s(s(z)), z)) | (~b(s(s(s(z))), z)) | (~b(s(z), s(s(s(z))))))),
% 3.13/3.36 inference(rewrite,[status(thm)],[])).
% 3.13/3.36 tff(13918,plain,
% 3.13/3.36 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), z)) | (~b(s(z), z)) | (~b(z, s(s(z)))) | (~b(s(s(s(z))), z)) | (~b(s(z), z)) | (~b(s(z), s(s(s(z))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(z)))) | (~b(s(z), z)) | (~b(s(s(z)), z)) | (~b(s(s(s(z))), z)) | (~b(s(z), s(s(s(z)))))))),
% 3.13/3.36 inference(monotonicity,[status(thm)],[13917])).
% 3.13/3.36 tff(13919,plain,
% 3.13/3.36 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), z)) | (~b(s(z), z)) | (~b(z, s(s(z)))) | (~b(s(s(s(z))), z)) | (~b(s(z), z)) | (~b(s(z), s(s(s(z))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(s(z)))) | (~b(s(z), z)) | (~b(s(s(z)), z)) | (~b(s(s(s(z))), z)) | (~b(s(z), s(s(s(z))))))),
% 3.13/3.36 inference(transitivity,[status(thm)],[13918, 13916])).
% 3.13/3.36 tff(13920,plain,
% 3.13/3.36 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), z)) | (~b(s(z), z)) | (~b(z, s(s(z)))) | (~b(s(s(s(z))), z)) | (~b(s(z), z)) | (~b(s(z), s(s(s(z))))))),
% 3.13/3.36 inference(quant_inst,[status(thm)],[])).
% 3.13/3.36 tff(13921,plain,
% 3.13/3.36 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(s(z)))) | (~b(s(z), z)) | (~b(s(s(z)), z)) | (~b(s(s(s(z))), z)) | (~b(s(z), s(s(s(z)))))),
% 3.13/3.36 inference(modus_ponens,[status(thm)],[13920, 13919])).
% 3.13/3.36 tff(13922,plain,
% 3.13/3.36 (~b(s(z), s(s(s(z))))),
% 3.13/3.36 inference(unit_resolution,[status(thm)],[13921, 166, 53, 10450, 13885, 13907])).
% 3.13/3.36 tff(13923,plain,
% 3.13/3.36 (r(s(z), s(s(s(z))))),
% 3.13/3.36 inference(unit_resolution,[status(thm)],[1674, 13922])).
% 3.13/3.36 tff(13924,plain,
% 3.13/3.36 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(z)))) | (~b(s(z), z)) | (~b(s(s(z)), z)) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(z))), z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(s(z)))) | (~b(s(z), z)) | (~b(s(s(z)), z)) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(z))), z)))),
% 3.13/3.36 inference(rewrite,[status(thm)],[])).
% 3.13/3.36 tff(13925,plain,
% 3.13/3.36 (((~b(s(s(z)), z)) | (~b(s(s(s(z))), z)) | (~b(z, s(s(z)))) | (~b(s(z), z)) | (~b(s(s(s(z))), z)) | (~b(s(s(s(z))), s(z)))) <=> ((~b(z, s(s(z)))) | (~b(s(z), z)) | (~b(s(s(z)), z)) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(z))), z)))),
% 3.13/3.36 inference(rewrite,[status(thm)],[])).
% 3.13/3.36 tff(13926,plain,
% 3.13/3.36 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), z)) | (~b(s(s(s(z))), z)) | (~b(z, s(s(z)))) | (~b(s(z), z)) | (~b(s(s(s(z))), z)) | (~b(s(s(s(z))), s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(z)))) | (~b(s(z), z)) | (~b(s(s(z)), z)) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(z))), z))))),
% 3.13/3.36 inference(monotonicity,[status(thm)],[13925])).
% 3.13/3.36 tff(13927,plain,
% 3.13/3.36 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), z)) | (~b(s(s(s(z))), z)) | (~b(z, s(s(z)))) | (~b(s(z), z)) | (~b(s(s(s(z))), z)) | (~b(s(s(s(z))), s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(s(z)))) | (~b(s(z), z)) | (~b(s(s(z)), z)) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(z))), z)))),
% 3.13/3.36 inference(transitivity,[status(thm)],[13926, 13924])).
% 3.13/3.36 tff(13928,plain,
% 3.13/3.36 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), z)) | (~b(s(s(s(z))), z)) | (~b(z, s(s(z)))) | (~b(s(z), z)) | (~b(s(s(s(z))), z)) | (~b(s(s(s(z))), s(z))))),
% 3.13/3.36 inference(quant_inst,[status(thm)],[])).
% 3.13/3.36 tff(13929,plain,
% 3.13/3.36 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(s(z)))) | (~b(s(z), z)) | (~b(s(s(z)), z)) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(z))), z))),
% 3.13/3.36 inference(modus_ponens,[status(thm)],[13928, 13927])).
% 3.13/3.36 tff(13930,plain,
% 3.13/3.36 (~b(s(s(s(z))), s(z))),
% 3.13/3.36 inference(unit_resolution,[status(thm)],[13929, 166, 53, 10450, 13885, 13907])).
% 3.13/3.36 tff(13931,plain,
% 3.13/3.36 (r(s(s(s(z))), s(z))),
% 3.13/3.36 inference(unit_resolution,[status(thm)],[1763, 13930])).
% 3.13/3.36 tff(13932,plain,
% 3.13/3.36 ($false),
% 3.13/3.36 inference(unit_resolution,[status(thm)],[5568, 197, 392, 13931, 13923, 13915])).
% 3.13/3.36 tff(13933,plain,((~r(z, s(z))) | (~r(s(s(z)), s(z))) | (~b(s(z), z)) | (~r(s(s(s(elem!1))), z)) | (~b(s(z), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(z))) | (s(s(s(elem!1))) = s(s(s(z)))) | (~r(s(z), s(s(elem!1))))), inference(lemma,lemma(discharge,[]))).
% 3.13/3.36 tff(13934,plain,
% 3.13/3.36 (~r(z, s(z))),
% 3.13/3.36 inference(unit_resolution,[status(thm)],[13933, 140, 53, 154, 241, 96, 392, 311])).
% 3.13/3.36 tff(13935,plain,
% 3.13/3.36 (b(z, s(z))),
% 3.13/3.36 inference(unit_resolution,[status(thm)],[321, 13934])).
% 3.13/3.36 tff(13936,plain,
% 3.13/3.36 (~b(z, s(s(s(elem!1))))),
% 3.13/3.36 inference(unit_resolution,[status(thm)],[249, 13935, 241, 96])).
% 3.13/3.36 tff(13937,plain,
% 3.13/3.36 (r(z, s(s(s(elem!1))))),
% 3.13/3.36 inference(unit_resolution,[status(thm)],[261, 13936])).
% 3.13/3.36 tff(13938,plain,
% 3.13/3.36 (~b(s(s(elem!1)), s(z))),
% 3.13/3.36 inference(unit_resolution,[status(thm)],[4277, 13935, 45, 53, 96])).
% 3.13/3.36 tff(13939,plain,
% 3.13/3.36 (r(s(s(elem!1)), s(z))),
% 3.13/3.36 inference(unit_resolution,[status(thm)],[1912, 13938])).
% 3.13/3.36 tff(13940,plain,
% 3.13/3.36 (~r(s(s(z)), s(s(elem!1)))),
% 3.13/3.36 inference(unit_resolution,[status(thm)],[4561, 197, 311, 13939, 392])).
% 3.13/3.36 tff(13941,plain,
% 3.13/3.36 (~r(s(s(elem!1)), s(s(z)))),
% 3.13/3.36 inference(unit_resolution,[status(thm)],[4565, 197, 311, 13939, 392])).
% 3.13/3.36 tff(13942,plain,
% 3.13/3.36 (b(s(s(z)), s(s(elem!1)))),
% 3.13/3.36 inference(unit_resolution,[status(thm)],[390, 13940, 52])).
% 3.13/3.36 tff(13943,plain,
% 3.13/3.36 (b(s(s(elem!1)), s(s(z)))),
% 3.13/3.36 inference(unit_resolution,[status(thm)],[441, 13941, 132])).
% 3.13/3.36 tff(13944,plain,
% 3.13/3.36 (~b(s(s(elem!1)), z)),
% 3.13/3.36 inference(unit_resolution,[status(thm)],[12470, 166, 13943, 10450, 13942])).
% 3.13/3.36 tff(13945,plain,
% 3.13/3.36 (r(s(s(elem!1)), z)),
% 3.13/3.36 inference(unit_resolution,[status(thm)],[608, 13944])).
% 3.13/3.36 tff(13946,plain,
% 3.13/3.36 (~r(s(s(elem!1)), s(s(s(elem!1))))),
% 3.13/3.36 inference(unit_resolution,[status(thm)],[4018, 13945, 154, 13937])).
% 3.13/3.36 tff(13947,plain,
% 3.13/3.36 (b(s(s(elem!1)), s(s(s(elem!1))))),
% 3.13/3.36 inference(unit_resolution,[status(thm)],[461, 13946, 45])).
% 3.13/3.36 tff(13948,plain,
% 3.13/3.36 (~b(s(s(z)), s(s(s(elem!1))))),
% 3.13/3.36 inference(unit_resolution,[status(thm)],[13320, 13947, 51, 96, 154, 13935, 53, 52, 13941, 13940])).
% 3.13/3.36 tff(13949,plain,
% 3.13/3.36 (r(s(s(z)), s(s(s(elem!1))))),
% 3.13/3.36 inference(unit_resolution,[status(thm)],[279, 13948])).
% 3.13/3.36 tff(13950,plain,
% 3.13/3.36 (~r(s(s(z)), z)),
% 3.13/3.36 inference(unit_resolution,[status(thm)],[13284, 13949, 154, 13937])).
% 3.13/3.36 tff(13951,plain,
% 3.13/3.36 (b(s(s(z)), z)),
% 3.13/3.36 inference(unit_resolution,[status(thm)],[186, 13950])).
% 3.13/3.36 tff(13952,plain,
% 3.13/3.36 (~b(s(z), s(s(z)))),
% 3.13/3.36 inference(unit_resolution,[status(thm)],[11973, 122, 10451, 118])).
% 3.13/3.36 tff(13953,plain,
% 3.13/3.36 (r(s(z), s(s(z)))),
% 3.13/3.36 inference(unit_resolution,[status(thm)],[427, 13952])).
% 3.13/3.36 tff(13954,plain,
% 3.13/3.36 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(z)), s(z))) | (~r(s(z), s(s(z)))) | (~r(s(s(s(z))), s(s(z)))) | (~r(s(s(s(z))), s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(z)), s(z))) | (~r(s(z), s(s(z)))) | (~r(s(s(s(z))), s(s(z)))) | (~r(s(s(s(z))), s(z))))),
% 3.13/3.36 inference(rewrite,[status(thm)],[])).
% 3.13/3.36 tff(13955,plain,
% 3.13/3.36 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(z)), s(z))) | (~r(s(z), s(s(z)))) | (~r(s(s(s(z))), s(s(z)))) | (~r(s(s(s(z))), s(z))))),
% 3.13/3.36 inference(quant_inst,[status(thm)],[])).
% 3.13/3.36 tff(13956,plain,
% 3.13/3.36 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(z)), s(z))) | (~r(s(z), s(s(z)))) | (~r(s(s(s(z))), s(s(z)))) | (~r(s(s(s(z))), s(z)))),
% 3.13/3.36 inference(modus_ponens,[status(thm)],[13955, 13954])).
% 3.13/3.36 tff(13957,plain,
% 3.13/3.36 (~r(s(s(s(z))), s(z))),
% 3.13/3.36 inference(unit_resolution,[status(thm)],[13956, 197, 13953, 392, 12298])).
% 3.13/3.36 tff(13958,plain,
% 3.13/3.36 (b(s(s(s(z))), s(z))),
% 3.13/3.36 inference(unit_resolution,[status(thm)],[1763, 13957])).
% 3.13/3.36 tff(13959,plain,
% 3.13/3.36 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(z))) | (~b(z, s(z))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(z))), z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(z))) | (~b(z, s(z))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(z))), z)))),
% 3.13/3.36 inference(rewrite,[status(thm)],[])).
% 3.13/3.36 tff(13960,plain,
% 3.13/3.36 (((~b(s(s(s(elem!1))), s(z))) | (~b(s(s(s(z))), s(z))) | (~b(s(z), s(s(s(elem!1))))) | (~b(z, s(z))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(z))), z))) <=> ((~b(s(z), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(z))) | (~b(z, s(z))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(z))), z)))),
% 3.13/3.36 inference(rewrite,[status(thm)],[])).
% 3.13/3.36 tff(13961,plain,
% 3.13/3.36 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), s(z))) | (~b(s(s(s(z))), s(z))) | (~b(s(z), s(s(s(elem!1))))) | (~b(z, s(z))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(z))), z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(z))) | (~b(z, s(z))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(z))), z))))),
% 3.13/3.37 inference(monotonicity,[status(thm)],[13960])).
% 3.13/3.37 tff(13962,plain,
% 3.13/3.37 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), s(z))) | (~b(s(s(s(z))), s(z))) | (~b(s(z), s(s(s(elem!1))))) | (~b(z, s(z))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(z))), z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(z))) | (~b(z, s(z))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(z))), z)))),
% 3.13/3.37 inference(transitivity,[status(thm)],[13961, 13959])).
% 3.13/3.37 tff(13963,plain,
% 3.13/3.37 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), s(z))) | (~b(s(s(s(z))), s(z))) | (~b(s(z), s(s(s(elem!1))))) | (~b(z, s(z))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(z))), z)))),
% 3.13/3.37 inference(quant_inst,[status(thm)],[])).
% 3.13/3.37 tff(13964,plain,
% 3.13/3.37 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(z))) | (~b(z, s(z))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(z))), z))),
% 3.13/3.37 inference(modus_ponens,[status(thm)],[13963, 13962])).
% 3.13/3.37 tff(13965,plain,
% 3.13/3.37 ($false),
% 3.13/3.37 inference(unit_resolution,[status(thm)],[13964, 166, 241, 96, 118, 1699, 13958])).
% 3.13/3.37 tff(13966,plain,((~b(s(s(s(z))), z)) | (~b(s(z), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(z))) | (~b(z, s(z))) | (~r(s(s(z)), s(z))) | (~b(z, s(s(z)))) | (~b(s(s(z)), z))), inference(lemma,lemma(discharge,[]))).
% 3.13/3.37 tff(13967,plain,
% 3.13/3.37 ((~b(s(s(s(z))), z)) | (~b(s(z), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(z))) | (~b(z, s(z))) | (~r(s(s(z)), s(z))) | (~b(s(s(z)), z))),
% 3.13/3.37 inference(unit_resolution,[status(thm)],[13966, 10450])).
% 3.13/3.37 tff(13968,plain,
% 3.13/3.37 (~b(s(s(s(z))), z)),
% 3.13/3.37 inference(unit_resolution,[status(thm)],[13967, 13951, 241, 96, 13935, 392])).
% 3.13/3.37 tff(13969,plain,
% 3.13/3.37 (r(s(s(s(z))), z)),
% 3.13/3.37 inference(unit_resolution,[status(thm)],[1713, 13968])).
% 3.13/3.37 tff(13970,plain,
% 3.13/3.37 (~b(z, s(s(elem!1)))),
% 3.13/3.37 inference(unit_resolution,[status(thm)],[12611, 13942, 13943])).
% 3.13/3.37 tff(13971,plain,
% 3.13/3.37 (r(z, s(s(elem!1)))),
% 3.13/3.37 inference(unit_resolution,[status(thm)],[1795, 13970])).
% 3.13/3.37 tff(13972,plain,
% 3.13/3.37 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(elem!1)))) | (~r(s(s(s(elem!1))), z)) | (~r(s(s(s(z))), z)) | (~r(s(s(s(z))), s(s(s(elem!1))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, s(s(elem!1)))) | (~r(s(s(s(elem!1))), z)) | (~r(s(s(s(z))), z)) | (~r(s(s(s(z))), s(s(s(elem!1))))))),
% 3.13/3.37 inference(rewrite,[status(thm)],[])).
% 3.13/3.37 tff(13973,plain,
% 3.13/3.37 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(elem!1)))) | (~r(s(s(s(elem!1))), z)) | (~r(s(s(s(z))), z)) | (~r(s(s(s(z))), s(s(s(elem!1))))))),
% 3.13/3.37 inference(quant_inst,[status(thm)],[])).
% 3.13/3.37 tff(13974,plain,
% 3.13/3.37 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, s(s(elem!1)))) | (~r(s(s(s(elem!1))), z)) | (~r(s(s(s(z))), z)) | (~r(s(s(s(z))), s(s(s(elem!1)))))),
% 3.13/3.37 inference(modus_ponens,[status(thm)],[13973, 13972])).
% 3.13/3.37 tff(13975,plain,
% 3.13/3.37 (~r(s(s(s(z))), s(s(s(elem!1))))),
% 3.13/3.37 inference(unit_resolution,[status(thm)],[13974, 197, 154, 13971, 13969])).
% 3.13/3.37 tff(13976,plain,
% 3.13/3.37 ((s(s(s(z))) = s(s(s(elem!1)))) | b(s(s(s(z))), s(s(s(elem!1))))),
% 3.13/3.37 inference(unit_resolution,[status(thm)],[10059, 79, 13975])).
% 3.13/3.37 tff(13977,plain,
% 3.13/3.37 (b(s(s(s(z))), s(s(s(elem!1))))),
% 3.13/3.37 inference(unit_resolution,[status(thm)],[13976, 13883])).
% 3.13/3.37 tff(13978,plain,
% 3.13/3.37 (~r(s(s(s(elem!1))), s(s(elem!1)))),
% 3.13/3.37 inference(unit_resolution,[status(thm)],[13310, 197, 154, 13971, 13945])).
% 3.13/3.37 tff(13979,plain,
% 3.13/3.37 (b(s(s(s(elem!1))), s(s(elem!1)))),
% 3.13/3.37 inference(unit_resolution,[status(thm)],[889, 13978, 51])).
% 3.13/3.37 tff(13980,plain,
% 3.13/3.37 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(s(s(z))), s(s(s(elem!1))))) | (~b(s(s(elem!1)), s(s(s(z))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(s(s(z))), s(s(s(elem!1))))) | (~b(s(s(elem!1)), s(s(s(z))))))),
% 3.13/3.37 inference(rewrite,[status(thm)],[])).
% 3.13/3.37 tff(13981,plain,
% 3.13/3.37 (((~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(s(s(z))), s(s(s(elem!1))))) | (~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(s(s(elem!1)), s(s(s(z)))))) <=> ((~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(s(s(z))), s(s(s(elem!1))))) | (~b(s(s(elem!1)), s(s(s(z))))))),
% 3.13/3.37 inference(rewrite,[status(thm)],[])).
% 3.13/3.37 tff(13982,plain,
% 3.13/3.37 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(s(s(z))), s(s(s(elem!1))))) | (~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(s(s(elem!1)), s(s(s(z))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(s(s(z))), s(s(s(elem!1))))) | (~b(s(s(elem!1)), s(s(s(z)))))))),
% 3.13/3.37 inference(monotonicity,[status(thm)],[13981])).
% 3.13/3.37 tff(13983,plain,
% 3.13/3.37 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(s(s(z))), s(s(s(elem!1))))) | (~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(s(s(elem!1)), s(s(s(z))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(s(s(z))), s(s(s(elem!1))))) | (~b(s(s(elem!1)), s(s(s(z))))))),
% 3.13/3.37 inference(transitivity,[status(thm)],[13982, 13980])).
% 3.13/3.37 tff(13984,plain,
% 3.13/3.37 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(s(s(z))), s(s(s(elem!1))))) | (~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(s(s(elem!1)), s(s(s(z))))))),
% 3.13/3.37 inference(quant_inst,[status(thm)],[])).
% 3.13/3.37 tff(13985,plain,
% 3.13/3.37 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(s(s(z))), s(s(s(elem!1))))) | (~b(s(s(elem!1)), s(s(s(z)))))),
% 3.13/3.37 inference(modus_ponens,[status(thm)],[13984, 13983])).
% 3.13/3.37 tff(13986,plain,
% 3.13/3.37 (~b(s(s(elem!1)), s(s(s(z))))),
% 3.13/3.37 inference(unit_resolution,[status(thm)],[13985, 166, 13947, 13979, 13977])).
% 3.13/3.37 tff(13987,plain,
% 3.13/3.37 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(elem!1)))) | (~r(s(s(elem!1)), z)) | (~r(s(s(s(z))), z)) | (~r(s(s(elem!1)), s(s(s(z))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, s(s(elem!1)))) | (~r(s(s(elem!1)), z)) | (~r(s(s(s(z))), z)) | (~r(s(s(elem!1)), s(s(s(z))))))),
% 3.13/3.37 inference(rewrite,[status(thm)],[])).
% 3.13/3.37 tff(13988,plain,
% 3.13/3.37 (((~r(z, s(s(elem!1)))) | (~r(s(s(s(z))), z)) | (~r(s(s(elem!1)), z)) | (~r(s(s(elem!1)), s(s(s(z)))))) <=> ((~r(z, s(s(elem!1)))) | (~r(s(s(elem!1)), z)) | (~r(s(s(s(z))), z)) | (~r(s(s(elem!1)), s(s(s(z))))))),
% 3.13/3.37 inference(rewrite,[status(thm)],[])).
% 3.13/3.37 tff(13989,plain,
% 3.13/3.37 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(elem!1)))) | (~r(s(s(s(z))), z)) | (~r(s(s(elem!1)), z)) | (~r(s(s(elem!1)), s(s(s(z))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(elem!1)))) | (~r(s(s(elem!1)), z)) | (~r(s(s(s(z))), z)) | (~r(s(s(elem!1)), s(s(s(z)))))))),
% 3.13/3.37 inference(monotonicity,[status(thm)],[13988])).
% 3.13/3.37 tff(13990,plain,
% 3.13/3.37 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(elem!1)))) | (~r(s(s(s(z))), z)) | (~r(s(s(elem!1)), z)) | (~r(s(s(elem!1)), s(s(s(z))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, s(s(elem!1)))) | (~r(s(s(elem!1)), z)) | (~r(s(s(s(z))), z)) | (~r(s(s(elem!1)), s(s(s(z))))))),
% 3.13/3.37 inference(transitivity,[status(thm)],[13989, 13987])).
% 3.13/3.37 tff(13991,plain,
% 3.13/3.37 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(elem!1)))) | (~r(s(s(s(z))), z)) | (~r(s(s(elem!1)), z)) | (~r(s(s(elem!1)), s(s(s(z))))))),
% 3.13/3.37 inference(quant_inst,[status(thm)],[])).
% 3.13/3.37 tff(13992,plain,
% 3.13/3.37 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, s(s(elem!1)))) | (~r(s(s(elem!1)), z)) | (~r(s(s(s(z))), z)) | (~r(s(s(elem!1)), s(s(s(z)))))),
% 3.13/3.37 inference(modus_ponens,[status(thm)],[13991, 13990])).
% 3.13/3.37 tff(13993,plain,
% 3.13/3.37 (~r(s(s(elem!1)), s(s(s(z))))),
% 3.13/3.37 inference(unit_resolution,[status(thm)],[13992, 197, 13971, 13945, 13969])).
% 3.13/3.37 tff(13994,plain,
% 3.13/3.37 ((s(s(elem!1)) = s(s(s(z)))) | b(s(s(elem!1)), s(s(s(z))))),
% 3.13/3.37 inference(unit_resolution,[status(thm)],[5091, 79, 13993])).
% 3.13/3.37 tff(13995,plain,
% 3.13/3.37 (s(s(elem!1)) = s(s(s(z)))),
% 3.13/3.37 inference(unit_resolution,[status(thm)],[13994, 13986])).
% 3.13/3.37 tff(13996,plain,
% 3.13/3.37 (s(s(s(elem!1))) = s(s(s(s(z))))),
% 3.13/3.37 inference(monotonicity,[status(thm)],[13995])).
% 3.13/3.37 tff(13997,plain,
% 3.13/3.37 (s(s(s(s(z)))) = s(s(s(elem!1)))),
% 3.13/3.37 inference(symmetry,[status(thm)],[13996])).
% 3.13/3.37 tff(13998,plain,
% 3.13/3.37 (s(s(s(s(elem!1)))) = s(s(s(s(s(z)))))),
% 3.13/3.37 inference(monotonicity,[status(thm)],[13996])).
% 3.13/3.37 tff(13999,plain,
% 3.13/3.37 (s(s(s(s(s(z))))) = s(s(s(s(elem!1))))),
% 3.13/3.37 inference(symmetry,[status(thm)],[13998])).
% 3.13/3.37 tff(14000,plain,
% 3.13/3.37 (r(s(s(s(s(s(z))))), s(s(s(s(z))))) <=> r(s(s(s(s(elem!1)))), s(s(s(elem!1))))),
% 3.13/3.37 inference(monotonicity,[status(thm)],[13999, 13997])).
% 3.13/3.37 tff(14001,plain,
% 3.13/3.37 (r(s(s(s(s(elem!1)))), s(s(s(elem!1)))) <=> r(s(s(s(s(s(z))))), s(s(s(s(z)))))),
% 3.13/3.37 inference(symmetry,[status(thm)],[14000])).
% 3.13/3.37 tff(14002,plain,
% 3.13/3.37 (b(s(s(s(s(elem!1)))), s(s(s(elem!1)))) <=> b(s(s(s(s(elem!1)))), s(s(s(s(z)))))),
% 3.13/3.37 inference(monotonicity,[status(thm)],[13996])).
% 3.13/3.37 tff(14003,plain,
% 3.13/3.37 (b(s(s(s(s(elem!1)))), s(s(s(s(z))))) <=> b(s(s(s(s(elem!1)))), s(s(s(elem!1))))),
% 3.13/3.37 inference(symmetry,[status(thm)],[14002])).
% 3.13/3.37 tff(14004,plain,
% 3.13/3.37 (b(s(s(s(s(s(z))))), s(s(s(s(z))))) <=> b(s(s(s(s(elem!1)))), s(s(s(s(z)))))),
% 3.13/3.37 inference(monotonicity,[status(thm)],[13999])).
% 3.13/3.37 tff(14005,plain,
% 3.13/3.37 (b(s(s(s(s(s(z))))), s(s(s(s(z))))) <=> b(s(s(s(s(elem!1)))), s(s(s(elem!1))))),
% 3.13/3.37 inference(transitivity,[status(thm)],[14004, 14003])).
% 3.13/3.37 tff(14006,plain,
% 3.13/3.37 ((~b(s(s(s(s(s(z))))), s(s(s(s(z)))))) <=> (~b(s(s(s(s(elem!1)))), s(s(s(elem!1)))))),
% 3.13/3.37 inference(monotonicity,[status(thm)],[14005])).
% 3.13/3.37 tff(14007,plain,
% 3.13/3.37 (b(s(s(s(s(s(z))))), s(z)) <=> b(s(s(s(s(elem!1)))), s(z))),
% 3.13/3.37 inference(monotonicity,[status(thm)],[13999])).
% 3.13/3.37 tff(14008,plain,
% 3.13/3.37 (b(s(s(s(s(elem!1)))), s(z)) <=> b(s(s(s(s(s(z))))), s(z))),
% 3.13/3.37 inference(symmetry,[status(thm)],[14007])).
% 3.13/3.37 tff(14009,plain,
% 3.13/3.37 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(z, s(s(z)))) | (~b(s(z), z)) | (~b(s(z), s(s(s(elem!1))))) | (~b(s(z), s(s(z)))) | (~b(s(s(z)), s(s(elem!1)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(z, s(s(z)))) | (~b(s(z), z)) | (~b(s(z), s(s(s(elem!1))))) | (~b(s(z), s(s(z)))) | (~b(s(s(z)), s(s(elem!1)))))),
% 3.13/3.37 inference(rewrite,[status(thm)],[])).
% 3.13/3.37 tff(14010,plain,
% 3.13/3.37 (((~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(s(z), s(s(s(elem!1))))) | (~b(s(s(z)), s(s(elem!1)))) | (~b(z, s(s(z)))) | (~b(s(z), s(s(z)))) | (~b(s(z), z))) <=> ((~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(z, s(s(z)))) | (~b(s(z), z)) | (~b(s(z), s(s(s(elem!1))))) | (~b(s(z), s(s(z)))) | (~b(s(s(z)), s(s(elem!1)))))),
% 3.13/3.37 inference(rewrite,[status(thm)],[])).
% 3.13/3.37 tff(14011,plain,
% 3.13/3.37 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(s(z), s(s(s(elem!1))))) | (~b(s(s(z)), s(s(elem!1)))) | (~b(z, s(s(z)))) | (~b(s(z), s(s(z)))) | (~b(s(z), z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(z, s(s(z)))) | (~b(s(z), z)) | (~b(s(z), s(s(s(elem!1))))) | (~b(s(z), s(s(z)))) | (~b(s(s(z)), s(s(elem!1))))))),
% 3.13/3.37 inference(monotonicity,[status(thm)],[14010])).
% 3.13/3.37 tff(14012,plain,
% 3.13/3.37 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(s(z), s(s(s(elem!1))))) | (~b(s(s(z)), s(s(elem!1)))) | (~b(z, s(s(z)))) | (~b(s(z), s(s(z)))) | (~b(s(z), z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(z, s(s(z)))) | (~b(s(z), z)) | (~b(s(z), s(s(s(elem!1))))) | (~b(s(z), s(s(z)))) | (~b(s(s(z)), s(s(elem!1)))))),
% 3.13/3.37 inference(transitivity,[status(thm)],[14011, 14009])).
% 3.13/3.37 tff(14013,plain,
% 3.13/3.37 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(s(z), s(s(s(elem!1))))) | (~b(s(s(z)), s(s(elem!1)))) | (~b(z, s(s(z)))) | (~b(s(z), s(s(z)))) | (~b(s(z), z)))),
% 3.13/3.37 inference(quant_inst,[status(thm)],[])).
% 3.13/3.37 tff(14014,plain,
% 3.13/3.37 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(z, s(s(z)))) | (~b(s(z), z)) | (~b(s(z), s(s(s(elem!1))))) | (~b(s(z), s(s(z)))) | (~b(s(s(z)), s(s(elem!1))))),
% 3.13/3.37 inference(modus_ponens,[status(thm)],[14013, 14012])).
% 3.13/3.37 tff(14015,plain,
% 3.13/3.37 ($false),
% 3.13/3.37 inference(unit_resolution,[status(thm)],[14014, 166, 463, 241, 53, 556, 10451, 446])).
% 3.13/3.37 tff(14016,plain,((~b(s(z), s(s(s(elem!1))))) | (~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(s(z), z)) | (~b(s(z), s(s(z)))) | (~b(z, s(s(z)))) | (~b(s(s(z)), s(s(elem!1))))), inference(lemma,lemma(discharge,[]))).
% 3.13/3.37 tff(14017,plain,
% 3.13/3.37 ((~b(s(z), s(s(s(elem!1))))) | (~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(s(z), z)) | (~b(s(z), s(s(z)))) | (~b(s(s(z)), s(s(elem!1))))),
% 3.13/3.37 inference(unit_resolution,[status(thm)],[14016, 10450])).
% 3.13/3.37 tff(14018,plain,
% 3.13/3.37 (~b(s(z), s(s(z)))),
% 3.13/3.37 inference(unit_resolution,[status(thm)],[14017, 13947, 53, 241, 13942])).
% 3.13/3.37 tff(14019,plain,
% 3.13/3.37 (r(s(z), s(s(z)))),
% 3.13/3.37 inference(unit_resolution,[status(thm)],[427, 14018])).
% 3.13/3.37 tff(14020,plain,
% 3.13/3.37 (b(s(s(elem!1)), s(s(z))) <=> b(s(s(s(z))), s(s(z)))),
% 3.13/3.37 inference(monotonicity,[status(thm)],[13995])).
% 3.13/3.37 tff(14021,plain,
% 3.13/3.37 (b(s(s(s(z))), s(s(z)))),
% 3.13/3.37 inference(modus_ponens,[status(thm)],[13943, 14020])).
% 3.13/3.37 tff(14022,plain,
% 3.13/3.37 (~b(s(z), s(s(s(z))))),
% 3.13/3.37 inference(unit_resolution,[status(thm)],[8841, 13977, 241, 96])).
% 3.13/3.37 tff(14023,plain,
% 3.13/3.37 (r(s(z), s(s(s(z))))),
% 3.13/3.37 inference(unit_resolution,[status(thm)],[1674, 14022])).
% 3.13/3.37 tff(14024,plain,
% 3.13/3.37 (~r(s(s(z)), s(s(s(z))))),
% 3.13/3.37 inference(unit_resolution,[status(thm)],[11884, 14023, 13969, 14019])).
% 3.13/3.37 tff(14025,plain,
% 3.13/3.37 (b(s(s(z)), s(s(s(z))))),
% 3.13/3.37 inference(unit_resolution,[status(thm)],[1730, 14024])).
% 3.13/3.37 tff(14026,plain,
% 3.13/3.37 ((s(s(z)) = s(s(s(s(s(z)))))) <=> (s(s(z)) = s(s(s(s(elem!1)))))),
% 3.13/3.37 inference(monotonicity,[status(thm)],[5168])).
% 3.13/3.37 tff(14027,plain,
% 3.13/3.37 ((s(s(z)) = s(s(s(s(s(z)))))) <=> (s(s(s(s(elem!1)))) = s(s(z)))),
% 3.13/3.37 inference(transitivity,[status(thm)],[14026, 1275])).
% 3.13/3.37 tff(14028,plain,
% 3.13/3.37 ((s(s(s(s(elem!1)))) = s(s(z))) <=> (s(s(z)) = s(s(s(s(s(z))))))),
% 3.13/3.37 inference(symmetry,[status(thm)],[14027])).
% 3.13/3.37 tff(14029,plain,
% 3.13/3.37 ((~(s(s(s(s(elem!1)))) = s(s(z)))) <=> (~(s(s(z)) = s(s(s(s(s(z)))))))),
% 3.13/3.37 inference(monotonicity,[status(thm)],[14028])).
% 3.13/3.37 tff(14030,plain,
% 3.13/3.37 (~(s(s(z)) = s(s(s(s(s(z))))))),
% 3.13/3.37 inference(modus_ponens,[status(thm)],[733, 14029])).
% 3.13/3.37 tff(14031,plain,
% 3.13/3.37 (s(s(s(z))) = s(s(elem!1))),
% 3.13/3.37 inference(symmetry,[status(thm)],[5163])).
% 3.13/3.37 tff(14032,plain,
% 3.13/3.37 ((s(s(s(s(elem!1)))) = s(s(s(z)))) <=> (s(s(s(s(elem!1)))) = s(s(elem!1)))),
% 3.13/3.37 inference(monotonicity,[status(thm)],[14031])).
% 3.13/3.37 tff(14033,plain,
% 3.13/3.37 ((s(s(s(s(elem!1)))) = s(s(s(z)))) <=> (s(s(elem!1)) = s(s(s(s(elem!1)))))),
% 3.13/3.37 inference(transitivity,[status(thm)],[14032, 123])).
% 3.13/3.37 tff(14034,plain,
% 3.13/3.37 ((s(s(s(s(elem!1)))) = s(s(s(z)))) <=> (s(s(s(s(elem!1)))) = s(s(elem!1)))),
% 3.13/3.37 inference(transitivity,[status(thm)],[14033, 124])).
% 3.13/3.37 tff(14035,plain,
% 3.13/3.37 ((~(s(s(s(s(elem!1)))) = s(s(s(z))))) <=> (~(s(s(s(s(elem!1)))) = s(s(elem!1))))),
% 3.13/3.37 inference(monotonicity,[status(thm)],[14034])).
% 3.13/3.37 tff(14036,plain,
% 3.13/3.37 (~(s(s(s(s(elem!1)))) = s(s(elem!1)))),
% 3.13/3.37 inference(modus_ponens,[status(thm)],[5112, 14035])).
% 3.13/3.37 tff(14037,plain,
% 3.13/3.37 (~r(s(s(s(s(elem!1)))), s(s(elem!1)))),
% 3.13/3.37 inference(unit_resolution,[status(thm)],[4643, 700, 120, 4577])).
% 3.13/3.37 tff(14038,plain,
% 3.13/3.37 (b(s(s(s(s(elem!1)))), s(s(elem!1)))),
% 3.13/3.37 inference(unit_resolution,[status(thm)],[813, 14037, 14036])).
% 3.13/3.37 tff(14039,plain,
% 3.13/3.37 (b(s(s(s(s(s(z))))), s(s(s(z))))),
% 3.13/3.37 inference(unit_resolution,[status(thm)],[5175, 14038, 5163])).
% 3.13/3.37 tff(14040,plain,
% 3.13/3.37 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), s(s(z)))) | (~b(s(s(z)), z)) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(z)), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), s(s(s(z))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(s(z)), z)) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(z)), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), s(s(s(z))))))),
% 3.13/3.37 inference(rewrite,[status(thm)],[])).
% 3.13/3.37 tff(14041,plain,
% 3.13/3.37 (((~b(s(s(z)), z)) | (~b(s(s(z)), z)) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(s(s(s(s(z))))), s(s(s(z))))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(z)), s(s(s(s(s(z)))))))) <=> ((~b(s(s(s(z))), s(s(z)))) | (~b(s(s(z)), z)) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(z)), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), s(s(s(z))))))),
% 3.13/3.37 inference(rewrite,[status(thm)],[])).
% 3.13/3.37 tff(14042,plain,
% 3.13/3.37 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), z)) | (~b(s(s(z)), z)) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(s(s(s(s(z))))), s(s(s(z))))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(z)), s(s(s(s(s(z))))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), s(s(z)))) | (~b(s(s(z)), z)) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(z)), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), s(s(s(z)))))))),
% 3.13/3.38 inference(monotonicity,[status(thm)],[14041])).
% 3.13/3.38 tff(14043,plain,
% 3.13/3.38 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), z)) | (~b(s(s(z)), z)) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(s(s(s(s(z))))), s(s(s(z))))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(z)), s(s(s(s(s(z))))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(s(z)), z)) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(z)), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), s(s(s(z))))))),
% 3.13/3.38 inference(transitivity,[status(thm)],[14042, 14040])).
% 3.13/3.38 tff(14044,plain,
% 3.13/3.38 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), z)) | (~b(s(s(z)), z)) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(s(s(s(s(z))))), s(s(s(z))))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(z)), s(s(s(s(s(z))))))))),
% 3.13/3.38 inference(quant_inst,[status(thm)],[])).
% 3.13/3.38 tff(14045,plain,
% 3.13/3.38 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(s(z)), z)) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(z)), s(s(s(s(s(z))))))) | (~b(s(s(s(s(s(z))))), s(s(s(z)))))),
% 3.13/3.38 inference(modus_ponens,[status(thm)],[14044, 14043])).
% 3.13/3.38 tff(14046,plain,
% 3.13/3.38 (~b(s(s(z)), s(s(s(s(s(z))))))),
% 3.13/3.38 inference(unit_resolution,[status(thm)],[14045, 166, 122, 986, 987, 14039])).
% 3.13/3.38 tff(14047,plain,
% 3.13/3.38 (r(s(s(s(s(s(z))))), s(z)) <=> r(s(s(s(s(elem!1)))), s(z))),
% 3.13/3.38 inference(monotonicity,[status(thm)],[5168])).
% 3.13/3.38 tff(14048,plain,
% 3.13/3.38 (r(s(s(s(s(elem!1)))), s(z)) <=> r(s(s(s(s(s(z))))), s(z))),
% 3.13/3.38 inference(symmetry,[status(thm)],[14047])).
% 3.13/3.38 tff(14049,plain,
% 3.13/3.38 (r(s(s(s(s(s(z))))), s(z))),
% 3.13/3.38 inference(modus_ponens,[status(thm)],[700, 14048])).
% 3.13/3.38 tff(14050,plain,
% 3.13/3.38 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(z)), s(z))) | (~r(s(z), s(s(z)))) | (~r(s(s(s(s(s(z))))), s(z))) | (~r(s(s(z)), s(s(s(s(s(z))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(z)), s(z))) | (~r(s(z), s(s(z)))) | (~r(s(s(s(s(s(z))))), s(z))) | (~r(s(s(z)), s(s(s(s(s(z))))))))),
% 3.13/3.38 inference(rewrite,[status(thm)],[])).
% 3.13/3.38 tff(14051,plain,
% 3.13/3.38 (((~r(s(z), s(s(z)))) | (~r(s(s(s(s(s(z))))), s(z))) | (~r(s(s(z)), s(z))) | (~r(s(s(z)), s(s(s(s(s(z)))))))) <=> ((~r(s(s(z)), s(z))) | (~r(s(z), s(s(z)))) | (~r(s(s(s(s(s(z))))), s(z))) | (~r(s(s(z)), s(s(s(s(s(z))))))))),
% 3.13/3.38 inference(rewrite,[status(thm)],[])).
% 3.13/3.38 tff(14052,plain,
% 3.13/3.38 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(s(z)))) | (~r(s(s(s(s(s(z))))), s(z))) | (~r(s(s(z)), s(z))) | (~r(s(s(z)), s(s(s(s(s(z))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(z)), s(z))) | (~r(s(z), s(s(z)))) | (~r(s(s(s(s(s(z))))), s(z))) | (~r(s(s(z)), s(s(s(s(s(z)))))))))),
% 3.13/3.38 inference(monotonicity,[status(thm)],[14051])).
% 3.13/3.38 tff(14053,plain,
% 3.13/3.38 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(s(z)))) | (~r(s(s(s(s(s(z))))), s(z))) | (~r(s(s(z)), s(z))) | (~r(s(s(z)), s(s(s(s(s(z))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(z)), s(z))) | (~r(s(z), s(s(z)))) | (~r(s(s(s(s(s(z))))), s(z))) | (~r(s(s(z)), s(s(s(s(s(z))))))))),
% 3.13/3.38 inference(transitivity,[status(thm)],[14052, 14050])).
% 3.13/3.38 tff(14054,plain,
% 3.13/3.38 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(s(z)))) | (~r(s(s(s(s(s(z))))), s(z))) | (~r(s(s(z)), s(z))) | (~r(s(s(z)), s(s(s(s(s(z))))))))),
% 3.13/3.38 inference(quant_inst,[status(thm)],[])).
% 3.13/3.38 tff(14055,plain,
% 3.13/3.38 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(z)), s(z))) | (~r(s(z), s(s(z)))) | (~r(s(s(s(s(s(z))))), s(z))) | (~r(s(s(z)), s(s(s(s(s(z)))))))),
% 3.13/3.38 inference(modus_ponens,[status(thm)],[14054, 14053])).
% 3.13/3.38 tff(14056,plain,
% 3.13/3.38 (~r(s(s(z)), s(s(s(s(s(z))))))),
% 3.13/3.38 inference(unit_resolution,[status(thm)],[14055, 197, 120, 392, 14049])).
% 3.13/3.38 tff(14057,plain,
% 3.13/3.38 ((s(s(z)) = s(s(s(s(s(z)))))) | b(s(s(z)), s(s(s(s(s(z))))))),
% 3.13/3.38 inference(unit_resolution,[status(thm)],[5216, 79, 14056])).
% 3.13/3.38 tff(14058,plain,
% 3.13/3.38 ($false),
% 3.13/3.38 inference(unit_resolution,[status(thm)],[14057, 14046, 14030])).
% 3.13/3.38 tff(14059,plain,((~r(s(s(s(s(elem!1)))), s(z))) | (~b(s(s(z)), z)) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(s(z))), s(s(z)))) | (~(s(s(elem!1)) = s(s(s(z))))) | (~r(s(z), s(s(z)))) | (~r(s(s(z)), s(z))) | (~r(s(s(elem!1)), s(z)))), inference(lemma,lemma(discharge,[]))).
% 3.13/3.38 tff(14060,plain,
% 3.13/3.38 (~r(s(s(s(s(elem!1)))), s(z))),
% 3.13/3.38 inference(unit_resolution,[status(thm)],[14059, 13951, 14025, 14021, 13995, 14019, 392, 13939])).
% 3.13/3.38 tff(14061,plain,
% 3.13/3.38 (b(s(s(s(s(elem!1)))), s(z))),
% 3.13/3.38 inference(unit_resolution,[status(thm)],[661, 14060])).
% 3.13/3.38 tff(14062,plain,
% 3.13/3.38 (b(s(s(s(s(s(z))))), s(z))),
% 3.13/3.38 inference(modus_ponens,[status(thm)],[14061, 14008])).
% 3.13/3.38 tff(14063,plain,
% 3.13/3.38 (b(s(s(s(elem!1))), s(z)) <=> b(s(s(s(s(z)))), s(z))),
% 3.13/3.38 inference(monotonicity,[status(thm)],[13996])).
% 3.13/3.38 tff(14064,plain,
% 3.13/3.38 (b(s(s(s(s(z)))), s(z))),
% 3.13/3.38 inference(modus_ponens,[status(thm)],[96, 14063])).
% 3.13/3.38 tff(14065,plain,
% 3.13/3.38 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), z)) | (~b(z, s(z))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~b(s(s(s(s(s(z))))), s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), z)) | (~b(z, s(z))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~b(s(s(s(s(s(z))))), s(z))))),
% 3.13/3.38 inference(rewrite,[status(thm)],[])).
% 3.13/3.38 tff(14066,plain,
% 3.13/3.38 (((~b(z, s(z))) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(s(z), z)) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(s(s(s(s(s(z))))), s(s(s(s(z))))))) <=> ((~b(s(z), z)) | (~b(z, s(z))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~b(s(s(s(s(s(z))))), s(z))))),
% 3.13/3.38 inference(rewrite,[status(thm)],[])).
% 3.13/3.38 tff(14067,plain,
% 3.13/3.38 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(z))) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(s(z), z)) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(s(s(s(s(s(z))))), s(s(s(s(z)))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), z)) | (~b(z, s(z))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~b(s(s(s(s(s(z))))), s(z)))))),
% 3.13/3.38 inference(monotonicity,[status(thm)],[14066])).
% 3.13/3.38 tff(14068,plain,
% 3.13/3.38 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(z))) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(s(z), z)) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(s(s(s(s(s(z))))), s(s(s(s(z)))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), z)) | (~b(z, s(z))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~b(s(s(s(s(s(z))))), s(z))))),
% 3.13/3.38 inference(transitivity,[status(thm)],[14067, 14065])).
% 3.13/3.38 tff(14069,plain,
% 3.13/3.38 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(z))) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(s(z), z)) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(s(s(z))))), s(z))) | (~b(s(s(s(s(s(z))))), s(s(s(s(z)))))))),
% 3.13/3.38 inference(quant_inst,[status(thm)],[])).
% 3.13/3.38 tff(14070,plain,
% 3.13/3.38 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), z)) | (~b(z, s(z))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~b(s(s(s(s(s(z))))), s(z)))),
% 3.13/3.38 inference(modus_ponens,[status(thm)],[14069, 14068])).
% 3.13/3.38 tff(14071,plain,
% 3.13/3.38 ((~b(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~b(s(s(s(s(s(z))))), s(z)))),
% 3.13/3.38 inference(unit_resolution,[status(thm)],[14070, 166, 53, 13935, 14064])).
% 3.13/3.38 tff(14072,plain,
% 3.13/3.38 (~b(s(s(s(s(s(z))))), s(s(s(s(z)))))),
% 3.13/3.38 inference(unit_resolution,[status(thm)],[14071, 14062])).
% 3.13/3.38 tff(14073,plain,
% 3.13/3.38 (~b(s(s(s(s(elem!1)))), s(s(s(elem!1))))),
% 3.13/3.38 inference(modus_ponens,[status(thm)],[14072, 14006])).
% 3.13/3.38 tff(14074,plain,
% 3.13/3.38 (r(s(s(s(s(elem!1)))), s(s(s(elem!1))))),
% 3.13/3.38 inference(unit_resolution,[status(thm)],[1065, 14073, 364])).
% 3.13/3.38 tff(14075,plain,
% 3.13/3.38 (r(s(s(s(s(s(z))))), s(s(s(s(z)))))),
% 3.13/3.38 inference(modus_ponens,[status(thm)],[14074, 14001])).
% 3.13/3.38 tff(14076,plain,
% 3.13/3.38 ((~b(s(s(s(s(s(z))))), s(z))) | (~b(s(s(s(s(s(z))))), z))),
% 3.13/3.38 inference(unit_resolution,[status(thm)],[7005, 166, 53, 13935])).
% 3.13/3.38 tff(14077,plain,
% 3.13/3.38 (~b(s(s(s(s(s(z))))), z)),
% 3.13/3.38 inference(unit_resolution,[status(thm)],[14076, 14062])).
% 3.13/3.38 tff(14078,plain,
% 3.13/3.38 (r(s(s(s(s(s(z))))), z)),
% 3.13/3.38 inference(unit_resolution,[status(thm)],[5198, 79, 5195, 14077])).
% 3.13/3.38 tff(14079,plain,
% 3.13/3.38 (r(s(s(s(elem!1))), z) <=> r(s(s(s(s(z)))), z)),
% 3.13/3.38 inference(monotonicity,[status(thm)],[13996])).
% 3.13/3.38 tff(14080,plain,
% 3.13/3.38 (r(s(s(s(s(z)))), z)),
% 3.13/3.38 inference(modus_ponens,[status(thm)],[154, 14079])).
% 3.13/3.38 tff(14081,plain,
% 3.13/3.38 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(z)))) | (~b(s(s(s(elem!1))), s(z))) | (~b(z, s(z))) | (~b(s(s(s(z))), s(s(s(elem!1))))) | (~b(z, s(s(s(z))))) | (~b(s(s(z)), s(s(s(z))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(s(z)))) | (~b(s(s(s(elem!1))), s(z))) | (~b(z, s(z))) | (~b(s(s(s(z))), s(s(s(elem!1))))) | (~b(z, s(s(s(z))))) | (~b(s(s(z)), s(s(s(z))))))),
% 3.13/3.38 inference(rewrite,[status(thm)],[])).
% 3.13/3.38 tff(14082,plain,
% 3.13/3.38 (((~b(s(s(s(elem!1))), s(z))) | (~b(z, s(z))) | (~b(s(s(s(z))), s(s(s(elem!1))))) | (~b(s(s(z)), s(s(s(z))))) | (~b(z, s(s(s(z))))) | (~b(z, s(s(z))))) <=> ((~b(z, s(s(z)))) | (~b(s(s(s(elem!1))), s(z))) | (~b(z, s(z))) | (~b(s(s(s(z))), s(s(s(elem!1))))) | (~b(z, s(s(s(z))))) | (~b(s(s(z)), s(s(s(z))))))),
% 3.13/3.38 inference(rewrite,[status(thm)],[])).
% 3.13/3.38 tff(14083,plain,
% 3.13/3.38 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), s(z))) | (~b(z, s(z))) | (~b(s(s(s(z))), s(s(s(elem!1))))) | (~b(s(s(z)), s(s(s(z))))) | (~b(z, s(s(s(z))))) | (~b(z, s(s(z)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(z)))) | (~b(s(s(s(elem!1))), s(z))) | (~b(z, s(z))) | (~b(s(s(s(z))), s(s(s(elem!1))))) | (~b(z, s(s(s(z))))) | (~b(s(s(z)), s(s(s(z)))))))),
% 3.13/3.38 inference(monotonicity,[status(thm)],[14082])).
% 3.13/3.38 tff(14084,plain,
% 3.13/3.38 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), s(z))) | (~b(z, s(z))) | (~b(s(s(s(z))), s(s(s(elem!1))))) | (~b(s(s(z)), s(s(s(z))))) | (~b(z, s(s(s(z))))) | (~b(z, s(s(z)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(s(z)))) | (~b(s(s(s(elem!1))), s(z))) | (~b(z, s(z))) | (~b(s(s(s(z))), s(s(s(elem!1))))) | (~b(z, s(s(s(z))))) | (~b(s(s(z)), s(s(s(z))))))),
% 3.13/3.38 inference(transitivity,[status(thm)],[14083, 14081])).
% 3.13/3.38 tff(14085,plain,
% 3.13/3.38 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), s(z))) | (~b(z, s(z))) | (~b(s(s(s(z))), s(s(s(elem!1))))) | (~b(s(s(z)), s(s(s(z))))) | (~b(z, s(s(s(z))))) | (~b(z, s(s(z)))))),
% 3.13/3.38 inference(quant_inst,[status(thm)],[])).
% 3.13/3.38 tff(14086,plain,
% 3.13/3.38 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(s(z)))) | (~b(s(s(s(elem!1))), s(z))) | (~b(z, s(z))) | (~b(s(s(s(z))), s(s(s(elem!1))))) | (~b(z, s(s(s(z))))) | (~b(s(s(z)), s(s(s(z)))))),
% 3.13/3.38 inference(modus_ponens,[status(thm)],[14085, 14084])).
% 3.13/3.38 tff(14087,plain,
% 3.13/3.38 (~b(z, s(s(s(z))))),
% 3.13/3.38 inference(unit_resolution,[status(thm)],[14086, 166, 10450, 96, 13935, 13977, 14025])).
% 3.13/3.38 tff(14088,plain,
% 3.13/3.38 (r(z, s(s(s(z))))),
% 3.13/3.38 inference(unit_resolution,[status(thm)],[1697, 14087])).
% 3.13/3.38 tff(14089,plain,
% 3.13/3.38 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(s(z))))) | (~r(s(s(s(s(z)))), z)) | (~r(s(s(s(s(s(z))))), z)) | (~r(s(s(s(s(s(z))))), s(s(s(s(z)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, s(s(s(z))))) | (~r(s(s(s(s(z)))), z)) | (~r(s(s(s(s(s(z))))), z)) | (~r(s(s(s(s(s(z))))), s(s(s(s(z)))))))),
% 3.13/3.38 inference(rewrite,[status(thm)],[])).
% 3.13/3.38 tff(14090,plain,
% 3.13/3.38 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(s(z))))) | (~r(s(s(s(s(z)))), z)) | (~r(s(s(s(s(s(z))))), z)) | (~r(s(s(s(s(s(z))))), s(s(s(s(z)))))))),
% 3.13/3.38 inference(quant_inst,[status(thm)],[])).
% 3.13/3.38 tff(14091,plain,
% 3.13/3.38 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, s(s(s(z))))) | (~r(s(s(s(s(z)))), z)) | (~r(s(s(s(s(s(z))))), z)) | (~r(s(s(s(s(s(z))))), s(s(s(s(z))))))),
% 3.13/3.38 inference(modus_ponens,[status(thm)],[14090, 14089])).
% 3.13/3.38 tff(14092,plain,
% 3.13/3.38 ($false),
% 3.13/3.38 inference(unit_resolution,[status(thm)],[14091, 197, 14088, 14080, 14078, 14075])).
% 3.13/3.38 tff(14093,plain,((s(s(z)) = s(s(elem!1))) | (~b(s(z), z)) | (~r(s(s(z)), s(z))) | (~b(s(s(s(elem!1))), s(z))) | (~r(s(s(s(elem!1))), z)) | (~b(s(z), s(s(s(elem!1))))) | (s(s(elem!1)) = s(s(s(elem!1)))) | (~r(s(z), s(s(elem!1))))), inference(lemma,lemma(discharge,[]))).
% 3.13/3.38 tff(14094,plain,
% 3.13/3.38 (s(s(z)) = s(s(elem!1))),
% 3.13/3.38 inference(unit_resolution,[status(thm)],[14093, 4143, 53, 13882, 13084, 13790, 13791, 85])).
% 3.13/3.38 tff(14095,plain,
% 3.13/3.38 (s(elem!1) = s(z)),
% 3.13/3.38 inference(unit_resolution,[status(thm)],[43, 14094])).
% 3.13/3.38 tff(14096,plain,
% 3.13/3.38 (z = elem!1),
% 3.13/3.38 inference(unit_resolution,[status(thm)],[30, 14095])).
% 3.13/3.38 tff(14097,plain,
% 3.13/3.38 ((s(s(s(s(elem!1)))) = z) <=> (s(s(s(s(elem!1)))) = elem!1)),
% 3.13/3.38 inference(monotonicity,[status(thm)],[14096])).
% 3.13/3.38 tff(14098,plain,
% 3.13/3.38 ((~(s(s(s(s(elem!1)))) = z)) <=> (~(s(s(s(s(elem!1)))) = elem!1))),
% 3.13/3.38 inference(monotonicity,[status(thm)],[14097])).
% 3.13/3.38 tff(14099,plain,
% 3.13/3.38 (~(s(s(s(s(elem!1)))) = elem!1)),
% 3.13/3.38 inference(modus_ponens,[status(thm)],[626, 14098])).
% 3.13/3.38 tff(14100,plain,
% 3.13/3.38 (~(s(s(s(elem!1))) = s(s(s(s(s(s(s(s(elem!1)))))))))),
% 3.13/3.38 inference(unit_resolution,[status(thm)],[13110, 14094])).
% 3.13/3.38 tff(14101,plain,
% 3.13/3.38 (~(s(s(s(s(s(s(s(s(elem!1)))))))) = s(s(s(elem!1))))),
% 3.13/3.38 inference(modus_ponens,[status(thm)],[14100, 13362])).
% 3.13/3.38 tff(14102,plain,
% 3.13/3.38 (r(s(s(s(elem!1))), elem!1)),
% 3.13/3.38 inference(unit_resolution,[status(thm)],[966, 14096, 13084])).
% 3.13/3.38 tff(14103,plain,
% 3.13/3.38 ((s(s(s(s(s(s(s(s(elem!1)))))))) = z) <=> (s(s(s(s(s(s(s(s(elem!1)))))))) = elem!1)),
% 3.13/3.38 inference(monotonicity,[status(thm)],[14096])).
% 3.13/3.38 tff(14104,plain,
% 3.13/3.38 ((~(s(s(s(s(s(s(s(s(elem!1)))))))) = z)) <=> (~(s(s(s(s(s(s(s(s(elem!1)))))))) = elem!1))),
% 3.13/3.38 inference(monotonicity,[status(thm)],[14103])).
% 3.13/3.38 tff(14105,plain,
% 3.13/3.38 (~(s(s(s(s(s(s(s(s(elem!1)))))))) = elem!1)),
% 3.13/3.38 inference(modus_ponens,[status(thm)],[13119, 14104])).
% 3.13/3.38 tff(14106,plain,
% 3.13/3.38 (b(s(z), z) <=> b(s(z), elem!1)),
% 3.13/3.38 inference(monotonicity,[status(thm)],[14096])).
% 3.13/3.38 tff(14107,plain,
% 3.13/3.38 (b(s(z), elem!1)),
% 3.13/3.38 inference(modus_ponens,[status(thm)],[53, 14106])).
% 3.13/3.38 tff(14108,plain,
% 3.13/3.38 (elem!1 = z),
% 3.13/3.38 inference(symmetry,[status(thm)],[14096])).
% 3.13/3.38 tff(14109,plain,
% 3.13/3.38 (b(elem!1, s(s(elem!1))) <=> b(z, s(s(elem!1)))),
% 3.13/3.38 inference(monotonicity,[status(thm)],[14108])).
% 3.13/3.38 tff(14110,plain,
% 3.13/3.38 (b(z, s(s(elem!1))) <=> b(elem!1, s(s(elem!1)))),
% 3.13/3.38 inference(symmetry,[status(thm)],[14109])).
% 3.13/3.38 tff(14111,plain,
% 3.13/3.38 (b(z, s(s(elem!1)))),
% 3.13/3.38 inference(unit_resolution,[status(thm)],[12671, 14094])).
% 3.13/3.38 tff(14112,plain,
% 3.13/3.38 (b(elem!1, s(s(elem!1)))),
% 3.13/3.38 inference(modus_ponens,[status(thm)],[14111, 14110])).
% 3.13/3.38 tff(14113,plain,
% 3.13/3.38 (~(s(s(s(s(s(s(s(s(elem!1)))))))) = s(s(elem!1)))),
% 3.13/3.38 inference(unit_resolution,[status(thm)],[13189, 14095])).
% 3.13/3.38 tff(14114,plain,
% 3.13/3.38 (~(s(s(s(s(s(s(s(s(elem!1)))))))) = s(z))),
% 3.13/3.38 inference(unit_resolution,[status(thm)],[13196, 14096])).
% 3.13/3.38 tff(14115,plain,
% 3.13/3.38 (~b(s(s(elem!1)), s(z))),
% 3.13/3.38 inference(unit_resolution,[status(thm)],[3938, 14094, 3936])).
% 3.13/3.38 tff(14116,plain,
% 3.13/3.38 (r(s(s(elem!1)), s(z))),
% 3.13/3.38 inference(unit_resolution,[status(thm)],[1912, 14115])).
% 3.13/3.38 tff(14117,plain,
% 3.13/3.38 (s(s(s(z))) = s(s(s(elem!1)))),
% 3.13/3.38 inference(monotonicity,[status(thm)],[14094])).
% 3.13/3.38 tff(14118,plain,
% 3.13/3.38 (b(s(s(s(z))), s(z)) <=> b(s(s(s(elem!1))), s(z))),
% 3.13/3.38 inference(monotonicity,[status(thm)],[14117])).
% 3.13/3.38 tff(14119,plain,
% 3.13/3.38 (b(s(s(s(elem!1))), s(z)) <=> b(s(s(s(z))), s(z))),
% 3.13/3.38 inference(symmetry,[status(thm)],[14118])).
% 3.13/3.38 tff(14120,plain,
% 3.13/3.38 (b(s(s(s(z))), s(z))),
% 3.13/3.38 inference(modus_ponens,[status(thm)],[13882, 14119])).
% 3.13/3.38 tff(14121,plain,
% 3.13/3.38 (~b(s(z), s(s(z)))),
% 3.13/3.38 inference(unit_resolution,[status(thm)],[4398, 14094, 54])).
% 3.13/3.38 tff(14122,plain,
% 3.13/3.38 (r(s(z), s(s(z)))),
% 3.13/3.38 inference(unit_resolution,[status(thm)],[427, 14121])).
% 3.13/3.38 tff(14123,plain,
% 3.13/3.38 (~(s(s(s(elem!1))) = s(s(s(s(s(s(s(s(elem!1)))))))))),
% 3.13/3.38 inference(unit_resolution,[status(thm)],[13110, 34])).
% 3.13/3.38 tff(14124,plain,
% 3.13/3.38 (~(s(s(s(s(s(s(s(s(elem!1)))))))) = s(s(s(elem!1))))),
% 3.13/3.38 inference(modus_ponens,[status(thm)],[14123, 13362])).
% 3.13/3.38 tff(14125,plain,
% 3.13/3.38 ((s(s(s(s(s(s(s(s(elem!1)))))))) = z) <=> (s(s(s(s(s(s(s(s(elem!1)))))))) = elem!1)),
% 3.13/3.38 inference(monotonicity,[status(thm)],[620])).
% 3.13/3.38 tff(14126,plain,
% 3.13/3.38 ((~(s(s(s(s(s(s(s(s(elem!1)))))))) = z)) <=> (~(s(s(s(s(s(s(s(s(elem!1)))))))) = elem!1))),
% 3.13/3.38 inference(monotonicity,[status(thm)],[14125])).
% 3.13/3.38 tff(14127,plain,
% 3.13/3.38 (~(s(s(s(s(s(s(s(s(elem!1)))))))) = elem!1)),
% 3.13/3.38 inference(modus_ponens,[status(thm)],[13119, 14126])).
% 3.13/3.38 tff(14128,plain,
% 3.13/3.38 (b(z, s(s(elem!1)))),
% 3.13/3.38 inference(unit_resolution,[status(thm)],[12671, 34])).
% 3.13/3.38 tff(14129,plain,
% 3.13/3.38 (b(elem!1, s(s(elem!1)))),
% 3.13/3.38 inference(modus_ponens,[status(thm)],[14128, 10705])).
% 3.13/3.38 tff(14130,plain,
% 3.13/3.38 (~(s(s(s(s(s(s(s(s(elem!1)))))))) = s(s(elem!1)))),
% 3.13/3.38 inference(unit_resolution,[status(thm)],[13189, 619])).
% 3.13/3.38 tff(14131,plain,
% 3.13/3.38 (~(s(s(s(s(s(s(s(s(elem!1)))))))) = s(z))),
% 3.13/3.38 inference(unit_resolution,[status(thm)],[13196, 620])).
% 3.13/3.38 tff(14132,plain,
% 3.13/3.38 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(z))) | (~r(s(s(z)), s(z))) | (~r(s(z), s(s(z)))) | (~r(s(s(z)), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, s(z))) | (~r(s(s(z)), s(z))) | (~r(s(z), s(s(z)))) | (~r(s(s(z)), z)))),
% 3.13/3.38 inference(rewrite,[status(thm)],[])).
% 3.13/3.38 tff(14133,plain,
% 3.13/3.38 (((~r(s(z), s(s(z)))) | (~r(z, s(z))) | (~r(s(s(z)), s(z))) | (~r(s(s(z)), z))) <=> ((~r(z, s(z))) | (~r(s(s(z)), s(z))) | (~r(s(z), s(s(z)))) | (~r(s(s(z)), z)))),
% 3.13/3.38 inference(rewrite,[status(thm)],[])).
% 3.13/3.38 tff(14134,plain,
% 3.13/3.38 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(s(z)))) | (~r(z, s(z))) | (~r(s(s(z)), s(z))) | (~r(s(s(z)), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(z))) | (~r(s(s(z)), s(z))) | (~r(s(z), s(s(z)))) | (~r(s(s(z)), z))))),
% 3.13/3.39 inference(monotonicity,[status(thm)],[14133])).
% 3.13/3.39 tff(14135,plain,
% 3.13/3.39 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(s(z)))) | (~r(z, s(z))) | (~r(s(s(z)), s(z))) | (~r(s(s(z)), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, s(z))) | (~r(s(s(z)), s(z))) | (~r(s(z), s(s(z)))) | (~r(s(s(z)), z)))),
% 3.13/3.39 inference(transitivity,[status(thm)],[14134, 14132])).
% 3.13/3.39 tff(14136,plain,
% 3.13/3.39 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(s(z)))) | (~r(z, s(z))) | (~r(s(s(z)), s(z))) | (~r(s(s(z)), z)))),
% 3.13/3.39 inference(quant_inst,[status(thm)],[])).
% 3.13/3.39 tff(14137,plain,
% 3.13/3.39 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, s(z))) | (~r(s(s(z)), s(z))) | (~r(s(z), s(s(z)))) | (~r(s(s(z)), z))),
% 3.13/3.39 inference(modus_ponens,[status(thm)],[14136, 14135])).
% 3.13/3.39 tff(14138,plain,
% 3.13/3.39 ($false),
% 3.13/3.39 inference(unit_resolution,[status(thm)],[14137, 197, 120, 323, 392, 866])).
% 3.13/3.39 tff(14139,plain,((~r(s(z), s(s(z)))) | (~r(z, s(z))) | (~r(s(s(z)), s(z))) | (~r(s(s(z)), z))), inference(lemma,lemma(discharge,[]))).
% 3.13/3.39 tff(14140,plain,
% 3.13/3.39 (~r(s(s(z)), z)),
% 3.13/3.39 inference(unit_resolution,[status(thm)],[14139, 323, 392, 120])).
% 3.13/3.39 tff(14141,plain,
% 3.13/3.39 (b(s(s(z)), z)),
% 3.13/3.39 inference(unit_resolution,[status(thm)],[186, 14140])).
% 3.13/3.39 tff(14142,plain,
% 3.13/3.39 (b(s(s(elem!1)), elem!1)),
% 3.13/3.39 inference(unit_resolution,[status(thm)],[8754, 14141, 34])).
% 3.13/3.39 tff(14143,plain,
% 3.13/3.39 (~b(s(s(s(s(s(s(s(s(elem!1)))))))), elem!1)),
% 3.13/3.39 inference(unit_resolution,[status(thm)],[13230, 14142, 4577, 14131, 14130, 14129, 642, 311])).
% 3.13/3.39 tff(14144,plain,
% 3.13/3.39 (r(s(s(s(s(s(s(s(s(elem!1)))))))), elem!1)),
% 3.13/3.39 inference(unit_resolution,[status(thm)],[13235, 14143, 14127])).
% 3.13/3.39 tff(14145,plain,
% 3.13/3.39 (r(elem!1, s(z))),
% 3.13/3.39 inference(unit_resolution,[status(thm)],[741, 323, 620])).
% 3.13/3.39 tff(14146,plain,
% 3.13/3.39 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(z))) | (~r(s(s(s(elem!1))), elem!1)) | (~r(s(s(s(s(s(s(s(s(elem!1)))))))), elem!1)) | (~r(s(s(s(s(s(s(s(s(elem!1)))))))), s(s(s(elem!1))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(elem!1, s(z))) | (~r(s(s(s(elem!1))), elem!1)) | (~r(s(s(s(s(s(s(s(s(elem!1)))))))), elem!1)) | (~r(s(s(s(s(s(s(s(s(elem!1)))))))), s(s(s(elem!1))))))),
% 3.13/3.39 inference(rewrite,[status(thm)],[])).
% 3.13/3.39 tff(14147,plain,
% 3.13/3.39 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(z))) | (~r(s(s(s(elem!1))), elem!1)) | (~r(s(s(s(s(s(s(s(s(elem!1)))))))), elem!1)) | (~r(s(s(s(s(s(s(s(s(elem!1)))))))), s(s(s(elem!1))))))),
% 3.13/3.39 inference(quant_inst,[status(thm)],[])).
% 3.13/3.39 tff(14148,plain,
% 3.13/3.39 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(elem!1, s(z))) | (~r(s(s(s(elem!1))), elem!1)) | (~r(s(s(s(s(s(s(s(s(elem!1)))))))), elem!1)) | (~r(s(s(s(s(s(s(s(s(elem!1)))))))), s(s(s(elem!1)))))),
% 3.13/3.39 inference(modus_ponens,[status(thm)],[14147, 14146])).
% 3.13/3.39 tff(14149,plain,
% 3.13/3.39 (~r(s(s(s(s(s(s(s(s(elem!1)))))))), s(s(s(elem!1))))),
% 3.13/3.39 inference(unit_resolution,[status(thm)],[14148, 197, 14145, 14144, 1013])).
% 3.13/3.39 tff(14150,plain,
% 3.13/3.39 ((s(s(s(s(s(s(s(s(elem!1)))))))) = s(s(s(elem!1)))) | b(s(s(s(s(s(s(s(s(elem!1)))))))), s(s(s(elem!1))))),
% 3.13/3.39 inference(unit_resolution,[status(thm)],[13243, 79, 14149])).
% 3.13/3.39 tff(14151,plain,
% 3.13/3.39 (b(s(s(s(s(s(s(s(s(elem!1)))))))), s(s(s(elem!1))))),
% 3.13/3.39 inference(unit_resolution,[status(thm)],[14150, 14124])).
% 3.13/3.39 tff(14152,plain,
% 3.13/3.39 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(s(s(s(s(s(s(s(elem!1)))))))), s(s(s(elem!1))))) | (~b(s(s(s(s(s(s(s(s(elem!1)))))))), s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(s(s(s(s(s(s(s(elem!1)))))))), s(s(s(elem!1))))) | (~b(s(s(s(s(s(s(s(s(elem!1)))))))), s(z))))),
% 3.13/3.39 inference(rewrite,[status(thm)],[])).
% 3.13/3.39 tff(14153,plain,
% 3.13/3.39 (((~b(s(z), s(s(s(elem!1))))) | (~b(s(s(s(s(s(s(s(s(elem!1)))))))), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(z), s(s(s(elem!1))))) | (~b(s(s(s(s(s(s(s(s(elem!1)))))))), s(s(s(elem!1))))) | (~b(s(s(s(s(s(s(s(s(elem!1)))))))), s(z)))) <=> ((~b(s(z), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(s(s(s(s(s(s(s(elem!1)))))))), s(s(s(elem!1))))) | (~b(s(s(s(s(s(s(s(s(elem!1)))))))), s(z))))),
% 3.13/3.39 inference(rewrite,[status(thm)],[])).
% 3.13/3.39 tff(14154,plain,
% 3.13/3.39 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(s(elem!1))))) | (~b(s(s(s(s(s(s(s(s(elem!1)))))))), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(z), s(s(s(elem!1))))) | (~b(s(s(s(s(s(s(s(s(elem!1)))))))), s(s(s(elem!1))))) | (~b(s(s(s(s(s(s(s(s(elem!1)))))))), s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(s(s(s(s(s(s(s(elem!1)))))))), s(s(s(elem!1))))) | (~b(s(s(s(s(s(s(s(s(elem!1)))))))), s(z)))))),
% 3.13/3.39 inference(monotonicity,[status(thm)],[14153])).
% 3.13/3.39 tff(14155,plain,
% 3.13/3.39 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(s(elem!1))))) | (~b(s(s(s(s(s(s(s(s(elem!1)))))))), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(z), s(s(s(elem!1))))) | (~b(s(s(s(s(s(s(s(s(elem!1)))))))), s(s(s(elem!1))))) | (~b(s(s(s(s(s(s(s(s(elem!1)))))))), s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(s(s(s(s(s(s(s(elem!1)))))))), s(s(s(elem!1))))) | (~b(s(s(s(s(s(s(s(s(elem!1)))))))), s(z))))),
% 3.13/3.39 inference(transitivity,[status(thm)],[14154, 14152])).
% 3.13/3.39 tff(14156,plain,
% 3.13/3.39 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(s(elem!1))))) | (~b(s(s(s(s(s(s(s(s(elem!1)))))))), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(z), s(s(s(elem!1))))) | (~b(s(s(s(s(s(s(s(s(elem!1)))))))), s(s(s(elem!1))))) | (~b(s(s(s(s(s(s(s(s(elem!1)))))))), s(z))))),
% 3.13/3.39 inference(quant_inst,[status(thm)],[])).
% 3.13/3.39 tff(14157,plain,
% 3.13/3.39 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(s(s(s(s(s(s(s(elem!1)))))))), s(s(s(elem!1))))) | (~b(s(s(s(s(s(s(s(s(elem!1)))))))), s(z)))),
% 3.13/3.39 inference(modus_ponens,[status(thm)],[14156, 14155])).
% 3.13/3.39 tff(14158,plain,
% 3.13/3.39 (~b(s(s(s(s(s(s(s(s(elem!1)))))))), s(z))),
% 3.13/3.39 inference(unit_resolution,[status(thm)],[14157, 166, 241, 96, 14151])).
% 3.13/3.39 tff(14159,plain,
% 3.13/3.39 (r(s(s(s(s(s(s(s(s(elem!1)))))))), s(z))),
% 3.13/3.39 inference(unit_resolution,[status(thm)],[13209, 79, 14131, 14158])).
% 3.13/3.39 tff(14160,plain,
% 3.13/3.39 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(s(elem!1)))) | (~r(elem!1, s(z))) | (~r(s(s(s(s(s(s(s(s(elem!1)))))))), elem!1)) | (~r(s(s(s(s(s(s(s(s(elem!1)))))))), s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(z), s(s(elem!1)))) | (~r(elem!1, s(z))) | (~r(s(s(s(s(s(s(s(s(elem!1)))))))), elem!1)) | (~r(s(s(s(s(s(s(s(s(elem!1)))))))), s(z))))),
% 3.13/3.39 inference(rewrite,[status(thm)],[])).
% 3.13/3.39 tff(14161,plain,
% 3.13/3.39 (((~r(s(z), s(s(elem!1)))) | (~r(elem!1, s(z))) | (~r(s(s(s(s(s(s(s(s(elem!1)))))))), s(z))) | (~r(s(s(s(s(s(s(s(s(elem!1)))))))), elem!1))) <=> ((~r(s(z), s(s(elem!1)))) | (~r(elem!1, s(z))) | (~r(s(s(s(s(s(s(s(s(elem!1)))))))), elem!1)) | (~r(s(s(s(s(s(s(s(s(elem!1)))))))), s(z))))),
% 3.13/3.39 inference(rewrite,[status(thm)],[])).
% 3.13/3.39 tff(14162,plain,
% 3.13/3.39 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(s(elem!1)))) | (~r(elem!1, s(z))) | (~r(s(s(s(s(s(s(s(s(elem!1)))))))), s(z))) | (~r(s(s(s(s(s(s(s(s(elem!1)))))))), elem!1)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(s(elem!1)))) | (~r(elem!1, s(z))) | (~r(s(s(s(s(s(s(s(s(elem!1)))))))), elem!1)) | (~r(s(s(s(s(s(s(s(s(elem!1)))))))), s(z)))))),
% 3.13/3.39 inference(monotonicity,[status(thm)],[14161])).
% 3.13/3.39 tff(14163,plain,
% 3.13/3.39 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(s(elem!1)))) | (~r(elem!1, s(z))) | (~r(s(s(s(s(s(s(s(s(elem!1)))))))), s(z))) | (~r(s(s(s(s(s(s(s(s(elem!1)))))))), elem!1)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(z), s(s(elem!1)))) | (~r(elem!1, s(z))) | (~r(s(s(s(s(s(s(s(s(elem!1)))))))), elem!1)) | (~r(s(s(s(s(s(s(s(s(elem!1)))))))), s(z))))),
% 3.13/3.39 inference(transitivity,[status(thm)],[14162, 14160])).
% 3.13/3.39 tff(14164,plain,
% 3.13/3.39 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(s(elem!1)))) | (~r(elem!1, s(z))) | (~r(s(s(s(s(s(s(s(s(elem!1)))))))), s(z))) | (~r(s(s(s(s(s(s(s(s(elem!1)))))))), elem!1)))),
% 3.13/3.39 inference(quant_inst,[status(thm)],[])).
% 3.13/3.39 tff(14165,plain,
% 3.13/3.39 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(z), s(s(elem!1)))) | (~r(elem!1, s(z))) | (~r(s(s(s(s(s(s(s(s(elem!1)))))))), elem!1)) | (~r(s(s(s(s(s(s(s(s(elem!1)))))))), s(z)))),
% 3.13/3.39 inference(modus_ponens,[status(thm)],[14164, 14163])).
% 3.13/3.39 tff(14166,plain,
% 3.13/3.39 ($false),
% 3.13/3.39 inference(unit_resolution,[status(thm)],[14165, 197, 311, 14145, 14144, 14159])).
% 3.13/3.39 tff(14167,plain,((~r(z, s(z))) | (~r(s(z), s(s(elem!1)))) | (~b(s(z), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(z))) | (~r(s(s(s(elem!1))), elem!1)) | (~r(s(s(elem!1)), s(z))) | (~b(s(z), elem!1)) | (~(s(s(z)) = s(s(elem!1)))) | (~r(s(s(z)), s(z))) | (~r(s(z), s(s(z))))), inference(lemma,lemma(discharge,[]))).
% 3.13/3.39 tff(14168,plain,
% 3.13/3.39 (~r(z, s(z))),
% 3.13/3.39 inference(unit_resolution,[status(thm)],[14167, 13790, 85, 13882, 14102, 14116, 14107, 14094, 4143, 14122])).
% 3.13/3.39 tff(14169,plain,
% 3.13/3.39 (b(z, s(z))),
% 3.13/3.39 inference(unit_resolution,[status(thm)],[321, 14168])).
% 3.13/3.39 tff(14170,plain,
% 3.13/3.39 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(elem!1)))) | (~b(s(z), z)) | (~b(z, s(z))) | (~b(s(s(s(z))), s(z))) | (~b(z, s(s(s(z))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(s(elem!1)))) | (~b(s(z), z)) | (~b(z, s(z))) | (~b(s(s(s(z))), s(z))) | (~b(z, s(s(s(z))))))),
% 3.13/3.39 inference(rewrite,[status(thm)],[])).
% 3.13/3.39 tff(14171,plain,
% 3.13/3.39 (((~b(z, s(s(elem!1)))) | (~b(z, s(s(elem!1)))) | (~b(s(z), z)) | (~b(s(s(s(z))), s(z))) | (~b(z, s(z))) | (~b(z, s(s(s(z)))))) <=> ((~b(z, s(s(elem!1)))) | (~b(s(z), z)) | (~b(z, s(z))) | (~b(s(s(s(z))), s(z))) | (~b(z, s(s(s(z))))))),
% 3.13/3.39 inference(rewrite,[status(thm)],[])).
% 3.13/3.39 tff(14172,plain,
% 3.13/3.39 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(elem!1)))) | (~b(z, s(s(elem!1)))) | (~b(s(z), z)) | (~b(s(s(s(z))), s(z))) | (~b(z, s(z))) | (~b(z, s(s(s(z))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(elem!1)))) | (~b(s(z), z)) | (~b(z, s(z))) | (~b(s(s(s(z))), s(z))) | (~b(z, s(s(s(z)))))))),
% 3.13/3.39 inference(monotonicity,[status(thm)],[14171])).
% 3.13/3.39 tff(14173,plain,
% 3.13/3.39 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(elem!1)))) | (~b(z, s(s(elem!1)))) | (~b(s(z), z)) | (~b(s(s(s(z))), s(z))) | (~b(z, s(z))) | (~b(z, s(s(s(z))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(s(elem!1)))) | (~b(s(z), z)) | (~b(z, s(z))) | (~b(s(s(s(z))), s(z))) | (~b(z, s(s(s(z))))))),
% 3.13/3.39 inference(transitivity,[status(thm)],[14172, 14170])).
% 3.13/3.39 tff(14174,plain,
% 3.13/3.39 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(elem!1)))) | (~b(z, s(s(elem!1)))) | (~b(s(z), z)) | (~b(s(s(s(z))), s(z))) | (~b(z, s(z))) | (~b(z, s(s(s(z))))))),
% 3.13/3.39 inference(quant_inst,[status(thm)],[])).
% 3.13/3.39 tff(14175,plain,
% 3.13/3.39 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(s(elem!1)))) | (~b(s(z), z)) | (~b(z, s(z))) | (~b(s(s(s(z))), s(z))) | (~b(z, s(s(s(z)))))),
% 3.13/3.39 inference(modus_ponens,[status(thm)],[14174, 14173])).
% 3.13/3.39 tff(14176,plain,
% 3.13/3.39 ($false),
% 3.13/3.39 inference(unit_resolution,[status(thm)],[14175, 166, 1820, 53, 118, 1700, 3240])).
% 3.13/3.39 tff(14177,plain,((~b(s(s(s(z))), s(z))) | (~b(z, s(s(elem!1)))) | (~b(s(z), z)) | (~b(z, s(z))) | (~b(z, s(s(s(z)))))), inference(lemma,lemma(discharge,[]))).
% 3.13/3.39 tff(14178,plain,
% 3.13/3.39 (~b(z, s(s(s(z))))),
% 3.13/3.39 inference(unit_resolution,[status(thm)],[14177, 14169, 53, 14120, 14111])).
% 3.13/3.39 tff(14179,plain,
% 3.13/3.39 (r(z, s(s(s(z))))),
% 3.13/3.39 inference(unit_resolution,[status(thm)],[1697, 14178])).
% 3.13/3.39 tff(14180,plain,
% 3.13/3.39 (~(s(s(s(elem!1))) = s(s(elem!1)))),
% 3.13/3.39 inference(unit_resolution,[status(thm)],[50, 13791])).
% 3.13/3.39 tff(14181,plain,
% 3.13/3.39 (b(s(z), s(s(s(z)))) <=> b(s(z), s(s(s(elem!1))))),
% 3.13/3.39 inference(monotonicity,[status(thm)],[14117])).
% 3.13/3.39 tff(14182,plain,
% 3.13/3.39 (b(s(z), s(s(s(elem!1)))) <=> b(s(z), s(s(s(z))))),
% 3.13/3.39 inference(symmetry,[status(thm)],[14181])).
% 3.13/3.39 tff(14183,plain,
% 3.13/3.39 (b(s(z), s(s(s(z))))),
% 3.13/3.39 inference(modus_ponens,[status(thm)],[13790, 14182])).
% 3.13/3.39 tff(14184,plain,
% 3.13/3.39 (b(z, s(z)) <=> b(elem!1, s(z))),
% 3.13/3.39 inference(monotonicity,[status(thm)],[14096])).
% 3.13/3.39 tff(14185,plain,
% 3.13/3.39 (b(elem!1, s(z))),
% 3.13/3.39 inference(modus_ponens,[status(thm)],[14169, 14184])).
% 3.13/3.39 tff(14186,plain,
% 3.13/3.39 (~r(s(s(z)), s(s(s(z))))),
% 3.13/3.39 inference(unit_resolution,[status(thm)],[12076, 866, 1677, 6298])).
% 3.13/3.39 tff(14187,plain,
% 3.13/3.39 (b(s(s(z)), s(s(s(z))))),
% 3.13/3.39 inference(unit_resolution,[status(thm)],[1730, 14186])).
% 3.13/3.39 tff(14188,plain,
% 3.13/3.39 (b(s(s(s(z))), s(s(z))) <=> b(s(s(s(z))), s(s(elem!1)))),
% 3.13/3.39 inference(monotonicity,[status(thm)],[34])).
% 3.13/3.39 tff(14189,plain,
% 3.13/3.39 (b(s(s(s(z))), s(s(elem!1))) <=> b(s(s(s(z))), s(s(z)))),
% 3.13/3.39 inference(symmetry,[status(thm)],[14188])).
% 3.13/3.39 tff(14190,plain,
% 3.13/3.39 (b(s(s(s(z))), s(s(elem!1))) <=> b(s(s(s(elem!1))), s(s(elem!1)))),
% 3.13/3.39 inference(monotonicity,[status(thm)],[1086])).
% 3.13/3.39 tff(14191,plain,
% 3.13/3.39 (b(s(s(s(elem!1))), s(s(elem!1))) <=> b(s(s(s(z))), s(s(elem!1)))),
% 3.13/3.39 inference(symmetry,[status(thm)],[14190])).
% 3.13/3.39 tff(14192,plain,
% 3.13/3.39 (b(s(s(s(elem!1))), s(s(elem!1))) <=> b(s(s(s(z))), s(s(z)))),
% 3.13/3.39 inference(transitivity,[status(thm)],[14191, 14189])).
% 3.13/3.39 tff(14193,plain,
% 3.13/3.39 (r(s(s(elem!1)), elem!1)),
% 3.13/3.39 inference(modus_ponens,[status(thm)],[866, 6287])).
% 3.13/3.39 tff(14194,plain,
% 3.13/3.39 (r(z, s(s(s(z)))) <=> r(elem!1, s(s(s(z))))),
% 3.13/3.39 inference(monotonicity,[status(thm)],[620])).
% 3.13/3.39 tff(14195,plain,
% 3.13/3.39 (r(z, s(s(s(z)))) <=> r(elem!1, s(s(s(elem!1))))),
% 3.13/3.39 inference(transitivity,[status(thm)],[14194, 3741])).
% 3.13/3.39 tff(14196,plain,
% 3.13/3.39 (r(elem!1, s(s(s(elem!1))))),
% 3.13/3.39 inference(modus_ponens,[status(thm)],[1677, 14195])).
% 3.13/3.39 tff(14197,plain,
% 3.13/3.39 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), s(s(elem!1)))) | (~r(s(s(elem!1)), elem!1)) | (~r(elem!1, s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), elem!1)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(elem!1))), s(s(elem!1)))) | (~r(s(s(elem!1)), elem!1)) | (~r(elem!1, s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), elem!1)))),
% 3.13/3.39 inference(rewrite,[status(thm)],[])).
% 3.13/3.39 tff(14198,plain,
% 3.13/3.39 (((~r(elem!1, s(s(s(elem!1))))) | (~r(s(s(elem!1)), elem!1)) | (~r(s(s(s(elem!1))), elem!1)) | (~r(s(s(s(elem!1))), s(s(elem!1))))) <=> ((~r(s(s(s(elem!1))), s(s(elem!1)))) | (~r(s(s(elem!1)), elem!1)) | (~r(elem!1, s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), elem!1)))),
% 3.13/3.39 inference(rewrite,[status(thm)],[])).
% 3.13/3.39 tff(14199,plain,
% 3.13/3.39 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(s(s(elem!1))))) | (~r(s(s(elem!1)), elem!1)) | (~r(s(s(s(elem!1))), elem!1)) | (~r(s(s(s(elem!1))), s(s(elem!1)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), s(s(elem!1)))) | (~r(s(s(elem!1)), elem!1)) | (~r(elem!1, s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), elem!1))))),
% 3.13/3.39 inference(monotonicity,[status(thm)],[14198])).
% 3.13/3.39 tff(14200,plain,
% 3.13/3.39 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(s(s(elem!1))))) | (~r(s(s(elem!1)), elem!1)) | (~r(s(s(s(elem!1))), elem!1)) | (~r(s(s(s(elem!1))), s(s(elem!1)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(elem!1))), s(s(elem!1)))) | (~r(s(s(elem!1)), elem!1)) | (~r(elem!1, s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), elem!1)))),
% 3.13/3.39 inference(transitivity,[status(thm)],[14199, 14197])).
% 3.13/3.39 tff(14201,plain,
% 3.13/3.39 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(s(s(elem!1))))) | (~r(s(s(elem!1)), elem!1)) | (~r(s(s(s(elem!1))), elem!1)) | (~r(s(s(s(elem!1))), s(s(elem!1)))))),
% 3.13/3.39 inference(quant_inst,[status(thm)],[])).
% 3.13/3.39 tff(14202,plain,
% 3.13/3.39 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(elem!1))), s(s(elem!1)))) | (~r(s(s(elem!1)), elem!1)) | (~r(elem!1, s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), elem!1))),
% 3.13/3.39 inference(modus_ponens,[status(thm)],[14201, 14200])).
% 3.13/3.39 tff(14203,plain,
% 3.13/3.39 (~r(s(s(s(elem!1))), s(s(elem!1)))),
% 3.13/3.39 inference(unit_resolution,[status(thm)],[14202, 197, 14196, 14193, 1013])).
% 3.13/3.39 tff(14204,plain,
% 3.13/3.39 (b(s(s(s(elem!1))), s(s(elem!1)))),
% 3.13/3.39 inference(unit_resolution,[status(thm)],[889, 14203, 1863])).
% 3.13/3.39 tff(14205,plain,
% 3.13/3.39 (b(s(s(s(z))), s(s(z)))),
% 3.13/3.39 inference(modus_ponens,[status(thm)],[14204, 14192])).
% 3.13/3.39 tff(14206,plain,
% 3.13/3.39 (~b(s(s(s(s(z)))), s(s(s(z))))),
% 3.13/3.39 inference(unit_resolution,[status(thm)],[4778, 14205, 120, 988, 3240, 14187])).
% 3.13/3.39 tff(14207,plain,
% 3.13/3.39 (r(s(s(s(s(z)))), s(s(s(z))))),
% 3.13/3.39 inference(unit_resolution,[status(thm)],[4662, 14206])).
% 3.13/3.39 tff(14208,plain,
% 3.13/3.39 (r(s(s(s(s(elem!1)))), s(s(s(elem!1))))),
% 3.13/3.39 inference(modus_ponens,[status(thm)],[14207, 6228])).
% 3.13/3.39 tff(14209,plain,
% 3.13/3.39 (b(s(s(elem!1)), s(s(s(elem!1))))),
% 3.13/3.39 inference(modus_ponens,[status(thm)],[14187, 6309])).
% 3.13/3.39 tff(14210,plain,
% 3.13/3.39 (~r(s(s(s(s(s(s(s(elem!1))))))), elem!1)),
% 3.13/3.39 inference(unit_resolution,[status(thm)],[6369, 14204, 34, 14193, 14209, 1013, 14196])).
% 3.13/3.39 tff(14211,plain,
% 3.13/3.39 (b(s(s(s(s(s(s(s(elem!1))))))), elem!1)),
% 3.13/3.39 inference(unit_resolution,[status(thm)],[6375, 14210, 6284])).
% 3.13/3.39 tff(14212,plain,
% 3.13/3.39 (~b(s(s(s(s(z)))), elem!1)),
% 3.13/3.39 inference(unit_resolution,[status(thm)],[4965, 14207, 6278, 6378, 1212, 642, 14211])).
% 3.13/3.39 tff(14213,plain,
% 3.13/3.39 (r(s(s(s(s(z)))), elem!1)),
% 3.13/3.39 inference(unit_resolution,[status(thm)],[6190, 14212, 6184])).
% 3.13/3.39 tff(14214,plain,
% 3.13/3.39 (r(s(s(s(s(elem!1)))), elem!1)),
% 3.13/3.39 inference(modus_ponens,[status(thm)],[14213, 10624])).
% 3.13/3.39 tff(14215,plain,
% 3.13/3.39 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), elem!1)) | (~r(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~r(s(s(s(s(elem!1)))), elem!1)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(elem!1, s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), elem!1)) | (~r(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~r(s(s(s(s(elem!1)))), elem!1)))),
% 3.23/3.40 inference(rewrite,[status(thm)],[])).
% 3.23/3.40 tff(14216,plain,
% 3.23/3.40 (((~r(s(s(s(elem!1))), elem!1)) | (~r(elem!1, s(s(s(elem!1))))) | (~r(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~r(s(s(s(s(elem!1)))), elem!1))) <=> ((~r(elem!1, s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), elem!1)) | (~r(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~r(s(s(s(s(elem!1)))), elem!1)))),
% 3.23/3.40 inference(rewrite,[status(thm)],[])).
% 3.23/3.40 tff(14217,plain,
% 3.23/3.40 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), elem!1)) | (~r(elem!1, s(s(s(elem!1))))) | (~r(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~r(s(s(s(s(elem!1)))), elem!1)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), elem!1)) | (~r(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~r(s(s(s(s(elem!1)))), elem!1))))),
% 3.23/3.40 inference(monotonicity,[status(thm)],[14216])).
% 3.23/3.40 tff(14218,plain,
% 3.23/3.40 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), elem!1)) | (~r(elem!1, s(s(s(elem!1))))) | (~r(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~r(s(s(s(s(elem!1)))), elem!1)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(elem!1, s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), elem!1)) | (~r(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~r(s(s(s(s(elem!1)))), elem!1)))),
% 3.23/3.40 inference(transitivity,[status(thm)],[14217, 14215])).
% 3.23/3.40 tff(14219,plain,
% 3.23/3.40 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), elem!1)) | (~r(elem!1, s(s(s(elem!1))))) | (~r(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~r(s(s(s(s(elem!1)))), elem!1)))),
% 3.23/3.40 inference(quant_inst,[status(thm)],[])).
% 3.23/3.40 tff(14220,plain,
% 3.23/3.40 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(elem!1, s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), elem!1)) | (~r(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~r(s(s(s(s(elem!1)))), elem!1))),
% 3.23/3.40 inference(modus_ponens,[status(thm)],[14219, 14218])).
% 3.23/3.40 tff(14221,plain,
% 3.23/3.40 ($false),
% 3.23/3.40 inference(unit_resolution,[status(thm)],[14220, 197, 14196, 14214, 14208, 1013])).
% 3.23/3.40 tff(14222,plain,((~r(s(s(z)), z)) | (~r(s(s(s(elem!1))), elem!1)) | (~(s(s(z)) = s(s(elem!1)))) | (~b(elem!1, s(z))) | (~b(s(z), elem!1)) | (~r(s(z), s(s(z)))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(z))), s(z))) | (s(s(s(elem!1))) = s(s(elem!1))) | (~r(z, s(s(s(z)))))), inference(lemma,lemma(discharge,[]))).
% 3.23/3.40 tff(14223,plain,
% 3.23/3.40 (~r(s(s(z)), z)),
% 3.23/3.40 inference(unit_resolution,[status(thm)],[14222, 14102, 14094, 14185, 14107, 14122, 14183, 14120, 14180, 14179])).
% 3.23/3.40 tff(14224,plain,
% 3.23/3.40 (b(s(s(z)), z)),
% 3.23/3.40 inference(unit_resolution,[status(thm)],[186, 14223])).
% 3.23/3.40 tff(14225,plain,
% 3.23/3.40 (b(s(s(elem!1)), elem!1)),
% 3.23/3.40 inference(unit_resolution,[status(thm)],[8754, 14224, 14094])).
% 3.23/3.40 tff(14226,plain,
% 3.23/3.40 (~b(s(s(s(s(s(s(s(s(elem!1)))))))), elem!1)),
% 3.23/3.40 inference(unit_resolution,[status(thm)],[13230, 14225, 14116, 14114, 14113, 14112, 14107, 85])).
% 3.23/3.40 tff(14227,plain,
% 3.23/3.40 (r(s(s(s(s(s(s(s(s(elem!1)))))))), elem!1)),
% 3.23/3.40 inference(unit_resolution,[status(thm)],[13235, 14226, 14105])).
% 3.23/3.40 tff(14228,plain,
% 3.23/3.40 (r(elem!1, s(s(s(z)))) <=> r(elem!1, s(s(s(elem!1))))),
% 3.23/3.40 inference(monotonicity,[status(thm)],[14117])).
% 3.23/3.40 tff(14229,plain,
% 3.23/3.40 (r(z, s(s(s(z)))) <=> r(elem!1, s(s(s(z))))),
% 3.23/3.40 inference(monotonicity,[status(thm)],[14096])).
% 3.23/3.40 tff(14230,plain,
% 3.23/3.40 (r(z, s(s(s(z)))) <=> r(elem!1, s(s(s(elem!1))))),
% 3.23/3.40 inference(transitivity,[status(thm)],[14229, 14228])).
% 3.23/3.40 tff(14231,plain,
% 3.23/3.40 (r(elem!1, s(s(s(elem!1))))),
% 3.23/3.40 inference(modus_ponens,[status(thm)],[14179, 14230])).
% 3.23/3.40 tff(14232,plain,
% 3.23/3.40 (~r(s(s(s(s(s(s(s(s(elem!1)))))))), s(s(s(elem!1))))),
% 3.23/3.40 inference(unit_resolution,[status(thm)],[13239, 197, 14231, 14227, 14102])).
% 3.23/3.40 tff(14233,plain,
% 3.23/3.40 ((s(s(s(s(s(s(s(s(elem!1)))))))) = s(s(s(elem!1)))) | b(s(s(s(s(s(s(s(s(elem!1)))))))), s(s(s(elem!1))))),
% 3.23/3.40 inference(unit_resolution,[status(thm)],[13243, 79, 14232])).
% 3.23/3.40 tff(14234,plain,
% 3.23/3.40 (b(s(s(s(s(s(s(s(s(elem!1)))))))), s(s(s(elem!1))))),
% 3.23/3.40 inference(unit_resolution,[status(thm)],[14233, 14101])).
% 3.23/3.40 tff(14235,plain,
% 3.23/3.40 (~b(s(s(s(s(s(s(s(s(elem!1)))))))), s(z))),
% 3.23/3.40 inference(unit_resolution,[status(thm)],[14157, 166, 13790, 13882, 14234])).
% 3.23/3.40 tff(14236,plain,
% 3.23/3.40 (r(s(s(s(s(s(s(s(s(elem!1)))))))), s(z))),
% 3.23/3.40 inference(unit_resolution,[status(thm)],[13209, 79, 14114, 14235])).
% 3.23/3.40 tff(14237,plain,
% 3.23/3.40 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(s(elem!1)))) | (~r(s(s(elem!1)), s(z))) | (~r(s(s(s(s(s(s(s(s(elem!1)))))))), s(z))) | (~r(s(s(s(s(s(s(s(s(elem!1)))))))), s(s(elem!1)))))),
% 3.23/3.40 inference(quant_inst,[status(thm)],[])).
% 3.23/3.40 tff(14238,plain,
% 3.23/3.40 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(z), s(s(elem!1)))) | (~r(s(s(elem!1)), s(z))) | (~r(s(s(s(s(s(s(s(s(elem!1)))))))), s(z))) | (~r(s(s(s(s(s(s(s(s(elem!1)))))))), s(s(elem!1))))),
% 3.23/3.40 inference(modus_ponens,[status(thm)],[14237, 13223])).
% 3.23/3.40 tff(14239,plain,
% 3.23/3.40 (~r(s(s(s(s(s(s(s(s(elem!1)))))))), s(s(elem!1)))),
% 3.23/3.40 inference(unit_resolution,[status(thm)],[14238, 197, 85, 14116, 14236])).
% 3.23/3.40 tff(14240,plain,
% 3.23/3.40 (b(s(s(s(s(s(s(s(s(elem!1)))))))), s(s(elem!1)))),
% 3.23/3.40 inference(unit_resolution,[status(thm)],[13221, 79, 14113, 14239])).
% 3.23/3.40 tff(14241,plain,
% 3.23/3.40 ((s(s(elem!1)) = s(s(s(s(s(s(s(s(elem!1))))))))) <=> (s(s(s(s(s(s(s(s(elem!1)))))))) = s(s(elem!1)))),
% 3.23/3.40 inference(commutativity,[status(thm)],[])).
% 3.23/3.40 tff(14242,plain,
% 3.23/3.40 ((s(s(s(s(s(s(s(s(elem!1)))))))) = s(s(elem!1))) <=> (s(s(elem!1)) = s(s(s(s(s(s(s(s(elem!1)))))))))),
% 3.23/3.40 inference(symmetry,[status(thm)],[14241])).
% 3.23/3.40 tff(14243,plain,
% 3.23/3.40 ((~(s(s(s(s(s(s(s(s(elem!1)))))))) = s(s(elem!1)))) <=> (~(s(s(elem!1)) = s(s(s(s(s(s(s(s(elem!1))))))))))),
% 3.23/3.40 inference(monotonicity,[status(thm)],[14242])).
% 3.23/3.40 tff(14244,plain,
% 3.23/3.40 (~(s(s(elem!1)) = s(s(s(s(s(s(s(s(elem!1)))))))))),
% 3.23/3.40 inference(modus_ponens,[status(thm)],[14113, 14243])).
% 3.23/3.40 tff(14245,plain,
% 3.23/3.40 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(s(elem!1)))) | (~r(s(s(elem!1)), s(z))) | (~r(s(s(s(s(s(s(s(s(elem!1)))))))), s(z))) | (~r(s(s(elem!1)), s(s(s(s(s(s(s(s(elem!1)))))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(z), s(s(elem!1)))) | (~r(s(s(elem!1)), s(z))) | (~r(s(s(s(s(s(s(s(s(elem!1)))))))), s(z))) | (~r(s(s(elem!1)), s(s(s(s(s(s(s(s(elem!1)))))))))))),
% 3.23/3.40 inference(rewrite,[status(thm)],[])).
% 3.23/3.40 tff(14246,plain,
% 3.23/3.40 (((~r(s(z), s(s(elem!1)))) | (~r(s(s(s(s(s(s(s(s(elem!1)))))))), s(z))) | (~r(s(s(elem!1)), s(z))) | (~r(s(s(elem!1)), s(s(s(s(s(s(s(s(elem!1))))))))))) <=> ((~r(s(z), s(s(elem!1)))) | (~r(s(s(elem!1)), s(z))) | (~r(s(s(s(s(s(s(s(s(elem!1)))))))), s(z))) | (~r(s(s(elem!1)), s(s(s(s(s(s(s(s(elem!1)))))))))))),
% 3.23/3.40 inference(rewrite,[status(thm)],[])).
% 3.23/3.40 tff(14247,plain,
% 3.23/3.40 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(s(elem!1)))) | (~r(s(s(s(s(s(s(s(s(elem!1)))))))), s(z))) | (~r(s(s(elem!1)), s(z))) | (~r(s(s(elem!1)), s(s(s(s(s(s(s(s(elem!1)))))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(s(elem!1)))) | (~r(s(s(elem!1)), s(z))) | (~r(s(s(s(s(s(s(s(s(elem!1)))))))), s(z))) | (~r(s(s(elem!1)), s(s(s(s(s(s(s(s(elem!1))))))))))))),
% 3.23/3.40 inference(monotonicity,[status(thm)],[14246])).
% 3.23/3.40 tff(14248,plain,
% 3.23/3.40 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(s(elem!1)))) | (~r(s(s(s(s(s(s(s(s(elem!1)))))))), s(z))) | (~r(s(s(elem!1)), s(z))) | (~r(s(s(elem!1)), s(s(s(s(s(s(s(s(elem!1)))))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(z), s(s(elem!1)))) | (~r(s(s(elem!1)), s(z))) | (~r(s(s(s(s(s(s(s(s(elem!1)))))))), s(z))) | (~r(s(s(elem!1)), s(s(s(s(s(s(s(s(elem!1)))))))))))),
% 3.23/3.40 inference(transitivity,[status(thm)],[14247, 14245])).
% 3.23/3.40 tff(14249,plain,
% 3.23/3.40 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(s(elem!1)))) | (~r(s(s(s(s(s(s(s(s(elem!1)))))))), s(z))) | (~r(s(s(elem!1)), s(z))) | (~r(s(s(elem!1)), s(s(s(s(s(s(s(s(elem!1)))))))))))),
% 3.23/3.40 inference(quant_inst,[status(thm)],[])).
% 3.23/3.40 tff(14250,plain,
% 3.23/3.40 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(z), s(s(elem!1)))) | (~r(s(s(elem!1)), s(z))) | (~r(s(s(s(s(s(s(s(s(elem!1)))))))), s(z))) | (~r(s(s(elem!1)), s(s(s(s(s(s(s(s(elem!1))))))))))),
% 3.23/3.40 inference(modus_ponens,[status(thm)],[14249, 14248])).
% 3.23/3.40 tff(14251,plain,
% 3.23/3.40 (~r(s(s(elem!1)), s(s(s(s(s(s(s(s(elem!1)))))))))),
% 3.23/3.40 inference(unit_resolution,[status(thm)],[14250, 197, 85, 14116, 14236])).
% 3.23/3.40 tff(14252,plain,
% 3.23/3.40 (((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((s(s(elem!1)) = s(s(s(s(s(s(s(s(elem!1))))))))) | b(s(s(elem!1)), s(s(s(s(s(s(s(s(elem!1))))))))) | r(s(s(elem!1)), s(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(s(elem!1))))))))) | b(s(s(elem!1)), s(s(s(s(s(s(s(s(elem!1))))))))) | r(s(s(elem!1)), s(s(s(s(s(s(s(s(elem!1))))))))))),
% 3.23/3.40 inference(rewrite,[status(thm)],[])).
% 3.23/3.40 tff(14253,plain,
% 3.23/3.40 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((s(s(elem!1)) = s(s(s(s(s(s(s(s(elem!1))))))))) | b(s(s(elem!1)), s(s(s(s(s(s(s(s(elem!1))))))))) | r(s(s(elem!1)), s(s(s(s(s(s(s(s(elem!1))))))))))),
% 3.23/3.40 inference(quant_inst,[status(thm)],[])).
% 3.23/3.40 tff(14254,plain,
% 3.23/3.40 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (s(s(elem!1)) = s(s(s(s(s(s(s(s(elem!1))))))))) | b(s(s(elem!1)), s(s(s(s(s(s(s(s(elem!1))))))))) | r(s(s(elem!1)), s(s(s(s(s(s(s(s(elem!1)))))))))),
% 3.23/3.40 inference(modus_ponens,[status(thm)],[14253, 14252])).
% 3.23/3.40 tff(14255,plain,
% 3.23/3.40 ((s(s(elem!1)) = s(s(s(s(s(s(s(s(elem!1))))))))) | b(s(s(elem!1)), s(s(s(s(s(s(s(s(elem!1)))))))))),
% 3.23/3.40 inference(unit_resolution,[status(thm)],[14254, 79, 14251])).
% 3.23/3.40 tff(14256,plain,
% 3.23/3.40 (b(s(s(elem!1)), s(s(s(s(s(s(s(s(elem!1)))))))))),
% 3.23/3.40 inference(unit_resolution,[status(thm)],[14255, 14244])).
% 3.23/3.40 tff(14257,plain,
% 3.23/3.40 ((s(s(s(s(elem!1)))) = s(s(z))) <=> (s(s(s(s(elem!1)))) = s(s(elem!1)))),
% 3.23/3.40 inference(monotonicity,[status(thm)],[14094])).
% 3.23/3.40 tff(14258,plain,
% 3.23/3.40 ((s(s(s(s(elem!1)))) = s(s(z))) <=> (s(s(elem!1)) = s(s(s(s(elem!1)))))),
% 3.23/3.40 inference(transitivity,[status(thm)],[14257, 123])).
% 3.23/3.40 tff(14259,plain,
% 3.23/3.40 ((s(s(s(s(elem!1)))) = s(s(z))) <=> (s(s(s(s(elem!1)))) = s(s(elem!1)))),
% 3.23/3.40 inference(transitivity,[status(thm)],[14258, 124])).
% 3.23/3.40 tff(14260,plain,
% 3.23/3.40 ((~(s(s(s(s(elem!1)))) = s(s(z)))) <=> (~(s(s(s(s(elem!1)))) = s(s(elem!1))))),
% 3.23/3.40 inference(monotonicity,[status(thm)],[14259])).
% 3.23/3.40 tff(14261,plain,
% 3.23/3.40 (~(s(s(s(s(elem!1)))) = s(s(elem!1)))),
% 3.23/3.40 inference(modus_ponens,[status(thm)],[733, 14260])).
% 3.23/3.40 tff(14262,plain,
% 3.23/3.40 ((~(s(s(s(s(elem!1)))) = s(s(z)))) <=> (~(s(s(elem!1)) = s(s(s(s(elem!1))))))),
% 3.23/3.40 inference(monotonicity,[status(thm)],[14258])).
% 3.23/3.40 tff(14263,plain,
% 3.23/3.40 (~(s(s(elem!1)) = s(s(s(s(elem!1)))))),
% 3.23/3.40 inference(modus_ponens,[status(thm)],[733, 14262])).
% 3.23/3.40 tff(14264,plain,
% 3.23/3.40 (~(s(s(s(elem!1))) = s(s(s(s(elem!1)))))),
% 3.23/3.40 inference(unit_resolution,[status(thm)],[357, 13791])).
% 3.23/3.40 tff(14265,plain,
% 3.23/3.40 (~r(s(s(s(elem!1))), s(s(s(s(s(s(s(s(elem!1)))))))))),
% 3.23/3.40 inference(unit_resolution,[status(thm)],[13353, 197, 14231, 14227, 14102])).
% 3.23/3.40 tff(14266,plain,
% 3.23/3.40 (b(s(s(s(elem!1))), s(s(s(s(s(s(s(s(elem!1)))))))))),
% 3.23/3.40 inference(unit_resolution,[status(thm)],[13358, 79, 14100, 14265])).
% 3.23/3.40 tff(14267,plain,
% 3.23/3.40 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), elem!1)) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(elem!1, s(z))) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(s(s(elem!1))), s(s(s(s(s(s(s(s(elem!1)))))))))) | (~b(s(s(s(s(s(s(s(s(elem!1)))))))), s(s(elem!1)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(elem!1)), elem!1)) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(elem!1, s(z))) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(s(s(elem!1))), s(s(s(s(s(s(s(s(elem!1)))))))))) | (~b(s(s(s(s(s(s(s(s(elem!1)))))))), s(s(elem!1)))))),
% 3.23/3.40 inference(rewrite,[status(thm)],[])).
% 3.23/3.40 tff(14268,plain,
% 3.23/3.40 (((~b(elem!1, s(z))) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(s(elem!1)), elem!1)) | (~b(s(s(s(s(s(s(s(s(elem!1)))))))), s(s(elem!1)))) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(s(s(elem!1))), s(s(s(s(s(s(s(s(elem!1))))))))))) <=> ((~b(s(s(elem!1)), elem!1)) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(elem!1, s(z))) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(s(s(elem!1))), s(s(s(s(s(s(s(s(elem!1)))))))))) | (~b(s(s(s(s(s(s(s(s(elem!1)))))))), s(s(elem!1)))))),
% 3.23/3.40 inference(rewrite,[status(thm)],[])).
% 3.23/3.40 tff(14269,plain,
% 3.23/3.40 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(z))) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(s(elem!1)), elem!1)) | (~b(s(s(s(s(s(s(s(s(elem!1)))))))), s(s(elem!1)))) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(s(s(elem!1))), s(s(s(s(s(s(s(s(elem!1)))))))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), elem!1)) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(elem!1, s(z))) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(s(s(elem!1))), s(s(s(s(s(s(s(s(elem!1)))))))))) | (~b(s(s(s(s(s(s(s(s(elem!1)))))))), s(s(elem!1))))))),
% 3.23/3.40 inference(monotonicity,[status(thm)],[14268])).
% 3.23/3.40 tff(14270,plain,
% 3.23/3.40 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(z))) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(s(elem!1)), elem!1)) | (~b(s(s(s(s(s(s(s(s(elem!1)))))))), s(s(elem!1)))) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(s(s(elem!1))), s(s(s(s(s(s(s(s(elem!1)))))))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(elem!1)), elem!1)) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(elem!1, s(z))) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(s(s(elem!1))), s(s(s(s(s(s(s(s(elem!1)))))))))) | (~b(s(s(s(s(s(s(s(s(elem!1)))))))), s(s(elem!1)))))),
% 3.23/3.40 inference(transitivity,[status(thm)],[14269, 14267])).
% 3.23/3.40 tff(14271,plain,
% 3.23/3.40 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(z))) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(s(elem!1)), elem!1)) | (~b(s(s(s(s(s(s(s(s(elem!1)))))))), s(s(elem!1)))) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(s(s(elem!1))), s(s(s(s(s(s(s(s(elem!1)))))))))))),
% 3.23/3.40 inference(quant_inst,[status(thm)],[])).
% 3.23/3.40 tff(14272,plain,
% 3.23/3.40 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(elem!1)), elem!1)) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(elem!1, s(z))) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(s(s(elem!1))), s(s(s(s(s(s(s(s(elem!1)))))))))) | (~b(s(s(s(s(s(s(s(s(elem!1)))))))), s(s(elem!1))))),
% 3.23/3.40 inference(modus_ponens,[status(thm)],[14271, 14270])).
% 3.23/3.40 tff(14273,plain,
% 3.23/3.40 (~b(s(s(s(elem!1))), s(s(elem!1)))),
% 3.23/3.40 inference(unit_resolution,[status(thm)],[14272, 166, 14225, 13882, 14185, 14266, 14240])).
% 3.23/3.40 tff(14274,plain,
% 3.23/3.40 (r(s(s(s(elem!1))), s(s(elem!1)))),
% 3.23/3.40 inference(unit_resolution,[status(thm)],[889, 14273, 14180])).
% 3.23/3.40 tff(14275,plain,
% 3.23/3.40 (~r(s(s(s(s(elem!1)))), s(s(elem!1)))),
% 3.23/3.40 inference(unit_resolution,[status(thm)],[5160, 14274, 85, 14122, 14264, 14116, 13790, 14261, 14263, 13882])).
% 3.23/3.40 tff(14276,plain,
% 3.23/3.40 (b(s(s(s(s(elem!1)))), s(s(elem!1)))),
% 3.23/3.40 inference(unit_resolution,[status(thm)],[813, 14275, 14261])).
% 3.23/3.40 tff(14277,plain,
% 3.23/3.40 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(elem!1)))), s(s(elem!1)))) | (~b(elem!1, s(s(elem!1)))) | (~b(s(s(s(s(elem!1)))), elem!1)) | (~b(s(s(elem!1)), s(s(s(s(s(s(s(s(elem!1)))))))))) | (~b(s(s(s(s(s(s(s(s(elem!1)))))))), s(s(elem!1)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(elem!1)))), s(s(elem!1)))) | (~b(elem!1, s(s(elem!1)))) | (~b(s(s(s(s(elem!1)))), elem!1)) | (~b(s(s(elem!1)), s(s(s(s(s(s(s(s(elem!1)))))))))) | (~b(s(s(s(s(s(s(s(s(elem!1)))))))), s(s(elem!1)))))),
% 3.23/3.40 inference(rewrite,[status(thm)],[])).
% 3.23/3.40 tff(14278,plain,
% 3.23/3.40 (((~b(s(s(s(s(s(s(s(s(elem!1)))))))), s(s(elem!1)))) | (~b(s(s(s(s(elem!1)))), s(s(elem!1)))) | (~b(s(s(elem!1)), s(s(s(s(s(s(s(s(elem!1)))))))))) | (~b(elem!1, s(s(elem!1)))) | (~b(s(s(s(s(elem!1)))), s(s(elem!1)))) | (~b(s(s(s(s(elem!1)))), elem!1))) <=> ((~b(s(s(s(s(elem!1)))), s(s(elem!1)))) | (~b(elem!1, s(s(elem!1)))) | (~b(s(s(s(s(elem!1)))), elem!1)) | (~b(s(s(elem!1)), s(s(s(s(s(s(s(s(elem!1)))))))))) | (~b(s(s(s(s(s(s(s(s(elem!1)))))))), s(s(elem!1)))))),
% 3.23/3.40 inference(rewrite,[status(thm)],[])).
% 3.23/3.40 tff(14279,plain,
% 3.23/3.40 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(s(s(s(elem!1)))))))), s(s(elem!1)))) | (~b(s(s(s(s(elem!1)))), s(s(elem!1)))) | (~b(s(s(elem!1)), s(s(s(s(s(s(s(s(elem!1)))))))))) | (~b(elem!1, s(s(elem!1)))) | (~b(s(s(s(s(elem!1)))), s(s(elem!1)))) | (~b(s(s(s(s(elem!1)))), elem!1)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(elem!1)))), s(s(elem!1)))) | (~b(elem!1, s(s(elem!1)))) | (~b(s(s(s(s(elem!1)))), elem!1)) | (~b(s(s(elem!1)), s(s(s(s(s(s(s(s(elem!1)))))))))) | (~b(s(s(s(s(s(s(s(s(elem!1)))))))), s(s(elem!1))))))),
% 3.23/3.40 inference(monotonicity,[status(thm)],[14278])).
% 3.23/3.40 tff(14280,plain,
% 3.23/3.40 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(s(s(s(elem!1)))))))), s(s(elem!1)))) | (~b(s(s(s(s(elem!1)))), s(s(elem!1)))) | (~b(s(s(elem!1)), s(s(s(s(s(s(s(s(elem!1)))))))))) | (~b(elem!1, s(s(elem!1)))) | (~b(s(s(s(s(elem!1)))), s(s(elem!1)))) | (~b(s(s(s(s(elem!1)))), elem!1)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(elem!1)))), s(s(elem!1)))) | (~b(elem!1, s(s(elem!1)))) | (~b(s(s(s(s(elem!1)))), elem!1)) | (~b(s(s(elem!1)), s(s(s(s(s(s(s(s(elem!1)))))))))) | (~b(s(s(s(s(s(s(s(s(elem!1)))))))), s(s(elem!1)))))),
% 3.23/3.40 inference(transitivity,[status(thm)],[14279, 14277])).
% 3.23/3.40 tff(14281,plain,
% 3.23/3.40 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(s(s(s(elem!1)))))))), s(s(elem!1)))) | (~b(s(s(s(s(elem!1)))), s(s(elem!1)))) | (~b(s(s(elem!1)), s(s(s(s(s(s(s(s(elem!1)))))))))) | (~b(elem!1, s(s(elem!1)))) | (~b(s(s(s(s(elem!1)))), s(s(elem!1)))) | (~b(s(s(s(s(elem!1)))), elem!1)))),
% 3.23/3.40 inference(quant_inst,[status(thm)],[])).
% 3.23/3.40 tff(14282,plain,
% 3.23/3.40 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(elem!1)))), s(s(elem!1)))) | (~b(elem!1, s(s(elem!1)))) | (~b(s(s(s(s(elem!1)))), elem!1)) | (~b(s(s(elem!1)), s(s(s(s(s(s(s(s(elem!1)))))))))) | (~b(s(s(s(s(s(s(s(s(elem!1)))))))), s(s(elem!1))))),
% 3.23/3.41 inference(modus_ponens,[status(thm)],[14281, 14280])).
% 3.23/3.41 tff(14283,plain,
% 3.23/3.41 (~b(s(s(s(s(elem!1)))), elem!1)),
% 3.23/3.41 inference(unit_resolution,[status(thm)],[14282, 166, 14112, 14276, 14256, 14240])).
% 3.23/3.41 tff(14284,plain,
% 3.23/3.41 (r(s(s(s(s(elem!1)))), elem!1)),
% 3.23/3.41 inference(unit_resolution,[status(thm)],[719, 14283, 14099])).
% 3.23/3.41 tff(14285,plain,
% 3.23/3.41 (~r(s(s(s(s(elem!1)))), s(s(s(s(s(s(s(s(elem!1)))))))))),
% 3.23/3.41 inference(unit_resolution,[status(thm)],[13261, 197, 14231, 14227, 14284])).
% 3.23/3.41 tff(14286,plain,
% 3.23/3.41 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(elem!1)))), s(s(elem!1)))) | (~b(s(s(elem!1)), s(s(s(s(s(s(s(s(elem!1)))))))))) | (~b(s(s(s(s(s(s(s(s(elem!1)))))))), s(s(elem!1)))) | (~b(s(s(s(s(elem!1)))), s(s(s(s(s(s(s(s(elem!1)))))))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(elem!1)))), s(s(elem!1)))) | (~b(s(s(elem!1)), s(s(s(s(s(s(s(s(elem!1)))))))))) | (~b(s(s(s(s(s(s(s(s(elem!1)))))))), s(s(elem!1)))) | (~b(s(s(s(s(elem!1)))), s(s(s(s(s(s(s(s(elem!1)))))))))))),
% 3.23/3.41 inference(rewrite,[status(thm)],[])).
% 3.23/3.41 tff(14287,plain,
% 3.23/3.41 (((~b(s(s(s(s(s(s(s(s(elem!1)))))))), s(s(elem!1)))) | (~b(s(s(s(s(elem!1)))), s(s(elem!1)))) | (~b(s(s(elem!1)), s(s(s(s(s(s(s(s(elem!1)))))))))) | (~b(s(s(s(s(s(s(s(s(elem!1)))))))), s(s(elem!1)))) | (~b(s(s(s(s(elem!1)))), s(s(elem!1)))) | (~b(s(s(s(s(elem!1)))), s(s(s(s(s(s(s(s(elem!1))))))))))) <=> ((~b(s(s(s(s(elem!1)))), s(s(elem!1)))) | (~b(s(s(elem!1)), s(s(s(s(s(s(s(s(elem!1)))))))))) | (~b(s(s(s(s(s(s(s(s(elem!1)))))))), s(s(elem!1)))) | (~b(s(s(s(s(elem!1)))), s(s(s(s(s(s(s(s(elem!1)))))))))))),
% 3.23/3.41 inference(rewrite,[status(thm)],[])).
% 3.23/3.41 tff(14288,plain,
% 3.23/3.41 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(s(s(s(elem!1)))))))), s(s(elem!1)))) | (~b(s(s(s(s(elem!1)))), s(s(elem!1)))) | (~b(s(s(elem!1)), s(s(s(s(s(s(s(s(elem!1)))))))))) | (~b(s(s(s(s(s(s(s(s(elem!1)))))))), s(s(elem!1)))) | (~b(s(s(s(s(elem!1)))), s(s(elem!1)))) | (~b(s(s(s(s(elem!1)))), s(s(s(s(s(s(s(s(elem!1)))))))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(elem!1)))), s(s(elem!1)))) | (~b(s(s(elem!1)), s(s(s(s(s(s(s(s(elem!1)))))))))) | (~b(s(s(s(s(s(s(s(s(elem!1)))))))), s(s(elem!1)))) | (~b(s(s(s(s(elem!1)))), s(s(s(s(s(s(s(s(elem!1))))))))))))),
% 3.23/3.41 inference(monotonicity,[status(thm)],[14287])).
% 3.23/3.41 tff(14289,plain,
% 3.23/3.41 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(s(s(s(elem!1)))))))), s(s(elem!1)))) | (~b(s(s(s(s(elem!1)))), s(s(elem!1)))) | (~b(s(s(elem!1)), s(s(s(s(s(s(s(s(elem!1)))))))))) | (~b(s(s(s(s(s(s(s(s(elem!1)))))))), s(s(elem!1)))) | (~b(s(s(s(s(elem!1)))), s(s(elem!1)))) | (~b(s(s(s(s(elem!1)))), s(s(s(s(s(s(s(s(elem!1)))))))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(elem!1)))), s(s(elem!1)))) | (~b(s(s(elem!1)), s(s(s(s(s(s(s(s(elem!1)))))))))) | (~b(s(s(s(s(s(s(s(s(elem!1)))))))), s(s(elem!1)))) | (~b(s(s(s(s(elem!1)))), s(s(s(s(s(s(s(s(elem!1)))))))))))),
% 3.23/3.41 inference(transitivity,[status(thm)],[14288, 14286])).
% 3.23/3.41 tff(14290,plain,
% 3.23/3.41 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(s(s(s(elem!1)))))))), s(s(elem!1)))) | (~b(s(s(s(s(elem!1)))), s(s(elem!1)))) | (~b(s(s(elem!1)), s(s(s(s(s(s(s(s(elem!1)))))))))) | (~b(s(s(s(s(s(s(s(s(elem!1)))))))), s(s(elem!1)))) | (~b(s(s(s(s(elem!1)))), s(s(elem!1)))) | (~b(s(s(s(s(elem!1)))), s(s(s(s(s(s(s(s(elem!1)))))))))))),
% 3.23/3.41 inference(quant_inst,[status(thm)],[])).
% 3.23/3.41 tff(14291,plain,
% 3.23/3.41 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(elem!1)))), s(s(elem!1)))) | (~b(s(s(elem!1)), s(s(s(s(s(s(s(s(elem!1)))))))))) | (~b(s(s(s(s(s(s(s(s(elem!1)))))))), s(s(elem!1)))) | (~b(s(s(s(s(elem!1)))), s(s(s(s(s(s(s(s(elem!1))))))))))),
% 3.23/3.41 inference(modus_ponens,[status(thm)],[14290, 14289])).
% 3.23/3.41 tff(14292,plain,
% 3.23/3.41 (~b(s(s(s(s(elem!1)))), s(s(s(s(s(s(s(s(elem!1)))))))))),
% 3.23/3.41 inference(unit_resolution,[status(thm)],[14291, 166, 14276, 14256, 14240])).
% 3.23/3.41 tff(14293,plain,
% 3.23/3.41 ((s(s(s(s(elem!1)))) = s(s(s(s(s(s(s(s(elem!1))))))))) | r(s(s(s(s(elem!1)))), s(s(s(s(s(s(s(s(elem!1)))))))))),
% 3.23/3.41 inference(unit_resolution,[status(thm)],[13265, 79, 14292])).
% 3.23/3.41 tff(14294,plain,
% 3.23/3.41 (s(s(s(s(elem!1)))) = s(s(s(s(s(s(s(s(elem!1))))))))),
% 3.23/3.41 inference(unit_resolution,[status(thm)],[14293, 14285])).
% 3.23/3.41 tff(14295,plain,
% 3.23/3.41 (s(s(s(s(s(s(s(s(elem!1)))))))) = s(s(s(s(elem!1))))),
% 3.23/3.41 inference(symmetry,[status(thm)],[14294])).
% 3.23/3.41 tff(14296,plain,
% 3.23/3.41 (inj_0(s(s(s(s(s(s(s(s(elem!1))))))))) = inj_0(s(s(s(s(elem!1)))))),
% 3.23/3.41 inference(monotonicity,[status(thm)],[14295])).
% 3.23/3.41 tff(14297,plain,
% 3.23/3.41 (inj_0(s(s(s(s(elem!1))))) = inj_0(s(s(s(s(s(s(s(s(elem!1)))))))))),
% 3.23/3.41 inference(symmetry,[status(thm)],[14296])).
% 3.23/3.41 tff(14298,plain,
% 3.23/3.41 (s(s(s(z))) = s(s(s(s(s(s(s(elem!1)))))))),
% 3.23/3.41 inference(transitivity,[status(thm)],[14117, 653, 14297, 10])).
% 3.23/3.41 tff(14299,plain,
% 3.23/3.41 (s(s(elem!1)) = s(s(z))),
% 3.23/3.41 inference(unit_resolution,[status(thm)],[17, 14096])).
% 3.23/3.41 tff(14300,plain,
% 3.23/3.41 (~(s(s(s(s(s(s(elem!1)))))) = s(s(elem!1)))),
% 3.23/3.41 inference(unit_resolution,[status(thm)],[4986, 14095])).
% 3.23/3.41 tff(14301,plain,
% 3.23/3.41 (~(s(s(s(z))) = s(s(s(s(s(s(s(elem!1))))))))),
% 3.23/3.41 inference(unit_resolution,[status(thm)],[4995, 14300, 14299])).
% 3.23/3.41 tff(14302,plain,
% 3.23/3.41 ($false),
% 3.23/3.41 inference(unit_resolution,[status(thm)],[14301, 14298])).
% 3.23/3.41 tff(14303,plain,(b(s(s(z)), s(z)) | (~b(s(z), z)) | b(s(z), s(s(elem!1)))), inference(lemma,lemma(discharge,[]))).
% 3.23/3.41 tff(14304,plain,
% 3.23/3.41 (b(s(s(z)), s(z))),
% 3.23/3.41 inference(unit_resolution,[status(thm)],[14303, 53, 54])).
% 3.23/3.41 tff(14305,plain,
% 3.23/3.41 ((~b(s(s(z)), s(z))) | (~b(s(z), z)) | (~b(z, s(z)))),
% 3.23/3.41 inference(unit_resolution,[status(thm)],[13598, 10450])).
% 3.23/3.41 tff(14306,plain,
% 3.23/3.41 (~b(z, s(z))),
% 3.23/3.41 inference(unit_resolution,[status(thm)],[14305, 14304, 53])).
% 3.23/3.41 tff(14307,plain,
% 3.23/3.41 (r(z, s(z))),
% 3.23/3.41 inference(unit_resolution,[status(thm)],[321, 14306])).
% 3.23/3.41 tff(14308,plain,
% 3.23/3.41 (~b(s(s(z)), z)),
% 3.23/3.41 inference(unit_resolution,[status(thm)],[12884, 166, 53, 10450, 14304])).
% 3.23/3.41 tff(14309,plain,
% 3.23/3.41 (r(s(s(z)), z)),
% 3.23/3.41 inference(unit_resolution,[status(thm)],[186, 14308])).
% 3.23/3.41 tff(14310,plain,
% 3.23/3.41 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(z))) | (~r(s(s(z)), z)) | (~r(s(s(s(elem!1))), z)) | (~r(s(s(s(elem!1))), s(s(z)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, s(z))) | (~r(s(s(z)), z)) | (~r(s(s(s(elem!1))), z)) | (~r(s(s(s(elem!1))), s(s(z)))))),
% 3.23/3.41 inference(rewrite,[status(thm)],[])).
% 3.23/3.41 tff(14311,plain,
% 3.23/3.41 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(z))) | (~r(s(s(z)), z)) | (~r(s(s(s(elem!1))), z)) | (~r(s(s(s(elem!1))), s(s(z)))))),
% 3.23/3.41 inference(quant_inst,[status(thm)],[])).
% 3.23/3.41 tff(14312,plain,
% 3.23/3.41 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, s(z))) | (~r(s(s(z)), z)) | (~r(s(s(s(elem!1))), z)) | (~r(s(s(s(elem!1))), s(s(z))))),
% 3.23/3.41 inference(modus_ponens,[status(thm)],[14311, 14310])).
% 3.23/3.41 tff(14313,plain,
% 3.23/3.41 ($false),
% 3.23/3.41 inference(unit_resolution,[status(thm)],[14312, 197, 154, 323, 866, 464])).
% 3.23/3.41 tff(14314,plain,((~r(s(s(s(elem!1))), s(s(z)))) | (~r(s(s(s(elem!1))), z)) | (~r(z, s(z))) | (~r(s(s(z)), z))), inference(lemma,lemma(discharge,[]))).
% 3.23/3.41 tff(14315,plain,
% 3.23/3.41 (~r(s(s(s(elem!1))), s(s(z)))),
% 3.23/3.41 inference(unit_resolution,[status(thm)],[14314, 14309, 13084, 14307])).
% 3.23/3.41 tff(14316,plain,
% 3.23/3.41 (b(s(s(s(elem!1))), s(s(z)))),
% 3.23/3.41 inference(unit_resolution,[status(thm)],[218, 14315])).
% 3.23/3.41 tff(14317,plain,
% 3.23/3.41 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), z)) | (~r(z, s(z))) | (~r(s(s(z)), z)) | (~r(s(s(z)), s(s(s(elem!1))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(elem!1))), z)) | (~r(z, s(z))) | (~r(s(s(z)), z)) | (~r(s(s(z)), s(s(s(elem!1))))))),
% 3.23/3.41 inference(rewrite,[status(thm)],[])).
% 3.23/3.41 tff(14318,plain,
% 3.23/3.41 (((~r(z, s(z))) | (~r(s(s(s(elem!1))), z)) | (~r(s(s(z)), z)) | (~r(s(s(z)), s(s(s(elem!1)))))) <=> ((~r(s(s(s(elem!1))), z)) | (~r(z, s(z))) | (~r(s(s(z)), z)) | (~r(s(s(z)), s(s(s(elem!1))))))),
% 3.23/3.41 inference(rewrite,[status(thm)],[])).
% 3.23/3.41 tff(14319,plain,
% 3.23/3.41 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(z))) | (~r(s(s(s(elem!1))), z)) | (~r(s(s(z)), z)) | (~r(s(s(z)), s(s(s(elem!1))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), z)) | (~r(z, s(z))) | (~r(s(s(z)), z)) | (~r(s(s(z)), s(s(s(elem!1)))))))),
% 3.23/3.41 inference(monotonicity,[status(thm)],[14318])).
% 3.23/3.41 tff(14320,plain,
% 3.23/3.41 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(z))) | (~r(s(s(s(elem!1))), z)) | (~r(s(s(z)), z)) | (~r(s(s(z)), s(s(s(elem!1))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(elem!1))), z)) | (~r(z, s(z))) | (~r(s(s(z)), z)) | (~r(s(s(z)), s(s(s(elem!1))))))),
% 3.23/3.41 inference(transitivity,[status(thm)],[14319, 14317])).
% 3.23/3.41 tff(14321,plain,
% 3.23/3.41 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(z))) | (~r(s(s(s(elem!1))), z)) | (~r(s(s(z)), z)) | (~r(s(s(z)), s(s(s(elem!1))))))),
% 3.23/3.41 inference(quant_inst,[status(thm)],[])).
% 3.23/3.41 tff(14322,plain,
% 3.23/3.41 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(elem!1))), z)) | (~r(z, s(z))) | (~r(s(s(z)), z)) | (~r(s(s(z)), s(s(s(elem!1)))))),
% 3.23/3.41 inference(modus_ponens,[status(thm)],[14321, 14320])).
% 3.23/3.41 tff(14323,plain,
% 3.23/3.41 (~r(s(s(z)), s(s(s(elem!1))))),
% 3.23/3.41 inference(unit_resolution,[status(thm)],[14322, 197, 13084, 14307, 14309])).
% 3.23/3.41 tff(14324,plain,
% 3.23/3.41 (b(s(s(z)), s(s(s(elem!1))))),
% 3.23/3.41 inference(unit_resolution,[status(thm)],[279, 14323])).
% 3.23/3.41 tff(14325,plain,
% 3.23/3.41 (~r(s(s(s(elem!1))), s(z))),
% 3.23/3.41 inference(unit_resolution,[status(thm)],[373, 14307, 85, 13084])).
% 3.23/3.41 tff(14326,plain,
% 3.23/3.41 (b(s(s(s(elem!1))), s(z))),
% 3.23/3.41 inference(unit_resolution,[status(thm)],[1849, 14325])).
% 3.23/3.41 tff(14327,plain,
% 3.23/3.41 (~b(s(z), s(s(s(elem!1))))),
% 3.23/3.41 inference(unit_resolution,[status(thm)],[271, 14324, 14304, 14326])).
% 3.23/3.41 tff(14328,plain,
% 3.23/3.41 (r(s(z), s(s(s(elem!1))))),
% 3.23/3.41 inference(unit_resolution,[status(thm)],[116, 14327])).
% 3.23/3.41 tff(14329,plain,
% 3.23/3.41 (~r(z, s(s(s(elem!1))))),
% 3.23/3.41 inference(unit_resolution,[status(thm)],[13506, 14328, 13084, 14307])).
% 3.23/3.41 tff(14330,plain,
% 3.23/3.41 (b(z, s(s(s(elem!1))))),
% 3.23/3.41 inference(unit_resolution,[status(thm)],[261, 14329])).
% 3.23/3.41 tff(14331,plain,
% 3.23/3.41 ($false),
% 3.23/3.41 inference(unit_resolution,[status(thm)],[10577, 166, 14330, 10450, 14324, 14316])).
% 3.23/3.41 tff(14332,plain,((~b(s(z), z)) | b(s(z), s(s(elem!1)))), inference(lemma,lemma(discharge,[]))).
% 3.23/3.41 tff(14333,plain,
% 3.23/3.41 (~b(s(z), z)),
% 3.23/3.41 inference(unit_resolution,[status(thm)],[14332, 54])).
% 3.23/3.41 tff(14334,plain,
% 3.23/3.41 (r(s(z), z)),
% 3.23/3.41 inference(unit_resolution,[status(thm)],[230, 14333])).
% 3.23/3.41 tff(14335,plain,
% 3.23/3.41 ($false),
% 3.23/3.41 inference(unit_resolution,[status(thm)],[12919, 166, 556, 10450, 118, 156])).
% 3.23/3.41 tff(14336,plain,((~b(s(z), s(s(z)))) | (~b(z, s(z))) | (~b(s(s(z)), s(z)))), inference(lemma,lemma(discharge,[]))).
% 3.23/3.41 tff(14337,plain,
% 3.23/3.41 (~b(s(z), s(s(z)))),
% 3.23/3.41 inference(unit_resolution,[status(thm)],[14336, 13574, 156])).
% 3.23/3.41 tff(14338,plain,
% 3.23/3.41 (r(s(z), s(s(z)))),
% 3.23/3.41 inference(unit_resolution,[status(thm)],[427, 14337])).
% 3.23/3.41 tff(14339,plain,
% 3.23/3.41 (~r(z, s(s(elem!1)))),
% 3.23/3.41 inference(unit_resolution,[status(thm)],[4466, 350, 154, 97])).
% 3.23/3.41 tff(14340,plain,
% 3.23/3.41 (b(z, s(s(elem!1)))),
% 3.23/3.41 inference(unit_resolution,[status(thm)],[1795, 14339])).
% 3.23/3.41 tff(14341,plain,
% 3.23/3.41 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), z)) | (~r(z, s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), s(z))) | (~r(s(z), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(elem!1))), z)) | (~r(z, s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), s(z))) | (~r(s(z), z)))),
% 3.23/3.41 inference(rewrite,[status(thm)],[])).
% 3.23/3.41 tff(14342,plain,
% 3.23/3.41 (((~r(z, s(s(s(elem!1))))) | (~r(s(z), z)) | (~r(s(s(s(elem!1))), z)) | (~r(s(s(s(elem!1))), s(z)))) <=> ((~r(s(s(s(elem!1))), z)) | (~r(z, s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), s(z))) | (~r(s(z), z)))),
% 3.23/3.41 inference(rewrite,[status(thm)],[])).
% 3.23/3.41 tff(14343,plain,
% 3.23/3.41 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(s(elem!1))))) | (~r(s(z), z)) | (~r(s(s(s(elem!1))), z)) | (~r(s(s(s(elem!1))), s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), z)) | (~r(z, s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), s(z))) | (~r(s(z), z))))),
% 3.23/3.41 inference(monotonicity,[status(thm)],[14342])).
% 3.23/3.41 tff(14344,plain,
% 3.23/3.41 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(s(elem!1))))) | (~r(s(z), z)) | (~r(s(s(s(elem!1))), z)) | (~r(s(s(s(elem!1))), s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(elem!1))), z)) | (~r(z, s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), s(z))) | (~r(s(z), z)))),
% 3.23/3.41 inference(transitivity,[status(thm)],[14343, 14341])).
% 3.23/3.41 tff(14345,plain,
% 3.23/3.41 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(s(elem!1))))) | (~r(s(z), z)) | (~r(s(s(s(elem!1))), z)) | (~r(s(s(s(elem!1))), s(z))))),
% 3.23/3.41 inference(quant_inst,[status(thm)],[])).
% 3.23/3.41 tff(14346,plain,
% 3.23/3.41 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(elem!1))), z)) | (~r(z, s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), s(z))) | (~r(s(z), z))),
% 3.23/3.41 inference(modus_ponens,[status(thm)],[14345, 14344])).
% 3.23/3.41 tff(14347,plain,
% 3.23/3.41 ($false),
% 3.23/3.41 inference(unit_resolution,[status(thm)],[14346, 197, 154, 350, 97, 282])).
% 3.23/3.41 tff(14348,plain,((~r(z, s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), z)) | (~r(s(s(s(elem!1))), s(z))) | (~r(s(z), z))), inference(lemma,lemma(discharge,[]))).
% 3.23/3.41 tff(14349,plain,
% 3.23/3.41 (~r(z, s(s(s(elem!1))))),
% 3.23/3.41 inference(unit_resolution,[status(thm)],[14348, 350, 154, 97])).
% 3.23/3.41 tff(14350,plain,
% 3.23/3.41 (b(z, s(s(s(elem!1))))),
% 3.23/3.41 inference(unit_resolution,[status(thm)],[261, 14349])).
% 3.23/3.41 tff(14351,plain,
% 3.23/3.41 (~b(s(z), s(s(z)))),
% 3.23/3.41 inference(unit_resolution,[status(thm)],[14336, 13796, 156])).
% 3.23/3.41 tff(14352,plain,
% 3.23/3.41 (r(s(z), s(s(z)))),
% 3.23/3.41 inference(unit_resolution,[status(thm)],[427, 14351])).
% 3.23/3.41 tff(14353,plain,
% 3.23/3.41 (~r(s(s(elem!1)), s(s(z)))),
% 3.23/3.41 inference(unit_resolution,[status(thm)],[4199, 905, 311, 350])).
% 3.23/3.41 tff(14354,plain,
% 3.23/3.41 (b(s(s(elem!1)), s(s(z)))),
% 3.23/3.41 inference(unit_resolution,[status(thm)],[441, 14353, 11])).
% 3.23/3.41 tff(14355,plain,
% 3.23/3.41 (~r(s(s(elem!1)), s(s(s(elem!1))))),
% 3.23/3.41 inference(unit_resolution,[status(thm)],[2627, 905, 350, 311])).
% 3.23/3.41 tff(14356,plain,
% 3.23/3.41 (b(s(s(elem!1)), s(s(s(elem!1))))),
% 3.23/3.41 inference(unit_resolution,[status(thm)],[461, 14355, 45])).
% 3.23/3.41 tff(14357,plain,
% 3.23/3.41 ($false),
% 3.23/3.41 inference(unit_resolution,[status(thm)],[1841, 197, 311, 350, 905, 1970])).
% 3.23/3.41 tff(14358,plain,((~r(s(s(elem!1)), z)) | (~r(s(z), s(s(elem!1)))) | (~r(s(s(s(elem!1))), s(z))) | (~r(s(s(s(elem!1))), s(s(elem!1))))), inference(lemma,lemma(discharge,[]))).
% 3.23/3.41 tff(14359,plain,
% 3.23/3.41 (~r(s(s(elem!1)), z)),
% 3.23/3.41 inference(unit_resolution,[status(thm)],[14358, 905, 350, 311])).
% 3.23/3.41 tff(14360,plain,
% 3.23/3.41 (b(s(s(elem!1)), z)),
% 3.23/3.41 inference(unit_resolution,[status(thm)],[608, 14359])).
% 3.23/3.41 tff(14361,plain,
% 3.23/3.41 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(z, s(s(z)))) | (~b(s(z), s(s(s(elem!1))))) | (~b(s(s(elem!1)), z)) | (~b(s(s(elem!1)), s(s(z)))) | (~b(s(s(z)), s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(z, s(s(z)))) | (~b(s(z), s(s(s(elem!1))))) | (~b(s(s(elem!1)), z)) | (~b(s(s(elem!1)), s(s(z)))) | (~b(s(s(z)), s(z))))),
% 3.23/3.41 inference(rewrite,[status(thm)],[])).
% 3.23/3.41 tff(14362,plain,
% 3.23/3.41 (((~b(s(z), s(s(s(elem!1))))) | (~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(s(s(z)), s(z))) | (~b(z, s(s(z)))) | (~b(s(s(elem!1)), s(s(z)))) | (~b(s(s(elem!1)), z))) <=> ((~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(z, s(s(z)))) | (~b(s(z), s(s(s(elem!1))))) | (~b(s(s(elem!1)), z)) | (~b(s(s(elem!1)), s(s(z)))) | (~b(s(s(z)), s(z))))),
% 3.23/3.41 inference(rewrite,[status(thm)],[])).
% 3.23/3.41 tff(14363,plain,
% 3.23/3.41 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(s(elem!1))))) | (~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(s(s(z)), s(z))) | (~b(z, s(s(z)))) | (~b(s(s(elem!1)), s(s(z)))) | (~b(s(s(elem!1)), z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(z, s(s(z)))) | (~b(s(z), s(s(s(elem!1))))) | (~b(s(s(elem!1)), z)) | (~b(s(s(elem!1)), s(s(z)))) | (~b(s(s(z)), s(z)))))),
% 3.23/3.41 inference(monotonicity,[status(thm)],[14362])).
% 3.23/3.41 tff(14364,plain,
% 3.23/3.41 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(s(elem!1))))) | (~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(s(s(z)), s(z))) | (~b(z, s(s(z)))) | (~b(s(s(elem!1)), s(s(z)))) | (~b(s(s(elem!1)), z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(z, s(s(z)))) | (~b(s(z), s(s(s(elem!1))))) | (~b(s(s(elem!1)), z)) | (~b(s(s(elem!1)), s(s(z)))) | (~b(s(s(z)), s(z))))),
% 3.23/3.41 inference(transitivity,[status(thm)],[14363, 14361])).
% 3.23/3.41 tff(14365,plain,
% 3.23/3.41 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(s(elem!1))))) | (~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(s(s(z)), s(z))) | (~b(z, s(s(z)))) | (~b(s(s(elem!1)), s(s(z)))) | (~b(s(s(elem!1)), z)))),
% 3.23/3.41 inference(quant_inst,[status(thm)],[])).
% 3.23/3.41 tff(14366,plain,
% 3.23/3.41 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(z, s(s(z)))) | (~b(s(z), s(s(s(elem!1))))) | (~b(s(s(elem!1)), z)) | (~b(s(s(elem!1)), s(s(z)))) | (~b(s(s(z)), s(z)))),
% 3.23/3.41 inference(modus_ponens,[status(thm)],[14365, 14364])).
% 3.23/3.41 tff(14367,plain,
% 3.23/3.41 ($false),
% 3.23/3.41 inference(unit_resolution,[status(thm)],[14366, 166, 463, 241, 405, 10450, 592, 156])).
% 3.23/3.41 tff(14368,plain,((~b(s(z), s(s(s(elem!1))))) | (~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(s(s(elem!1)), s(s(z)))) | (~b(s(s(elem!1)), z)) | (~b(s(s(z)), s(z)))), inference(lemma,lemma(discharge,[]))).
% 3.23/3.41 tff(14369,plain,
% 3.23/3.41 (~b(s(z), s(s(s(elem!1))))),
% 3.23/3.41 inference(unit_resolution,[status(thm)],[14368, 14356, 14354, 14360, 156])).
% 3.23/3.41 tff(14370,plain,
% 3.23/3.41 (r(s(z), s(s(s(elem!1))))),
% 3.23/3.41 inference(unit_resolution,[status(thm)],[116, 14369])).
% 3.23/3.41 tff(14371,plain,
% 3.23/3.41 (~r(s(s(z)), s(s(s(elem!1))))),
% 3.23/3.41 inference(unit_resolution,[status(thm)],[2304, 14370, 154, 14352])).
% 3.23/3.41 tff(14372,plain,
% 3.23/3.41 (r(s(s(s(elem!1))), s(s(z)))),
% 3.23/3.41 inference(unit_resolution,[status(thm)],[501, 14371, 14356, 14354])).
% 3.23/3.41 tff(14373,plain,
% 3.23/3.42 (~r(s(s(z)), z)),
% 3.23/3.42 inference(unit_resolution,[status(thm)],[874, 14372, 350, 14352])).
% 3.23/3.42 tff(14374,plain,
% 3.23/3.42 (b(s(s(z)), z)),
% 3.23/3.42 inference(unit_resolution,[status(thm)],[186, 14373])).
% 3.23/3.42 tff(14375,plain,
% 3.23/3.42 (~r(z, elem!1)),
% 3.23/3.42 inference(unit_resolution,[status(thm)],[2489, 14369, 154, 97])).
% 3.23/3.42 tff(14376,plain,
% 3.23/3.42 (b(z, elem!1)),
% 3.23/3.42 inference(unit_resolution,[status(thm)],[2514, 14375, 18])).
% 3.23/3.42 tff(14377,plain,
% 3.23/3.42 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(z)))) | (~b(z, s(s(elem!1)))) | (~b(s(s(elem!1)), s(s(z)))) | (~b(z, elem!1)) | (~b(s(s(z)), z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(s(z)))) | (~b(z, s(s(elem!1)))) | (~b(s(s(elem!1)), s(s(z)))) | (~b(z, elem!1)) | (~b(s(s(z)), z)))),
% 3.23/3.42 inference(rewrite,[status(thm)],[])).
% 3.23/3.42 tff(14378,plain,
% 3.23/3.42 (((~b(z, elem!1)) | (~b(z, elem!1)) | (~b(s(s(z)), z)) | (~b(s(s(elem!1)), s(s(z)))) | (~b(z, s(s(z)))) | (~b(z, s(s(elem!1))))) <=> ((~b(z, s(s(z)))) | (~b(z, s(s(elem!1)))) | (~b(s(s(elem!1)), s(s(z)))) | (~b(z, elem!1)) | (~b(s(s(z)), z)))),
% 3.23/3.42 inference(rewrite,[status(thm)],[])).
% 3.23/3.42 tff(14379,plain,
% 3.23/3.42 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, elem!1)) | (~b(z, elem!1)) | (~b(s(s(z)), z)) | (~b(s(s(elem!1)), s(s(z)))) | (~b(z, s(s(z)))) | (~b(z, s(s(elem!1)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(z)))) | (~b(z, s(s(elem!1)))) | (~b(s(s(elem!1)), s(s(z)))) | (~b(z, elem!1)) | (~b(s(s(z)), z))))),
% 3.23/3.42 inference(monotonicity,[status(thm)],[14378])).
% 3.23/3.42 tff(14380,plain,
% 3.23/3.42 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, elem!1)) | (~b(z, elem!1)) | (~b(s(s(z)), z)) | (~b(s(s(elem!1)), s(s(z)))) | (~b(z, s(s(z)))) | (~b(z, s(s(elem!1)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(s(z)))) | (~b(z, s(s(elem!1)))) | (~b(s(s(elem!1)), s(s(z)))) | (~b(z, elem!1)) | (~b(s(s(z)), z)))),
% 3.23/3.42 inference(transitivity,[status(thm)],[14379, 14377])).
% 3.23/3.42 tff(14381,plain,
% 3.23/3.42 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, elem!1)) | (~b(z, elem!1)) | (~b(s(s(z)), z)) | (~b(s(s(elem!1)), s(s(z)))) | (~b(z, s(s(z)))) | (~b(z, s(s(elem!1)))))),
% 3.23/3.42 inference(quant_inst,[status(thm)],[])).
% 3.23/3.42 tff(14382,plain,
% 3.23/3.42 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(s(z)))) | (~b(z, s(s(elem!1)))) | (~b(s(s(elem!1)), s(s(z)))) | (~b(z, elem!1)) | (~b(s(s(z)), z))),
% 3.23/3.42 inference(modus_ponens,[status(thm)],[14381, 14380])).
% 3.23/3.42 tff(14383,plain,
% 3.23/3.42 ($false),
% 3.23/3.42 inference(unit_resolution,[status(thm)],[14382, 166, 14376, 14340, 14354, 10450, 14374])).
% 3.23/3.42 tff(14384,plain,((~r(s(s(s(elem!1))), s(s(elem!1)))) | (~r(s(s(s(elem!1))), s(z))) | (~r(s(s(s(elem!1))), z)) | (~r(s(z), z)) | (~b(s(s(z)), s(z))) | (~r(s(z), s(s(elem!1)))) | (s(s(elem!1)) = s(s(z))) | (s(s(elem!1)) = s(s(s(elem!1))))), inference(lemma,lemma(discharge,[]))).
% 3.23/3.42 tff(14385,plain,
% 3.23/3.42 (~r(s(s(s(elem!1))), s(s(elem!1)))),
% 3.23/3.42 inference(unit_resolution,[status(thm)],[14384, 45, 154, 97, 156, 311, 11, 350])).
% 3.23/3.42 tff(14386,plain,
% 3.23/3.42 (~r(s(s(elem!1)), s(z))),
% 3.23/3.42 inference(unit_resolution,[status(thm)],[6958, 240, 311, 350, 1820, 45])).
% 3.23/3.42 tff(14387,plain,
% 3.23/3.42 (b(s(s(elem!1)), s(z))),
% 3.23/3.42 inference(unit_resolution,[status(thm)],[1912, 14386])).
% 3.23/3.42 tff(14388,plain,
% 3.23/3.42 (r(s(s(elem!1)), s(s(s(elem!1))))),
% 3.23/3.42 inference(unit_resolution,[status(thm)],[1834, 1823, 45, 1820, 240])).
% 3.23/3.42 tff(14389,plain,
% 3.23/3.42 (~r(s(z), s(s(s(elem!1))))),
% 3.23/3.42 inference(unit_resolution,[status(thm)],[764, 14388, 311, 350])).
% 3.23/3.42 tff(14390,plain,
% 3.23/3.42 (b(s(z), s(s(s(elem!1))))),
% 3.23/3.42 inference(unit_resolution,[status(thm)],[116, 14389])).
% 3.23/3.42 tff(14391,plain,
% 3.23/3.42 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(z, s(s(s(elem!1))))) | (~b(s(z), s(s(s(elem!1))))) | (~b(z, s(z))) | (~b(s(s(elem!1)), s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(z, s(s(s(elem!1))))) | (~b(s(z), s(s(s(elem!1))))) | (~b(z, s(z))) | (~b(s(s(elem!1)), s(z))))),
% 3.23/3.42 inference(rewrite,[status(thm)],[])).
% 3.23/3.42 tff(14392,plain,
% 3.23/3.42 (((~b(s(s(elem!1)), s(z))) | (~b(z, s(z))) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(z), s(s(s(elem!1))))) | (~b(z, s(s(s(elem!1))))) | (~b(z, s(z)))) <=> ((~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(z, s(s(s(elem!1))))) | (~b(s(z), s(s(s(elem!1))))) | (~b(z, s(z))) | (~b(s(s(elem!1)), s(z))))),
% 3.23/3.42 inference(rewrite,[status(thm)],[])).
% 3.23/3.42 tff(14393,plain,
% 3.23/3.42 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), s(z))) | (~b(z, s(z))) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(z), s(s(s(elem!1))))) | (~b(z, s(s(s(elem!1))))) | (~b(z, s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(z, s(s(s(elem!1))))) | (~b(s(z), s(s(s(elem!1))))) | (~b(z, s(z))) | (~b(s(s(elem!1)), s(z)))))),
% 3.23/3.42 inference(monotonicity,[status(thm)],[14392])).
% 3.23/3.42 tff(14394,plain,
% 3.23/3.42 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), s(z))) | (~b(z, s(z))) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(z), s(s(s(elem!1))))) | (~b(z, s(s(s(elem!1))))) | (~b(z, s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(z, s(s(s(elem!1))))) | (~b(s(z), s(s(s(elem!1))))) | (~b(z, s(z))) | (~b(s(s(elem!1)), s(z))))),
% 3.23/3.42 inference(transitivity,[status(thm)],[14393, 14391])).
% 3.23/3.42 tff(14395,plain,
% 3.23/3.42 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), s(z))) | (~b(z, s(z))) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(z), s(s(s(elem!1))))) | (~b(z, s(s(s(elem!1))))) | (~b(z, s(z))))),
% 3.23/3.42 inference(quant_inst,[status(thm)],[])).
% 3.23/3.42 tff(14396,plain,
% 3.23/3.42 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(z, s(s(s(elem!1))))) | (~b(s(z), s(s(s(elem!1))))) | (~b(z, s(z))) | (~b(s(s(elem!1)), s(z)))),
% 3.23/3.42 inference(modus_ponens,[status(thm)],[14395, 14394])).
% 3.23/3.42 tff(14397,plain,
% 3.23/3.42 ($false),
% 3.23/3.42 inference(unit_resolution,[status(thm)],[14396, 166, 2329, 14390, 240, 118, 14387])).
% 3.23/3.42 tff(14398,plain,(r(s(s(s(elem!1))), s(s(elem!1))) | (~b(z, s(s(s(elem!1))))) | (~b(z, s(z))) | (~r(s(z), s(s(elem!1)))) | (~r(s(s(s(elem!1))), s(z))) | (s(s(elem!1)) = s(s(s(elem!1)))) | (~b(z, s(s(elem!1))))), inference(lemma,lemma(discharge,[]))).
% 3.23/3.42 tff(14399,plain,
% 3.23/3.42 ($false),
% 3.23/3.42 inference(unit_resolution,[status(thm)],[14398, 14385, 45, 13796, 311, 350, 14350, 14340])).
% 3.23/3.42 tff(14400,plain,((s(s(elem!1)) = s(s(s(elem!1)))) | (~r(s(z), s(s(elem!1)))) | (~r(s(s(s(elem!1))), s(z))) | (~r(s(s(s(elem!1))), z)) | (~r(s(z), z)) | (~b(s(s(z)), s(z))) | (s(s(elem!1)) = s(s(z)))), inference(lemma,lemma(discharge,[]))).
% 3.23/3.42 tff(14401,plain,
% 3.23/3.42 (s(s(elem!1)) = s(s(s(elem!1)))),
% 3.23/3.42 inference(unit_resolution,[status(thm)],[14400, 3953, 311, 154, 97, 156, 11])).
% 3.23/3.42 tff(14402,plain,
% 3.23/3.42 (~b(s(s(elem!1)), s(z))),
% 3.23/3.42 inference(unit_resolution,[status(thm)],[3849, 14401, 3846])).
% 3.23/3.42 tff(14403,plain,
% 3.23/3.42 (r(s(s(elem!1)), s(z))),
% 3.23/3.42 inference(unit_resolution,[status(thm)],[1912, 14402])).
% 3.23/3.42 tff(14404,plain,
% 3.23/3.42 (r(s(s(z)), s(s(elem!1)))),
% 3.23/3.42 inference(unit_resolution,[status(thm)],[11731, 14402, 97])).
% 3.23/3.42 tff(14405,plain,
% 3.23/3.42 ($false),
% 3.23/3.42 inference(unit_resolution,[status(thm)],[6744, 14404, 14403, 311, 14338])).
% 3.23/3.42 tff(14406,plain,(b(s(s(s(elem!1))), s(z)) | (~r(s(z), s(s(elem!1)))) | (~r(s(z), z)) | (~r(s(s(s(elem!1))), z)) | (~b(s(s(z)), s(z))) | (s(s(elem!1)) = s(s(z)))), inference(lemma,lemma(discharge,[]))).
% 3.23/3.42 tff(14407,plain,
% 3.23/3.42 (b(s(s(s(elem!1))), s(z))),
% 3.23/3.42 inference(unit_resolution,[status(thm)],[14406, 132, 14334, 13084, 156, 85])).
% 3.23/3.42 tff(14408,plain,
% 3.23/3.42 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), z)) | (~r(z, s(z))) | (~r(s(z), z)) | (~r(s(z), s(s(s(elem!1))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(elem!1))), z)) | (~r(z, s(z))) | (~r(s(z), z)) | (~r(s(z), s(s(s(elem!1))))))),
% 3.23/3.42 inference(rewrite,[status(thm)],[])).
% 3.23/3.42 tff(14409,plain,
% 3.23/3.42 (((~r(z, s(z))) | (~r(s(s(s(elem!1))), z)) | (~r(s(z), z)) | (~r(s(z), s(s(s(elem!1)))))) <=> ((~r(s(s(s(elem!1))), z)) | (~r(z, s(z))) | (~r(s(z), z)) | (~r(s(z), s(s(s(elem!1))))))),
% 3.23/3.42 inference(rewrite,[status(thm)],[])).
% 3.23/3.42 tff(14410,plain,
% 3.23/3.42 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(z))) | (~r(s(s(s(elem!1))), z)) | (~r(s(z), z)) | (~r(s(z), s(s(s(elem!1))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), z)) | (~r(z, s(z))) | (~r(s(z), z)) | (~r(s(z), s(s(s(elem!1)))))))),
% 3.23/3.42 inference(monotonicity,[status(thm)],[14409])).
% 3.23/3.42 tff(14411,plain,
% 3.23/3.42 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(z))) | (~r(s(s(s(elem!1))), z)) | (~r(s(z), z)) | (~r(s(z), s(s(s(elem!1))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(elem!1))), z)) | (~r(z, s(z))) | (~r(s(z), z)) | (~r(s(z), s(s(s(elem!1))))))),
% 3.23/3.42 inference(transitivity,[status(thm)],[14410, 14408])).
% 3.23/3.42 tff(14412,plain,
% 3.23/3.42 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(z))) | (~r(s(s(s(elem!1))), z)) | (~r(s(z), z)) | (~r(s(z), s(s(s(elem!1))))))),
% 3.23/3.42 inference(quant_inst,[status(thm)],[])).
% 3.23/3.42 tff(14413,plain,
% 3.23/3.42 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(elem!1))), z)) | (~r(z, s(z))) | (~r(s(z), z)) | (~r(s(z), s(s(s(elem!1)))))),
% 3.23/3.42 inference(modus_ponens,[status(thm)],[14412, 14411])).
% 3.23/3.42 tff(14414,plain,
% 3.23/3.42 (~r(s(z), s(s(s(elem!1))))),
% 3.23/3.42 inference(unit_resolution,[status(thm)],[14413, 197, 13084, 323, 14334])).
% 3.23/3.42 tff(14415,plain,
% 3.23/3.42 (b(s(z), s(s(s(elem!1))))),
% 3.23/3.42 inference(unit_resolution,[status(thm)],[116, 14414])).
% 3.23/3.42 tff(14416,plain,
% 3.23/3.42 (~(s(s(elem!1)) = s(s(s(elem!1))))),
% 3.23/3.42 inference(unit_resolution,[status(thm)],[12329, 14415, 54])).
% 3.23/3.42 tff(14417,plain,
% 3.23/3.42 (~b(s(s(z)), s(s(s(elem!1))))),
% 3.23/3.42 inference(unit_resolution,[status(thm)],[271, 14415, 156, 14407])).
% 3.23/3.42 tff(14418,plain,
% 3.23/3.42 (r(s(s(z)), s(s(s(elem!1))))),
% 3.23/3.42 inference(unit_resolution,[status(thm)],[279, 14417])).
% 3.23/3.42 tff(14419,plain,
% 3.23/3.42 (b(s(s(elem!1)), s(s(s(elem!1))))),
% 3.23/3.42 inference(unit_resolution,[status(thm)],[12416, 365, 54, 323, 14415])).
% 3.23/3.42 tff(14420,plain,
% 3.23/3.42 (~r(s(s(elem!1)), s(z))),
% 3.23/3.42 inference(unit_resolution,[status(thm)],[8600, 365, 85, 323])).
% 3.23/3.42 tff(14421,plain,
% 3.23/3.42 (b(s(s(elem!1)), s(z))),
% 3.23/3.42 inference(unit_resolution,[status(thm)],[1912, 14420])).
% 3.23/3.42 tff(14422,plain,
% 3.23/3.42 ($false),
% 3.23/3.42 inference(unit_resolution,[status(thm)],[1994, 14421, 14419, 96, 14415])).
% 3.23/3.42 tff(14423,plain,((~r(z, s(s(elem!1)))) | (~b(s(s(s(elem!1))), s(z))) | b(s(z), s(s(elem!1))) | (~r(z, s(z)))), inference(lemma,lemma(discharge,[]))).
% 3.23/3.42 tff(14424,plain,
% 3.23/3.42 (~r(z, s(s(elem!1)))),
% 3.23/3.42 inference(unit_resolution,[status(thm)],[14423, 323, 54, 14407])).
% 3.23/3.42 tff(14425,plain,
% 3.23/3.42 (b(z, s(s(elem!1)))),
% 3.23/3.42 inference(unit_resolution,[status(thm)],[1795, 14424])).
% 3.23/3.42 tff(14426,plain,
% 3.23/3.42 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), z)) | (~r(s(s(elem!1)), s(s(s(elem!1))))) | (~r(s(s(elem!1)), s(s(z)))) | (~r(s(s(z)), s(s(s(elem!1))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(elem!1))), z)) | (~r(s(s(elem!1)), s(s(s(elem!1))))) | (~r(s(s(elem!1)), s(s(z)))) | (~r(s(s(z)), s(s(s(elem!1))))))),
% 3.23/3.42 inference(rewrite,[status(thm)],[])).
% 3.23/3.42 tff(14427,plain,
% 3.23/3.42 (((~r(s(s(s(elem!1))), z)) | (~r(s(s(z)), s(s(s(elem!1))))) | (~r(s(s(elem!1)), s(s(s(elem!1))))) | (~r(s(s(elem!1)), s(s(z))))) <=> ((~r(s(s(s(elem!1))), z)) | (~r(s(s(elem!1)), s(s(s(elem!1))))) | (~r(s(s(elem!1)), s(s(z)))) | (~r(s(s(z)), s(s(s(elem!1))))))),
% 3.23/3.42 inference(rewrite,[status(thm)],[])).
% 3.23/3.42 tff(14428,plain,
% 3.23/3.42 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), z)) | (~r(s(s(z)), s(s(s(elem!1))))) | (~r(s(s(elem!1)), s(s(s(elem!1))))) | (~r(s(s(elem!1)), s(s(z)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), z)) | (~r(s(s(elem!1)), s(s(s(elem!1))))) | (~r(s(s(elem!1)), s(s(z)))) | (~r(s(s(z)), s(s(s(elem!1)))))))),
% 3.23/3.42 inference(monotonicity,[status(thm)],[14427])).
% 3.23/3.42 tff(14429,plain,
% 3.23/3.42 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), z)) | (~r(s(s(z)), s(s(s(elem!1))))) | (~r(s(s(elem!1)), s(s(s(elem!1))))) | (~r(s(s(elem!1)), s(s(z)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(elem!1))), z)) | (~r(s(s(elem!1)), s(s(s(elem!1))))) | (~r(s(s(elem!1)), s(s(z)))) | (~r(s(s(z)), s(s(s(elem!1))))))),
% 3.23/3.42 inference(transitivity,[status(thm)],[14428, 14426])).
% 3.23/3.42 tff(14430,plain,
% 3.23/3.42 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), z)) | (~r(s(s(z)), s(s(s(elem!1))))) | (~r(s(s(elem!1)), s(s(s(elem!1))))) | (~r(s(s(elem!1)), s(s(z)))))),
% 3.23/3.42 inference(quant_inst,[status(thm)],[])).
% 3.23/3.42 tff(14431,plain,
% 3.23/3.42 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(elem!1))), z)) | (~r(s(s(elem!1)), s(s(s(elem!1))))) | (~r(s(s(elem!1)), s(s(z)))) | (~r(s(s(z)), s(s(s(elem!1)))))),
% 3.23/3.42 inference(modus_ponens,[status(thm)],[14430, 14429])).
% 3.23/3.42 tff(14432,plain,
% 3.23/3.42 (~r(s(s(elem!1)), s(s(z)))),
% 3.23/3.42 inference(unit_resolution,[status(thm)],[14431, 197, 154, 377, 281])).
% 3.23/3.42 tff(14433,plain,
% 3.23/3.42 (b(s(s(elem!1)), s(s(z)))),
% 3.23/3.42 inference(unit_resolution,[status(thm)],[441, 14432, 132])).
% 3.23/3.42 tff(14434,plain,
% 3.23/3.42 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), z)) | (~r(s(s(elem!1)), s(s(s(elem!1))))) | (~r(s(s(z)), s(s(elem!1)))) | (~r(s(s(z)), s(s(s(elem!1))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(elem!1))), z)) | (~r(s(s(elem!1)), s(s(s(elem!1))))) | (~r(s(s(z)), s(s(elem!1)))) | (~r(s(s(z)), s(s(s(elem!1))))))),
% 3.23/3.42 inference(rewrite,[status(thm)],[])).
% 3.23/3.42 tff(14435,plain,
% 3.23/3.42 (((~r(s(s(s(elem!1))), z)) | (~r(s(s(elem!1)), s(s(s(elem!1))))) | (~r(s(s(z)), s(s(s(elem!1))))) | (~r(s(s(z)), s(s(elem!1))))) <=> ((~r(s(s(s(elem!1))), z)) | (~r(s(s(elem!1)), s(s(s(elem!1))))) | (~r(s(s(z)), s(s(elem!1)))) | (~r(s(s(z)), s(s(s(elem!1))))))),
% 3.23/3.42 inference(rewrite,[status(thm)],[])).
% 3.23/3.42 tff(14436,plain,
% 3.23/3.42 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), z)) | (~r(s(s(elem!1)), s(s(s(elem!1))))) | (~r(s(s(z)), s(s(s(elem!1))))) | (~r(s(s(z)), s(s(elem!1)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), z)) | (~r(s(s(elem!1)), s(s(s(elem!1))))) | (~r(s(s(z)), s(s(elem!1)))) | (~r(s(s(z)), s(s(s(elem!1)))))))),
% 3.23/3.42 inference(monotonicity,[status(thm)],[14435])).
% 3.23/3.42 tff(14437,plain,
% 3.23/3.42 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), z)) | (~r(s(s(elem!1)), s(s(s(elem!1))))) | (~r(s(s(z)), s(s(s(elem!1))))) | (~r(s(s(z)), s(s(elem!1)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(elem!1))), z)) | (~r(s(s(elem!1)), s(s(s(elem!1))))) | (~r(s(s(z)), s(s(elem!1)))) | (~r(s(s(z)), s(s(s(elem!1))))))),
% 3.23/3.42 inference(transitivity,[status(thm)],[14436, 14434])).
% 3.23/3.42 tff(14438,plain,
% 3.23/3.42 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), z)) | (~r(s(s(elem!1)), s(s(s(elem!1))))) | (~r(s(s(z)), s(s(s(elem!1))))) | (~r(s(s(z)), s(s(elem!1)))))),
% 3.23/3.42 inference(quant_inst,[status(thm)],[])).
% 3.23/3.42 tff(14439,plain,
% 3.23/3.42 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(elem!1))), z)) | (~r(s(s(elem!1)), s(s(s(elem!1))))) | (~r(s(s(z)), s(s(elem!1)))) | (~r(s(s(z)), s(s(s(elem!1)))))),
% 3.23/3.42 inference(modus_ponens,[status(thm)],[14438, 14437])).
% 3.23/3.42 tff(14440,plain,
% 3.23/3.42 (~r(s(s(z)), s(s(elem!1)))),
% 3.23/3.42 inference(unit_resolution,[status(thm)],[14439, 197, 154, 377, 281])).
% 3.23/3.42 tff(14441,plain,
% 3.23/3.42 (b(s(s(z)), s(s(elem!1)))),
% 3.23/3.42 inference(unit_resolution,[status(thm)],[390, 14440, 52])).
% 3.23/3.42 tff(14442,plain,
% 3.23/3.42 ($false),
% 3.23/3.42 inference(unit_resolution,[status(thm)],[12611, 14441, 14433, 1820])).
% 3.23/3.42 tff(14443,plain,((~r(s(s(elem!1)), s(s(s(elem!1))))) | (~b(z, s(s(elem!1)))) | (s(s(z)) = s(s(elem!1))) | (~r(s(s(s(elem!1))), z)) | (~r(s(s(z)), s(s(s(elem!1)))))), inference(lemma,lemma(discharge,[]))).
% 3.23/3.42 tff(14444,plain,
% 3.23/3.42 (~r(s(s(elem!1)), s(s(s(elem!1))))),
% 3.23/3.42 inference(unit_resolution,[status(thm)],[14443, 14425, 52, 13084, 14418])).
% 3.23/3.42 tff(14445,plain,
% 3.23/3.42 (b(s(s(elem!1)), s(s(s(elem!1))))),
% 3.23/3.42 inference(unit_resolution,[status(thm)],[461, 14444, 14416])).
% 3.23/3.42 tff(14446,plain,
% 3.23/3.42 (~b(s(s(elem!1)), s(z))),
% 3.23/3.42 inference(unit_resolution,[status(thm)],[1994, 14445, 14407, 14415])).
% 3.23/3.42 tff(14447,plain,
% 3.23/3.42 (r(s(s(z)), s(s(elem!1)))),
% 3.23/3.42 inference(unit_resolution,[status(thm)],[11731, 14446, 14334])).
% 3.23/3.42 tff(14448,plain,
% 3.23/3.42 (r(s(s(elem!1)), s(z))),
% 3.23/3.42 inference(unit_resolution,[status(thm)],[1912, 14446])).
% 3.23/3.42 tff(14449,plain,
% 3.23/3.42 (~r(s(s(elem!1)), z)),
% 3.23/3.42 inference(unit_resolution,[status(thm)],[8490, 14448, 14334, 323])).
% 3.23/3.42 tff(14450,plain,
% 3.23/3.42 (b(s(s(elem!1)), z)),
% 3.23/3.42 inference(unit_resolution,[status(thm)],[608, 14449])).
% 3.23/3.42 tff(14451,plain,
% 3.23/3.42 (~b(s(s(elem!1)), s(s(z)))),
% 3.23/3.42 inference(unit_resolution,[status(thm)],[14368, 14450, 14415, 14445, 156])).
% 3.23/3.42 tff(14452,plain,
% 3.23/3.42 (r(s(s(elem!1)), s(s(z)))),
% 3.23/3.42 inference(unit_resolution,[status(thm)],[441, 14451, 132])).
% 3.23/3.42 tff(14453,plain,
% 3.23/3.42 (~r(s(s(s(z))), s(s(elem!1)))),
% 3.23/3.42 inference(unit_resolution,[status(thm)],[4435, 14452, 85, 156, 14447])).
% 3.23/3.42 tff(14454,plain,
% 3.23/3.42 (~r(s(z), s(s(z)))),
% 3.23/3.42 inference(unit_resolution,[status(thm)],[6744, 14447, 85, 14448])).
% 3.23/3.42 tff(14455,plain,
% 3.23/3.42 (b(s(z), s(s(z)))),
% 3.23/3.42 inference(unit_resolution,[status(thm)],[427, 14454])).
% 3.23/3.42 tff(14456,plain,
% 3.23/3.42 (~b(s(s(s(elem!1))), s(s(z)))),
% 3.23/3.42 inference(unit_resolution,[status(thm)],[9072, 166, 14415, 14407, 156])).
% 3.23/3.42 tff(14457,plain,
% 3.23/3.42 (r(s(s(s(elem!1))), s(s(z)))),
% 3.23/3.42 inference(unit_resolution,[status(thm)],[218, 14456])).
% 3.23/3.42 tff(14458,plain,
% 3.23/3.42 (~(s(s(s(elem!1))) = s(s(s(s(elem!1)))))),
% 3.23/3.42 inference(unit_resolution,[status(thm)],[357, 14416])).
% 3.23/3.42 tff(14459,plain,
% 3.23/3.42 (~(s(s(s(s(elem!1)))) = s(s(s(elem!1))))),
% 3.23/3.42 inference(unit_resolution,[status(thm)],[363, 14458])).
% 3.23/3.42 tff(14460,assumption,(s(s(s(z))) = s(s(elem!1))), introduced(assumption)).
% 3.23/3.42 tff(14461,plain,
% 3.23/3.42 (s(s(s(s(z)))) = s(s(s(elem!1)))),
% 3.23/3.43 inference(monotonicity,[status(thm)],[14460])).
% 3.23/3.43 tff(14462,plain,
% 3.23/3.43 (s(s(s(elem!1))) = s(s(s(s(z))))),
% 3.23/3.43 inference(symmetry,[status(thm)],[14461])).
% 3.23/3.43 tff(14463,plain,
% 3.23/3.43 (r(s(s(s(z))), s(z)) <=> r(s(s(elem!1)), s(z))),
% 3.23/3.43 inference(monotonicity,[status(thm)],[14460])).
% 3.23/3.43 tff(14464,plain,
% 3.23/3.43 (r(s(s(elem!1)), s(z)) <=> r(s(s(s(z))), s(z))),
% 3.23/3.43 inference(symmetry,[status(thm)],[14463])).
% 3.23/3.43 tff(14465,plain,
% 3.23/3.43 (r(s(s(s(z))), s(z))),
% 3.23/3.43 inference(modus_ponens,[status(thm)],[4577, 14464])).
% 3.23/3.43 tff(14466,plain,
% 3.23/3.43 (~r(s(s(s(s(elem!1)))), s(z))),
% 3.23/3.43 inference(unit_resolution,[status(thm)],[9373, 14465, 97, 1820, 14462, 311, 323])).
% 3.23/3.43 tff(14467,plain,
% 3.23/3.43 (b(s(s(s(s(elem!1)))), s(z))),
% 3.23/3.43 inference(unit_resolution,[status(thm)],[661, 14466])).
% 3.23/3.43 tff(14468,plain,
% 3.23/3.43 (inj_0(s(s(s(z)))) = inj_0(s(s(elem!1)))),
% 3.23/3.43 inference(monotonicity,[status(thm)],[14460])).
% 3.23/3.43 tff(14469,plain,
% 3.23/3.43 (s(s(z)) = s(elem!1)),
% 3.23/3.43 inference(transitivity,[status(thm)],[1666, 14468, 38])).
% 3.23/3.43 tff(14470,plain,
% 3.23/3.43 (b(s(z), s(s(z))) <=> b(s(z), s(elem!1))),
% 3.23/3.43 inference(monotonicity,[status(thm)],[14469])).
% 3.23/3.43 tff(14471,plain,
% 3.23/3.43 (b(s(z), s(elem!1))),
% 3.23/3.43 inference(modus_ponens,[status(thm)],[556, 14470])).
% 3.23/3.43 tff(14472,plain,
% 3.23/3.43 (b(s(s(z)), s(z)) <=> b(s(elem!1), s(z))),
% 3.23/3.43 inference(monotonicity,[status(thm)],[14469])).
% 3.23/3.43 tff(14473,plain,
% 3.23/3.43 (b(s(elem!1), s(z))),
% 3.23/3.43 inference(modus_ponens,[status(thm)],[156, 14472])).
% 3.23/3.43 tff(14474,plain,
% 3.23/3.43 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), s(z))) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(z), s(elem!1))) | (~b(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~b(s(s(s(s(elem!1)))), s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(elem!1), s(z))) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(z), s(elem!1))) | (~b(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~b(s(s(s(s(elem!1)))), s(z))))),
% 3.23/3.43 inference(rewrite,[status(thm)],[])).
% 3.23/3.43 tff(14475,plain,
% 3.23/3.43 (((~b(s(elem!1), s(z))) | (~b(s(s(s(s(elem!1)))), s(z))) | (~b(s(z), s(elem!1))) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(s(s(s(elem!1)))), s(z))) | (~b(s(s(s(s(elem!1)))), s(s(s(elem!1)))))) <=> ((~b(s(elem!1), s(z))) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(z), s(elem!1))) | (~b(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~b(s(s(s(s(elem!1)))), s(z))))),
% 3.23/3.43 inference(rewrite,[status(thm)],[])).
% 3.23/3.43 tff(14476,plain,
% 3.23/3.43 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), s(z))) | (~b(s(s(s(s(elem!1)))), s(z))) | (~b(s(z), s(elem!1))) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(s(s(s(elem!1)))), s(z))) | (~b(s(s(s(s(elem!1)))), s(s(s(elem!1))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), s(z))) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(z), s(elem!1))) | (~b(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~b(s(s(s(s(elem!1)))), s(z)))))),
% 3.23/3.43 inference(monotonicity,[status(thm)],[14475])).
% 3.23/3.43 tff(14477,plain,
% 3.23/3.43 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), s(z))) | (~b(s(s(s(s(elem!1)))), s(z))) | (~b(s(z), s(elem!1))) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(s(s(s(elem!1)))), s(z))) | (~b(s(s(s(s(elem!1)))), s(s(s(elem!1))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(elem!1), s(z))) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(z), s(elem!1))) | (~b(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~b(s(s(s(s(elem!1)))), s(z))))),
% 3.23/3.43 inference(transitivity,[status(thm)],[14476, 14474])).
% 3.23/3.43 tff(14478,plain,
% 3.23/3.43 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), s(z))) | (~b(s(s(s(s(elem!1)))), s(z))) | (~b(s(z), s(elem!1))) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(s(s(s(elem!1)))), s(z))) | (~b(s(s(s(s(elem!1)))), s(s(s(elem!1))))))),
% 3.23/3.43 inference(quant_inst,[status(thm)],[])).
% 3.23/3.43 tff(14479,plain,
% 3.23/3.43 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(elem!1), s(z))) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(z), s(elem!1))) | (~b(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~b(s(s(s(s(elem!1)))), s(z)))),
% 3.23/3.43 inference(modus_ponens,[status(thm)],[14478, 14477])).
% 3.23/3.43 tff(14480,plain,
% 3.23/3.43 (~b(s(s(s(s(elem!1)))), s(s(s(elem!1))))),
% 3.23/3.43 inference(unit_resolution,[status(thm)],[14479, 166, 14473, 96, 14471, 14467])).
% 3.23/3.43 tff(14481,plain,
% 3.23/3.43 (r(s(s(s(s(elem!1)))), s(s(s(elem!1))))),
% 3.23/3.43 inference(unit_resolution,[status(thm)],[1065, 14480, 1058])).
% 3.23/3.43 tff(14482,plain,
% 3.23/3.43 (r(s(s(s(s(elem!1)))), s(s(z))) <=> r(s(s(s(s(elem!1)))), s(elem!1))),
% 3.23/3.43 inference(monotonicity,[status(thm)],[14469])).
% 3.23/3.43 tff(14483,plain,
% 3.23/3.43 (b(s(s(s(s(elem!1)))), s(s(z))) <=> b(s(s(s(s(elem!1)))), s(elem!1))),
% 3.23/3.43 inference(monotonicity,[status(thm)],[14469])).
% 3.23/3.43 tff(14484,plain,
% 3.23/3.43 (b(s(s(s(s(elem!1)))), s(elem!1)) <=> b(s(s(s(s(elem!1)))), s(s(z)))),
% 3.23/3.43 inference(symmetry,[status(thm)],[14483])).
% 3.23/3.43 tff(14485,plain,
% 3.23/3.43 ((~b(s(s(s(s(elem!1)))), s(elem!1))) <=> (~b(s(s(s(s(elem!1)))), s(s(z))))),
% 3.23/3.43 inference(monotonicity,[status(thm)],[14484])).
% 3.23/3.43 tff(14486,plain,
% 3.23/3.43 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), s(z))) | (~b(s(z), s(elem!1))) | (~b(s(s(s(s(elem!1)))), s(elem!1))) | (~b(s(s(s(s(elem!1)))), s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(elem!1), s(z))) | (~b(s(z), s(elem!1))) | (~b(s(s(s(s(elem!1)))), s(elem!1))) | (~b(s(s(s(s(elem!1)))), s(z))))),
% 3.23/3.43 inference(rewrite,[status(thm)],[])).
% 3.23/3.43 tff(14487,plain,
% 3.23/3.43 (((~b(s(elem!1), s(z))) | (~b(s(s(s(s(elem!1)))), s(z))) | (~b(s(z), s(elem!1))) | (~b(s(elem!1), s(z))) | (~b(s(s(s(s(elem!1)))), s(z))) | (~b(s(s(s(s(elem!1)))), s(elem!1)))) <=> ((~b(s(elem!1), s(z))) | (~b(s(z), s(elem!1))) | (~b(s(s(s(s(elem!1)))), s(elem!1))) | (~b(s(s(s(s(elem!1)))), s(z))))),
% 3.23/3.43 inference(rewrite,[status(thm)],[])).
% 3.23/3.43 tff(14488,plain,
% 3.23/3.43 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), s(z))) | (~b(s(s(s(s(elem!1)))), s(z))) | (~b(s(z), s(elem!1))) | (~b(s(elem!1), s(z))) | (~b(s(s(s(s(elem!1)))), s(z))) | (~b(s(s(s(s(elem!1)))), s(elem!1))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), s(z))) | (~b(s(z), s(elem!1))) | (~b(s(s(s(s(elem!1)))), s(elem!1))) | (~b(s(s(s(s(elem!1)))), s(z)))))),
% 3.23/3.43 inference(monotonicity,[status(thm)],[14487])).
% 3.23/3.43 tff(14489,plain,
% 3.23/3.43 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), s(z))) | (~b(s(s(s(s(elem!1)))), s(z))) | (~b(s(z), s(elem!1))) | (~b(s(elem!1), s(z))) | (~b(s(s(s(s(elem!1)))), s(z))) | (~b(s(s(s(s(elem!1)))), s(elem!1))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(elem!1), s(z))) | (~b(s(z), s(elem!1))) | (~b(s(s(s(s(elem!1)))), s(elem!1))) | (~b(s(s(s(s(elem!1)))), s(z))))),
% 3.23/3.43 inference(transitivity,[status(thm)],[14488, 14486])).
% 3.23/3.43 tff(14490,plain,
% 3.23/3.43 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), s(z))) | (~b(s(s(s(s(elem!1)))), s(z))) | (~b(s(z), s(elem!1))) | (~b(s(elem!1), s(z))) | (~b(s(s(s(s(elem!1)))), s(z))) | (~b(s(s(s(s(elem!1)))), s(elem!1))))),
% 3.23/3.43 inference(quant_inst,[status(thm)],[])).
% 3.23/3.43 tff(14491,plain,
% 3.23/3.43 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(elem!1), s(z))) | (~b(s(z), s(elem!1))) | (~b(s(s(s(s(elem!1)))), s(elem!1))) | (~b(s(s(s(s(elem!1)))), s(z)))),
% 3.23/3.43 inference(modus_ponens,[status(thm)],[14490, 14489])).
% 3.23/3.43 tff(14492,plain,
% 3.23/3.43 (~b(s(s(s(s(elem!1)))), s(elem!1))),
% 3.23/3.43 inference(unit_resolution,[status(thm)],[14491, 166, 14473, 14471, 14467])).
% 3.23/3.43 tff(14493,plain,
% 3.23/3.43 (~b(s(s(s(s(elem!1)))), s(s(z)))),
% 3.23/3.43 inference(modus_ponens,[status(thm)],[14492, 14485])).
% 3.23/3.43 tff(14494,plain,
% 3.23/3.43 (r(s(s(s(s(elem!1)))), s(s(z)))),
% 3.23/3.43 inference(unit_resolution,[status(thm)],[1299, 14493])).
% 3.23/3.43 tff(14495,plain,
% 3.23/3.43 (r(s(s(s(s(elem!1)))), s(elem!1))),
% 3.23/3.43 inference(modus_ponens,[status(thm)],[14494, 14482])).
% 3.23/3.43 tff(14496,plain,
% 3.23/3.43 (r(s(s(z)), s(s(s(elem!1)))) <=> r(s(elem!1), s(s(s(elem!1))))),
% 3.23/3.43 inference(monotonicity,[status(thm)],[14469])).
% 3.23/3.43 tff(14497,plain,
% 3.23/3.43 (r(s(elem!1), s(s(s(elem!1))))),
% 3.23/3.43 inference(modus_ponens,[status(thm)],[281, 14496])).
% 3.23/3.43 tff(14498,plain,
% 3.23/3.43 (r(s(s(s(elem!1))), s(s(z))) <=> r(s(s(s(elem!1))), s(elem!1))),
% 3.23/3.43 inference(monotonicity,[status(thm)],[14469])).
% 3.23/3.43 tff(14499,plain,
% 3.23/3.43 (r(s(s(s(elem!1))), s(elem!1))),
% 3.23/3.43 inference(modus_ponens,[status(thm)],[464, 14498])).
% 3.23/3.43 tff(14500,plain,
% 3.23/3.43 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(elem!1), s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), s(elem!1))) | (~r(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~r(s(s(s(s(elem!1)))), s(elem!1))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(elem!1), s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), s(elem!1))) | (~r(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~r(s(s(s(s(elem!1)))), s(elem!1))))),
% 3.23/3.43 inference(rewrite,[status(thm)],[])).
% 3.23/3.43 tff(14501,plain,
% 3.23/3.43 (((~r(s(s(s(elem!1))), s(elem!1))) | (~r(s(elem!1), s(s(s(elem!1))))) | (~r(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~r(s(s(s(s(elem!1)))), s(elem!1)))) <=> ((~r(s(elem!1), s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), s(elem!1))) | (~r(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~r(s(s(s(s(elem!1)))), s(elem!1))))),
% 3.23/3.43 inference(rewrite,[status(thm)],[])).
% 3.23/3.43 tff(14502,plain,
% 3.23/3.43 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), s(elem!1))) | (~r(s(elem!1), s(s(s(elem!1))))) | (~r(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~r(s(s(s(s(elem!1)))), s(elem!1))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(elem!1), s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), s(elem!1))) | (~r(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~r(s(s(s(s(elem!1)))), s(elem!1)))))),
% 3.23/3.43 inference(monotonicity,[status(thm)],[14501])).
% 3.23/3.43 tff(14503,plain,
% 3.23/3.43 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), s(elem!1))) | (~r(s(elem!1), s(s(s(elem!1))))) | (~r(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~r(s(s(s(s(elem!1)))), s(elem!1))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(elem!1), s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), s(elem!1))) | (~r(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~r(s(s(s(s(elem!1)))), s(elem!1))))),
% 3.23/3.43 inference(transitivity,[status(thm)],[14502, 14500])).
% 3.23/3.43 tff(14504,plain,
% 3.23/3.43 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), s(elem!1))) | (~r(s(elem!1), s(s(s(elem!1))))) | (~r(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~r(s(s(s(s(elem!1)))), s(elem!1))))),
% 3.23/3.43 inference(quant_inst,[status(thm)],[])).
% 3.23/3.43 tff(14505,plain,
% 3.23/3.43 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(elem!1), s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), s(elem!1))) | (~r(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~r(s(s(s(s(elem!1)))), s(elem!1)))),
% 3.23/3.43 inference(modus_ponens,[status(thm)],[14504, 14503])).
% 3.23/3.43 tff(14506,plain,
% 3.23/3.43 ($false),
% 3.23/3.43 inference(unit_resolution,[status(thm)],[14505, 197, 14499, 14497, 14495, 14481])).
% 3.23/3.43 tff(14507,plain,((~(s(s(s(z))) = s(s(elem!1)))) | (s(s(s(s(elem!1)))) = s(s(s(elem!1)))) | (~b(s(s(s(elem!1))), s(z))) | (~r(s(z), z)) | (~b(z, s(s(elem!1)))) | (~r(s(z), s(s(elem!1)))) | (~r(z, s(z))) | (~r(s(s(s(elem!1))), s(s(z)))) | (~r(s(s(z)), s(s(s(elem!1))))) | (~b(s(s(z)), s(z))) | (~b(s(z), s(s(z)))) | (~r(s(s(elem!1)), s(z)))), inference(lemma,lemma(discharge,[]))).
% 3.23/3.43 tff(14508,plain,
% 3.23/3.43 (~(s(s(s(z))) = s(s(elem!1)))),
% 3.23/3.43 inference(unit_resolution,[status(thm)],[14507, 14459, 14407, 14334, 14425, 85, 323, 14457, 14418, 156, 14455, 14448])).
% 3.23/3.43 tff(14509,plain,
% 3.23/3.43 ($false),
% 3.23/3.43 inference(unit_resolution,[status(thm)],[4523, 79, 8907, 5534, 5536])).
% 3.23/3.43 tff(14510,plain,(b(s(s(s(z))), s(s(elem!1))) | (s(s(s(z))) = s(s(elem!1))) | r(s(s(s(z))), s(s(elem!1)))), inference(lemma,lemma(discharge,[]))).
% 3.23/3.43 tff(14511,plain,
% 3.23/3.43 (b(s(s(s(z))), s(s(elem!1)))),
% 3.23/3.43 inference(unit_resolution,[status(thm)],[14510, 14508, 14453])).
% 3.23/3.43 tff(14512,plain,
% 3.23/3.43 (~(s(s(s(elem!1))) = s(s(elem!1)))),
% 3.23/3.43 inference(unit_resolution,[status(thm)],[50, 14416])).
% 3.23/3.43 tff(14513,plain,
% 3.23/3.43 (~r(s(s(s(elem!1))), s(s(elem!1)))),
% 3.23/3.43 inference(unit_resolution,[status(thm)],[9441, 14447, 14448, 14457])).
% 3.23/3.43 tff(14514,plain,
% 3.23/3.43 (b(s(s(s(elem!1))), s(s(elem!1)))),
% 3.23/3.43 inference(unit_resolution,[status(thm)],[889, 14513, 14512])).
% 3.23/3.43 tff(14515,plain,
% 3.23/3.43 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(s(s(elem!1))), s(s(s(z))))) | (~b(s(s(s(z))), s(s(elem!1)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(s(s(elem!1))), s(s(s(z))))) | (~b(s(s(s(z))), s(s(elem!1)))))),
% 3.23/3.43 inference(rewrite,[status(thm)],[])).
% 3.23/3.43 tff(14516,plain,
% 3.23/3.43 (((~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(s(s(s(z))), s(s(elem!1)))) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(s(s(elem!1))), s(s(s(z)))))) <=> ((~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(s(s(elem!1))), s(s(s(z))))) | (~b(s(s(s(z))), s(s(elem!1)))))),
% 3.23/3.43 inference(rewrite,[status(thm)],[])).
% 3.23/3.43 tff(14517,plain,
% 3.23/3.43 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(s(s(s(z))), s(s(elem!1)))) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(s(s(elem!1))), s(s(s(z))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(s(s(elem!1))), s(s(s(z))))) | (~b(s(s(s(z))), s(s(elem!1))))))),
% 3.23/3.43 inference(monotonicity,[status(thm)],[14516])).
% 3.23/3.43 tff(14518,plain,
% 3.23/3.43 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(s(s(s(z))), s(s(elem!1)))) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(s(s(elem!1))), s(s(s(z))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(s(s(elem!1))), s(s(s(z))))) | (~b(s(s(s(z))), s(s(elem!1)))))),
% 3.23/3.43 inference(transitivity,[status(thm)],[14517, 14515])).
% 3.23/3.43 tff(14519,plain,
% 3.23/3.43 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(s(s(s(z))), s(s(elem!1)))) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(s(s(elem!1))), s(s(s(z))))))),
% 3.23/3.43 inference(quant_inst,[status(thm)],[])).
% 3.23/3.43 tff(14520,plain,
% 3.23/3.43 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(s(s(elem!1))), s(s(s(z))))) | (~b(s(s(s(z))), s(s(elem!1))))),
% 3.23/3.43 inference(modus_ponens,[status(thm)],[14519, 14518])).
% 3.23/3.43 tff(14521,plain,
% 3.23/3.43 (~b(s(s(s(elem!1))), s(s(s(z))))),
% 3.23/3.43 inference(unit_resolution,[status(thm)],[14520, 166, 14445, 14514, 14511])).
% 3.23/3.43 tff(14522,plain,
% 3.23/3.43 (r(s(s(s(elem!1))), s(s(s(z))))),
% 3.23/3.43 inference(unit_resolution,[status(thm)],[3574, 14521, 140])).
% 3.23/3.43 tff(14523,plain,
% 3.23/3.43 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(z, s(s(elem!1)))) | (~b(s(s(s(z))), z)) | (~b(s(s(s(z))), s(s(elem!1)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(z, s(s(elem!1)))) | (~b(s(s(s(z))), z)) | (~b(s(s(s(z))), s(s(elem!1)))))),
% 3.23/3.43 inference(rewrite,[status(thm)],[])).
% 3.23/3.43 tff(14524,plain,
% 3.23/3.43 (((~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(s(s(z))), s(s(elem!1)))) | (~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(z, s(s(elem!1)))) | (~b(s(s(s(z))), s(s(elem!1)))) | (~b(s(s(s(z))), z))) <=> ((~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(z, s(s(elem!1)))) | (~b(s(s(s(z))), z)) | (~b(s(s(s(z))), s(s(elem!1)))))),
% 3.23/3.43 inference(rewrite,[status(thm)],[])).
% 3.23/3.43 tff(14525,plain,
% 3.23/3.43 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(s(s(z))), s(s(elem!1)))) | (~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(z, s(s(elem!1)))) | (~b(s(s(s(z))), s(s(elem!1)))) | (~b(s(s(s(z))), z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(z, s(s(elem!1)))) | (~b(s(s(s(z))), z)) | (~b(s(s(s(z))), s(s(elem!1))))))),
% 3.23/3.43 inference(monotonicity,[status(thm)],[14524])).
% 3.23/3.43 tff(14526,plain,
% 3.23/3.43 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(s(s(z))), s(s(elem!1)))) | (~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(z, s(s(elem!1)))) | (~b(s(s(s(z))), s(s(elem!1)))) | (~b(s(s(s(z))), z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(z, s(s(elem!1)))) | (~b(s(s(s(z))), z)) | (~b(s(s(s(z))), s(s(elem!1)))))),
% 3.23/3.43 inference(transitivity,[status(thm)],[14525, 14523])).
% 3.23/3.43 tff(14527,plain,
% 3.23/3.43 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(s(s(z))), s(s(elem!1)))) | (~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(z, s(s(elem!1)))) | (~b(s(s(s(z))), s(s(elem!1)))) | (~b(s(s(s(z))), z)))),
% 3.23/3.43 inference(quant_inst,[status(thm)],[])).
% 3.23/3.43 tff(14528,plain,
% 3.23/3.43 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(z, s(s(elem!1)))) | (~b(s(s(s(z))), z)) | (~b(s(s(s(z))), s(s(elem!1))))),
% 3.23/3.44 inference(modus_ponens,[status(thm)],[14527, 14526])).
% 3.23/3.44 tff(14529,plain,
% 3.23/3.44 (~b(s(s(s(z))), z)),
% 3.23/3.44 inference(unit_resolution,[status(thm)],[14528, 166, 14445, 14514, 14425, 14511])).
% 3.23/3.44 tff(14530,plain,
% 3.23/3.44 (r(s(s(s(z))), z)),
% 3.23/3.44 inference(unit_resolution,[status(thm)],[1713, 14529])).
% 3.23/3.44 tff(14531,plain,
% 3.23/3.44 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(z, s(s(elem!1)))) | (~b(z, s(s(s(z))))) | (~b(s(s(s(z))), s(s(elem!1)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(z, s(s(elem!1)))) | (~b(z, s(s(s(z))))) | (~b(s(s(s(z))), s(s(elem!1)))))),
% 3.23/3.44 inference(rewrite,[status(thm)],[])).
% 3.23/3.44 tff(14532,plain,
% 3.23/3.44 (((~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(z, s(s(elem!1)))) | (~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(s(s(s(z))), s(s(elem!1)))) | (~b(z, s(s(elem!1)))) | (~b(z, s(s(s(z)))))) <=> ((~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(z, s(s(elem!1)))) | (~b(z, s(s(s(z))))) | (~b(s(s(s(z))), s(s(elem!1)))))),
% 3.23/3.44 inference(rewrite,[status(thm)],[])).
% 3.23/3.44 tff(14533,plain,
% 3.23/3.44 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(z, s(s(elem!1)))) | (~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(s(s(s(z))), s(s(elem!1)))) | (~b(z, s(s(elem!1)))) | (~b(z, s(s(s(z))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(z, s(s(elem!1)))) | (~b(z, s(s(s(z))))) | (~b(s(s(s(z))), s(s(elem!1))))))),
% 3.23/3.44 inference(monotonicity,[status(thm)],[14532])).
% 3.23/3.44 tff(14534,plain,
% 3.23/3.44 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(z, s(s(elem!1)))) | (~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(s(s(s(z))), s(s(elem!1)))) | (~b(z, s(s(elem!1)))) | (~b(z, s(s(s(z))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(z, s(s(elem!1)))) | (~b(z, s(s(s(z))))) | (~b(s(s(s(z))), s(s(elem!1)))))),
% 3.23/3.44 inference(transitivity,[status(thm)],[14533, 14531])).
% 3.23/3.44 tff(14535,plain,
% 3.23/3.44 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(z, s(s(elem!1)))) | (~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(s(s(s(z))), s(s(elem!1)))) | (~b(z, s(s(elem!1)))) | (~b(z, s(s(s(z))))))),
% 3.23/3.44 inference(quant_inst,[status(thm)],[])).
% 3.23/3.44 tff(14536,plain,
% 3.23/3.44 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(z, s(s(elem!1)))) | (~b(z, s(s(s(z))))) | (~b(s(s(s(z))), s(s(elem!1))))),
% 3.23/3.44 inference(modus_ponens,[status(thm)],[14535, 14534])).
% 3.23/3.44 tff(14537,plain,
% 3.23/3.44 (~b(z, s(s(s(z))))),
% 3.23/3.44 inference(unit_resolution,[status(thm)],[14536, 166, 14445, 14514, 14425, 14511])).
% 3.23/3.44 tff(14538,plain,
% 3.23/3.44 (r(z, s(s(s(z))))),
% 3.23/3.44 inference(unit_resolution,[status(thm)],[1697, 14537])).
% 3.23/3.44 tff(14539,plain,
% 3.23/3.44 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), z)) | (~r(s(s(s(elem!1))), s(s(s(z))))) | (~r(z, s(s(s(z))))) | (~r(s(s(s(z))), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(elem!1))), z)) | (~r(s(s(s(elem!1))), s(s(s(z))))) | (~r(z, s(s(s(z))))) | (~r(s(s(s(z))), z)))),
% 3.23/3.44 inference(rewrite,[status(thm)],[])).
% 3.23/3.44 tff(14540,plain,
% 3.23/3.44 (((~r(z, s(s(s(z))))) | (~r(s(s(s(z))), z)) | (~r(s(s(s(elem!1))), z)) | (~r(s(s(s(elem!1))), s(s(s(z)))))) <=> ((~r(s(s(s(elem!1))), z)) | (~r(s(s(s(elem!1))), s(s(s(z))))) | (~r(z, s(s(s(z))))) | (~r(s(s(s(z))), z)))),
% 3.23/3.44 inference(rewrite,[status(thm)],[])).
% 3.23/3.44 tff(14541,plain,
% 3.23/3.44 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(s(z))))) | (~r(s(s(s(z))), z)) | (~r(s(s(s(elem!1))), z)) | (~r(s(s(s(elem!1))), s(s(s(z))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), z)) | (~r(s(s(s(elem!1))), s(s(s(z))))) | (~r(z, s(s(s(z))))) | (~r(s(s(s(z))), z))))),
% 3.23/3.44 inference(monotonicity,[status(thm)],[14540])).
% 3.23/3.44 tff(14542,plain,
% 3.23/3.44 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(s(z))))) | (~r(s(s(s(z))), z)) | (~r(s(s(s(elem!1))), z)) | (~r(s(s(s(elem!1))), s(s(s(z))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(elem!1))), z)) | (~r(s(s(s(elem!1))), s(s(s(z))))) | (~r(z, s(s(s(z))))) | (~r(s(s(s(z))), z)))),
% 3.23/3.44 inference(transitivity,[status(thm)],[14541, 14539])).
% 3.23/3.44 tff(14543,plain,
% 3.23/3.44 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(s(z))))) | (~r(s(s(s(z))), z)) | (~r(s(s(s(elem!1))), z)) | (~r(s(s(s(elem!1))), s(s(s(z))))))),
% 3.23/3.44 inference(quant_inst,[status(thm)],[])).
% 3.23/3.44 tff(14544,plain,
% 3.23/3.44 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(elem!1))), z)) | (~r(s(s(s(elem!1))), s(s(s(z))))) | (~r(z, s(s(s(z))))) | (~r(s(s(s(z))), z))),
% 3.23/3.44 inference(modus_ponens,[status(thm)],[14543, 14542])).
% 3.23/3.44 tff(14545,plain,
% 3.23/3.44 ($false),
% 3.23/3.44 inference(unit_resolution,[status(thm)],[14544, 197, 13084, 14538, 14530, 14522])).
% 3.23/3.44 tff(14546,plain,((~r(z, s(z))) | (~b(s(s(z)), s(z))) | (s(s(z)) = s(s(elem!1))) | b(s(z), s(s(elem!1)))), inference(lemma,lemma(discharge,[]))).
% 3.23/3.44 tff(14547,plain,
% 3.23/3.44 (~r(z, s(z))),
% 3.23/3.44 inference(unit_resolution,[status(thm)],[14546, 52, 156, 54])).
% 3.23/3.44 tff(14548,plain,
% 3.23/3.44 (b(z, s(z))),
% 3.23/3.44 inference(unit_resolution,[status(thm)],[321, 14547])).
% 3.23/3.44 tff(14549,plain,
% 3.23/3.44 (~b(s(z), s(s(s(elem!1))))),
% 3.23/3.44 inference(unit_resolution,[status(thm)],[12629, 14548, 156, 14407])).
% 3.23/3.44 tff(14550,plain,
% 3.23/3.44 (r(s(z), s(s(s(elem!1))))),
% 3.23/3.44 inference(unit_resolution,[status(thm)],[116, 14549])).
% 3.23/3.44 tff(14551,plain,
% 3.23/3.44 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), z)) | (~r(z, s(s(elem!1)))) | (~r(s(z), z)) | (~r(s(z), s(s(s(elem!1))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(elem!1))), z)) | (~r(z, s(s(elem!1)))) | (~r(s(z), z)) | (~r(s(z), s(s(s(elem!1))))))),
% 3.23/3.44 inference(rewrite,[status(thm)],[])).
% 3.23/3.44 tff(14552,plain,
% 3.23/3.44 (((~r(z, s(s(elem!1)))) | (~r(s(s(s(elem!1))), z)) | (~r(s(z), z)) | (~r(s(z), s(s(s(elem!1)))))) <=> ((~r(s(s(s(elem!1))), z)) | (~r(z, s(s(elem!1)))) | (~r(s(z), z)) | (~r(s(z), s(s(s(elem!1))))))),
% 3.23/3.44 inference(rewrite,[status(thm)],[])).
% 3.23/3.44 tff(14553,plain,
% 3.23/3.44 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(elem!1)))) | (~r(s(s(s(elem!1))), z)) | (~r(s(z), z)) | (~r(s(z), s(s(s(elem!1))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), z)) | (~r(z, s(s(elem!1)))) | (~r(s(z), z)) | (~r(s(z), s(s(s(elem!1)))))))),
% 3.23/3.44 inference(monotonicity,[status(thm)],[14552])).
% 3.23/3.44 tff(14554,plain,
% 3.23/3.44 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(elem!1)))) | (~r(s(s(s(elem!1))), z)) | (~r(s(z), z)) | (~r(s(z), s(s(s(elem!1))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(elem!1))), z)) | (~r(z, s(s(elem!1)))) | (~r(s(z), z)) | (~r(s(z), s(s(s(elem!1))))))),
% 3.23/3.44 inference(transitivity,[status(thm)],[14553, 14551])).
% 3.23/3.44 tff(14555,plain,
% 3.23/3.44 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(elem!1)))) | (~r(s(s(s(elem!1))), z)) | (~r(s(z), z)) | (~r(s(z), s(s(s(elem!1))))))),
% 3.23/3.44 inference(quant_inst,[status(thm)],[])).
% 3.23/3.44 tff(14556,plain,
% 3.23/3.44 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(elem!1))), z)) | (~r(z, s(s(elem!1)))) | (~r(s(z), z)) | (~r(s(z), s(s(s(elem!1)))))),
% 3.23/3.44 inference(modus_ponens,[status(thm)],[14555, 14554])).
% 3.23/3.44 tff(14557,plain,
% 3.23/3.44 ($false),
% 3.23/3.44 inference(unit_resolution,[status(thm)],[14556, 197, 154, 97, 365, 119])).
% 3.23/3.44 tff(14558,plain,((~r(z, s(s(elem!1)))) | (~r(s(s(s(elem!1))), z)) | (~r(s(z), z)) | (~r(s(z), s(s(s(elem!1)))))), inference(lemma,lemma(discharge,[]))).
% 3.23/3.44 tff(14559,plain,
% 3.23/3.44 (~r(z, s(s(elem!1)))),
% 3.23/3.44 inference(unit_resolution,[status(thm)],[14558, 14550, 14334, 13084])).
% 3.23/3.44 tff(14560,plain,
% 3.23/3.44 (b(z, s(s(elem!1)))),
% 3.23/3.44 inference(unit_resolution,[status(thm)],[1795, 14559])).
% 3.23/3.44 tff(14561,plain,
% 3.23/3.44 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), z)) | (~r(s(z), s(s(elem!1)))) | (~r(s(z), s(s(s(elem!1))))) | (~r(s(s(elem!1)), s(s(s(elem!1))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(elem!1))), z)) | (~r(s(z), s(s(elem!1)))) | (~r(s(z), s(s(s(elem!1))))) | (~r(s(s(elem!1)), s(s(s(elem!1))))))),
% 3.23/3.44 inference(rewrite,[status(thm)],[])).
% 3.23/3.44 tff(14562,plain,
% 3.23/3.44 (((~r(s(s(s(elem!1))), z)) | (~r(s(s(elem!1)), s(s(s(elem!1))))) | (~r(s(z), s(s(s(elem!1))))) | (~r(s(z), s(s(elem!1))))) <=> ((~r(s(s(s(elem!1))), z)) | (~r(s(z), s(s(elem!1)))) | (~r(s(z), s(s(s(elem!1))))) | (~r(s(s(elem!1)), s(s(s(elem!1))))))),
% 3.23/3.44 inference(rewrite,[status(thm)],[])).
% 3.23/3.44 tff(14563,plain,
% 3.23/3.44 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), z)) | (~r(s(s(elem!1)), s(s(s(elem!1))))) | (~r(s(z), s(s(s(elem!1))))) | (~r(s(z), s(s(elem!1)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), z)) | (~r(s(z), s(s(elem!1)))) | (~r(s(z), s(s(s(elem!1))))) | (~r(s(s(elem!1)), s(s(s(elem!1)))))))),
% 3.23/3.44 inference(monotonicity,[status(thm)],[14562])).
% 3.23/3.44 tff(14564,plain,
% 3.23/3.44 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), z)) | (~r(s(s(elem!1)), s(s(s(elem!1))))) | (~r(s(z), s(s(s(elem!1))))) | (~r(s(z), s(s(elem!1)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(elem!1))), z)) | (~r(s(z), s(s(elem!1)))) | (~r(s(z), s(s(s(elem!1))))) | (~r(s(s(elem!1)), s(s(s(elem!1))))))),
% 3.23/3.44 inference(transitivity,[status(thm)],[14563, 14561])).
% 3.23/3.44 tff(14565,plain,
% 3.23/3.44 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), z)) | (~r(s(s(elem!1)), s(s(s(elem!1))))) | (~r(s(z), s(s(s(elem!1))))) | (~r(s(z), s(s(elem!1)))))),
% 3.23/3.44 inference(quant_inst,[status(thm)],[])).
% 3.23/3.44 tff(14566,plain,
% 3.23/3.44 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(elem!1))), z)) | (~r(s(z), s(s(elem!1)))) | (~r(s(z), s(s(s(elem!1))))) | (~r(s(s(elem!1)), s(s(s(elem!1)))))),
% 3.23/3.44 inference(modus_ponens,[status(thm)],[14565, 14564])).
% 3.23/3.44 tff(14567,plain,
% 3.23/3.44 ($false),
% 3.23/3.44 inference(unit_resolution,[status(thm)],[14566, 197, 311, 154, 377, 119])).
% 3.23/3.44 tff(14568,plain,((~r(s(s(elem!1)), s(s(s(elem!1))))) | (~r(s(z), s(s(elem!1)))) | (~r(s(s(s(elem!1))), z)) | (~r(s(z), s(s(s(elem!1)))))), inference(lemma,lemma(discharge,[]))).
% 3.23/3.44 tff(14569,plain,
% 3.23/3.44 (~r(s(s(elem!1)), s(s(s(elem!1))))),
% 3.23/3.44 inference(unit_resolution,[status(thm)],[14568, 14550, 13084, 85])).
% 3.23/3.44 tff(14570,plain,
% 3.23/3.44 (~b(s(z), s(s(z)))),
% 3.23/3.44 inference(unit_resolution,[status(thm)],[14336, 14548, 156])).
% 3.23/3.44 tff(14571,plain,
% 3.23/3.44 (r(s(z), s(s(z)))),
% 3.23/3.44 inference(unit_resolution,[status(thm)],[427, 14570])).
% 3.23/3.44 tff(14572,plain,
% 3.23/3.44 (~r(s(s(z)), s(s(s(elem!1))))),
% 3.23/3.44 inference(unit_resolution,[status(thm)],[2304, 14550, 13084, 14571])).
% 3.23/3.44 tff(14573,plain,
% 3.23/3.44 (b(s(s(z)), s(s(s(elem!1))))),
% 3.23/3.44 inference(unit_resolution,[status(thm)],[279, 14572])).
% 3.23/3.44 tff(14574,plain,
% 3.23/3.44 (~b(s(s(elem!1)), s(s(z)))),
% 3.23/3.44 inference(unit_resolution,[status(thm)],[12004, 14560, 14407, 14573, 14548])).
% 3.23/3.44 tff(14575,plain,
% 3.23/3.44 (r(s(s(elem!1)), s(s(z)))),
% 3.23/3.44 inference(unit_resolution,[status(thm)],[441, 14574, 132])).
% 3.23/3.44 tff(14576,plain,
% 3.23/3.44 ($false),
% 3.23/3.44 inference(unit_resolution,[status(thm)],[13481, 197, 311, 393, 905, 119])).
% 3.23/3.44 tff(14577,plain,((~r(s(s(s(elem!1))), s(s(elem!1)))) | (~r(s(z), s(s(elem!1)))) | (~r(s(s(elem!1)), s(s(z)))) | (~r(s(z), s(s(s(elem!1)))))), inference(lemma,lemma(discharge,[]))).
% 3.23/3.44 tff(14578,plain,
% 3.23/3.44 (~r(s(s(s(elem!1))), s(s(elem!1)))),
% 3.23/3.44 inference(unit_resolution,[status(thm)],[14577, 14575, 85, 14550])).
% 3.23/3.44 tff(14579,plain,
% 3.23/3.44 (s(s(elem!1)) = s(s(s(elem!1)))),
% 3.23/3.44 inference(unit_resolution,[status(thm)],[12051, 14578, 14334, 14550, 14569, 14560])).
% 3.23/3.44 tff(14580,plain,
% 3.23/3.44 (s(s(s(elem!1))) = s(s(elem!1))),
% 3.23/3.44 inference(symmetry,[status(thm)],[14579])).
% 3.23/3.44 tff(14581,plain,
% 3.23/3.44 ((s(s(s(elem!1))) = s(s(s(z)))) <=> (s(s(elem!1)) = s(s(s(z))))),
% 3.23/3.44 inference(monotonicity,[status(thm)],[14580])).
% 3.23/3.44 tff(14582,plain,
% 3.23/3.44 ((s(s(s(elem!1))) = s(s(s(z)))) <=> (s(s(s(z))) = s(s(elem!1)))),
% 3.23/3.44 inference(transitivity,[status(thm)],[14581, 4437])).
% 3.23/3.44 tff(14583,plain,
% 3.23/3.44 ((~(s(s(s(elem!1))) = s(s(s(z))))) <=> (~(s(s(s(z))) = s(s(elem!1))))),
% 3.23/3.44 inference(monotonicity,[status(thm)],[14582])).
% 3.23/3.44 tff(14584,plain,
% 3.23/3.44 (~(s(s(s(z))) = s(s(elem!1)))),
% 3.23/3.44 inference(modus_ponens,[status(thm)],[140, 14583])).
% 3.23/3.44 tff(14585,plain,
% 3.23/3.44 (r(s(s(s(z))), s(s(s(elem!1)))) <=> r(s(s(s(z))), s(s(elem!1)))),
% 3.23/3.44 inference(monotonicity,[status(thm)],[14580])).
% 3.23/3.44 tff(14586,plain,
% 3.23/3.44 ((~r(s(s(s(z))), s(s(s(elem!1))))) <=> (~r(s(s(s(z))), s(s(elem!1))))),
% 3.23/3.44 inference(monotonicity,[status(thm)],[14585])).
% 3.23/3.44 tff(14587,plain,
% 3.23/3.44 (r(s(s(elem!1)), s(s(z))) <=> r(s(s(s(elem!1))), s(s(z)))),
% 3.23/3.44 inference(monotonicity,[status(thm)],[14579])).
% 3.23/3.44 tff(14588,plain,
% 3.23/3.44 (r(s(s(s(elem!1))), s(s(z)))),
% 3.23/3.44 inference(modus_ponens,[status(thm)],[14575, 14587])).
% 3.23/3.44 tff(14589,plain,
% 3.23/3.44 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(s(s(elem!1))))) | (~r(s(z), s(s(z)))) | (~r(s(s(s(elem!1))), s(s(z)))) | (~r(s(s(z)), s(s(s(z))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(z), s(s(s(elem!1))))) | (~r(s(z), s(s(z)))) | (~r(s(s(s(elem!1))), s(s(z)))) | (~r(s(s(z)), s(s(s(z))))))),
% 3.23/3.44 inference(rewrite,[status(thm)],[])).
% 3.23/3.44 tff(14590,plain,
% 3.23/3.44 (((~r(s(s(z)), s(s(s(z))))) | (~r(s(s(s(elem!1))), s(s(z)))) | (~r(s(z), s(s(z)))) | (~r(s(z), s(s(s(elem!1)))))) <=> ((~r(s(z), s(s(s(elem!1))))) | (~r(s(z), s(s(z)))) | (~r(s(s(s(elem!1))), s(s(z)))) | (~r(s(s(z)), s(s(s(z))))))),
% 3.23/3.44 inference(rewrite,[status(thm)],[])).
% 3.23/3.44 tff(14591,plain,
% 3.23/3.44 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(z)), s(s(s(z))))) | (~r(s(s(s(elem!1))), s(s(z)))) | (~r(s(z), s(s(z)))) | (~r(s(z), s(s(s(elem!1))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(s(s(elem!1))))) | (~r(s(z), s(s(z)))) | (~r(s(s(s(elem!1))), s(s(z)))) | (~r(s(s(z)), s(s(s(z)))))))),
% 3.23/3.44 inference(monotonicity,[status(thm)],[14590])).
% 3.23/3.44 tff(14592,plain,
% 3.23/3.44 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(z)), s(s(s(z))))) | (~r(s(s(s(elem!1))), s(s(z)))) | (~r(s(z), s(s(z)))) | (~r(s(z), s(s(s(elem!1))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(z), s(s(s(elem!1))))) | (~r(s(z), s(s(z)))) | (~r(s(s(s(elem!1))), s(s(z)))) | (~r(s(s(z)), s(s(s(z))))))),
% 3.23/3.44 inference(transitivity,[status(thm)],[14591, 14589])).
% 3.23/3.44 tff(14593,plain,
% 3.23/3.44 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(z)), s(s(s(z))))) | (~r(s(s(s(elem!1))), s(s(z)))) | (~r(s(z), s(s(z)))) | (~r(s(z), s(s(s(elem!1))))))),
% 3.23/3.44 inference(quant_inst,[status(thm)],[])).
% 3.23/3.44 tff(14594,plain,
% 3.23/3.44 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(z), s(s(s(elem!1))))) | (~r(s(z), s(s(z)))) | (~r(s(s(s(elem!1))), s(s(z)))) | (~r(s(s(z)), s(s(s(z)))))),
% 3.23/3.44 inference(modus_ponens,[status(thm)],[14593, 14592])).
% 3.23/3.44 tff(14595,plain,
% 3.23/3.44 ($false),
% 3.23/3.44 inference(unit_resolution,[status(thm)],[14594, 197, 120, 119, 464, 1732])).
% 3.23/3.44 tff(14596,plain,((~r(s(s(z)), s(s(s(z))))) | (~r(s(z), s(s(z)))) | (~r(s(z), s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), s(s(z))))), inference(lemma,lemma(discharge,[]))).
% 3.23/3.44 tff(14597,plain,
% 3.23/3.44 (~r(s(s(z)), s(s(s(z))))),
% 3.23/3.44 inference(unit_resolution,[status(thm)],[14596, 14571, 14550, 14588])).
% 3.23/3.44 tff(14598,plain,
% 3.23/3.44 (b(s(s(z)), s(s(s(z))))),
% 3.23/3.44 inference(unit_resolution,[status(thm)],[1730, 14597])).
% 3.23/3.44 tff(14599,assumption,(r(s(s(s(z))), s(s(s(elem!1))))), introduced(assumption)).
% 3.23/3.44 tff(14600,plain,
% 3.23/3.44 ((~r(s(s(s(z))), s(s(s(elem!1))))) | (~r(s(s(s(z))), s(z)))),
% 3.23/3.44 inference(unit_resolution,[status(thm)],[4090, 197, 154, 119])).
% 3.23/3.44 tff(14601,plain,
% 3.23/3.44 (~r(s(s(s(z))), s(z))),
% 3.23/3.44 inference(unit_resolution,[status(thm)],[14600, 14599])).
% 3.23/3.44 tff(14602,plain,
% 3.23/3.44 (b(s(s(s(z))), s(z))),
% 3.23/3.44 inference(unit_resolution,[status(thm)],[1763, 14601])).
% 3.23/3.44 tff(14603,plain,
% 3.23/3.44 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(z))), s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), z)) | (~r(s(z), s(s(s(elem!1))))) | (~r(s(z), s(s(s(z))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(z))), s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), z)) | (~r(s(z), s(s(s(elem!1))))) | (~r(s(z), s(s(s(z))))))),
% 3.23/3.44 inference(rewrite,[status(thm)],[])).
% 3.23/3.44 tff(14604,plain,
% 3.23/3.44 (((~r(s(s(s(elem!1))), z)) | (~r(s(s(s(z))), s(s(s(elem!1))))) | (~r(s(z), s(s(s(elem!1))))) | (~r(s(z), s(s(s(z)))))) <=> ((~r(s(s(s(z))), s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), z)) | (~r(s(z), s(s(s(elem!1))))) | (~r(s(z), s(s(s(z))))))),
% 3.23/3.44 inference(rewrite,[status(thm)],[])).
% 3.23/3.44 tff(14605,plain,
% 3.23/3.44 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), z)) | (~r(s(s(s(z))), s(s(s(elem!1))))) | (~r(s(z), s(s(s(elem!1))))) | (~r(s(z), s(s(s(z))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(z))), s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), z)) | (~r(s(z), s(s(s(elem!1))))) | (~r(s(z), s(s(s(z)))))))),
% 3.23/3.44 inference(monotonicity,[status(thm)],[14604])).
% 3.23/3.44 tff(14606,plain,
% 3.23/3.44 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), z)) | (~r(s(s(s(z))), s(s(s(elem!1))))) | (~r(s(z), s(s(s(elem!1))))) | (~r(s(z), s(s(s(z))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(z))), s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), z)) | (~r(s(z), s(s(s(elem!1))))) | (~r(s(z), s(s(s(z))))))),
% 3.23/3.44 inference(transitivity,[status(thm)],[14605, 14603])).
% 3.23/3.44 tff(14607,plain,
% 3.23/3.44 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), z)) | (~r(s(s(s(z))), s(s(s(elem!1))))) | (~r(s(z), s(s(s(elem!1))))) | (~r(s(z), s(s(s(z))))))),
% 3.23/3.44 inference(quant_inst,[status(thm)],[])).
% 3.23/3.44 tff(14608,plain,
% 3.23/3.44 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(z))), s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), z)) | (~r(s(z), s(s(s(elem!1))))) | (~r(s(z), s(s(s(z)))))),
% 3.23/3.45 inference(modus_ponens,[status(thm)],[14607, 14606])).
% 3.23/3.45 tff(14609,plain,
% 3.23/3.45 ((~r(s(s(s(z))), s(s(s(elem!1))))) | (~r(s(z), s(s(s(z)))))),
% 3.23/3.45 inference(unit_resolution,[status(thm)],[14608, 197, 154, 119])).
% 3.23/3.45 tff(14610,plain,
% 3.23/3.45 (~r(s(z), s(s(s(z))))),
% 3.23/3.45 inference(unit_resolution,[status(thm)],[14609, 14599])).
% 3.23/3.45 tff(14611,plain,
% 3.23/3.45 (b(s(z), s(s(s(z))))),
% 3.23/3.45 inference(unit_resolution,[status(thm)],[1674, 14610])).
% 3.23/3.45 tff(14612,plain,
% 3.23/3.45 ($false),
% 3.23/3.45 inference(unit_resolution,[status(thm)],[3248, 14611, 14602, 156, 986])).
% 3.23/3.45 tff(14613,plain,((~r(s(s(s(z))), s(s(s(elem!1))))) | (~b(s(s(z)), s(z))) | (~b(s(s(z)), s(s(s(z))))) | (~r(s(s(s(elem!1))), z)) | (~r(s(z), s(s(s(elem!1)))))), inference(lemma,lemma(discharge,[]))).
% 3.23/3.45 tff(14614,plain,
% 3.23/3.45 (~r(s(s(s(z))), s(s(s(elem!1))))),
% 3.23/3.45 inference(unit_resolution,[status(thm)],[14613, 14598, 156, 13084, 14550])).
% 3.23/3.45 tff(14615,plain,
% 3.23/3.45 (~r(s(s(s(z))), s(s(elem!1)))),
% 3.23/3.45 inference(modus_ponens,[status(thm)],[14614, 14586])).
% 3.23/3.45 tff(14616,plain,
% 3.23/3.45 (b(s(s(s(z))), s(s(elem!1)))),
% 3.23/3.45 inference(unit_resolution,[status(thm)],[14510, 14615, 14584])).
% 3.23/3.45 tff(14617,plain,
% 3.23/3.45 ((~b(s(z), s(s(s(z))))) | (~b(z, s(s(elem!1)))) | (~b(z, s(z))) | (~b(s(s(z)), s(z))) | (~b(s(s(s(z))), s(s(elem!1))))),
% 3.23/3.45 inference(unit_resolution,[status(thm)],[10866, 10450])).
% 3.23/3.45 tff(14618,plain,
% 3.23/3.45 (~b(s(z), s(s(s(z))))),
% 3.23/3.45 inference(unit_resolution,[status(thm)],[14617, 14616, 156, 14548, 14560])).
% 3.23/3.45 tff(14619,plain,
% 3.23/3.45 (r(s(z), s(s(s(z))))),
% 3.23/3.45 inference(unit_resolution,[status(thm)],[1674, 14618])).
% 3.23/3.45 tff(14620,plain,
% 3.23/3.45 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(s(s(elem!1))))) | (~r(s(z), s(s(z)))) | (~r(s(s(z)), z)) | (~r(s(s(s(elem!1))), s(s(z)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(z), s(s(s(elem!1))))) | (~r(s(z), s(s(z)))) | (~r(s(s(z)), z)) | (~r(s(s(s(elem!1))), s(s(z)))))),
% 3.23/3.45 inference(rewrite,[status(thm)],[])).
% 3.23/3.45 tff(14621,plain,
% 3.23/3.45 (((~r(s(s(z)), z)) | (~r(s(s(s(elem!1))), s(s(z)))) | (~r(s(z), s(s(z)))) | (~r(s(z), s(s(s(elem!1)))))) <=> ((~r(s(z), s(s(s(elem!1))))) | (~r(s(z), s(s(z)))) | (~r(s(s(z)), z)) | (~r(s(s(s(elem!1))), s(s(z)))))),
% 3.23/3.45 inference(rewrite,[status(thm)],[])).
% 3.23/3.45 tff(14622,plain,
% 3.23/3.45 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(z)), z)) | (~r(s(s(s(elem!1))), s(s(z)))) | (~r(s(z), s(s(z)))) | (~r(s(z), s(s(s(elem!1))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(s(s(elem!1))))) | (~r(s(z), s(s(z)))) | (~r(s(s(z)), z)) | (~r(s(s(s(elem!1))), s(s(z))))))),
% 3.23/3.45 inference(monotonicity,[status(thm)],[14621])).
% 3.23/3.45 tff(14623,plain,
% 3.23/3.45 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(z)), z)) | (~r(s(s(s(elem!1))), s(s(z)))) | (~r(s(z), s(s(z)))) | (~r(s(z), s(s(s(elem!1))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(z), s(s(s(elem!1))))) | (~r(s(z), s(s(z)))) | (~r(s(s(z)), z)) | (~r(s(s(s(elem!1))), s(s(z)))))),
% 3.23/3.45 inference(transitivity,[status(thm)],[14622, 14620])).
% 3.23/3.45 tff(14624,plain,
% 3.23/3.45 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(z)), z)) | (~r(s(s(s(elem!1))), s(s(z)))) | (~r(s(z), s(s(z)))) | (~r(s(z), s(s(s(elem!1))))))),
% 3.23/3.45 inference(quant_inst,[status(thm)],[])).
% 3.23/3.45 tff(14625,plain,
% 3.23/3.45 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(z), s(s(s(elem!1))))) | (~r(s(z), s(s(z)))) | (~r(s(s(z)), z)) | (~r(s(s(s(elem!1))), s(s(z))))),
% 3.23/3.45 inference(modus_ponens,[status(thm)],[14624, 14623])).
% 3.23/3.45 tff(14626,plain,
% 3.23/3.45 ($false),
% 3.23/3.45 inference(unit_resolution,[status(thm)],[14625, 197, 120, 119, 866, 464])).
% 3.23/3.45 tff(14627,plain,((~r(s(s(z)), z)) | (~r(s(z), s(s(z)))) | (~r(s(z), s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), s(s(z))))), inference(lemma,lemma(discharge,[]))).
% 3.23/3.45 tff(14628,plain,
% 3.23/3.45 (~r(s(s(z)), z)),
% 3.23/3.45 inference(unit_resolution,[status(thm)],[14627, 14571, 14550, 14588])).
% 3.23/3.45 tff(14629,plain,
% 3.23/3.45 (b(s(s(z)), z)),
% 3.23/3.45 inference(unit_resolution,[status(thm)],[186, 14628])).
% 3.23/3.45 tff(14630,plain,
% 3.23/3.45 (~r(s(s(z)), s(s(elem!1)))),
% 3.23/3.45 inference(unit_resolution,[status(thm)],[338, 14579, 14572])).
% 3.23/3.45 tff(14631,plain,
% 3.23/3.45 (b(s(s(z)), s(s(elem!1)))),
% 3.23/3.45 inference(unit_resolution,[status(thm)],[390, 14630, 52])).
% 3.23/3.45 tff(14632,plain,
% 3.23/3.45 ((~b(s(s(s(z))), z)) | (~b(s(s(z)), s(s(elem!1)))) | (~b(s(s(z)), z)) | (~b(s(s(z)), s(s(s(z)))))),
% 3.23/3.45 inference(unit_resolution,[status(thm)],[10794, 10450])).
% 3.23/3.45 tff(14633,plain,
% 3.23/3.45 (~b(s(s(s(z))), z)),
% 3.23/3.45 inference(unit_resolution,[status(thm)],[14632, 14598, 14631, 14629])).
% 3.23/3.45 tff(14634,plain,
% 3.23/3.45 (r(s(s(s(z))), z)),
% 3.23/3.45 inference(unit_resolution,[status(thm)],[1713, 14633])).
% 3.23/3.45 tff(14635,plain,
% 3.23/3.45 (s(s(s(elem!1))) = s(s(elem!1))),
% 3.23/3.45 inference(unit_resolution,[status(thm)],[4030, 14579])).
% 3.23/3.45 tff(14636,plain,
% 3.23/3.45 (~(s(s(s(z))) = elem!1)),
% 3.23/3.45 inference(unit_resolution,[status(thm)],[3122, 14579])).
% 3.23/3.45 tff(14637,plain,
% 3.23/3.45 (s(s(s(elem!1))) = s(elem!1)),
% 3.23/3.45 inference(unit_resolution,[status(thm)],[2594, 14579])).
% 3.23/3.45 tff(14638,plain,
% 3.23/3.45 (s(elem!1) = s(s(s(elem!1)))),
% 3.23/3.45 inference(symmetry,[status(thm)],[14637])).
% 3.23/3.45 tff(14639,plain,
% 3.23/3.45 (inj_0(s(elem!1)) = inj_0(s(s(s(elem!1))))),
% 3.23/3.45 inference(monotonicity,[status(thm)],[14638])).
% 3.23/3.45 tff(14640,plain,
% 3.23/3.45 (elem!1 = s(s(elem!1))),
% 3.23/3.45 inference(transitivity,[status(thm)],[1170, 14639, 104])).
% 3.23/3.45 tff(14641,plain,
% 3.23/3.45 (r(s(s(s(z))), elem!1) <=> r(s(s(s(z))), s(s(elem!1)))),
% 3.23/3.45 inference(monotonicity,[status(thm)],[14640])).
% 3.23/3.45 tff(14642,plain,
% 3.23/3.45 (r(s(s(s(z))), s(s(elem!1))) <=> r(s(s(s(z))), elem!1)),
% 3.23/3.45 inference(symmetry,[status(thm)],[14641])).
% 3.23/3.45 tff(14643,plain,
% 3.23/3.45 (r(s(s(s(z))), s(s(s(elem!1)))) <=> r(s(s(s(z))), elem!1)),
% 3.23/3.45 inference(transitivity,[status(thm)],[14585, 14642])).
% 3.23/3.45 tff(14644,plain,
% 3.23/3.45 ((~r(s(s(s(z))), s(s(s(elem!1))))) <=> (~r(s(s(s(z))), elem!1))),
% 3.23/3.45 inference(monotonicity,[status(thm)],[14643])).
% 3.23/3.45 tff(14645,plain,
% 3.23/3.45 (~r(s(s(s(z))), elem!1)),
% 3.23/3.45 inference(modus_ponens,[status(thm)],[14614, 14644])).
% 3.23/3.45 tff(14646,plain,
% 3.23/3.45 (b(s(s(s(z))), elem!1)),
% 3.23/3.45 inference(unit_resolution,[status(thm)],[2826, 14645, 14636])).
% 3.23/3.45 tff(14647,plain,
% 3.23/3.45 (b(s(s(s(z))), s(s(s(elem!1))))),
% 3.23/3.45 inference(unit_resolution,[status(thm)],[4078, 14646, 14635])).
% 3.23/3.45 tff(14648,plain,
% 3.23/3.45 ($false),
% 3.23/3.45 inference(unit_resolution,[status(thm)],[14086, 166, 10450, 96, 118, 6552, 986, 1700])).
% 3.23/3.45 tff(14649,plain,((~b(s(s(s(z))), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(z))) | (~b(z, s(z))) | (~b(s(s(z)), s(s(s(z))))) | (~b(z, s(s(s(z)))))), inference(lemma,lemma(discharge,[]))).
% 3.23/3.45 tff(14650,plain,
% 3.23/3.45 (~b(z, s(s(s(z))))),
% 3.23/3.45 inference(unit_resolution,[status(thm)],[14649, 14647, 14548, 14598, 14407])).
% 3.23/3.45 tff(14651,plain,
% 3.23/3.45 (r(z, s(s(s(z))))),
% 3.23/3.45 inference(unit_resolution,[status(thm)],[1697, 14650])).
% 3.23/3.45 tff(14652,plain,
% 3.23/3.45 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(s(z))))) | (~r(s(z), z)) | (~r(s(s(s(z))), z)) | (~r(s(z), s(s(s(z))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, s(s(s(z))))) | (~r(s(z), z)) | (~r(s(s(s(z))), z)) | (~r(s(z), s(s(s(z))))))),
% 3.23/3.45 inference(rewrite,[status(thm)],[])).
% 3.23/3.45 tff(14653,plain,
% 3.23/3.45 (((~r(s(s(s(z))), z)) | (~r(z, s(s(s(z))))) | (~r(s(z), s(s(s(z))))) | (~r(s(z), z))) <=> ((~r(z, s(s(s(z))))) | (~r(s(z), z)) | (~r(s(s(s(z))), z)) | (~r(s(z), s(s(s(z))))))),
% 3.23/3.45 inference(rewrite,[status(thm)],[])).
% 3.23/3.45 tff(14654,plain,
% 3.23/3.45 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(z))), z)) | (~r(z, s(s(s(z))))) | (~r(s(z), s(s(s(z))))) | (~r(s(z), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(s(z))))) | (~r(s(z), z)) | (~r(s(s(s(z))), z)) | (~r(s(z), s(s(s(z)))))))),
% 3.23/3.45 inference(monotonicity,[status(thm)],[14653])).
% 3.23/3.45 tff(14655,plain,
% 3.23/3.45 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(z))), z)) | (~r(z, s(s(s(z))))) | (~r(s(z), s(s(s(z))))) | (~r(s(z), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, s(s(s(z))))) | (~r(s(z), z)) | (~r(s(s(s(z))), z)) | (~r(s(z), s(s(s(z))))))),
% 3.23/3.45 inference(transitivity,[status(thm)],[14654, 14652])).
% 3.23/3.45 tff(14656,plain,
% 3.23/3.45 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(z))), z)) | (~r(z, s(s(s(z))))) | (~r(s(z), s(s(s(z))))) | (~r(s(z), z)))),
% 3.23/3.45 inference(quant_inst,[status(thm)],[])).
% 3.23/3.45 tff(14657,plain,
% 3.23/3.45 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, s(s(s(z))))) | (~r(s(z), z)) | (~r(s(s(s(z))), z)) | (~r(s(z), s(s(s(z)))))),
% 3.23/3.45 inference(modus_ponens,[status(thm)],[14656, 14655])).
% 3.23/3.45 tff(14658,plain,
% 3.23/3.45 ($false),
% 3.23/3.45 inference(unit_resolution,[status(thm)],[14657, 197, 14334, 14651, 14634, 14619])).
% 3.23/3.45 tff(14659,plain,((s(s(z)) = s(s(elem!1))) | (~b(s(s(z)), s(z))) | b(s(z), s(s(elem!1)))), inference(lemma,lemma(discharge,[]))).
% 3.23/3.45 tff(14660,plain,
% 3.23/3.45 (s(s(z)) = s(s(elem!1))),
% 3.23/3.45 inference(unit_resolution,[status(thm)],[14659, 156, 54])).
% 3.23/3.45 tff(14661,plain,
% 3.23/3.45 (s(elem!1) = s(z)),
% 3.23/3.45 inference(unit_resolution,[status(thm)],[43, 14660])).
% 3.23/3.45 tff(14662,plain,
% 3.23/3.45 (z = elem!1),
% 3.23/3.45 inference(unit_resolution,[status(thm)],[30, 14661])).
% 3.23/3.45 tff(14663,plain,
% 3.23/3.45 (b(s(z), z) <=> b(s(z), elem!1)),
% 3.23/3.45 inference(monotonicity,[status(thm)],[14662])).
% 3.23/3.45 tff(14664,plain,
% 3.23/3.45 ((~b(s(z), z)) <=> (~b(s(z), elem!1))),
% 3.23/3.45 inference(monotonicity,[status(thm)],[14663])).
% 3.23/3.45 tff(14665,plain,
% 3.23/3.45 (~b(s(z), elem!1)),
% 3.23/3.45 inference(modus_ponens,[status(thm)],[14333, 14664])).
% 3.23/3.45 tff(14666,plain,
% 3.23/3.45 (~r(elem!1, s(s(s(elem!1))))),
% 3.23/3.45 inference(unit_resolution,[status(thm)],[5446, 14349, 620])).
% 3.23/3.45 tff(14667,plain,
% 3.23/3.45 (b(elem!1, s(s(s(elem!1))))),
% 3.23/3.45 inference(unit_resolution,[status(thm)],[5451, 14666, 6292])).
% 3.23/3.45 tff(14668,plain,
% 3.23/3.45 (r(s(s(s(z))), elem!1)),
% 3.23/3.45 inference(modus_ponens,[status(thm)],[10748, 6296])).
% 3.23/3.45 tff(14669,plain,
% 3.23/3.45 ((elem!1 = s(z)) <=> (z = s(z))),
% 3.23/3.45 inference(monotonicity,[status(thm)],[752])).
% 3.23/3.45 tff(14670,plain,
% 3.23/3.45 ((elem!1 = s(z)) <=> (s(z) = z)),
% 3.23/3.45 inference(transitivity,[status(thm)],[14669, 313])).
% 3.23/3.45 tff(14671,plain,
% 3.23/3.45 ((s(z) = z) <=> (elem!1 = s(z))),
% 3.23/3.45 inference(symmetry,[status(thm)],[14670])).
% 3.23/3.45 tff(14672,plain,
% 3.23/3.45 ((~(s(z) = z)) <=> (~(elem!1 = s(z)))),
% 3.23/3.45 inference(monotonicity,[status(thm)],[14671])).
% 3.23/3.45 tff(14673,plain,
% 3.23/3.45 (~(elem!1 = s(z))),
% 3.23/3.45 inference(modus_ponens,[status(thm)],[225, 14672])).
% 3.23/3.45 tff(14674,plain,
% 3.23/3.45 (b(elem!1, s(z))),
% 3.23/3.45 inference(unit_resolution,[status(thm)],[10376, 350, 10748, 9912, 14673])).
% 3.23/3.45 tff(14675,plain,
% 3.23/3.45 (r(s(s(s(elem!1))), s(s(elem!1)))),
% 3.23/3.45 inference(unit_resolution,[status(thm)],[14398, 118, 10529, 311, 350, 240, 14128])).
% 3.23/3.45 tff(14676,plain,
% 3.23/3.45 (~r(s(s(elem!1)), s(s(s(elem!1))))),
% 3.23/3.45 inference(unit_resolution,[status(thm)],[2627, 14675, 350, 311])).
% 3.23/3.45 tff(14677,plain,
% 3.23/3.45 (b(s(s(elem!1)), s(s(s(elem!1))))),
% 3.23/3.45 inference(unit_resolution,[status(thm)],[461, 14676, 10529])).
% 3.23/3.45 tff(14678,plain,
% 3.23/3.45 (b(s(s(z)), s(s(s(z))))),
% 3.23/3.45 inference(modus_ponens,[status(thm)],[14677, 6153])).
% 3.23/3.45 tff(14679,plain,
% 3.23/3.45 (~r(s(s(elem!1)), elem!1)),
% 3.23/3.45 inference(unit_resolution,[status(thm)],[13053, 14675, 311, 350])).
% 3.23/3.45 tff(14680,plain,
% 3.23/3.45 (b(s(s(elem!1)), elem!1)),
% 3.23/3.45 inference(unit_resolution,[status(thm)],[784, 14679, 756])).
% 3.23/3.45 tff(14681,plain,
% 3.23/3.45 (b(s(s(elem!1)), elem!1) <=> b(s(s(z)), elem!1)),
% 3.23/3.45 inference(monotonicity,[status(thm)],[128])).
% 3.23/3.45 tff(14682,plain,
% 3.23/3.45 (b(s(s(z)), elem!1)),
% 3.23/3.45 inference(modus_ponens,[status(thm)],[786, 14681])).
% 3.23/3.45 tff(14683,assumption,(~b(s(s(z)), elem!1)), introduced(assumption)).
% 3.23/3.45 tff(14684,plain,
% 3.23/3.45 ($false),
% 3.23/3.45 inference(unit_resolution,[status(thm)],[14683, 14682])).
% 3.23/3.45 tff(14685,plain,(b(s(s(z)), elem!1) | (~b(s(s(elem!1)), elem!1)) | (~(s(s(elem!1)) = s(s(z))))), inference(lemma,lemma(discharge,[]))).
% 3.23/3.45 tff(14686,plain,
% 3.23/3.45 (b(s(s(z)), elem!1)),
% 3.23/3.45 inference(unit_resolution,[status(thm)],[14685, 14680, 2153])).
% 3.23/3.45 tff(14687,plain,
% 3.23/3.45 (r(s(s(s(s(elem!1)))), s(s(s(elem!1)))) <=> r(s(s(s(s(z)))), s(s(s(z))))),
% 3.23/3.45 inference(symmetry,[status(thm)],[6228])).
% 3.23/3.45 tff(14688,plain,
% 3.23/3.45 ((~r(s(s(s(s(elem!1)))), s(s(s(elem!1))))) <=> (~r(s(s(s(s(z)))), s(s(s(z)))))),
% 3.23/3.45 inference(monotonicity,[status(thm)],[14687])).
% 3.23/3.45 tff(14689,plain,
% 3.23/3.45 (~r(s(s(s(s(z)))), s(s(s(z))))),
% 3.23/3.45 inference(modus_ponens,[status(thm)],[1059, 14688])).
% 3.23/3.45 tff(14690,plain,
% 3.23/3.45 (b(s(s(s(s(z)))), s(s(s(z))))),
% 3.23/3.45 inference(unit_resolution,[status(thm)],[4662, 14689])).
% 3.23/3.45 tff(14691,assumption,(b(s(z), s(s(s(s(z)))))), introduced(assumption)).
% 3.23/3.45 tff(14692,assumption,(b(s(s(z)), elem!1)), introduced(assumption)).
% 3.23/3.45 tff(14693,plain,
% 3.23/3.45 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(z))) | (~b(s(s(z)), elem!1)) | (~b(s(s(z)), s(z))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(s(z))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(z))) | (~b(s(s(z)), elem!1)) | (~b(s(s(z)), s(z))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(s(z))))))),
% 3.23/3.45 inference(rewrite,[status(thm)],[])).
% 3.23/3.45 tff(14694,plain,
% 3.23/3.45 (((~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(z), s(s(s(s(z)))))) | (~b(elem!1, s(z))) | (~b(s(s(z)), s(z))) | (~b(s(s(z)), elem!1))) <=> ((~b(elem!1, s(z))) | (~b(s(s(z)), elem!1)) | (~b(s(s(z)), s(z))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(s(z))))))),
% 3.23/3.45 inference(rewrite,[status(thm)],[])).
% 3.23/3.45 tff(14695,plain,
% 3.23/3.45 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(z), s(s(s(s(z)))))) | (~b(elem!1, s(z))) | (~b(s(s(z)), s(z))) | (~b(s(s(z)), elem!1)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(z))) | (~b(s(s(z)), elem!1)) | (~b(s(s(z)), s(z))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(s(z)))))))),
% 3.23/3.45 inference(monotonicity,[status(thm)],[14694])).
% 3.23/3.45 tff(14696,plain,
% 3.23/3.45 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(z), s(s(s(s(z)))))) | (~b(elem!1, s(z))) | (~b(s(s(z)), s(z))) | (~b(s(s(z)), elem!1)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(z))) | (~b(s(s(z)), elem!1)) | (~b(s(s(z)), s(z))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(s(z))))))),
% 3.23/3.45 inference(transitivity,[status(thm)],[14695, 14693])).
% 3.23/3.45 tff(14697,plain,
% 3.23/3.45 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(z), s(s(s(s(z)))))) | (~b(elem!1, s(z))) | (~b(s(s(z)), s(z))) | (~b(s(s(z)), elem!1)))),
% 3.23/3.45 inference(quant_inst,[status(thm)],[])).
% 3.23/3.45 tff(14698,plain,
% 3.23/3.45 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(z))) | (~b(s(s(z)), elem!1)) | (~b(s(s(z)), s(z))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(s(z)))))),
% 3.23/3.45 inference(modus_ponens,[status(thm)],[14697, 14696])).
% 3.23/3.45 tff(14699,plain,
% 3.23/3.45 ($false),
% 3.23/3.45 inference(unit_resolution,[status(thm)],[14698, 166, 1212, 14692, 156, 986, 14691, 4732])).
% 3.23/3.45 tff(14700,plain,((~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(elem!1, s(z))) | (~b(s(s(z)), elem!1)) | (~b(s(s(z)), s(z))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(z), s(s(s(s(z))))))), inference(lemma,lemma(discharge,[]))).
% 3.23/3.45 tff(14701,plain,
% 3.23/3.45 (~b(s(z), s(s(s(s(z)))))),
% 3.23/3.45 inference(unit_resolution,[status(thm)],[14700, 14690, 156, 14686, 1212, 14678])).
% 3.23/3.45 tff(14702,plain,
% 3.23/3.45 (b(s(z), s(s(s(s(z))))) <=> b(s(z), s(s(s(s(elem!1)))))),
% 3.23/3.45 inference(monotonicity,[status(thm)],[2197])).
% 3.23/3.45 tff(14703,plain,
% 3.23/3.45 (b(s(z), s(s(s(s(elem!1))))) <=> b(s(z), s(s(s(s(z)))))),
% 3.23/3.45 inference(symmetry,[status(thm)],[14702])).
% 3.23/3.45 tff(14704,plain,
% 3.23/3.45 (b(s(z), s(s(s(s(z)))))),
% 3.23/3.45 inference(modus_ponens,[status(thm)],[1327, 14703])).
% 3.23/3.45 tff(14705,assumption,(~b(s(z), s(s(s(s(z)))))), introduced(assumption)).
% 3.23/3.45 tff(14706,plain,
% 3.23/3.45 ($false),
% 3.23/3.45 inference(unit_resolution,[status(thm)],[14705, 14704])).
% 3.23/3.45 tff(14707,plain,(b(s(z), s(s(s(s(z))))) | (~b(s(z), s(s(s(s(elem!1)))))) | (~(s(s(elem!1)) = s(s(z))))), inference(lemma,lemma(discharge,[]))).
% 3.23/3.45 tff(14708,plain,
% 3.23/3.45 (~b(s(z), s(s(s(s(elem!1)))))),
% 3.23/3.45 inference(unit_resolution,[status(thm)],[14707, 14701, 2153])).
% 3.23/3.45 tff(14709,plain,
% 3.23/3.45 (r(s(z), s(s(s(s(elem!1)))))),
% 3.23/3.45 inference(unit_resolution,[status(thm)],[681, 14708])).
% 3.23/3.45 tff(14710,plain,
% 3.23/3.45 ((s(s(s(s(elem!1)))) = s(s(s(z)))) <=> (s(s(s(s(elem!1)))) = s(s(s(elem!1))))),
% 3.23/3.45 inference(monotonicity,[status(thm)],[1086])).
% 3.23/3.45 tff(14711,plain,
% 3.23/3.45 ((s(s(s(s(elem!1)))) = s(s(s(z)))) <=> (s(s(s(elem!1))) = s(s(s(s(elem!1)))))),
% 3.23/3.45 inference(transitivity,[status(thm)],[14710, 1191])).
% 3.23/3.45 tff(14712,plain,
% 3.23/3.45 ((s(s(s(s(elem!1)))) = s(s(s(z)))) <=> (s(s(s(s(elem!1)))) = s(s(s(elem!1))))),
% 3.23/3.45 inference(transitivity,[status(thm)],[14711, 3797])).
% 3.23/3.45 tff(14713,plain,
% 3.23/3.45 ((~(s(s(s(s(elem!1)))) = s(s(s(z))))) <=> (~(s(s(s(s(elem!1)))) = s(s(s(elem!1)))))),
% 3.23/3.45 inference(monotonicity,[status(thm)],[14712])).
% 3.23/3.45 tff(14714,plain,
% 3.23/3.45 (~(s(s(s(s(elem!1)))) = s(s(s(elem!1))))),
% 3.23/3.45 inference(modus_ponens,[status(thm)],[5112, 14713])).
% 3.23/3.45 tff(14715,plain,
% 3.23/3.45 (b(s(s(s(s(elem!1)))), s(s(s(elem!1))))),
% 3.23/3.45 inference(unit_resolution,[status(thm)],[1065, 1059, 14714])).
% 3.23/3.45 tff(14716,plain,
% 3.23/3.45 ((~(s(s(s(s(elem!1)))) = s(s(s(z))))) <=> (~(s(s(s(elem!1))) = s(s(s(s(elem!1))))))),
% 3.23/3.45 inference(monotonicity,[status(thm)],[14711])).
% 3.23/3.45 tff(14717,plain,
% 3.23/3.45 (~(s(s(s(elem!1))) = s(s(s(s(elem!1)))))),
% 3.23/3.45 inference(modus_ponens,[status(thm)],[5112, 14716])).
% 3.23/3.45 tff(14718,plain,
% 3.23/3.45 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(s(s(elem!1)), elem!1)) | (~b(s(s(s(s(elem!1)))), s(s(elem!1)))) | (~b(elem!1, s(s(elem!1)))) | (~b(s(s(s(s(elem!1)))), elem!1)) | (~b(s(s(s(s(elem!1)))), s(s(s(elem!1))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(s(s(elem!1)), elem!1)) | (~b(s(s(s(s(elem!1)))), s(s(elem!1)))) | (~b(elem!1, s(s(elem!1)))) | (~b(s(s(s(s(elem!1)))), elem!1)) | (~b(s(s(s(s(elem!1)))), s(s(s(elem!1))))))),
% 3.23/3.45 inference(rewrite,[status(thm)],[])).
% 3.23/3.45 tff(14719,plain,
% 3.23/3.45 (((~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~b(elem!1, s(s(elem!1)))) | (~b(s(s(elem!1)), elem!1)) | (~b(s(s(s(s(elem!1)))), elem!1)) | (~b(s(s(s(s(elem!1)))), s(s(elem!1))))) <=> ((~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(s(s(elem!1)), elem!1)) | (~b(s(s(s(s(elem!1)))), s(s(elem!1)))) | (~b(elem!1, s(s(elem!1)))) | (~b(s(s(s(s(elem!1)))), elem!1)) | (~b(s(s(s(s(elem!1)))), s(s(s(elem!1))))))),
% 3.23/3.45 inference(rewrite,[status(thm)],[])).
% 3.23/3.45 tff(14720,plain,
% 3.23/3.45 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~b(elem!1, s(s(elem!1)))) | (~b(s(s(elem!1)), elem!1)) | (~b(s(s(s(s(elem!1)))), elem!1)) | (~b(s(s(s(s(elem!1)))), s(s(elem!1)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(s(s(elem!1)), elem!1)) | (~b(s(s(s(s(elem!1)))), s(s(elem!1)))) | (~b(elem!1, s(s(elem!1)))) | (~b(s(s(s(s(elem!1)))), elem!1)) | (~b(s(s(s(s(elem!1)))), s(s(s(elem!1)))))))),
% 3.23/3.45 inference(monotonicity,[status(thm)],[14719])).
% 3.23/3.45 tff(14721,plain,
% 3.23/3.45 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~b(elem!1, s(s(elem!1)))) | (~b(s(s(elem!1)), elem!1)) | (~b(s(s(s(s(elem!1)))), elem!1)) | (~b(s(s(s(s(elem!1)))), s(s(elem!1)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(s(s(elem!1)), elem!1)) | (~b(s(s(s(s(elem!1)))), s(s(elem!1)))) | (~b(elem!1, s(s(elem!1)))) | (~b(s(s(s(s(elem!1)))), elem!1)) | (~b(s(s(s(s(elem!1)))), s(s(s(elem!1))))))),
% 3.23/3.45 inference(transitivity,[status(thm)],[14720, 14718])).
% 3.23/3.45 tff(14722,plain,
% 3.23/3.45 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~b(elem!1, s(s(elem!1)))) | (~b(s(s(elem!1)), elem!1)) | (~b(s(s(s(s(elem!1)))), elem!1)) | (~b(s(s(s(s(elem!1)))), s(s(elem!1)))))),
% 3.23/3.45 inference(quant_inst,[status(thm)],[])).
% 3.23/3.45 tff(14723,plain,
% 3.23/3.45 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(s(s(elem!1)), elem!1)) | (~b(s(s(s(s(elem!1)))), s(s(elem!1)))) | (~b(elem!1, s(s(elem!1)))) | (~b(s(s(s(s(elem!1)))), elem!1)) | (~b(s(s(s(s(elem!1)))), s(s(s(elem!1)))))),
% 3.23/3.45 inference(modus_ponens,[status(thm)],[14722, 14721])).
% 3.23/3.45 tff(14724,plain,
% 3.23/3.45 ((~b(s(s(s(s(elem!1)))), s(s(elem!1)))) | (~b(s(s(s(s(elem!1)))), elem!1))),
% 3.23/3.45 inference(unit_resolution,[status(thm)],[14723, 166, 463, 786, 14129, 1107])).
% 3.23/3.45 tff(14725,plain,
% 3.23/3.45 (~b(s(s(s(s(elem!1)))), s(s(elem!1)))),
% 3.23/3.45 inference(unit_resolution,[status(thm)],[14724, 640])).
% 3.23/3.45 tff(14726,plain,
% 3.23/3.45 (~b(s(s(s(s(elem!1)))), s(s(z)))),
% 3.23/3.45 inference(modus_ponens,[status(thm)],[14725, 2156])).
% 3.23/3.45 tff(14727,plain,
% 3.23/3.45 (r(s(s(s(s(elem!1)))), s(s(z)))),
% 3.23/3.45 inference(unit_resolution,[status(thm)],[1299, 14726])).
% 3.23/3.45 tff(14728,plain,
% 3.23/3.45 (~r(s(s(elem!1)), s(s(s(s(elem!1)))))),
% 3.23/3.45 inference(unit_resolution,[status(thm)],[2176, 14727, 311, 699])).
% 3.23/3.45 tff(14729,plain,
% 3.23/3.45 (b(s(s(elem!1)), s(s(s(s(elem!1)))))),
% 3.23/3.45 inference(unit_resolution,[status(thm)],[827, 14728, 816])).
% 3.23/3.45 tff(14730,plain,
% 3.23/3.45 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(s(s(elem!1)), elem!1)) | (~b(elem!1, s(z))) | (~b(s(z), s(s(s(elem!1))))) | (~b(s(s(elem!1)), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), elem!1)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(s(s(elem!1)), elem!1)) | (~b(elem!1, s(z))) | (~b(s(z), s(s(s(elem!1))))) | (~b(s(s(elem!1)), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), elem!1)))),
% 3.23/3.45 inference(rewrite,[status(thm)],[])).
% 3.23/3.45 tff(14731,plain,
% 3.23/3.45 (((~b(s(z), s(s(s(elem!1))))) | (~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(elem!1, s(z))) | (~b(s(s(s(s(elem!1)))), elem!1)) | (~b(s(s(elem!1)), elem!1)) | (~b(s(s(elem!1)), s(s(s(s(elem!1))))))) <=> ((~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(s(s(elem!1)), elem!1)) | (~b(elem!1, s(z))) | (~b(s(z), s(s(s(elem!1))))) | (~b(s(s(elem!1)), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), elem!1)))),
% 3.23/3.46 inference(rewrite,[status(thm)],[])).
% 3.23/3.46 tff(14732,plain,
% 3.23/3.46 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(s(elem!1))))) | (~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(elem!1, s(z))) | (~b(s(s(s(s(elem!1)))), elem!1)) | (~b(s(s(elem!1)), elem!1)) | (~b(s(s(elem!1)), s(s(s(s(elem!1)))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(s(s(elem!1)), elem!1)) | (~b(elem!1, s(z))) | (~b(s(z), s(s(s(elem!1))))) | (~b(s(s(elem!1)), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), elem!1))))),
% 3.23/3.46 inference(monotonicity,[status(thm)],[14731])).
% 3.23/3.46 tff(14733,plain,
% 3.23/3.46 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(s(elem!1))))) | (~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(elem!1, s(z))) | (~b(s(s(s(s(elem!1)))), elem!1)) | (~b(s(s(elem!1)), elem!1)) | (~b(s(s(elem!1)), s(s(s(s(elem!1)))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(s(s(elem!1)), elem!1)) | (~b(elem!1, s(z))) | (~b(s(z), s(s(s(elem!1))))) | (~b(s(s(elem!1)), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), elem!1)))),
% 3.23/3.46 inference(transitivity,[status(thm)],[14732, 14730])).
% 3.23/3.46 tff(14734,plain,
% 3.23/3.46 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(s(elem!1))))) | (~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(elem!1, s(z))) | (~b(s(s(s(s(elem!1)))), elem!1)) | (~b(s(s(elem!1)), elem!1)) | (~b(s(s(elem!1)), s(s(s(s(elem!1)))))))),
% 3.23/3.46 inference(quant_inst,[status(thm)],[])).
% 3.23/3.46 tff(14735,plain,
% 3.23/3.46 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(s(s(elem!1)), elem!1)) | (~b(elem!1, s(z))) | (~b(s(z), s(s(s(elem!1))))) | (~b(s(s(elem!1)), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), elem!1))),
% 3.23/3.46 inference(modus_ponens,[status(thm)],[14734, 14733])).
% 3.23/3.46 tff(14736,plain,
% 3.23/3.46 ($false),
% 3.23/3.46 inference(unit_resolution,[status(thm)],[14735, 166, 463, 786, 241, 1212, 14729, 640])).
% 3.23/3.46 tff(14737,plain,((~b(s(s(s(s(elem!1)))), elem!1)) | (~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(s(s(elem!1)), elem!1)) | (~b(s(z), s(s(s(elem!1))))) | (~b(elem!1, s(z))) | (~r(s(z), s(s(elem!1)))) | (~r(s(z), s(s(s(s(elem!1)))))) | (~(s(s(z)) = s(s(elem!1)))) | (~b(s(s(s(s(elem!1)))), s(s(s(elem!1)))))), inference(lemma,lemma(discharge,[]))).
% 3.23/3.46 tff(14738,plain,
% 3.23/3.46 (~b(s(s(s(s(elem!1)))), elem!1)),
% 3.23/3.46 inference(unit_resolution,[status(thm)],[14737, 14709, 14680, 241, 1212, 311, 14677, 34, 14715])).
% 3.23/3.46 tff(14739,plain,
% 3.23/3.46 (r(s(s(s(s(elem!1)))), elem!1)),
% 3.23/3.46 inference(unit_resolution,[status(thm)],[719, 14738, 627])).
% 3.23/3.46 tff(14740,plain,
% 3.23/3.46 (~r(elem!1, s(s(s(s(elem!1)))))),
% 3.23/3.46 inference(unit_resolution,[status(thm)],[10678, 14739, 2381, 14709])).
% 3.23/3.46 tff(14741,plain,
% 3.23/3.46 (b(elem!1, s(s(s(s(elem!1)))))),
% 3.23/3.46 inference(unit_resolution,[status(thm)],[2427, 14740, 2377])).
% 3.23/3.46 tff(14742,plain,
% 3.23/3.46 (~b(s(s(s(elem!1))), s(s(s(s(elem!1)))))),
% 3.23/3.46 inference(unit_resolution,[status(thm)],[1313, 1046, 463, 1107])).
% 3.23/3.46 tff(14743,plain,
% 3.23/3.46 (r(s(s(s(elem!1))), s(s(s(s(elem!1)))))),
% 3.23/3.46 inference(unit_resolution,[status(thm)],[696, 14742, 361])).
% 3.23/3.46 tff(14744,plain,
% 3.23/3.46 (~r(s(s(s(s(elem!1)))), s(z))),
% 3.23/3.46 inference(unit_resolution,[status(thm)],[3469, 14743, 311, 350])).
% 3.23/3.46 tff(14745,plain,
% 3.23/3.46 (b(s(s(s(s(elem!1)))), s(z))),
% 3.23/3.46 inference(unit_resolution,[status(thm)],[661, 14744])).
% 3.23/3.46 tff(14746,plain,
% 3.23/3.46 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(s(elem!1))))) | (~b(elem!1, s(s(s(elem!1))))) | (~b(elem!1, s(s(elem!1)))) | (~b(s(s(elem!1)), s(s(s(s(elem!1)))))) | (~b(elem!1, s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), s(s(s(elem!1))))) | (~b(elem!1, s(s(s(elem!1))))) | (~b(elem!1, s(s(elem!1)))) | (~b(s(s(elem!1)), s(s(s(s(elem!1)))))) | (~b(elem!1, s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), s(z))))),
% 3.23/3.46 inference(rewrite,[status(thm)],[])).
% 3.23/3.46 tff(14747,plain,
% 3.23/3.46 (((~b(s(z), s(s(s(elem!1))))) | (~b(elem!1, s(s(s(elem!1))))) | (~b(s(s(s(s(elem!1)))), s(z))) | (~b(s(s(elem!1)), s(s(s(s(elem!1)))))) | (~b(elem!1, s(s(s(s(elem!1)))))) | (~b(elem!1, s(s(elem!1))))) <=> ((~b(s(z), s(s(s(elem!1))))) | (~b(elem!1, s(s(s(elem!1))))) | (~b(elem!1, s(s(elem!1)))) | (~b(s(s(elem!1)), s(s(s(s(elem!1)))))) | (~b(elem!1, s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), s(z))))),
% 3.23/3.46 inference(rewrite,[status(thm)],[])).
% 3.23/3.46 tff(14748,plain,
% 3.23/3.46 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(s(elem!1))))) | (~b(elem!1, s(s(s(elem!1))))) | (~b(s(s(s(s(elem!1)))), s(z))) | (~b(s(s(elem!1)), s(s(s(s(elem!1)))))) | (~b(elem!1, s(s(s(s(elem!1)))))) | (~b(elem!1, s(s(elem!1)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(s(elem!1))))) | (~b(elem!1, s(s(s(elem!1))))) | (~b(elem!1, s(s(elem!1)))) | (~b(s(s(elem!1)), s(s(s(s(elem!1)))))) | (~b(elem!1, s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), s(z)))))),
% 3.23/3.46 inference(monotonicity,[status(thm)],[14747])).
% 3.23/3.46 tff(14749,plain,
% 3.23/3.46 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(s(elem!1))))) | (~b(elem!1, s(s(s(elem!1))))) | (~b(s(s(s(s(elem!1)))), s(z))) | (~b(s(s(elem!1)), s(s(s(s(elem!1)))))) | (~b(elem!1, s(s(s(s(elem!1)))))) | (~b(elem!1, s(s(elem!1)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), s(s(s(elem!1))))) | (~b(elem!1, s(s(s(elem!1))))) | (~b(elem!1, s(s(elem!1)))) | (~b(s(s(elem!1)), s(s(s(s(elem!1)))))) | (~b(elem!1, s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), s(z))))),
% 3.23/3.46 inference(transitivity,[status(thm)],[14748, 14746])).
% 3.23/3.46 tff(14750,plain,
% 3.23/3.46 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(s(elem!1))))) | (~b(elem!1, s(s(s(elem!1))))) | (~b(s(s(s(s(elem!1)))), s(z))) | (~b(s(s(elem!1)), s(s(s(s(elem!1)))))) | (~b(elem!1, s(s(s(s(elem!1)))))) | (~b(elem!1, s(s(elem!1)))))),
% 3.23/3.46 inference(quant_inst,[status(thm)],[])).
% 3.23/3.46 tff(14751,plain,
% 3.23/3.46 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), s(s(s(elem!1))))) | (~b(elem!1, s(s(s(elem!1))))) | (~b(elem!1, s(s(elem!1)))) | (~b(s(s(elem!1)), s(s(s(s(elem!1)))))) | (~b(elem!1, s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), s(z)))),
% 3.23/3.46 inference(modus_ponens,[status(thm)],[14750, 14749])).
% 3.23/3.46 tff(14752,plain,
% 3.23/3.46 ($false),
% 3.23/3.46 inference(unit_resolution,[status(thm)],[14751, 166, 643, 241, 1046, 14745, 10960, 1108])).
% 3.23/3.46 tff(14753,plain,((~b(s(s(elem!1)), s(s(s(s(elem!1)))))) | (~b(elem!1, s(s(s(elem!1))))) | (~b(s(z), s(s(s(elem!1))))) | (~b(elem!1, s(s(elem!1)))) | (~b(elem!1, s(s(s(s(elem!1)))))) | (~r(s(z), s(s(elem!1)))) | (~r(s(s(s(elem!1))), s(z))) | (s(s(s(elem!1))) = s(s(s(s(elem!1))))) | (~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(s(s(s(s(elem!1)))), s(s(s(elem!1)))))), inference(lemma,lemma(discharge,[]))).
% 3.23/3.46 tff(14754,plain,
% 3.23/3.46 (~b(s(s(elem!1)), s(s(s(s(elem!1)))))),
% 3.23/3.46 inference(unit_resolution,[status(thm)],[14753, 14741, 241, 14129, 643, 311, 350, 14717, 14677, 14715])).
% 3.23/3.46 tff(14755,plain,
% 3.23/3.46 (r(s(s(elem!1)), s(s(s(s(elem!1)))))),
% 3.23/3.46 inference(unit_resolution,[status(thm)],[827, 14754, 816])).
% 3.23/3.46 tff(14756,plain,
% 3.23/3.46 (~r(s(s(s(s(elem!1)))), s(z))),
% 3.23/3.46 inference(unit_resolution,[status(thm)],[11805, 14755, 311, 14709])).
% 3.23/3.46 tff(14757,plain,
% 3.23/3.46 (b(s(s(s(s(elem!1)))), s(z))),
% 3.23/3.46 inference(unit_resolution,[status(thm)],[661, 14756])).
% 3.23/3.46 tff(14758,plain,
% 3.23/3.46 (~r(s(s(s(s(elem!1)))), s(s(z)))),
% 3.23/3.46 inference(unit_resolution,[status(thm)],[2176, 14755, 311, 14709])).
% 3.23/3.46 tff(14759,plain,
% 3.23/3.46 (b(s(s(s(s(elem!1)))), s(s(z)))),
% 3.23/3.46 inference(unit_resolution,[status(thm)],[1299, 14758])).
% 3.23/3.46 tff(14760,plain,
% 3.23/3.46 (s(s(z)) = s(s(elem!1))),
% 3.23/3.46 inference(unit_resolution,[status(thm)],[131, 128])).
% 3.23/3.46 tff(14761,plain,
% 3.23/3.46 (s(elem!1) = s(z)),
% 3.23/3.46 inference(unit_resolution,[status(thm)],[43, 14760])).
% 3.23/3.46 tff(14762,plain,
% 3.23/3.46 (z = elem!1),
% 3.23/3.46 inference(unit_resolution,[status(thm)],[30, 14761])).
% 3.23/3.46 tff(14763,plain,
% 3.23/3.46 (elem!1 = z),
% 3.23/3.46 inference(symmetry,[status(thm)],[14762])).
% 3.23/3.46 tff(14764,plain,
% 3.23/3.46 ((elem!1 = s(s(s(s(z))))) <=> (z = s(s(s(s(z)))))),
% 3.23/3.46 inference(monotonicity,[status(thm)],[14763])).
% 3.23/3.46 tff(14765,plain,
% 3.23/3.46 ((elem!1 = s(s(s(s(z))))) <=> (s(s(s(s(z)))) = z)),
% 3.23/3.46 inference(transitivity,[status(thm)],[14764, 12709])).
% 3.23/3.46 tff(14766,plain,
% 3.23/3.46 ((s(s(s(s(z)))) = z) <=> (elem!1 = s(s(s(s(z)))))),
% 3.23/3.46 inference(symmetry,[status(thm)],[14765])).
% 3.23/3.46 tff(14767,plain,
% 3.23/3.46 ((~(s(s(s(s(z)))) = z)) <=> (~(elem!1 = s(s(s(s(z))))))),
% 3.23/3.46 inference(monotonicity,[status(thm)],[14766])).
% 3.23/3.46 tff(14768,plain,
% 3.23/3.46 (~(elem!1 = s(s(s(s(z)))))),
% 3.23/3.46 inference(modus_ponens,[status(thm)],[1044, 14767])).
% 3.23/3.46 tff(14769,plain,
% 3.23/3.46 (b(elem!1, s(s(z))) <=> b(elem!1, s(s(elem!1)))),
% 3.23/3.46 inference(monotonicity,[status(thm)],[4988])).
% 3.23/3.46 tff(14770,plain,
% 3.23/3.46 (b(elem!1, s(s(elem!1))) <=> b(elem!1, s(s(z)))),
% 3.23/3.46 inference(symmetry,[status(thm)],[14769])).
% 3.23/3.46 tff(14771,plain,
% 3.23/3.46 (b(elem!1, s(s(z)))),
% 3.23/3.46 inference(modus_ponens,[status(thm)],[10960, 14770])).
% 3.23/3.46 tff(14772,plain,
% 3.23/3.46 (b(s(s(s(s(z)))), s(s(z))) <=> b(s(s(s(s(elem!1)))), s(s(z)))),
% 3.23/3.46 inference(monotonicity,[status(thm)],[2197])).
% 3.23/3.46 tff(14773,plain,
% 3.23/3.46 (b(s(s(s(s(elem!1)))), s(s(z))) <=> b(s(s(s(s(z)))), s(s(z)))),
% 3.23/3.46 inference(symmetry,[status(thm)],[14772])).
% 3.23/3.46 tff(14774,plain,
% 3.23/3.46 (b(s(s(s(s(z)))), s(s(z)))),
% 3.23/3.46 inference(modus_ponens,[status(thm)],[3039, 14773])).
% 3.23/3.46 tff(14775,plain,
% 3.23/3.46 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(z))) | (~b(s(s(z)), elem!1)) | (~b(elem!1, s(s(z)))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(elem!1, s(s(s(s(z)))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(z))) | (~b(s(s(z)), elem!1)) | (~b(elem!1, s(s(z)))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(elem!1, s(s(s(s(z)))))))),
% 3.23/3.46 inference(rewrite,[status(thm)],[])).
% 3.23/3.46 tff(14776,plain,
% 3.23/3.46 (((~b(elem!1, s(z))) | (~b(elem!1, s(z))) | (~b(s(s(z)), elem!1)) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(elem!1, s(s(z)))) | (~b(elem!1, s(s(s(s(z))))))) <=> ((~b(elem!1, s(z))) | (~b(s(s(z)), elem!1)) | (~b(elem!1, s(s(z)))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(elem!1, s(s(s(s(z)))))))),
% 3.23/3.46 inference(rewrite,[status(thm)],[])).
% 3.23/3.46 tff(14777,plain,
% 3.23/3.46 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(z))) | (~b(elem!1, s(z))) | (~b(s(s(z)), elem!1)) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(elem!1, s(s(z)))) | (~b(elem!1, s(s(s(s(z)))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(z))) | (~b(s(s(z)), elem!1)) | (~b(elem!1, s(s(z)))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(elem!1, s(s(s(s(z))))))))),
% 3.23/3.46 inference(monotonicity,[status(thm)],[14776])).
% 3.23/3.46 tff(14778,plain,
% 3.23/3.46 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(z))) | (~b(elem!1, s(z))) | (~b(s(s(z)), elem!1)) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(elem!1, s(s(z)))) | (~b(elem!1, s(s(s(s(z)))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(z))) | (~b(s(s(z)), elem!1)) | (~b(elem!1, s(s(z)))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(elem!1, s(s(s(s(z)))))))),
% 3.23/3.46 inference(transitivity,[status(thm)],[14777, 14775])).
% 3.23/3.46 tff(14779,plain,
% 3.23/3.46 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(z))) | (~b(elem!1, s(z))) | (~b(s(s(z)), elem!1)) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(elem!1, s(s(z)))) | (~b(elem!1, s(s(s(s(z)))))))),
% 3.23/3.46 inference(quant_inst,[status(thm)],[])).
% 3.23/3.46 tff(14780,plain,
% 3.23/3.46 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(z))) | (~b(s(s(z)), elem!1)) | (~b(elem!1, s(s(z)))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(elem!1, s(s(s(s(z))))))),
% 3.23/3.46 inference(modus_ponens,[status(thm)],[14779, 14778])).
% 3.23/3.46 tff(14781,plain,
% 3.23/3.46 ((~b(elem!1, s(s(z)))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(elem!1, s(s(s(s(z))))))),
% 3.23/3.46 inference(unit_resolution,[status(thm)],[14780, 166, 1212, 14692])).
% 3.23/3.46 tff(14782,plain,
% 3.23/3.46 (~b(elem!1, s(s(s(s(z)))))),
% 3.23/3.46 inference(unit_resolution,[status(thm)],[14781, 14774, 14771])).
% 3.23/3.46 tff(14783,plain,
% 3.23/3.46 ((elem!1 = s(s(s(s(z))))) | r(elem!1, s(s(s(s(z)))))),
% 3.23/3.46 inference(unit_resolution,[status(thm)],[1097, 79, 14782])).
% 3.23/3.46 tff(14784,plain,
% 3.23/3.46 (r(elem!1, s(s(s(s(z)))))),
% 3.23/3.46 inference(unit_resolution,[status(thm)],[14783, 14768])).
% 3.23/3.46 tff(14785,plain,
% 3.23/3.46 ((s(s(s(s(z)))) = elem!1) <=> (s(s(s(s(z)))) = z)),
% 3.23/3.46 inference(monotonicity,[status(thm)],[14763])).
% 3.23/3.46 tff(14786,plain,
% 3.23/3.46 ((s(s(s(s(z)))) = z) <=> (s(s(s(s(z)))) = elem!1)),
% 3.23/3.46 inference(symmetry,[status(thm)],[14785])).
% 3.23/3.46 tff(14787,plain,
% 3.23/3.46 ((~(s(s(s(s(z)))) = z)) <=> (~(s(s(s(s(z)))) = elem!1))),
% 3.23/3.46 inference(monotonicity,[status(thm)],[14786])).
% 3.23/3.46 tff(14788,plain,
% 3.23/3.46 (~(s(s(s(s(z)))) = elem!1)),
% 3.23/3.46 inference(modus_ponens,[status(thm)],[1044, 14787])).
% 3.23/3.46 tff(14789,plain,
% 3.23/3.46 (b(s(s(s(s(z)))), s(z)) <=> b(s(s(s(s(elem!1)))), s(z))),
% 3.23/3.46 inference(monotonicity,[status(thm)],[2197])).
% 3.23/3.46 tff(14790,plain,
% 3.23/3.46 (b(s(s(s(s(elem!1)))), s(z)) <=> b(s(s(s(s(z)))), s(z))),
% 3.23/3.46 inference(symmetry,[status(thm)],[14789])).
% 3.23/3.46 tff(14791,plain,
% 3.23/3.46 (b(s(s(s(s(z)))), s(z))),
% 3.23/3.46 inference(modus_ponens,[status(thm)],[1402, 14790])).
% 3.23/3.46 tff(14792,plain,
% 3.23/3.46 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), elem!1)) | (~b(elem!1, s(s(z)))) | (~b(s(s(z)), s(z))) | (~b(s(s(s(s(z)))), elem!1)) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(s(z)))), s(s(z)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(z)), elem!1)) | (~b(elem!1, s(s(z)))) | (~b(s(s(z)), s(z))) | (~b(s(s(s(s(z)))), elem!1)) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(s(z)))), s(s(z)))))),
% 3.23/3.46 inference(rewrite,[status(thm)],[])).
% 3.23/3.46 tff(14793,plain,
% 3.23/3.46 (((~b(s(s(z)), s(z))) | (~b(s(s(s(s(z)))), s(z))) | (~b(elem!1, s(s(z)))) | (~b(s(s(z)), elem!1)) | (~b(s(s(s(s(z)))), elem!1)) | (~b(s(s(s(s(z)))), s(s(z))))) <=> ((~b(s(s(z)), elem!1)) | (~b(elem!1, s(s(z)))) | (~b(s(s(z)), s(z))) | (~b(s(s(s(s(z)))), elem!1)) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(s(z)))), s(s(z)))))),
% 3.23/3.46 inference(rewrite,[status(thm)],[])).
% 3.23/3.46 tff(14794,plain,
% 3.23/3.46 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), s(z))) | (~b(s(s(s(s(z)))), s(z))) | (~b(elem!1, s(s(z)))) | (~b(s(s(z)), elem!1)) | (~b(s(s(s(s(z)))), elem!1)) | (~b(s(s(s(s(z)))), s(s(z)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), elem!1)) | (~b(elem!1, s(s(z)))) | (~b(s(s(z)), s(z))) | (~b(s(s(s(s(z)))), elem!1)) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(s(z)))), s(s(z))))))),
% 3.23/3.46 inference(monotonicity,[status(thm)],[14793])).
% 3.23/3.46 tff(14795,plain,
% 3.23/3.46 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), s(z))) | (~b(s(s(s(s(z)))), s(z))) | (~b(elem!1, s(s(z)))) | (~b(s(s(z)), elem!1)) | (~b(s(s(s(s(z)))), elem!1)) | (~b(s(s(s(s(z)))), s(s(z)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(z)), elem!1)) | (~b(elem!1, s(s(z)))) | (~b(s(s(z)), s(z))) | (~b(s(s(s(s(z)))), elem!1)) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(s(z)))), s(s(z)))))),
% 3.23/3.46 inference(transitivity,[status(thm)],[14794, 14792])).
% 3.23/3.46 tff(14796,plain,
% 3.23/3.46 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), s(z))) | (~b(s(s(s(s(z)))), s(z))) | (~b(elem!1, s(s(z)))) | (~b(s(s(z)), elem!1)) | (~b(s(s(s(s(z)))), elem!1)) | (~b(s(s(s(s(z)))), s(s(z)))))),
% 3.23/3.46 inference(quant_inst,[status(thm)],[])).
% 3.23/3.46 tff(14797,plain,
% 3.23/3.46 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(z)), elem!1)) | (~b(elem!1, s(s(z)))) | (~b(s(s(z)), s(z))) | (~b(s(s(s(s(z)))), elem!1)) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(s(z)))), s(s(z))))),
% 3.23/3.46 inference(modus_ponens,[status(thm)],[14796, 14795])).
% 3.23/3.46 tff(14798,plain,
% 3.23/3.46 ((~b(elem!1, s(s(z)))) | (~b(s(s(s(s(z)))), elem!1)) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(s(z)))), s(s(z))))),
% 3.23/3.46 inference(unit_resolution,[status(thm)],[14797, 166, 14692, 156])).
% 3.23/3.46 tff(14799,plain,
% 3.23/3.46 (~b(s(s(s(s(z)))), elem!1)),
% 3.23/3.46 inference(unit_resolution,[status(thm)],[14798, 14771, 14791, 14774])).
% 3.23/3.46 tff(14800,plain,
% 3.23/3.46 ((s(s(s(s(z)))) = elem!1) | r(s(s(s(s(z)))), elem!1)),
% 3.23/3.46 inference(unit_resolution,[status(thm)],[6189, 79, 14799])).
% 3.23/3.46 tff(14801,plain,
% 3.23/3.46 (r(s(s(s(s(z)))), elem!1)),
% 3.23/3.46 inference(unit_resolution,[status(thm)],[14800, 14788])).
% 3.23/3.46 tff(14802,plain,
% 3.23/3.46 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(z))), s(s(s(s(z)))))) | (~r(s(s(s(s(z)))), elem!1)) | (~r(elem!1, s(s(s(s(z)))))) | (~r(s(s(s(z))), elem!1)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(z))), s(s(s(s(z)))))) | (~r(s(s(s(s(z)))), elem!1)) | (~r(elem!1, s(s(s(s(z)))))) | (~r(s(s(s(z))), elem!1)))),
% 3.23/3.46 inference(rewrite,[status(thm)],[])).
% 3.23/3.46 tff(14803,plain,
% 3.23/3.46 (((~r(elem!1, s(s(s(s(z)))))) | (~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))), s(s(s(s(z)))))) | (~r(s(s(s(s(z)))), elem!1)) | (~r(elem!1, s(s(s(s(z)))))) | (~r(s(s(s(z))), elem!1)))),
% 3.23/3.46 inference(rewrite,[status(thm)],[])).
% 3.23/3.46 tff(14804,plain,
% 3.23/3.46 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(s(s(s(z)))))) | (~r(s(s(s(s(z)))), elem!1)) | (~r(s(s(s(z))), elem!1)) | (~r(s(s(s(z))), s(s(s(s(z)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(z))), s(s(s(s(z)))))) | (~r(s(s(s(s(z)))), elem!1)) | (~r(elem!1, s(s(s(s(z)))))) | (~r(s(s(s(z))), elem!1))))),
% 3.23/3.46 inference(monotonicity,[status(thm)],[14803])).
% 3.23/3.46 tff(14805,plain,
% 3.23/3.46 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(s(s(s(z)))))) | (~r(s(s(s(s(z)))), elem!1)) | (~r(s(s(s(z))), elem!1)) | (~r(s(s(s(z))), s(s(s(s(z)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(z))), s(s(s(s(z)))))) | (~r(s(s(s(s(z)))), elem!1)) | (~r(elem!1, s(s(s(s(z)))))) | (~r(s(s(s(z))), elem!1)))),
% 3.23/3.46 inference(transitivity,[status(thm)],[14804, 14802])).
% 3.23/3.47 tff(14806,plain,
% 3.23/3.47 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(s(s(s(z)))))) | (~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)))))))),
% 3.23/3.47 inference(quant_inst,[status(thm)],[])).
% 3.23/3.47 tff(14807,plain,
% 3.23/3.47 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(z))), s(s(s(s(z)))))) | (~r(s(s(s(s(z)))), elem!1)) | (~r(elem!1, s(s(s(s(z)))))) | (~r(s(s(s(z))), elem!1))),
% 3.23/3.47 inference(modus_ponens,[status(thm)],[14806, 14805])).
% 3.23/3.47 tff(14808,plain,
% 3.23/3.47 ($false),
% 3.23/3.47 inference(unit_resolution,[status(thm)],[14807, 197, 2208, 8074, 14801, 14784])).
% 3.23/3.47 tff(14809,plain,((~b(s(s(z)), elem!1)) | (~r(s(s(s(z))), s(s(s(s(z)))))) | (~r(s(s(s(z))), elem!1)) | (~b(elem!1, s(z))) | (~b(s(s(z)), s(z))) | (~b(s(s(s(s(elem!1)))), s(s(z)))) | (~(s(s(elem!1)) = s(s(z)))) | (~b(s(s(s(s(elem!1)))), s(z))) | (~b(elem!1, s(s(elem!1))))), inference(lemma,lemma(discharge,[]))).
% 3.23/3.47 tff(14810,plain,
% 3.23/3.47 (~r(s(s(s(z))), s(s(s(s(z)))))),
% 3.23/3.47 inference(unit_resolution,[status(thm)],[14809, 14759, 156, 14129, 8074, 1212, 2153, 14686, 14757])).
% 3.23/3.47 tff(14811,plain,
% 3.23/3.47 (b(s(s(s(z))), s(s(s(s(z)))))),
% 3.23/3.47 inference(unit_resolution,[status(thm)],[2233, 14810])).
% 3.23/3.47 tff(14812,plain,
% 3.23/3.47 (b(s(s(s(elem!1))), s(s(s(s(elem!1)))))),
% 3.23/3.47 inference(modus_ponens,[status(thm)],[14811, 2374])).
% 3.23/3.47 tff(14813,plain,
% 3.23/3.47 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(z, s(s(s(elem!1))))) | (~b(z, s(s(elem!1)))) | (~b(z, s(z))) | (~b(s(s(s(elem!1))), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(z, s(s(s(elem!1))))) | (~b(z, s(s(elem!1)))) | (~b(z, s(z))) | (~b(s(s(s(elem!1))), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), s(z))))),
% 3.23/3.47 inference(rewrite,[status(thm)],[])).
% 3.23/3.47 tff(14814,plain,
% 3.23/3.47 (((~b(s(s(s(s(elem!1)))), s(z))) | (~b(z, s(z))) | (~b(s(s(s(elem!1))), s(s(s(s(elem!1)))))) | (~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(z, s(s(s(elem!1))))) | (~b(z, s(s(elem!1))))) <=> ((~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(z, s(s(s(elem!1))))) | (~b(z, s(s(elem!1)))) | (~b(z, s(z))) | (~b(s(s(s(elem!1))), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), s(z))))),
% 3.23/3.47 inference(rewrite,[status(thm)],[])).
% 3.23/3.47 tff(14815,plain,
% 3.23/3.47 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(elem!1)))), s(z))) | (~b(z, s(z))) | (~b(s(s(s(elem!1))), s(s(s(s(elem!1)))))) | (~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(z, s(s(s(elem!1))))) | (~b(z, s(s(elem!1)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(z, s(s(s(elem!1))))) | (~b(z, s(s(elem!1)))) | (~b(z, s(z))) | (~b(s(s(s(elem!1))), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), s(z)))))),
% 3.23/3.47 inference(monotonicity,[status(thm)],[14814])).
% 3.23/3.47 tff(14816,plain,
% 3.23/3.47 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(elem!1)))), s(z))) | (~b(z, s(z))) | (~b(s(s(s(elem!1))), s(s(s(s(elem!1)))))) | (~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(z, s(s(s(elem!1))))) | (~b(z, s(s(elem!1)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(z, s(s(s(elem!1))))) | (~b(z, s(s(elem!1)))) | (~b(z, s(z))) | (~b(s(s(s(elem!1))), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), s(z))))),
% 3.23/3.47 inference(transitivity,[status(thm)],[14815, 14813])).
% 3.23/3.47 tff(14817,plain,
% 3.23/3.47 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(elem!1)))), s(z))) | (~b(z, s(z))) | (~b(s(s(s(elem!1))), s(s(s(s(elem!1)))))) | (~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(z, s(s(s(elem!1))))) | (~b(z, s(s(elem!1)))))),
% 3.23/3.47 inference(quant_inst,[status(thm)],[])).
% 3.23/3.47 tff(14818,plain,
% 3.23/3.47 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(z, s(s(s(elem!1))))) | (~b(z, s(s(elem!1)))) | (~b(z, s(z))) | (~b(s(s(s(elem!1))), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), s(z)))),
% 3.23/3.47 inference(modus_ponens,[status(thm)],[14817, 14816])).
% 3.23/3.47 tff(14819,plain,
% 3.23/3.47 ($false),
% 3.23/3.47 inference(unit_resolution,[status(thm)],[14818, 166, 463, 240, 1820, 118, 1402, 1311])).
% 3.23/3.47 tff(14820,plain,((~b(s(s(s(elem!1))), s(s(s(s(elem!1)))))) | (~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(z, s(s(s(elem!1))))) | (~b(z, s(s(elem!1)))) | (~b(z, s(z))) | (~b(s(s(s(s(elem!1)))), s(z)))), inference(lemma,lemma(discharge,[]))).
% 3.23/3.47 tff(14821,plain,
% 3.23/3.47 (~b(s(s(s(elem!1))), s(s(s(s(elem!1)))))),
% 3.23/3.47 inference(unit_resolution,[status(thm)],[14820, 14757, 118, 14128, 240, 14677])).
% 3.23/3.47 tff(14822,plain,
% 3.23/3.47 ($false),
% 3.23/3.47 inference(unit_resolution,[status(thm)],[14821, 14812])).
% 3.23/3.47 tff(14823,plain,(r(s(s(s(s(elem!1)))), s(s(s(elem!1)))) | (~(s(s(z)) = s(s(elem!1)))) | (~b(s(s(z)), s(z))) | (~r(s(s(s(z))), elem!1)) | (~b(elem!1, s(z))) | (~b(z, s(z))) | (~b(z, s(s(s(elem!1))))) | (~r(s(z), s(s(elem!1)))) | (~b(s(z), s(s(s(elem!1))))) | (~b(elem!1, s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), s(z))) | (~r(s(z), elem!1))), inference(lemma,lemma(discharge,[]))).
% 3.23/3.47 tff(14824,plain,
% 3.23/3.47 (r(s(s(s(s(elem!1)))), s(s(s(elem!1))))),
% 3.23/3.47 inference(unit_resolution,[status(thm)],[14823, 14674, 156, 14668, 34, 13796, 14350, 311, 241, 14667, 350, 10623])).
% 3.23/3.47 tff(14825,plain,
% 3.23/3.47 ($false),
% 3.23/3.47 inference(unit_resolution,[status(thm)],[5790, 197, 311, 350, 700, 1048])).
% 3.23/3.47 tff(14826,plain,((~r(s(s(s(s(elem!1)))), s(z))) | (~r(s(z), s(s(elem!1)))) | (~r(s(s(s(elem!1))), s(z))) | (~r(s(s(s(s(elem!1)))), s(s(s(elem!1)))))), inference(lemma,lemma(discharge,[]))).
% 3.23/3.47 tff(14827,plain,
% 3.23/3.47 (~r(s(s(s(s(elem!1)))), s(z))),
% 3.23/3.47 inference(unit_resolution,[status(thm)],[14826, 350, 311, 14824])).
% 3.23/3.47 tff(14828,plain,
% 3.23/3.47 (b(s(s(s(s(elem!1)))), s(z))),
% 3.23/3.47 inference(unit_resolution,[status(thm)],[661, 14827])).
% 3.23/3.47 tff(14829,plain,
% 3.23/3.47 (r(s(s(s(elem!1))), s(s(elem!1)))),
% 3.23/3.47 inference(unit_resolution,[status(thm)],[14398, 13796, 10529, 311, 350, 14350, 14128])).
% 3.23/3.47 tff(14830,plain,
% 3.23/3.47 (~r(s(s(elem!1)), elem!1)),
% 3.23/3.47 inference(unit_resolution,[status(thm)],[13053, 14829, 311, 350])).
% 3.23/3.47 tff(14831,plain,
% 3.23/3.47 (b(s(s(elem!1)), elem!1)),
% 3.23/3.47 inference(unit_resolution,[status(thm)],[784, 14830, 756])).
% 3.23/3.47 tff(14832,plain,
% 3.23/3.47 (b(s(s(z)), elem!1)),
% 3.23/3.47 inference(unit_resolution,[status(thm)],[14685, 14831, 2153])).
% 3.23/3.47 tff(14833,plain,
% 3.23/3.47 (~r(s(s(elem!1)), s(s(s(elem!1))))),
% 3.23/3.47 inference(unit_resolution,[status(thm)],[2627, 14829, 350, 311])).
% 3.23/3.47 tff(14834,plain,
% 3.23/3.47 (b(s(s(elem!1)), s(s(s(elem!1))))),
% 3.23/3.47 inference(unit_resolution,[status(thm)],[461, 14833, 10529])).
% 3.23/3.47 tff(14835,plain,
% 3.23/3.47 (~b(s(s(s(elem!1))), s(s(s(s(elem!1)))))),
% 3.23/3.47 inference(unit_resolution,[status(thm)],[14820, 14828, 13796, 14128, 14350, 14834])).
% 3.23/3.47 tff(14836,plain,
% 3.23/3.47 (b(s(s(s(elem!1))), s(s(s(s(elem!1)))))),
% 3.23/3.47 inference(modus_ponens,[status(thm)],[3252, 2374])).
% 3.23/3.47 tff(14837,plain,
% 3.23/3.47 ($false),
% 3.23/3.47 inference(unit_resolution,[status(thm)],[691, 14836])).
% 3.23/3.47 tff(14838,plain,((~b(s(s(s(z))), s(s(s(s(z)))))) | b(s(s(s(elem!1))), s(s(s(s(elem!1))))) | (~(s(s(z)) = s(s(elem!1))))), inference(lemma,lemma(discharge,[]))).
% 3.23/3.47 tff(14839,plain,
% 3.23/3.47 (~b(s(s(s(z))), s(s(s(s(z)))))),
% 3.23/3.47 inference(unit_resolution,[status(thm)],[14838, 14835, 34])).
% 3.23/3.47 tff(14840,plain,
% 3.23/3.47 (r(s(s(s(z))), s(s(s(s(z)))))),
% 3.23/3.47 inference(unit_resolution,[status(thm)],[2233, 14839])).
% 3.23/3.47 tff(14841,plain,
% 3.23/3.47 (~b(s(s(s(s(elem!1)))), s(s(z)))),
% 3.23/3.47 inference(unit_resolution,[status(thm)],[14809, 14840, 156, 14129, 14668, 14674, 2153, 14832, 14828])).
% 3.23/3.47 tff(14842,plain,
% 3.23/3.47 (r(s(s(s(s(elem!1)))), s(s(z)))),
% 3.23/3.47 inference(unit_resolution,[status(thm)],[1299, 14841])).
% 3.23/3.47 tff(14843,plain,
% 3.23/3.47 (r(s(s(s(s(elem!1)))), s(s(elem!1)))),
% 3.23/3.47 inference(unit_resolution,[status(thm)],[4866, 14842, 34])).
% 3.23/3.47 tff(14844,plain,
% 3.23/3.47 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(elem!1)))) | (~b(z, s(z))) | (~b(s(s(elem!1)), s(z))) | (~b(s(s(s(s(elem!1)))), s(z))) | (~b(s(z), s(s(s(s(elem!1)))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(s(elem!1)))) | (~b(z, s(z))) | (~b(s(s(elem!1)), s(z))) | (~b(s(s(s(s(elem!1)))), s(z))) | (~b(s(z), s(s(s(s(elem!1)))))))),
% 3.23/3.47 inference(rewrite,[status(thm)],[])).
% 3.23/3.47 tff(14845,plain,
% 3.23/3.47 (((~b(s(s(s(s(elem!1)))), s(z))) | (~b(z, s(z))) | (~b(s(z), s(s(s(s(elem!1)))))) | (~b(s(s(elem!1)), s(z))) | (~b(z, s(z))) | (~b(z, s(s(elem!1))))) <=> ((~b(z, s(s(elem!1)))) | (~b(z, s(z))) | (~b(s(s(elem!1)), s(z))) | (~b(s(s(s(s(elem!1)))), s(z))) | (~b(s(z), s(s(s(s(elem!1)))))))),
% 3.23/3.47 inference(rewrite,[status(thm)],[])).
% 3.23/3.47 tff(14846,plain,
% 3.23/3.47 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(elem!1)))), s(z))) | (~b(z, s(z))) | (~b(s(z), s(s(s(s(elem!1)))))) | (~b(s(s(elem!1)), s(z))) | (~b(z, s(z))) | (~b(z, s(s(elem!1)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(elem!1)))) | (~b(z, s(z))) | (~b(s(s(elem!1)), s(z))) | (~b(s(s(s(s(elem!1)))), s(z))) | (~b(s(z), s(s(s(s(elem!1))))))))),
% 3.23/3.47 inference(monotonicity,[status(thm)],[14845])).
% 3.23/3.47 tff(14847,plain,
% 3.23/3.47 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(elem!1)))), s(z))) | (~b(z, s(z))) | (~b(s(z), s(s(s(s(elem!1)))))) | (~b(s(s(elem!1)), s(z))) | (~b(z, s(z))) | (~b(z, s(s(elem!1)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(s(elem!1)))) | (~b(z, s(z))) | (~b(s(s(elem!1)), s(z))) | (~b(s(s(s(s(elem!1)))), s(z))) | (~b(s(z), s(s(s(s(elem!1)))))))),
% 3.23/3.47 inference(transitivity,[status(thm)],[14846, 14844])).
% 3.23/3.47 tff(14848,plain,
% 3.23/3.47 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(elem!1)))), s(z))) | (~b(z, s(z))) | (~b(s(z), s(s(s(s(elem!1)))))) | (~b(s(s(elem!1)), s(z))) | (~b(z, s(z))) | (~b(z, s(s(elem!1)))))),
% 3.23/3.47 inference(quant_inst,[status(thm)],[])).
% 3.23/3.47 tff(14849,plain,
% 3.23/3.47 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(s(elem!1)))) | (~b(z, s(z))) | (~b(s(s(elem!1)), s(z))) | (~b(s(s(s(s(elem!1)))), s(z))) | (~b(s(z), s(s(s(s(elem!1))))))),
% 3.23/3.47 inference(modus_ponens,[status(thm)],[14848, 14847])).
% 3.23/3.47 tff(14850,plain,
% 3.23/3.47 ($false),
% 3.23/3.47 inference(unit_resolution,[status(thm)],[14849, 166, 1820, 118, 310, 1402, 1327])).
% 3.23/3.47 tff(14851,plain,((~b(s(z), s(s(s(s(elem!1)))))) | (~b(z, s(s(elem!1)))) | (~b(z, s(z))) | (~b(s(s(elem!1)), s(z))) | (~b(s(s(s(s(elem!1)))), s(z)))), inference(lemma,lemma(discharge,[]))).
% 3.23/3.47 tff(14852,plain,
% 3.23/3.47 (~b(s(z), s(s(s(s(elem!1)))))),
% 3.23/3.47 inference(unit_resolution,[status(thm)],[14851, 1402, 118, 1820, 310])).
% 3.23/3.47 tff(14853,plain,
% 3.23/3.47 (r(s(z), s(s(s(s(elem!1)))))),
% 3.23/3.47 inference(unit_resolution,[status(thm)],[681, 14852])).
% 3.23/3.47 tff(14854,plain,
% 3.23/3.47 (~r(s(s(elem!1)), s(s(s(s(elem!1)))))),
% 3.23/3.47 inference(unit_resolution,[status(thm)],[2176, 14853, 311, 2168])).
% 3.23/3.47 tff(14855,plain,
% 3.23/3.47 (b(s(s(elem!1)), s(s(s(s(elem!1)))))),
% 3.23/3.47 inference(unit_resolution,[status(thm)],[827, 14854, 2395])).
% 3.23/3.47 tff(14856,plain,
% 3.23/3.47 (~b(elem!1, s(s(s(s(elem!1)))))),
% 3.23/3.47 inference(unit_resolution,[status(thm)],[14751, 166, 643, 241, 14855, 1402, 10960])).
% 3.23/3.47 tff(14857,plain,
% 3.23/3.47 (r(elem!1, s(s(s(s(elem!1)))))),
% 3.23/3.47 inference(unit_resolution,[status(thm)],[2427, 14856, 2422])).
% 3.23/3.47 tff(14858,plain,
% 3.23/3.47 ($false),
% 3.23/3.47 inference(unit_resolution,[status(thm)],[3820, 197, 2381, 14853, 3408, 14857])).
% 3.23/3.47 tff(14859,plain,((~b(s(s(s(s(elem!1)))), s(z))) | (~r(s(z), elem!1)) | (~r(s(s(s(s(elem!1)))), s(s(elem!1)))) | (elem!1 = s(s(s(s(elem!1))))) | (~b(elem!1, s(s(s(elem!1))))) | (~b(s(z), s(s(s(elem!1))))) | (~b(elem!1, s(s(elem!1)))) | (s(s(elem!1)) = s(s(s(s(elem!1))))) | (~r(s(z), s(s(elem!1)))) | (~r(s(s(s(s(elem!1)))), s(s(z)))) | (~b(z, s(z))) | (~b(z, s(s(elem!1)))) | (~b(s(s(elem!1)), s(z)))), inference(lemma,lemma(discharge,[]))).
% 3.23/3.47 tff(14860,plain,
% 3.23/3.47 ($false),
% 3.23/3.47 inference(unit_resolution,[status(thm)],[14859, 14843, 14842, 10623, 2377, 14667, 241, 14129, 816, 311, 14828, 13796, 14128, 6315])).
% 3.23/3.47 tff(14861,plain,((~r(s(s(s(elem!1))), s(z))) | (~b(s(z), s(s(s(elem!1))))) | (~r(s(z), s(s(elem!1)))) | (~(s(s(z)) = s(s(elem!1)))) | (~b(s(s(z)), s(z))) | b(s(z), elem!1) | (~r(s(s(s(elem!1))), z)) | (~r(s(z), z))), inference(lemma,lemma(discharge,[]))).
% 3.23/3.47 tff(14862,plain,
% 3.23/3.47 (~r(s(s(s(elem!1))), s(z))),
% 3.23/3.47 inference(unit_resolution,[status(thm)],[14861, 241, 311, 34, 156, 9912, 154, 97])).
% 3.23/3.47 tff(14863,plain,
% 3.23/3.47 (b(s(s(s(elem!1))), s(z))),
% 3.23/3.47 inference(unit_resolution,[status(thm)],[1849, 14862])).
% 3.23/3.47 tff(14864,plain,
% 3.23/3.47 (~b(z, s(z))),
% 3.23/3.47 inference(unit_resolution,[status(thm)],[12629, 14863, 156, 241])).
% 3.23/3.47 tff(14865,plain,
% 3.23/3.47 (r(z, s(z))),
% 3.23/3.47 inference(unit_resolution,[status(thm)],[321, 14864])).
% 3.23/3.47 tff(14866,plain,
% 3.23/3.47 (r(elem!1, s(z))),
% 3.23/3.47 inference(unit_resolution,[status(thm)],[741, 14865, 620])).
% 3.23/3.47 tff(14867,plain,
% 3.23/3.47 (~r(s(s(s(s(elem!1)))), elem!1)),
% 3.23/3.47 inference(unit_resolution,[status(thm)],[11173, 14866, 10748, 10623, 14717, 14863, 241])).
% 3.23/3.47 tff(14868,plain,
% 3.23/3.47 (b(s(s(s(s(elem!1)))), elem!1)),
% 3.23/3.47 inference(unit_resolution,[status(thm)],[719, 14867, 627])).
% 3.23/3.47 tff(14869,plain,
% 3.23/3.47 (~b(s(s(s(elem!1))), s(s(elem!1)))),
% 3.23/3.47 inference(unit_resolution,[status(thm)],[12346, 166, 241, 14863, 6315])).
% 3.23/3.47 tff(14870,plain,
% 3.23/3.47 (r(s(s(s(elem!1))), s(s(elem!1)))),
% 3.23/3.47 inference(unit_resolution,[status(thm)],[889, 14869, 3345])).
% 3.23/3.47 tff(14871,plain,
% 3.23/3.47 (~r(s(s(elem!1)), elem!1)),
% 3.23/3.47 inference(unit_resolution,[status(thm)],[1018, 14870, 10748, 14866])).
% 3.23/3.47 tff(14872,plain,
% 3.23/3.47 (b(s(s(elem!1)), elem!1)),
% 3.23/3.47 inference(unit_resolution,[status(thm)],[784, 14871, 756])).
% 3.23/3.47 tff(14873,plain,
% 3.23/3.47 (~b(s(s(s(s(elem!1)))), s(s(elem!1)))),
% 3.23/3.47 inference(unit_resolution,[status(thm)],[11180, 166, 14872, 14129, 14868])).
% 3.23/3.47 tff(14874,plain,
% 3.23/3.47 (r(s(s(s(s(elem!1)))), s(s(elem!1)))),
% 3.23/3.47 inference(unit_resolution,[status(thm)],[813, 14873, 734])).
% 3.23/3.47 tff(14875,plain,
% 3.23/3.47 (~b(s(s(elem!1)), s(s(s(elem!1))))),
% 3.23/3.47 inference(unit_resolution,[status(thm)],[1994, 14863, 241, 6315])).
% 3.23/3.47 tff(14876,plain,
% 3.23/3.47 (r(s(s(elem!1)), s(s(s(elem!1))))),
% 3.23/3.47 inference(unit_resolution,[status(thm)],[461, 14875, 10529])).
% 3.23/3.47 tff(14877,plain,
% 3.23/3.47 (~b(s(s(s(s(elem!1)))), s(z))),
% 3.23/3.47 inference(unit_resolution,[status(thm)],[12705, 14870, 6315, 734, 14714, 241, 14863, 14876])).
% 3.23/3.47 tff(14878,plain,
% 3.23/3.47 (r(s(s(s(s(elem!1)))), s(z))),
% 3.23/3.47 inference(unit_resolution,[status(thm)],[661, 14877])).
% 3.23/3.47 tff(14879,plain,
% 3.23/3.47 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(s(elem!1)))) | (~r(s(s(elem!1)), s(s(s(elem!1))))) | (~r(s(s(s(s(elem!1)))), s(z))) | (~r(s(s(s(s(elem!1)))), s(s(elem!1)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(z), s(s(elem!1)))) | (~r(s(s(elem!1)), s(s(s(elem!1))))) | (~r(s(s(s(s(elem!1)))), s(z))) | (~r(s(s(s(s(elem!1)))), s(s(elem!1)))))),
% 3.23/3.47 inference(rewrite,[status(thm)],[])).
% 3.23/3.47 tff(14880,plain,
% 3.23/3.47 (((~r(s(s(elem!1)), s(s(s(elem!1))))) | (~r(s(z), s(s(elem!1)))) | (~r(s(s(s(s(elem!1)))), s(s(elem!1)))) | (~r(s(s(s(s(elem!1)))), s(z)))) <=> ((~r(s(z), s(s(elem!1)))) | (~r(s(s(elem!1)), s(s(s(elem!1))))) | (~r(s(s(s(s(elem!1)))), s(z))) | (~r(s(s(s(s(elem!1)))), s(s(elem!1)))))),
% 3.23/3.47 inference(rewrite,[status(thm)],[])).
% 3.23/3.47 tff(14881,plain,
% 3.23/3.47 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(elem!1)), s(s(s(elem!1))))) | (~r(s(z), s(s(elem!1)))) | (~r(s(s(s(s(elem!1)))), s(s(elem!1)))) | (~r(s(s(s(s(elem!1)))), s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(s(elem!1)))) | (~r(s(s(elem!1)), s(s(s(elem!1))))) | (~r(s(s(s(s(elem!1)))), s(z))) | (~r(s(s(s(s(elem!1)))), s(s(elem!1))))))),
% 3.23/3.47 inference(monotonicity,[status(thm)],[14880])).
% 3.23/3.47 tff(14882,plain,
% 3.23/3.47 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(elem!1)), s(s(s(elem!1))))) | (~r(s(z), s(s(elem!1)))) | (~r(s(s(s(s(elem!1)))), s(s(elem!1)))) | (~r(s(s(s(s(elem!1)))), s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(z), s(s(elem!1)))) | (~r(s(s(elem!1)), s(s(s(elem!1))))) | (~r(s(s(s(s(elem!1)))), s(z))) | (~r(s(s(s(s(elem!1)))), s(s(elem!1)))))),
% 3.23/3.47 inference(transitivity,[status(thm)],[14881, 14879])).
% 3.23/3.47 tff(14883,plain,
% 3.23/3.47 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(elem!1)), s(s(s(elem!1))))) | (~r(s(z), s(s(elem!1)))) | (~r(s(s(s(s(elem!1)))), s(s(elem!1)))) | (~r(s(s(s(s(elem!1)))), s(z))))),
% 3.23/3.47 inference(quant_inst,[status(thm)],[])).
% 3.23/3.47 tff(14884,plain,
% 3.23/3.47 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(z), s(s(elem!1)))) | (~r(s(s(elem!1)), s(s(s(elem!1))))) | (~r(s(s(s(s(elem!1)))), s(z))) | (~r(s(s(s(s(elem!1)))), s(s(elem!1))))),
% 3.23/3.47 inference(modus_ponens,[status(thm)],[14883, 14882])).
% 3.23/3.47 tff(14885,plain,
% 3.23/3.47 ($false),
% 3.23/3.47 inference(unit_resolution,[status(thm)],[14884, 197, 311, 14876, 14878, 14874])).
% 3.23/3.47 tff(14886,plain,((~b(s(z), s(s(s(elem!1))))) | (~r(s(z), s(s(elem!1)))) | (~b(s(s(z)), s(z))) | (~(s(s(z)) = s(s(elem!1)))) | b(s(z), elem!1) | (~r(s(s(s(elem!1))), z)) | (~r(s(z), z))), inference(lemma,lemma(discharge,[]))).
% 3.23/3.47 tff(14887,plain,
% 3.23/3.47 (~b(s(z), s(s(s(elem!1))))),
% 3.23/3.47 inference(unit_resolution,[status(thm)],[14886, 156, 85, 14660, 14665, 13084, 14334])).
% 3.23/3.47 tff(14888,plain,
% 3.23/3.47 (r(s(z), s(s(s(elem!1))))),
% 3.23/3.47 inference(unit_resolution,[status(thm)],[116, 14887])).
% 3.23/3.47 tff(14889,plain,
% 3.23/3.47 (~b(s(z), s(s(z)))),
% 3.23/3.47 inference(unit_resolution,[status(thm)],[4398, 14660, 54])).
% 3.23/3.47 tff(14890,plain,
% 3.23/3.47 (r(s(z), s(s(z)))),
% 3.23/3.47 inference(unit_resolution,[status(thm)],[427, 14889])).
% 3.23/3.47 tff(14891,plain,
% 3.23/3.47 (b(z, s(s(elem!1)))),
% 3.23/3.47 inference(unit_resolution,[status(thm)],[12671, 14660])).
% 3.23/3.47 tff(14892,plain,
% 3.23/3.47 (~r(s(s(elem!1)), s(s(s(elem!1))))),
% 3.23/3.47 inference(unit_resolution,[status(thm)],[14568, 14888, 13084, 85])).
% 3.23/3.47 tff(14893,plain,
% 3.23/3.47 ((s(s(z)) = s(s(s(elem!1)))) <=> (s(s(elem!1)) = s(s(s(elem!1))))),
% 3.23/3.47 inference(monotonicity,[status(thm)],[14660])).
% 3.23/3.47 tff(14894,plain,
% 3.23/3.47 ((~(s(s(z)) = s(s(s(elem!1))))) <=> (~(s(s(elem!1)) = s(s(s(elem!1)))))),
% 3.23/3.47 inference(monotonicity,[status(thm)],[14893])).
% 3.23/3.47 tff(14895,plain,
% 3.23/3.47 (~(s(s(elem!1)) = s(s(s(elem!1))))),
% 3.23/3.47 inference(modus_ponens,[status(thm)],[209, 14894])).
% 3.23/3.47 tff(14896,plain,
% 3.23/3.47 (r(s(s(s(elem!1))), s(s(elem!1)))),
% 3.23/3.47 inference(unit_resolution,[status(thm)],[12051, 14888, 14334, 14895, 14892, 14891])).
% 3.23/3.47 tff(14897,plain,
% 3.23/3.47 (r(s(s(s(elem!1))), s(s(z)))),
% 3.23/3.47 inference(unit_resolution,[status(thm)],[3454, 14896, 14660])).
% 3.23/3.47 tff(14898,plain,
% 3.23/3.47 (~r(s(s(z)), s(s(s(z))))),
% 3.23/3.47 inference(unit_resolution,[status(thm)],[14596, 14897, 14890, 14888])).
% 3.23/3.47 tff(14899,plain,
% 3.23/3.47 (b(s(s(z)), s(s(s(z))))),
% 3.23/3.47 inference(unit_resolution,[status(thm)],[1730, 14898])).
% 3.23/3.47 tff(14900,plain,
% 3.23/3.47 (r(s(s(s(z))), z) <=> r(s(s(s(z))), elem!1)),
% 3.23/3.47 inference(monotonicity,[status(thm)],[14662])).
% 3.23/3.47 tff(14901,plain,
% 3.23/3.47 (r(s(s(s(z))), elem!1) <=> r(s(s(s(z))), z)),
% 3.23/3.47 inference(symmetry,[status(thm)],[14900])).
% 3.23/3.47 tff(14902,plain,
% 3.23/3.47 (s(s(s(z))) = s(s(s(elem!1)))),
% 3.23/3.48 inference(monotonicity,[status(thm)],[14660])).
% 3.23/3.48 tff(14903,plain,
% 3.23/3.48 (r(s(s(s(z))), elem!1) <=> r(s(s(s(elem!1))), elem!1)),
% 3.23/3.48 inference(monotonicity,[status(thm)],[14902])).
% 3.23/3.48 tff(14904,plain,
% 3.23/3.48 (r(s(s(s(elem!1))), elem!1) <=> r(s(s(s(z))), elem!1)),
% 3.23/3.48 inference(symmetry,[status(thm)],[14903])).
% 3.23/3.48 tff(14905,plain,
% 3.23/3.48 (r(s(s(s(elem!1))), elem!1) <=> r(s(s(s(z))), z)),
% 3.23/3.48 inference(transitivity,[status(thm)],[14904, 14901])).
% 3.23/3.48 tff(14906,plain,
% 3.23/3.48 (r(s(s(s(elem!1))), elem!1)),
% 3.23/3.48 inference(unit_resolution,[status(thm)],[966, 14662, 13084])).
% 3.23/3.48 tff(14907,plain,
% 3.23/3.48 (r(s(s(s(z))), z)),
% 3.23/3.48 inference(modus_ponens,[status(thm)],[14906, 14905])).
% 3.23/3.48 tff(14908,plain,
% 3.23/3.48 ((s(s(s(s(elem!1)))) = s(s(s(z)))) <=> (s(s(s(s(elem!1)))) = s(s(s(elem!1))))),
% 3.23/3.48 inference(monotonicity,[status(thm)],[14902])).
% 3.23/3.48 tff(14909,plain,
% 3.23/3.48 ((s(s(s(s(elem!1)))) = s(s(s(z)))) <=> (s(s(s(elem!1))) = s(s(s(s(elem!1)))))),
% 3.23/3.48 inference(transitivity,[status(thm)],[14908, 1191])).
% 3.23/3.48 tff(14910,plain,
% 3.23/3.48 ((~(s(s(s(s(elem!1)))) = s(s(s(z))))) <=> (~(s(s(s(elem!1))) = s(s(s(s(elem!1))))))),
% 3.23/3.48 inference(monotonicity,[status(thm)],[14909])).
% 3.23/3.48 tff(14911,plain,
% 3.23/3.48 (~(s(s(s(elem!1))) = s(s(s(s(elem!1)))))),
% 3.23/3.48 inference(modus_ponens,[status(thm)],[5112, 14910])).
% 3.23/3.48 tff(14912,plain,
% 3.23/3.48 ((s(s(z)) = s(s(s(elem!1)))) <=> (s(s(s(elem!1))) = s(s(elem!1)))),
% 3.23/3.48 inference(transitivity,[status(thm)],[14893, 3341])).
% 3.23/3.48 tff(14913,plain,
% 3.23/3.48 ((~(s(s(z)) = s(s(s(elem!1))))) <=> (~(s(s(s(elem!1))) = s(s(elem!1))))),
% 3.23/3.48 inference(monotonicity,[status(thm)],[14912])).
% 3.23/3.48 tff(14914,plain,
% 3.23/3.48 (~(s(s(s(elem!1))) = s(s(elem!1)))),
% 3.23/3.48 inference(modus_ponens,[status(thm)],[209, 14913])).
% 3.23/3.48 tff(14915,plain,
% 3.23/3.48 (elem!1 = z),
% 3.23/3.48 inference(symmetry,[status(thm)],[14662])).
% 3.23/3.48 tff(14916,plain,
% 3.23/3.48 ((s(s(elem!1)) = elem!1) <=> (s(s(elem!1)) = z)),
% 3.23/3.48 inference(monotonicity,[status(thm)],[14915])).
% 3.23/3.48 tff(14917,plain,
% 3.23/3.48 ((s(s(elem!1)) = z) <=> (s(s(elem!1)) = elem!1)),
% 3.23/3.48 inference(symmetry,[status(thm)],[14916])).
% 3.23/3.48 tff(14918,plain,
% 3.23/3.48 ((~(s(s(elem!1)) = z)) <=> (~(s(s(elem!1)) = elem!1))),
% 3.23/3.48 inference(monotonicity,[status(thm)],[14917])).
% 3.23/3.48 tff(14919,plain,
% 3.23/3.48 (~(s(s(elem!1)) = elem!1)),
% 3.23/3.48 inference(modus_ponens,[status(thm)],[108, 14918])).
% 3.23/3.48 tff(14920,plain,
% 3.23/3.48 (b(s(s(z)), s(z)) <=> b(s(s(elem!1)), s(z))),
% 3.23/3.48 inference(monotonicity,[status(thm)],[14660])).
% 3.23/3.48 tff(14921,plain,
% 3.23/3.48 (b(s(s(elem!1)), s(z))),
% 3.23/3.48 inference(modus_ponens,[status(thm)],[156, 14920])).
% 3.23/3.48 tff(14922,plain,
% 3.23/3.48 (s(s(elem!1)) = s(s(z))),
% 3.23/3.48 inference(unit_resolution,[status(thm)],[17, 14662])).
% 3.23/3.48 tff(14923,plain,
% 3.23/3.48 (b(s(s(elem!1)), s(s(s(elem!1))))),
% 3.23/3.48 inference(unit_resolution,[status(thm)],[461, 14892, 14895])).
% 3.23/3.48 tff(14924,plain,
% 3.23/3.48 (r(s(s(s(elem!1))), z) <=> r(s(s(s(elem!1))), elem!1)),
% 3.23/3.48 inference(monotonicity,[status(thm)],[14762])).
% 3.23/3.48 tff(14925,plain,
% 3.23/3.48 (r(s(s(s(elem!1))), elem!1) <=> r(s(s(s(elem!1))), z)),
% 3.23/3.48 inference(symmetry,[status(thm)],[14924])).
% 3.23/3.48 tff(14926,plain,
% 3.23/3.48 (r(s(s(s(z))), elem!1) <=> r(s(s(s(elem!1))), elem!1)),
% 3.23/3.48 inference(monotonicity,[status(thm)],[2201])).
% 3.23/3.48 tff(14927,plain,
% 3.23/3.48 (r(s(s(s(z))), elem!1) <=> r(s(s(s(elem!1))), z)),
% 3.23/3.48 inference(transitivity,[status(thm)],[14926, 14925])).
% 3.23/3.48 tff(14928,plain,
% 3.23/3.48 ((~r(s(s(s(z))), elem!1)) <=> (~r(s(s(s(elem!1))), z))),
% 3.23/3.48 inference(monotonicity,[status(thm)],[14927])).
% 3.23/3.48 tff(14929,plain,
% 3.23/3.48 (b(elem!1, s(s(elem!1))) <=> b(z, s(s(z)))),
% 3.23/3.48 inference(monotonicity,[status(thm)],[14763, 128])).
% 3.23/3.48 tff(14930,plain,
% 3.23/3.48 (b(z, s(s(z))) <=> b(elem!1, s(s(elem!1)))),
% 3.23/3.48 inference(symmetry,[status(thm)],[14929])).
% 3.23/3.48 tff(14931,plain,
% 3.23/3.48 (b(elem!1, s(s(elem!1)))),
% 3.23/3.48 inference(modus_ponens,[status(thm)],[10451, 14930])).
% 3.23/3.48 tff(14932,plain,
% 3.23/3.48 ((s(s(s(elem!1))) = s(s(s(s(elem!1))))) <=> (s(s(s(z))) = s(s(s(s(z)))))),
% 3.23/3.48 inference(monotonicity,[status(thm)],[2195, 2196])).
% 3.23/3.48 tff(14933,plain,
% 3.23/3.48 ((~(s(s(s(elem!1))) = s(s(s(s(elem!1)))))) <=> (~(s(s(s(z))) = s(s(s(s(z))))))),
% 3.23/3.48 inference(monotonicity,[status(thm)],[14932])).
% 3.23/3.48 tff(14934,plain,
% 3.23/3.48 (~(s(s(s(z))) = s(s(s(s(z)))))),
% 3.23/3.48 inference(modus_ponens,[status(thm)],[361, 14933])).
% 3.23/3.48 tff(14935,plain,
% 3.23/3.48 (b(s(s(s(elem!1))), s(s(s(s(elem!1))))) <=> b(s(s(s(z))), s(s(s(s(z)))))),
% 3.23/3.48 inference(monotonicity,[status(thm)],[2195, 2196])).
% 3.23/3.48 tff(14936,plain,
% 3.23/3.48 ((~b(s(s(s(elem!1))), s(s(s(s(elem!1)))))) <=> (~b(s(s(s(z))), s(s(s(s(z))))))),
% 3.23/3.48 inference(monotonicity,[status(thm)],[14935])).
% 3.23/3.48 tff(14937,plain,
% 3.23/3.48 (b(z, s(s(s(elem!1)))) <=> b(elem!1, s(s(s(elem!1))))),
% 3.23/3.48 inference(monotonicity,[status(thm)],[14762])).
% 3.23/3.48 tff(14938,plain,
% 3.23/3.48 (b(elem!1, s(s(s(elem!1)))) <=> b(z, s(s(s(elem!1))))),
% 3.23/3.48 inference(symmetry,[status(thm)],[14937])).
% 3.23/3.48 tff(14939,plain,
% 3.23/3.48 ((elem!1 = s(s(s(elem!1)))) <=> (z = s(s(s(elem!1))))),
% 3.23/3.48 inference(monotonicity,[status(thm)],[14763])).
% 3.23/3.48 tff(14940,plain,
% 3.23/3.48 ((elem!1 = s(s(s(elem!1)))) <=> (s(s(s(elem!1))) = z)),
% 3.23/3.48 inference(transitivity,[status(thm)],[14939, 7746])).
% 3.23/3.48 tff(14941,plain,
% 3.23/3.48 ((s(s(s(elem!1))) = z) <=> (elem!1 = s(s(s(elem!1))))),
% 3.23/3.48 inference(symmetry,[status(thm)],[14940])).
% 3.23/3.48 tff(14942,plain,
% 3.23/3.48 ((~(s(s(s(elem!1))) = z)) <=> (~(elem!1 = s(s(s(elem!1)))))),
% 3.23/3.48 inference(monotonicity,[status(thm)],[14941])).
% 3.23/3.48 tff(14943,plain,
% 3.23/3.48 (~(elem!1 = s(s(s(elem!1))))),
% 3.23/3.48 inference(modus_ponens,[status(thm)],[89, 14942])).
% 3.23/3.48 tff(14944,plain,
% 3.23/3.48 (r(s(elem!1), elem!1) <=> r(s(z), elem!1)),
% 3.23/3.48 inference(monotonicity,[status(thm)],[14761])).
% 3.23/3.48 tff(14945,plain,
% 3.23/3.48 (r(s(z), elem!1) <=> r(s(elem!1), elem!1)),
% 3.23/3.48 inference(symmetry,[status(thm)],[14944])).
% 3.23/3.48 tff(14946,plain,
% 3.23/3.48 (r(s(z), z) <=> r(s(z), elem!1)),
% 3.23/3.48 inference(monotonicity,[status(thm)],[14762])).
% 3.23/3.48 tff(14947,plain,
% 3.23/3.48 (r(s(z), z) <=> r(s(elem!1), elem!1)),
% 3.23/3.48 inference(transitivity,[status(thm)],[14946, 14945])).
% 3.23/3.48 tff(14948,plain,
% 3.23/3.48 (~b(s(z), z)),
% 3.23/3.48 inference(unit_resolution,[status(thm)],[13808, 118, 10451, 1820, 310])).
% 3.23/3.48 tff(14949,plain,
% 3.23/3.48 (r(s(z), z)),
% 3.23/3.48 inference(unit_resolution,[status(thm)],[230, 14948])).
% 3.23/3.48 tff(14950,plain,
% 3.23/3.48 (r(s(elem!1), elem!1)),
% 3.23/3.48 inference(modus_ponens,[status(thm)],[14949, 14947])).
% 3.23/3.48 tff(14951,plain,
% 3.23/3.48 (r(s(elem!1), s(s(s(elem!1)))) <=> r(s(z), s(s(s(elem!1))))),
% 3.23/3.48 inference(monotonicity,[status(thm)],[14761])).
% 3.23/3.48 tff(14952,plain,
% 3.23/3.48 (r(s(z), s(s(s(elem!1)))) <=> r(s(elem!1), s(s(s(elem!1))))),
% 3.23/3.48 inference(symmetry,[status(thm)],[14951])).
% 3.23/3.48 tff(14953,plain,
% 3.23/3.48 (r(s(elem!1), s(s(s(elem!1))))),
% 3.23/3.48 inference(modus_ponens,[status(thm)],[119, 14952])).
% 3.23/3.48 tff(14954,plain,
% 3.23/3.48 (b(s(s(elem!1)), z) <=> b(s(s(z)), z)),
% 3.23/3.48 inference(monotonicity,[status(thm)],[128])).
% 3.23/3.48 tff(14955,plain,
% 3.23/3.48 (b(s(s(z)), z) <=> b(s(s(elem!1)), z)),
% 3.23/3.48 inference(symmetry,[status(thm)],[14954])).
% 3.23/3.48 tff(14956,plain,
% 3.23/3.48 (b(s(s(z)), z) <=> b(s(s(z)), elem!1)),
% 3.23/3.48 inference(monotonicity,[status(thm)],[14762])).
% 3.23/3.48 tff(14957,plain,
% 3.23/3.48 (b(s(s(z)), elem!1) <=> b(s(s(z)), z)),
% 3.23/3.48 inference(symmetry,[status(thm)],[14956])).
% 3.23/3.48 tff(14958,plain,
% 3.23/3.48 (b(s(s(z)), elem!1) <=> b(s(s(elem!1)), z)),
% 3.23/3.48 inference(transitivity,[status(thm)],[14957, 14955])).
% 3.23/3.48 tff(14959,plain,
% 3.23/3.48 (b(s(s(s(elem!1))), s(s(elem!1))) <=> b(s(s(s(elem!1))), s(s(z)))),
% 3.23/3.48 inference(monotonicity,[status(thm)],[128])).
% 3.23/3.48 tff(14960,plain,
% 3.23/3.48 (b(s(s(s(elem!1))), s(s(z))) <=> b(s(s(s(elem!1))), s(s(elem!1)))),
% 3.23/3.48 inference(symmetry,[status(thm)],[14959])).
% 3.23/3.48 tff(14961,plain,
% 3.23/3.48 (b(s(s(s(z))), s(s(z))) <=> b(s(s(s(elem!1))), s(s(z)))),
% 3.23/3.48 inference(monotonicity,[status(thm)],[2201])).
% 3.23/3.48 tff(14962,plain,
% 3.23/3.48 (b(s(s(s(z))), s(s(z))) <=> b(s(s(s(elem!1))), s(s(elem!1)))),
% 3.23/3.48 inference(transitivity,[status(thm)],[14961, 14960])).
% 3.23/3.48 tff(14963,plain,
% 3.23/3.48 ((~b(s(s(s(z))), s(s(z)))) <=> (~b(s(s(s(elem!1))), s(s(elem!1))))),
% 3.23/3.48 inference(monotonicity,[status(thm)],[14962])).
% 3.23/3.48 tff(14964,plain,
% 3.23/3.48 (b(s(s(z)), s(s(s(z)))) <=> b(s(s(z)), s(s(s(elem!1))))),
% 3.23/3.48 inference(monotonicity,[status(thm)],[2201])).
% 3.23/3.48 tff(14965,plain,
% 3.23/3.48 (b(s(s(z)), s(s(s(elem!1)))) <=> b(s(s(z)), s(s(s(z))))),
% 3.23/3.48 inference(symmetry,[status(thm)],[14964])).
% 3.23/3.48 tff(14966,plain,
% 3.23/3.48 (b(s(s(elem!1)), s(s(s(elem!1)))) <=> b(s(s(z)), s(s(s(elem!1))))),
% 3.23/3.48 inference(monotonicity,[status(thm)],[128])).
% 3.23/3.48 tff(14967,plain,
% 3.23/3.48 (b(s(s(z)), s(s(s(elem!1))))),
% 3.23/3.48 inference(modus_ponens,[status(thm)],[463, 14966])).
% 3.23/3.48 tff(14968,plain,
% 3.23/3.48 (b(s(s(z)), s(s(s(z))))),
% 3.23/3.48 inference(modus_ponens,[status(thm)],[14967, 14965])).
% 3.23/3.48 tff(14969,plain,
% 3.23/3.48 ((~r(s(s(s(elem!1))), elem!1)) <=> (~r(s(s(s(elem!1))), z))),
% 3.23/3.48 inference(monotonicity,[status(thm)],[14925])).
% 3.23/3.48 tff(14970,assumption,(r(s(elem!1), s(s(s(elem!1))))), introduced(assumption)).
% 3.23/3.48 tff(14971,plain,
% 3.23/3.48 (b(z, s(s(s(z)))) <=> b(elem!1, s(s(s(elem!1))))),
% 3.23/3.48 inference(monotonicity,[status(thm)],[14762, 2201])).
% 3.23/3.48 tff(14972,plain,
% 3.23/3.48 (b(elem!1, s(s(s(z)))) <=> b(z, s(s(s(z))))),
% 3.23/3.48 inference(monotonicity,[status(thm)],[14763])).
% 3.23/3.48 tff(14973,plain,
% 3.23/3.48 (b(elem!1, s(s(s(z)))) <=> b(elem!1, s(s(s(elem!1))))),
% 3.23/3.48 inference(transitivity,[status(thm)],[14972, 14971])).
% 3.23/3.48 tff(14974,plain,
% 3.23/3.48 ((~b(elem!1, s(s(s(z))))) <=> (~b(elem!1, s(s(s(elem!1)))))),
% 3.23/3.48 inference(monotonicity,[status(thm)],[14973])).
% 3.23/3.48 tff(14975,plain,
% 3.23/3.48 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), s(s(z)))) | (~b(elem!1, s(s(z)))) | (~b(s(s(z)), s(s(s(z))))) | (~b(elem!1, s(s(s(z))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(z))), s(s(z)))) | (~b(elem!1, s(s(z)))) | (~b(s(s(z)), s(s(s(z))))) | (~b(elem!1, s(s(s(z))))))),
% 3.23/3.48 inference(rewrite,[status(thm)],[])).
% 3.23/3.48 tff(14976,plain,
% 3.23/3.48 (((~b(s(s(s(z))), s(s(z)))) | (~b(elem!1, s(s(z)))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(s(z))), s(s(z)))) | (~b(elem!1, s(s(z)))) | (~b(elem!1, s(s(s(z)))))) <=> ((~b(s(s(s(z))), s(s(z)))) | (~b(elem!1, s(s(z)))) | (~b(s(s(z)), s(s(s(z))))) | (~b(elem!1, s(s(s(z))))))),
% 3.23/3.48 inference(rewrite,[status(thm)],[])).
% 3.23/3.48 tff(14977,plain,
% 3.23/3.48 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), s(s(z)))) | (~b(elem!1, s(s(z)))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(s(z))), s(s(z)))) | (~b(elem!1, s(s(z)))) | (~b(elem!1, s(s(s(z))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), s(s(z)))) | (~b(elem!1, s(s(z)))) | (~b(s(s(z)), s(s(s(z))))) | (~b(elem!1, s(s(s(z)))))))),
% 3.23/3.48 inference(monotonicity,[status(thm)],[14976])).
% 3.23/3.48 tff(14978,plain,
% 3.23/3.48 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), s(s(z)))) | (~b(elem!1, s(s(z)))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(s(z))), s(s(z)))) | (~b(elem!1, s(s(z)))) | (~b(elem!1, s(s(s(z))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(z))), s(s(z)))) | (~b(elem!1, s(s(z)))) | (~b(s(s(z)), s(s(s(z))))) | (~b(elem!1, s(s(s(z))))))),
% 3.23/3.48 inference(transitivity,[status(thm)],[14977, 14975])).
% 3.23/3.48 tff(14979,plain,
% 3.23/3.48 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), s(s(z)))) | (~b(elem!1, s(s(z)))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(s(z))), s(s(z)))) | (~b(elem!1, s(s(z)))) | (~b(elem!1, s(s(s(z))))))),
% 3.23/3.48 inference(quant_inst,[status(thm)],[])).
% 3.23/3.48 tff(14980,plain,
% 3.23/3.48 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(z))), s(s(z)))) | (~b(elem!1, s(s(z)))) | (~b(s(s(z)), s(s(s(z))))) | (~b(elem!1, s(s(s(z)))))),
% 3.23/3.48 inference(modus_ponens,[status(thm)],[14979, 14978])).
% 3.23/3.48 tff(14981,plain,
% 3.23/3.48 ((~b(elem!1, s(s(z)))) | (~b(elem!1, s(s(s(z)))))),
% 3.23/3.48 inference(unit_resolution,[status(thm)],[14980, 166, 986, 987])).
% 3.23/3.48 tff(14982,plain,
% 3.23/3.48 (~b(elem!1, s(s(s(z))))),
% 3.23/3.48 inference(unit_resolution,[status(thm)],[14981, 14771])).
% 3.23/3.48 tff(14983,plain,
% 3.23/3.48 (~b(elem!1, s(s(s(elem!1))))),
% 3.23/3.48 inference(modus_ponens,[status(thm)],[14982, 14974])).
% 3.23/3.48 tff(14984,plain,
% 3.23/3.48 (r(elem!1, s(s(s(elem!1))))),
% 3.23/3.48 inference(unit_resolution,[status(thm)],[5451, 14983, 14943])).
% 3.23/3.48 tff(14985,plain,
% 3.23/3.48 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(elem!1), elem!1)) | (~r(s(elem!1), s(s(s(elem!1))))) | (~r(elem!1, s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), elem!1)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(elem!1), elem!1)) | (~r(s(elem!1), s(s(s(elem!1))))) | (~r(elem!1, s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), elem!1)))),
% 3.23/3.48 inference(rewrite,[status(thm)],[])).
% 3.23/3.48 tff(14986,plain,
% 3.23/3.48 (((~r(s(s(s(elem!1))), elem!1)) | (~r(elem!1, s(s(s(elem!1))))) | (~r(s(elem!1), s(s(s(elem!1))))) | (~r(s(elem!1), elem!1))) <=> ((~r(s(elem!1), elem!1)) | (~r(s(elem!1), s(s(s(elem!1))))) | (~r(elem!1, s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), elem!1)))),
% 3.23/3.48 inference(rewrite,[status(thm)],[])).
% 3.23/3.48 tff(14987,plain,
% 3.23/3.48 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), elem!1)) | (~r(elem!1, s(s(s(elem!1))))) | (~r(s(elem!1), s(s(s(elem!1))))) | (~r(s(elem!1), elem!1)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(elem!1), elem!1)) | (~r(s(elem!1), s(s(s(elem!1))))) | (~r(elem!1, s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), elem!1))))),
% 3.23/3.48 inference(monotonicity,[status(thm)],[14986])).
% 3.23/3.48 tff(14988,plain,
% 3.23/3.48 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), elem!1)) | (~r(elem!1, s(s(s(elem!1))))) | (~r(s(elem!1), s(s(s(elem!1))))) | (~r(s(elem!1), elem!1)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(elem!1), elem!1)) | (~r(s(elem!1), s(s(s(elem!1))))) | (~r(elem!1, s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), elem!1)))),
% 3.23/3.48 inference(transitivity,[status(thm)],[14987, 14985])).
% 3.23/3.48 tff(14989,plain,
% 3.23/3.48 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), elem!1)) | (~r(elem!1, s(s(s(elem!1))))) | (~r(s(elem!1), s(s(s(elem!1))))) | (~r(s(elem!1), elem!1)))),
% 3.23/3.48 inference(quant_inst,[status(thm)],[])).
% 3.23/3.48 tff(14990,plain,
% 3.23/3.48 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(elem!1), elem!1)) | (~r(s(elem!1), s(s(s(elem!1))))) | (~r(elem!1, s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), elem!1))),
% 3.23/3.48 inference(modus_ponens,[status(thm)],[14989, 14988])).
% 3.23/3.48 tff(14991,plain,
% 3.23/3.48 ((~r(s(elem!1), elem!1)) | (~r(s(elem!1), s(s(s(elem!1))))) | (~r(elem!1, s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), elem!1))),
% 3.23/3.48 inference(unit_resolution,[status(thm)],[14990, 197])).
% 3.23/3.48 tff(14992,plain,
% 3.23/3.48 (~r(s(s(s(elem!1))), elem!1)),
% 3.23/3.48 inference(unit_resolution,[status(thm)],[14991, 14984, 14970, 3728])).
% 3.23/3.48 tff(14993,plain,
% 3.23/3.48 (~r(s(s(s(elem!1))), z)),
% 3.23/3.48 inference(modus_ponens,[status(thm)],[14992, 14969])).
% 3.23/3.48 tff(14994,plain,
% 3.23/3.48 (b(s(s(s(elem!1))), z) <=> b(s(s(s(elem!1))), elem!1)),
% 3.23/3.48 inference(monotonicity,[status(thm)],[14762])).
% 3.23/3.48 tff(14995,plain,
% 3.23/3.48 (b(s(s(s(elem!1))), elem!1) <=> b(s(s(s(elem!1))), z)),
% 3.23/3.48 inference(symmetry,[status(thm)],[14994])).
% 3.23/3.48 tff(14996,plain,
% 3.23/3.48 (b(s(s(s(z))), z) <=> b(s(s(s(elem!1))), elem!1)),
% 3.23/3.48 inference(monotonicity,[status(thm)],[2201, 14762])).
% 3.23/3.48 tff(14997,plain,
% 3.23/3.48 (b(s(s(s(z))), elem!1) <=> b(s(s(s(z))), z)),
% 3.23/3.48 inference(monotonicity,[status(thm)],[14763])).
% 3.23/3.48 tff(14998,plain,
% 3.23/3.48 (b(s(s(s(z))), elem!1) <=> b(s(s(s(elem!1))), z)),
% 3.23/3.48 inference(transitivity,[status(thm)],[14997, 14996, 14995])).
% 3.23/3.48 tff(14999,plain,
% 3.23/3.48 ((~b(s(s(s(z))), elem!1)) <=> (~b(s(s(s(elem!1))), z))),
% 3.23/3.48 inference(monotonicity,[status(thm)],[14998])).
% 3.23/3.48 tff(15000,plain,
% 3.23/3.48 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), s(s(z)))) | (~b(elem!1, s(s(z)))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(s(z))), elem!1)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(z))), s(s(z)))) | (~b(elem!1, s(s(z)))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(s(z))), elem!1)))),
% 3.23/3.48 inference(rewrite,[status(thm)],[])).
% 3.23/3.48 tff(15001,plain,
% 3.23/3.48 (((~b(s(s(s(z))), s(s(z)))) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(s(z)), s(s(s(z))))) | (~b(elem!1, s(s(z)))) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(s(s(z))), elem!1))) <=> ((~b(s(s(s(z))), s(s(z)))) | (~b(elem!1, s(s(z)))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(s(z))), elem!1)))),
% 3.23/3.48 inference(rewrite,[status(thm)],[])).
% 3.23/3.48 tff(15002,plain,
% 3.23/3.48 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), s(s(z)))) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(s(z)), s(s(s(z))))) | (~b(elem!1, s(s(z)))) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(s(s(z))), elem!1)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), s(s(z)))) | (~b(elem!1, s(s(z)))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(s(z))), elem!1))))),
% 3.23/3.48 inference(monotonicity,[status(thm)],[15001])).
% 3.23/3.48 tff(15003,plain,
% 3.23/3.48 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), s(s(z)))) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(s(z)), s(s(s(z))))) | (~b(elem!1, s(s(z)))) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(s(s(z))), elem!1)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(z))), s(s(z)))) | (~b(elem!1, s(s(z)))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(s(z))), elem!1)))),
% 3.23/3.48 inference(transitivity,[status(thm)],[15002, 15000])).
% 3.23/3.48 tff(15004,plain,
% 3.23/3.48 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), s(s(z)))) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(s(z)), s(s(s(z))))) | (~b(elem!1, s(s(z)))) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(s(s(z))), elem!1)))),
% 3.23/3.48 inference(quant_inst,[status(thm)],[])).
% 3.23/3.48 tff(15005,plain,
% 3.23/3.48 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(z))), s(s(z)))) | (~b(elem!1, s(s(z)))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(s(z))), elem!1))),
% 3.23/3.48 inference(modus_ponens,[status(thm)],[15004, 15003])).
% 3.23/3.48 tff(15006,plain,
% 3.23/3.48 ((~b(elem!1, s(s(z)))) | (~b(s(s(s(z))), elem!1))),
% 3.23/3.48 inference(unit_resolution,[status(thm)],[15005, 166, 986, 987])).
% 3.23/3.48 tff(15007,plain,
% 3.23/3.48 (~b(s(s(s(z))), elem!1)),
% 3.23/3.48 inference(unit_resolution,[status(thm)],[15006, 14771])).
% 3.23/3.48 tff(15008,plain,
% 3.23/3.48 (~b(s(s(s(elem!1))), z)),
% 3.23/3.48 inference(modus_ponens,[status(thm)],[15007, 14999])).
% 3.23/3.48 tff(15009,plain,
% 3.23/3.48 (r(s(s(s(elem!1))), z)),
% 3.23/3.48 inference(unit_resolution,[status(thm)],[94, 15008])).
% 3.23/3.48 tff(15010,plain,
% 3.23/3.48 ($false),
% 3.23/3.48 inference(unit_resolution,[status(thm)],[15009, 14993])).
% 3.23/3.48 tff(15011,plain,((~b(s(s(s(z))), s(s(z)))) | (~r(s(elem!1), s(s(s(elem!1))))) | (~r(s(elem!1), elem!1)) | (~(s(s(elem!1)) = s(s(z)))) | (~b(s(s(z)), s(s(s(z))))) | (~b(elem!1, s(s(elem!1))))), inference(lemma,lemma(discharge,[]))).
% 3.23/3.48 tff(15012,plain,
% 3.23/3.48 (~b(s(s(s(z))), s(s(z)))),
% 3.23/3.48 inference(unit_resolution,[status(thm)],[15011, 14953, 14950, 128, 14968, 14931])).
% 3.23/3.48 tff(15013,plain,
% 3.23/3.48 (~b(s(s(s(elem!1))), s(s(elem!1)))),
% 3.23/3.48 inference(modus_ponens,[status(thm)],[15012, 14963])).
% 3.23/3.48 tff(15014,plain,
% 3.23/3.48 (r(s(s(s(elem!1))), s(s(elem!1)))),
% 3.23/3.48 inference(unit_resolution,[status(thm)],[889, 15013, 1863])).
% 3.23/3.48 tff(15015,plain,
% 3.23/3.48 (~r(s(s(elem!1)), elem!1)),
% 3.23/3.48 inference(unit_resolution,[status(thm)],[2508, 15014, 311, 119])).
% 3.23/3.48 tff(15016,plain,
% 3.23/3.48 (b(s(s(elem!1)), elem!1)),
% 3.23/3.48 inference(unit_resolution,[status(thm)],[784, 15015, 767])).
% 3.23/3.48 tff(15017,plain,
% 3.23/3.48 (b(s(s(z)), elem!1)),
% 3.23/3.48 inference(unit_resolution,[status(thm)],[14685, 15016, 128])).
% 3.23/3.48 tff(15018,plain,
% 3.23/3.48 (b(s(s(elem!1)), z)),
% 3.23/3.48 inference(modus_ponens,[status(thm)],[15017, 14958])).
% 3.23/3.48 tff(15019,plain,
% 3.23/3.48 (~b(s(s(s(elem!1))), z)),
% 3.23/3.48 inference(unit_resolution,[status(thm)],[3593, 15018, 1820, 463])).
% 3.23/3.48 tff(15020,plain,
% 3.23/3.48 (r(s(s(s(elem!1))), z)),
% 3.23/3.48 inference(unit_resolution,[status(thm)],[94, 15019])).
% 3.23/3.48 tff(15021,plain,
% 3.23/3.48 (r(s(s(s(elem!1))), elem!1)),
% 3.23/3.48 inference(unit_resolution,[status(thm)],[966, 15020, 14762])).
% 3.23/3.48 tff(15022,plain,
% 3.23/3.48 (~r(elem!1, s(s(s(elem!1))))),
% 3.23/3.48 inference(unit_resolution,[status(thm)],[14991, 15021, 14953, 14950])).
% 3.23/3.48 tff(15023,plain,
% 3.23/3.48 (b(elem!1, s(s(s(elem!1))))),
% 3.23/3.48 inference(unit_resolution,[status(thm)],[5451, 15022, 14943])).
% 3.23/3.48 tff(15024,plain,
% 3.23/3.48 (b(z, s(s(s(elem!1))))),
% 3.23/3.48 inference(modus_ponens,[status(thm)],[15023, 14938])).
% 3.23/3.48 tff(15025,plain,
% 3.23/3.48 (r(s(s(s(z))), s(s(z))) <=> r(s(s(s(elem!1))), s(s(z)))),
% 3.23/3.48 inference(monotonicity,[status(thm)],[2201])).
% 3.23/3.48 tff(15026,plain,
% 3.23/3.48 (r(s(s(s(elem!1))), s(s(z))) <=> r(s(s(s(z))), s(s(z)))),
% 3.23/3.48 inference(symmetry,[status(thm)],[15025])).
% 3.23/3.48 tff(15027,plain,
% 3.23/3.48 (r(s(s(s(elem!1))), s(s(elem!1))) <=> r(s(s(s(elem!1))), s(s(z)))),
% 3.23/3.48 inference(monotonicity,[status(thm)],[128])).
% 3.23/3.48 tff(15028,plain,
% 3.23/3.48 (r(s(s(s(elem!1))), s(s(elem!1))) <=> r(s(s(s(z))), s(s(z)))),
% 3.23/3.48 inference(transitivity,[status(thm)],[15027, 15026])).
% 3.23/3.48 tff(15029,plain,
% 3.23/3.48 (r(s(s(s(z))), s(s(z)))),
% 3.23/3.48 inference(modus_ponens,[status(thm)],[15014, 15028])).
% 3.23/3.48 tff(15030,plain,
% 3.23/3.48 (b(z, s(z)) <=> b(elem!1, s(z))),
% 3.23/3.48 inference(monotonicity,[status(thm)],[14762])).
% 3.23/3.48 tff(15031,plain,
% 3.23/3.48 (b(elem!1, s(z))),
% 3.23/3.48 inference(modus_ponens,[status(thm)],[118, 15030])).
% 3.23/3.48 tff(15032,plain,
% 3.23/3.48 (b(s(s(elem!1)), s(z)) <=> b(s(s(z)), s(z))),
% 3.23/3.48 inference(monotonicity,[status(thm)],[128])).
% 3.23/3.48 tff(15033,plain,
% 3.23/3.48 (b(s(s(z)), s(z))),
% 3.23/3.48 inference(modus_ponens,[status(thm)],[310, 15032])).
% 3.23/3.48 tff(15034,plain,
% 3.23/3.48 (b(elem!1, s(s(s(elem!1)))) <=> b(z, s(s(s(z))))),
% 3.23/3.48 inference(symmetry,[status(thm)],[14971])).
% 3.23/3.48 tff(15035,plain,
% 3.23/3.48 (b(z, s(s(s(z))))),
% 3.23/3.48 inference(modus_ponens,[status(thm)],[15023, 15034])).
% 3.23/3.48 tff(15036,plain,
% 3.23/3.48 (b(z, s(s(s(z)))) <=> b(elem!1, s(s(s(z))))),
% 3.23/3.48 inference(symmetry,[status(thm)],[14972])).
% 3.23/3.48 tff(15037,plain,
% 3.23/3.48 (b(elem!1, s(s(s(z))))),
% 3.23/3.48 inference(modus_ponens,[status(thm)],[1700, 15036])).
% 3.23/3.48 tff(15038,assumption,(~(s(s(s(z))) = s(s(s(s(z)))))), introduced(assumption)).
% 3.23/3.48 tff(15039,plain,
% 3.23/3.48 (~(s(s(s(s(z)))) = s(s(s(z))))),
% 3.23/3.48 inference(modus_ponens,[status(thm)],[15038, 4656])).
% 3.23/3.48 tff(15040,plain,
% 3.23/3.48 (~r(s(s(s(s(z)))), s(s(s(z))))),
% 3.23/3.48 inference(unit_resolution,[status(thm)],[7867, 700, 1676, 128, 119])).
% 3.23/3.48 tff(15041,plain,
% 3.23/3.48 ((s(s(s(s(z)))) = s(s(s(z)))) | b(s(s(s(s(z)))), s(s(s(z))))),
% 3.23/3.48 inference(unit_resolution,[status(thm)],[4660, 79, 15040])).
% 3.23/3.48 tff(15042,plain,
% 3.23/3.48 (b(s(s(s(s(z)))), s(s(s(z))))),
% 3.23/3.48 inference(unit_resolution,[status(thm)],[15041, 15039])).
% 3.23/3.48 tff(15043,plain,
% 3.23/3.48 (r(s(s(s(elem!1))), s(s(s(s(elem!1))))) <=> r(s(s(s(z))), s(s(s(s(z)))))),
% 3.23/3.48 inference(monotonicity,[status(thm)],[2195, 2196])).
% 3.23/3.48 tff(15044,plain,
% 3.23/3.48 ((~r(s(s(s(elem!1))), s(s(s(s(elem!1)))))) <=> (~r(s(s(s(z))), s(s(s(s(z))))))),
% 3.23/3.48 inference(monotonicity,[status(thm)],[15043])).
% 3.23/3.48 tff(15045,plain,
% 3.23/3.48 (~b(s(z), s(s(s(s(z)))))),
% 3.23/3.48 inference(unit_resolution,[status(thm)],[14700, 15042, 14692, 156, 986, 1212])).
% 3.23/3.48 tff(15046,plain,
% 3.23/3.48 (~b(s(z), s(s(s(s(elem!1)))))),
% 3.23/3.48 inference(unit_resolution,[status(thm)],[14707, 15045, 128])).
% 3.23/3.48 tff(15047,plain,
% 3.23/3.48 (r(s(z), s(s(s(s(elem!1)))))),
% 3.23/3.48 inference(unit_resolution,[status(thm)],[680, 15046, 676])).
% 3.23/3.48 tff(15048,plain,
% 3.23/3.48 (~r(s(s(s(elem!1))), s(s(s(s(elem!1)))))),
% 3.23/3.48 inference(unit_resolution,[status(thm)],[708, 15047, 119, 700])).
% 3.23/3.48 tff(15049,plain,
% 3.23/3.48 (~r(s(s(s(z))), s(s(s(s(z)))))),
% 3.23/3.48 inference(modus_ponens,[status(thm)],[15048, 15044])).
% 3.23/3.48 tff(15050,plain,
% 3.23/3.48 (b(s(s(s(z))), s(s(s(s(z)))))),
% 3.23/3.48 inference(unit_resolution,[status(thm)],[2232, 15049, 15038])).
% 3.23/3.48 tff(15051,plain,
% 3.23/3.48 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), elem!1)) | (~b(s(s(z)), s(s(s(z))))) | (~b(elem!1, s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(z))), s(s(s(s(z)))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(z)), elem!1)) | (~b(s(s(z)), s(s(s(z))))) | (~b(elem!1, s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(z))), s(s(s(s(z)))))))),
% 3.23/3.49 inference(rewrite,[status(thm)],[])).
% 3.23/3.49 tff(15052,plain,
% 3.23/3.49 (((~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(elem!1, s(s(s(z))))) | (~b(s(s(z)), 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))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(z))), s(s(s(s(z)))))))),
% 3.23/3.49 inference(rewrite,[status(thm)],[])).
% 3.23/3.49 tff(15053,plain,
% 3.23/3.49 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(elem!1, s(s(s(z))))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(z)), elem!1)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), elem!1)) | (~b(s(s(z)), s(s(s(z))))) | (~b(elem!1, s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(z))), s(s(s(s(z))))))))),
% 3.23/3.49 inference(monotonicity,[status(thm)],[15052])).
% 3.23/3.49 tff(15054,plain,
% 3.23/3.49 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(elem!1, s(s(s(z))))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(z)), elem!1)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(z)), elem!1)) | (~b(s(s(z)), s(s(s(z))))) | (~b(elem!1, s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(z))), s(s(s(s(z)))))))),
% 3.23/3.49 inference(transitivity,[status(thm)],[15053, 15051])).
% 3.23/3.49 tff(15055,plain,
% 3.23/3.49 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(elem!1, s(s(s(z))))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(z)), elem!1)))),
% 3.23/3.49 inference(quant_inst,[status(thm)],[])).
% 3.23/3.49 tff(15056,plain,
% 3.23/3.49 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(z)), elem!1)) | (~b(s(s(z)), s(s(s(z))))) | (~b(elem!1, s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(z))), s(s(s(s(z))))))),
% 3.23/3.49 inference(modus_ponens,[status(thm)],[15055, 15054])).
% 3.23/3.49 tff(15057,plain,
% 3.23/3.49 ($false),
% 3.23/3.49 inference(unit_resolution,[status(thm)],[15056, 166, 14692, 986, 15050, 15042, 15037])).
% 3.23/3.49 tff(15058,plain,((~r(s(s(s(s(elem!1)))), s(z))) | (~b(s(s(z)), elem!1)) | (~b(s(s(z)), s(s(s(z))))) | (~b(z, s(s(s(z))))) | (s(s(s(z))) = s(s(s(s(z))))) | (~(s(s(elem!1)) = s(s(z)))) | (~r(s(z), s(s(s(elem!1))))) | (~b(s(s(z)), s(z))) | (~b(elem!1, s(z))) | (~r(s(s(s(z))), s(s(z))))), inference(lemma,lemma(discharge,[]))).
% 3.23/3.49 tff(15059,plain,
% 3.23/3.49 (~r(s(s(s(s(elem!1)))), s(z))),
% 3.23/3.49 inference(unit_resolution,[status(thm)],[15058, 15017, 14968, 15035, 14934, 128, 119, 15033, 15031, 15029])).
% 3.23/3.49 tff(15060,plain,
% 3.23/3.49 (b(s(s(s(s(elem!1)))), s(z))),
% 3.23/3.49 inference(unit_resolution,[status(thm)],[660, 15059, 656])).
% 3.23/3.49 tff(15061,plain,
% 3.23/3.49 (~b(s(s(s(elem!1))), s(s(s(s(elem!1)))))),
% 3.23/3.49 inference(unit_resolution,[status(thm)],[14820, 15060, 15024, 1820, 118, 463])).
% 3.23/3.49 tff(15062,plain,
% 3.23/3.49 (~b(s(s(s(z))), s(s(s(s(z)))))),
% 3.23/3.49 inference(modus_ponens,[status(thm)],[15061, 14936])).
% 3.23/3.49 tff(15063,plain,
% 3.23/3.49 (r(s(s(s(z))), s(s(s(s(z)))))),
% 3.23/3.49 inference(unit_resolution,[status(thm)],[2232, 15062, 14934])).
% 3.23/3.49 tff(15064,plain,
% 3.23/3.49 (~b(s(z), s(s(s(s(elem!1)))))),
% 3.23/3.49 inference(unit_resolution,[status(thm)],[14851, 15060, 118, 310, 1820])).
% 3.23/3.49 tff(15065,plain,
% 3.23/3.49 (r(s(z), s(s(s(s(elem!1)))))),
% 3.23/3.49 inference(unit_resolution,[status(thm)],[680, 15064, 676])).
% 3.23/3.49 tff(15066,plain,
% 3.23/3.49 (~r(s(s(s(s(elem!1)))), s(s(z)))),
% 3.23/3.49 inference(unit_resolution,[status(thm)],[2217, 15063, 15065, 128, 119])).
% 3.23/3.49 tff(15067,plain,
% 3.23/3.49 (b(s(s(s(s(elem!1)))), s(s(z)))),
% 3.23/3.49 inference(unit_resolution,[status(thm)],[1299, 15066])).
% 3.23/3.49 tff(15068,plain,
% 3.23/3.49 (~r(s(s(s(z))), elem!1)),
% 3.23/3.49 inference(unit_resolution,[status(thm)],[14809, 15067, 15017, 15031, 15033, 15060, 128, 15063, 14931])).
% 3.23/3.49 tff(15069,plain,
% 3.23/3.49 (~r(s(s(s(elem!1))), z)),
% 3.23/3.49 inference(modus_ponens,[status(thm)],[15068, 14928])).
% 3.23/3.49 tff(15070,plain,
% 3.23/3.49 ($false),
% 3.23/3.49 inference(unit_resolution,[status(thm)],[15020, 15069])).
% 3.23/3.49 tff(15071,plain,((~(s(s(elem!1)) = s(s(z)))) | (~r(s(z), s(s(s(elem!1))))) | (~b(z, s(s(elem!1)))) | (~b(z, s(z))) | (~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(s(s(elem!1)), s(z))) | (s(s(elem!1)) = elem!1) | (~r(s(z), s(s(elem!1)))) | (s(s(s(elem!1))) = s(s(elem!1))) | (s(s(s(elem!1))) = s(s(s(s(elem!1))))) | (~b(z, s(s(z))))), inference(lemma,lemma(discharge,[]))).
% 3.23/3.49 tff(15072,plain,
% 3.23/3.49 ((~(s(s(elem!1)) = s(s(z)))) | (~r(s(z), s(s(s(elem!1))))) | (~b(z, s(s(elem!1)))) | (~b(z, s(z))) | (~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(s(s(elem!1)), s(z))) | (s(s(elem!1)) = elem!1) | (~r(s(z), s(s(elem!1)))) | (s(s(s(elem!1))) = s(s(elem!1))) | (s(s(s(elem!1))) = s(s(s(s(elem!1)))))),
% 3.23/3.49 inference(unit_resolution,[status(thm)],[15071, 10450])).
% 3.23/3.49 tff(15073,plain,
% 3.23/3.49 (~b(z, s(z))),
% 3.23/3.49 inference(unit_resolution,[status(thm)],[15072, 14923, 14922, 14891, 14921, 14919, 14888, 85, 14914, 14911])).
% 3.23/3.49 tff(15074,plain,
% 3.23/3.49 (r(z, s(z))),
% 3.23/3.49 inference(unit_resolution,[status(thm)],[321, 15073])).
% 3.23/3.49 tff(15075,plain,
% 3.23/3.49 (~r(s(z), s(s(s(z))))),
% 3.23/3.49 inference(unit_resolution,[status(thm)],[8876, 15074, 14907, 14334])).
% 3.23/3.49 tff(15076,plain,
% 3.23/3.49 (b(s(z), s(s(s(z))))),
% 3.23/3.49 inference(unit_resolution,[status(thm)],[1674, 15075])).
% 3.23/3.49 tff(15077,plain,
% 3.23/3.49 (~r(s(s(s(z))), s(z))),
% 3.23/3.49 inference(unit_resolution,[status(thm)],[3213, 15074, 14907, 14890])).
% 3.23/3.49 tff(15078,plain,
% 3.23/3.49 (b(s(s(s(z))), s(z))),
% 3.23/3.49 inference(unit_resolution,[status(thm)],[1763, 15077])).
% 3.23/3.49 tff(15079,plain,
% 3.23/3.49 ($false),
% 3.23/3.49 inference(unit_resolution,[status(thm)],[3248, 15078, 15076, 156, 14899])).
% 3.23/3.49 tff(15080,plain,((~b(s(s(z)), s(z))) | b(s(z), s(s(elem!1)))), inference(lemma,lemma(discharge,[]))).
% 3.23/3.49 tff(15081,plain,
% 3.23/3.49 (~b(s(s(z)), s(z))),
% 3.23/3.49 inference(unit_resolution,[status(thm)],[15080, 54])).
% 3.23/3.49 tff(15082,plain,
% 3.23/3.49 (r(s(s(z)), s(z))),
% 3.23/3.49 inference(unit_resolution,[status(thm)],[308, 15081])).
% 3.23/3.49 tff(15083,plain,
% 3.23/3.49 (b(s(s(elem!1)), s(z))),
% 3.23/3.49 inference(unit_resolution,[status(thm)],[11987, 15082, 14334])).
% 3.23/3.49 tff(15084,plain,
% 3.23/3.49 (~(s(s(z)) = s(s(elem!1)))),
% 3.23/3.49 inference(unit_resolution,[status(thm)],[3938, 15083, 15081])).
% 3.23/3.49 tff(15085,plain,
% 3.23/3.49 (~r(s(s(z)), z)),
% 3.23/3.49 inference(unit_resolution,[status(thm)],[12769, 197, 85, 323, 15082])).
% 3.23/3.49 tff(15086,plain,
% 3.23/3.49 (b(s(s(z)), z)),
% 3.23/3.49 inference(unit_resolution,[status(thm)],[186, 15085])).
% 3.23/3.49 tff(15087,plain,
% 3.23/3.49 (~(s(s(elem!1)) = s(s(z)))),
% 3.23/3.49 inference(unit_resolution,[status(thm)],[131, 15084])).
% 3.23/3.49 tff(15088,plain,
% 3.23/3.49 (~r(z, s(s(elem!1)))),
% 3.23/3.49 inference(unit_resolution,[status(thm)],[14558, 119, 97, 154])).
% 3.23/3.49 tff(15089,plain,
% 3.23/3.49 (b(z, s(s(elem!1)))),
% 3.23/3.49 inference(unit_resolution,[status(thm)],[1795, 15088])).
% 3.23/3.49 tff(15090,plain,
% 3.23/3.49 (~r(s(s(elem!1)), s(s(s(elem!1))))),
% 3.23/3.49 inference(unit_resolution,[status(thm)],[14568, 119, 154, 311])).
% 3.23/3.49 tff(15091,plain,
% 3.23/3.49 (b(s(s(elem!1)), s(z))),
% 3.23/3.49 inference(unit_resolution,[status(thm)],[11987, 392, 97])).
% 3.23/3.49 tff(15092,plain,
% 3.23/3.49 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), z)) | (~r(s(z), s(s(s(elem!1))))) | (~r(s(s(z)), s(z))) | (~r(s(s(z)), s(s(s(elem!1))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(elem!1))), z)) | (~r(s(z), s(s(s(elem!1))))) | (~r(s(s(z)), s(z))) | (~r(s(s(z)), s(s(s(elem!1))))))),
% 3.23/3.49 inference(rewrite,[status(thm)],[])).
% 3.23/3.49 tff(15093,plain,
% 3.23/3.49 (((~r(s(s(s(elem!1))), z)) | (~r(s(z), s(s(s(elem!1))))) | (~r(s(s(z)), s(s(s(elem!1))))) | (~r(s(s(z)), s(z)))) <=> ((~r(s(s(s(elem!1))), z)) | (~r(s(z), s(s(s(elem!1))))) | (~r(s(s(z)), s(z))) | (~r(s(s(z)), s(s(s(elem!1))))))),
% 3.23/3.49 inference(rewrite,[status(thm)],[])).
% 3.23/3.49 tff(15094,plain,
% 3.23/3.49 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), z)) | (~r(s(z), s(s(s(elem!1))))) | (~r(s(s(z)), s(s(s(elem!1))))) | (~r(s(s(z)), s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), z)) | (~r(s(z), s(s(s(elem!1))))) | (~r(s(s(z)), s(z))) | (~r(s(s(z)), s(s(s(elem!1)))))))),
% 3.23/3.49 inference(monotonicity,[status(thm)],[15093])).
% 3.23/3.49 tff(15095,plain,
% 3.23/3.49 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), z)) | (~r(s(z), s(s(s(elem!1))))) | (~r(s(s(z)), s(s(s(elem!1))))) | (~r(s(s(z)), s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(elem!1))), z)) | (~r(s(z), s(s(s(elem!1))))) | (~r(s(s(z)), s(z))) | (~r(s(s(z)), s(s(s(elem!1))))))),
% 3.23/3.49 inference(transitivity,[status(thm)],[15094, 15092])).
% 3.23/3.49 tff(15096,plain,
% 3.23/3.49 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), z)) | (~r(s(z), s(s(s(elem!1))))) | (~r(s(s(z)), s(s(s(elem!1))))) | (~r(s(s(z)), s(z))))),
% 3.23/3.49 inference(quant_inst,[status(thm)],[])).
% 3.23/3.49 tff(15097,plain,
% 3.23/3.49 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(elem!1))), z)) | (~r(s(z), s(s(s(elem!1))))) | (~r(s(s(z)), s(z))) | (~r(s(s(z)), s(s(s(elem!1)))))),
% 3.23/3.49 inference(modus_ponens,[status(thm)],[15096, 15095])).
% 3.23/3.49 tff(15098,plain,
% 3.23/3.49 ($false),
% 3.23/3.49 inference(unit_resolution,[status(thm)],[15097, 197, 154, 392, 119, 281])).
% 3.23/3.49 tff(15099,plain,((~r(s(s(z)), s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), z)) | (~r(s(s(z)), s(z))) | (~r(s(z), s(s(s(elem!1)))))), inference(lemma,lemma(discharge,[]))).
% 3.23/3.49 tff(15100,plain,
% 3.23/3.49 (~r(s(s(z)), s(s(s(elem!1))))),
% 3.23/3.49 inference(unit_resolution,[status(thm)],[15099, 119, 392, 154])).
% 3.23/3.49 tff(15101,plain,
% 3.23/3.49 (b(s(s(z)), s(s(s(elem!1))))),
% 3.23/3.49 inference(unit_resolution,[status(thm)],[279, 15100])).
% 3.23/3.49 tff(15102,plain,
% 3.23/3.49 ($false),
% 3.23/3.49 inference(unit_resolution,[status(thm)],[14413, 197, 154, 323, 97, 119])).
% 3.23/3.49 tff(15103,plain,((~r(z, s(z))) | (~r(s(s(s(elem!1))), z)) | (~r(s(z), z)) | (~r(s(z), s(s(s(elem!1)))))), inference(lemma,lemma(discharge,[]))).
% 3.23/3.49 tff(15104,plain,
% 3.23/3.49 (~r(z, s(z))),
% 3.23/3.49 inference(unit_resolution,[status(thm)],[15103, 119, 97, 154])).
% 3.23/3.49 tff(15105,plain,
% 3.23/3.49 (b(z, s(z))),
% 3.23/3.49 inference(unit_resolution,[status(thm)],[321, 15104])).
% 3.23/3.49 tff(15106,plain,
% 3.23/3.49 (r(s(s(elem!1)), s(s(z))) <=> r(s(s(s(elem!1))), s(s(z)))),
% 3.23/3.49 inference(monotonicity,[status(thm)],[334])).
% 3.23/3.49 tff(15107,plain,
% 3.23/3.49 (b(s(s(s(elem!1))), s(z))),
% 3.23/3.49 inference(unit_resolution,[status(thm)],[3849, 334, 310])).
% 3.23/3.49 tff(15108,plain,
% 3.23/3.49 (~b(s(s(elem!1)), s(s(z)))),
% 3.23/3.49 inference(unit_resolution,[status(thm)],[12004, 15107, 1820, 263, 118])).
% 3.23/3.49 tff(15109,plain,
% 3.23/3.49 (r(s(s(elem!1)), s(s(z)))),
% 3.23/3.49 inference(unit_resolution,[status(thm)],[441, 15108, 11])).
% 3.23/3.49 tff(15110,plain,
% 3.23/3.49 (r(s(s(s(elem!1))), s(s(z)))),
% 3.23/3.49 inference(modus_ponens,[status(thm)],[15109, 15106])).
% 3.23/3.49 tff(15111,plain,
% 3.23/3.49 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(z)))) | (~b(s(s(s(elem!1))), s(z))) | (~b(z, s(z))) | (~b(s(z), s(s(z)))) | (~b(s(s(z)), s(s(s(elem!1))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(s(z)))) | (~b(s(s(s(elem!1))), s(z))) | (~b(z, s(z))) | (~b(s(z), s(s(z)))) | (~b(s(s(z)), s(s(s(elem!1))))))),
% 3.23/3.49 inference(rewrite,[status(thm)],[])).
% 3.23/3.49 tff(15112,plain,
% 3.23/3.49 (((~b(s(s(s(elem!1))), s(z))) | (~b(z, s(z))) | (~b(s(s(z)), s(s(s(elem!1))))) | (~b(s(z), s(s(z)))) | (~b(z, s(s(z)))) | (~b(z, s(z)))) <=> ((~b(z, s(s(z)))) | (~b(s(s(s(elem!1))), s(z))) | (~b(z, s(z))) | (~b(s(z), s(s(z)))) | (~b(s(s(z)), s(s(s(elem!1))))))),
% 3.23/3.49 inference(rewrite,[status(thm)],[])).
% 3.23/3.49 tff(15113,plain,
% 3.23/3.49 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), s(z))) | (~b(z, s(z))) | (~b(s(s(z)), s(s(s(elem!1))))) | (~b(s(z), s(s(z)))) | (~b(z, s(s(z)))) | (~b(z, s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(z)))) | (~b(s(s(s(elem!1))), s(z))) | (~b(z, s(z))) | (~b(s(z), s(s(z)))) | (~b(s(s(z)), s(s(s(elem!1)))))))),
% 3.23/3.49 inference(monotonicity,[status(thm)],[15112])).
% 3.23/3.49 tff(15114,plain,
% 3.23/3.49 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), s(z))) | (~b(z, s(z))) | (~b(s(s(z)), s(s(s(elem!1))))) | (~b(s(z), s(s(z)))) | (~b(z, s(s(z)))) | (~b(z, s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(s(z)))) | (~b(s(s(s(elem!1))), s(z))) | (~b(z, s(z))) | (~b(s(z), s(s(z)))) | (~b(s(s(z)), s(s(s(elem!1))))))),
% 3.23/3.49 inference(transitivity,[status(thm)],[15113, 15111])).
% 3.23/3.49 tff(15115,plain,
% 3.23/3.49 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), s(z))) | (~b(z, s(z))) | (~b(s(s(z)), s(s(s(elem!1))))) | (~b(s(z), s(s(z)))) | (~b(z, s(s(z)))) | (~b(z, s(z))))),
% 3.23/3.49 inference(quant_inst,[status(thm)],[])).
% 3.23/3.49 tff(15116,plain,
% 3.23/3.49 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(s(z)))) | (~b(s(s(s(elem!1))), s(z))) | (~b(z, s(z))) | (~b(s(z), s(s(z)))) | (~b(s(s(z)), s(s(s(elem!1)))))),
% 3.23/3.49 inference(modus_ponens,[status(thm)],[15115, 15114])).
% 3.23/3.49 tff(15117,plain,
% 3.23/3.49 ($false),
% 3.23/3.49 inference(unit_resolution,[status(thm)],[15116, 166, 556, 10450, 96, 118, 263])).
% 3.23/3.49 tff(15118,plain,((~b(s(z), s(s(z)))) | (~b(s(s(s(elem!1))), s(z))) | (~b(z, s(z))) | (~b(s(s(z)), s(s(s(elem!1)))))), inference(lemma,lemma(discharge,[]))).
% 3.23/3.49 tff(15119,plain,
% 3.23/3.49 (~b(s(z), s(s(z)))),
% 3.23/3.49 inference(unit_resolution,[status(thm)],[15118, 15107, 118, 263])).
% 3.23/3.49 tff(15120,plain,
% 3.23/3.49 (r(s(z), s(s(z)))),
% 3.23/3.49 inference(unit_resolution,[status(thm)],[427, 15119])).
% 3.23/3.49 tff(15121,plain,
% 3.23/3.49 ($false),
% 3.23/3.49 inference(unit_resolution,[status(thm)],[13786, 197, 15120, 392, 119, 15110])).
% 3.23/3.49 tff(15122,plain,((~(s(s(elem!1)) = s(s(s(elem!1))))) | (~r(s(s(z)), s(z))) | (~r(s(z), s(s(s(elem!1))))) | (~b(z, s(z))) | (~b(s(s(z)), s(s(s(elem!1))))) | (s(s(elem!1)) = s(s(z))) | (~b(z, s(s(elem!1)))) | (~b(s(s(elem!1)), s(z)))), inference(lemma,lemma(discharge,[]))).
% 3.23/3.49 tff(15123,plain,
% 3.23/3.49 (~(s(s(elem!1)) = s(s(s(elem!1))))),
% 3.23/3.49 inference(unit_resolution,[status(thm)],[15122, 119, 392, 15105, 15101, 132, 15089, 15091])).
% 3.23/3.49 tff(15124,plain,
% 3.23/3.49 (r(s(s(s(elem!1))), s(s(elem!1)))),
% 3.23/3.49 inference(unit_resolution,[status(thm)],[12051, 15123, 97, 119, 15090, 15089])).
% 3.23/3.49 tff(15125,plain,
% 3.23/3.49 (b(s(s(elem!1)), s(s(s(elem!1))))),
% 3.23/3.49 inference(unit_resolution,[status(thm)],[461, 15123, 15090])).
% 3.23/3.49 tff(15126,plain,
% 3.23/3.49 (~r(s(s(s(elem!1))), s(z))),
% 3.23/3.49 inference(unit_resolution,[status(thm)],[13490, 15123, 311, 392, 119, 52])).
% 3.23/3.49 tff(15127,plain,
% 3.23/3.49 (b(s(s(s(elem!1))), s(z))),
% 3.23/3.49 inference(unit_resolution,[status(thm)],[1849, 15126])).
% 3.23/3.49 tff(15128,plain,
% 3.23/3.49 (~r(s(s(s(elem!1))), s(s(z)))),
% 3.23/3.49 inference(unit_resolution,[status(thm)],[12006, 15124, 392, 132, 15089, 119, 15105, 15127])).
% 3.23/3.49 tff(15129,plain,
% 3.23/3.49 ($false),
% 3.23/3.49 inference(unit_resolution,[status(thm)],[13483, 15128, 15125, 311, 392, 132, 119, 15124])).
% 3.23/3.49 tff(15130,plain,((~r(s(z), s(s(s(elem!1))))) | (~r(s(z), s(s(elem!1)))) | (~r(s(s(z)), s(z))) | (~r(s(z), z)) | (s(s(z)) = s(s(elem!1))) | (~r(s(s(s(elem!1))), z))), inference(lemma,lemma(discharge,[]))).
% 3.23/3.49 tff(15131,plain,
% 3.23/3.49 (~r(s(z), s(s(s(elem!1))))),
% 3.23/3.49 inference(unit_resolution,[status(thm)],[15130, 85, 15082, 14334, 15084, 13084])).
% 3.23/3.49 tff(15132,plain,
% 3.23/3.49 (b(s(z), s(s(s(elem!1))))),
% 3.23/3.49 inference(unit_resolution,[status(thm)],[116, 15131])).
% 3.23/3.49 tff(15133,plain,
% 3.23/3.49 (~(s(s(elem!1)) = s(s(s(elem!1))))),
% 3.23/3.49 inference(unit_resolution,[status(thm)],[12329, 15132, 54])).
% 3.23/3.49 tff(15134,plain,
% 3.23/3.49 (~(s(s(s(elem!1))) = s(s(elem!1)))),
% 3.23/3.49 inference(unit_resolution,[status(thm)],[50, 15133])).
% 3.23/3.49 tff(15135,plain,
% 3.23/3.49 (~r(s(s(s(elem!1))), s(z))),
% 3.23/3.49 inference(unit_resolution,[status(thm)],[373, 323, 85, 13084])).
% 3.23/3.49 tff(15136,plain,
% 3.23/3.49 (b(s(s(s(elem!1))), s(z))),
% 3.23/3.49 inference(unit_resolution,[status(thm)],[1849, 15135])).
% 3.23/3.49 tff(15137,plain,
% 3.23/3.49 (~b(s(s(s(elem!1))), s(s(elem!1)))),
% 3.23/3.49 inference(unit_resolution,[status(thm)],[12346, 166, 15132, 15136, 15083])).
% 3.23/3.49 tff(15138,plain,
% 3.23/3.49 (r(s(s(s(elem!1))), s(s(elem!1)))),
% 3.23/3.49 inference(unit_resolution,[status(thm)],[889, 15137, 15134])).
% 3.23/3.49 tff(15139,plain,
% 3.23/3.49 (~b(s(s(elem!1)), s(s(s(elem!1))))),
% 3.23/3.49 inference(unit_resolution,[status(thm)],[1994, 15136, 15132, 15083])).
% 3.23/3.49 tff(15140,plain,
% 3.23/3.49 (r(s(s(elem!1)), s(s(s(elem!1))))),
% 3.23/3.49 inference(unit_resolution,[status(thm)],[461, 15139, 15133])).
% 3.23/3.49 tff(15141,plain,
% 3.23/3.49 (~r(z, s(s(elem!1)))),
% 3.23/3.49 inference(unit_resolution,[status(thm)],[14423, 15136, 54, 323])).
% 3.23/3.49 tff(15142,plain,
% 3.23/3.49 (b(z, s(s(elem!1)))),
% 3.23/3.49 inference(unit_resolution,[status(thm)],[1795, 15141])).
% 3.23/3.49 tff(15143,plain,
% 3.23/3.49 (~r(s(s(z)), s(s(elem!1)))),
% 3.23/3.49 inference(unit_resolution,[status(thm)],[4253, 2060, 311, 96, 377])).
% 3.23/3.49 tff(15144,plain,
% 3.23/3.49 (b(s(s(z)), s(s(elem!1)))),
% 3.23/3.49 inference(unit_resolution,[status(thm)],[390, 15143, 52])).
% 3.23/3.49 tff(15145,plain,
% 3.23/3.49 (~b(s(z), s(s(z)))),
% 3.23/3.49 inference(unit_resolution,[status(thm)],[4226, 15144, 96, 310, 2060])).
% 3.23/3.49 tff(15146,plain,
% 3.23/3.49 (r(s(z), s(s(z)))),
% 3.23/3.49 inference(unit_resolution,[status(thm)],[427, 15145])).
% 3.23/3.49 tff(15147,plain,
% 3.23/3.49 (~b(s(s(elem!1)), s(s(z)))),
% 3.23/3.49 inference(unit_resolution,[status(thm)],[12611, 15144, 1820])).
% 3.23/3.49 tff(15148,plain,
% 3.23/3.49 (r(s(s(elem!1)), s(s(z)))),
% 3.23/3.49 inference(unit_resolution,[status(thm)],[441, 15147, 132])).
% 3.23/3.49 tff(15149,plain,
% 3.23/3.49 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(s(elem!1)))) | (~r(s(s(z)), s(z))) | (~r(s(z), s(s(z)))) | (~r(s(s(elem!1)), s(s(z)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(z), s(s(elem!1)))) | (~r(s(s(z)), s(z))) | (~r(s(z), s(s(z)))) | (~r(s(s(elem!1)), s(s(z)))))),
% 3.23/3.49 inference(rewrite,[status(thm)],[])).
% 3.23/3.49 tff(15150,plain,
% 3.23/3.49 (((~r(s(s(z)), s(z))) | (~r(s(s(elem!1)), s(s(z)))) | (~r(s(z), s(s(z)))) | (~r(s(z), s(s(elem!1))))) <=> ((~r(s(z), s(s(elem!1)))) | (~r(s(s(z)), s(z))) | (~r(s(z), s(s(z)))) | (~r(s(s(elem!1)), s(s(z)))))),
% 3.23/3.49 inference(rewrite,[status(thm)],[])).
% 3.23/3.49 tff(15151,plain,
% 3.23/3.49 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(z)), s(z))) | (~r(s(s(elem!1)), s(s(z)))) | (~r(s(z), s(s(z)))) | (~r(s(z), s(s(elem!1)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(s(elem!1)))) | (~r(s(s(z)), s(z))) | (~r(s(z), s(s(z)))) | (~r(s(s(elem!1)), s(s(z))))))),
% 3.23/3.49 inference(monotonicity,[status(thm)],[15150])).
% 3.23/3.49 tff(15152,plain,
% 3.23/3.49 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(z)), s(z))) | (~r(s(s(elem!1)), s(s(z)))) | (~r(s(z), s(s(z)))) | (~r(s(z), s(s(elem!1)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(z), s(s(elem!1)))) | (~r(s(s(z)), s(z))) | (~r(s(z), s(s(z)))) | (~r(s(s(elem!1)), s(s(z)))))),
% 3.23/3.49 inference(transitivity,[status(thm)],[15151, 15149])).
% 3.23/3.50 tff(15153,plain,
% 3.23/3.50 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(z)), s(z))) | (~r(s(s(elem!1)), s(s(z)))) | (~r(s(z), s(s(z)))) | (~r(s(z), s(s(elem!1)))))),
% 3.23/3.50 inference(quant_inst,[status(thm)],[])).
% 3.23/3.50 tff(15154,plain,
% 3.23/3.50 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(z), s(s(elem!1)))) | (~r(s(s(z)), s(z))) | (~r(s(z), s(s(z)))) | (~r(s(s(elem!1)), s(s(z))))),
% 3.23/3.50 inference(modus_ponens,[status(thm)],[15153, 15152])).
% 3.23/3.50 tff(15155,plain,
% 3.23/3.50 ($false),
% 3.23/3.50 inference(unit_resolution,[status(thm)],[15154, 197, 311, 15148, 15146, 392])).
% 3.23/3.50 tff(15156,plain,((~b(s(s(s(elem!1))), s(s(z)))) | (~r(s(z), s(s(elem!1)))) | (~r(s(s(z)), s(z))) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(s(elem!1)), s(z))) | (~b(z, s(s(elem!1)))) | (s(s(z)) = s(s(elem!1))) | (~r(s(s(elem!1)), s(s(s(elem!1)))))), inference(lemma,lemma(discharge,[]))).
% 3.23/3.50 tff(15157,plain,
% 3.23/3.50 (~b(s(s(s(elem!1))), s(s(z)))),
% 3.23/3.50 inference(unit_resolution,[status(thm)],[15156, 15136, 15082, 85, 15083, 15142, 15084, 15140])).
% 3.23/3.50 tff(15158,plain,
% 3.23/3.50 (r(s(s(s(elem!1))), s(s(z)))),
% 3.23/3.50 inference(unit_resolution,[status(thm)],[218, 15157])).
% 3.23/3.50 tff(15159,plain,
% 3.23/3.50 (~r(s(s(elem!1)), s(s(z)))),
% 3.23/3.50 inference(unit_resolution,[status(thm)],[4313, 15158, 15082, 15138])).
% 3.23/3.50 tff(15160,plain,
% 3.23/3.50 (b(s(s(elem!1)), s(s(z)))),
% 3.23/3.50 inference(unit_resolution,[status(thm)],[441, 15159, 15087])).
% 3.23/3.50 tff(15161,plain,
% 3.23/3.50 ($false),
% 3.23/3.50 inference(unit_resolution,[status(thm)],[12388, 166, 15142, 15160, 10450, 15086])).
% 3.23/3.50 tff(15162,plain,((~r(z, s(z))) | b(s(z), s(s(elem!1)))), inference(lemma,lemma(discharge,[]))).
% 3.23/3.50 tff(15163,plain,
% 3.23/3.50 (~r(z, s(z))),
% 3.23/3.50 inference(unit_resolution,[status(thm)],[15162, 54])).
% 3.23/3.50 tff(15164,plain,
% 3.23/3.50 (b(z, s(z))),
% 3.23/3.50 inference(unit_resolution,[status(thm)],[321, 15163])).
% 3.23/3.50 tff(15165,plain,
% 3.23/3.50 (~r(s(s(z)), z)),
% 3.23/3.50 inference(unit_resolution,[status(thm)],[11980, 365, 97, 392])).
% 3.23/3.50 tff(15166,plain,
% 3.23/3.50 (b(s(s(z)), z)),
% 3.23/3.50 inference(unit_resolution,[status(thm)],[186, 15165])).
% 3.23/3.50 tff(15167,plain,
% 3.23/3.50 (~r(s(s(elem!1)), z)),
% 3.23/3.50 inference(unit_resolution,[status(thm)],[4478, 365, 311, 97])).
% 3.23/3.50 tff(15168,plain,
% 3.23/3.50 (b(s(s(elem!1)), z)),
% 3.23/3.50 inference(unit_resolution,[status(thm)],[608, 15167])).
% 3.23/3.50 tff(15169,plain,
% 3.23/3.50 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(s(elem!1)))) | (~r(z, s(s(elem!1)))) | (~r(s(z), z)) | (~r(s(s(elem!1)), s(s(z)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(z), s(s(elem!1)))) | (~r(z, s(s(elem!1)))) | (~r(s(z), z)) | (~r(s(s(elem!1)), s(s(z)))))),
% 3.23/3.50 inference(rewrite,[status(thm)],[])).
% 3.23/3.50 tff(15170,plain,
% 3.23/3.50 (((~r(s(s(elem!1)), s(s(z)))) | (~r(z, s(s(elem!1)))) | (~r(s(z), s(s(elem!1)))) | (~r(s(z), z))) <=> ((~r(s(z), s(s(elem!1)))) | (~r(z, s(s(elem!1)))) | (~r(s(z), z)) | (~r(s(s(elem!1)), s(s(z)))))),
% 3.23/3.50 inference(rewrite,[status(thm)],[])).
% 3.23/3.50 tff(15171,plain,
% 3.33/3.50 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(elem!1)), s(s(z)))) | (~r(z, s(s(elem!1)))) | (~r(s(z), s(s(elem!1)))) | (~r(s(z), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(s(elem!1)))) | (~r(z, s(s(elem!1)))) | (~r(s(z), z)) | (~r(s(s(elem!1)), s(s(z))))))),
% 3.33/3.50 inference(monotonicity,[status(thm)],[15170])).
% 3.33/3.50 tff(15172,plain,
% 3.33/3.50 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(elem!1)), s(s(z)))) | (~r(z, s(s(elem!1)))) | (~r(s(z), s(s(elem!1)))) | (~r(s(z), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(z), s(s(elem!1)))) | (~r(z, s(s(elem!1)))) | (~r(s(z), z)) | (~r(s(s(elem!1)), s(s(z)))))),
% 3.33/3.50 inference(transitivity,[status(thm)],[15171, 15169])).
% 3.33/3.50 tff(15173,plain,
% 3.33/3.50 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(elem!1)), s(s(z)))) | (~r(z, s(s(elem!1)))) | (~r(s(z), s(s(elem!1)))) | (~r(s(z), z)))),
% 3.33/3.50 inference(quant_inst,[status(thm)],[])).
% 3.33/3.50 tff(15174,plain,
% 3.33/3.50 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(z), s(s(elem!1)))) | (~r(z, s(s(elem!1)))) | (~r(s(z), z)) | (~r(s(s(elem!1)), s(s(z))))),
% 3.33/3.50 inference(modus_ponens,[status(thm)],[15173, 15172])).
% 3.33/3.50 tff(15175,plain,
% 3.33/3.50 ($false),
% 3.33/3.50 inference(unit_resolution,[status(thm)],[15174, 197, 311, 393, 97, 365])).
% 3.33/3.50 tff(15176,plain,((~r(s(s(elem!1)), s(s(z)))) | (~r(s(z), s(s(elem!1)))) | (~r(s(z), z)) | (~r(z, s(s(elem!1))))), inference(lemma,lemma(discharge,[]))).
% 3.33/3.50 tff(15177,plain,
% 3.33/3.50 (~r(s(s(elem!1)), s(s(z)))),
% 3.33/3.50 inference(unit_resolution,[status(thm)],[15176, 365, 97, 311])).
% 3.33/3.50 tff(15178,plain,
% 3.33/3.50 (b(s(s(elem!1)), s(s(z)))),
% 3.33/3.50 inference(unit_resolution,[status(thm)],[441, 15177, 11])).
% 3.33/3.50 tff(15179,plain,
% 3.33/3.50 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(z)))) | (~b(s(s(elem!1)), z)) | (~b(s(s(elem!1)), s(s(z)))) | (~b(s(s(z)), z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(s(z)))) | (~b(s(s(elem!1)), z)) | (~b(s(s(elem!1)), s(s(z)))) | (~b(s(s(z)), z)))),
% 3.33/3.50 inference(rewrite,[status(thm)],[])).
% 3.33/3.50 tff(15180,plain,
% 3.33/3.50 (((~b(z, s(s(z)))) | (~b(s(s(elem!1)), s(s(z)))) | (~b(s(s(z)), z)) | (~b(z, s(s(z)))) | (~b(s(s(elem!1)), s(s(z)))) | (~b(s(s(elem!1)), z))) <=> ((~b(z, s(s(z)))) | (~b(s(s(elem!1)), z)) | (~b(s(s(elem!1)), s(s(z)))) | (~b(s(s(z)), z)))),
% 3.33/3.50 inference(rewrite,[status(thm)],[])).
% 3.33/3.50 tff(15181,plain,
% 3.33/3.50 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(z)))) | (~b(s(s(elem!1)), s(s(z)))) | (~b(s(s(z)), z)) | (~b(z, s(s(z)))) | (~b(s(s(elem!1)), s(s(z)))) | (~b(s(s(elem!1)), z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(z)))) | (~b(s(s(elem!1)), z)) | (~b(s(s(elem!1)), s(s(z)))) | (~b(s(s(z)), z))))),
% 3.33/3.50 inference(monotonicity,[status(thm)],[15180])).
% 3.33/3.50 tff(15182,plain,
% 3.33/3.50 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(z)))) | (~b(s(s(elem!1)), s(s(z)))) | (~b(s(s(z)), z)) | (~b(z, s(s(z)))) | (~b(s(s(elem!1)), s(s(z)))) | (~b(s(s(elem!1)), z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(s(z)))) | (~b(s(s(elem!1)), z)) | (~b(s(s(elem!1)), s(s(z)))) | (~b(s(s(z)), z)))),
% 3.33/3.50 inference(transitivity,[status(thm)],[15181, 15179])).
% 3.33/3.50 tff(15183,plain,
% 3.33/3.50 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(z)))) | (~b(s(s(elem!1)), s(s(z)))) | (~b(s(s(z)), z)) | (~b(z, s(s(z)))) | (~b(s(s(elem!1)), s(s(z)))) | (~b(s(s(elem!1)), z)))),
% 3.33/3.50 inference(quant_inst,[status(thm)],[])).
% 3.33/3.50 tff(15184,plain,
% 3.33/3.50 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(s(z)))) | (~b(s(s(elem!1)), z)) | (~b(s(s(elem!1)), s(s(z)))) | (~b(s(s(z)), z))),
% 3.33/3.50 inference(modus_ponens,[status(thm)],[15183, 15182])).
% 3.33/3.50 tff(15185,plain,
% 3.33/3.50 ($false),
% 3.33/3.50 inference(unit_resolution,[status(thm)],[15184, 166, 15178, 10450, 15168, 15166])).
% 3.33/3.50 tff(15186,plain,((~r(z, s(s(elem!1)))) | (s(s(elem!1)) = s(s(z))) | (~r(s(z), z)) | (~r(s(z), s(s(elem!1)))) | (~r(s(s(z)), s(z)))), inference(lemma,lemma(discharge,[]))).
% 3.33/3.50 tff(15187,plain,
% 3.33/3.50 (~r(z, s(s(elem!1)))),
% 3.33/3.50 inference(unit_resolution,[status(thm)],[15186, 11, 97, 311, 392])).
% 3.33/3.50 tff(15188,plain,
% 3.33/3.50 (b(z, s(s(elem!1)))),
% 3.33/3.50 inference(unit_resolution,[status(thm)],[1795, 15187])).
% 3.33/3.50 tff(15189,plain,
% 3.33/3.50 (r(s(s(s(elem!1))), s(s(elem!1)))),
% 3.33/3.50 inference(unit_resolution,[status(thm)],[14398, 14350, 45, 311, 118, 350, 15188])).
% 3.33/3.50 tff(15190,plain,
% 3.33/3.50 (~r(s(s(elem!1)), s(s(s(elem!1))))),
% 3.33/3.50 inference(unit_resolution,[status(thm)],[2627, 15189, 350, 311])).
% 3.33/3.50 tff(15191,plain,
% 3.33/3.50 (b(s(s(elem!1)), s(s(s(elem!1))))),
% 3.33/3.50 inference(unit_resolution,[status(thm)],[461, 15190, 45])).
% 3.33/3.50 tff(15192,plain,
% 3.33/3.50 (~r(s(s(elem!1)), s(s(z)))),
% 3.33/3.50 inference(unit_resolution,[status(thm)],[4199, 15189, 311, 350])).
% 3.33/3.50 tff(15193,plain,
% 3.33/3.50 (b(s(s(elem!1)), s(s(z)))),
% 3.33/3.50 inference(unit_resolution,[status(thm)],[441, 15192, 11])).
% 3.33/3.50 tff(15194,plain,
% 3.33/3.50 ($false),
% 3.33/3.50 inference(unit_resolution,[status(thm)],[501, 15193, 15191, 13486, 13471])).
% 3.33/3.50 tff(15195,plain,((~r(s(s(s(elem!1))), s(z))) | (s(s(elem!1)) = s(s(z))) | (s(s(elem!1)) = s(s(s(elem!1)))) | (~r(s(z), s(s(elem!1)))) | (~b(z, s(z))) | (~r(s(s(z)), s(z))) | (~r(s(s(s(elem!1))), z)) | (~r(s(z), z))), inference(lemma,lemma(discharge,[]))).
% 3.33/3.50 tff(15196,plain,
% 3.33/3.50 (~r(s(s(s(elem!1))), s(z))),
% 3.33/3.50 inference(unit_resolution,[status(thm)],[15195, 15087, 15133, 85, 15164, 15082, 13084, 14334])).
% 3.33/3.50 tff(15197,plain,
% 3.33/3.50 (b(s(s(s(elem!1))), s(z))),
% 3.33/3.50 inference(unit_resolution,[status(thm)],[1849, 15196])).
% 3.33/3.50 tff(15198,plain,
% 3.33/3.50 (~r(z, s(s(elem!1)))),
% 3.33/3.50 inference(unit_resolution,[status(thm)],[15186, 15087, 14334, 85, 15082])).
% 3.33/3.50 tff(15199,plain,
% 3.33/3.50 (b(z, s(s(elem!1)))),
% 3.33/3.50 inference(unit_resolution,[status(thm)],[1795, 15198])).
% 3.33/3.50 tff(15200,plain,
% 3.33/3.50 (~b(s(s(elem!1)), s(s(s(elem!1))))),
% 3.33/3.50 inference(unit_resolution,[status(thm)],[1994, 15197, 15132, 15083])).
% 3.33/3.50 tff(15201,plain,
% 3.33/3.50 (r(s(s(elem!1)), s(s(s(elem!1))))),
% 3.33/3.50 inference(unit_resolution,[status(thm)],[461, 15200, 15133])).
% 3.33/3.50 tff(15202,plain,
% 3.33/3.50 (~r(s(s(z)), s(s(s(elem!1))))),
% 3.33/3.50 inference(unit_resolution,[status(thm)],[14443, 15201, 15084, 13084, 15199])).
% 3.33/3.50 tff(15203,plain,
% 3.33/3.50 (b(s(s(z)), s(s(s(elem!1))))),
% 3.33/3.50 inference(unit_resolution,[status(thm)],[279, 15202])).
% 3.33/3.50 tff(15204,plain,
% 3.33/3.50 (~b(s(s(elem!1)), s(s(z)))),
% 3.33/3.50 inference(unit_resolution,[status(thm)],[12004, 15203, 15164, 15199, 15197])).
% 3.33/3.50 tff(15205,plain,
% 3.33/3.50 (~b(z, s(s(s(elem!1))))),
% 3.33/3.50 inference(unit_resolution,[status(thm)],[249, 15197, 15132, 15164])).
% 3.33/3.50 tff(15206,plain,
% 3.33/3.50 (r(z, s(s(s(elem!1))))),
% 3.33/3.50 inference(unit_resolution,[status(thm)],[261, 15205])).
% 3.33/3.50 tff(15207,plain,
% 3.33/3.50 (~r(s(s(elem!1)), z)),
% 3.33/3.50 inference(unit_resolution,[status(thm)],[4018, 15206, 13084, 15201])).
% 3.33/3.50 tff(15208,plain,
% 3.33/3.50 (b(s(s(elem!1)), z)),
% 3.33/3.50 inference(unit_resolution,[status(thm)],[608, 15207])).
% 3.33/3.50 tff(15209,plain,
% 3.33/3.50 (~b(s(s(z)), s(s(elem!1)))),
% 3.33/3.50 inference(unit_resolution,[status(thm)],[11837, 15208, 15199])).
% 3.33/3.50 tff(15210,plain,
% 3.33/3.50 ($false),
% 3.33/3.50 inference(unit_resolution,[status(thm)],[13102, 15209, 15204, 15082, 85, 15084])).
% 3.33/3.50 tff(15211,plain,(b(s(z), s(s(elem!1)))), inference(lemma,lemma(discharge,[]))).
% 3.33/3.50 tff(15212,plain,
% 3.33/3.50 (~(s(s(z)) = s(s(elem!1)))),
% 3.33/3.50 inference(unit_resolution,[status(thm)],[5435, 5433, 376])).
% 3.33/3.50 tff(15213,plain,
% 3.33/3.50 (~(s(s(elem!1)) = s(s(z)))),
% 3.33/3.50 inference(unit_resolution,[status(thm)],[131, 15212])).
% 3.33/3.50 tff(15214,plain,
% 3.33/3.50 (~r(s(s(z)), s(s(elem!1)))),
% 3.33/3.50 inference(unit_resolution,[status(thm)],[5384, 12399, 10521, 392])).
% 3.33/3.50 tff(15215,plain,
% 3.33/3.50 (b(s(s(z)), s(s(elem!1)))),
% 3.33/3.50 inference(unit_resolution,[status(thm)],[390, 15212, 15214])).
% 3.33/3.50 tff(15216,plain,
% 3.33/3.50 (~r(s(s(elem!1)), s(s(z)))),
% 3.33/3.50 inference(unit_resolution,[status(thm)],[5362, 120, 10521, 392])).
% 3.33/3.50 tff(15217,plain,
% 3.33/3.50 (b(s(s(elem!1)), s(s(z)))),
% 3.33/3.50 inference(unit_resolution,[status(thm)],[441, 11, 15216])).
% 3.33/3.50 tff(15218,plain,
% 3.33/3.50 (~b(z, s(s(elem!1)))),
% 3.33/3.50 inference(unit_resolution,[status(thm)],[10727, 15217, 10451, 446])).
% 3.33/3.50 tff(15219,plain,
% 3.33/3.50 (r(z, s(s(elem!1)))),
% 3.33/3.50 inference(unit_resolution,[status(thm)],[1795, 15218])).
% 3.33/3.50 tff(15220,plain,
% 3.33/3.50 (~b(s(s(elem!1)), s(s(s(elem!1))))),
% 3.33/3.50 inference(unit_resolution,[status(thm)],[6083, 350, 10521, 120, 392, 11])).
% 3.33/3.50 tff(15221,plain,
% 3.33/3.50 (r(s(s(elem!1)), s(s(s(elem!1))))),
% 3.33/3.50 inference(unit_resolution,[status(thm)],[461, 15220, 45])).
% 3.33/3.50 tff(15222,plain,
% 3.33/3.50 (~r(s(s(elem!1)), s(s(s(elem!1))))),
% 3.33/3.50 inference(unit_resolution,[status(thm)],[10564, 197, 12399, 350, 10521])).
% 3.33/3.50 tff(15223,plain,
% 3.33/3.50 (~r(s(z), s(s(s(elem!1))))),
% 3.33/3.50 inference(unit_resolution,[status(thm)],[6892, 333, 4577, 392])).
% 3.33/3.50 tff(15224,plain,
% 3.33/3.50 (b(s(z), s(s(s(elem!1))))),
% 3.33/3.50 inference(unit_resolution,[status(thm)],[116, 15223])).
% 3.33/3.50 tff(15225,plain,
% 3.33/3.50 (r(s(s(s(elem!1))), s(s(elem!1)))),
% 3.33/3.50 inference(unit_resolution,[status(thm)],[6040, 1863, 15224, 1821, 376])).
% 3.33/3.50 tff(15226,plain,
% 3.33/3.50 (~r(s(s(s(elem!1))), s(s(z)))),
% 3.33/3.50 inference(unit_resolution,[status(thm)],[9439, 197, 4577, 333, 905])).
% 3.33/3.50 tff(15227,plain,
% 3.33/3.50 (~r(s(s(z)), s(s(s(elem!1))))),
% 3.33/3.50 inference(unit_resolution,[status(thm)],[8675, 197, 4577, 333, 905])).
% 3.33/3.50 tff(15228,plain,
% 3.33/3.50 (~b(s(s(elem!1)), s(s(z)))),
% 3.33/3.50 inference(unit_resolution,[status(thm)],[501, 15227, 463, 15226])).
% 3.33/3.50 tff(15229,plain,
% 3.33/3.50 (r(s(s(elem!1)), s(s(z)))),
% 3.33/3.50 inference(unit_resolution,[status(thm)],[441, 15228, 11])).
% 3.33/3.50 tff(15230,plain,
% 3.33/3.50 (b(s(s(s(elem!1))), s(s(z)))),
% 3.33/3.50 inference(unit_resolution,[status(thm)],[218, 15226])).
% 3.33/3.50 tff(15231,plain,
% 3.33/3.50 (b(s(s(z)), s(s(s(elem!1))))),
% 3.33/3.50 inference(unit_resolution,[status(thm)],[279, 15227])).
% 3.33/3.50 tff(15232,plain,
% 3.33/3.50 (~b(s(z), s(s(z)))),
% 3.33/3.50 inference(unit_resolution,[status(thm)],[12045, 15231, 10451, 118, 15230])).
% 3.33/3.50 tff(15233,plain,
% 3.33/3.50 (r(s(z), s(s(z)))),
% 3.33/3.50 inference(unit_resolution,[status(thm)],[427, 15232])).
% 3.33/3.50 tff(15234,plain,
% 3.33/3.50 ($false),
% 3.33/3.50 inference(unit_resolution,[status(thm)],[5362, 15233, 15229, 392, 4577])).
% 3.33/3.50 tff(15235,plain,((~r(s(s(s(elem!1))), s(s(elem!1)))) | (~r(s(s(z)), s(z))) | (~r(s(s(elem!1)), s(z))) | (s(s(elem!1)) = s(s(z))) | (~b(z, s(s(z)))) | (~b(z, s(z))) | (~b(s(s(elem!1)), s(s(s(elem!1))))) | (~r(s(s(z)), s(s(elem!1))))), inference(lemma,lemma(discharge,[]))).
% 3.33/3.50 tff(15236,plain,
% 3.33/3.50 ($false),
% 3.33/3.50 inference(unit_resolution,[status(thm)],[15235, 6030, 15225, 4577, 11, 10451, 118, 392, 333])).
% 3.33/3.50 tff(15237,plain,((s(s(s(elem!1))) = s(s(elem!1))) | (~r(s(s(elem!1)), s(z))) | (s(s(elem!1)) = s(s(z))) | (~b(z, s(s(z)))) | (~b(z, s(z))) | (~r(s(s(z)), s(z))) | (~r(s(s(z)), s(s(elem!1)))) | r(s(s(elem!1)), s(s(s(elem!1)))) | (~b(s(z), s(s(elem!1))))), inference(lemma,lemma(discharge,[]))).
% 3.33/3.50 tff(15238,plain,
% 3.33/3.50 (s(s(s(elem!1))) = s(s(elem!1))),
% 3.33/3.50 inference(unit_resolution,[status(thm)],[15237, 333, 11, 10451, 118, 392, 4577, 1821, 376])).
% 3.33/3.50 tff(15239,plain,
% 3.33/3.50 (s(s(elem!1)) = s(s(s(elem!1)))),
% 3.33/3.50 inference(unit_resolution,[status(thm)],[50, 15238])).
% 3.33/3.50 tff(15240,plain,
% 3.33/3.50 (s(s(s(elem!1))) = s(elem!1)),
% 3.33/3.50 inference(unit_resolution,[status(thm)],[2594, 15239])).
% 3.33/3.50 tff(15241,plain,
% 3.33/3.50 (s(elem!1) = s(s(s(elem!1)))),
% 3.33/3.50 inference(symmetry,[status(thm)],[15240])).
% 3.33/3.50 tff(15242,plain,
% 3.33/3.50 (s(elem!1) = s(s(elem!1))),
% 3.33/3.50 inference(transitivity,[status(thm)],[15241, 15238])).
% 3.33/3.50 tff(15243,plain,
% 3.33/3.50 (inj_0(s(elem!1)) = inj_0(s(s(elem!1)))),
% 3.33/3.50 inference(monotonicity,[status(thm)],[15242])).
% 3.33/3.50 tff(15244,plain,
% 3.33/3.50 (inj_0(s(s(elem!1))) = inj_0(s(elem!1))),
% 3.33/3.50 inference(symmetry,[status(thm)],[15243])).
% 3.33/3.50 tff(15245,plain,
% 3.33/3.50 (s(s(elem!1)) = s(s(s(elem!1)))),
% 3.33/3.50 inference(symmetry,[status(thm)],[15238])).
% 3.33/3.50 tff(15246,plain,
% 3.33/3.50 (s(s(elem!1)) = elem!1),
% 3.33/3.50 inference(transitivity,[status(thm)],[15245, 15240, 39, 15244, 20])).
% 3.33/3.50 tff(15247,plain,
% 3.33/3.50 (r(s(s(s(z))), s(s(elem!1))) <=> r(s(s(s(z))), elem!1)),
% 3.33/3.50 inference(monotonicity,[status(thm)],[15246])).
% 3.33/3.50 tff(15248,plain,
% 3.33/3.50 (r(s(s(s(z))), elem!1) <=> r(s(s(s(z))), s(s(elem!1)))),
% 3.33/3.50 inference(symmetry,[status(thm)],[15247])).
% 3.33/3.50 tff(15249,plain,
% 3.33/3.50 (~(s(s(s(z))) = elem!1)),
% 3.33/3.50 inference(unit_resolution,[status(thm)],[3122, 15239])).
% 3.33/3.50 tff(15250,plain,
% 3.33/3.50 (~r(s(z), z)),
% 3.33/3.50 inference(unit_resolution,[status(thm)],[6771, 333, 4577, 392])).
% 3.33/3.50 tff(15251,plain,
% 3.33/3.50 (b(s(z), z)),
% 3.33/3.50 inference(unit_resolution,[status(thm)],[230, 15250])).
% 3.33/3.50 tff(15252,plain,
% 3.33/3.50 (~r(s(z), s(s(z)))),
% 3.33/3.50 inference(unit_resolution,[status(thm)],[5384, 333, 4577, 392])).
% 3.33/3.50 tff(15253,plain,
% 3.33/3.50 (b(s(z), s(s(z)))),
% 3.33/3.50 inference(unit_resolution,[status(thm)],[427, 15252])).
% 3.33/3.50 tff(15254,plain,
% 3.33/3.50 (r(s(s(z)), s(s(s(elem!1))))),
% 3.33/3.50 inference(unit_resolution,[status(thm)],[338, 15239, 333])).
% 3.33/3.50 tff(15255,plain,
% 3.33/3.50 (~b(s(s(z)), z)),
% 3.33/3.50 inference(unit_resolution,[status(thm)],[11973, 15253, 10451, 118])).
% 3.33/3.50 tff(15256,plain,
% 3.33/3.50 (r(s(s(z)), z)),
% 3.33/3.50 inference(unit_resolution,[status(thm)],[186, 15255])).
% 3.33/3.50 tff(15257,plain,
% 3.33/3.50 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(elem!1)))) | (~r(s(s(z)), s(s(elem!1)))) | (~r(s(s(elem!1)), s(z))) | (~r(s(s(z)), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, s(s(elem!1)))) | (~r(s(s(z)), s(s(elem!1)))) | (~r(s(s(elem!1)), s(z))) | (~r(s(s(z)), z)))),
% 3.33/3.50 inference(rewrite,[status(thm)],[])).
% 3.33/3.50 tff(15258,plain,
% 3.33/3.50 (((~r(s(s(elem!1)), s(z))) | (~r(z, s(s(elem!1)))) | (~r(s(s(z)), s(s(elem!1)))) | (~r(s(s(z)), z))) <=> ((~r(z, s(s(elem!1)))) | (~r(s(s(z)), s(s(elem!1)))) | (~r(s(s(elem!1)), s(z))) | (~r(s(s(z)), z)))),
% 3.33/3.50 inference(rewrite,[status(thm)],[])).
% 3.33/3.50 tff(15259,plain,
% 3.33/3.50 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(elem!1)), s(z))) | (~r(z, s(s(elem!1)))) | (~r(s(s(z)), s(s(elem!1)))) | (~r(s(s(z)), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(elem!1)))) | (~r(s(s(z)), s(s(elem!1)))) | (~r(s(s(elem!1)), s(z))) | (~r(s(s(z)), z))))),
% 3.33/3.50 inference(monotonicity,[status(thm)],[15258])).
% 3.33/3.50 tff(15260,plain,
% 3.33/3.50 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(elem!1)), s(z))) | (~r(z, s(s(elem!1)))) | (~r(s(s(z)), s(s(elem!1)))) | (~r(s(s(z)), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, s(s(elem!1)))) | (~r(s(s(z)), s(s(elem!1)))) | (~r(s(s(elem!1)), s(z))) | (~r(s(s(z)), z)))),
% 3.33/3.50 inference(transitivity,[status(thm)],[15259, 15257])).
% 3.33/3.50 tff(15261,plain,
% 3.33/3.50 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(elem!1)), s(z))) | (~r(z, s(s(elem!1)))) | (~r(s(s(z)), s(s(elem!1)))) | (~r(s(s(z)), z)))),
% 3.33/3.50 inference(quant_inst,[status(thm)],[])).
% 3.33/3.50 tff(15262,plain,
% 3.33/3.50 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, s(s(elem!1)))) | (~r(s(s(z)), s(s(elem!1)))) | (~r(s(s(elem!1)), s(z))) | (~r(s(s(z)), z))),
% 3.33/3.50 inference(modus_ponens,[status(thm)],[15261, 15260])).
% 3.33/3.50 tff(15263,plain,
% 3.33/3.50 ($false),
% 3.33/3.50 inference(unit_resolution,[status(thm)],[15262, 197, 4577, 333, 365, 866])).
% 3.33/3.50 tff(15264,plain,((~r(s(s(z)), s(s(elem!1)))) | (~r(s(s(elem!1)), s(z))) | (~r(z, s(s(elem!1)))) | (~r(s(s(z)), z))), inference(lemma,lemma(discharge,[]))).
% 3.33/3.50 tff(15265,plain,
% 3.33/3.50 (~r(z, s(s(elem!1)))),
% 3.33/3.50 inference(unit_resolution,[status(thm)],[15264, 15256, 4577, 333])).
% 3.33/3.50 tff(15266,plain,
% 3.33/3.50 (b(z, s(s(elem!1)))),
% 3.33/3.50 inference(unit_resolution,[status(thm)],[1795, 15265])).
% 3.33/3.50 tff(15267,plain,
% 3.33/3.50 (~r(s(z), s(s(s(z))))),
% 3.33/3.50 inference(unit_resolution,[status(thm)],[8655, 333, 4577, 392])).
% 3.33/3.50 tff(15268,plain,
% 3.33/3.50 (b(s(z), s(s(s(z))))),
% 3.33/3.50 inference(unit_resolution,[status(thm)],[1674, 15267])).
% 3.33/3.50 tff(15269,plain,
% 3.33/3.50 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(elem!1)))) | (~b(s(z), z)) | (~b(s(z), s(s(elem!1)))) | (~b(s(s(elem!1)), s(s(z)))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(z)), s(s(s(z))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(s(elem!1)))) | (~b(s(z), z)) | (~b(s(z), s(s(elem!1)))) | (~b(s(s(elem!1)), s(s(z)))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(z)), s(s(s(z))))))),
% 3.33/3.50 inference(rewrite,[status(thm)],[])).
% 3.33/3.50 tff(15270,plain,
% 3.33/3.50 (((~b(s(s(z)), s(s(s(z))))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(elem!1)), s(s(z)))) | (~b(z, s(s(elem!1)))) | (~b(s(z), s(s(elem!1)))) | (~b(s(z), z))) <=> ((~b(z, s(s(elem!1)))) | (~b(s(z), z)) | (~b(s(z), s(s(elem!1)))) | (~b(s(s(elem!1)), s(s(z)))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(z)), s(s(s(z))))))),
% 3.33/3.50 inference(rewrite,[status(thm)],[])).
% 3.33/3.50 tff(15271,plain,
% 3.33/3.50 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), s(s(s(z))))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(elem!1)), s(s(z)))) | (~b(z, s(s(elem!1)))) | (~b(s(z), s(s(elem!1)))) | (~b(s(z), z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(elem!1)))) | (~b(s(z), z)) | (~b(s(z), s(s(elem!1)))) | (~b(s(s(elem!1)), s(s(z)))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(z)), s(s(s(z)))))))),
% 3.33/3.50 inference(monotonicity,[status(thm)],[15270])).
% 3.33/3.50 tff(15272,plain,
% 3.33/3.50 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), s(s(s(z))))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(elem!1)), s(s(z)))) | (~b(z, s(s(elem!1)))) | (~b(s(z), s(s(elem!1)))) | (~b(s(z), z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(s(elem!1)))) | (~b(s(z), z)) | (~b(s(z), s(s(elem!1)))) | (~b(s(s(elem!1)), s(s(z)))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(z)), s(s(s(z))))))),
% 3.33/3.50 inference(transitivity,[status(thm)],[15271, 15269])).
% 3.33/3.50 tff(15273,plain,
% 3.33/3.50 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), s(s(s(z))))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(elem!1)), s(s(z)))) | (~b(z, s(s(elem!1)))) | (~b(s(z), s(s(elem!1)))) | (~b(s(z), z)))),
% 3.33/3.50 inference(quant_inst,[status(thm)],[])).
% 3.33/3.50 tff(15274,plain,
% 3.33/3.50 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(s(elem!1)))) | (~b(s(z), z)) | (~b(s(z), s(s(elem!1)))) | (~b(s(s(elem!1)), s(s(z)))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(z)), s(s(s(z)))))),
% 3.33/3.50 inference(modus_ponens,[status(thm)],[15273, 15272])).
% 3.33/3.50 tff(15275,plain,
% 3.33/3.50 ($false),
% 3.33/3.50 inference(unit_resolution,[status(thm)],[15274, 166, 376, 1820, 53, 405, 988, 986])).
% 3.33/3.50 tff(15276,plain,((~b(s(s(z)), s(s(s(z))))) | (~b(s(z), s(s(elem!1)))) | (~b(z, s(s(elem!1)))) | (~b(s(z), z)) | (~b(s(s(elem!1)), s(s(z)))) | (~b(s(z), s(s(s(z)))))), inference(lemma,lemma(discharge,[]))).
% 3.33/3.50 tff(15277,plain,
% 3.33/3.50 (~b(s(s(z)), s(s(s(z))))),
% 3.33/3.50 inference(unit_resolution,[status(thm)],[15276, 405, 1820, 53, 376, 988])).
% 3.33/3.50 tff(15278,plain,
% 3.33/3.50 (r(s(s(z)), s(s(s(z))))),
% 3.33/3.50 inference(unit_resolution,[status(thm)],[1730, 15277])).
% 3.33/3.50 tff(15279,plain,
% 3.33/3.50 (~r(s(s(s(z))), elem!1)),
% 3.33/3.50 inference(unit_resolution,[status(thm)],[8084, 15278, 350, 281, 4066])).
% 3.33/3.50 tff(15280,plain,
% 3.33/3.50 (b(s(s(s(z))), elem!1)),
% 3.33/3.50 inference(unit_resolution,[status(thm)],[2826, 15279, 10809])).
% 3.33/3.50 tff(15281,plain,
% 3.33/3.50 (b(s(s(s(z))), s(s(elem!1)))),
% 3.33/3.50 inference(modus_ponens,[status(thm)],[15280, 4072])).
% 3.33/3.50 tff(15282,plain,
% 3.33/3.50 (~r(s(s(s(z))), elem!1)),
% 3.33/3.50 inference(unit_resolution,[status(thm)],[8084, 1732, 350, 281, 4066])).
% 3.33/3.50 tff(15283,plain,
% 3.33/3.50 (b(s(s(s(z))), elem!1)),
% 3.33/3.50 inference(unit_resolution,[status(thm)],[2826, 15282, 10809])).
% 3.33/3.50 tff(15284,plain,
% 3.33/3.50 (b(s(s(s(z))), s(s(elem!1)))),
% 3.33/3.50 inference(modus_ponens,[status(thm)],[15283, 4072])).
% 3.33/3.50 tff(15285,plain,
% 3.33/3.50 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(z)))) | (~b(s(s(elem!1)), s(s(z)))) | (~b(z, s(z))) | (~b(s(z), s(s(s(z))))) | (~b(z, s(s(s(z))))) | (~b(s(s(s(z))), s(s(elem!1)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(s(z)))) | (~b(s(s(elem!1)), s(s(z)))) | (~b(z, s(z))) | (~b(s(z), s(s(s(z))))) | (~b(z, s(s(s(z))))) | (~b(s(s(s(z))), s(s(elem!1)))))),
% 3.33/3.51 inference(rewrite,[status(thm)],[])).
% 3.33/3.51 tff(15286,plain,
% 3.33/3.51 (((~b(s(s(elem!1)), s(s(z)))) | (~b(z, s(s(z)))) | (~b(s(s(s(z))), s(s(elem!1)))) | (~b(s(z), s(s(s(z))))) | (~b(z, s(s(s(z))))) | (~b(z, s(z)))) <=> ((~b(z, s(s(z)))) | (~b(s(s(elem!1)), s(s(z)))) | (~b(z, s(z))) | (~b(s(z), s(s(s(z))))) | (~b(z, s(s(s(z))))) | (~b(s(s(s(z))), s(s(elem!1)))))),
% 3.33/3.51 inference(rewrite,[status(thm)],[])).
% 3.33/3.51 tff(15287,plain,
% 3.33/3.51 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), s(s(z)))) | (~b(z, s(s(z)))) | (~b(s(s(s(z))), s(s(elem!1)))) | (~b(s(z), s(s(s(z))))) | (~b(z, s(s(s(z))))) | (~b(z, s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(z)))) | (~b(s(s(elem!1)), s(s(z)))) | (~b(z, s(z))) | (~b(s(z), s(s(s(z))))) | (~b(z, s(s(s(z))))) | (~b(s(s(s(z))), s(s(elem!1))))))),
% 3.33/3.51 inference(monotonicity,[status(thm)],[15286])).
% 3.33/3.51 tff(15288,plain,
% 3.33/3.51 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), s(s(z)))) | (~b(z, s(s(z)))) | (~b(s(s(s(z))), s(s(elem!1)))) | (~b(s(z), s(s(s(z))))) | (~b(z, s(s(s(z))))) | (~b(z, s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(s(z)))) | (~b(s(s(elem!1)), s(s(z)))) | (~b(z, s(z))) | (~b(s(z), s(s(s(z))))) | (~b(z, s(s(s(z))))) | (~b(s(s(s(z))), s(s(elem!1)))))),
% 3.33/3.51 inference(transitivity,[status(thm)],[15287, 15285])).
% 3.33/3.51 tff(15289,plain,
% 3.33/3.51 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), s(s(z)))) | (~b(z, s(s(z)))) | (~b(s(s(s(z))), s(s(elem!1)))) | (~b(s(z), s(s(s(z))))) | (~b(z, s(s(s(z))))) | (~b(z, s(z))))),
% 3.33/3.51 inference(quant_inst,[status(thm)],[])).
% 3.33/3.51 tff(15290,plain,
% 3.33/3.51 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(s(z)))) | (~b(s(s(elem!1)), s(s(z)))) | (~b(z, s(z))) | (~b(s(z), s(s(s(z))))) | (~b(z, s(s(s(z))))) | (~b(s(s(s(z))), s(s(elem!1))))),
% 3.33/3.51 inference(modus_ponens,[status(thm)],[15289, 15288])).
% 3.33/3.51 tff(15291,plain,
% 3.33/3.51 (~b(z, s(s(s(z))))),
% 3.33/3.51 inference(unit_resolution,[status(thm)],[15290, 166, 405, 10451, 118, 988, 15284])).
% 3.33/3.51 tff(15292,plain,
% 3.33/3.51 (r(z, s(s(s(z))))),
% 3.33/3.51 inference(unit_resolution,[status(thm)],[1697, 15291])).
% 3.33/3.51 tff(15293,plain,
% 3.33/3.51 ($false),
% 3.33/3.51 inference(unit_resolution,[status(thm)],[12074, 197, 866, 15292, 1733, 1732])).
% 3.33/3.51 tff(15294,plain,((~r(s(s(z)), s(s(s(z))))) | (~r(s(s(z)), z)) | (~r(s(s(s(z))), z)) | (~b(s(s(elem!1)), s(s(z)))) | (~b(z, s(s(z)))) | (~b(z, s(z))) | (~b(s(z), s(s(s(z))))) | (~(s(s(s(elem!1))) = s(s(elem!1)))) | (~r(s(s(s(elem!1))), s(z))) | (~r(s(s(z)), s(s(s(elem!1)))))), inference(lemma,lemma(discharge,[]))).
% 3.33/3.51 tff(15295,plain,
% 3.33/3.51 (~r(s(s(s(z))), z)),
% 3.33/3.51 inference(unit_resolution,[status(thm)],[15294, 15278, 866, 405, 10451, 118, 988, 47, 350, 281])).
% 3.33/3.51 tff(15296,plain,
% 3.33/3.51 (b(s(s(s(z))), z)),
% 3.33/3.51 inference(unit_resolution,[status(thm)],[1713, 15295])).
% 3.33/3.51 tff(15297,plain,
% 3.33/3.51 (~b(z, s(s(s(z))))),
% 3.33/3.51 inference(unit_resolution,[status(thm)],[1708, 15296, 53, 988])).
% 3.33/3.51 tff(15298,plain,
% 3.33/3.51 (r(z, s(s(s(z))))),
% 3.33/3.51 inference(unit_resolution,[status(thm)],[1697, 15297])).
% 3.33/3.51 tff(15299,plain,
% 3.33/3.51 (~r(s(s(s(z))), s(z))),
% 3.33/3.51 inference(unit_resolution,[status(thm)],[1754, 15298, 866, 15278])).
% 3.33/3.51 tff(15300,plain,
% 3.33/3.51 (b(s(s(s(z))), s(z))),
% 3.33/3.51 inference(unit_resolution,[status(thm)],[1763, 15299])).
% 3.33/3.51 tff(15301,plain,
% 3.33/3.51 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), z)) | (~b(s(z), s(s(elem!1)))) | (~b(z, s(z))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(z))), z)) | (~b(s(s(s(z))), s(s(elem!1)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), z)) | (~b(s(z), s(s(elem!1)))) | (~b(z, s(z))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(z))), z)) | (~b(s(s(s(z))), s(s(elem!1)))))),
% 3.33/3.51 inference(rewrite,[status(thm)],[])).
% 3.33/3.51 tff(15302,plain,
% 3.33/3.51 (((~b(s(z), s(s(elem!1)))) | (~b(s(s(s(z))), s(s(elem!1)))) | (~b(z, s(z))) | (~b(s(z), z)) | (~b(s(s(s(z))), z)) | (~b(s(s(s(z))), s(z)))) <=> ((~b(s(z), z)) | (~b(s(z), s(s(elem!1)))) | (~b(z, s(z))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(z))), z)) | (~b(s(s(s(z))), s(s(elem!1)))))),
% 3.33/3.51 inference(rewrite,[status(thm)],[])).
% 3.33/3.51 tff(15303,plain,
% 3.33/3.51 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(elem!1)))) | (~b(s(s(s(z))), s(s(elem!1)))) | (~b(z, s(z))) | (~b(s(z), z)) | (~b(s(s(s(z))), z)) | (~b(s(s(s(z))), s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), z)) | (~b(s(z), s(s(elem!1)))) | (~b(z, s(z))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(z))), z)) | (~b(s(s(s(z))), s(s(elem!1))))))),
% 3.33/3.51 inference(monotonicity,[status(thm)],[15302])).
% 3.33/3.51 tff(15304,plain,
% 3.33/3.51 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(elem!1)))) | (~b(s(s(s(z))), s(s(elem!1)))) | (~b(z, s(z))) | (~b(s(z), z)) | (~b(s(s(s(z))), z)) | (~b(s(s(s(z))), s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), z)) | (~b(s(z), s(s(elem!1)))) | (~b(z, s(z))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(z))), z)) | (~b(s(s(s(z))), s(s(elem!1)))))),
% 3.33/3.51 inference(transitivity,[status(thm)],[15303, 15301])).
% 3.33/3.51 tff(15305,plain,
% 3.33/3.51 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(elem!1)))) | (~b(s(s(s(z))), s(s(elem!1)))) | (~b(z, s(z))) | (~b(s(z), z)) | (~b(s(s(s(z))), z)) | (~b(s(s(s(z))), s(z))))),
% 3.33/3.51 inference(quant_inst,[status(thm)],[])).
% 3.33/3.51 tff(15306,plain,
% 3.33/3.51 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), z)) | (~b(s(z), s(s(elem!1)))) | (~b(z, s(z))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(z))), z)) | (~b(s(s(s(z))), s(s(elem!1))))),
% 3.33/3.51 inference(modus_ponens,[status(thm)],[15305, 15304])).
% 3.33/3.51 tff(15307,plain,
% 3.33/3.51 ($false),
% 3.33/3.51 inference(unit_resolution,[status(thm)],[15306, 166, 376, 53, 118, 15296, 15300, 15281])).
% 3.33/3.51 tff(15308,plain,((~b(s(s(elem!1)), s(s(z)))) | (~b(s(z), s(s(elem!1)))) | (~b(s(z), z)) | (~b(z, s(z))) | (~(s(s(s(elem!1))) = s(s(elem!1)))) | (~r(s(s(z)), z)) | (~b(s(z), s(s(s(z))))) | (~b(z, s(s(z)))) | (~r(s(s(s(elem!1))), s(z))) | (~r(s(s(z)), s(s(s(elem!1))))) | (~b(z, s(s(elem!1))))), inference(lemma,lemma(discharge,[]))).
% 3.33/3.51 tff(15309,plain,
% 3.33/3.51 (~b(s(s(elem!1)), s(s(z)))),
% 3.33/3.51 inference(unit_resolution,[status(thm)],[15308, 15254, 15251, 118, 376, 15256, 15268, 10451, 350, 15238, 15266])).
% 3.33/3.51 tff(15310,plain,
% 3.33/3.51 (r(s(s(elem!1)), s(s(z)))),
% 3.33/3.51 inference(unit_resolution,[status(thm)],[441, 15309, 11])).
% 3.33/3.51 tff(15311,plain,
% 3.33/3.51 (s(s(s(s(elem!1)))) = s(s(s(elem!1)))),
% 3.33/3.51 inference(monotonicity,[status(thm)],[47])).
% 3.33/3.51 tff(15312,plain,
% 3.33/3.51 (s(s(s(elem!1))) = s(s(s(s(elem!1))))),
% 3.33/3.51 inference(symmetry,[status(thm)],[15311])).
% 3.33/3.51 tff(15313,plain,
% 3.33/3.51 (elem!1 = s(s(s(s(elem!1))))),
% 3.33/3.51 inference(transitivity,[status(thm)],[1170, 4070, 38, 4068, 15312])).
% 3.33/3.51 tff(15314,plain,
% 3.33/3.51 (b(elem!1, s(s(s(z)))) <=> b(s(s(s(s(elem!1)))), s(s(s(z))))),
% 3.33/3.51 inference(monotonicity,[status(thm)],[15313])).
% 3.33/3.51 tff(15315,plain,
% 3.33/3.51 (b(s(s(s(s(elem!1)))), s(s(s(z)))) <=> b(elem!1, s(s(s(z))))),
% 3.33/3.51 inference(symmetry,[status(thm)],[15314])).
% 3.33/3.51 tff(15316,plain,
% 3.33/3.51 (s(s(elem!1)) = s(s(s(s(elem!1))))),
% 3.33/3.51 inference(transitivity,[status(thm)],[8229, 15312])).
% 3.33/3.51 tff(15317,plain,
% 3.33/3.51 (b(s(s(elem!1)), s(s(s(z)))) <=> b(s(s(s(s(elem!1)))), s(s(s(z))))),
% 3.33/3.51 inference(monotonicity,[status(thm)],[15316])).
% 3.33/3.51 tff(15318,plain,
% 3.33/3.51 (b(s(s(elem!1)), s(s(s(z)))) <=> b(elem!1, s(s(s(z))))),
% 3.33/3.51 inference(transitivity,[status(thm)],[15317, 15315])).
% 3.33/3.51 tff(15319,plain,
% 3.33/3.51 ((~b(s(s(elem!1)), s(s(s(z))))) <=> (~b(elem!1, s(s(s(z)))))),
% 3.33/3.51 inference(monotonicity,[status(thm)],[15318])).
% 3.33/3.51 tff(15320,plain,
% 3.33/3.51 (~b(s(s(elem!1)), s(s(s(z))))),
% 3.33/3.51 inference(unit_resolution,[status(thm)],[5548, 15284, 988, 376])).
% 3.33/3.51 tff(15321,plain,
% 3.33/3.51 (~b(elem!1, s(s(s(z))))),
% 3.33/3.51 inference(modus_ponens,[status(thm)],[15320, 15319])).
% 3.33/3.51 tff(15322,plain,
% 3.33/3.51 (r(elem!1, s(s(s(z))))),
% 3.33/3.51 inference(unit_resolution,[status(thm)],[1619, 15321, 10810])).
% 3.33/3.51 tff(15323,plain,
% 3.33/3.51 (r(s(s(elem!1)), s(s(s(z))))),
% 3.33/3.51 inference(modus_ponens,[status(thm)],[15322, 8232])).
% 3.33/3.51 tff(15324,plain,
% 3.33/3.51 (~b(s(s(s(z))), z)),
% 3.33/3.51 inference(unit_resolution,[status(thm)],[5676, 53, 376, 118, 988])).
% 3.33/3.51 tff(15325,plain,
% 3.33/3.51 (r(s(s(s(z))), z)),
% 3.33/3.51 inference(unit_resolution,[status(thm)],[1713, 15324])).
% 3.33/3.51 tff(15326,plain,
% 3.33/3.51 (~r(z, s(s(s(z))))),
% 3.33/3.51 inference(unit_resolution,[status(thm)],[12076, 1732, 15325, 866])).
% 3.33/3.51 tff(15327,plain,
% 3.33/3.51 (b(z, s(s(s(z))))),
% 3.33/3.51 inference(unit_resolution,[status(thm)],[1697, 15326])).
% 3.33/3.51 tff(15328,plain,
% 3.33/3.51 (~b(s(s(s(z))), s(z))),
% 3.33/3.51 inference(unit_resolution,[status(thm)],[14177, 15327, 53, 118, 1820])).
% 3.33/3.51 tff(15329,plain,
% 3.33/3.51 (r(s(s(s(z))), s(z))),
% 3.33/3.51 inference(unit_resolution,[status(thm)],[1763, 15328])).
% 3.33/3.51 tff(15330,plain,
% 3.33/3.51 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(elem!1)), s(s(z)))) | (~r(s(s(z)), s(s(s(z))))) | (~r(s(s(s(z))), s(z))) | (~r(s(s(elem!1)), s(s(s(z))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(elem!1)), s(s(z)))) | (~r(s(s(z)), s(s(s(z))))) | (~r(s(s(s(z))), s(z))) | (~r(s(s(elem!1)), s(s(s(z))))))),
% 3.33/3.51 inference(rewrite,[status(thm)],[])).
% 3.33/3.51 tff(15331,plain,
% 3.33/3.51 (((~r(s(s(s(z))), s(z))) | (~r(s(s(z)), s(s(s(z))))) | (~r(s(s(elem!1)), s(s(s(z))))) | (~r(s(s(elem!1)), s(s(z))))) <=> ((~r(s(s(elem!1)), s(s(z)))) | (~r(s(s(z)), s(s(s(z))))) | (~r(s(s(s(z))), s(z))) | (~r(s(s(elem!1)), s(s(s(z))))))),
% 3.33/3.51 inference(rewrite,[status(thm)],[])).
% 3.33/3.51 tff(15332,plain,
% 3.33/3.51 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(z))), s(z))) | (~r(s(s(z)), s(s(s(z))))) | (~r(s(s(elem!1)), s(s(s(z))))) | (~r(s(s(elem!1)), s(s(z)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(elem!1)), s(s(z)))) | (~r(s(s(z)), s(s(s(z))))) | (~r(s(s(s(z))), s(z))) | (~r(s(s(elem!1)), s(s(s(z)))))))),
% 3.33/3.51 inference(monotonicity,[status(thm)],[15331])).
% 3.33/3.51 tff(15333,plain,
% 3.33/3.51 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(z))), s(z))) | (~r(s(s(z)), s(s(s(z))))) | (~r(s(s(elem!1)), s(s(s(z))))) | (~r(s(s(elem!1)), s(s(z)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(elem!1)), s(s(z)))) | (~r(s(s(z)), s(s(s(z))))) | (~r(s(s(s(z))), s(z))) | (~r(s(s(elem!1)), s(s(s(z))))))),
% 3.33/3.51 inference(transitivity,[status(thm)],[15332, 15330])).
% 3.33/3.51 tff(15334,plain,
% 3.33/3.51 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(z))), s(z))) | (~r(s(s(z)), s(s(s(z))))) | (~r(s(s(elem!1)), s(s(s(z))))) | (~r(s(s(elem!1)), s(s(z)))))),
% 3.33/3.51 inference(quant_inst,[status(thm)],[])).
% 3.33/3.51 tff(15335,plain,
% 3.33/3.51 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(elem!1)), s(s(z)))) | (~r(s(s(z)), s(s(s(z))))) | (~r(s(s(s(z))), s(z))) | (~r(s(s(elem!1)), s(s(s(z)))))),
% 3.33/3.51 inference(modus_ponens,[status(thm)],[15334, 15333])).
% 3.33/3.51 tff(15336,plain,
% 3.33/3.51 ($false),
% 3.33/3.51 inference(unit_resolution,[status(thm)],[15335, 197, 393, 15329, 1732, 15323])).
% 3.33/3.51 tff(15337,plain,((~r(s(s(z)), s(s(s(z))))) | (~r(s(s(elem!1)), s(s(z)))) | (~(s(s(s(elem!1))) = s(s(elem!1)))) | (~b(s(z), s(s(s(z))))) | (~b(s(z), s(s(elem!1)))) | (~b(s(z), z)) | (~b(z, s(z))) | (~b(z, s(s(elem!1)))) | (~r(s(s(z)), z)) | (~r(s(s(s(elem!1))), s(z))) | (~r(s(s(z)), s(s(s(elem!1)))))), inference(lemma,lemma(discharge,[]))).
% 3.33/3.51 tff(15338,plain,
% 3.33/3.51 (~r(s(s(z)), s(s(s(z))))),
% 3.33/3.51 inference(unit_resolution,[status(thm)],[15337, 15310, 15238, 15268, 376, 15251, 118, 15266, 15256, 350, 15254])).
% 3.33/3.51 tff(15339,plain,
% 3.33/3.51 (b(s(s(z)), s(s(s(z))))),
% 3.33/3.51 inference(unit_resolution,[status(thm)],[1730, 15338])).
% 3.33/3.51 tff(15340,plain,
% 3.33/3.51 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(z)))) | (~b(s(z), z)) | (~b(s(z), s(s(s(elem!1))))) | (~b(s(z), s(s(z)))) | (~b(s(s(s(z))), s(s(s(elem!1))))) | (~b(s(s(z)), s(s(s(z))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(s(z)))) | (~b(s(z), z)) | (~b(s(z), s(s(s(elem!1))))) | (~b(s(z), s(s(z)))) | (~b(s(s(s(z))), s(s(s(elem!1))))) | (~b(s(s(z)), s(s(s(z))))))),
% 3.33/3.51 inference(rewrite,[status(thm)],[])).
% 3.33/3.51 tff(15341,plain,
% 3.33/3.51 (((~b(s(s(s(z))), s(s(s(elem!1))))) | (~b(s(z), s(s(s(elem!1))))) | (~b(s(s(z)), s(s(s(z))))) | (~b(z, s(s(z)))) | (~b(s(z), s(s(z)))) | (~b(s(z), z))) <=> ((~b(z, s(s(z)))) | (~b(s(z), z)) | (~b(s(z), s(s(s(elem!1))))) | (~b(s(z), s(s(z)))) | (~b(s(s(s(z))), s(s(s(elem!1))))) | (~b(s(s(z)), s(s(s(z))))))),
% 3.33/3.51 inference(rewrite,[status(thm)],[])).
% 3.33/3.51 tff(15342,plain,
% 3.33/3.51 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), s(s(s(elem!1))))) | (~b(s(z), s(s(s(elem!1))))) | (~b(s(s(z)), s(s(s(z))))) | (~b(z, s(s(z)))) | (~b(s(z), s(s(z)))) | (~b(s(z), z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(z)))) | (~b(s(z), z)) | (~b(s(z), s(s(s(elem!1))))) | (~b(s(z), s(s(z)))) | (~b(s(s(s(z))), s(s(s(elem!1))))) | (~b(s(s(z)), s(s(s(z)))))))),
% 3.33/3.51 inference(monotonicity,[status(thm)],[15341])).
% 3.33/3.51 tff(15343,plain,
% 3.33/3.51 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), s(s(s(elem!1))))) | (~b(s(z), s(s(s(elem!1))))) | (~b(s(s(z)), s(s(s(z))))) | (~b(z, s(s(z)))) | (~b(s(z), s(s(z)))) | (~b(s(z), z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(s(z)))) | (~b(s(z), z)) | (~b(s(z), s(s(s(elem!1))))) | (~b(s(z), s(s(z)))) | (~b(s(s(s(z))), s(s(s(elem!1))))) | (~b(s(s(z)), s(s(s(z))))))),
% 3.33/3.51 inference(transitivity,[status(thm)],[15342, 15340])).
% 3.33/3.51 tff(15344,plain,
% 3.33/3.51 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), s(s(s(elem!1))))) | (~b(s(z), s(s(s(elem!1))))) | (~b(s(s(z)), s(s(s(z))))) | (~b(z, s(s(z)))) | (~b(s(z), s(s(z)))) | (~b(s(z), z)))),
% 3.33/3.51 inference(quant_inst,[status(thm)],[])).
% 3.33/3.51 tff(15345,plain,
% 3.33/3.51 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(s(z)))) | (~b(s(z), z)) | (~b(s(z), s(s(s(elem!1))))) | (~b(s(z), s(s(z)))) | (~b(s(s(s(z))), s(s(s(elem!1))))) | (~b(s(s(z)), s(s(s(z)))))),
% 3.33/3.51 inference(modus_ponens,[status(thm)],[15344, 15343])).
% 3.33/3.51 tff(15346,plain,
% 3.33/3.51 ($false),
% 3.33/3.51 inference(unit_resolution,[status(thm)],[15345, 166, 241, 53, 556, 10451, 6552, 986])).
% 3.33/3.51 tff(15347,plain,((~b(z, s(s(z)))) | (~b(s(z), s(s(s(elem!1))))) | (~b(s(z), z)) | (~b(s(z), s(s(z)))) | (~b(s(s(s(z))), s(s(s(elem!1))))) | (~b(s(s(z)), s(s(s(z)))))), inference(lemma,lemma(discharge,[]))).
% 3.33/3.51 tff(15348,plain,
% 3.33/3.51 (~b(s(s(s(z))), s(s(s(elem!1))))),
% 3.33/3.51 inference(unit_resolution,[status(thm)],[15347, 15339, 10451, 15253, 15251, 15224])).
% 3.33/3.51 tff(15349,plain,
% 3.33/3.51 (~b(s(s(s(z))), elem!1)),
% 3.33/3.51 inference(unit_resolution,[status(thm)],[4078, 15348, 15238])).
% 3.33/3.51 tff(15350,plain,
% 3.33/3.51 (r(s(s(s(z))), elem!1)),
% 3.33/3.51 inference(unit_resolution,[status(thm)],[2826, 15349, 15249])).
% 3.33/3.51 tff(15351,plain,
% 3.33/3.51 (r(s(s(s(z))), s(s(elem!1)))),
% 3.33/3.51 inference(modus_ponens,[status(thm)],[15350, 15248])).
% 3.33/3.51 tff(15352,plain,
% 3.33/3.51 (~b(s(s(s(z))), s(s(z)))),
% 3.33/3.51 inference(unit_resolution,[status(thm)],[996, 15339, 15253, 15268])).
% 3.33/3.51 tff(15353,plain,
% 3.33/3.51 (r(s(s(s(z))), s(s(z)))),
% 3.33/3.51 inference(unit_resolution,[status(thm)],[1010, 15352])).
% 3.33/3.51 tff(15354,plain,
% 3.33/3.51 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(elem!1)), s(s(z)))) | (~r(s(s(z)), s(s(elem!1)))) | (~r(s(s(s(z))), s(s(elem!1)))) | (~r(s(s(s(z))), s(s(z)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(elem!1)), s(s(z)))) | (~r(s(s(z)), s(s(elem!1)))) | (~r(s(s(s(z))), s(s(elem!1)))) | (~r(s(s(s(z))), s(s(z)))))),
% 3.33/3.51 inference(rewrite,[status(thm)],[])).
% 3.33/3.51 tff(15355,plain,
% 3.33/3.51 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(elem!1)), s(s(z)))) | (~r(s(s(z)), s(s(elem!1)))) | (~r(s(s(s(z))), s(s(elem!1)))) | (~r(s(s(s(z))), s(s(z)))))),
% 3.33/3.51 inference(quant_inst,[status(thm)],[])).
% 3.33/3.51 tff(15356,plain,
% 3.33/3.51 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(elem!1)), s(s(z)))) | (~r(s(s(z)), s(s(elem!1)))) | (~r(s(s(s(z))), s(s(elem!1)))) | (~r(s(s(s(z))), s(s(z))))),
% 3.33/3.51 inference(modus_ponens,[status(thm)],[15355, 15354])).
% 3.33/3.51 tff(15357,plain,
% 3.33/3.51 (~r(s(s(s(z))), s(s(elem!1)))),
% 3.33/3.51 inference(unit_resolution,[status(thm)],[15356, 197, 15310, 333, 15353])).
% 3.33/3.51 tff(15358,plain,
% 3.33/3.51 ($false),
% 3.33/3.51 inference(unit_resolution,[status(thm)],[15357, 15351])).
% 3.33/3.51 tff(15359,plain,((~r(s(s(z)), s(s(elem!1)))) | (~b(z, s(s(z)))) | (~b(s(z), s(s(elem!1)))) | (~b(z, s(z))) | (~r(s(s(s(elem!1))), s(z))) | (s(s(elem!1)) = s(s(z))) | (~r(s(s(z)), s(z))) | (~r(s(s(elem!1)), s(z))) | r(s(s(elem!1)), s(s(s(elem!1))))), inference(lemma,lemma(discharge,[]))).
% 3.33/3.51 tff(15360,plain,
% 3.33/3.51 (~r(s(s(z)), s(s(elem!1)))),
% 3.33/3.51 inference(unit_resolution,[status(thm)],[15359, 1821, 376, 118, 350, 132, 392, 10521, 10451])).
% 3.33/3.51 tff(15361,plain,
% 3.33/3.51 (~r(s(z), z)),
% 3.33/3.51 inference(unit_resolution,[status(thm)],[11730, 15360, 10451, 4568])).
% 3.33/3.51 tff(15362,plain,
% 3.33/3.51 (b(s(z), z)),
% 3.33/3.51 inference(unit_resolution,[status(thm)],[230, 15361])).
% 3.33/3.51 tff(15363,plain,
% 3.33/3.51 (b(s(s(z)), s(s(elem!1)))),
% 3.33/3.51 inference(unit_resolution,[status(thm)],[390, 15360, 52])).
% 3.33/3.51 tff(15364,plain,
% 3.33/3.51 (~r(s(z), s(s(z)))),
% 3.33/3.51 inference(unit_resolution,[status(thm)],[6083, 463, 392, 350, 11, 4577])).
% 3.33/3.51 tff(15365,plain,
% 3.33/3.51 (b(s(z), s(s(z)))),
% 3.33/3.51 inference(unit_resolution,[status(thm)],[427, 15364])).
% 3.33/3.51 tff(15366,plain,
% 3.33/3.51 (~b(s(z), s(s(s(elem!1))))),
% 3.33/3.52 inference(unit_resolution,[status(thm)],[14016, 463, 53, 15365, 10451, 446])).
% 3.33/3.52 tff(15367,plain,
% 3.33/3.52 (r(s(z), s(s(s(elem!1))))),
% 3.33/3.52 inference(unit_resolution,[status(thm)],[116, 15366])).
% 3.33/3.52 tff(15368,plain,
% 3.33/3.52 (~r(s(s(s(elem!1))), s(s(z)))),
% 3.33/3.52 inference(unit_resolution,[status(thm)],[7534, 15367, 392, 350])).
% 3.33/3.52 tff(15369,plain,
% 3.33/3.52 (b(s(s(s(elem!1))), s(s(z)))),
% 3.33/3.52 inference(unit_resolution,[status(thm)],[218, 15368])).
% 3.33/3.52 tff(15370,plain,
% 3.33/3.52 (~b(s(s(s(elem!1))), s(s(elem!1)))),
% 3.33/3.52 inference(unit_resolution,[status(thm)],[2068, 15369, 446, 463])).
% 3.33/3.52 tff(15371,plain,
% 3.33/3.52 (~b(s(s(z)), s(s(s(elem!1))))),
% 3.33/3.52 inference(unit_resolution,[status(thm)],[12045, 15369, 10451, 118, 15365])).
% 3.33/3.52 tff(15372,plain,
% 3.33/3.52 (r(s(s(z)), s(s(s(elem!1))))),
% 3.33/3.52 inference(unit_resolution,[status(thm)],[279, 15371])).
% 3.33/3.52 tff(15373,plain,
% 3.33/3.52 (~r(s(s(s(elem!1))), s(s(elem!1)))),
% 3.33/3.52 inference(unit_resolution,[status(thm)],[913, 117, 392, 281])).
% 3.33/3.52 tff(15374,plain,
% 3.33/3.52 (~(s(s(elem!1)) = s(s(s(elem!1))))),
% 3.33/3.52 inference(unit_resolution,[status(thm)],[5500, 98, 376])).
% 3.33/3.52 tff(15375,plain,
% 3.33/3.52 (~(s(s(s(elem!1))) = s(s(elem!1)))),
% 3.33/3.52 inference(unit_resolution,[status(thm)],[50, 15374])).
% 3.33/3.52 tff(15376,plain,
% 3.33/3.52 ($false),
% 3.33/3.52 inference(unit_resolution,[status(thm)],[889, 15375, 15373, 12348])).
% 3.33/3.52 tff(15377,plain,(b(s(z), s(s(s(elem!1)))) | b(s(s(s(elem!1))), s(s(elem!1))) | (~r(s(s(z)), s(z))) | (~r(s(s(z)), s(s(s(elem!1))))) | (~b(s(z), s(s(elem!1))))), inference(lemma,lemma(discharge,[]))).
% 3.33/3.52 tff(15378,plain,
% 3.33/3.52 ($false),
% 3.33/3.52 inference(unit_resolution,[status(thm)],[15377, 15372, 15370, 392, 15366, 376])).
% 3.33/3.52 tff(15379,plain,((~b(s(s(elem!1)), s(s(s(elem!1))))) | (~r(s(s(z)), s(z))) | (~b(s(z), s(s(elem!1)))) | (~b(s(s(z)), s(s(elem!1)))) | (~b(z, s(s(z)))) | (~b(z, s(z))) | (~r(s(s(s(elem!1))), s(z))) | (~b(s(z), z)) | (s(s(elem!1)) = s(s(z))) | (~r(s(s(elem!1)), s(z)))), inference(lemma,lemma(discharge,[]))).
% 3.33/3.52 tff(15380,plain,
% 3.33/3.52 (~b(s(s(elem!1)), s(s(s(elem!1))))),
% 3.33/3.52 inference(unit_resolution,[status(thm)],[15379, 15363, 376, 392, 10451, 118, 350, 15362, 132, 10521])).
% 3.33/3.52 tff(15381,plain,
% 3.33/3.52 (s(s(elem!1)) = s(s(s(elem!1)))),
% 3.33/3.52 inference(unit_resolution,[status(thm)],[461, 15380, 1821])).
% 3.33/3.52 tff(15382,plain,
% 3.33/3.52 (s(s(s(elem!1))) = s(elem!1)),
% 3.33/3.52 inference(unit_resolution,[status(thm)],[2594, 15381])).
% 3.33/3.52 tff(15383,plain,
% 3.33/3.52 (s(elem!1) = s(s(s(elem!1)))),
% 3.33/3.52 inference(symmetry,[status(thm)],[15382])).
% 3.33/3.52 tff(15384,plain,
% 3.33/3.52 (inj_0(s(elem!1)) = inj_0(s(s(s(elem!1))))),
% 3.33/3.52 inference(monotonicity,[status(thm)],[15383])).
% 3.33/3.52 tff(15385,plain,
% 3.33/3.52 (inj_0(s(s(s(elem!1)))) = inj_0(s(elem!1))),
% 3.33/3.52 inference(symmetry,[status(thm)],[15384])).
% 3.33/3.52 tff(15386,plain,
% 3.33/3.52 (s(s(s(elem!1))) = s(s(elem!1))),
% 3.33/3.52 inference(symmetry,[status(thm)],[15381])).
% 3.33/3.52 tff(15387,plain,
% 3.33/3.52 (s(s(s(elem!1))) = elem!1),
% 3.33/3.52 inference(transitivity,[status(thm)],[15386, 105, 15385, 20])).
% 3.33/3.52 tff(15388,plain,
% 3.33/3.52 (r(s(s(s(elem!1))), s(s(s(z)))) <=> r(elem!1, s(s(s(z))))),
% 3.33/3.52 inference(monotonicity,[status(thm)],[15387])).
% 3.33/3.52 tff(15389,plain,
% 3.33/3.52 (r(elem!1, s(s(s(z)))) <=> r(s(s(s(elem!1))), s(s(s(z))))),
% 3.33/3.52 inference(symmetry,[status(thm)],[15388])).
% 3.33/3.52 tff(15390,plain,
% 3.33/3.52 (~(s(s(s(z))) = elem!1)),
% 3.33/3.52 inference(unit_resolution,[status(thm)],[3122, 15381])).
% 3.33/3.52 tff(15391,plain,
% 3.33/3.52 (~(elem!1 = s(s(s(z))))),
% 3.33/3.52 inference(unit_resolution,[status(thm)],[1564, 15390])).
% 3.33/3.52 tff(15392,plain,
% 3.33/3.52 (elem!1 = s(s(elem!1))),
% 3.33/3.52 inference(transitivity,[status(thm)],[1170, 15384, 104])).
% 3.33/3.52 tff(15393,plain,
% 3.33/3.52 (b(elem!1, s(s(s(z)))) <=> b(s(s(elem!1)), s(s(s(z))))),
% 3.33/3.52 inference(monotonicity,[status(thm)],[15392])).
% 3.33/3.52 tff(15394,plain,
% 3.33/3.52 (b(s(s(elem!1)), s(s(s(z)))) <=> b(elem!1, s(s(s(z))))),
% 3.33/3.52 inference(symmetry,[status(thm)],[15393])).
% 3.33/3.52 tff(15395,plain,
% 3.33/3.52 ((~b(s(s(elem!1)), s(s(s(z))))) <=> (~b(elem!1, s(s(s(z)))))),
% 3.33/3.52 inference(monotonicity,[status(thm)],[15394])).
% 3.33/3.52 tff(15396,plain,
% 3.33/3.52 (b(s(s(z)), s(s(s(elem!1))))),
% 3.33/3.52 inference(unit_resolution,[status(thm)],[6647, 15381, 15363])).
% 3.33/3.52 tff(15397,plain,
% 3.33/3.52 (b(elem!1, s(s(s(z)))) <=> b(s(s(elem!1)), s(s(s(z))))),
% 3.33/3.52 inference(monotonicity,[status(thm)],[4025])).
% 3.33/3.52 tff(15398,plain,
% 3.33/3.52 ((~r(s(s(s(elem!1))), s(s(s(z))))) <=> (~r(elem!1, s(s(s(z)))))),
% 3.33/3.52 inference(monotonicity,[status(thm)],[13584])).
% 3.33/3.52 tff(15399,plain,
% 3.33/3.52 (~b(elem!1, s(s(s(z))))),
% 3.33/3.52 inference(unit_resolution,[status(thm)],[13610, 1699, 10451, 2060, 334, 53, 118])).
% 3.33/3.52 tff(15400,plain,
% 3.33/3.52 (r(elem!1, s(s(s(z))))),
% 3.33/3.52 inference(unit_resolution,[status(thm)],[1619, 15399, 8222])).
% 3.33/3.52 tff(15401,plain,
% 3.33/3.52 (r(s(s(s(elem!1))), s(s(s(z))))),
% 3.33/3.52 inference(modus_ponens,[status(thm)],[15400, 13585])).
% 3.33/3.52 tff(15402,plain,
% 3.33/3.52 (~r(s(s(s(elem!1))), s(s(s(z))))),
% 3.33/3.52 inference(unit_resolution,[status(thm)],[6678, 197, 120, 350, 4047])).
% 3.33/3.52 tff(15403,plain,
% 3.33/3.52 ($false),
% 3.33/3.52 inference(unit_resolution,[status(thm)],[15402, 15401])).
% 3.33/3.52 tff(15404,plain,((~b(s(s(s(z))), z)) | (~(s(s(elem!1)) = s(s(s(elem!1))))) | (~r(s(z), s(s(z)))) | (~r(s(s(s(elem!1))), s(z))) | (~b(s(z), z)) | (~b(z, s(z))) | (~b(z, s(s(z)))) | (~b(s(s(s(elem!1))), s(s(z))))), inference(lemma,lemma(discharge,[]))).
% 3.33/3.52 tff(15405,plain,
% 3.33/3.52 (~b(s(s(s(z))), z)),
% 3.33/3.52 inference(unit_resolution,[status(thm)],[15404, 120, 334, 350, 53, 118, 10451, 7200])).
% 3.33/3.52 tff(15406,plain,
% 3.33/3.52 (r(s(s(s(z))), z)),
% 3.33/3.52 inference(unit_resolution,[status(thm)],[1713, 15405])).
% 3.33/3.52 tff(15407,plain,
% 3.33/3.52 (b(s(s(elem!1)), s(s(z)))),
% 3.33/3.52 inference(unit_resolution,[status(thm)],[441, 6070, 11])).
% 3.33/3.52 tff(15408,plain,
% 3.33/3.52 (~b(z, s(s(elem!1)))),
% 3.33/3.52 inference(unit_resolution,[status(thm)],[10727, 15407, 10451, 446])).
% 3.33/3.52 tff(15409,plain,
% 3.33/3.52 (~b(z, s(s(s(elem!1))))),
% 3.33/3.52 inference(unit_resolution,[status(thm)],[4345, 15408, 334])).
% 3.33/3.52 tff(15410,plain,
% 3.33/3.52 (r(z, s(s(s(elem!1))))),
% 3.33/3.52 inference(unit_resolution,[status(thm)],[261, 15409])).
% 3.33/3.52 tff(15411,plain,
% 3.33/3.52 (~b(s(s(s(elem!1))), z)),
% 3.33/3.52 inference(unit_resolution,[status(thm)],[12429, 5555, 10451, 446, 53, 376])).
% 3.33/3.52 tff(15412,plain,
% 3.33/3.52 (r(s(s(s(elem!1))), z)),
% 3.33/3.52 inference(unit_resolution,[status(thm)],[94, 15411])).
% 3.33/3.52 tff(15413,plain,
% 3.33/3.52 (~r(s(s(s(elem!1))), s(s(s(z))))),
% 3.33/3.52 inference(unit_resolution,[status(thm)],[13638, 197, 15412, 15410, 15406])).
% 3.33/3.52 tff(15414,plain,
% 3.33/3.52 (~r(elem!1, s(s(s(z))))),
% 3.33/3.52 inference(modus_ponens,[status(thm)],[15413, 15398])).
% 3.33/3.52 tff(15415,plain,
% 3.33/3.52 (b(elem!1, s(s(s(z))))),
% 3.33/3.52 inference(unit_resolution,[status(thm)],[1619, 15414, 8222])).
% 3.33/3.52 tff(15416,plain,
% 3.33/3.52 (b(s(s(elem!1)), s(s(s(z))))),
% 3.33/3.52 inference(modus_ponens,[status(thm)],[15415, 15397])).
% 3.33/3.52 tff(15417,plain,
% 3.33/3.52 (~r(s(s(z)), z)),
% 3.33/3.52 inference(unit_resolution,[status(thm)],[13666, 15406, 334, 15410, 7200, 15412])).
% 3.33/3.52 tff(15418,plain,
% 3.33/3.52 (b(s(s(z)), z)),
% 3.33/3.52 inference(unit_resolution,[status(thm)],[186, 15417])).
% 3.33/3.52 tff(15419,plain,
% 3.33/3.52 (~r(s(z), s(s(s(z))))),
% 3.33/3.52 inference(unit_resolution,[status(thm)],[13688, 15418, 392, 53, 118, 120, 334, 15412, 15410, 10451, 446, 7200])).
% 3.33/3.52 tff(15420,plain,
% 3.33/3.52 (b(s(z), s(s(s(z))))),
% 3.33/3.52 inference(unit_resolution,[status(thm)],[1674, 15419])).
% 3.33/3.52 tff(15421,plain,
% 3.33/3.52 (~r(s(s(s(z))), s(s(s(elem!1))))),
% 3.33/3.52 inference(unit_resolution,[status(thm)],[13628, 197, 15412, 15410, 15406])).
% 3.33/3.52 tff(15422,plain,
% 3.33/3.52 (~r(s(s(s(z))), elem!1)),
% 3.33/3.52 inference(modus_ponens,[status(thm)],[15421, 13654])).
% 3.33/3.52 tff(15423,plain,
% 3.33/3.52 (b(s(s(s(z))), elem!1)),
% 3.33/3.52 inference(unit_resolution,[status(thm)],[2826, 15422, 4027])).
% 3.33/3.52 tff(15424,plain,
% 3.33/3.52 (b(s(s(s(z))), s(s(s(elem!1))))),
% 3.33/3.52 inference(unit_resolution,[status(thm)],[4078, 15423, 4031])).
% 3.33/3.52 tff(15425,plain,
% 3.33/3.52 (b(s(s(s(z))), s(s(elem!1)))),
% 3.33/3.52 inference(unit_resolution,[status(thm)],[8909, 15424, 4031])).
% 3.33/3.52 tff(15426,plain,
% 3.33/3.52 (~b(s(s(elem!1)), s(s(s(z))))),
% 3.33/3.52 inference(unit_resolution,[status(thm)],[5548, 15425, 15420, 376])).
% 3.33/3.52 tff(15427,plain,
% 3.33/3.52 ($false),
% 3.33/3.52 inference(unit_resolution,[status(thm)],[15426, 15416])).
% 3.33/3.52 tff(15428,plain,((~r(s(z), s(s(z)))) | (~b(s(z), s(s(elem!1)))) | (~(s(s(elem!1)) = s(s(s(elem!1))))) | (~r(s(s(z)), s(z))) | (~b(s(z), z)) | (~b(z, s(z))) | (~b(z, s(s(z)))) | (~b(s(s(z)), s(s(elem!1)))) | (~r(s(s(s(elem!1))), s(z))) | (s(s(elem!1)) = s(s(z))) | (~r(s(s(elem!1)), s(z)))), inference(lemma,lemma(discharge,[]))).
% 3.33/3.52 tff(15429,plain,
% 3.33/3.52 (~r(s(z), s(s(z)))),
% 3.33/3.52 inference(unit_resolution,[status(thm)],[15428, 15381, 376, 392, 15362, 118, 10451, 15363, 350, 132, 10521])).
% 3.33/3.52 tff(15430,plain,
% 3.33/3.52 (b(s(z), s(s(z)))),
% 3.33/3.52 inference(unit_resolution,[status(thm)],[427, 15429])).
% 3.33/3.52 tff(15431,plain,
% 3.33/3.52 (~b(s(s(s(elem!1))), s(s(z)))),
% 3.33/3.52 inference(unit_resolution,[status(thm)],[12045, 15430, 10451, 118, 15396])).
% 3.33/3.52 tff(15432,plain,
% 3.33/3.52 (r(s(s(s(elem!1))), s(s(z)))),
% 3.33/3.52 inference(unit_resolution,[status(thm)],[218, 15431])).
% 3.33/3.52 tff(15433,plain,
% 3.33/3.52 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), s(z))) | (~r(s(s(z)), s(z))) | (~r(s(s(s(elem!1))), s(s(z)))) | (~r(s(z), s(s(s(z))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(elem!1))), s(z))) | (~r(s(s(z)), s(z))) | (~r(s(s(s(elem!1))), s(s(z)))) | (~r(s(z), s(s(s(z))))))),
% 3.33/3.52 inference(rewrite,[status(thm)],[])).
% 3.33/3.52 tff(15434,plain,
% 3.33/3.52 (((~r(s(z), s(s(s(z))))) | (~r(s(s(z)), s(z))) | (~r(s(s(s(elem!1))), s(z))) | (~r(s(s(s(elem!1))), s(s(z))))) <=> ((~r(s(s(s(elem!1))), s(z))) | (~r(s(s(z)), s(z))) | (~r(s(s(s(elem!1))), s(s(z)))) | (~r(s(z), s(s(s(z))))))),
% 3.33/3.52 inference(rewrite,[status(thm)],[])).
% 3.33/3.52 tff(15435,plain,
% 3.33/3.52 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(s(s(z))))) | (~r(s(s(z)), s(z))) | (~r(s(s(s(elem!1))), s(z))) | (~r(s(s(s(elem!1))), s(s(z)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), s(z))) | (~r(s(s(z)), s(z))) | (~r(s(s(s(elem!1))), s(s(z)))) | (~r(s(z), s(s(s(z)))))))),
% 3.33/3.52 inference(monotonicity,[status(thm)],[15434])).
% 3.33/3.52 tff(15436,plain,
% 3.33/3.52 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(s(s(z))))) | (~r(s(s(z)), s(z))) | (~r(s(s(s(elem!1))), s(z))) | (~r(s(s(s(elem!1))), s(s(z)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(elem!1))), s(z))) | (~r(s(s(z)), s(z))) | (~r(s(s(s(elem!1))), s(s(z)))) | (~r(s(z), s(s(s(z))))))),
% 3.33/3.52 inference(transitivity,[status(thm)],[15435, 15433])).
% 3.33/3.52 tff(15437,plain,
% 3.33/3.52 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(s(s(z))))) | (~r(s(s(z)), s(z))) | (~r(s(s(s(elem!1))), s(z))) | (~r(s(s(s(elem!1))), s(s(z)))))),
% 3.33/3.52 inference(quant_inst,[status(thm)],[])).
% 3.33/3.52 tff(15438,plain,
% 3.33/3.52 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(elem!1))), s(z))) | (~r(s(s(z)), s(z))) | (~r(s(s(s(elem!1))), s(s(z)))) | (~r(s(z), s(s(s(z)))))),
% 3.33/3.52 inference(modus_ponens,[status(thm)],[15437, 15436])).
% 3.33/3.52 tff(15439,plain,
% 3.33/3.52 ($false),
% 3.33/3.52 inference(unit_resolution,[status(thm)],[15438, 197, 350, 392, 464, 1653])).
% 3.33/3.52 tff(15440,plain,((~r(s(z), s(s(s(z))))) | (~r(s(s(s(elem!1))), s(z))) | (~r(s(s(z)), s(z))) | (~r(s(s(s(elem!1))), s(s(z))))), inference(lemma,lemma(discharge,[]))).
% 3.33/3.52 tff(15441,plain,
% 3.33/3.52 (~r(s(z), s(s(s(z))))),
% 3.33/3.52 inference(unit_resolution,[status(thm)],[15440, 15432, 392, 350])).
% 3.33/3.52 tff(15442,plain,
% 3.33/3.52 (b(s(z), s(s(s(z))))),
% 3.33/3.52 inference(unit_resolution,[status(thm)],[1674, 15441])).
% 3.33/3.52 tff(15443,plain,
% 3.33/3.52 (b(s(s(s(elem!1))), s(s(s(z)))) <=> b(s(s(elem!1)), s(s(s(z))))),
% 3.33/3.52 inference(monotonicity,[status(thm)],[2591])).
% 3.33/3.52 tff(15444,plain,
% 3.33/3.52 (b(s(s(elem!1)), s(s(s(z)))) <=> b(s(s(s(elem!1))), s(s(s(z))))),
% 3.33/3.52 inference(symmetry,[status(thm)],[15443])).
% 3.33/3.52 tff(15445,plain,
% 3.33/3.52 (b(s(s(s(elem!1))), s(s(s(z))))),
% 3.33/3.52 inference(modus_ponens,[status(thm)],[5539, 15444])).
% 3.33/3.52 tff(15446,plain,
% 3.33/3.52 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(z)))) | (~b(s(z), z)) | (~b(s(z), s(s(z)))) | (~b(s(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, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(s(z)))) | (~b(s(z), z)) | (~b(s(z), s(s(z)))) | (~b(s(s(z)), s(s(s(elem!1))))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(elem!1))), s(s(s(z))))))),
% 3.33/3.52 inference(rewrite,[status(thm)],[])).
% 3.33/3.52 tff(15447,plain,
% 3.33/3.52 (((~b(s(s(s(elem!1))), s(s(s(z))))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(z)), s(s(s(elem!1))))) | (~b(z, s(s(z)))) | (~b(s(z), s(s(z)))) | (~b(s(z), z))) <=> ((~b(z, s(s(z)))) | (~b(s(z), z)) | (~b(s(z), s(s(z)))) | (~b(s(s(z)), s(s(s(elem!1))))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(elem!1))), s(s(s(z))))))),
% 3.33/3.52 inference(rewrite,[status(thm)],[])).
% 3.33/3.52 tff(15448,plain,
% 3.33/3.52 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), s(s(s(z))))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(z)), s(s(s(elem!1))))) | (~b(z, s(s(z)))) | (~b(s(z), s(s(z)))) | (~b(s(z), z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(z)))) | (~b(s(z), z)) | (~b(s(z), s(s(z)))) | (~b(s(s(z)), s(s(s(elem!1))))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(elem!1))), s(s(s(z)))))))),
% 3.33/3.52 inference(monotonicity,[status(thm)],[15447])).
% 3.33/3.52 tff(15449,plain,
% 3.33/3.52 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), s(s(s(z))))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(z)), s(s(s(elem!1))))) | (~b(z, s(s(z)))) | (~b(s(z), s(s(z)))) | (~b(s(z), z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(s(z)))) | (~b(s(z), z)) | (~b(s(z), s(s(z)))) | (~b(s(s(z)), s(s(s(elem!1))))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(elem!1))), s(s(s(z))))))),
% 3.33/3.52 inference(transitivity,[status(thm)],[15448, 15446])).
% 3.33/3.52 tff(15450,plain,
% 3.33/3.52 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), s(s(s(z))))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(z)), s(s(s(elem!1))))) | (~b(z, s(s(z)))) | (~b(s(z), s(s(z)))) | (~b(s(z), z)))),
% 3.33/3.52 inference(quant_inst,[status(thm)],[])).
% 3.33/3.52 tff(15451,plain,
% 3.33/3.52 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(s(z)))) | (~b(s(z), z)) | (~b(s(z), s(s(z)))) | (~b(s(s(z)), s(s(s(elem!1))))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(elem!1))), s(s(s(z)))))),
% 3.33/3.52 inference(modus_ponens,[status(thm)],[15450, 15449])).
% 3.33/3.52 tff(15452,plain,
% 3.33/3.52 (~b(s(s(s(elem!1))), s(s(s(z))))),
% 3.33/3.52 inference(unit_resolution,[status(thm)],[15451, 166, 53, 556, 10451, 263, 988])).
% 3.33/3.52 tff(15453,plain,
% 3.33/3.52 ($false),
% 3.33/3.52 inference(unit_resolution,[status(thm)],[15452, 15445])).
% 3.33/3.52 tff(15454,plain,((~b(s(s(elem!1)), s(s(s(z))))) | (~(s(s(elem!1)) = s(s(s(elem!1))))) | (~b(s(z), z)) | (~b(s(z), s(s(z)))) | (~b(z, s(s(z)))) | (~b(s(s(z)), s(s(s(elem!1))))) | (~b(s(z), s(s(s(z)))))), inference(lemma,lemma(discharge,[]))).
% 3.33/3.52 tff(15455,plain,
% 3.33/3.52 (~b(s(s(elem!1)), s(s(s(z))))),
% 3.33/3.52 inference(unit_resolution,[status(thm)],[15454, 15381, 15362, 15430, 10451, 15396, 15442])).
% 3.33/3.52 tff(15456,plain,
% 3.33/3.52 (~b(elem!1, s(s(s(z))))),
% 3.33/3.52 inference(modus_ponens,[status(thm)],[15455, 15395])).
% 3.33/3.52 tff(15457,plain,
% 3.33/3.52 (r(elem!1, s(s(s(z))))),
% 3.33/3.52 inference(unit_resolution,[status(thm)],[1619, 15456, 15391])).
% 3.33/3.52 tff(15458,plain,
% 3.33/3.52 (r(s(s(s(elem!1))), s(s(s(z))))),
% 3.33/3.52 inference(modus_ponens,[status(thm)],[15457, 15389])).
% 3.33/3.52 tff(15459,plain,
% 3.33/3.52 (b(s(z), s(s(s(elem!1))))),
% 3.33/3.52 inference(unit_resolution,[status(thm)],[5500, 15381, 376])).
% 3.33/3.52 tff(15460,plain,
% 3.33/3.52 (~b(s(s(s(z))), s(s(s(elem!1))))),
% 3.33/3.52 inference(unit_resolution,[status(thm)],[15347, 986, 10451, 556, 53, 241])).
% 3.33/3.52 tff(15461,plain,
% 3.33/3.52 (~b(s(s(s(z))), elem!1)),
% 3.33/3.52 inference(unit_resolution,[status(thm)],[4078, 15460, 4031])).
% 3.33/3.52 tff(15462,plain,
% 3.33/3.52 (r(s(s(s(z))), elem!1)),
% 3.33/3.52 inference(unit_resolution,[status(thm)],[2826, 15461, 4027])).
% 3.33/3.52 tff(15463,plain,
% 3.33/3.52 (r(s(s(s(z))), s(s(s(elem!1))))),
% 3.33/3.52 inference(modus_ponens,[status(thm)],[15462, 8073])).
% 3.33/3.52 tff(15464,plain,
% 3.33/3.52 (~b(s(s(s(z))), s(s(z)))),
% 3.33/3.52 inference(unit_resolution,[status(thm)],[996, 986, 556, 988])).
% 3.33/3.52 tff(15465,plain,
% 3.33/3.52 (r(s(s(s(z))), s(s(z)))),
% 3.33/3.52 inference(unit_resolution,[status(thm)],[1010, 15464])).
% 3.33/3.52 tff(15466,plain,
% 3.33/3.52 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(z)), s(z))) | (~r(s(s(s(elem!1))), s(s(z)))) | (~r(s(s(s(z))), s(s(z)))) | (~r(s(s(s(z))), s(s(s(elem!1))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(z)), s(z))) | (~r(s(s(s(elem!1))), s(s(z)))) | (~r(s(s(s(z))), s(s(z)))) | (~r(s(s(s(z))), s(s(s(elem!1))))))),
% 3.33/3.52 inference(rewrite,[status(thm)],[])).
% 3.33/3.52 tff(15467,plain,
% 3.33/3.52 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(z)), s(z))) | (~r(s(s(s(elem!1))), s(s(z)))) | (~r(s(s(s(z))), s(s(z)))) | (~r(s(s(s(z))), s(s(s(elem!1))))))),
% 3.33/3.52 inference(quant_inst,[status(thm)],[])).
% 3.33/3.52 tff(15468,plain,
% 3.33/3.52 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(z)), s(z))) | (~r(s(s(s(elem!1))), s(s(z)))) | (~r(s(s(s(z))), s(s(z)))) | (~r(s(s(s(z))), s(s(s(elem!1)))))),
% 3.33/3.52 inference(modus_ponens,[status(thm)],[15467, 15466])).
% 3.33/3.52 tff(15469,plain,
% 3.33/3.52 ($false),
% 3.33/3.52 inference(unit_resolution,[status(thm)],[15468, 197, 392, 464, 15465, 15463])).
% 3.33/3.52 tff(15470,plain,((~b(s(s(z)), s(s(s(z))))) | (~r(s(s(z)), s(z))) | (~r(s(s(s(elem!1))), s(s(z)))) | (~(s(s(elem!1)) = s(s(s(elem!1))))) | (~b(z, s(s(z)))) | (~b(s(z), s(s(z)))) | (~b(s(z), z)) | (~b(s(z), s(s(s(elem!1))))) | (~b(s(z), s(s(s(z)))))), inference(lemma,lemma(discharge,[]))).
% 3.33/3.52 tff(15471,plain,
% 3.33/3.52 (~b(s(s(z)), s(s(s(z))))),
% 3.33/3.52 inference(unit_resolution,[status(thm)],[15470, 15432, 392, 15381, 10451, 15430, 15362, 15459, 15442])).
% 3.33/3.52 tff(15472,plain,
% 3.33/3.52 (r(s(s(z)), s(s(s(z))))),
% 3.33/3.52 inference(unit_resolution,[status(thm)],[1730, 15471])).
% 3.33/3.52 tff(15473,plain,
% 3.33/3.52 ((s(s(elem!1)) = elem!1) <=> (s(s(s(elem!1))) = elem!1)),
% 3.33/3.52 inference(monotonicity,[status(thm)],[15381])).
% 3.33/3.52 tff(15474,plain,
% 3.33/3.52 ((s(s(elem!1)) = elem!1) <=> (elem!1 = s(s(s(elem!1))))),
% 3.33/3.52 inference(transitivity,[status(thm)],[15473, 5406])).
% 3.33/3.52 tff(15475,plain,
% 3.33/3.52 (s(s(elem!1)) = elem!1),
% 3.33/3.52 inference(unit_resolution,[status(thm)],[10139, 15382])).
% 3.33/3.52 tff(15476,plain,
% 3.33/3.52 (elem!1 = s(s(s(elem!1)))),
% 3.33/3.52 inference(modus_ponens,[status(thm)],[15475, 15474])).
% 3.33/3.52 tff(15477,plain,
% 3.33/3.52 (~b(s(s(z)), z)),
% 3.33/3.52 inference(unit_resolution,[status(thm)],[11973, 15430, 10451, 118])).
% 3.33/3.52 tff(15478,plain,
% 3.33/3.52 (r(s(s(z)), z)),
% 3.33/3.52 inference(unit_resolution,[status(thm)],[186, 15477])).
% 3.33/3.52 tff(15479,plain,
% 3.33/3.52 (elem!1 = s(s(s(elem!1)))),
% 3.33/3.52 inference(transitivity,[status(thm)],[1170, 15384, 104, 15381])).
% 3.33/3.52 tff(15480,plain,
% 3.33/3.52 (r(elem!1, z) <=> r(s(s(s(elem!1))), z)),
% 3.33/3.52 inference(monotonicity,[status(thm)],[15479])).
% 3.33/3.52 tff(15481,plain,
% 3.33/3.52 (r(s(s(s(elem!1))), z) <=> r(elem!1, z)),
% 3.33/3.52 inference(symmetry,[status(thm)],[15480])).
% 3.33/3.52 tff(15482,plain,
% 3.33/3.52 (~b(s(s(s(elem!1))), z)),
% 3.33/3.52 inference(unit_resolution,[status(thm)],[12429, 15459, 10451, 15363, 15362, 376])).
% 3.33/3.52 tff(15483,plain,
% 3.33/3.52 (r(s(s(s(elem!1))), z)),
% 3.33/3.52 inference(unit_resolution,[status(thm)],[94, 15482])).
% 3.33/3.52 tff(15484,plain,
% 3.33/3.52 (r(elem!1, z)),
% 3.33/3.52 inference(modus_ponens,[status(thm)],[15483, 15481])).
% 3.33/3.52 tff(15485,plain,
% 3.33/3.52 (~b(s(s(elem!1)), s(s(z)))),
% 3.33/3.52 inference(unit_resolution,[status(thm)],[558, 15430, 376, 15363])).
% 3.33/3.52 tff(15486,plain,
% 3.33/3.52 (r(s(s(elem!1)), s(s(z)))),
% 3.33/3.52 inference(unit_resolution,[status(thm)],[441, 15485, 132])).
% 3.33/3.52 tff(15487,plain,
% 3.33/3.52 (r(elem!1, s(s(z)))),
% 3.33/3.52 inference(unit_resolution,[status(thm)],[3656, 15486, 15382])).
% 3.33/3.52 tff(15488,plain,
% 3.33/3.52 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, z)) | (~r(z, elem!1)) | (~r(s(s(z)), z)) | (~r(elem!1, s(s(z)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(elem!1, z)) | (~r(z, elem!1)) | (~r(s(s(z)), z)) | (~r(elem!1, s(s(z)))))),
% 3.33/3.52 inference(rewrite,[status(thm)],[])).
% 3.33/3.52 tff(15489,plain,
% 3.33/3.52 (((~r(z, elem!1)) | (~r(s(s(z)), z)) | (~r(elem!1, z)) | (~r(elem!1, s(s(z))))) <=> ((~r(elem!1, z)) | (~r(z, elem!1)) | (~r(s(s(z)), z)) | (~r(elem!1, s(s(z)))))),
% 3.33/3.52 inference(rewrite,[status(thm)],[])).
% 3.33/3.52 tff(15490,plain,
% 3.33/3.52 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, elem!1)) | (~r(s(s(z)), z)) | (~r(elem!1, z)) | (~r(elem!1, s(s(z)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, z)) | (~r(z, elem!1)) | (~r(s(s(z)), z)) | (~r(elem!1, s(s(z))))))),
% 3.33/3.52 inference(monotonicity,[status(thm)],[15489])).
% 3.33/3.52 tff(15491,plain,
% 3.33/3.52 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, elem!1)) | (~r(s(s(z)), z)) | (~r(elem!1, z)) | (~r(elem!1, s(s(z)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(elem!1, z)) | (~r(z, elem!1)) | (~r(s(s(z)), z)) | (~r(elem!1, s(s(z)))))),
% 3.33/3.53 inference(transitivity,[status(thm)],[15490, 15488])).
% 3.33/3.53 tff(15492,plain,
% 3.33/3.53 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, elem!1)) | (~r(s(s(z)), z)) | (~r(elem!1, z)) | (~r(elem!1, s(s(z)))))),
% 3.33/3.53 inference(quant_inst,[status(thm)],[])).
% 3.33/3.53 tff(15493,plain,
% 3.33/3.53 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(elem!1, z)) | (~r(z, elem!1)) | (~r(s(s(z)), z)) | (~r(elem!1, s(s(z))))),
% 3.33/3.53 inference(modus_ponens,[status(thm)],[15492, 15491])).
% 3.33/3.53 tff(15494,plain,
% 3.33/3.53 ((~r(elem!1, z)) | (~r(z, elem!1)) | (~r(s(s(z)), z)) | (~r(elem!1, s(s(z))))),
% 3.33/3.53 inference(unit_resolution,[status(thm)],[15493, 197])).
% 3.33/3.53 tff(15495,plain,
% 3.33/3.53 (~r(z, elem!1)),
% 3.33/3.53 inference(unit_resolution,[status(thm)],[15494, 15487, 15484, 15478])).
% 3.33/3.53 tff(15496,plain,
% 3.33/3.53 (b(z, elem!1)),
% 3.33/3.53 inference(unit_resolution,[status(thm)],[2514, 15495, 1146])).
% 3.33/3.53 tff(15497,plain,
% 3.33/3.53 (b(z, s(s(s(elem!1))))),
% 3.33/3.53 inference(unit_resolution,[status(thm)],[11488, 15496, 15476])).
% 3.33/3.53 tff(15498,plain,
% 3.33/3.53 (b(z, s(s(elem!1)))),
% 3.33/3.53 inference(unit_resolution,[status(thm)],[4345, 15497, 15381])).
% 3.33/3.53 tff(15499,plain,
% 3.33/3.53 (~b(s(s(s(z))), z)),
% 3.33/3.53 inference(unit_resolution,[status(thm)],[5676, 15442, 376, 118, 15362])).
% 3.33/3.53 tff(15500,plain,
% 3.33/3.53 (r(s(s(s(z))), z)),
% 3.33/3.53 inference(unit_resolution,[status(thm)],[1713, 15499])).
% 3.33/3.53 tff(15501,plain,
% 3.33/3.53 (~r(z, s(s(s(z))))),
% 3.33/3.53 inference(unit_resolution,[status(thm)],[12076, 15472, 15478, 15500])).
% 3.33/3.53 tff(15502,plain,
% 3.33/3.53 (b(z, s(s(s(z))))),
% 3.33/3.53 inference(unit_resolution,[status(thm)],[1697, 15501])).
% 3.33/3.53 tff(15503,plain,
% 3.33/3.53 (~b(s(s(s(z))), s(z))),
% 3.33/3.53 inference(unit_resolution,[status(thm)],[14177, 15502, 15362, 118, 15498])).
% 3.33/3.53 tff(15504,plain,
% 3.33/3.53 (r(s(s(s(z))), s(z))),
% 3.33/3.53 inference(unit_resolution,[status(thm)],[1763, 15503])).
% 3.33/3.53 tff(15505,plain,
% 3.33/3.53 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), s(s(s(z))))) | (~r(s(s(s(elem!1))), s(s(z)))) | (~r(s(s(z)), s(s(s(z))))) | (~r(s(s(s(z))), s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(elem!1))), s(s(s(z))))) | (~r(s(s(s(elem!1))), s(s(z)))) | (~r(s(s(z)), s(s(s(z))))) | (~r(s(s(s(z))), s(z))))),
% 3.33/3.53 inference(rewrite,[status(thm)],[])).
% 3.33/3.53 tff(15506,plain,
% 3.33/3.53 (((~r(s(s(s(z))), s(z))) | (~r(s(s(z)), s(s(s(z))))) | (~r(s(s(s(elem!1))), s(s(s(z))))) | (~r(s(s(s(elem!1))), s(s(z))))) <=> ((~r(s(s(s(elem!1))), s(s(s(z))))) | (~r(s(s(s(elem!1))), s(s(z)))) | (~r(s(s(z)), s(s(s(z))))) | (~r(s(s(s(z))), s(z))))),
% 3.33/3.53 inference(rewrite,[status(thm)],[])).
% 3.33/3.53 tff(15507,plain,
% 3.33/3.53 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(z))), s(z))) | (~r(s(s(z)), s(s(s(z))))) | (~r(s(s(s(elem!1))), s(s(s(z))))) | (~r(s(s(s(elem!1))), s(s(z)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), s(s(s(z))))) | (~r(s(s(s(elem!1))), s(s(z)))) | (~r(s(s(z)), s(s(s(z))))) | (~r(s(s(s(z))), s(z)))))),
% 3.33/3.53 inference(monotonicity,[status(thm)],[15506])).
% 3.33/3.53 tff(15508,plain,
% 3.33/3.53 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(z))), s(z))) | (~r(s(s(z)), s(s(s(z))))) | (~r(s(s(s(elem!1))), s(s(s(z))))) | (~r(s(s(s(elem!1))), s(s(z)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(elem!1))), s(s(s(z))))) | (~r(s(s(s(elem!1))), s(s(z)))) | (~r(s(s(z)), s(s(s(z))))) | (~r(s(s(s(z))), s(z))))),
% 3.33/3.53 inference(transitivity,[status(thm)],[15507, 15505])).
% 3.33/3.53 tff(15509,plain,
% 3.33/3.53 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(z))), s(z))) | (~r(s(s(z)), s(s(s(z))))) | (~r(s(s(s(elem!1))), s(s(s(z))))) | (~r(s(s(s(elem!1))), s(s(z)))))),
% 3.33/3.53 inference(quant_inst,[status(thm)],[])).
% 3.33/3.53 tff(15510,plain,
% 3.33/3.53 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(elem!1))), s(s(s(z))))) | (~r(s(s(s(elem!1))), s(s(z)))) | (~r(s(s(z)), s(s(s(z))))) | (~r(s(s(s(z))), s(z)))),
% 3.33/3.53 inference(modus_ponens,[status(thm)],[15509, 15508])).
% 3.33/3.53 tff(15511,plain,
% 3.33/3.53 ($false),
% 3.33/3.53 inference(unit_resolution,[status(thm)],[15510, 197, 15432, 15504, 15472, 15458])).
% 3.33/3.53 tff(15512,plain,(r(s(s(elem!1)), s(s(s(elem!1)))) | (~b(z, s(z))) | (~r(s(s(z)), s(z))) | (~b(z, s(s(z)))) | (~b(s(z), s(s(elem!1)))) | (~r(s(s(s(elem!1))), s(z))) | b(s(s(elem!1)), s(z)) | (s(s(z)) = s(s(elem!1)))), inference(lemma,lemma(discharge,[]))).
% 3.33/3.53 tff(15513,plain,
% 3.33/3.53 (s(s(z)) = s(s(elem!1))),
% 3.33/3.53 inference(unit_resolution,[status(thm)],[15512, 15222, 392, 10451, 376, 350, 4568, 118])).
% 3.33/3.53 tff(15514,plain,
% 3.33/3.53 (b(s(z), s(s(z))) <=> b(s(z), s(s(elem!1)))),
% 3.33/3.53 inference(monotonicity,[status(thm)],[15513])).
% 3.33/3.53 tff(15515,plain,
% 3.33/3.53 (b(s(z), s(s(elem!1))) <=> b(s(z), s(s(z)))),
% 3.33/3.53 inference(symmetry,[status(thm)],[15514])).
% 3.33/3.53 tff(15516,plain,
% 3.33/3.53 (b(s(z), s(s(z)))),
% 3.33/3.53 inference(modus_ponens,[status(thm)],[376, 15515])).
% 3.33/3.53 tff(15517,plain,
% 3.33/3.53 ($false),
% 3.33/3.53 inference(unit_resolution,[status(thm)],[5433, 15516])).
% 3.33/3.53 tff(15518,plain,(b(s(z), s(s(z))) | (~b(s(z), s(s(elem!1)))) | (~r(s(s(z)), s(z))) | (~b(z, s(s(z)))) | (~r(s(s(s(elem!1))), s(z))) | b(s(s(elem!1)), s(z)) | (~b(z, s(z)))), inference(lemma,lemma(discharge,[]))).
% 3.33/3.53 tff(15519,plain,
% 3.33/3.53 (b(s(z), s(s(z)))),
% 3.33/3.53 inference(unit_resolution,[status(thm)],[15518, 392, 376, 10451, 350, 4568, 118])).
% 3.33/3.53 tff(15520,plain,
% 3.33/3.53 (~r(s(s(s(elem!1))), s(s(z)))),
% 3.33/3.53 inference(unit_resolution,[status(thm)],[15440, 1653, 392, 350])).
% 3.33/3.53 tff(15521,plain,
% 3.33/3.53 (b(s(s(s(elem!1))), s(s(z)))),
% 3.33/3.53 inference(unit_resolution,[status(thm)],[218, 15520])).
% 3.33/3.53 tff(15522,plain,
% 3.33/3.53 (~b(s(s(z)), s(s(s(elem!1))))),
% 3.33/3.53 inference(unit_resolution,[status(thm)],[12045, 15521, 10451, 118, 556])).
% 3.33/3.53 tff(15523,plain,
% 3.33/3.53 (r(s(s(z)), s(s(s(elem!1))))),
% 3.33/3.53 inference(unit_resolution,[status(thm)],[279, 15522])).
% 3.33/3.53 tff(15524,plain,
% 3.33/3.53 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), s(z))) | (~r(s(s(z)), s(z))) | (~r(s(s(z)), s(s(s(elem!1))))) | (~r(s(z), s(s(s(z))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(elem!1))), s(z))) | (~r(s(s(z)), s(z))) | (~r(s(s(z)), s(s(s(elem!1))))) | (~r(s(z), s(s(s(z))))))),
% 3.33/3.53 inference(rewrite,[status(thm)],[])).
% 3.33/3.53 tff(15525,plain,
% 3.33/3.53 (((~r(s(z), s(s(s(z))))) | (~r(s(s(s(elem!1))), s(z))) | (~r(s(s(z)), s(z))) | (~r(s(s(z)), s(s(s(elem!1)))))) <=> ((~r(s(s(s(elem!1))), s(z))) | (~r(s(s(z)), s(z))) | (~r(s(s(z)), s(s(s(elem!1))))) | (~r(s(z), s(s(s(z))))))),
% 3.33/3.53 inference(rewrite,[status(thm)],[])).
% 3.33/3.53 tff(15526,plain,
% 3.33/3.53 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(s(s(z))))) | (~r(s(s(s(elem!1))), s(z))) | (~r(s(s(z)), s(z))) | (~r(s(s(z)), s(s(s(elem!1))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), s(z))) | (~r(s(s(z)), s(z))) | (~r(s(s(z)), s(s(s(elem!1))))) | (~r(s(z), s(s(s(z)))))))),
% 3.33/3.53 inference(monotonicity,[status(thm)],[15525])).
% 3.33/3.53 tff(15527,plain,
% 3.33/3.53 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(s(s(z))))) | (~r(s(s(s(elem!1))), s(z))) | (~r(s(s(z)), s(z))) | (~r(s(s(z)), s(s(s(elem!1))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(elem!1))), s(z))) | (~r(s(s(z)), s(z))) | (~r(s(s(z)), s(s(s(elem!1))))) | (~r(s(z), s(s(s(z))))))),
% 3.33/3.53 inference(transitivity,[status(thm)],[15526, 15524])).
% 3.33/3.53 tff(15528,plain,
% 3.33/3.53 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(s(s(z))))) | (~r(s(s(s(elem!1))), s(z))) | (~r(s(s(z)), s(z))) | (~r(s(s(z)), s(s(s(elem!1))))))),
% 3.33/3.53 inference(quant_inst,[status(thm)],[])).
% 3.33/3.53 tff(15529,plain,
% 3.33/3.53 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(elem!1))), s(z))) | (~r(s(s(z)), s(z))) | (~r(s(s(z)), s(s(s(elem!1))))) | (~r(s(z), s(s(s(z)))))),
% 3.33/3.53 inference(modus_ponens,[status(thm)],[15528, 15527])).
% 3.33/3.53 tff(15530,plain,
% 3.33/3.53 ($false),
% 3.33/3.53 inference(unit_resolution,[status(thm)],[15529, 197, 350, 392, 15523, 1653])).
% 3.33/3.53 tff(15531,plain,((~r(s(z), s(s(s(z))))) | (~r(s(s(s(elem!1))), s(z))) | (~r(s(s(z)), s(z))) | (~b(z, s(s(z)))) | (~b(z, s(z))) | (~b(s(z), s(s(z))))), inference(lemma,lemma(discharge,[]))).
% 3.33/3.53 tff(15532,plain,
% 3.33/3.53 (~r(s(z), s(s(s(z))))),
% 3.33/3.53 inference(unit_resolution,[status(thm)],[15531, 556, 392, 10451, 118, 350])).
% 3.33/3.53 tff(15533,plain,
% 3.33/3.53 (b(s(z), s(s(s(z))))),
% 3.33/3.53 inference(unit_resolution,[status(thm)],[1674, 15532])).
% 3.33/3.53 tff(15534,plain,
% 3.33/3.53 (~r(s(z), z)),
% 3.33/3.53 inference(unit_resolution,[status(thm)],[11986, 392, 10451, 4568])).
% 3.33/3.53 tff(15535,plain,
% 3.33/3.53 (b(s(z), z)),
% 3.33/3.53 inference(unit_resolution,[status(thm)],[230, 15534])).
% 3.33/3.53 tff(15536,plain,
% 3.33/3.53 (~b(s(s(s(z))), z)),
% 3.33/3.53 inference(unit_resolution,[status(thm)],[5676, 15533, 376, 118, 15535])).
% 3.33/3.53 tff(15537,plain,
% 3.33/3.53 (r(s(s(s(z))), z)),
% 3.33/3.53 inference(unit_resolution,[status(thm)],[1713, 15536])).
% 3.33/3.53 tff(15538,plain,
% 3.33/3.53 (~b(s(s(z)), z)),
% 3.33/3.53 inference(unit_resolution,[status(thm)],[11973, 556, 10451, 118])).
% 3.33/3.53 tff(15539,plain,
% 3.33/3.53 (r(s(s(z)), z)),
% 3.33/3.53 inference(unit_resolution,[status(thm)],[186, 15538])).
% 3.33/3.53 tff(15540,plain,
% 3.33/3.53 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(elem!1)))) | (~r(s(s(z)), z)) | (~r(s(s(z)), s(s(s(z))))) | (~r(s(s(s(z))), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, s(s(elem!1)))) | (~r(s(s(z)), z)) | (~r(s(s(z)), s(s(s(z))))) | (~r(s(s(s(z))), z)))),
% 3.33/3.53 inference(rewrite,[status(thm)],[])).
% 3.33/3.53 tff(15541,plain,
% 3.33/3.53 (((~r(z, s(s(elem!1)))) | (~r(s(s(s(z))), z)) | (~r(s(s(z)), z)) | (~r(s(s(z)), s(s(s(z)))))) <=> ((~r(z, s(s(elem!1)))) | (~r(s(s(z)), z)) | (~r(s(s(z)), s(s(s(z))))) | (~r(s(s(s(z))), z)))),
% 3.33/3.53 inference(rewrite,[status(thm)],[])).
% 3.33/3.53 tff(15542,plain,
% 3.33/3.53 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(elem!1)))) | (~r(s(s(s(z))), z)) | (~r(s(s(z)), z)) | (~r(s(s(z)), s(s(s(z))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(elem!1)))) | (~r(s(s(z)), z)) | (~r(s(s(z)), s(s(s(z))))) | (~r(s(s(s(z))), z))))),
% 3.33/3.53 inference(monotonicity,[status(thm)],[15541])).
% 3.33/3.53 tff(15543,plain,
% 3.33/3.53 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(elem!1)))) | (~r(s(s(s(z))), z)) | (~r(s(s(z)), z)) | (~r(s(s(z)), s(s(s(z))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, s(s(elem!1)))) | (~r(s(s(z)), z)) | (~r(s(s(z)), s(s(s(z))))) | (~r(s(s(s(z))), z)))),
% 3.33/3.53 inference(transitivity,[status(thm)],[15542, 15540])).
% 3.33/3.53 tff(15544,plain,
% 3.33/3.53 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(elem!1)))) | (~r(s(s(s(z))), z)) | (~r(s(s(z)), z)) | (~r(s(s(z)), s(s(s(z))))))),
% 3.33/3.53 inference(quant_inst,[status(thm)],[])).
% 3.33/3.53 tff(15545,plain,
% 3.33/3.53 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, s(s(elem!1)))) | (~r(s(s(z)), z)) | (~r(s(s(z)), s(s(s(z))))) | (~r(s(s(s(z))), z))),
% 3.33/3.53 inference(modus_ponens,[status(thm)],[15544, 15543])).
% 3.33/3.53 tff(15546,plain,
% 3.33/3.53 (~r(s(s(z)), s(s(s(z))))),
% 3.33/3.53 inference(unit_resolution,[status(thm)],[15545, 197, 365, 15539, 1733])).
% 3.33/3.53 tff(15547,plain,
% 3.33/3.53 (b(s(s(z)), s(s(s(z))))),
% 3.33/3.53 inference(unit_resolution,[status(thm)],[1730, 15546])).
% 3.33/3.53 tff(15548,plain,
% 3.33/3.53 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(elem!1)))) | (~r(s(s(z)), z)) | (~r(s(s(s(z))), z)) | (~r(s(s(s(z))), s(s(z)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, s(s(elem!1)))) | (~r(s(s(z)), z)) | (~r(s(s(s(z))), z)) | (~r(s(s(s(z))), s(s(z)))))),
% 3.33/3.53 inference(rewrite,[status(thm)],[])).
% 3.33/3.53 tff(15549,plain,
% 3.33/3.53 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(elem!1)))) | (~r(s(s(z)), z)) | (~r(s(s(s(z))), z)) | (~r(s(s(s(z))), s(s(z)))))),
% 3.33/3.53 inference(quant_inst,[status(thm)],[])).
% 3.33/3.53 tff(15550,plain,
% 3.33/3.53 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, s(s(elem!1)))) | (~r(s(s(z)), z)) | (~r(s(s(s(z))), z)) | (~r(s(s(s(z))), s(s(z))))),
% 3.33/3.53 inference(modus_ponens,[status(thm)],[15549, 15548])).
% 3.33/3.53 tff(15551,plain,
% 3.33/3.53 (~r(s(s(s(z))), s(s(z)))),
% 3.33/3.53 inference(unit_resolution,[status(thm)],[15550, 197, 365, 15539, 1733])).
% 3.33/3.53 tff(15552,plain,
% 3.33/3.53 (b(s(s(s(z))), s(s(z)))),
% 3.33/3.53 inference(unit_resolution,[status(thm)],[1010, 15551])).
% 3.33/3.53 tff(15553,plain,
% 3.33/3.53 ($false),
% 3.33/3.53 inference(unit_resolution,[status(thm)],[996, 15552, 15547, 556, 988])).
% 3.33/3.53 tff(15554,plain,((~b(s(z), s(s(z)))) | (~b(s(z), s(s(s(z))))) | (~r(z, s(s(elem!1)))) | (~r(s(s(s(z))), z)) | (~b(z, s(s(z)))) | (~b(z, s(z)))), inference(lemma,lemma(discharge,[]))).
% 3.33/3.53 tff(15555,plain,
% 3.33/3.53 (~r(z, s(s(elem!1)))),
% 3.33/3.53 inference(unit_resolution,[status(thm)],[15554, 15537, 556, 15533, 10451, 118])).
% 3.33/3.53 tff(15556,plain,
% 3.33/3.53 (b(z, s(s(elem!1)))),
% 3.33/3.53 inference(unit_resolution,[status(thm)],[1795, 15555])).
% 3.33/3.53 tff(15557,plain,
% 3.33/3.53 (~b(s(s(z)), s(s(s(elem!1))))),
% 3.33/3.53 inference(unit_resolution,[status(thm)],[12045, 3962, 10451, 118, 556])).
% 3.33/3.53 tff(15558,plain,
% 3.33/3.53 (r(s(s(z)), s(s(s(elem!1))))),
% 3.33/3.53 inference(unit_resolution,[status(thm)],[279, 15557])).
% 3.33/3.53 tff(15559,plain,
% 3.33/3.53 (r(s(s(elem!1)), s(s(s(elem!1))))),
% 3.33/3.53 inference(unit_resolution,[status(thm)],[15512, 52, 392, 10451, 376, 350, 4568, 118])).
% 3.33/3.53 tff(15560,plain,
% 3.33/3.53 (~r(s(z), s(s(s(elem!1))))),
% 3.33/3.53 inference(unit_resolution,[status(thm)],[6892, 2073, 10521, 392])).
% 3.33/3.53 tff(15561,plain,
% 3.33/3.53 (b(s(z), s(s(s(elem!1))))),
% 3.33/3.53 inference(unit_resolution,[status(thm)],[116, 15560])).
% 3.33/3.53 tff(15562,plain,
% 3.33/3.53 (~b(s(s(s(elem!1))), z)),
% 3.33/3.53 inference(unit_resolution,[status(thm)],[7322, 15561, 376, 15535, 118])).
% 3.33/3.53 tff(15563,plain,
% 3.33/3.53 (r(s(s(s(elem!1))), z)),
% 3.33/3.53 inference(unit_resolution,[status(thm)],[94, 15562])).
% 3.33/3.53 tff(15564,plain,
% 3.33/3.53 ($false),
% 3.33/3.53 inference(unit_resolution,[status(thm)],[14439, 197, 15563, 15559, 2073, 281])).
% 3.33/3.53 tff(15565,plain,((s(s(z)) = s(s(elem!1))) | (~r(s(s(z)), s(s(s(elem!1))))) | (~b(s(z), s(s(elem!1)))) | (~b(z, s(z))) | (~r(s(s(z)), s(z))) | b(s(s(z)), s(s(elem!1))) | (~b(z, s(s(z)))) | (~r(s(s(s(elem!1))), s(z))) | b(s(s(elem!1)), s(z))), inference(lemma,lemma(discharge,[]))).
% 3.33/3.53 tff(15566,plain,
% 3.33/3.53 (b(s(s(z)), s(s(elem!1)))),
% 3.33/3.53 inference(unit_resolution,[status(thm)],[15565, 52, 376, 118, 392, 281, 10451, 350, 4568])).
% 3.33/3.53 tff(15567,plain,
% 3.33/3.53 (~b(s(s(elem!1)), s(s(z)))),
% 3.33/3.53 inference(unit_resolution,[status(thm)],[558, 15566, 376, 556])).
% 3.33/3.53 tff(15568,plain,
% 3.33/3.53 (r(s(s(elem!1)), s(s(z)))),
% 3.33/3.53 inference(unit_resolution,[status(thm)],[441, 15567, 132])).
% 3.33/3.53 tff(15569,plain,
% 3.33/3.53 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), s(z))) | (~r(s(s(elem!1)), s(s(s(elem!1))))) | (~r(s(s(elem!1)), s(s(z)))) | (~r(s(s(z)), s(s(s(elem!1))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(elem!1))), s(z))) | (~r(s(s(elem!1)), s(s(s(elem!1))))) | (~r(s(s(elem!1)), s(s(z)))) | (~r(s(s(z)), s(s(s(elem!1))))))),
% 3.33/3.53 inference(rewrite,[status(thm)],[])).
% 3.33/3.53 tff(15570,plain,
% 3.33/3.53 (((~r(s(s(s(elem!1))), s(z))) | (~r(s(s(z)), s(s(s(elem!1))))) | (~r(s(s(elem!1)), s(s(s(elem!1))))) | (~r(s(s(elem!1)), s(s(z))))) <=> ((~r(s(s(s(elem!1))), s(z))) | (~r(s(s(elem!1)), s(s(s(elem!1))))) | (~r(s(s(elem!1)), s(s(z)))) | (~r(s(s(z)), s(s(s(elem!1))))))),
% 3.33/3.53 inference(rewrite,[status(thm)],[])).
% 3.33/3.53 tff(15571,plain,
% 3.33/3.53 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), s(z))) | (~r(s(s(z)), s(s(s(elem!1))))) | (~r(s(s(elem!1)), s(s(s(elem!1))))) | (~r(s(s(elem!1)), s(s(z)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), s(z))) | (~r(s(s(elem!1)), s(s(s(elem!1))))) | (~r(s(s(elem!1)), s(s(z)))) | (~r(s(s(z)), s(s(s(elem!1)))))))),
% 3.33/3.53 inference(monotonicity,[status(thm)],[15570])).
% 3.33/3.53 tff(15572,plain,
% 3.33/3.53 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), s(z))) | (~r(s(s(z)), s(s(s(elem!1))))) | (~r(s(s(elem!1)), s(s(s(elem!1))))) | (~r(s(s(elem!1)), s(s(z)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(elem!1))), s(z))) | (~r(s(s(elem!1)), s(s(s(elem!1))))) | (~r(s(s(elem!1)), s(s(z)))) | (~r(s(s(z)), s(s(s(elem!1))))))),
% 3.33/3.53 inference(transitivity,[status(thm)],[15571, 15569])).
% 3.33/3.53 tff(15573,plain,
% 3.33/3.53 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), s(z))) | (~r(s(s(z)), s(s(s(elem!1))))) | (~r(s(s(elem!1)), s(s(s(elem!1))))) | (~r(s(s(elem!1)), s(s(z)))))),
% 3.33/3.53 inference(quant_inst,[status(thm)],[])).
% 3.33/3.53 tff(15574,plain,
% 3.33/3.53 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(elem!1))), s(z))) | (~r(s(s(elem!1)), s(s(s(elem!1))))) | (~r(s(s(elem!1)), s(s(z)))) | (~r(s(s(z)), s(s(s(elem!1)))))),
% 3.33/3.53 inference(modus_ponens,[status(thm)],[15573, 15572])).
% 3.33/3.53 tff(15575,plain,
% 3.33/3.53 ($false),
% 3.33/3.53 inference(unit_resolution,[status(thm)],[15574, 197, 15568, 350, 15559, 281])).
% 3.33/3.53 tff(15576,plain,((s(s(z)) = s(s(elem!1))) | (~r(s(s(s(elem!1))), s(z))) | (~r(s(s(z)), s(s(s(elem!1))))) | (~b(s(z), s(s(elem!1)))) | (~b(s(z), s(s(z)))) | (~b(z, s(z))) | (~r(s(s(z)), s(z))) | (~b(z, s(s(z)))) | b(s(s(elem!1)), s(z))), inference(lemma,lemma(discharge,[]))).
% 3.33/3.53 tff(15577,plain,
% 3.33/3.53 (s(s(z)) = s(s(elem!1))),
% 3.33/3.53 inference(unit_resolution,[status(thm)],[15576, 15558, 350, 376, 556, 118, 392, 10451, 4568])).
% 3.33/3.53 tff(15578,plain,
% 3.33/3.53 (s(elem!1) = s(z)),
% 3.33/3.53 inference(unit_resolution,[status(thm)],[43, 15577])).
% 3.33/3.53 tff(15579,plain,
% 3.33/3.53 (~r(s(z), s(s(s(s(elem!1)))))),
% 3.33/3.53 inference(unit_resolution,[status(thm)],[1323, 15558, 350, 392])).
% 3.33/3.53 tff(15580,plain,
% 3.33/3.53 (b(s(z), s(s(s(s(elem!1)))))),
% 3.33/3.53 inference(unit_resolution,[status(thm)],[681, 15579])).
% 3.33/3.53 tff(15581,plain,
% 3.33/3.53 (r(s(s(s(z))), elem!1)),
% 3.33/3.53 inference(modus_ponens,[status(thm)],[1733, 6293])).
% 3.33/3.53 tff(15582,plain,
% 3.33/3.53 (r(s(s(s(elem!1))), elem!1)),
% 3.33/3.53 inference(modus_ponens,[status(thm)],[15581, 6295])).
% 3.33/3.53 tff(15583,plain,
% 3.33/3.53 (r(s(s(elem!1)), s(s(s(elem!1))))),
% 3.33/3.53 inference(modus_ponens,[status(thm)],[281, 10526])).
% 3.33/3.53 tff(15584,plain,
% 3.33/3.53 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(s(s(s(elem!1)))))) | (~r(s(s(elem!1)), elem!1)) | (~r(s(s(elem!1)), s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), elem!1)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(elem!1, s(s(s(s(elem!1)))))) | (~r(s(s(elem!1)), elem!1)) | (~r(s(s(elem!1)), s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), elem!1)))),
% 3.33/3.53 inference(rewrite,[status(thm)],[])).
% 3.33/3.53 tff(15585,plain,
% 3.33/3.53 (((~r(elem!1, s(s(s(s(elem!1)))))) | (~r(s(s(s(elem!1))), elem!1)) | (~r(s(s(elem!1)), elem!1)) | (~r(s(s(elem!1)), s(s(s(elem!1)))))) <=> ((~r(elem!1, s(s(s(s(elem!1)))))) | (~r(s(s(elem!1)), elem!1)) | (~r(s(s(elem!1)), s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), elem!1)))),
% 3.33/3.53 inference(rewrite,[status(thm)],[])).
% 3.33/3.53 tff(15586,plain,
% 3.33/3.53 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(s(s(s(elem!1)))))) | (~r(s(s(s(elem!1))), elem!1)) | (~r(s(s(elem!1)), elem!1)) | (~r(s(s(elem!1)), s(s(s(elem!1))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(s(s(s(elem!1)))))) | (~r(s(s(elem!1)), elem!1)) | (~r(s(s(elem!1)), s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), elem!1))))),
% 3.33/3.54 inference(monotonicity,[status(thm)],[15585])).
% 3.33/3.54 tff(15587,plain,
% 3.33/3.54 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(s(s(s(elem!1)))))) | (~r(s(s(s(elem!1))), elem!1)) | (~r(s(s(elem!1)), elem!1)) | (~r(s(s(elem!1)), s(s(s(elem!1))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(elem!1, s(s(s(s(elem!1)))))) | (~r(s(s(elem!1)), elem!1)) | (~r(s(s(elem!1)), s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), elem!1)))),
% 3.33/3.54 inference(transitivity,[status(thm)],[15586, 15584])).
% 3.33/3.54 tff(15588,plain,
% 3.33/3.54 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(s(s(s(elem!1)))))) | (~r(s(s(s(elem!1))), elem!1)) | (~r(s(s(elem!1)), elem!1)) | (~r(s(s(elem!1)), s(s(s(elem!1))))))),
% 3.33/3.54 inference(quant_inst,[status(thm)],[])).
% 3.33/3.54 tff(15589,plain,
% 3.33/3.54 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(elem!1, s(s(s(s(elem!1)))))) | (~r(s(s(elem!1)), elem!1)) | (~r(s(s(elem!1)), s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), elem!1))),
% 3.33/3.54 inference(modus_ponens,[status(thm)],[15588, 15587])).
% 3.33/3.54 tff(15590,plain,
% 3.33/3.54 ($false),
% 3.33/3.54 inference(unit_resolution,[status(thm)],[15589, 197, 768, 377, 1013, 1047])).
% 3.33/3.54 tff(15591,plain,((~r(elem!1, s(s(s(s(elem!1)))))) | (~r(s(s(elem!1)), elem!1)) | (~r(s(s(elem!1)), s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), elem!1))), inference(lemma,lemma(discharge,[]))).
% 3.33/3.54 tff(15592,plain,
% 3.33/3.54 (~r(elem!1, s(s(s(s(elem!1)))))),
% 3.33/3.54 inference(unit_resolution,[status(thm)],[15591, 10546, 15583, 15582])).
% 3.33/3.54 tff(15593,plain,
% 3.33/3.54 (~r(elem!1, s(s(s(s(z)))))),
% 3.33/3.54 inference(unit_resolution,[status(thm)],[1093, 15592, 34])).
% 3.33/3.54 tff(15594,plain,
% 3.33/3.54 (b(elem!1, s(s(s(s(z)))))),
% 3.33/3.54 inference(unit_resolution,[status(thm)],[1098, 15593, 1045])).
% 3.33/3.54 tff(15595,plain,
% 3.33/3.54 (b(elem!1, s(s(s(s(elem!1)))))),
% 3.33/3.54 inference(unit_resolution,[status(thm)],[1105, 15594, 34])).
% 3.33/3.54 tff(15596,plain,
% 3.33/3.54 (~r(s(s(s(elem!1))), s(s(elem!1)))),
% 3.33/3.54 inference(unit_resolution,[status(thm)],[3454, 34, 213])).
% 3.33/3.54 tff(15597,plain,
% 3.33/3.54 (b(s(s(s(elem!1))), s(s(elem!1)))),
% 3.33/3.54 inference(unit_resolution,[status(thm)],[889, 15596, 1863])).
% 3.33/3.54 tff(15598,plain,
% 3.33/3.54 (~b(s(s(s(s(elem!1)))), s(s(s(elem!1))))),
% 3.33/3.54 inference(unit_resolution,[status(thm)],[6387, 15597, 376, 637, 1327, 15595])).
% 3.33/3.54 tff(15599,plain,
% 3.33/3.54 (r(s(s(s(s(elem!1)))), s(s(s(elem!1))))),
% 3.33/3.54 inference(unit_resolution,[status(thm)],[1065, 15598, 1058])).
% 3.33/3.54 tff(15600,plain,
% 3.33/3.54 (~r(s(s(elem!1)), s(s(s(s(elem!1)))))),
% 3.33/3.54 inference(unit_resolution,[status(thm)],[7704, 197, 350, 15583, 15599])).
% 3.33/3.54 tff(15601,plain,
% 3.33/3.54 (b(s(s(elem!1)), s(s(s(s(elem!1)))))),
% 3.33/3.54 inference(unit_resolution,[status(thm)],[827, 15600, 2395])).
% 3.33/3.54 tff(15602,plain,
% 3.33/3.54 (~r(s(s(s(z))), s(s(z)))),
% 3.33/3.54 inference(unit_resolution,[status(thm)],[4714, 34, 213])).
% 3.33/3.54 tff(15603,plain,
% 3.33/3.54 (b(s(s(s(z))), s(s(z)))),
% 3.33/3.54 inference(unit_resolution,[status(thm)],[1010, 15602])).
% 3.33/3.54 tff(15604,plain,
% 3.33/3.54 (~b(s(s(z)), s(s(s(z))))),
% 3.33/3.54 inference(unit_resolution,[status(thm)],[996, 15603, 556, 988])).
% 3.33/3.54 tff(15605,plain,
% 3.33/3.54 (r(s(s(z)), s(s(s(z))))),
% 3.33/3.54 inference(unit_resolution,[status(thm)],[1730, 15604])).
% 3.33/3.54 tff(15606,plain,
% 3.33/3.54 (~r(z, s(s(s(z))))),
% 3.33/3.54 inference(unit_resolution,[status(thm)],[12076, 15605, 866, 1733])).
% 3.33/3.54 tff(15607,plain,
% 3.33/3.54 (b(z, s(s(s(z))))),
% 3.33/3.54 inference(unit_resolution,[status(thm)],[1697, 15606])).
% 3.33/3.54 tff(15608,plain,
% 3.33/3.54 (b(elem!1, s(s(s(z))))),
% 3.33/3.54 inference(modus_ponens,[status(thm)],[15607, 4840])).
% 3.33/3.54 tff(15609,plain,
% 3.33/3.54 (b(elem!1, s(s(s(elem!1))))),
% 3.33/3.54 inference(modus_ponens,[status(thm)],[15608, 4839])).
% 3.33/3.54 tff(15610,plain,
% 3.33/3.54 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(z), s(s(s(elem!1))))) | (~b(elem!1, s(s(s(elem!1))))) | (~b(s(z), elem!1)) | (~b(s(s(elem!1)), s(s(s(s(elem!1)))))) | (~b(s(z), s(s(s(s(elem!1)))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(z), s(s(s(elem!1))))) | (~b(elem!1, s(s(s(elem!1))))) | (~b(s(z), elem!1)) | (~b(s(s(elem!1)), s(s(s(s(elem!1)))))) | (~b(s(z), s(s(s(s(elem!1)))))))),
% 3.33/3.54 inference(rewrite,[status(thm)],[])).
% 3.33/3.54 tff(15611,plain,
% 3.33/3.54 (((~b(s(s(elem!1)), s(s(s(s(elem!1)))))) | (~b(s(z), s(s(s(s(elem!1)))))) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(elem!1, s(s(s(elem!1))))) | (~b(s(z), s(s(s(elem!1))))) | (~b(s(z), elem!1))) <=> ((~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(z), s(s(s(elem!1))))) | (~b(elem!1, s(s(s(elem!1))))) | (~b(s(z), elem!1)) | (~b(s(s(elem!1)), s(s(s(s(elem!1)))))) | (~b(s(z), s(s(s(s(elem!1)))))))),
% 3.33/3.54 inference(rewrite,[status(thm)],[])).
% 3.33/3.54 tff(15612,plain,
% 3.33/3.54 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), s(s(s(s(elem!1)))))) | (~b(s(z), s(s(s(s(elem!1)))))) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(elem!1, s(s(s(elem!1))))) | (~b(s(z), s(s(s(elem!1))))) | (~b(s(z), elem!1)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(z), s(s(s(elem!1))))) | (~b(elem!1, s(s(s(elem!1))))) | (~b(s(z), elem!1)) | (~b(s(s(elem!1)), s(s(s(s(elem!1)))))) | (~b(s(z), s(s(s(s(elem!1))))))))),
% 3.33/3.54 inference(monotonicity,[status(thm)],[15611])).
% 3.33/3.54 tff(15613,plain,
% 3.33/3.54 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), s(s(s(s(elem!1)))))) | (~b(s(z), s(s(s(s(elem!1)))))) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(elem!1, s(s(s(elem!1))))) | (~b(s(z), s(s(s(elem!1))))) | (~b(s(z), elem!1)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(z), s(s(s(elem!1))))) | (~b(elem!1, s(s(s(elem!1))))) | (~b(s(z), elem!1)) | (~b(s(s(elem!1)), s(s(s(s(elem!1)))))) | (~b(s(z), s(s(s(s(elem!1)))))))),
% 3.33/3.54 inference(transitivity,[status(thm)],[15612, 15610])).
% 3.33/3.54 tff(15614,plain,
% 3.33/3.54 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), s(s(s(s(elem!1)))))) | (~b(s(z), s(s(s(s(elem!1)))))) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(elem!1, s(s(s(elem!1))))) | (~b(s(z), s(s(s(elem!1))))) | (~b(s(z), elem!1)))),
% 3.33/3.54 inference(quant_inst,[status(thm)],[])).
% 3.33/3.54 tff(15615,plain,
% 3.33/3.54 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(z), s(s(s(elem!1))))) | (~b(elem!1, s(s(s(elem!1))))) | (~b(s(z), elem!1)) | (~b(s(s(elem!1)), s(s(s(s(elem!1)))))) | (~b(s(z), s(s(s(s(elem!1))))))),
% 3.33/3.54 inference(modus_ponens,[status(thm)],[15614, 15613])).
% 3.33/3.54 tff(15616,plain,
% 3.33/3.54 ($false),
% 3.33/3.54 inference(unit_resolution,[status(thm)],[15615, 166, 15597, 15609, 4785, 637, 15601, 1327])).
% 3.33/3.54 tff(15617,plain,((~(s(s(z)) = s(s(elem!1)))) | (~b(s(z), s(s(s(s(elem!1)))))) | (s(s(elem!1)) = s(s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), s(z))) | (s(s(s(s(elem!1)))) = s(s(s(elem!1)))) | (~b(s(z), s(s(elem!1)))) | (~b(s(z), s(s(s(z))))) | (~r(s(s(s(z))), z)) | (~b(s(z), z)) | (~r(s(s(z)), z)) | (~r(s(s(z)), s(s(s(elem!1))))) | (~b(s(z), s(s(z)))) | (s(s(s(elem!1))) = s(s(elem!1))) | r(s(s(s(elem!1))), s(s(z)))), inference(lemma,lemma(discharge,[]))).
% 3.33/3.54 tff(15618,plain,
% 3.33/3.54 (s(s(elem!1)) = s(s(s(s(elem!1))))),
% 3.33/3.54 inference(unit_resolution,[status(thm)],[15617, 15577, 15580, 350, 1058, 376, 15533, 15537, 15535, 15539, 15558, 556, 1863, 213])).
% 3.33/3.54 tff(15619,plain,
% 3.33/3.54 (s(s(s(s(elem!1)))) = s(s(elem!1))),
% 3.33/3.54 inference(unit_resolution,[status(thm)],[1159, 15618])).
% 3.33/3.54 tff(15620,plain,
% 3.33/3.54 (s(s(s(elem!1))) = s(elem!1)),
% 3.33/3.54 inference(unit_resolution,[status(thm)],[1166, 15619])).
% 3.33/3.54 tff(15621,plain,
% 3.33/3.54 (s(s(s(elem!1))) = s(z)),
% 3.33/3.54 inference(transitivity,[status(thm)],[15620, 15578])).
% 3.33/3.54 tff(15622,plain,
% 3.33/3.54 ($false),
% 3.33/3.54 inference(unit_resolution,[status(thm)],[110, 15621])).
% 3.33/3.54 tff(15623,plain,(r(s(s(s(elem!1))), s(s(z))) | (~r(s(s(s(elem!1))), s(z))) | (s(s(s(s(elem!1)))) = s(s(s(elem!1)))) | (~b(s(z), s(s(elem!1)))) | (~b(s(z), s(s(z)))) | (s(s(s(elem!1))) = s(s(elem!1))) | (~b(z, s(z))) | (~r(s(s(z)), s(z))) | (~b(z, s(s(z)))) | b(s(s(elem!1)), s(z))), inference(lemma,lemma(discharge,[]))).
% 3.33/3.54 tff(15624,plain,
% 3.33/3.54 (r(s(s(s(elem!1))), s(s(z)))),
% 3.33/3.54 inference(unit_resolution,[status(thm)],[15623, 556, 364, 376, 350, 51, 118, 392, 10451, 4568])).
% 3.33/3.54 tff(15625,plain,
% 3.33/3.54 (~r(s(z), s(s(s(elem!1))))),
% 3.33/3.54 inference(unit_resolution,[status(thm)],[7534, 15624, 392, 350])).
% 3.33/3.54 tff(15626,plain,
% 3.33/3.54 (b(s(z), s(s(s(elem!1))))),
% 3.33/3.54 inference(unit_resolution,[status(thm)],[116, 15625])).
% 3.33/3.54 tff(15627,plain,
% 3.33/3.54 (s(s(z)) = s(s(elem!1))),
% 3.33/3.54 inference(unit_resolution,[status(thm)],[15512, 1821, 392, 10451, 376, 350, 4568, 118])).
% 3.33/3.54 tff(15628,plain,
% 3.33/3.54 (s(elem!1) = s(z)),
% 3.33/3.54 inference(unit_resolution,[status(thm)],[43, 15627])).
% 3.33/3.54 tff(15629,plain,
% 3.33/3.54 (z = elem!1),
% 3.33/3.54 inference(unit_resolution,[status(thm)],[30, 15628])).
% 3.33/3.54 tff(15630,plain,
% 3.33/3.54 ((s(s(s(s(z)))) = z) <=> (s(s(s(s(z)))) = elem!1)),
% 3.33/3.54 inference(monotonicity,[status(thm)],[15629])).
% 3.33/3.54 tff(15631,plain,
% 3.33/3.54 ((s(s(s(s(z)))) = z) <=> (elem!1 = s(s(s(s(z)))))),
% 3.33/3.54 inference(transitivity,[status(thm)],[15630, 1039])).
% 3.33/3.54 tff(15632,plain,
% 3.33/3.54 ((~(s(s(s(s(z)))) = z)) <=> (~(elem!1 = s(s(s(s(z))))))),
% 3.33/3.54 inference(monotonicity,[status(thm)],[15631])).
% 3.33/3.54 tff(15633,plain,
% 3.33/3.54 (~(elem!1 = s(s(s(s(z)))))),
% 3.33/3.54 inference(modus_ponens,[status(thm)],[1044, 15632])).
% 3.33/3.54 tff(15634,plain,
% 3.33/3.54 (~b(s(s(s(elem!1))), z)),
% 3.33/3.54 inference(unit_resolution,[status(thm)],[7322, 241, 376, 15535, 118])).
% 3.33/3.54 tff(15635,plain,
% 3.33/3.54 (r(s(s(s(elem!1))), z)),
% 3.33/3.54 inference(unit_resolution,[status(thm)],[94, 15634])).
% 3.33/3.54 tff(15636,plain,
% 3.33/3.54 (r(s(s(s(elem!1))), elem!1)),
% 3.33/3.54 inference(unit_resolution,[status(thm)],[966, 15629, 15635])).
% 3.33/3.54 tff(15637,plain,
% 3.33/3.54 (r(s(s(s(elem!1))), s(s(elem!1)))),
% 3.33/3.54 inference(unit_resolution,[status(thm)],[6040, 1821, 51, 241, 376])).
% 3.33/3.54 tff(15638,plain,
% 3.33/3.54 (r(s(s(elem!1)), z) <=> r(s(s(elem!1)), elem!1)),
% 3.33/3.54 inference(monotonicity,[status(thm)],[15629])).
% 3.33/3.54 tff(15639,plain,
% 3.33/3.54 (r(s(s(z)), z) <=> r(s(s(elem!1)), z)),
% 3.33/3.54 inference(monotonicity,[status(thm)],[15627])).
% 3.33/3.54 tff(15640,plain,
% 3.33/3.54 (r(s(s(elem!1)), z)),
% 3.33/3.54 inference(modus_ponens,[status(thm)],[866, 15639])).
% 3.33/3.54 tff(15641,plain,
% 3.33/3.54 (r(s(s(elem!1)), elem!1)),
% 3.33/3.54 inference(modus_ponens,[status(thm)],[15640, 15638])).
% 3.33/3.54 tff(15642,plain,
% 3.33/3.54 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(s(s(s(elem!1)))))) | (~r(s(s(s(elem!1))), s(s(elem!1)))) | (~r(s(s(elem!1)), elem!1)) | (~r(s(s(s(elem!1))), elem!1)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(elem!1, s(s(s(s(elem!1)))))) | (~r(s(s(s(elem!1))), s(s(elem!1)))) | (~r(s(s(elem!1)), elem!1)) | (~r(s(s(s(elem!1))), elem!1)))),
% 3.33/3.54 inference(rewrite,[status(thm)],[])).
% 3.33/3.54 tff(15643,plain,
% 3.33/3.54 (((~r(elem!1, s(s(s(s(elem!1)))))) | (~r(s(s(elem!1)), elem!1)) | (~r(s(s(s(elem!1))), elem!1)) | (~r(s(s(s(elem!1))), s(s(elem!1))))) <=> ((~r(elem!1, s(s(s(s(elem!1)))))) | (~r(s(s(s(elem!1))), s(s(elem!1)))) | (~r(s(s(elem!1)), elem!1)) | (~r(s(s(s(elem!1))), elem!1)))),
% 3.33/3.54 inference(rewrite,[status(thm)],[])).
% 3.33/3.54 tff(15644,plain,
% 3.33/3.54 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(s(s(s(elem!1)))))) | (~r(s(s(elem!1)), elem!1)) | (~r(s(s(s(elem!1))), elem!1)) | (~r(s(s(s(elem!1))), s(s(elem!1)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(s(s(s(elem!1)))))) | (~r(s(s(s(elem!1))), s(s(elem!1)))) | (~r(s(s(elem!1)), elem!1)) | (~r(s(s(s(elem!1))), elem!1))))),
% 3.33/3.54 inference(monotonicity,[status(thm)],[15643])).
% 3.33/3.54 tff(15645,plain,
% 3.33/3.54 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(s(s(s(elem!1)))))) | (~r(s(s(elem!1)), elem!1)) | (~r(s(s(s(elem!1))), elem!1)) | (~r(s(s(s(elem!1))), s(s(elem!1)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(elem!1, s(s(s(s(elem!1)))))) | (~r(s(s(s(elem!1))), s(s(elem!1)))) | (~r(s(s(elem!1)), elem!1)) | (~r(s(s(s(elem!1))), elem!1)))),
% 3.33/3.54 inference(transitivity,[status(thm)],[15644, 15642])).
% 3.33/3.54 tff(15646,plain,
% 3.33/3.54 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(s(s(s(elem!1)))))) | (~r(s(s(elem!1)), elem!1)) | (~r(s(s(s(elem!1))), elem!1)) | (~r(s(s(s(elem!1))), s(s(elem!1)))))),
% 3.33/3.54 inference(quant_inst,[status(thm)],[])).
% 3.33/3.54 tff(15647,plain,
% 3.33/3.54 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(elem!1, s(s(s(s(elem!1)))))) | (~r(s(s(s(elem!1))), s(s(elem!1)))) | (~r(s(s(elem!1)), elem!1)) | (~r(s(s(s(elem!1))), elem!1))),
% 3.33/3.54 inference(modus_ponens,[status(thm)],[15646, 15645])).
% 3.33/3.54 tff(15648,plain,
% 3.33/3.54 ($false),
% 3.33/3.54 inference(unit_resolution,[status(thm)],[15647, 197, 768, 905, 1013, 1047])).
% 3.33/3.54 tff(15649,plain,((~r(elem!1, s(s(s(s(elem!1)))))) | (~r(s(s(elem!1)), elem!1)) | (~r(s(s(s(elem!1))), s(s(elem!1)))) | (~r(s(s(s(elem!1))), elem!1))), inference(lemma,lemma(discharge,[]))).
% 3.33/3.54 tff(15650,plain,
% 3.33/3.54 (~r(elem!1, s(s(s(s(elem!1)))))),
% 3.33/3.54 inference(unit_resolution,[status(thm)],[15649, 15641, 15637, 15636])).
% 3.33/3.54 tff(15651,plain,
% 3.33/3.54 (~r(elem!1, s(s(s(s(z)))))),
% 3.33/3.54 inference(unit_resolution,[status(thm)],[1093, 15650, 15627])).
% 3.33/3.54 tff(15652,plain,
% 3.33/3.54 (b(elem!1, s(s(s(s(z)))))),
% 3.33/3.54 inference(unit_resolution,[status(thm)],[1098, 15651, 15633])).
% 3.33/3.54 tff(15653,plain,
% 3.33/3.54 (b(elem!1, s(s(s(s(elem!1)))))),
% 3.33/3.54 inference(unit_resolution,[status(thm)],[1105, 15652, 15627])).
% 3.33/3.54 tff(15654,plain,
% 3.33/3.54 ((s(s(s(s(elem!1)))) = s(s(z))) <=> (s(s(s(s(elem!1)))) = s(s(elem!1)))),
% 3.33/3.54 inference(monotonicity,[status(thm)],[15627])).
% 3.33/3.54 tff(15655,plain,
% 3.33/3.54 ((s(s(s(s(elem!1)))) = s(s(z))) <=> (s(s(elem!1)) = s(s(s(s(elem!1)))))),
% 3.33/3.54 inference(transitivity,[status(thm)],[15654, 123])).
% 3.33/3.54 tff(15656,plain,
% 3.33/3.54 ((s(s(s(s(elem!1)))) = s(s(z))) <=> (s(s(s(s(elem!1)))) = s(s(elem!1)))),
% 3.33/3.54 inference(transitivity,[status(thm)],[15655, 124])).
% 3.33/3.54 tff(15657,plain,
% 3.33/3.54 ((~(s(s(s(s(elem!1)))) = s(s(z)))) <=> (~(s(s(s(s(elem!1)))) = s(s(elem!1))))),
% 3.33/3.54 inference(monotonicity,[status(thm)],[15656])).
% 3.33/3.54 tff(15658,plain,
% 3.33/3.54 (~(s(s(s(s(elem!1)))) = s(s(elem!1)))),
% 3.33/3.54 inference(modus_ponens,[status(thm)],[733, 15657])).
% 3.33/3.54 tff(15659,plain,
% 3.33/3.54 (b(s(elem!1), s(s(s(elem!1))))),
% 3.33/3.54 inference(unit_resolution,[status(thm)],[8725, 15629, 241])).
% 3.33/3.54 tff(15660,plain,
% 3.33/3.54 (b(s(elem!1), elem!1) <=> b(s(z), elem!1)),
% 3.33/3.54 inference(monotonicity,[status(thm)],[15628])).
% 3.33/3.54 tff(15661,plain,
% 3.33/3.54 (b(s(z), elem!1) <=> b(s(elem!1), elem!1)),
% 3.33/3.54 inference(symmetry,[status(thm)],[15660])).
% 3.33/3.54 tff(15662,plain,
% 3.33/3.54 (b(s(z), z) <=> b(s(z), elem!1)),
% 3.33/3.54 inference(monotonicity,[status(thm)],[15629])).
% 3.33/3.54 tff(15663,plain,
% 3.33/3.54 (b(s(z), z) <=> b(s(elem!1), elem!1)),
% 3.33/3.54 inference(transitivity,[status(thm)],[15662, 15661])).
% 3.33/3.54 tff(15664,plain,
% 3.33/3.54 (b(s(elem!1), elem!1)),
% 3.33/3.54 inference(modus_ponens,[status(thm)],[15535, 15663])).
% 3.33/3.54 tff(15665,plain,
% 3.33/3.54 ((s(s(s(elem!1))) = z) <=> (s(s(s(elem!1))) = elem!1)),
% 3.33/3.54 inference(monotonicity,[status(thm)],[15629])).
% 3.33/3.54 tff(15666,plain,
% 3.33/3.54 ((s(s(s(elem!1))) = z) <=> (elem!1 = s(s(s(elem!1))))),
% 3.33/3.54 inference(transitivity,[status(thm)],[15665, 5406])).
% 3.33/3.54 tff(15667,plain,
% 3.33/3.54 ((~(s(s(s(elem!1))) = z)) <=> (~(elem!1 = s(s(s(elem!1)))))),
% 3.33/3.54 inference(monotonicity,[status(thm)],[15666])).
% 3.33/3.54 tff(15668,plain,
% 3.33/3.54 (~(elem!1 = s(s(s(elem!1))))),
% 3.33/3.54 inference(modus_ponens,[status(thm)],[89, 15667])).
% 3.33/3.54 tff(15669,plain,
% 3.33/3.54 ($false),
% 3.33/3.54 inference(unit_resolution,[status(thm)],[14202, 197, 942, 768, 905, 1013])).
% 3.33/3.54 tff(15670,plain,((~r(elem!1, s(s(s(elem!1))))) | (~r(s(s(elem!1)), elem!1)) | (~r(s(s(s(elem!1))), s(s(elem!1)))) | (~r(s(s(s(elem!1))), elem!1))), inference(lemma,lemma(discharge,[]))).
% 3.33/3.54 tff(15671,plain,
% 3.33/3.54 (~r(elem!1, s(s(s(elem!1))))),
% 3.33/3.54 inference(unit_resolution,[status(thm)],[15670, 15641, 15637, 15636])).
% 3.33/3.54 tff(15672,plain,
% 3.33/3.54 (b(elem!1, s(s(s(elem!1))))),
% 3.33/3.54 inference(unit_resolution,[status(thm)],[5451, 15671, 15668])).
% 3.33/3.54 tff(15673,plain,
% 3.33/3.54 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), s(s(elem!1)))) | (~r(s(s(elem!1)), elem!1)) | (~r(s(s(s(elem!1))), s(s(s(s(elem!1)))))) | (~r(s(s(s(s(elem!1)))), s(s(elem!1)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(elem!1))), s(s(elem!1)))) | (~r(s(s(elem!1)), elem!1)) | (~r(s(s(s(elem!1))), s(s(s(s(elem!1)))))) | (~r(s(s(s(s(elem!1)))), s(s(elem!1)))))),
% 3.33/3.54 inference(rewrite,[status(thm)],[])).
% 3.33/3.54 tff(15674,plain,
% 3.33/3.54 (((~r(s(s(elem!1)), elem!1)) | (~r(s(s(s(s(elem!1)))), s(s(elem!1)))) | (~r(s(s(s(elem!1))), s(s(elem!1)))) | (~r(s(s(s(elem!1))), s(s(s(s(elem!1))))))) <=> ((~r(s(s(s(elem!1))), s(s(elem!1)))) | (~r(s(s(elem!1)), elem!1)) | (~r(s(s(s(elem!1))), s(s(s(s(elem!1)))))) | (~r(s(s(s(s(elem!1)))), s(s(elem!1)))))),
% 3.33/3.54 inference(rewrite,[status(thm)],[])).
% 3.33/3.54 tff(15675,plain,
% 3.33/3.54 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(elem!1)), elem!1)) | (~r(s(s(s(s(elem!1)))), s(s(elem!1)))) | (~r(s(s(s(elem!1))), s(s(elem!1)))) | (~r(s(s(s(elem!1))), s(s(s(s(elem!1)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), s(s(elem!1)))) | (~r(s(s(elem!1)), elem!1)) | (~r(s(s(s(elem!1))), s(s(s(s(elem!1)))))) | (~r(s(s(s(s(elem!1)))), s(s(elem!1))))))),
% 3.33/3.54 inference(monotonicity,[status(thm)],[15674])).
% 3.33/3.54 tff(15676,plain,
% 3.33/3.54 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(elem!1)), elem!1)) | (~r(s(s(s(s(elem!1)))), s(s(elem!1)))) | (~r(s(s(s(elem!1))), s(s(elem!1)))) | (~r(s(s(s(elem!1))), s(s(s(s(elem!1)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(elem!1))), s(s(elem!1)))) | (~r(s(s(elem!1)), elem!1)) | (~r(s(s(s(elem!1))), s(s(s(s(elem!1)))))) | (~r(s(s(s(s(elem!1)))), s(s(elem!1)))))),
% 3.33/3.54 inference(transitivity,[status(thm)],[15675, 15673])).
% 3.33/3.54 tff(15677,plain,
% 3.33/3.54 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(elem!1)), elem!1)) | (~r(s(s(s(s(elem!1)))), s(s(elem!1)))) | (~r(s(s(s(elem!1))), s(s(elem!1)))) | (~r(s(s(s(elem!1))), s(s(s(s(elem!1)))))))),
% 3.33/3.54 inference(quant_inst,[status(thm)],[])).
% 3.33/3.54 tff(15678,plain,
% 3.33/3.54 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(elem!1))), s(s(elem!1)))) | (~r(s(s(elem!1)), elem!1)) | (~r(s(s(s(elem!1))), s(s(s(s(elem!1)))))) | (~r(s(s(s(s(elem!1)))), s(s(elem!1))))),
% 3.33/3.54 inference(modus_ponens,[status(thm)],[15677, 15676])).
% 3.33/3.54 tff(15679,plain,
% 3.33/3.54 (~r(s(s(s(elem!1))), s(s(s(s(elem!1)))))),
% 3.33/3.54 inference(unit_resolution,[status(thm)],[15678, 197, 768, 905, 3408])).
% 3.33/3.54 tff(15680,plain,
% 3.33/3.54 (b(s(s(s(elem!1))), s(s(s(s(elem!1)))))),
% 3.33/3.54 inference(unit_resolution,[status(thm)],[694, 79, 361, 15679])).
% 3.33/3.54 tff(15681,plain,
% 3.33/3.54 ((~(s(s(s(elem!1))) = s(s(s(s(elem!1)))))) <=> (~(s(s(s(s(elem!1)))) = s(s(s(elem!1)))))),
% 3.33/3.54 inference(monotonicity,[status(thm)],[3797])).
% 3.33/3.54 tff(15682,plain,
% 3.33/3.54 (~(s(s(s(s(elem!1)))) = s(s(s(elem!1))))),
% 3.33/3.54 inference(modus_ponens,[status(thm)],[361, 15681])).
% 3.33/3.54 tff(15683,plain,
% 3.33/3.54 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(elem!1)), elem!1)) | (~r(s(s(s(elem!1))), s(s(elem!1)))) | (~r(s(s(s(s(elem!1)))), s(s(elem!1)))) | (~r(s(s(s(s(elem!1)))), s(s(s(elem!1))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(elem!1)), elem!1)) | (~r(s(s(s(elem!1))), s(s(elem!1)))) | (~r(s(s(s(s(elem!1)))), s(s(elem!1)))) | (~r(s(s(s(s(elem!1)))), s(s(s(elem!1))))))),
% 3.33/3.54 inference(rewrite,[status(thm)],[])).
% 3.33/3.54 tff(15684,plain,
% 3.33/3.54 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(elem!1)), elem!1)) | (~r(s(s(s(elem!1))), s(s(elem!1)))) | (~r(s(s(s(s(elem!1)))), s(s(elem!1)))) | (~r(s(s(s(s(elem!1)))), s(s(s(elem!1))))))),
% 3.33/3.54 inference(quant_inst,[status(thm)],[])).
% 3.33/3.54 tff(15685,plain,
% 3.33/3.54 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(elem!1)), elem!1)) | (~r(s(s(s(elem!1))), s(s(elem!1)))) | (~r(s(s(s(s(elem!1)))), s(s(elem!1)))) | (~r(s(s(s(s(elem!1)))), s(s(s(elem!1)))))),
% 3.33/3.54 inference(modus_ponens,[status(thm)],[15684, 15683])).
% 3.33/3.54 tff(15686,plain,
% 3.33/3.54 (~r(s(s(s(s(elem!1)))), s(s(s(elem!1))))),
% 3.33/3.54 inference(unit_resolution,[status(thm)],[15685, 197, 768, 905, 3408])).
% 3.33/3.54 tff(15687,plain,
% 3.33/3.54 ((s(s(s(s(elem!1)))) = s(s(s(elem!1)))) | b(s(s(s(s(elem!1)))), s(s(s(elem!1))))),
% 3.33/3.54 inference(unit_resolution,[status(thm)],[1063, 79, 15686])).
% 3.33/3.54 tff(15688,plain,
% 3.33/3.54 (b(s(s(s(s(elem!1)))), s(s(s(elem!1))))),
% 3.33/3.54 inference(unit_resolution,[status(thm)],[15687, 15682])).
% 3.33/3.54 tff(15689,assumption,(b(s(elem!1), s(s(s(elem!1))))), introduced(assumption)).
% 3.33/3.54 tff(15690,plain,
% 3.33/3.54 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), s(s(s(elem!1))))) | (~b(s(elem!1), elem!1)) | (~b(elem!1, s(s(s(elem!1))))) | (~b(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(s(s(s(elem!1)))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(elem!1), s(s(s(elem!1))))) | (~b(s(elem!1), elem!1)) | (~b(elem!1, s(s(s(elem!1))))) | (~b(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(s(s(s(elem!1)))))))),
% 3.33/3.54 inference(rewrite,[status(thm)],[])).
% 3.33/3.54 tff(15691,plain,
% 3.33/3.54 (((~b(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~b(s(elem!1), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(s(s(s(elem!1)))))) | (~b(elem!1, s(s(s(elem!1))))) | (~b(s(elem!1), s(s(s(elem!1))))) | (~b(s(elem!1), elem!1))) <=> ((~b(s(elem!1), s(s(s(elem!1))))) | (~b(s(elem!1), elem!1)) | (~b(elem!1, s(s(s(elem!1))))) | (~b(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(s(s(s(elem!1)))))))),
% 3.33/3.54 inference(rewrite,[status(thm)],[])).
% 3.33/3.54 tff(15692,plain,
% 3.33/3.54 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~b(s(elem!1), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(s(s(s(elem!1)))))) | (~b(elem!1, s(s(s(elem!1))))) | (~b(s(elem!1), s(s(s(elem!1))))) | (~b(s(elem!1), elem!1)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), s(s(s(elem!1))))) | (~b(s(elem!1), elem!1)) | (~b(elem!1, s(s(s(elem!1))))) | (~b(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(s(s(s(elem!1))))))))),
% 3.33/3.54 inference(monotonicity,[status(thm)],[15691])).
% 3.33/3.54 tff(15693,plain,
% 3.33/3.54 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~b(s(elem!1), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(s(s(s(elem!1)))))) | (~b(elem!1, s(s(s(elem!1))))) | (~b(s(elem!1), s(s(s(elem!1))))) | (~b(s(elem!1), elem!1)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(elem!1), s(s(s(elem!1))))) | (~b(s(elem!1), elem!1)) | (~b(elem!1, s(s(s(elem!1))))) | (~b(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(s(s(s(elem!1)))))))),
% 3.33/3.55 inference(transitivity,[status(thm)],[15692, 15690])).
% 3.33/3.55 tff(15694,plain,
% 3.33/3.55 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~b(s(elem!1), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(s(s(s(elem!1)))))) | (~b(elem!1, s(s(s(elem!1))))) | (~b(s(elem!1), s(s(s(elem!1))))) | (~b(s(elem!1), elem!1)))),
% 3.33/3.55 inference(quant_inst,[status(thm)],[])).
% 3.33/3.55 tff(15695,plain,
% 3.33/3.55 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(elem!1), s(s(s(elem!1))))) | (~b(s(elem!1), elem!1)) | (~b(elem!1, s(s(s(elem!1))))) | (~b(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(s(s(s(elem!1))))))),
% 3.33/3.55 inference(modus_ponens,[status(thm)],[15694, 15693])).
% 3.33/3.55 tff(15696,plain,
% 3.33/3.55 ($false),
% 3.33/3.55 inference(unit_resolution,[status(thm)],[15695, 166, 15689, 1213, 643, 15688, 15680])).
% 3.33/3.55 tff(15697,plain,((~r(s(s(s(s(elem!1)))), s(s(elem!1)))) | (~b(s(elem!1), s(s(s(elem!1))))) | (~b(s(elem!1), elem!1)) | (~b(elem!1, s(s(s(elem!1))))) | (s(s(s(elem!1))) = s(s(s(s(elem!1))))) | (~r(s(s(elem!1)), elem!1)) | (~r(s(s(s(elem!1))), s(s(elem!1))))), inference(lemma,lemma(discharge,[]))).
% 3.33/3.55 tff(15698,plain,
% 3.33/3.55 (~r(s(s(s(s(elem!1)))), s(s(elem!1)))),
% 3.33/3.55 inference(unit_resolution,[status(thm)],[15697, 15672, 15637, 15664, 358, 15641, 15659])).
% 3.33/3.55 tff(15699,plain,
% 3.33/3.55 (b(s(s(s(s(elem!1)))), s(s(elem!1)))),
% 3.33/3.55 inference(unit_resolution,[status(thm)],[813, 15698, 15658])).
% 3.33/3.55 tff(15700,plain,
% 3.33/3.55 (~r(s(z), s(s(s(s(elem!1)))))),
% 3.33/3.55 inference(unit_resolution,[status(thm)],[10419, 15637, 10521, 350])).
% 3.33/3.55 tff(15701,plain,
% 3.33/3.55 (b(s(z), s(s(s(s(elem!1)))))),
% 3.33/3.55 inference(unit_resolution,[status(thm)],[681, 15700])).
% 3.33/3.55 tff(15702,plain,
% 3.33/3.55 (b(z, s(z)) <=> b(elem!1, s(z))),
% 3.33/3.55 inference(monotonicity,[status(thm)],[15629])).
% 3.33/3.55 tff(15703,plain,
% 3.33/3.55 (b(elem!1, s(z))),
% 3.33/3.55 inference(modus_ponens,[status(thm)],[118, 15702])).
% 3.33/3.55 tff(15704,plain,
% 3.33/3.55 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(elem!1, s(z))) | (~b(elem!1, s(s(s(elem!1))))) | (~b(s(s(s(s(elem!1)))), s(s(elem!1)))) | (~b(elem!1, s(s(s(s(elem!1)))))) | (~b(s(z), s(s(s(s(elem!1)))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(elem!1, s(z))) | (~b(elem!1, s(s(s(elem!1))))) | (~b(s(s(s(s(elem!1)))), s(s(elem!1)))) | (~b(elem!1, s(s(s(s(elem!1)))))) | (~b(s(z), s(s(s(s(elem!1)))))))),
% 3.33/3.55 inference(rewrite,[status(thm)],[])).
% 3.33/3.55 tff(15705,plain,
% 3.33/3.55 (((~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(elem!1, s(s(s(elem!1))))) | (~b(s(s(s(s(elem!1)))), s(s(elem!1)))) | (~b(s(z), s(s(s(s(elem!1)))))) | (~b(elem!1, s(s(s(s(elem!1)))))) | (~b(elem!1, s(z)))) <=> ((~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(elem!1, s(z))) | (~b(elem!1, s(s(s(elem!1))))) | (~b(s(s(s(s(elem!1)))), s(s(elem!1)))) | (~b(elem!1, s(s(s(s(elem!1)))))) | (~b(s(z), s(s(s(s(elem!1)))))))),
% 3.33/3.55 inference(rewrite,[status(thm)],[])).
% 3.33/3.55 tff(15706,plain,
% 3.33/3.55 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(elem!1, s(s(s(elem!1))))) | (~b(s(s(s(s(elem!1)))), s(s(elem!1)))) | (~b(s(z), s(s(s(s(elem!1)))))) | (~b(elem!1, s(s(s(s(elem!1)))))) | (~b(elem!1, s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(elem!1, s(z))) | (~b(elem!1, s(s(s(elem!1))))) | (~b(s(s(s(s(elem!1)))), s(s(elem!1)))) | (~b(elem!1, s(s(s(s(elem!1)))))) | (~b(s(z), s(s(s(s(elem!1))))))))),
% 3.33/3.55 inference(monotonicity,[status(thm)],[15705])).
% 3.33/3.55 tff(15707,plain,
% 3.33/3.55 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(elem!1, s(s(s(elem!1))))) | (~b(s(s(s(s(elem!1)))), s(s(elem!1)))) | (~b(s(z), s(s(s(s(elem!1)))))) | (~b(elem!1, s(s(s(s(elem!1)))))) | (~b(elem!1, s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(elem!1, s(z))) | (~b(elem!1, s(s(s(elem!1))))) | (~b(s(s(s(s(elem!1)))), s(s(elem!1)))) | (~b(elem!1, s(s(s(s(elem!1)))))) | (~b(s(z), s(s(s(s(elem!1)))))))),
% 3.33/3.55 inference(transitivity,[status(thm)],[15706, 15704])).
% 3.33/3.55 tff(15708,plain,
% 3.33/3.55 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(elem!1, s(s(s(elem!1))))) | (~b(s(s(s(s(elem!1)))), s(s(elem!1)))) | (~b(s(z), s(s(s(s(elem!1)))))) | (~b(elem!1, s(s(s(s(elem!1)))))) | (~b(elem!1, s(z))))),
% 3.33/3.55 inference(quant_inst,[status(thm)],[])).
% 3.33/3.55 tff(15709,plain,
% 3.33/3.55 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(elem!1, s(z))) | (~b(elem!1, s(s(s(elem!1))))) | (~b(s(s(s(s(elem!1)))), s(s(elem!1)))) | (~b(elem!1, s(s(s(s(elem!1)))))) | (~b(s(z), s(s(s(s(elem!1))))))),
% 3.33/3.55 inference(modus_ponens,[status(thm)],[15708, 15707])).
% 3.33/3.55 tff(15710,plain,
% 3.33/3.55 ($false),
% 3.33/3.55 inference(unit_resolution,[status(thm)],[15709, 166, 13515, 15672, 15703, 15701, 15699, 15653])).
% 3.33/3.55 tff(15711,plain,(r(s(s(elem!1)), s(s(s(elem!1)))) | (~r(s(s(s(elem!1))), s(z))) | (~b(z, s(z))) | (~r(s(s(z)), z)) | (~b(s(z), s(s(s(elem!1))))) | (~b(s(z), s(s(elem!1)))) | (s(s(elem!1)) = s(s(s(elem!1)))) | (~r(s(s(z)), s(z))) | (~b(z, s(s(z)))) | b(s(s(elem!1)), s(z))), inference(lemma,lemma(discharge,[]))).
% 3.33/3.55 tff(15712,plain,
% 3.33/3.55 (r(s(s(elem!1)), s(s(s(elem!1))))),
% 3.33/3.55 inference(unit_resolution,[status(thm)],[15711, 15539, 118, 350, 15626, 376, 45, 392, 10451, 4568])).
% 3.33/3.55 tff(15713,plain,
% 3.33/3.55 (~b(s(s(s(elem!1))), s(s(elem!1)))),
% 3.33/3.55 inference(unit_resolution,[status(thm)],[12016, 12008, 556, 10451, 118, 1820])).
% 3.33/3.55 tff(15714,plain,
% 3.33/3.55 (r(s(s(s(elem!1))), s(s(elem!1)))),
% 3.33/3.55 inference(unit_resolution,[status(thm)],[889, 15713, 1863])).
% 3.33/3.55 tff(15715,plain,
% 3.33/3.55 (~r(s(s(z)), s(s(elem!1)))),
% 3.33/3.55 inference(unit_resolution,[status(thm)],[9441, 15714, 4577, 464])).
% 3.33/3.55 tff(15716,plain,
% 3.33/3.55 (~r(s(s(elem!1)), s(s(z)))),
% 3.33/3.55 inference(unit_resolution,[status(thm)],[4313, 15714, 392, 464])).
% 3.33/3.55 tff(15717,plain,
% 3.33/3.55 (s(s(z)) = s(s(elem!1))),
% 3.33/3.55 inference(unit_resolution,[status(thm)],[5300, 15716, 556, 376, 15715])).
% 3.33/3.55 tff(15718,plain,
% 3.33/3.55 (r(s(s(z)), s(s(s(elem!1)))) <=> r(s(s(elem!1)), s(s(s(elem!1))))),
% 3.33/3.55 inference(monotonicity,[status(thm)],[15717])).
% 3.33/3.55 tff(15719,plain,
% 3.33/3.55 (r(s(s(elem!1)), s(s(s(elem!1)))) <=> r(s(s(z)), s(s(s(elem!1))))),
% 3.33/3.55 inference(symmetry,[status(thm)],[15718])).
% 3.33/3.55 tff(15720,plain,
% 3.33/3.55 (r(s(s(z)), s(s(s(elem!1))))),
% 3.33/3.55 inference(modus_ponens,[status(thm)],[377, 15719])).
% 3.33/3.55 tff(15721,plain,
% 3.33/3.55 ($false),
% 3.33/3.55 inference(unit_resolution,[status(thm)],[273, 15720])).
% 3.33/3.55 tff(15722,plain,(r(s(s(z)), s(s(s(elem!1)))) | (~r(s(s(elem!1)), s(s(s(elem!1))))) | (~b(s(z), s(s(z)))) | (~b(s(z), s(s(elem!1)))) | (~r(s(s(z)), s(z))) | (~r(s(s(s(elem!1))), s(s(z)))) | (~r(s(s(elem!1)), s(z))) | (s(s(s(elem!1))) = s(s(elem!1))) | (~b(z, s(s(z)))) | (~b(z, s(z))) | (~b(z, s(s(elem!1))))), inference(lemma,lemma(discharge,[]))).
% 3.33/3.55 tff(15723,plain,
% 3.33/3.55 (r(s(s(z)), s(s(s(elem!1))))),
% 3.33/3.55 inference(unit_resolution,[status(thm)],[15722, 15712, 556, 376, 392, 15624, 10521, 51, 10451, 118, 15556])).
% 3.33/3.55 tff(15724,plain,
% 3.33/3.55 (s(s(z)) = s(s(elem!1))),
% 3.33/3.55 inference(unit_resolution,[status(thm)],[15576, 15723, 350, 376, 556, 118, 392, 10451, 4568])).
% 3.33/3.55 tff(15725,plain,
% 3.33/3.55 ((s(s(s(s(elem!1)))) = s(s(z))) <=> (s(s(s(s(elem!1)))) = s(s(elem!1)))),
% 3.33/3.55 inference(monotonicity,[status(thm)],[15724])).
% 3.33/3.55 tff(15726,plain,
% 3.33/3.55 ((s(s(s(s(elem!1)))) = s(s(z))) <=> (s(s(elem!1)) = s(s(s(s(elem!1)))))),
% 3.33/3.55 inference(transitivity,[status(thm)],[15725, 123])).
% 3.33/3.55 tff(15727,plain,
% 3.33/3.55 ((s(s(s(s(elem!1)))) = s(s(z))) <=> (s(s(s(s(elem!1)))) = s(s(elem!1)))),
% 3.33/3.55 inference(transitivity,[status(thm)],[15726, 124])).
% 3.33/3.55 tff(15728,plain,
% 3.33/3.55 ((~(s(s(s(s(elem!1)))) = s(s(z)))) <=> (~(s(s(s(s(elem!1)))) = s(s(elem!1))))),
% 3.33/3.55 inference(monotonicity,[status(thm)],[15727])).
% 3.33/3.55 tff(15729,plain,
% 3.33/3.55 (~(s(s(s(s(elem!1)))) = s(s(elem!1)))),
% 3.33/3.55 inference(modus_ponens,[status(thm)],[733, 15728])).
% 3.33/3.55 tff(15730,plain,
% 3.33/3.55 (s(elem!1) = s(z)),
% 3.33/3.55 inference(unit_resolution,[status(thm)],[43, 15724])).
% 3.33/3.55 tff(15731,plain,
% 3.33/3.55 (z = elem!1),
% 3.33/3.55 inference(unit_resolution,[status(thm)],[30, 15730])).
% 3.33/3.55 tff(15732,plain,
% 3.33/3.55 (b(s(elem!1), s(s(s(elem!1))))),
% 3.33/3.55 inference(unit_resolution,[status(thm)],[8725, 15731, 15626])).
% 3.33/3.55 tff(15733,plain,
% 3.33/3.55 (r(s(s(elem!1)), z) <=> r(s(s(elem!1)), elem!1)),
% 3.33/3.55 inference(monotonicity,[status(thm)],[15731])).
% 3.33/3.55 tff(15734,plain,
% 3.33/3.55 (r(s(s(z)), z) <=> r(s(s(elem!1)), z)),
% 3.33/3.55 inference(monotonicity,[status(thm)],[15724])).
% 3.33/3.55 tff(15735,plain,
% 3.33/3.55 (r(s(s(elem!1)), z)),
% 3.33/3.55 inference(modus_ponens,[status(thm)],[15539, 15734])).
% 3.33/3.55 tff(15736,plain,
% 3.33/3.55 (r(s(s(elem!1)), elem!1)),
% 3.33/3.55 inference(modus_ponens,[status(thm)],[15735, 15733])).
% 3.33/3.55 tff(15737,plain,
% 3.33/3.55 (b(z, s(s(s(elem!1)))) <=> b(elem!1, s(s(s(elem!1))))),
% 3.33/3.55 inference(monotonicity,[status(thm)],[15731])).
% 3.33/3.55 tff(15738,plain,
% 3.33/3.55 (~b(s(s(s(elem!1))), z)),
% 3.33/3.55 inference(unit_resolution,[status(thm)],[7322, 15626, 376, 15535, 118])).
% 3.33/3.55 tff(15739,plain,
% 3.33/3.55 (r(s(s(s(elem!1))), z)),
% 3.33/3.55 inference(unit_resolution,[status(thm)],[94, 15738])).
% 3.33/3.55 tff(15740,plain,
% 3.33/3.55 (~r(z, s(s(s(elem!1))))),
% 3.33/3.55 inference(unit_resolution,[status(thm)],[13284, 15723, 15739, 15539])).
% 3.33/3.55 tff(15741,plain,
% 3.33/3.55 (b(z, s(s(s(elem!1))))),
% 3.33/3.55 inference(unit_resolution,[status(thm)],[261, 15740])).
% 3.33/3.55 tff(15742,plain,
% 3.33/3.55 (b(elem!1, s(s(s(elem!1))))),
% 3.33/3.55 inference(modus_ponens,[status(thm)],[15741, 15737])).
% 3.33/3.55 tff(15743,plain,
% 3.33/3.55 (r(s(s(s(elem!1))), s(s(z))) <=> r(s(s(s(elem!1))), s(s(elem!1)))),
% 3.33/3.55 inference(monotonicity,[status(thm)],[15724])).
% 3.33/3.55 tff(15744,plain,
% 3.33/3.55 (r(s(s(s(elem!1))), s(s(elem!1)))),
% 3.33/3.55 inference(modus_ponens,[status(thm)],[15624, 15743])).
% 3.33/3.55 tff(15745,plain,
% 3.33/3.55 (b(s(elem!1), elem!1) <=> b(s(z), elem!1)),
% 3.33/3.55 inference(monotonicity,[status(thm)],[15730])).
% 3.33/3.55 tff(15746,plain,
% 3.33/3.55 (b(s(z), elem!1) <=> b(s(elem!1), elem!1)),
% 3.33/3.55 inference(symmetry,[status(thm)],[15745])).
% 3.33/3.55 tff(15747,plain,
% 3.33/3.55 (b(s(z), z) <=> b(s(z), elem!1)),
% 3.33/3.55 inference(monotonicity,[status(thm)],[15731])).
% 3.33/3.55 tff(15748,plain,
% 3.33/3.55 (b(s(z), z) <=> b(s(elem!1), elem!1)),
% 3.33/3.55 inference(transitivity,[status(thm)],[15747, 15746])).
% 3.33/3.55 tff(15749,plain,
% 3.33/3.55 (b(s(elem!1), elem!1)),
% 3.33/3.55 inference(modus_ponens,[status(thm)],[15535, 15748])).
% 3.33/3.55 tff(15750,plain,
% 3.33/3.55 (~r(s(s(s(s(elem!1)))), s(s(elem!1)))),
% 3.33/3.55 inference(unit_resolution,[status(thm)],[15697, 15749, 15744, 15742, 358, 15736, 15732])).
% 3.33/3.55 tff(15751,plain,
% 3.33/3.55 (b(s(s(s(s(elem!1)))), s(s(elem!1)))),
% 3.33/3.55 inference(unit_resolution,[status(thm)],[813, 15750, 15729])).
% 3.33/3.55 tff(15752,plain,
% 3.33/3.55 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), s(z))) | (~r(s(s(elem!1)), s(s(s(elem!1))))) | (~r(s(s(elem!1)), s(z))) | (~r(s(z), s(s(s(s(elem!1)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(elem!1))), s(z))) | (~r(s(s(elem!1)), s(s(s(elem!1))))) | (~r(s(s(elem!1)), s(z))) | (~r(s(z), s(s(s(s(elem!1)))))))),
% 3.33/3.55 inference(rewrite,[status(thm)],[])).
% 3.33/3.55 tff(15753,plain,
% 3.33/3.55 (((~r(s(z), s(s(s(s(elem!1)))))) | (~r(s(s(s(elem!1))), s(z))) | (~r(s(s(elem!1)), s(z))) | (~r(s(s(elem!1)), s(s(s(elem!1)))))) <=> ((~r(s(s(s(elem!1))), s(z))) | (~r(s(s(elem!1)), s(s(s(elem!1))))) | (~r(s(s(elem!1)), s(z))) | (~r(s(z), s(s(s(s(elem!1)))))))),
% 3.33/3.55 inference(rewrite,[status(thm)],[])).
% 3.33/3.55 tff(15754,plain,
% 3.33/3.55 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(s(s(s(elem!1)))))) | (~r(s(s(s(elem!1))), s(z))) | (~r(s(s(elem!1)), s(z))) | (~r(s(s(elem!1)), s(s(s(elem!1))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), s(z))) | (~r(s(s(elem!1)), s(s(s(elem!1))))) | (~r(s(s(elem!1)), s(z))) | (~r(s(z), s(s(s(s(elem!1))))))))),
% 3.33/3.55 inference(monotonicity,[status(thm)],[15753])).
% 3.33/3.55 tff(15755,plain,
% 3.33/3.55 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(s(s(s(elem!1)))))) | (~r(s(s(s(elem!1))), s(z))) | (~r(s(s(elem!1)), s(z))) | (~r(s(s(elem!1)), s(s(s(elem!1))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(elem!1))), s(z))) | (~r(s(s(elem!1)), s(s(s(elem!1))))) | (~r(s(s(elem!1)), s(z))) | (~r(s(z), s(s(s(s(elem!1)))))))),
% 3.33/3.55 inference(transitivity,[status(thm)],[15754, 15752])).
% 3.33/3.55 tff(15756,plain,
% 3.33/3.55 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(s(s(s(elem!1)))))) | (~r(s(s(s(elem!1))), s(z))) | (~r(s(s(elem!1)), s(z))) | (~r(s(s(elem!1)), s(s(s(elem!1))))))),
% 3.33/3.55 inference(quant_inst,[status(thm)],[])).
% 3.33/3.55 tff(15757,plain,
% 3.33/3.55 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(elem!1))), s(z))) | (~r(s(s(elem!1)), s(s(s(elem!1))))) | (~r(s(s(elem!1)), s(z))) | (~r(s(z), s(s(s(s(elem!1))))))),
% 3.33/3.55 inference(modus_ponens,[status(thm)],[15756, 15755])).
% 3.33/3.55 tff(15758,plain,
% 3.33/3.55 ($false),
% 3.33/3.55 inference(unit_resolution,[status(thm)],[15757, 197, 350, 4577, 377, 699])).
% 3.33/3.55 tff(15759,plain,((~r(s(z), s(s(s(s(elem!1)))))) | (~r(s(s(s(elem!1))), s(z))) | (~r(s(s(elem!1)), s(z))) | (~r(s(s(elem!1)), s(s(s(elem!1)))))), inference(lemma,lemma(discharge,[]))).
% 3.33/3.55 tff(15760,plain,
% 3.33/3.55 (~r(s(z), s(s(s(s(elem!1)))))),
% 3.33/3.55 inference(unit_resolution,[status(thm)],[15759, 15712, 10521, 350])).
% 3.33/3.55 tff(15761,plain,
% 3.33/3.55 (b(s(z), s(s(s(s(elem!1)))))),
% 3.33/3.55 inference(unit_resolution,[status(thm)],[681, 15760])).
% 3.33/3.55 tff(15762,plain,
% 3.33/3.55 ((~(s(s(s(s(elem!1)))) = s(s(z)))) <=> (~(s(s(elem!1)) = s(s(s(s(elem!1))))))),
% 3.33/3.55 inference(monotonicity,[status(thm)],[15726])).
% 3.33/3.55 tff(15763,plain,
% 3.33/3.55 (~(s(s(elem!1)) = s(s(s(s(elem!1)))))),
% 3.33/3.55 inference(modus_ponens,[status(thm)],[733, 15762])).
% 3.33/3.55 tff(15764,plain,
% 3.33/3.55 (b(s(z), elem!1)),
% 3.33/3.55 inference(modus_ponens,[status(thm)],[15535, 15747])).
% 3.33/3.55 tff(15765,plain,
% 3.33/3.55 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(s(elem!1))))) | (~b(elem!1, s(s(s(elem!1))))) | (~b(s(s(s(s(elem!1)))), s(s(elem!1)))) | (~b(s(z), s(s(elem!1)))) | (~b(s(z), elem!1)) | (~b(s(s(s(elem!1))), s(s(s(s(elem!1)))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), s(s(s(elem!1))))) | (~b(elem!1, s(s(s(elem!1))))) | (~b(s(s(s(s(elem!1)))), s(s(elem!1)))) | (~b(s(z), s(s(elem!1)))) | (~b(s(z), elem!1)) | (~b(s(s(s(elem!1))), s(s(s(s(elem!1)))))))),
% 3.33/3.55 inference(rewrite,[status(thm)],[])).
% 3.33/3.55 tff(15766,plain,
% 3.33/3.55 (((~b(s(s(s(s(elem!1)))), s(s(elem!1)))) | (~b(s(z), s(s(elem!1)))) | (~b(s(s(s(elem!1))), s(s(s(s(elem!1)))))) | (~b(elem!1, s(s(s(elem!1))))) | (~b(s(z), s(s(s(elem!1))))) | (~b(s(z), elem!1))) <=> ((~b(s(z), s(s(s(elem!1))))) | (~b(elem!1, s(s(s(elem!1))))) | (~b(s(s(s(s(elem!1)))), s(s(elem!1)))) | (~b(s(z), s(s(elem!1)))) | (~b(s(z), elem!1)) | (~b(s(s(s(elem!1))), s(s(s(s(elem!1)))))))),
% 3.33/3.55 inference(rewrite,[status(thm)],[])).
% 3.33/3.55 tff(15767,plain,
% 3.33/3.55 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(elem!1)))), s(s(elem!1)))) | (~b(s(z), s(s(elem!1)))) | (~b(s(s(s(elem!1))), s(s(s(s(elem!1)))))) | (~b(elem!1, s(s(s(elem!1))))) | (~b(s(z), s(s(s(elem!1))))) | (~b(s(z), elem!1)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(s(elem!1))))) | (~b(elem!1, s(s(s(elem!1))))) | (~b(s(s(s(s(elem!1)))), s(s(elem!1)))) | (~b(s(z), s(s(elem!1)))) | (~b(s(z), elem!1)) | (~b(s(s(s(elem!1))), s(s(s(s(elem!1))))))))),
% 3.33/3.55 inference(monotonicity,[status(thm)],[15766])).
% 3.33/3.55 tff(15768,plain,
% 3.33/3.55 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(elem!1)))), s(s(elem!1)))) | (~b(s(z), s(s(elem!1)))) | (~b(s(s(s(elem!1))), s(s(s(s(elem!1)))))) | (~b(elem!1, s(s(s(elem!1))))) | (~b(s(z), s(s(s(elem!1))))) | (~b(s(z), elem!1)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), s(s(s(elem!1))))) | (~b(elem!1, s(s(s(elem!1))))) | (~b(s(s(s(s(elem!1)))), s(s(elem!1)))) | (~b(s(z), s(s(elem!1)))) | (~b(s(z), elem!1)) | (~b(s(s(s(elem!1))), s(s(s(s(elem!1)))))))),
% 3.33/3.55 inference(transitivity,[status(thm)],[15767, 15765])).
% 3.33/3.55 tff(15769,plain,
% 3.33/3.55 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(elem!1)))), s(s(elem!1)))) | (~b(s(z), s(s(elem!1)))) | (~b(s(s(s(elem!1))), s(s(s(s(elem!1)))))) | (~b(elem!1, s(s(s(elem!1))))) | (~b(s(z), s(s(s(elem!1))))) | (~b(s(z), elem!1)))),
% 3.33/3.55 inference(quant_inst,[status(thm)],[])).
% 3.33/3.55 tff(15770,plain,
% 3.33/3.55 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), s(s(s(elem!1))))) | (~b(elem!1, s(s(s(elem!1))))) | (~b(s(s(s(s(elem!1)))), s(s(elem!1)))) | (~b(s(z), s(s(elem!1)))) | (~b(s(z), elem!1)) | (~b(s(s(s(elem!1))), s(s(s(s(elem!1))))))),
% 3.33/3.55 inference(modus_ponens,[status(thm)],[15769, 15768])).
% 3.33/3.55 tff(15771,plain,
% 3.33/3.55 ($false),
% 3.33/3.55 inference(unit_resolution,[status(thm)],[15770, 166, 376, 643, 241, 642, 3457, 1311])).
% 3.33/3.55 tff(15772,plain,((~b(s(s(s(elem!1))), s(s(s(s(elem!1)))))) | (~b(s(z), s(s(elem!1)))) | (~b(elem!1, s(s(s(elem!1))))) | (~b(s(z), s(s(s(elem!1))))) | (~b(s(z), elem!1)) | (~b(s(s(s(s(elem!1)))), s(s(elem!1))))), inference(lemma,lemma(discharge,[]))).
% 3.33/3.55 tff(15773,plain,
% 3.33/3.55 (~b(s(s(s(elem!1))), s(s(s(s(elem!1)))))),
% 3.33/3.55 inference(unit_resolution,[status(thm)],[15772, 15742, 376, 15626, 15764, 15751])).
% 3.33/3.55 tff(15774,plain,
% 3.33/3.55 (r(s(s(s(elem!1))), s(s(s(s(elem!1)))))),
% 3.33/3.55 inference(unit_resolution,[status(thm)],[696, 15773, 358])).
% 3.33/3.55 tff(15775,plain,
% 3.33/3.55 ((s(s(s(s(elem!1)))) = z) <=> (s(s(s(s(elem!1)))) = elem!1)),
% 3.33/3.55 inference(monotonicity,[status(thm)],[15731])).
% 3.33/3.55 tff(15776,plain,
% 3.33/3.55 ((~(s(s(s(s(elem!1)))) = z)) <=> (~(s(s(s(s(elem!1)))) = elem!1))),
% 3.33/3.55 inference(monotonicity,[status(thm)],[15775])).
% 3.33/3.55 tff(15777,plain,
% 3.33/3.55 (~(s(s(s(s(elem!1)))) = elem!1)),
% 3.33/3.55 inference(modus_ponens,[status(thm)],[626, 15776])).
% 3.33/3.55 tff(15778,plain,
% 3.33/3.55 ((s(s(s(s(elem!1)))) = z) <=> (elem!1 = s(s(s(s(elem!1)))))),
% 3.33/3.55 inference(transitivity,[status(thm)],[15775, 2287])).
% 3.33/3.55 tff(15779,plain,
% 3.33/3.55 ((~(s(s(s(s(elem!1)))) = z)) <=> (~(elem!1 = s(s(s(s(elem!1))))))),
% 3.33/3.55 inference(monotonicity,[status(thm)],[15778])).
% 3.33/3.55 tff(15780,plain,
% 3.33/3.55 (~(elem!1 = s(s(s(s(elem!1)))))),
% 3.33/3.55 inference(modus_ponens,[status(thm)],[626, 15779])).
% 3.33/3.55 tff(15781,plain,
% 3.33/3.55 (r(s(s(s(elem!1))), elem!1)),
% 3.33/3.55 inference(unit_resolution,[status(thm)],[966, 15731, 15739])).
% 3.33/3.55 tff(15782,plain,
% 3.33/3.55 (~r(elem!1, s(s(s(s(elem!1)))))),
% 3.33/3.55 inference(unit_resolution,[status(thm)],[15649, 15736, 15744, 15781])).
% 3.33/3.55 tff(15783,plain,
% 3.33/3.55 (b(elem!1, s(s(s(s(elem!1)))))),
% 3.33/3.55 inference(unit_resolution,[status(thm)],[2427, 15782, 15780])).
% 3.33/3.55 tff(15784,plain,
% 3.33/3.55 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(s(elem!1))))) | (~b(elem!1, s(s(s(elem!1))))) | (~b(s(z), elem!1)) | (~b(s(s(s(s(elem!1)))), elem!1)) | (~b(elem!1, s(s(s(s(elem!1)))))) | (~b(s(z), s(s(s(s(elem!1)))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), s(s(s(elem!1))))) | (~b(elem!1, s(s(s(elem!1))))) | (~b(s(z), elem!1)) | (~b(s(s(s(s(elem!1)))), elem!1)) | (~b(elem!1, s(s(s(s(elem!1)))))) | (~b(s(z), s(s(s(s(elem!1)))))))),
% 3.33/3.56 inference(rewrite,[status(thm)],[])).
% 3.33/3.56 tff(15785,plain,
% 3.33/3.56 (((~b(elem!1, s(s(s(elem!1))))) | (~b(s(z), s(s(s(elem!1))))) | (~b(s(s(s(s(elem!1)))), elem!1)) | (~b(elem!1, s(s(s(s(elem!1)))))) | (~b(s(z), s(s(s(s(elem!1)))))) | (~b(s(z), elem!1))) <=> ((~b(s(z), s(s(s(elem!1))))) | (~b(elem!1, s(s(s(elem!1))))) | (~b(s(z), elem!1)) | (~b(s(s(s(s(elem!1)))), elem!1)) | (~b(elem!1, s(s(s(s(elem!1)))))) | (~b(s(z), s(s(s(s(elem!1)))))))),
% 3.33/3.56 inference(rewrite,[status(thm)],[])).
% 3.33/3.56 tff(15786,plain,
% 3.33/3.56 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(s(s(elem!1))))) | (~b(s(z), s(s(s(elem!1))))) | (~b(s(s(s(s(elem!1)))), elem!1)) | (~b(elem!1, s(s(s(s(elem!1)))))) | (~b(s(z), s(s(s(s(elem!1)))))) | (~b(s(z), elem!1)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(s(elem!1))))) | (~b(elem!1, s(s(s(elem!1))))) | (~b(s(z), elem!1)) | (~b(s(s(s(s(elem!1)))), elem!1)) | (~b(elem!1, s(s(s(s(elem!1)))))) | (~b(s(z), s(s(s(s(elem!1))))))))),
% 3.33/3.56 inference(monotonicity,[status(thm)],[15785])).
% 3.33/3.56 tff(15787,plain,
% 3.33/3.56 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(s(s(elem!1))))) | (~b(s(z), s(s(s(elem!1))))) | (~b(s(s(s(s(elem!1)))), elem!1)) | (~b(elem!1, s(s(s(s(elem!1)))))) | (~b(s(z), s(s(s(s(elem!1)))))) | (~b(s(z), elem!1)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), s(s(s(elem!1))))) | (~b(elem!1, s(s(s(elem!1))))) | (~b(s(z), elem!1)) | (~b(s(s(s(s(elem!1)))), elem!1)) | (~b(elem!1, s(s(s(s(elem!1)))))) | (~b(s(z), s(s(s(s(elem!1)))))))),
% 3.33/3.56 inference(transitivity,[status(thm)],[15786, 15784])).
% 3.33/3.56 tff(15788,plain,
% 3.33/3.56 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(s(s(elem!1))))) | (~b(s(z), s(s(s(elem!1))))) | (~b(s(s(s(s(elem!1)))), elem!1)) | (~b(elem!1, s(s(s(s(elem!1)))))) | (~b(s(z), s(s(s(s(elem!1)))))) | (~b(s(z), elem!1)))),
% 3.33/3.56 inference(quant_inst,[status(thm)],[])).
% 3.33/3.56 tff(15789,plain,
% 3.33/3.56 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), s(s(s(elem!1))))) | (~b(elem!1, s(s(s(elem!1))))) | (~b(s(z), elem!1)) | (~b(s(s(s(s(elem!1)))), elem!1)) | (~b(elem!1, s(s(s(s(elem!1)))))) | (~b(s(z), s(s(s(s(elem!1))))))),
% 3.33/3.56 inference(modus_ponens,[status(thm)],[15788, 15787])).
% 3.33/3.56 tff(15790,plain,
% 3.33/3.56 ((~b(s(z), s(s(s(elem!1))))) | (~b(elem!1, s(s(s(elem!1))))) | (~b(s(z), elem!1)) | (~b(s(s(s(s(elem!1)))), elem!1)) | (~b(elem!1, s(s(s(s(elem!1)))))) | (~b(s(z), s(s(s(s(elem!1))))))),
% 3.33/3.56 inference(unit_resolution,[status(thm)],[15789, 166])).
% 3.33/3.56 tff(15791,plain,
% 3.33/3.56 (~b(s(s(s(s(elem!1)))), elem!1)),
% 3.33/3.56 inference(unit_resolution,[status(thm)],[15790, 15783, 15626, 15742, 15764, 15761])).
% 3.33/3.56 tff(15792,plain,
% 3.33/3.56 (r(s(s(s(s(elem!1)))), elem!1)),
% 3.33/3.56 inference(unit_resolution,[status(thm)],[719, 15791, 15777])).
% 3.33/3.56 tff(15793,plain,
% 3.33/3.56 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(elem!1)), s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), s(s(s(s(elem!1)))))) | (~r(s(s(s(s(elem!1)))), elem!1)) | (~r(s(s(elem!1)), s(s(s(s(elem!1)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(elem!1)), s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), s(s(s(s(elem!1)))))) | (~r(s(s(s(s(elem!1)))), elem!1)) | (~r(s(s(elem!1)), s(s(s(s(elem!1)))))))),
% 3.33/3.56 inference(rewrite,[status(thm)],[])).
% 3.33/3.56 tff(15794,plain,
% 3.33/3.56 (((~r(s(s(s(s(elem!1)))), elem!1)) | (~r(s(s(s(elem!1))), s(s(s(s(elem!1)))))) | (~r(s(s(elem!1)), s(s(s(s(elem!1)))))) | (~r(s(s(elem!1)), s(s(s(elem!1)))))) <=> ((~r(s(s(elem!1)), s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), s(s(s(s(elem!1)))))) | (~r(s(s(s(s(elem!1)))), elem!1)) | (~r(s(s(elem!1)), s(s(s(s(elem!1)))))))),
% 3.33/3.56 inference(rewrite,[status(thm)],[])).
% 3.33/3.56 tff(15795,plain,
% 3.33/3.56 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(elem!1)))), elem!1)) | (~r(s(s(s(elem!1))), s(s(s(s(elem!1)))))) | (~r(s(s(elem!1)), s(s(s(s(elem!1)))))) | (~r(s(s(elem!1)), s(s(s(elem!1))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(elem!1)), s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), s(s(s(s(elem!1)))))) | (~r(s(s(s(s(elem!1)))), elem!1)) | (~r(s(s(elem!1)), s(s(s(s(elem!1))))))))),
% 3.33/3.56 inference(monotonicity,[status(thm)],[15794])).
% 3.33/3.56 tff(15796,plain,
% 3.33/3.56 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(elem!1)))), elem!1)) | (~r(s(s(s(elem!1))), s(s(s(s(elem!1)))))) | (~r(s(s(elem!1)), s(s(s(s(elem!1)))))) | (~r(s(s(elem!1)), s(s(s(elem!1))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(elem!1)), s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), s(s(s(s(elem!1)))))) | (~r(s(s(s(s(elem!1)))), elem!1)) | (~r(s(s(elem!1)), s(s(s(s(elem!1)))))))),
% 3.33/3.56 inference(transitivity,[status(thm)],[15795, 15793])).
% 3.33/3.56 tff(15797,plain,
% 3.33/3.56 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(elem!1)))), elem!1)) | (~r(s(s(s(elem!1))), s(s(s(s(elem!1)))))) | (~r(s(s(elem!1)), s(s(s(s(elem!1)))))) | (~r(s(s(elem!1)), s(s(s(elem!1))))))),
% 3.33/3.56 inference(quant_inst,[status(thm)],[])).
% 3.33/3.56 tff(15798,plain,
% 3.33/3.56 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(elem!1)), s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), s(s(s(s(elem!1)))))) | (~r(s(s(s(s(elem!1)))), elem!1)) | (~r(s(s(elem!1)), s(s(s(s(elem!1))))))),
% 3.33/3.56 inference(modus_ponens,[status(thm)],[15797, 15796])).
% 3.33/3.56 tff(15799,plain,
% 3.33/3.56 ($false),
% 3.33/3.56 inference(unit_resolution,[status(thm)],[15798, 197, 377, 561, 743, 698])).
% 3.33/3.56 tff(15800,plain,((~r(s(s(elem!1)), s(s(s(s(elem!1)))))) | (~r(s(s(elem!1)), s(s(s(elem!1))))) | (~r(s(s(s(s(elem!1)))), elem!1)) | (~r(s(s(s(elem!1))), s(s(s(s(elem!1))))))), inference(lemma,lemma(discharge,[]))).
% 3.33/3.56 tff(15801,plain,
% 3.33/3.56 (~r(s(s(elem!1)), s(s(s(s(elem!1)))))),
% 3.33/3.56 inference(unit_resolution,[status(thm)],[15800, 15712, 15792, 15774])).
% 3.33/3.56 tff(15802,plain,
% 3.33/3.56 (b(s(s(elem!1)), s(s(s(s(elem!1)))))),
% 3.33/3.56 inference(unit_resolution,[status(thm)],[827, 15801, 15763])).
% 3.33/3.56 tff(15803,plain,
% 3.33/3.56 (((~b(s(s(elem!1)), s(s(s(s(elem!1)))))) | (~b(s(z), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), s(s(elem!1)))) | (~b(s(s(elem!1)), s(s(s(s(elem!1)))))) | (~b(s(z), s(s(s(s(elem!1)))))) | (~b(s(z), s(s(elem!1))))) <=> ((~b(s(s(s(s(elem!1)))), s(s(elem!1)))) | (~b(s(z), s(s(elem!1)))) | (~b(s(s(elem!1)), s(s(s(s(elem!1)))))) | (~b(s(z), s(s(s(s(elem!1)))))))),
% 3.33/3.56 inference(rewrite,[status(thm)],[])).
% 3.33/3.56 tff(15804,plain,
% 3.33/3.56 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), s(s(s(s(elem!1)))))) | (~b(s(z), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), s(s(elem!1)))) | (~b(s(s(elem!1)), s(s(s(s(elem!1)))))) | (~b(s(z), s(s(s(s(elem!1)))))) | (~b(s(z), s(s(elem!1)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(elem!1)))), s(s(elem!1)))) | (~b(s(z), s(s(elem!1)))) | (~b(s(s(elem!1)), s(s(s(s(elem!1)))))) | (~b(s(z), s(s(s(s(elem!1))))))))),
% 3.33/3.56 inference(monotonicity,[status(thm)],[15803])).
% 3.33/3.56 tff(15805,plain,
% 3.33/3.56 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), s(s(s(s(elem!1)))))) | (~b(s(z), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), s(s(elem!1)))) | (~b(s(s(elem!1)), s(s(s(s(elem!1)))))) | (~b(s(z), s(s(s(s(elem!1)))))) | (~b(s(z), s(s(elem!1)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(elem!1)))), s(s(elem!1)))) | (~b(s(z), s(s(elem!1)))) | (~b(s(s(elem!1)), s(s(s(s(elem!1)))))) | (~b(s(z), s(s(s(s(elem!1)))))))),
% 3.33/3.56 inference(transitivity,[status(thm)],[15804, 7780])).
% 3.33/3.56 tff(15806,plain,
% 3.33/3.56 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), s(s(s(s(elem!1)))))) | (~b(s(z), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), s(s(elem!1)))) | (~b(s(s(elem!1)), s(s(s(s(elem!1)))))) | (~b(s(z), s(s(s(s(elem!1)))))) | (~b(s(z), s(s(elem!1)))))),
% 3.33/3.56 inference(quant_inst,[status(thm)],[])).
% 3.33/3.56 tff(15807,plain,
% 3.33/3.56 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(elem!1)))), s(s(elem!1)))) | (~b(s(z), s(s(elem!1)))) | (~b(s(s(elem!1)), s(s(s(s(elem!1)))))) | (~b(s(z), s(s(s(s(elem!1))))))),
% 3.33/3.56 inference(modus_ponens,[status(thm)],[15806, 15805])).
% 3.33/3.56 tff(15808,plain,
% 3.33/3.56 ($false),
% 3.33/3.56 inference(unit_resolution,[status(thm)],[15807, 166, 376, 15802, 15761, 15751])).
% 3.33/3.56 tff(15809,plain,((~b(s(z), s(s(z)))) | (~b(s(z), s(s(elem!1)))) | (~r(s(s(s(elem!1))), s(z))) | (~b(z, s(z))) | (~r(s(s(z)), s(z))) | (~b(z, s(s(z)))) | b(s(s(elem!1)), s(z)) | (s(s(elem!1)) = s(s(s(elem!1))))), inference(lemma,lemma(discharge,[]))).
% 3.33/3.56 tff(15810,plain,
% 3.33/3.56 (s(s(elem!1)) = s(s(s(elem!1)))),
% 3.33/3.56 inference(unit_resolution,[status(thm)],[15809, 15519, 350, 118, 392, 10451, 4568, 376])).
% 3.33/3.56 tff(15811,plain,
% 3.33/3.56 ((s(s(elem!1)) = s(s(z))) <=> (s(s(s(elem!1))) = s(s(z)))),
% 3.33/3.56 inference(monotonicity,[status(thm)],[15810])).
% 3.33/3.56 tff(15812,plain,
% 3.33/3.56 ((s(s(elem!1)) = s(s(z))) <=> (s(s(z)) = s(s(s(elem!1))))),
% 3.33/3.56 inference(transitivity,[status(thm)],[15811, 487])).
% 3.33/3.56 tff(15813,plain,
% 3.33/3.56 ((s(s(z)) = s(s(s(elem!1)))) <=> (s(s(elem!1)) = s(s(z)))),
% 3.33/3.56 inference(symmetry,[status(thm)],[15812])).
% 3.33/3.56 tff(15814,plain,
% 3.33/3.56 ((s(s(z)) = s(s(s(elem!1)))) <=> (s(s(z)) = s(s(elem!1)))),
% 3.33/3.56 inference(transitivity,[status(thm)],[15813, 127])).
% 3.33/3.56 tff(15815,plain,
% 3.33/3.56 ((~(s(s(z)) = s(s(s(elem!1))))) <=> (~(s(s(z)) = s(s(elem!1))))),
% 3.33/3.56 inference(monotonicity,[status(thm)],[15814])).
% 3.33/3.56 tff(15816,plain,
% 3.33/3.56 (~(s(s(z)) = s(s(elem!1)))),
% 3.33/3.56 inference(modus_ponens,[status(thm)],[209, 15815])).
% 3.33/3.56 tff(15817,plain,
% 3.33/3.56 (r(s(s(elem!1)), s(s(s(elem!1)))) <=> r(s(s(s(elem!1))), s(s(s(elem!1))))),
% 3.33/3.56 inference(monotonicity,[status(thm)],[15810])).
% 3.33/3.56 tff(15818,plain,
% 3.33/3.56 (r(s(s(s(elem!1))), s(s(s(elem!1)))) <=> r(s(s(elem!1)), s(s(s(elem!1))))),
% 3.33/3.56 inference(symmetry,[status(thm)],[15817])).
% 3.33/3.56 tff(15819,plain,
% 3.33/3.56 ((~r(s(s(s(elem!1))), s(s(s(elem!1))))) <=> (~r(s(s(elem!1)), s(s(s(elem!1)))))),
% 3.33/3.56 inference(monotonicity,[status(thm)],[15818])).
% 3.33/3.56 tff(15820,plain,
% 3.33/3.56 (~r(s(s(elem!1)), s(s(s(elem!1))))),
% 3.33/3.56 inference(modus_ponens,[status(thm)],[3149, 15819])).
% 3.33/3.56 tff(15821,plain,
% 3.33/3.56 ($false),
% 3.33/3.56 inference(unit_resolution,[status(thm)],[15512, 15820, 15816, 392, 10451, 376, 350, 4568, 118])).
% 3.33/3.56 tff(15822,plain,((~r(s(s(z)), s(z))) | (~b(z, s(s(z)))) | (~b(s(z), s(s(elem!1)))) | (~r(s(s(s(elem!1))), s(z))) | b(s(s(elem!1)), s(z)) | (~b(z, s(z)))), inference(lemma,lemma(discharge,[]))).
% 3.33/3.56 tff(15823,plain,
% 3.33/3.56 (~b(z, s(z))),
% 3.33/3.56 inference(unit_resolution,[status(thm)],[15822, 350, 10451, 376, 392, 4568])).
% 3.33/3.56 tff(15824,plain,
% 3.33/3.56 (r(z, s(z))),
% 3.33/3.56 inference(unit_resolution,[status(thm)],[321, 15823])).
% 3.33/3.56 tff(15825,plain,
% 3.33/3.56 (~r(s(s(z)), z)),
% 3.33/3.56 inference(unit_resolution,[status(thm)],[14139, 15824, 392, 120])).
% 3.33/3.56 tff(15826,plain,
% 3.33/3.56 (b(s(s(z)), z)),
% 3.33/3.56 inference(unit_resolution,[status(thm)],[186, 15825])).
% 3.33/3.56 tff(15827,plain,
% 3.33/3.56 (~b(s(s(s(elem!1))), z)),
% 3.33/3.56 inference(unit_resolution,[status(thm)],[10745, 15826, 10451, 350, 120])).
% 3.33/3.56 tff(15828,plain,
% 3.33/3.56 (r(s(s(s(elem!1))), z)),
% 3.33/3.56 inference(unit_resolution,[status(thm)],[94, 15827])).
% 3.33/3.56 tff(15829,plain,
% 3.33/3.56 (~r(s(z), s(s(s(elem!1))))),
% 3.33/3.56 inference(unit_resolution,[status(thm)],[8626, 15824, 10521, 15219])).
% 3.33/3.56 tff(15830,plain,
% 3.33/3.56 (b(s(z), s(s(s(elem!1))))),
% 3.33/3.56 inference(unit_resolution,[status(thm)],[116, 15829])).
% 3.33/3.56 tff(15831,plain,
% 3.33/3.56 (~b(s(s(s(elem!1))), s(s(elem!1)))),
% 3.33/3.56 inference(unit_resolution,[status(thm)],[5396, 15830, 376, 15217, 446])).
% 3.33/3.56 tff(15832,plain,
% 3.33/3.56 (r(s(s(s(elem!1))), s(s(elem!1)))),
% 3.33/3.56 inference(unit_resolution,[status(thm)],[889, 15831, 51])).
% 3.33/3.56 tff(15833,plain,
% 3.33/3.56 ($false),
% 3.33/3.56 inference(unit_resolution,[status(thm)],[1386, 15832, 15828, 15221, 15219])).
% 3.33/3.56 tff(15834,plain,((~r(s(s(s(elem!1))), s(z))) | (~b(s(z), s(s(elem!1)))) | (~b(s(s(z)), s(s(elem!1)))) | (~b(z, s(s(z)))) | (~r(s(z), s(s(z)))) | (~r(s(s(z)), s(z))) | (s(s(elem!1)) = s(s(s(elem!1)))) | (s(s(elem!1)) = s(s(z))) | b(s(s(elem!1)), s(z))), inference(lemma,lemma(discharge,[]))).
% 3.33/3.56 tff(15835,plain,
% 3.33/3.56 (~r(s(s(s(elem!1))), s(z))),
% 3.33/3.56 inference(unit_resolution,[status(thm)],[15834, 15215, 376, 10451, 12399, 392, 45, 15213, 4568])).
% 3.33/3.56 tff(15836,plain,
% 3.33/3.56 (b(s(s(s(elem!1))), s(z))),
% 3.33/3.56 inference(unit_resolution,[status(thm)],[1849, 15835])).
% 3.33/3.56 tff(15837,plain,
% 3.33/3.56 (~r(s(s(z)), s(s(elem!1)))),
% 3.33/3.56 inference(unit_resolution,[status(thm)],[5384, 120, 4577, 392])).
% 3.33/3.56 tff(15838,plain,
% 3.33/3.56 (b(s(s(z)), s(s(elem!1)))),
% 3.33/3.56 inference(unit_resolution,[status(thm)],[390, 52, 15837])).
% 3.33/3.56 tff(15839,plain,
% 3.33/3.56 (~r(s(s(elem!1)), s(s(z)))),
% 3.33/3.56 inference(unit_resolution,[status(thm)],[5362, 120, 4577, 392])).
% 3.33/3.56 tff(15840,plain,
% 3.33/3.56 (b(s(s(elem!1)), s(s(z)))),
% 3.33/3.56 inference(unit_resolution,[status(thm)],[441, 132, 15839])).
% 3.33/3.56 tff(15841,plain,
% 3.33/3.56 (~b(z, s(s(elem!1)))),
% 3.33/3.56 inference(unit_resolution,[status(thm)],[10727, 15840, 10451, 15838])).
% 3.33/3.56 tff(15842,plain,
% 3.33/3.56 (r(z, s(s(elem!1)))),
% 3.33/3.56 inference(unit_resolution,[status(thm)],[1795, 15841])).
% 3.33/3.56 tff(15843,plain,
% 3.33/3.56 (~b(s(s(elem!1)), z)),
% 3.33/3.56 inference(unit_resolution,[status(thm)],[12470, 166, 15840, 10451, 15838])).
% 3.33/3.56 tff(15844,plain,
% 3.33/3.56 (r(s(s(elem!1)), z)),
% 3.33/3.56 inference(unit_resolution,[status(thm)],[608, 15843])).
% 3.33/3.56 tff(15845,plain,
% 3.33/3.56 (~r(s(s(elem!1)), s(s(s(elem!1))))),
% 3.33/3.56 inference(unit_resolution,[status(thm)],[4018, 15844, 282, 154])).
% 3.33/3.56 tff(15846,plain,
% 3.33/3.56 (b(s(s(elem!1)), s(s(s(elem!1))))),
% 3.33/3.56 inference(unit_resolution,[status(thm)],[461, 15845, 45])).
% 3.33/3.56 tff(15847,plain,
% 3.33/3.56 (~b(z, s(s(elem!1)))),
% 3.33/3.56 inference(unit_resolution,[status(thm)],[10727, 15838, 10451, 15840])).
% 3.33/3.56 tff(15848,plain,
% 3.33/3.56 (r(z, s(s(elem!1)))),
% 3.33/3.56 inference(unit_resolution,[status(thm)],[1795, 15847])).
% 3.33/3.56 tff(15849,plain,
% 3.33/3.56 (~r(s(s(s(elem!1))), s(z))),
% 3.33/3.56 inference(unit_resolution,[status(thm)],[6083, 15846, 4577, 120, 392, 132])).
% 3.33/3.56 tff(15850,plain,
% 3.33/3.56 (b(s(s(s(elem!1))), s(z))),
% 3.33/3.56 inference(unit_resolution,[status(thm)],[1849, 15849])).
% 3.33/3.56 tff(15851,plain,
% 3.33/3.56 (~r(s(s(s(elem!1))), s(s(elem!1)))),
% 3.33/3.56 inference(unit_resolution,[status(thm)],[1937, 15850, 376, 15848, 15846])).
% 3.33/3.56 tff(15852,plain,
% 3.33/3.56 (~b(s(z), s(s(s(elem!1))))),
% 3.33/3.56 inference(unit_resolution,[status(thm)],[6040, 15851, 376, 15845, 51])).
% 3.33/3.56 tff(15853,plain,
% 3.33/3.56 (r(s(z), s(s(s(elem!1))))),
% 3.33/3.56 inference(unit_resolution,[status(thm)],[116, 15852])).
% 3.33/3.56 tff(15854,plain,
% 3.33/3.56 (~r(s(s(z)), s(s(s(elem!1))))),
% 3.33/3.56 inference(unit_resolution,[status(thm)],[2304, 15853, 120, 154])).
% 3.33/3.56 tff(15855,plain,
% 3.33/3.56 (b(s(s(z)), s(s(s(elem!1))))),
% 3.33/3.56 inference(unit_resolution,[status(thm)],[279, 15854])).
% 3.33/3.56 tff(15856,plain,
% 3.33/3.56 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(s(z), s(s(elem!1)))) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(s(z)), s(s(elem!1)))) | (~b(s(s(z)), s(s(s(elem!1))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(s(z), s(s(elem!1)))) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(s(z)), s(s(elem!1)))) | (~b(s(s(z)), s(s(s(elem!1))))))),
% 3.33/3.56 inference(rewrite,[status(thm)],[])).
% 3.33/3.56 tff(15857,plain,
% 3.33/3.56 (((~b(s(z), s(s(elem!1)))) | (~b(s(s(z)), s(s(elem!1)))) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(s(s(z)), s(s(s(elem!1))))) | (~b(s(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(s(s(elem!1))), s(z))) | (~b(s(s(z)), s(s(elem!1)))) | (~b(s(s(z)), s(s(s(elem!1))))))),
% 3.33/3.56 inference(rewrite,[status(thm)],[])).
% 3.33/3.56 tff(15858,plain,
% 3.33/3.56 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(elem!1)))) | (~b(s(s(z)), s(s(elem!1)))) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(s(s(z)), s(s(s(elem!1))))) | (~b(s(s(z)), s(s(elem!1)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(s(z), s(s(elem!1)))) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(s(z)), s(s(elem!1)))) | (~b(s(s(z)), s(s(s(elem!1)))))))),
% 3.33/3.56 inference(monotonicity,[status(thm)],[15857])).
% 3.33/3.56 tff(15859,plain,
% 3.33/3.56 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(elem!1)))) | (~b(s(s(z)), s(s(elem!1)))) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(s(s(z)), s(s(s(elem!1))))) | (~b(s(s(z)), s(s(elem!1)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(s(z), s(s(elem!1)))) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(s(z)), s(s(elem!1)))) | (~b(s(s(z)), s(s(s(elem!1))))))),
% 3.33/3.56 inference(transitivity,[status(thm)],[15858, 15856])).
% 3.33/3.56 tff(15860,plain,
% 3.33/3.56 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(elem!1)))) | (~b(s(s(z)), s(s(elem!1)))) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(s(s(z)), s(s(s(elem!1))))) | (~b(s(s(z)), s(s(elem!1)))))),
% 3.33/3.56 inference(quant_inst,[status(thm)],[])).
% 3.33/3.56 tff(15861,plain,
% 3.33/3.56 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(s(z), s(s(elem!1)))) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(s(z)), s(s(elem!1)))) | (~b(s(s(z)), s(s(s(elem!1)))))),
% 3.33/3.56 inference(modus_ponens,[status(thm)],[15860, 15859])).
% 3.33/3.56 tff(15862,plain,
% 3.33/3.56 ($false),
% 3.33/3.56 inference(unit_resolution,[status(thm)],[15861, 166, 376, 15846, 15850, 15838, 15855])).
% 3.33/3.56 tff(15863,plain,((s(s(z)) = s(s(elem!1))) | (~b(s(z), s(s(elem!1)))) | (~r(s(z), s(s(z)))) | (~r(s(s(s(elem!1))), z)) | (~r(s(s(elem!1)), s(z))) | (~r(s(s(z)), s(z))) | (s(s(elem!1)) = s(s(s(elem!1)))) | (~r(z, s(s(s(elem!1))))) | (~b(z, s(s(z))))), inference(lemma,lemma(discharge,[]))).
% 3.33/3.56 tff(15864,plain,
% 3.33/3.56 (~r(z, s(s(s(elem!1))))),
% 3.33/3.56 inference(unit_resolution,[status(thm)],[15863, 154, 120, 52, 4577, 392, 45, 376, 10451])).
% 3.33/3.56 tff(15865,plain,
% 3.33/3.56 (b(z, s(s(s(elem!1))))),
% 3.33/3.56 inference(unit_resolution,[status(thm)],[261, 15864])).
% 3.33/3.56 tff(15866,plain,
% 3.33/3.56 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(z)))) | (~b(z, s(s(s(elem!1))))) | (~b(s(z), s(s(elem!1)))) | (~b(s(s(elem!1)), s(s(z)))) | (~b(s(s(s(elem!1))), s(z))) | (~b(z, s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(s(z)))) | (~b(z, s(s(s(elem!1))))) | (~b(s(z), s(s(elem!1)))) | (~b(s(s(elem!1)), s(s(z)))) | (~b(s(s(s(elem!1))), s(z))) | (~b(z, s(z))))),
% 3.33/3.57 inference(rewrite,[status(thm)],[])).
% 3.33/3.57 tff(15867,plain,
% 3.33/3.57 (((~b(s(s(elem!1)), s(s(z)))) | (~b(z, s(s(z)))) | (~b(s(z), s(s(elem!1)))) | (~b(s(s(s(elem!1))), s(z))) | (~b(z, s(z))) | (~b(z, s(s(s(elem!1)))))) <=> ((~b(z, s(s(z)))) | (~b(z, s(s(s(elem!1))))) | (~b(s(z), s(s(elem!1)))) | (~b(s(s(elem!1)), s(s(z)))) | (~b(s(s(s(elem!1))), s(z))) | (~b(z, s(z))))),
% 3.33/3.57 inference(rewrite,[status(thm)],[])).
% 3.33/3.57 tff(15868,plain,
% 3.33/3.57 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), s(s(z)))) | (~b(z, s(s(z)))) | (~b(s(z), s(s(elem!1)))) | (~b(s(s(s(elem!1))), s(z))) | (~b(z, s(z))) | (~b(z, s(s(s(elem!1))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(z)))) | (~b(z, s(s(s(elem!1))))) | (~b(s(z), s(s(elem!1)))) | (~b(s(s(elem!1)), s(s(z)))) | (~b(s(s(s(elem!1))), s(z))) | (~b(z, s(z)))))),
% 3.33/3.57 inference(monotonicity,[status(thm)],[15867])).
% 3.33/3.57 tff(15869,plain,
% 3.33/3.57 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), s(s(z)))) | (~b(z, s(s(z)))) | (~b(s(z), s(s(elem!1)))) | (~b(s(s(s(elem!1))), s(z))) | (~b(z, s(z))) | (~b(z, s(s(s(elem!1))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(s(z)))) | (~b(z, s(s(s(elem!1))))) | (~b(s(z), s(s(elem!1)))) | (~b(s(s(elem!1)), s(s(z)))) | (~b(s(s(s(elem!1))), s(z))) | (~b(z, s(z))))),
% 3.33/3.57 inference(transitivity,[status(thm)],[15868, 15866])).
% 3.33/3.57 tff(15870,plain,
% 3.33/3.57 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), s(s(z)))) | (~b(z, s(s(z)))) | (~b(s(z), s(s(elem!1)))) | (~b(s(s(s(elem!1))), s(z))) | (~b(z, s(z))) | (~b(z, s(s(s(elem!1))))))),
% 3.33/3.57 inference(quant_inst,[status(thm)],[])).
% 3.33/3.57 tff(15871,plain,
% 3.33/3.57 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(s(z)))) | (~b(z, s(s(s(elem!1))))) | (~b(s(z), s(s(elem!1)))) | (~b(s(s(elem!1)), s(s(z)))) | (~b(s(s(s(elem!1))), s(z))) | (~b(z, s(z)))),
% 3.33/3.57 inference(modus_ponens,[status(thm)],[15870, 15869])).
% 3.33/3.57 tff(15872,plain,
% 3.33/3.57 ((~b(z, s(s(s(elem!1))))) | (~b(z, s(z)))),
% 3.33/3.57 inference(unit_resolution,[status(thm)],[15871, 166, 376, 15840, 10451, 96])).
% 3.33/3.57 tff(15873,plain,
% 3.33/3.57 (~b(z, s(z))),
% 3.33/3.57 inference(unit_resolution,[status(thm)],[15872, 15865])).
% 3.33/3.57 tff(15874,plain,
% 3.33/3.57 (r(z, s(z))),
% 3.33/3.57 inference(unit_resolution,[status(thm)],[321, 15873])).
% 3.33/3.57 tff(15875,plain,
% 3.33/3.57 (~r(s(z), s(s(s(elem!1))))),
% 3.33/3.57 inference(unit_resolution,[status(thm)],[8626, 15874, 4577, 15842])).
% 3.33/3.57 tff(15876,plain,
% 3.33/3.57 (b(s(z), s(s(s(elem!1))))),
% 3.33/3.57 inference(unit_resolution,[status(thm)],[116, 15875])).
% 3.33/3.57 tff(15877,plain,
% 3.33/3.57 (~b(s(s(s(elem!1))), s(s(elem!1)))),
% 3.33/3.57 inference(unit_resolution,[status(thm)],[5396, 15876, 376, 15840, 15838])).
% 3.33/3.57 tff(15878,plain,
% 3.33/3.57 (r(s(s(s(elem!1))), s(s(elem!1)))),
% 3.33/3.57 inference(unit_resolution,[status(thm)],[889, 15877, 51])).
% 3.33/3.57 tff(15879,plain,
% 3.33/3.57 (~r(s(s(elem!1)), s(s(s(elem!1))))),
% 3.33/3.57 inference(unit_resolution,[status(thm)],[1386, 15878, 154, 15842])).
% 3.33/3.57 tff(15880,plain,
% 3.33/3.57 (~b(s(s(elem!1)), s(s(s(elem!1))))),
% 3.33/3.57 inference(unit_resolution,[status(thm)],[1937, 15878, 376, 15842, 96])).
% 3.33/3.57 tff(15881,plain,
% 3.33/3.57 ($false),
% 3.33/3.57 inference(unit_resolution,[status(thm)],[461, 15880, 15879, 45])).
% 3.33/3.57 tff(15882,plain,((~r(s(s(s(elem!1))), z)) | (s(s(elem!1)) = s(s(s(elem!1)))) | (~b(s(z), s(s(elem!1)))) | (~b(s(s(s(elem!1))), s(z))) | (~r(s(s(elem!1)), s(z))) | (~b(z, s(s(z)))) | (~r(s(z), s(s(z)))) | (s(s(z)) = s(s(elem!1))) | (~r(s(s(z)), s(z)))), inference(lemma,lemma(discharge,[]))).
% 3.33/3.57 tff(15883,plain,
% 3.33/3.57 (~r(s(s(s(elem!1))), z)),
% 3.33/3.57 inference(unit_resolution,[status(thm)],[15882, 15836, 376, 45, 10521, 10451, 12399, 15212, 392])).
% 3.33/3.57 tff(15884,plain,
% 3.33/3.57 (b(s(s(s(elem!1))), z)),
% 3.33/3.57 inference(unit_resolution,[status(thm)],[94, 15883])).
% 3.33/3.57 tff(15885,plain,
% 3.33/3.57 (~r(s(s(elem!1)), s(s(z)))),
% 3.33/3.57 inference(unit_resolution,[status(thm)],[5362, 12399, 10521, 392])).
% 3.33/3.57 tff(15886,plain,
% 3.33/3.57 (b(s(s(elem!1)), s(s(z)))),
% 3.33/3.57 inference(unit_resolution,[status(thm)],[441, 15213, 15885])).
% 3.33/3.57 tff(15887,plain,
% 3.33/3.57 (~b(z, s(s(elem!1)))),
% 3.33/3.57 inference(unit_resolution,[status(thm)],[10727, 15886, 10451, 15215])).
% 3.33/3.57 tff(15888,plain,
% 3.33/3.57 (r(z, s(s(elem!1)))),
% 3.33/3.57 inference(unit_resolution,[status(thm)],[1795, 15887])).
% 3.33/3.57 tff(15889,plain,
% 3.33/3.57 (~b(s(z), s(s(s(elem!1))))),
% 3.33/3.57 inference(unit_resolution,[status(thm)],[12429, 15884, 10451, 15215, 53, 376])).
% 3.33/3.57 tff(15890,plain,
% 3.33/3.57 (r(s(z), s(s(s(elem!1))))),
% 3.33/3.57 inference(unit_resolution,[status(thm)],[116, 15889])).
% 3.33/3.57 tff(15891,plain,
% 3.33/3.57 (~r(z, s(z))),
% 3.33/3.57 inference(unit_resolution,[status(thm)],[8626, 15890, 10521, 15888])).
% 3.33/3.57 tff(15892,plain,
% 3.33/3.57 (b(z, s(z))),
% 3.33/3.57 inference(unit_resolution,[status(thm)],[321, 15891])).
% 3.33/3.57 tff(15893,plain,
% 3.33/3.57 ($false),
% 3.33/3.57 inference(unit_resolution,[status(thm)],[3997, 166, 53, 15836, 15892, 15884])).
% 3.33/3.57 tff(15894,plain,(b(s(z), s(s(z))) | (~b(s(z), z)) | (~b(z, s(s(z)))) | (~b(s(z), s(s(elem!1)))) | (s(s(elem!1)) = s(s(s(elem!1)))) | (~r(s(s(z)), s(z))) | b(s(s(elem!1)), s(z))), inference(lemma,lemma(discharge,[]))).
% 3.33/3.57 tff(15895,plain,
% 3.33/3.57 (b(s(z), s(s(z)))),
% 3.33/3.57 inference(unit_resolution,[status(thm)],[15894, 4568, 10451, 376, 45, 392, 53])).
% 3.33/3.57 tff(15896,plain,
% 3.33/3.57 (~r(s(s(z)), s(z))),
% 3.33/3.57 inference(unit_resolution,[status(thm)],[15822, 376, 10451, 350, 4568, 118])).
% 3.33/3.57 tff(15897,plain,
% 3.33/3.57 (b(s(s(z)), s(z))),
% 3.33/3.57 inference(unit_resolution,[status(thm)],[308, 15896])).
% 3.33/3.57 tff(15898,plain,
% 3.33/3.57 (~b(s(z), z)),
% 3.33/3.57 inference(unit_resolution,[status(thm)],[13598, 15897, 10451, 118])).
% 3.33/3.57 tff(15899,plain,
% 3.33/3.57 (r(s(z), z)),
% 3.33/3.57 inference(unit_resolution,[status(thm)],[230, 15898])).
% 3.33/3.57 tff(15900,plain,
% 3.33/3.57 (r(s(s(z)), s(s(elem!1)))),
% 3.33/3.57 inference(unit_resolution,[status(thm)],[11730, 15899, 10451, 4568])).
% 3.33/3.57 tff(15901,plain,
% 3.33/3.57 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(z)))) | (~b(s(z), s(s(elem!1)))) | (~b(s(s(elem!1)), s(s(z)))) | (~b(z, s(z))) | (~b(s(s(z)), s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(s(z)))) | (~b(s(z), s(s(elem!1)))) | (~b(s(s(elem!1)), s(s(z)))) | (~b(z, s(z))) | (~b(s(s(z)), s(z))))),
% 3.33/3.57 inference(rewrite,[status(thm)],[])).
% 3.33/3.57 tff(15902,plain,
% 3.33/3.57 (((~b(s(s(elem!1)), s(s(z)))) | (~b(z, s(s(z)))) | (~b(s(z), s(s(elem!1)))) | (~b(s(s(z)), s(z))) | (~b(z, s(z))) | (~b(z, s(s(z))))) <=> ((~b(z, s(s(z)))) | (~b(s(z), s(s(elem!1)))) | (~b(s(s(elem!1)), s(s(z)))) | (~b(z, s(z))) | (~b(s(s(z)), s(z))))),
% 3.33/3.57 inference(rewrite,[status(thm)],[])).
% 3.33/3.57 tff(15903,plain,
% 3.33/3.57 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), s(s(z)))) | (~b(z, s(s(z)))) | (~b(s(z), s(s(elem!1)))) | (~b(s(s(z)), s(z))) | (~b(z, s(z))) | (~b(z, s(s(z)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(z)))) | (~b(s(z), s(s(elem!1)))) | (~b(s(s(elem!1)), s(s(z)))) | (~b(z, s(z))) | (~b(s(s(z)), s(z)))))),
% 3.33/3.57 inference(monotonicity,[status(thm)],[15902])).
% 3.33/3.57 tff(15904,plain,
% 3.33/3.57 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), s(s(z)))) | (~b(z, s(s(z)))) | (~b(s(z), s(s(elem!1)))) | (~b(s(s(z)), s(z))) | (~b(z, s(z))) | (~b(z, s(s(z)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(s(z)))) | (~b(s(z), s(s(elem!1)))) | (~b(s(s(elem!1)), s(s(z)))) | (~b(z, s(z))) | (~b(s(s(z)), s(z))))),
% 3.33/3.57 inference(transitivity,[status(thm)],[15903, 15901])).
% 3.33/3.57 tff(15905,plain,
% 3.33/3.57 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), s(s(z)))) | (~b(z, s(s(z)))) | (~b(s(z), s(s(elem!1)))) | (~b(s(s(z)), s(z))) | (~b(z, s(z))) | (~b(z, s(s(z)))))),
% 3.33/3.57 inference(quant_inst,[status(thm)],[])).
% 3.33/3.57 tff(15906,plain,
% 3.33/3.57 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(s(z)))) | (~b(s(z), s(s(elem!1)))) | (~b(s(s(elem!1)), s(s(z)))) | (~b(z, s(z))) | (~b(s(s(z)), s(z)))),
% 3.33/3.57 inference(modus_ponens,[status(thm)],[15905, 15904])).
% 3.33/3.57 tff(15907,plain,
% 3.33/3.57 ($false),
% 3.33/3.57 inference(unit_resolution,[status(thm)],[15906, 166, 376, 405, 10451, 118, 156])).
% 3.33/3.57 tff(15908,plain,((~b(s(s(elem!1)), s(s(z)))) | (~b(s(z), s(s(elem!1)))) | (~b(z, s(s(z)))) | (~b(z, s(z))) | (~b(s(s(z)), s(z)))), inference(lemma,lemma(discharge,[]))).
% 3.33/3.57 tff(15909,plain,
% 3.33/3.57 (~b(s(s(elem!1)), s(s(z)))),
% 3.33/3.57 inference(unit_resolution,[status(thm)],[15908, 376, 10451, 118, 15897])).
% 3.33/3.57 tff(15910,plain,
% 3.33/3.57 (~r(s(s(elem!1)), s(s(z)))),
% 3.33/3.57 inference(unit_resolution,[status(thm)],[7518, 120, 4577, 333])).
% 3.33/3.57 tff(15911,plain,
% 3.33/3.57 (s(s(elem!1)) = s(s(z))),
% 3.33/3.57 inference(unit_resolution,[status(thm)],[441, 15910, 2076])).
% 3.33/3.57 tff(15912,plain,
% 3.33/3.57 (s(s(z)) = s(s(elem!1))),
% 3.33/3.57 inference(unit_resolution,[status(thm)],[131, 15911])).
% 3.33/3.57 tff(15913,plain,
% 3.33/3.57 (b(z, s(s(elem!1)))),
% 3.33/3.57 inference(unit_resolution,[status(thm)],[10937, 15912, 10451])).
% 3.33/3.57 tff(15914,plain,
% 3.33/3.57 (~r(s(s(s(elem!1))), z)),
% 3.33/3.57 inference(unit_resolution,[status(thm)],[10769, 15912, 97, 350, 7420, 7424])).
% 3.33/3.57 tff(15915,plain,
% 3.33/3.57 (b(s(s(s(elem!1))), z)),
% 3.33/3.57 inference(unit_resolution,[status(thm)],[94, 15914])).
% 3.33/3.57 tff(15916,plain,
% 3.33/3.57 (~b(s(s(z)), z)),
% 3.33/3.57 inference(unit_resolution,[status(thm)],[10745, 15915, 350, 10451, 120])).
% 3.33/3.57 tff(15917,plain,
% 3.33/3.57 (r(s(s(z)), z)),
% 3.33/3.57 inference(unit_resolution,[status(thm)],[186, 15916])).
% 3.33/3.57 tff(15918,plain,
% 3.33/3.57 (~r(z, s(s(s(elem!1))))),
% 3.33/3.57 inference(unit_resolution,[status(thm)],[10496, 15917, 97, 120])).
% 3.33/3.57 tff(15919,plain,
% 3.33/3.57 (b(z, s(s(s(elem!1))))),
% 3.33/3.57 inference(unit_resolution,[status(thm)],[261, 15918])).
% 3.33/3.57 tff(15920,plain,
% 3.33/3.57 (s(s(elem!1)) = s(s(s(elem!1)))),
% 3.33/3.57 inference(unit_resolution,[status(thm)],[1834, 15919, 15913, 7424, 7420])).
% 3.33/3.57 tff(15921,plain,
% 3.33/3.57 (s(s(z)) = s(s(elem!1))),
% 3.33/3.57 inference(symmetry,[status(thm)],[15911])).
% 3.33/3.57 tff(15922,plain,
% 3.33/3.57 (s(s(z)) = s(s(s(elem!1)))),
% 3.33/3.57 inference(transitivity,[status(thm)],[15921, 15920])).
% 3.33/3.57 tff(15923,plain,
% 3.33/3.57 ($false),
% 3.33/3.57 inference(unit_resolution,[status(thm)],[209, 15922])).
% 3.33/3.57 tff(15924,plain,((~r(s(z), s(s(z)))) | (~r(s(z), z)) | (~r(s(s(s(elem!1))), s(z))) | (~b(z, s(s(z)))) | b(s(s(elem!1)), s(s(z))) | (~r(s(s(elem!1)), s(z))) | (~r(s(s(z)), s(s(elem!1))))), inference(lemma,lemma(discharge,[]))).
% 3.33/3.57 tff(15925,plain,
% 3.33/3.57 (~r(s(z), s(s(z)))),
% 3.33/3.57 inference(unit_resolution,[status(thm)],[15924, 15899, 350, 10451, 15909, 10521, 15900])).
% 3.33/3.57 tff(15926,plain,
% 3.33/3.57 (b(s(z), s(s(z)))),
% 3.33/3.57 inference(unit_resolution,[status(thm)],[427, 15925])).
% 3.33/3.57 tff(15927,plain,
% 3.33/3.57 ($false),
% 3.33/3.57 inference(unit_resolution,[status(thm)],[12919, 166, 15926, 10451, 118, 15897])).
% 3.33/3.57 tff(15928,plain,((~b(s(z), s(s(elem!1)))) | (~b(z, s(s(z)))) | (~b(z, s(z))) | (~r(s(s(s(elem!1))), s(z))) | b(s(s(elem!1)), s(z))), inference(lemma,lemma(discharge,[]))).
% 3.33/3.57 tff(15929,plain,
% 3.33/3.57 (~r(s(s(s(elem!1))), s(z))),
% 3.33/3.57 inference(unit_resolution,[status(thm)],[15928, 118, 10451, 376, 4568])).
% 3.33/3.57 tff(15930,plain,
% 3.33/3.57 (b(s(s(s(elem!1))), s(z))),
% 3.33/3.57 inference(unit_resolution,[status(thm)],[1849, 15929])).
% 3.33/3.57 tff(15931,plain,
% 3.33/3.57 (~b(s(s(z)), z)),
% 3.33/3.57 inference(unit_resolution,[status(thm)],[12846, 556, 53, 10451])).
% 3.33/3.57 tff(15932,plain,
% 3.33/3.57 (r(s(s(z)), z)),
% 3.33/3.57 inference(unit_resolution,[status(thm)],[186, 15931])).
% 3.33/3.57 tff(15933,plain,
% 3.33/3.57 (~b(s(s(s(elem!1))), z)),
% 3.33/3.57 inference(unit_resolution,[status(thm)],[3997, 166, 53, 15930, 118])).
% 3.33/3.57 tff(15934,plain,
% 3.33/3.57 (r(s(s(s(elem!1))), z)),
% 3.33/3.57 inference(unit_resolution,[status(thm)],[94, 15933])).
% 3.33/3.57 tff(15935,plain,
% 3.33/3.57 (r(s(s(s(elem!1))), s(s(z)))),
% 3.33/3.57 inference(unit_resolution,[status(thm)],[5253, 15934, 556, 15932, 53, 15930, 118])).
% 3.33/3.57 tff(15936,plain,
% 3.33/3.57 (~b(z, s(s(s(elem!1))))),
% 3.33/3.57 inference(unit_resolution,[status(thm)],[3989, 166, 53, 15930, 118])).
% 3.33/3.57 tff(15937,plain,
% 3.33/3.57 (r(z, s(s(s(elem!1))))),
% 3.33/3.57 inference(unit_resolution,[status(thm)],[261, 15936])).
% 3.33/3.57 tff(15938,plain,
% 3.33/3.57 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), z)) | (~r(z, s(s(s(elem!1))))) | (~r(s(s(z)), z)) | (~r(s(s(s(elem!1))), s(s(z)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(elem!1))), z)) | (~r(z, s(s(s(elem!1))))) | (~r(s(s(z)), z)) | (~r(s(s(s(elem!1))), s(s(z)))))),
% 3.33/3.57 inference(rewrite,[status(thm)],[])).
% 3.33/3.57 tff(15939,plain,
% 3.33/3.57 (((~r(z, s(s(s(elem!1))))) | (~r(s(s(z)), z)) | (~r(s(s(s(elem!1))), z)) | (~r(s(s(s(elem!1))), s(s(z))))) <=> ((~r(s(s(s(elem!1))), z)) | (~r(z, s(s(s(elem!1))))) | (~r(s(s(z)), z)) | (~r(s(s(s(elem!1))), s(s(z)))))),
% 3.33/3.57 inference(rewrite,[status(thm)],[])).
% 3.33/3.57 tff(15940,plain,
% 3.33/3.57 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(s(elem!1))))) | (~r(s(s(z)), z)) | (~r(s(s(s(elem!1))), z)) | (~r(s(s(s(elem!1))), s(s(z)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), z)) | (~r(z, s(s(s(elem!1))))) | (~r(s(s(z)), z)) | (~r(s(s(s(elem!1))), s(s(z))))))),
% 3.33/3.57 inference(monotonicity,[status(thm)],[15939])).
% 3.33/3.57 tff(15941,plain,
% 3.33/3.57 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(s(elem!1))))) | (~r(s(s(z)), z)) | (~r(s(s(s(elem!1))), z)) | (~r(s(s(s(elem!1))), s(s(z)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(elem!1))), z)) | (~r(z, s(s(s(elem!1))))) | (~r(s(s(z)), z)) | (~r(s(s(s(elem!1))), s(s(z)))))),
% 3.33/3.57 inference(transitivity,[status(thm)],[15940, 15938])).
% 3.33/3.57 tff(15942,plain,
% 3.33/3.57 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(s(elem!1))))) | (~r(s(s(z)), z)) | (~r(s(s(s(elem!1))), z)) | (~r(s(s(s(elem!1))), s(s(z)))))),
% 3.33/3.57 inference(quant_inst,[status(thm)],[])).
% 3.33/3.57 tff(15943,plain,
% 3.33/3.57 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(elem!1))), z)) | (~r(z, s(s(s(elem!1))))) | (~r(s(s(z)), z)) | (~r(s(s(s(elem!1))), s(s(z))))),
% 3.33/3.57 inference(modus_ponens,[status(thm)],[15942, 15941])).
% 3.33/3.57 tff(15944,plain,
% 3.33/3.57 ($false),
% 3.33/3.57 inference(unit_resolution,[status(thm)],[15943, 197, 15934, 15937, 15932, 15935])).
% 3.33/3.57 tff(15945,plain,((~b(z, s(z))) | (~b(s(z), s(s(z)))) | (~b(s(z), z)) | (~b(z, s(s(z)))) | (~b(s(z), s(s(elem!1)))) | b(s(s(elem!1)), s(z))), inference(lemma,lemma(discharge,[]))).
% 3.33/3.57 tff(15946,plain,
% 3.33/3.57 (~b(z, s(z))),
% 3.33/3.57 inference(unit_resolution,[status(thm)],[15945, 15895, 53, 10451, 376, 4568])).
% 3.33/3.57 tff(15947,plain,
% 3.33/3.57 (r(z, s(z))),
% 3.33/3.57 inference(unit_resolution,[status(thm)],[321, 15946])).
% 3.33/3.57 tff(15948,plain,
% 3.33/3.57 (~b(s(s(z)), z)),
% 3.33/3.57 inference(unit_resolution,[status(thm)],[12846, 15895, 53, 10451])).
% 3.33/3.57 tff(15949,plain,
% 3.33/3.57 (r(s(s(z)), z)),
% 3.33/3.57 inference(unit_resolution,[status(thm)],[186, 15948])).
% 3.33/3.57 tff(15950,plain,
% 3.33/3.57 (~r(s(z), s(s(s(z))))),
% 3.33/3.57 inference(unit_resolution,[status(thm)],[1661, 15947, 392, 15949])).
% 3.33/3.57 tff(15951,plain,
% 3.33/3.57 (b(s(z), s(s(s(z))))),
% 3.33/3.57 inference(unit_resolution,[status(thm)],[1674, 15950])).
% 3.33/3.57 tff(15952,plain,
% 3.33/3.57 (~r(s(s(s(z))), z)),
% 3.33/3.57 inference(unit_resolution,[status(thm)],[8748, 15895, 15951, 15947, 15949])).
% 3.33/3.57 tff(15953,plain,
% 3.33/3.57 (b(s(s(s(z))), z)),
% 3.33/3.57 inference(unit_resolution,[status(thm)],[1713, 15952])).
% 3.33/3.57 tff(15954,plain,
% 3.33/3.57 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(z)))) | (~b(s(z), z)) | (~b(s(z), s(s(elem!1)))) | (~b(s(s(z)), s(s(elem!1)))) | (~b(s(s(s(z))), z)) | (~b(s(z), s(s(s(z))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(s(z)))) | (~b(s(z), z)) | (~b(s(z), s(s(elem!1)))) | (~b(s(s(z)), s(s(elem!1)))) | (~b(s(s(s(z))), z)) | (~b(s(z), s(s(s(z))))))),
% 3.33/3.57 inference(rewrite,[status(thm)],[])).
% 3.33/3.57 tff(15955,plain,
% 3.33/3.57 (((~b(s(s(z)), s(s(elem!1)))) | (~b(s(z), s(s(elem!1)))) | (~b(z, s(s(z)))) | (~b(s(s(s(z))), z)) | (~b(s(z), z)) | (~b(s(z), s(s(s(z)))))) <=> ((~b(z, s(s(z)))) | (~b(s(z), z)) | (~b(s(z), s(s(elem!1)))) | (~b(s(s(z)), s(s(elem!1)))) | (~b(s(s(s(z))), z)) | (~b(s(z), s(s(s(z))))))),
% 3.33/3.57 inference(rewrite,[status(thm)],[])).
% 3.33/3.57 tff(15956,plain,
% 3.33/3.57 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), s(s(elem!1)))) | (~b(s(z), s(s(elem!1)))) | (~b(z, s(s(z)))) | (~b(s(s(s(z))), z)) | (~b(s(z), z)) | (~b(s(z), s(s(s(z))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(z)))) | (~b(s(z), z)) | (~b(s(z), s(s(elem!1)))) | (~b(s(s(z)), s(s(elem!1)))) | (~b(s(s(s(z))), z)) | (~b(s(z), s(s(s(z)))))))),
% 3.33/3.57 inference(monotonicity,[status(thm)],[15955])).
% 3.33/3.57 tff(15957,plain,
% 3.33/3.57 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), s(s(elem!1)))) | (~b(s(z), s(s(elem!1)))) | (~b(z, s(s(z)))) | (~b(s(s(s(z))), z)) | (~b(s(z), z)) | (~b(s(z), s(s(s(z))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(s(z)))) | (~b(s(z), z)) | (~b(s(z), s(s(elem!1)))) | (~b(s(s(z)), s(s(elem!1)))) | (~b(s(s(s(z))), z)) | (~b(s(z), s(s(s(z))))))),
% 3.33/3.57 inference(transitivity,[status(thm)],[15956, 15954])).
% 3.33/3.57 tff(15958,plain,
% 3.33/3.57 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), s(s(elem!1)))) | (~b(s(z), s(s(elem!1)))) | (~b(z, s(s(z)))) | (~b(s(s(s(z))), z)) | (~b(s(z), z)) | (~b(s(z), s(s(s(z))))))),
% 3.33/3.57 inference(quant_inst,[status(thm)],[])).
% 3.33/3.57 tff(15959,plain,
% 3.33/3.57 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(s(z)))) | (~b(s(z), z)) | (~b(s(z), s(s(elem!1)))) | (~b(s(s(z)), s(s(elem!1)))) | (~b(s(s(s(z))), z)) | (~b(s(z), s(s(s(z)))))),
% 3.33/3.57 inference(modus_ponens,[status(thm)],[15958, 15957])).
% 3.33/3.57 tff(15960,plain,
% 3.33/3.57 ($false),
% 3.33/3.57 inference(unit_resolution,[status(thm)],[15959, 166, 376, 53, 10451, 446, 988, 1699])).
% 3.33/3.57 tff(15961,plain,((~b(s(s(z)), s(s(elem!1)))) | (~b(s(z), s(s(elem!1)))) | (~b(s(z), z)) | (~b(z, s(s(z)))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(z))), z))), inference(lemma,lemma(discharge,[]))).
% 3.33/3.57 tff(15962,plain,
% 3.33/3.57 (~b(s(s(z)), s(s(elem!1)))),
% 3.33/3.57 inference(unit_resolution,[status(thm)],[15961, 15951, 53, 10451, 376, 15953])).
% 3.33/3.57 tff(15963,plain,
% 3.33/3.57 (~b(z, s(s(s(z))))),
% 3.33/3.57 inference(unit_resolution,[status(thm)],[1708, 15953, 53, 15951])).
% 3.33/3.57 tff(15964,plain,
% 3.33/3.57 (r(z, s(s(s(z))))),
% 3.33/3.57 inference(unit_resolution,[status(thm)],[1697, 15963])).
% 3.33/3.57 tff(15965,plain,
% 3.33/3.57 (~r(z, s(s(elem!1)))),
% 3.33/3.57 inference(unit_resolution,[status(thm)],[15264, 333, 4577, 866])).
% 3.33/3.57 tff(15966,plain,
% 3.33/3.57 (b(z, s(s(elem!1)))),
% 3.33/3.57 inference(unit_resolution,[status(thm)],[1795, 15965])).
% 3.33/3.57 tff(15967,plain,
% 3.33/3.57 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(s(z))))) | (~r(s(s(elem!1)), z)) | (~r(s(s(z)), s(s(elem!1)))) | (~r(s(s(z)), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, s(s(s(z))))) | (~r(s(s(elem!1)), z)) | (~r(s(s(z)), s(s(elem!1)))) | (~r(s(s(z)), z)))),
% 3.33/3.58 inference(rewrite,[status(thm)],[])).
% 3.33/3.58 tff(15968,plain,
% 3.33/3.58 (((~r(z, s(s(s(z))))) | (~r(s(s(elem!1)), z)) | (~r(s(s(z)), z)) | (~r(s(s(z)), s(s(elem!1))))) <=> ((~r(z, s(s(s(z))))) | (~r(s(s(elem!1)), z)) | (~r(s(s(z)), s(s(elem!1)))) | (~r(s(s(z)), z)))),
% 3.33/3.58 inference(rewrite,[status(thm)],[])).
% 3.33/3.58 tff(15969,plain,
% 3.33/3.58 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(s(z))))) | (~r(s(s(elem!1)), z)) | (~r(s(s(z)), z)) | (~r(s(s(z)), s(s(elem!1)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(s(z))))) | (~r(s(s(elem!1)), z)) | (~r(s(s(z)), s(s(elem!1)))) | (~r(s(s(z)), z))))),
% 3.33/3.58 inference(monotonicity,[status(thm)],[15968])).
% 3.33/3.58 tff(15970,plain,
% 3.33/3.58 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(s(z))))) | (~r(s(s(elem!1)), z)) | (~r(s(s(z)), z)) | (~r(s(s(z)), s(s(elem!1)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, s(s(s(z))))) | (~r(s(s(elem!1)), z)) | (~r(s(s(z)), s(s(elem!1)))) | (~r(s(s(z)), z)))),
% 3.33/3.58 inference(transitivity,[status(thm)],[15969, 15967])).
% 3.33/3.58 tff(15971,plain,
% 3.33/3.58 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(s(z))))) | (~r(s(s(elem!1)), z)) | (~r(s(s(z)), z)) | (~r(s(s(z)), s(s(elem!1)))))),
% 3.33/3.58 inference(quant_inst,[status(thm)],[])).
% 3.33/3.58 tff(15972,plain,
% 3.33/3.58 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, s(s(s(z))))) | (~r(s(s(elem!1)), z)) | (~r(s(s(z)), s(s(elem!1)))) | (~r(s(s(z)), z))),
% 3.33/3.58 inference(modus_ponens,[status(thm)],[15971, 15970])).
% 3.33/3.58 tff(15973,plain,
% 3.33/3.58 ($false),
% 3.33/3.58 inference(unit_resolution,[status(thm)],[15972, 197, 333, 1970, 866, 1677])).
% 3.33/3.58 tff(15974,plain,((~r(z, s(s(s(z))))) | (~r(s(s(z)), s(s(elem!1)))) | (~r(s(s(elem!1)), z)) | (~r(s(s(z)), z))), inference(lemma,lemma(discharge,[]))).
% 3.33/3.58 tff(15975,plain,
% 3.33/3.58 (~r(s(s(elem!1)), z)),
% 3.33/3.58 inference(unit_resolution,[status(thm)],[15974, 333, 866, 1677])).
% 3.33/3.58 tff(15976,plain,
% 3.33/3.58 (b(s(s(elem!1)), z)),
% 3.33/3.58 inference(unit_resolution,[status(thm)],[608, 15975])).
% 3.33/3.58 tff(15977,plain,
% 3.33/3.58 ($false),
% 3.33/3.58 inference(unit_resolution,[status(thm)],[5377, 15976, 15966, 376, 53])).
% 3.33/3.58 tff(15978,plain,((~r(s(s(z)), s(s(elem!1)))) | (~b(s(z), s(s(elem!1)))) | (~b(s(z), z)) | (~r(s(s(z)), z)) | (~r(z, s(s(s(z))))) | (~r(s(s(elem!1)), s(z)))), inference(lemma,lemma(discharge,[]))).
% 3.33/3.58 tff(15979,plain,
% 3.33/3.58 (~r(s(s(z)), s(s(elem!1)))),
% 3.33/3.58 inference(unit_resolution,[status(thm)],[15978, 15949, 53, 376, 15964, 10521])).
% 3.33/3.58 tff(15980,plain,
% 3.33/3.58 (s(s(z)) = s(s(elem!1))),
% 3.33/3.58 inference(unit_resolution,[status(thm)],[390, 15979, 15962])).
% 3.33/3.58 tff(15981,plain,
% 3.33/3.58 (s(elem!1) = s(z)),
% 3.33/3.58 inference(unit_resolution,[status(thm)],[43, 15980])).
% 3.33/3.58 tff(15982,plain,
% 3.33/3.58 (z = elem!1),
% 3.33/3.58 inference(unit_resolution,[status(thm)],[30, 15981])).
% 3.33/3.58 tff(15983,plain,
% 3.33/3.58 (r(elem!1, s(z))),
% 3.33/3.58 inference(unit_resolution,[status(thm)],[741, 15982, 15947])).
% 3.33/3.58 tff(15984,plain,
% 3.33/3.58 ((s(s(s(s(elem!1)))) = z) <=> (s(s(s(s(elem!1)))) = elem!1)),
% 3.33/3.58 inference(monotonicity,[status(thm)],[15982])).
% 3.33/3.58 tff(15985,plain,
% 3.33/3.58 ((~(s(s(s(s(elem!1)))) = z)) <=> (~(s(s(s(s(elem!1)))) = elem!1))),
% 3.33/3.58 inference(monotonicity,[status(thm)],[15984])).
% 3.33/3.58 tff(15986,plain,
% 3.33/3.58 (~(s(s(s(s(elem!1)))) = elem!1)),
% 3.33/3.58 inference(modus_ponens,[status(thm)],[626, 15985])).
% 3.33/3.58 tff(15987,plain,
% 3.33/3.58 (~r(s(z), s(s(s(elem!1))))),
% 3.33/3.58 inference(unit_resolution,[status(thm)],[12271, 15947, 392, 15949])).
% 3.33/3.58 tff(15988,plain,
% 3.33/3.58 (b(s(z), s(s(s(elem!1))))),
% 3.33/3.58 inference(unit_resolution,[status(thm)],[116, 15987])).
% 3.33/3.58 tff(15989,plain,
% 3.33/3.58 (s(s(s(z))) = s(s(s(elem!1)))),
% 3.33/3.58 inference(monotonicity,[status(thm)],[15980])).
% 3.33/3.58 tff(15990,plain,
% 3.33/3.58 (b(s(s(s(z))), elem!1) <=> b(s(s(s(elem!1))), elem!1)),
% 3.33/3.58 inference(monotonicity,[status(thm)],[15989])).
% 3.33/3.58 tff(15991,plain,
% 3.33/3.58 (b(s(s(s(z))), z) <=> b(s(s(s(z))), elem!1)),
% 3.33/3.58 inference(monotonicity,[status(thm)],[15982])).
% 3.33/3.58 tff(15992,plain,
% 3.33/3.58 (b(s(s(s(z))), elem!1)),
% 3.33/3.58 inference(modus_ponens,[status(thm)],[15953, 15991])).
% 3.33/3.58 tff(15993,plain,
% 3.33/3.58 (b(s(s(s(elem!1))), elem!1)),
% 3.33/3.58 inference(modus_ponens,[status(thm)],[15992, 15990])).
% 3.33/3.58 tff(15994,plain,
% 3.33/3.58 (b(s(z), z) <=> b(s(z), elem!1)),
% 3.33/3.58 inference(monotonicity,[status(thm)],[15982])).
% 3.33/3.58 tff(15995,plain,
% 3.33/3.58 (b(s(z), elem!1)),
% 3.33/3.58 inference(modus_ponens,[status(thm)],[53, 15994])).
% 3.33/3.58 tff(15996,plain,
% 3.33/3.58 ((s(s(s(s(elem!1)))) = z) <=> (elem!1 = s(s(s(s(elem!1)))))),
% 3.33/3.58 inference(transitivity,[status(thm)],[15984, 2287])).
% 3.33/3.58 tff(15997,plain,
% 3.33/3.58 ((~(s(s(s(s(elem!1)))) = z)) <=> (~(elem!1 = s(s(s(s(elem!1))))))),
% 3.33/3.58 inference(monotonicity,[status(thm)],[15996])).
% 3.33/3.58 tff(15998,plain,
% 3.33/3.58 (~(elem!1 = s(s(s(s(elem!1)))))),
% 3.33/3.58 inference(modus_ponens,[status(thm)],[626, 15997])).
% 3.33/3.58 tff(15999,plain,
% 3.33/3.58 (b(z, s(s(elem!1)))),
% 3.33/3.58 inference(unit_resolution,[status(thm)],[10937, 15980, 10451])).
% 3.33/3.58 tff(16000,plain,
% 3.33/3.58 (~b(s(s(elem!1)), z)),
% 3.33/3.58 inference(unit_resolution,[status(thm)],[5377, 15999, 376, 53])).
% 3.33/3.58 tff(16001,plain,
% 3.33/3.58 (r(s(s(elem!1)), z)),
% 3.33/3.58 inference(unit_resolution,[status(thm)],[608, 16000])).
% 3.33/3.58 tff(16002,plain,
% 3.33/3.58 (r(s(s(elem!1)), elem!1)),
% 3.33/3.58 inference(unit_resolution,[status(thm)],[3398, 16001, 15982])).
% 3.33/3.58 tff(16003,plain,
% 3.33/3.58 ((s(s(s(s(elem!1)))) = s(s(z))) <=> (s(s(s(s(elem!1)))) = s(s(elem!1)))),
% 3.33/3.58 inference(monotonicity,[status(thm)],[15980])).
% 3.33/3.58 tff(16004,plain,
% 3.33/3.58 ((s(s(s(s(elem!1)))) = s(s(z))) <=> (s(s(elem!1)) = s(s(s(s(elem!1)))))),
% 3.33/3.58 inference(transitivity,[status(thm)],[16003, 123])).
% 3.33/3.58 tff(16005,plain,
% 3.33/3.58 ((~(s(s(s(s(elem!1)))) = s(s(z)))) <=> (~(s(s(elem!1)) = s(s(s(s(elem!1))))))),
% 3.33/3.58 inference(monotonicity,[status(thm)],[16004])).
% 3.33/3.58 tff(16006,plain,
% 3.33/3.58 (~(s(s(elem!1)) = s(s(s(s(elem!1)))))),
% 3.33/3.58 inference(modus_ponens,[status(thm)],[733, 16005])).
% 3.33/3.58 tff(16007,plain,
% 3.33/3.58 (elem!1 = z),
% 3.33/3.58 inference(symmetry,[status(thm)],[15982])).
% 3.33/3.58 tff(16008,plain,
% 3.33/3.58 (b(elem!1, s(s(elem!1))) <=> b(z, s(s(elem!1)))),
% 3.33/3.58 inference(monotonicity,[status(thm)],[16007])).
% 3.33/3.58 tff(16009,plain,
% 3.33/3.58 (b(z, s(s(elem!1))) <=> b(elem!1, s(s(elem!1)))),
% 3.33/3.58 inference(symmetry,[status(thm)],[16008])).
% 3.33/3.58 tff(16010,plain,
% 3.33/3.58 (b(elem!1, s(s(elem!1)))),
% 3.33/3.58 inference(modus_ponens,[status(thm)],[15999, 16009])).
% 3.33/3.58 tff(16011,plain,
% 3.33/3.58 (~r(s(z), s(s(s(s(elem!1)))))),
% 3.33/3.58 inference(unit_resolution,[status(thm)],[9645, 15983, 10521, 16002])).
% 3.33/3.58 tff(16012,plain,
% 3.33/3.58 (b(s(z), s(s(s(s(elem!1)))))),
% 3.33/3.58 inference(unit_resolution,[status(thm)],[681, 16011])).
% 3.33/3.58 tff(16013,plain,
% 3.33/3.58 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(s(elem!1))))) | (~b(elem!1, s(s(elem!1)))) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(z), elem!1)) | (~b(s(s(elem!1)), s(s(s(s(elem!1)))))) | (~b(s(z), s(s(s(s(elem!1)))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), s(s(s(elem!1))))) | (~b(elem!1, s(s(elem!1)))) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(z), elem!1)) | (~b(s(s(elem!1)), s(s(s(s(elem!1)))))) | (~b(s(z), s(s(s(s(elem!1)))))))),
% 3.33/3.58 inference(rewrite,[status(thm)],[])).
% 3.33/3.58 tff(16014,plain,
% 3.33/3.58 (((~b(s(s(elem!1)), s(s(s(s(elem!1)))))) | (~b(s(z), s(s(s(s(elem!1)))))) | (~b(elem!1, s(s(elem!1)))) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(z), elem!1)) | (~b(s(z), s(s(s(elem!1)))))) <=> ((~b(s(z), s(s(s(elem!1))))) | (~b(elem!1, s(s(elem!1)))) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(z), elem!1)) | (~b(s(s(elem!1)), s(s(s(s(elem!1)))))) | (~b(s(z), s(s(s(s(elem!1)))))))),
% 3.33/3.58 inference(rewrite,[status(thm)],[])).
% 3.33/3.58 tff(16015,plain,
% 3.33/3.58 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), s(s(s(s(elem!1)))))) | (~b(s(z), s(s(s(s(elem!1)))))) | (~b(elem!1, s(s(elem!1)))) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(z), elem!1)) | (~b(s(z), s(s(s(elem!1))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(s(elem!1))))) | (~b(elem!1, s(s(elem!1)))) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(z), elem!1)) | (~b(s(s(elem!1)), s(s(s(s(elem!1)))))) | (~b(s(z), s(s(s(s(elem!1))))))))),
% 3.33/3.58 inference(monotonicity,[status(thm)],[16014])).
% 3.33/3.58 tff(16016,plain,
% 3.33/3.58 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), s(s(s(s(elem!1)))))) | (~b(s(z), s(s(s(s(elem!1)))))) | (~b(elem!1, s(s(elem!1)))) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(z), elem!1)) | (~b(s(z), s(s(s(elem!1))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), s(s(s(elem!1))))) | (~b(elem!1, s(s(elem!1)))) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(z), elem!1)) | (~b(s(s(elem!1)), s(s(s(s(elem!1)))))) | (~b(s(z), s(s(s(s(elem!1)))))))),
% 3.33/3.58 inference(transitivity,[status(thm)],[16015, 16013])).
% 3.33/3.58 tff(16017,plain,
% 3.33/3.58 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), s(s(s(s(elem!1)))))) | (~b(s(z), s(s(s(s(elem!1)))))) | (~b(elem!1, s(s(elem!1)))) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(z), elem!1)) | (~b(s(z), s(s(s(elem!1))))))),
% 3.33/3.58 inference(quant_inst,[status(thm)],[])).
% 3.33/3.58 tff(16018,plain,
% 3.33/3.58 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), s(s(s(elem!1))))) | (~b(elem!1, s(s(elem!1)))) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(z), elem!1)) | (~b(s(s(elem!1)), s(s(s(s(elem!1)))))) | (~b(s(z), s(s(s(s(elem!1))))))),
% 3.33/3.58 inference(modus_ponens,[status(thm)],[16017, 16016])).
% 3.33/3.58 tff(16019,plain,
% 3.33/3.58 ($false),
% 3.33/3.58 inference(unit_resolution,[status(thm)],[16018, 166, 241, 642, 1046, 1327, 10960, 641])).
% 3.33/3.58 tff(16020,plain,((~b(s(z), s(s(s(s(elem!1)))))) | (~b(s(z), s(s(s(elem!1))))) | (~b(s(z), elem!1)) | (~b(s(s(elem!1)), s(s(s(s(elem!1)))))) | (~b(elem!1, s(s(elem!1)))) | (~b(s(s(s(elem!1))), elem!1))), inference(lemma,lemma(discharge,[]))).
% 3.33/3.58 tff(16021,plain,
% 3.33/3.58 (~b(s(s(elem!1)), s(s(s(s(elem!1)))))),
% 3.33/3.58 inference(unit_resolution,[status(thm)],[16020, 16012, 15995, 15988, 16010, 15993])).
% 3.33/3.58 tff(16022,plain,
% 3.33/3.58 (r(s(s(elem!1)), s(s(s(s(elem!1)))))),
% 3.33/3.58 inference(unit_resolution,[status(thm)],[827, 16021, 16006])).
% 3.33/3.58 tff(16023,plain,
% 3.33/3.58 (~r(s(s(s(s(elem!1)))), s(s(s(elem!1))))),
% 3.33/3.58 inference(unit_resolution,[status(thm)],[9699, 16022, 16002, 15998, 15995, 15993, 15988, 15986, 15983])).
% 3.33/3.58 tff(16024,plain,
% 3.33/3.58 (b(s(s(s(s(elem!1)))), s(s(s(elem!1))))),
% 3.33/3.58 inference(unit_resolution,[status(thm)],[1065, 16023, 364])).
% 3.33/3.58 tff(16025,plain,
% 3.33/3.58 (b(s(s(s(z))), s(z)) <=> b(s(s(s(elem!1))), s(z))),
% 3.33/3.58 inference(monotonicity,[status(thm)],[15989])).
% 3.33/3.58 tff(16026,plain,
% 3.33/3.58 (b(s(s(s(elem!1))), z) <=> b(s(s(s(elem!1))), elem!1)),
% 3.33/3.58 inference(monotonicity,[status(thm)],[15982])).
% 3.33/3.58 tff(16027,plain,
% 3.33/3.58 (b(s(s(s(elem!1))), elem!1) <=> b(s(s(s(elem!1))), z)),
% 3.33/3.58 inference(symmetry,[status(thm)],[16026])).
% 3.33/3.58 tff(16028,plain,
% 3.33/3.58 (b(s(s(s(z))), elem!1) <=> b(s(s(s(elem!1))), z)),
% 3.33/3.58 inference(transitivity,[status(thm)],[15990, 16027])).
% 3.33/3.58 tff(16029,plain,
% 3.33/3.58 (b(s(s(s(elem!1))), z)),
% 3.33/3.58 inference(modus_ponens,[status(thm)],[15992, 16028])).
% 3.33/3.58 tff(16030,plain,
% 3.33/3.58 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(z)))) | (~b(s(z), z)) | (~b(s(z), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), z)) | (~b(s(z), s(s(s(z))))) | (~b(s(s(z)), s(s(s(z))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(s(z)))) | (~b(s(z), z)) | (~b(s(z), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), z)) | (~b(s(z), s(s(s(z))))) | (~b(s(s(z)), s(s(s(z))))))),
% 3.33/3.58 inference(rewrite,[status(thm)],[])).
% 3.33/3.58 tff(16031,plain,
% 3.33/3.58 (((~b(s(s(z)), s(s(s(z))))) | (~b(s(z), s(s(s(z))))) | (~b(z, s(s(z)))) | (~b(s(s(s(elem!1))), z)) | (~b(s(z), z)) | (~b(s(z), s(s(s(elem!1)))))) <=> ((~b(z, s(s(z)))) | (~b(s(z), z)) | (~b(s(z), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), z)) | (~b(s(z), s(s(s(z))))) | (~b(s(s(z)), s(s(s(z))))))),
% 3.33/3.58 inference(rewrite,[status(thm)],[])).
% 3.33/3.58 tff(16032,plain,
% 3.33/3.58 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), s(s(s(z))))) | (~b(s(z), s(s(s(z))))) | (~b(z, s(s(z)))) | (~b(s(s(s(elem!1))), z)) | (~b(s(z), z)) | (~b(s(z), s(s(s(elem!1))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(z)))) | (~b(s(z), z)) | (~b(s(z), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), z)) | (~b(s(z), s(s(s(z))))) | (~b(s(s(z)), s(s(s(z)))))))),
% 3.33/3.58 inference(monotonicity,[status(thm)],[16031])).
% 3.33/3.58 tff(16033,plain,
% 3.33/3.58 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), s(s(s(z))))) | (~b(s(z), s(s(s(z))))) | (~b(z, s(s(z)))) | (~b(s(s(s(elem!1))), z)) | (~b(s(z), z)) | (~b(s(z), s(s(s(elem!1))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(s(z)))) | (~b(s(z), z)) | (~b(s(z), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), z)) | (~b(s(z), s(s(s(z))))) | (~b(s(s(z)), s(s(s(z))))))),
% 3.33/3.58 inference(transitivity,[status(thm)],[16032, 16030])).
% 3.33/3.58 tff(16034,plain,
% 3.33/3.58 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), s(s(s(z))))) | (~b(s(z), s(s(s(z))))) | (~b(z, s(s(z)))) | (~b(s(s(s(elem!1))), z)) | (~b(s(z), z)) | (~b(s(z), s(s(s(elem!1))))))),
% 3.33/3.58 inference(quant_inst,[status(thm)],[])).
% 3.33/3.58 tff(16035,plain,
% 3.33/3.58 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(s(z)))) | (~b(s(z), z)) | (~b(s(z), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), z)) | (~b(s(z), s(s(s(z))))) | (~b(s(s(z)), s(s(s(z)))))),
% 3.33/3.58 inference(modus_ponens,[status(thm)],[16034, 16033])).
% 3.33/3.58 tff(16036,plain,
% 3.33/3.58 ($false),
% 3.33/3.58 inference(unit_resolution,[status(thm)],[16035, 166, 241, 53, 10451, 121, 988, 986])).
% 3.33/3.58 tff(16037,plain,((~b(z, s(s(z)))) | (~b(s(z), s(s(s(elem!1))))) | (~b(s(z), z)) | (~b(s(s(s(elem!1))), z)) | (~b(s(z), s(s(s(z))))) | (~b(s(s(z)), s(s(s(z)))))), inference(lemma,lemma(discharge,[]))).
% 3.33/3.58 tff(16038,plain,
% 3.33/3.58 (~b(s(s(z)), s(s(s(z))))),
% 3.33/3.58 inference(unit_resolution,[status(thm)],[16037, 16029, 10451, 53, 15951, 15988])).
% 3.33/3.58 tff(16039,plain,
% 3.33/3.58 (r(s(s(z)), s(s(s(z))))),
% 3.33/3.58 inference(unit_resolution,[status(thm)],[1730, 16038])).
% 3.33/3.58 tff(16040,plain,
% 3.33/3.58 (~r(s(s(s(z))), s(z))),
% 3.33/3.58 inference(unit_resolution,[status(thm)],[1754, 16039, 15949, 15964])).
% 3.33/3.58 tff(16041,plain,
% 3.33/3.58 (b(s(s(s(z))), s(z))),
% 3.33/3.58 inference(unit_resolution,[status(thm)],[1763, 16040])).
% 3.33/3.58 tff(16042,plain,
% 3.33/3.58 (b(s(s(s(elem!1))), s(z))),
% 3.33/3.58 inference(modus_ponens,[status(thm)],[16041, 16025])).
% 3.33/3.58 tff(16043,plain,
% 3.33/3.58 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(s(elem!1))))) | (~b(s(z), s(s(elem!1)))) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~b(s(z), s(s(s(s(elem!1)))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), s(s(s(elem!1))))) | (~b(s(z), s(s(elem!1)))) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~b(s(z), s(s(s(s(elem!1)))))))),
% 3.33/3.58 inference(rewrite,[status(thm)],[])).
% 3.33/3.58 tff(16044,plain,
% 3.33/3.58 (((~b(s(z), s(s(elem!1)))) | (~b(s(z), s(s(elem!1)))) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~b(s(z), s(s(s(elem!1))))) | (~b(s(z), s(s(s(s(elem!1))))))) <=> ((~b(s(z), s(s(s(elem!1))))) | (~b(s(z), s(s(elem!1)))) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~b(s(z), s(s(s(s(elem!1)))))))),
% 3.33/3.58 inference(rewrite,[status(thm)],[])).
% 3.33/3.58 tff(16045,plain,
% 3.33/3.58 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(elem!1)))) | (~b(s(z), s(s(elem!1)))) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~b(s(z), s(s(s(elem!1))))) | (~b(s(z), s(s(s(s(elem!1)))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(s(elem!1))))) | (~b(s(z), s(s(elem!1)))) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~b(s(z), s(s(s(s(elem!1))))))))),
% 3.33/3.58 inference(monotonicity,[status(thm)],[16044])).
% 3.33/3.58 tff(16046,plain,
% 3.33/3.58 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(elem!1)))) | (~b(s(z), s(s(elem!1)))) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~b(s(z), s(s(s(elem!1))))) | (~b(s(z), s(s(s(s(elem!1)))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), s(s(s(elem!1))))) | (~b(s(z), s(s(elem!1)))) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~b(s(z), s(s(s(s(elem!1)))))))),
% 3.33/3.58 inference(transitivity,[status(thm)],[16045, 16043])).
% 3.33/3.58 tff(16047,plain,
% 3.33/3.58 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(elem!1)))) | (~b(s(z), s(s(elem!1)))) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~b(s(z), s(s(s(elem!1))))) | (~b(s(z), s(s(s(s(elem!1)))))))),
% 3.33/3.58 inference(quant_inst,[status(thm)],[])).
% 3.33/3.58 tff(16048,plain,
% 3.33/3.58 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), s(s(s(elem!1))))) | (~b(s(z), s(s(elem!1)))) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~b(s(z), s(s(s(s(elem!1))))))),
% 3.33/3.58 inference(modus_ponens,[status(thm)],[16047, 16046])).
% 3.33/3.58 tff(16049,plain,
% 3.33/3.58 ($false),
% 3.33/3.58 inference(unit_resolution,[status(thm)],[16048, 166, 376, 15988, 16042, 16012, 16024])).
% 3.33/3.58 tff(16050,plain,(b(s(s(elem!1)), s(z)) | (~b(s(z), s(s(elem!1)))) | (~b(z, s(s(z)))) | (~b(s(z), z)) | (~r(s(s(z)), s(z))) | (s(s(elem!1)) = s(s(s(elem!1))))), inference(lemma,lemma(discharge,[]))).
% 3.33/3.58 tff(16051,plain,
% 3.33/3.58 (b(s(s(elem!1)), s(z))),
% 3.33/3.58 inference(unit_resolution,[status(thm)],[16050, 45, 10451, 53, 4143, 376])).
% 3.33/3.58 tff(16052,plain,
% 3.33/3.58 (~(s(s(z)) = s(s(elem!1)))),
% 3.33/3.58 inference(unit_resolution,[status(thm)],[3938, 16051, 3936])).
% 3.33/3.58 tff(16053,plain,
% 3.33/3.58 (b(s(s(elem!1)), s(z))),
% 3.33/3.58 inference(unit_resolution,[status(thm)],[16050, 45, 10451, 53, 392, 376])).
% 3.33/3.58 tff(16054,plain,
% 3.33/3.58 (~b(z, s(s(elem!1)))),
% 3.33/3.58 inference(unit_resolution,[status(thm)],[8791, 16053, 53, 376])).
% 3.33/3.58 tff(16055,plain,
% 3.33/3.58 (r(z, s(s(elem!1)))),
% 3.33/3.58 inference(unit_resolution,[status(thm)],[1795, 16054])).
% 3.33/3.58 tff(16056,plain,
% 3.33/3.58 (~r(s(s(z)), s(s(s(elem!1))))),
% 3.33/3.58 inference(unit_resolution,[status(thm)],[6048, 197, 350, 392, 117])).
% 3.33/3.58 tff(16057,plain,
% 3.33/3.58 (b(s(s(z)), s(s(s(elem!1))))),
% 3.33/3.58 inference(unit_resolution,[status(thm)],[279, 16056])).
% 3.33/3.58 tff(16058,plain,
% 3.33/3.58 (~r(s(s(s(elem!1))), s(s(z)))),
% 3.33/3.58 inference(unit_resolution,[status(thm)],[7534, 350, 392, 117])).
% 3.33/3.58 tff(16059,plain,
% 3.33/3.58 (b(s(s(s(elem!1))), s(s(z)))),
% 3.33/3.58 inference(unit_resolution,[status(thm)],[218, 16058])).
% 3.33/3.58 tff(16060,plain,
% 3.33/3.58 (~b(z, s(s(s(elem!1))))),
% 3.33/3.58 inference(unit_resolution,[status(thm)],[10577, 166, 10451, 16057, 16059])).
% 3.33/3.58 tff(16061,plain,
% 3.33/3.58 (r(z, s(s(s(elem!1))))),
% 3.33/3.58 inference(unit_resolution,[status(thm)],[261, 16060])).
% 3.33/3.58 tff(16062,plain,
% 3.33/3.58 (~r(z, s(z))),
% 3.33/3.58 inference(unit_resolution,[status(thm)],[587, 16061, 117, 350])).
% 3.33/3.58 tff(16063,plain,
% 3.33/3.58 (b(z, s(z))),
% 3.33/3.58 inference(unit_resolution,[status(thm)],[321, 16062])).
% 3.33/3.58 tff(16064,plain,
% 3.33/3.58 (~b(s(z), s(s(z)))),
% 3.33/3.58 inference(unit_resolution,[status(thm)],[12045, 16063, 10451, 16059, 16057])).
% 3.33/3.58 tff(16065,plain,
% 3.33/3.58 (r(s(z), s(s(z)))),
% 3.33/3.58 inference(unit_resolution,[status(thm)],[427, 16064])).
% 3.33/3.58 tff(16066,plain,
% 3.33/3.58 (~b(s(s(s(z))), z)),
% 3.33/3.58 inference(unit_resolution,[status(thm)],[5078, 118, 392, 53, 122, 120])).
% 3.33/3.58 tff(16067,plain,
% 3.33/3.58 (r(s(s(s(z))), z)),
% 3.33/3.58 inference(unit_resolution,[status(thm)],[1713, 16066])).
% 3.33/3.58 tff(16068,plain,
% 3.33/3.58 (~b(s(s(s(elem!1))), s(z))),
% 3.33/3.58 inference(unit_resolution,[status(thm)],[4277, 118, 53, 45, 16053])).
% 3.33/3.58 tff(16069,plain,
% 3.33/3.58 (r(s(s(s(elem!1))), s(z))),
% 3.33/3.58 inference(unit_resolution,[status(thm)],[1849, 16068])).
% 3.33/3.58 tff(16070,plain,
% 3.33/3.58 (~r(s(s(s(elem!1))), s(s(z)))),
% 3.33/3.58 inference(unit_resolution,[status(thm)],[7534, 16069, 392, 119])).
% 3.33/3.58 tff(16071,plain,
% 3.33/3.58 (b(s(s(s(elem!1))), s(s(z)))),
% 3.33/3.58 inference(unit_resolution,[status(thm)],[218, 16070])).
% 3.33/3.58 tff(16072,plain,
% 3.33/3.58 (~b(s(s(s(elem!1))), z)),
% 3.33/3.58 inference(unit_resolution,[status(thm)],[10745, 16069, 10451, 122, 120])).
% 3.33/3.58 tff(16073,plain,
% 3.33/3.58 (r(s(s(s(elem!1))), z)),
% 3.33/3.58 inference(unit_resolution,[status(thm)],[94, 16072])).
% 3.33/3.58 tff(16074,plain,
% 3.33/3.58 (~r(s(s(z)), s(s(s(elem!1))))),
% 3.33/3.58 inference(unit_resolution,[status(thm)],[2304, 16073, 120, 119])).
% 3.33/3.58 tff(16075,plain,
% 3.33/3.58 (b(s(s(z)), s(s(s(elem!1))))),
% 3.33/3.58 inference(unit_resolution,[status(thm)],[279, 16074])).
% 3.33/3.58 tff(16076,plain,
% 3.33/3.58 (~b(z, s(s(s(elem!1))))),
% 3.33/3.58 inference(unit_resolution,[status(thm)],[10577, 166, 10451, 16075, 16071])).
% 3.33/3.58 tff(16077,plain,
% 3.33/3.58 (r(z, s(s(s(elem!1))))),
% 3.33/3.58 inference(unit_resolution,[status(thm)],[261, 16076])).
% 3.33/3.58 tff(16078,plain,
% 3.33/3.58 (~r(s(s(s(z))), s(s(s(elem!1))))),
% 3.33/3.58 inference(unit_resolution,[status(thm)],[13628, 197, 16073, 16077, 16067])).
% 3.33/3.58 tff(16079,plain,
% 3.33/3.58 ((s(s(s(z))) = s(s(s(elem!1)))) | b(s(s(s(z))), s(s(s(elem!1))))),
% 3.33/3.58 inference(unit_resolution,[status(thm)],[10059, 79, 16078])).
% 3.33/3.58 tff(16080,plain,
% 3.33/3.58 (b(s(s(s(z))), s(s(s(elem!1))))),
% 3.33/3.58 inference(unit_resolution,[status(thm)],[16079, 10056])).
% 3.33/3.58 tff(16081,plain,
% 3.33/3.58 (~b(s(s(elem!1)), z)),
% 3.33/3.58 inference(unit_resolution,[status(thm)],[7172, 166, 376, 118, 16053])).
% 3.33/3.58 tff(16082,plain,
% 3.33/3.58 (r(s(s(elem!1)), z)),
% 3.33/3.58 inference(unit_resolution,[status(thm)],[608, 16081])).
% 3.33/3.58 tff(16083,plain,
% 3.33/3.58 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), z)) | (~r(z, s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), s(s(elem!1)))) | (~r(s(s(elem!1)), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(elem!1))), z)) | (~r(z, s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), s(s(elem!1)))) | (~r(s(s(elem!1)), z)))),
% 3.33/3.58 inference(rewrite,[status(thm)],[])).
% 3.33/3.58 tff(16084,plain,
% 3.33/3.58 (((~r(z, s(s(s(elem!1))))) | (~r(s(s(elem!1)), z)) | (~r(s(s(s(elem!1))), z)) | (~r(s(s(s(elem!1))), s(s(elem!1))))) <=> ((~r(s(s(s(elem!1))), z)) | (~r(z, s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), s(s(elem!1)))) | (~r(s(s(elem!1)), z)))),
% 3.33/3.58 inference(rewrite,[status(thm)],[])).
% 3.33/3.58 tff(16085,plain,
% 3.33/3.58 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(s(elem!1))))) | (~r(s(s(elem!1)), z)) | (~r(s(s(s(elem!1))), z)) | (~r(s(s(s(elem!1))), s(s(elem!1)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), z)) | (~r(z, s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), s(s(elem!1)))) | (~r(s(s(elem!1)), z))))),
% 3.33/3.58 inference(monotonicity,[status(thm)],[16084])).
% 3.33/3.58 tff(16086,plain,
% 3.33/3.58 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(s(elem!1))))) | (~r(s(s(elem!1)), z)) | (~r(s(s(s(elem!1))), z)) | (~r(s(s(s(elem!1))), s(s(elem!1)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(elem!1))), z)) | (~r(z, s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), s(s(elem!1)))) | (~r(s(s(elem!1)), z)))),
% 3.33/3.59 inference(transitivity,[status(thm)],[16085, 16083])).
% 3.33/3.59 tff(16087,plain,
% 3.33/3.59 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(s(elem!1))))) | (~r(s(s(elem!1)), z)) | (~r(s(s(s(elem!1))), z)) | (~r(s(s(s(elem!1))), s(s(elem!1)))))),
% 3.33/3.59 inference(quant_inst,[status(thm)],[])).
% 3.33/3.59 tff(16088,plain,
% 3.33/3.59 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(elem!1))), z)) | (~r(z, s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), s(s(elem!1)))) | (~r(s(s(elem!1)), z))),
% 3.33/3.59 inference(modus_ponens,[status(thm)],[16087, 16086])).
% 3.33/3.59 tff(16089,plain,
% 3.33/3.59 (~r(s(s(s(elem!1))), s(s(elem!1)))),
% 3.33/3.59 inference(unit_resolution,[status(thm)],[16088, 197, 16073, 16077, 16082])).
% 3.33/3.59 tff(16090,plain,
% 3.33/3.59 (b(s(s(s(elem!1))), s(s(elem!1)))),
% 3.33/3.59 inference(unit_resolution,[status(thm)],[889, 16089, 51])).
% 3.33/3.59 tff(16091,plain,
% 3.33/3.59 (~r(s(s(elem!1)), s(s(s(elem!1))))),
% 3.33/3.59 inference(unit_resolution,[status(thm)],[933, 16077, 365, 16069])).
% 3.33/3.59 tff(16092,plain,
% 3.33/3.59 (b(s(s(elem!1)), s(s(s(elem!1))))),
% 3.33/3.59 inference(unit_resolution,[status(thm)],[461, 16091, 45])).
% 3.33/3.59 tff(16093,plain,
% 3.33/3.59 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(s(s(z))), s(s(s(elem!1))))) | (~b(s(s(s(z))), s(s(elem!1)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(s(s(z))), s(s(s(elem!1))))) | (~b(s(s(s(z))), s(s(elem!1)))))),
% 3.33/3.59 inference(rewrite,[status(thm)],[])).
% 3.33/3.59 tff(16094,plain,
% 3.33/3.59 (((~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(s(s(s(z))), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(s(s(s(z))), s(s(s(elem!1))))) | (~b(s(s(s(z))), s(s(elem!1))))) <=> ((~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(s(s(z))), s(s(s(elem!1))))) | (~b(s(s(s(z))), s(s(elem!1)))))),
% 3.33/3.59 inference(rewrite,[status(thm)],[])).
% 3.33/3.59 tff(16095,plain,
% 3.33/3.59 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(s(s(s(z))), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(s(s(s(z))), s(s(s(elem!1))))) | (~b(s(s(s(z))), s(s(elem!1)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(s(s(z))), s(s(s(elem!1))))) | (~b(s(s(s(z))), s(s(elem!1))))))),
% 3.33/3.59 inference(monotonicity,[status(thm)],[16094])).
% 3.33/3.59 tff(16096,plain,
% 3.33/3.59 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(s(s(s(z))), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(s(s(s(z))), s(s(s(elem!1))))) | (~b(s(s(s(z))), s(s(elem!1)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(s(s(z))), s(s(s(elem!1))))) | (~b(s(s(s(z))), s(s(elem!1)))))),
% 3.33/3.59 inference(transitivity,[status(thm)],[16095, 16093])).
% 3.33/3.59 tff(16097,plain,
% 3.33/3.59 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(s(s(s(z))), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(s(s(s(z))), s(s(s(elem!1))))) | (~b(s(s(s(z))), s(s(elem!1)))))),
% 3.33/3.59 inference(quant_inst,[status(thm)],[])).
% 3.33/3.59 tff(16098,plain,
% 3.33/3.59 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(s(s(z))), s(s(s(elem!1))))) | (~b(s(s(s(z))), s(s(elem!1))))),
% 3.33/3.59 inference(modus_ponens,[status(thm)],[16097, 16096])).
% 3.33/3.59 tff(16099,plain,
% 3.33/3.59 (~b(s(s(s(z))), s(s(elem!1)))),
% 3.33/3.59 inference(unit_resolution,[status(thm)],[16098, 166, 16092, 16090, 16080])).
% 3.33/3.59 tff(16100,plain,
% 3.33/3.59 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(elem!1)))) | (~r(s(s(elem!1)), z)) | (~r(s(s(s(z))), z)) | (~r(s(s(s(z))), s(s(elem!1)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, s(s(elem!1)))) | (~r(s(s(elem!1)), z)) | (~r(s(s(s(z))), z)) | (~r(s(s(s(z))), s(s(elem!1)))))),
% 3.33/3.59 inference(rewrite,[status(thm)],[])).
% 3.33/3.59 tff(16101,plain,
% 3.33/3.59 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(elem!1)))) | (~r(s(s(elem!1)), z)) | (~r(s(s(s(z))), z)) | (~r(s(s(s(z))), s(s(elem!1)))))),
% 3.33/3.59 inference(quant_inst,[status(thm)],[])).
% 3.33/3.59 tff(16102,plain,
% 3.33/3.59 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, s(s(elem!1)))) | (~r(s(s(elem!1)), z)) | (~r(s(s(s(z))), z)) | (~r(s(s(s(z))), s(s(elem!1))))),
% 3.33/3.59 inference(modus_ponens,[status(thm)],[16101, 16100])).
% 3.33/3.59 tff(16103,plain,
% 3.33/3.59 (~r(s(s(s(z))), s(s(elem!1)))),
% 3.33/3.59 inference(unit_resolution,[status(thm)],[16102, 197, 365, 16082, 16067])).
% 3.33/3.59 tff(16104,plain,
% 3.33/3.59 ((s(s(s(z))) = s(s(elem!1))) | b(s(s(s(z))), s(s(elem!1)))),
% 3.33/3.59 inference(unit_resolution,[status(thm)],[4523, 79, 16103])).
% 3.33/3.59 tff(16105,plain,
% 3.33/3.59 (s(s(s(z))) = s(s(elem!1))),
% 3.33/3.59 inference(unit_resolution,[status(thm)],[16104, 16099])).
% 3.33/3.59 tff(16106,plain,
% 3.33/3.59 (inj_0(s(s(z))) = inj_0(s(elem!1))),
% 3.33/3.59 inference(monotonicity,[status(thm)],[14469])).
% 3.33/3.59 tff(16107,plain,
% 3.33/3.59 (inj_0(s(elem!1)) = inj_0(s(s(z)))),
% 3.33/3.59 inference(symmetry,[status(thm)],[16106])).
% 3.33/3.59 tff(16108,plain,
% 3.33/3.59 (elem!1 = s(z)),
% 3.33/3.59 inference(transitivity,[status(thm)],[1170, 16107, 33])).
% 3.33/3.59 tff(16109,plain,
% 3.33/3.59 ($false),
% 3.33/3.59 inference(unit_resolution,[status(thm)],[10358, 16108])).
% 3.33/3.59 tff(16110,plain,((~(s(s(s(z))) = s(s(elem!1)))) | (elem!1 = s(z))), inference(lemma,lemma(discharge,[]))).
% 3.33/3.59 tff(16111,plain,
% 3.33/3.59 (elem!1 = s(z)),
% 3.33/3.59 inference(unit_resolution,[status(thm)],[16110, 16105])).
% 3.33/3.59 tff(16112,plain,
% 3.33/3.59 (r(elem!1, s(s(s(s(elem!1))))) <=> r(s(z), s(s(s(s(elem!1)))))),
% 3.33/3.59 inference(monotonicity,[status(thm)],[16111])).
% 3.33/3.59 tff(16113,plain,
% 3.33/3.59 (r(s(z), s(s(s(s(elem!1))))) <=> r(elem!1, s(s(s(s(elem!1)))))),
% 3.33/3.59 inference(symmetry,[status(thm)],[16112])).
% 3.33/3.59 tff(16114,plain,
% 3.33/3.59 (~b(s(s(elem!1)), s(s(s(z))))),
% 3.33/3.59 inference(unit_resolution,[status(thm)],[13985, 166, 16092, 16090, 16080])).
% 3.33/3.59 tff(16115,plain,
% 3.33/3.59 (~r(s(s(elem!1)), s(s(s(z))))),
% 3.33/3.59 inference(unit_resolution,[status(thm)],[13992, 197, 365, 16082, 16067])).
% 3.33/3.59 tff(16116,plain,
% 3.33/3.59 ((s(s(elem!1)) = s(s(s(z)))) | b(s(s(elem!1)), s(s(s(z))))),
% 3.33/3.59 inference(unit_resolution,[status(thm)],[5091, 79, 16115])).
% 3.33/3.59 tff(16117,plain,
% 3.33/3.59 (s(s(elem!1)) = s(s(s(z)))),
% 3.33/3.59 inference(unit_resolution,[status(thm)],[16116, 16114])).
% 3.33/3.59 tff(16118,plain,
% 3.33/3.59 (s(s(s(elem!1))) = s(s(s(s(z))))),
% 3.33/3.59 inference(monotonicity,[status(thm)],[16117])).
% 3.33/3.59 tff(16119,plain,
% 3.33/3.59 (b(s(s(s(s(elem!1)))), s(s(s(elem!1)))) <=> b(s(s(s(s(elem!1)))), s(s(s(s(z)))))),
% 3.33/3.59 inference(monotonicity,[status(thm)],[16118])).
% 3.33/3.59 tff(16120,plain,
% 3.33/3.59 (b(s(s(s(s(elem!1)))), s(s(s(s(z))))) <=> b(s(s(s(s(elem!1)))), s(s(s(elem!1))))),
% 3.33/3.59 inference(symmetry,[status(thm)],[16119])).
% 3.33/3.59 tff(16121,plain,
% 3.33/3.59 (s(s(s(s(elem!1)))) = s(s(s(s(s(z)))))),
% 3.33/3.59 inference(monotonicity,[status(thm)],[16118])).
% 3.33/3.59 tff(16122,plain,
% 3.33/3.59 (s(s(s(s(s(z))))) = s(s(s(s(elem!1))))),
% 3.33/3.59 inference(symmetry,[status(thm)],[16121])).
% 3.33/3.59 tff(16123,plain,
% 3.33/3.59 (b(s(s(s(s(s(z))))), s(s(s(s(z))))) <=> b(s(s(s(s(elem!1)))), s(s(s(s(z)))))),
% 3.33/3.59 inference(monotonicity,[status(thm)],[16122])).
% 3.33/3.59 tff(16124,plain,
% 3.33/3.59 (b(s(s(s(s(s(z))))), s(s(s(s(z))))) <=> b(s(s(s(s(elem!1)))), s(s(s(elem!1))))),
% 3.33/3.59 inference(transitivity,[status(thm)],[16123, 16120])).
% 3.33/3.59 tff(16125,plain,
% 3.33/3.59 ((~b(s(s(s(s(s(z))))), s(s(s(s(z)))))) <=> (~b(s(s(s(s(elem!1)))), s(s(s(elem!1)))))),
% 3.33/3.59 inference(monotonicity,[status(thm)],[16124])).
% 3.33/3.59 tff(16126,plain,
% 3.33/3.59 (s(s(s(s(z)))) = s(s(s(elem!1)))),
% 3.33/3.59 inference(symmetry,[status(thm)],[16118])).
% 3.33/3.59 tff(16127,plain,
% 3.33/3.59 (b(s(s(z)), s(s(s(s(z))))) <=> b(s(s(z)), s(s(s(elem!1))))),
% 3.33/3.59 inference(monotonicity,[status(thm)],[16126])).
% 3.33/3.59 tff(16128,plain,
% 3.33/3.59 (b(s(s(z)), s(s(s(elem!1)))) <=> b(s(s(z)), s(s(s(s(z)))))),
% 3.33/3.59 inference(symmetry,[status(thm)],[16127])).
% 3.33/3.59 tff(16129,plain,
% 3.33/3.59 (b(s(s(z)), s(s(s(s(z)))))),
% 3.33/3.59 inference(modus_ponens,[status(thm)],[16075, 16128])).
% 3.33/3.59 tff(16130,plain,
% 3.33/3.59 (b(s(s(s(s(z)))), s(s(s(z)))) <=> b(s(s(s(elem!1))), s(s(s(z))))),
% 3.33/3.59 inference(monotonicity,[status(thm)],[16126])).
% 3.33/3.59 tff(16131,plain,
% 3.33/3.59 (b(s(s(s(elem!1))), s(s(s(z)))) <=> b(s(s(s(s(z)))), s(s(s(z))))),
% 3.33/3.59 inference(symmetry,[status(thm)],[16130])).
% 3.33/3.59 tff(16132,plain,
% 3.33/3.59 (~r(s(s(s(elem!1))), s(s(s(z))))),
% 3.33/3.59 inference(unit_resolution,[status(thm)],[13638, 197, 16073, 16077, 16067])).
% 3.33/3.59 tff(16133,plain,
% 3.33/3.59 (b(s(s(s(elem!1))), s(s(s(z))))),
% 3.33/3.59 inference(unit_resolution,[status(thm)],[3574, 16132, 3567])).
% 3.33/3.59 tff(16134,plain,
% 3.33/3.59 (b(s(s(s(s(z)))), s(s(s(z))))),
% 3.33/3.59 inference(modus_ponens,[status(thm)],[16133, 16131])).
% 3.33/3.59 tff(16135,plain,
% 3.33/3.59 (b(s(s(s(z))), s(s(s(s(z))))) <=> b(s(s(s(z))), s(s(s(elem!1))))),
% 3.33/3.59 inference(monotonicity,[status(thm)],[16126])).
% 3.33/3.59 tff(16136,plain,
% 3.33/3.59 (b(s(s(s(z))), s(s(s(elem!1)))) <=> b(s(s(s(z))), s(s(s(s(z)))))),
% 3.33/3.59 inference(symmetry,[status(thm)],[16135])).
% 3.33/3.59 tff(16137,plain,
% 3.33/3.59 (b(s(s(s(z))), s(s(s(s(z)))))),
% 3.33/3.59 inference(modus_ponens,[status(thm)],[16080, 16136])).
% 3.33/3.59 tff(16138,plain,
% 3.33/3.59 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(s(z)), s(s(s(elem!1))))) | (~b(s(s(s(z))), s(s(s(elem!1))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(s(z)), s(s(s(elem!1))))) | (~b(s(s(s(z))), s(s(s(elem!1))))))),
% 3.33/3.59 inference(rewrite,[status(thm)],[])).
% 3.33/3.59 tff(16139,plain,
% 3.33/3.59 (((~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(s(s(s(z))), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(s(z)), s(s(s(elem!1))))) | (~b(s(s(s(z))), s(s(s(elem!1))))) | (~b(s(s(s(z))), s(s(z))))) <=> ((~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(s(z)), s(s(s(elem!1))))) | (~b(s(s(s(z))), s(s(s(elem!1))))))),
% 3.33/3.59 inference(rewrite,[status(thm)],[])).
% 3.33/3.59 tff(16140,plain,
% 3.33/3.59 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(s(s(s(z))), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(s(z)), s(s(s(elem!1))))) | (~b(s(s(s(z))), s(s(s(elem!1))))) | (~b(s(s(s(z))), s(s(z)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(s(z)), s(s(s(elem!1))))) | (~b(s(s(s(z))), s(s(s(elem!1)))))))),
% 3.33/3.59 inference(monotonicity,[status(thm)],[16139])).
% 3.33/3.59 tff(16141,plain,
% 3.33/3.59 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(s(s(s(z))), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(s(z)), s(s(s(elem!1))))) | (~b(s(s(s(z))), s(s(s(elem!1))))) | (~b(s(s(s(z))), s(s(z)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(s(z)), s(s(s(elem!1))))) | (~b(s(s(s(z))), s(s(s(elem!1))))))),
% 3.33/3.59 inference(transitivity,[status(thm)],[16140, 16138])).
% 3.33/3.59 tff(16142,plain,
% 3.33/3.59 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(s(s(s(z))), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(s(z)), s(s(s(elem!1))))) | (~b(s(s(s(z))), s(s(s(elem!1))))) | (~b(s(s(s(z))), s(s(z)))))),
% 3.33/3.59 inference(quant_inst,[status(thm)],[])).
% 3.33/3.59 tff(16143,plain,
% 3.33/3.59 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(s(z)), s(s(s(elem!1))))) | (~b(s(s(s(z))), s(s(s(elem!1)))))),
% 3.33/3.59 inference(modus_ponens,[status(thm)],[16142, 16141])).
% 3.33/3.59 tff(16144,plain,
% 3.33/3.59 (~b(s(s(s(z))), s(s(z)))),
% 3.33/3.59 inference(unit_resolution,[status(thm)],[16143, 166, 16092, 16090, 16075, 16080])).
% 3.33/3.59 tff(16145,plain,
% 3.33/3.59 (r(s(s(s(z))), s(s(z)))),
% 3.33/3.59 inference(unit_resolution,[status(thm)],[1010, 16144])).
% 3.33/3.59 tff(16146,plain,
% 3.33/3.59 (r(s(s(s(s(elem!1)))), s(s(z))) <=> r(s(s(s(s(s(z))))), s(s(z)))),
% 3.33/3.59 inference(symmetry,[status(thm)],[7206])).
% 3.33/3.59 tff(16147,plain,
% 3.33/3.59 ((~b(s(s(s(s(s(z))))), s(s(z)))) <=> (~b(s(s(s(s(elem!1)))), s(s(z))))),
% 3.33/3.59 inference(monotonicity,[status(thm)],[7204])).
% 3.33/3.59 tff(16148,assumption,(b(s(s(s(s(s(z))))), s(s(s(s(z)))))), introduced(assumption)).
% 3.33/3.59 tff(16149,plain,
% 3.33/3.59 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~b(s(s(s(s(s(z))))), s(s(z)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~b(s(s(s(s(s(z))))), s(s(z)))))),
% 3.33/3.59 inference(rewrite,[status(thm)],[])).
% 3.33/3.59 tff(16150,plain,
% 3.33/3.59 (((~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~b(s(s(s(s(s(z))))), s(s(z))))) <=> ((~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~b(s(s(s(s(s(z))))), s(s(z)))))),
% 3.33/3.59 inference(rewrite,[status(thm)],[])).
% 3.33/3.59 tff(16151,plain,
% 3.33/3.59 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~b(s(s(s(s(s(z))))), s(s(z)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~b(s(s(s(s(s(z))))), s(s(z))))))),
% 3.33/3.59 inference(monotonicity,[status(thm)],[16150])).
% 3.33/3.59 tff(16152,plain,
% 3.33/3.59 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~b(s(s(s(s(s(z))))), s(s(z)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~b(s(s(s(s(s(z))))), s(s(z)))))),
% 3.33/3.59 inference(transitivity,[status(thm)],[16151, 16149])).
% 3.33/3.59 tff(16153,plain,
% 3.33/3.59 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~b(s(s(s(s(s(z))))), s(s(z)))))),
% 3.33/3.59 inference(quant_inst,[status(thm)],[])).
% 3.33/3.59 tff(16154,plain,
% 3.33/3.59 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~b(s(s(s(s(s(z))))), s(s(z))))),
% 3.33/3.59 inference(modus_ponens,[status(thm)],[16153, 16152])).
% 3.33/3.59 tff(16155,plain,
% 3.33/3.59 (~b(s(s(s(s(s(z))))), s(s(z)))),
% 3.33/3.59 inference(unit_resolution,[status(thm)],[16154, 166, 3252, 4732, 4733, 16148])).
% 3.33/3.59 tff(16156,plain,
% 3.33/3.59 (~b(s(s(s(s(elem!1)))), s(s(z)))),
% 3.33/3.59 inference(modus_ponens,[status(thm)],[16155, 16147])).
% 3.33/3.59 tff(16157,plain,
% 3.33/3.59 (r(s(s(s(s(elem!1)))), s(s(z)))),
% 3.33/3.59 inference(unit_resolution,[status(thm)],[1299, 16156])).
% 3.33/3.59 tff(16158,plain,
% 3.33/3.59 (r(s(s(s(s(s(z))))), s(s(z)))),
% 3.33/3.59 inference(modus_ponens,[status(thm)],[16157, 16146])).
% 3.33/3.59 tff(16159,plain,
% 3.33/3.59 (r(s(s(s(s(s(z))))), s(s(s(z)))) <=> r(s(s(s(s(elem!1)))), s(s(elem!1)))),
% 3.33/3.59 inference(monotonicity,[status(thm)],[5168, 14031])).
% 3.33/3.59 tff(16160,plain,
% 3.33/3.59 (r(s(s(s(s(elem!1)))), s(s(elem!1))) <=> r(s(s(s(s(s(z))))), s(s(s(z))))),
% 3.33/3.59 inference(symmetry,[status(thm)],[16159])).
% 3.33/3.59 tff(16161,plain,
% 3.33/3.59 (inj_0(s(s(elem!1))) = inj_0(s(s(s(z))))),
% 3.33/3.59 inference(monotonicity,[status(thm)],[5163])).
% 3.33/3.59 tff(16162,plain,
% 3.33/3.59 (s(elem!1) = s(s(z))),
% 3.33/3.59 inference(transitivity,[status(thm)],[39, 16161, 134])).
% 3.33/3.59 tff(16163,plain,
% 3.33/3.59 ((s(s(s(elem!1))) = s(elem!1)) <=> (s(s(s(elem!1))) = s(s(z)))),
% 3.33/3.59 inference(monotonicity,[status(thm)],[16162])).
% 3.33/3.59 tff(16164,plain,
% 3.33/3.59 ((s(s(s(elem!1))) = s(elem!1)) <=> (s(s(z)) = s(s(s(elem!1))))),
% 3.33/3.59 inference(transitivity,[status(thm)],[16163, 487])).
% 3.33/3.59 tff(16165,plain,
% 3.33/3.59 ((s(s(z)) = s(s(s(elem!1)))) <=> (s(s(s(elem!1))) = s(elem!1))),
% 3.33/3.59 inference(symmetry,[status(thm)],[16164])).
% 3.33/3.59 tff(16166,plain,
% 3.33/3.59 ((~(s(s(z)) = s(s(s(elem!1))))) <=> (~(s(s(s(elem!1))) = s(elem!1)))),
% 3.33/3.59 inference(monotonicity,[status(thm)],[16165])).
% 3.33/3.59 tff(16167,plain,
% 3.33/3.59 (~(s(s(s(elem!1))) = s(elem!1))),
% 3.33/3.59 inference(modus_ponens,[status(thm)],[209, 16166])).
% 3.33/3.59 tff(16168,plain,
% 3.33/3.59 (~(s(s(s(s(elem!1)))) = s(s(elem!1)))),
% 3.33/3.59 inference(unit_resolution,[status(thm)],[1166, 16167])).
% 3.33/3.59 tff(16169,plain,
% 3.33/3.59 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~b(s(s(s(s(s(z))))), s(s(s(z))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~b(s(s(s(s(s(z))))), s(s(s(z))))))),
% 3.33/3.59 inference(rewrite,[status(thm)],[])).
% 3.33/3.59 tff(16170,plain,
% 3.33/3.59 (((~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~b(s(s(s(s(s(z))))), s(s(s(z)))))) <=> ((~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~b(s(s(s(s(s(z))))), s(s(s(z))))))),
% 3.43/3.60 inference(rewrite,[status(thm)],[])).
% 3.43/3.60 tff(16171,plain,
% 3.43/3.60 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~b(s(s(s(s(s(z))))), s(s(s(z))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~b(s(s(s(s(s(z))))), s(s(s(z)))))))),
% 3.43/3.60 inference(monotonicity,[status(thm)],[16170])).
% 3.43/3.60 tff(16172,plain,
% 3.43/3.60 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~b(s(s(s(s(s(z))))), s(s(s(z))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~b(s(s(s(s(s(z))))), s(s(s(z))))))),
% 3.43/3.60 inference(transitivity,[status(thm)],[16171, 16169])).
% 3.43/3.60 tff(16173,plain,
% 3.43/3.60 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~b(s(s(s(s(s(z))))), s(s(s(z))))))),
% 3.43/3.60 inference(quant_inst,[status(thm)],[])).
% 3.43/3.60 tff(16174,plain,
% 3.43/3.60 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~b(s(s(s(s(s(z))))), s(s(s(z)))))),
% 3.43/3.60 inference(modus_ponens,[status(thm)],[16173, 16172])).
% 3.43/3.60 tff(16175,plain,
% 3.43/3.60 (~b(s(s(s(s(s(z))))), s(s(s(z))))),
% 3.43/3.60 inference(unit_resolution,[status(thm)],[16174, 166, 3252, 4732, 16148])).
% 3.43/3.60 tff(16176,plain,
% 3.43/3.60 (~b(s(s(s(s(elem!1)))), s(s(elem!1)))),
% 3.43/3.60 inference(modus_ponens,[status(thm)],[16175, 5171])).
% 3.43/3.60 tff(16177,plain,
% 3.43/3.60 (r(s(s(s(s(elem!1)))), s(s(elem!1)))),
% 3.43/3.60 inference(unit_resolution,[status(thm)],[813, 16176, 16168])).
% 3.43/3.60 tff(16178,plain,
% 3.43/3.60 (r(s(s(s(s(s(z))))), s(s(s(z))))),
% 3.43/3.60 inference(modus_ponens,[status(thm)],[16177, 16160])).
% 3.43/3.60 tff(16179,plain,
% 3.43/3.60 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(z)), s(z))) | (~r(s(s(s(z))), s(s(z)))) | (~r(s(s(s(s(s(z))))), s(s(z)))) | (~r(s(s(s(s(s(z))))), s(s(s(z))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(z)), s(z))) | (~r(s(s(s(z))), s(s(z)))) | (~r(s(s(s(s(s(z))))), s(s(z)))) | (~r(s(s(s(s(s(z))))), s(s(s(z))))))),
% 3.43/3.60 inference(rewrite,[status(thm)],[])).
% 3.43/3.60 tff(16180,plain,
% 3.43/3.60 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(z)), s(z))) | (~r(s(s(s(z))), s(s(z)))) | (~r(s(s(s(s(s(z))))), s(s(z)))) | (~r(s(s(s(s(s(z))))), s(s(s(z))))))),
% 3.43/3.60 inference(quant_inst,[status(thm)],[])).
% 3.43/3.60 tff(16181,plain,
% 3.43/3.60 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(z)), s(z))) | (~r(s(s(s(z))), s(s(z)))) | (~r(s(s(s(s(s(z))))), s(s(z)))) | (~r(s(s(s(s(s(z))))), s(s(s(z)))))),
% 3.43/3.60 inference(modus_ponens,[status(thm)],[16180, 16179])).
% 3.43/3.60 tff(16182,plain,
% 3.43/3.60 (~r(s(s(s(s(s(z))))), s(s(z)))),
% 3.43/3.60 inference(unit_resolution,[status(thm)],[16181, 197, 392, 1676, 16178])).
% 3.43/3.60 tff(16183,plain,
% 3.43/3.60 ($false),
% 3.43/3.60 inference(unit_resolution,[status(thm)],[16182, 16158])).
% 3.43/3.60 tff(16184,plain,((~b(s(s(s(s(s(z))))), s(s(s(s(z)))))) | (~(s(s(elem!1)) = s(s(s(z))))) | (~r(s(s(z)), s(z))) | (~r(s(s(s(z))), s(s(z)))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(z)), s(s(s(s(z))))))), inference(lemma,lemma(discharge,[]))).
% 3.43/3.60 tff(16185,plain,
% 3.43/3.60 (~b(s(s(s(s(s(z))))), s(s(s(s(z)))))),
% 3.43/3.60 inference(unit_resolution,[status(thm)],[16184, 16117, 392, 16145, 16137, 16134, 16129])).
% 3.43/3.60 tff(16186,plain,
% 3.43/3.60 (~b(s(s(s(s(elem!1)))), s(s(s(elem!1))))),
% 3.43/3.60 inference(modus_ponens,[status(thm)],[16185, 16125])).
% 3.43/3.60 tff(16187,plain,
% 3.43/3.60 (r(s(s(s(s(elem!1)))), s(s(s(elem!1))))),
% 3.43/3.60 inference(unit_resolution,[status(thm)],[1065, 16186, 364])).
% 3.43/3.60 tff(16188,plain,
% 3.43/3.60 (~b(s(z), s(s(s(s(elem!1)))))),
% 3.43/3.60 inference(unit_resolution,[status(thm)],[1514, 16187, 16069, 53, 16077])).
% 3.43/3.60 tff(16189,plain,
% 3.43/3.60 (r(s(z), s(s(s(s(elem!1)))))),
% 3.43/3.60 inference(unit_resolution,[status(thm)],[681, 16188])).
% 3.43/3.60 tff(16190,plain,
% 3.43/3.60 (r(elem!1, s(s(s(s(elem!1)))))),
% 3.43/3.60 inference(modus_ponens,[status(thm)],[16189, 16113])).
% 3.43/3.60 tff(16191,plain,
% 3.43/3.60 (r(elem!1, s(s(s(elem!1)))) <=> r(s(z), s(s(s(elem!1))))),
% 3.43/3.60 inference(monotonicity,[status(thm)],[16111])).
% 3.43/3.60 tff(16192,plain,
% 3.43/3.60 (r(s(z), s(s(s(elem!1)))) <=> r(elem!1, s(s(s(elem!1))))),
% 3.43/3.60 inference(symmetry,[status(thm)],[16191])).
% 3.43/3.60 tff(16193,plain,
% 3.43/3.60 (r(elem!1, s(s(s(elem!1))))),
% 3.43/3.60 inference(modus_ponens,[status(thm)],[119, 16192])).
% 3.43/3.60 tff(16194,plain,
% 3.43/3.60 (~r(elem!1, s(s(s(s(elem!1)))))),
% 3.43/3.60 inference(unit_resolution,[status(thm)],[1056, 16187, 16069, 16193])).
% 3.43/3.60 tff(16195,plain,
% 3.43/3.60 ($false),
% 3.43/3.60 inference(unit_resolution,[status(thm)],[16194, 16190])).
% 3.43/3.60 tff(16196,plain,((~b(z, s(z))) | (~b(s(z), z)) | (~r(s(s(z)), s(z))) | (~r(s(z), s(s(s(elem!1))))) | (s(s(s(elem!1))) = s(s(s(z)))) | (s(s(elem!1)) = s(s(s(elem!1)))) | (~r(z, s(s(elem!1)))) | (~b(z, s(s(z)))) | (~b(s(z), s(s(elem!1)))) | (~r(s(z), s(s(z)))) | (~b(s(s(z)), z))), inference(lemma,lemma(discharge,[]))).
% 3.43/3.60 tff(16197,plain,
% 3.43/3.60 (~b(z, s(z))),
% 3.43/3.60 inference(unit_resolution,[status(thm)],[16196, 365, 392, 117, 3567, 45, 53, 10451, 376, 120, 122])).
% 3.43/3.60 tff(16198,plain,
% 3.43/3.60 (r(z, s(z))),
% 3.43/3.60 inference(unit_resolution,[status(thm)],[321, 16197])).
% 3.43/3.60 tff(16199,plain,
% 3.43/3.60 (~b(s(s(s(elem!1))), s(s(elem!1)))),
% 3.43/3.60 inference(unit_resolution,[status(thm)],[1858, 96, 376, 310])).
% 3.43/3.60 tff(16200,plain,
% 3.43/3.60 (~r(s(s(z)), s(s(s(elem!1))))),
% 3.43/3.60 inference(unit_resolution,[status(thm)],[15377, 16199, 376, 392, 98])).
% 3.43/3.60 tff(16201,plain,
% 3.43/3.60 (b(s(s(z)), s(s(s(elem!1))))),
% 3.43/3.60 inference(unit_resolution,[status(thm)],[279, 16200])).
% 3.43/3.60 tff(16202,plain,
% 3.43/3.60 (r(s(s(s(elem!1))), s(s(elem!1)))),
% 3.43/3.60 inference(unit_resolution,[status(thm)],[889, 16199, 51])).
% 3.43/3.60 tff(16203,plain,
% 3.43/3.60 (~b(s(s(elem!1)), s(s(s(elem!1))))),
% 3.43/3.60 inference(unit_resolution,[status(thm)],[1937, 16202, 376, 365, 96])).
% 3.43/3.60 tff(16204,plain,
% 3.43/3.60 (r(s(s(elem!1)), s(s(s(elem!1))))),
% 3.43/3.60 inference(unit_resolution,[status(thm)],[461, 16203, 45])).
% 3.43/3.60 tff(16205,plain,
% 3.43/3.60 (~r(s(s(s(elem!1))), z)),
% 3.43/3.60 inference(unit_resolution,[status(thm)],[1386, 16204, 365, 16202])).
% 3.43/3.60 tff(16206,plain,
% 3.43/3.60 (b(s(s(s(elem!1))), z)),
% 3.43/3.60 inference(unit_resolution,[status(thm)],[94, 16205])).
% 3.43/3.60 tff(16207,plain,
% 3.43/3.60 ($false),
% 3.43/3.60 inference(unit_resolution,[status(thm)],[10468, 166, 10451, 16206, 16201, 122])).
% 3.43/3.60 tff(16208,plain,((~b(s(s(s(elem!1))), s(z))) | (~b(z, s(s(z)))) | (~b(s(s(z)), z)) | (~r(z, s(s(elem!1)))) | (s(s(elem!1)) = s(s(s(elem!1)))) | (~b(s(z), s(s(elem!1)))) | (~r(s(s(z)), s(z))) | b(s(z), s(s(s(elem!1)))) | (~b(s(s(elem!1)), s(z)))), inference(lemma,lemma(discharge,[]))).
% 3.43/3.60 tff(16209,plain,
% 3.43/3.60 (~b(s(s(s(elem!1))), s(z))),
% 3.43/3.60 inference(unit_resolution,[status(thm)],[16208, 365, 122, 10451, 45, 376, 392, 98, 16053])).
% 3.43/3.60 tff(16210,plain,
% 3.43/3.60 (r(s(s(s(elem!1))), s(z))),
% 3.43/3.60 inference(unit_resolution,[status(thm)],[1849, 16209])).
% 3.43/3.60 tff(16211,plain,
% 3.43/3.60 (~b(s(s(s(elem!1))), z)),
% 3.43/3.60 inference(unit_resolution,[status(thm)],[10745, 16210, 10451, 122, 120])).
% 3.43/3.60 tff(16212,plain,
% 3.43/3.60 (r(s(s(s(elem!1))), z)),
% 3.43/3.60 inference(unit_resolution,[status(thm)],[94, 16211])).
% 3.43/3.60 tff(16213,plain,
% 3.43/3.60 ($false),
% 3.43/3.60 inference(unit_resolution,[status(thm)],[10031, 197, 16212, 120, 16210, 16198])).
% 3.43/3.60 tff(16214,plain,((~r(z, s(s(elem!1)))) | (~r(s(z), s(s(z)))) | (~b(z, s(s(z)))) | (~b(s(s(z)), z)) | (s(s(elem!1)) = s(s(s(elem!1)))) | (~b(s(z), s(s(elem!1)))) | (~r(s(s(z)), s(z))) | b(s(z), s(s(s(elem!1)))) | (s(s(s(elem!1))) = s(s(s(z)))) | (~b(s(z), z))), inference(lemma,lemma(discharge,[]))).
% 3.43/3.60 tff(16215,plain,
% 3.43/3.60 (~b(s(s(z)), z)),
% 3.43/3.60 inference(unit_resolution,[status(thm)],[16214, 16065, 10451, 16055, 45, 376, 392, 98, 140, 53])).
% 3.43/3.60 tff(16216,plain,
% 3.43/3.60 (r(s(s(z)), z)),
% 3.43/3.60 inference(unit_resolution,[status(thm)],[186, 16215])).
% 3.43/3.60 tff(16217,plain,
% 3.43/3.60 (~r(s(s(elem!1)), s(s(s(elem!1))))),
% 3.43/3.60 inference(unit_resolution,[status(thm)],[933, 16061, 16055, 350])).
% 3.43/3.60 tff(16218,plain,
% 3.43/3.60 (b(s(s(elem!1)), s(s(s(elem!1))))),
% 3.43/3.60 inference(unit_resolution,[status(thm)],[461, 16217, 45])).
% 3.43/3.60 tff(16219,plain,
% 3.43/3.60 (~b(s(s(z)), s(s(elem!1)))),
% 3.43/3.60 inference(unit_resolution,[status(thm)],[13098, 166, 16218, 16057, 16059])).
% 3.43/3.60 tff(16220,plain,
% 3.43/3.60 (r(s(s(z)), s(s(elem!1)))),
% 3.43/3.60 inference(unit_resolution,[status(thm)],[390, 16219, 52])).
% 3.43/3.60 tff(16221,plain,
% 3.43/3.60 (~b(s(s(elem!1)), s(s(z)))),
% 3.43/3.60 inference(unit_resolution,[status(thm)],[501, 16218, 16056, 16058])).
% 3.43/3.60 tff(16222,plain,
% 3.43/3.60 (r(s(s(elem!1)), s(s(z)))),
% 3.43/3.60 inference(unit_resolution,[status(thm)],[441, 16221, 132])).
% 3.43/3.60 tff(16223,plain,
% 3.43/3.60 ($false),
% 3.43/3.60 inference(unit_resolution,[status(thm)],[12437, 197, 16222, 16220, 16055, 16216])).
% 3.43/3.60 tff(16224,plain,((~r(s(s(s(elem!1))), s(z))) | (s(s(z)) = s(s(elem!1))) | (~b(z, s(s(z)))) | (s(s(elem!1)) = s(s(s(elem!1)))) | (~b(s(z), s(s(elem!1)))) | (~r(s(s(z)), s(z))) | b(s(z), s(s(s(elem!1)))) | (~b(s(z), z))), inference(lemma,lemma(discharge,[]))).
% 3.43/3.60 tff(16225,plain,
% 3.43/3.60 (~r(s(s(s(elem!1))), s(z))),
% 3.43/3.60 inference(unit_resolution,[status(thm)],[16224, 98, 10451, 45, 376, 392, 52, 53])).
% 3.43/3.60 tff(16226,plain,
% 3.43/3.60 (b(s(s(s(elem!1))), s(z))),
% 3.43/3.60 inference(unit_resolution,[status(thm)],[1849, 16225])).
% 3.43/3.60 tff(16227,plain,
% 3.43/3.60 (~b(z, s(z))),
% 3.43/3.60 inference(unit_resolution,[status(thm)],[4277, 16226, 53, 45, 16053])).
% 3.43/3.60 tff(16228,plain,
% 3.43/3.60 (r(z, s(z))),
% 3.43/3.60 inference(unit_resolution,[status(thm)],[321, 16227])).
% 3.43/3.60 tff(16229,plain,
% 3.43/3.60 (~b(s(s(z)), z)),
% 3.43/3.60 inference(unit_resolution,[status(thm)],[16208, 16226, 16055, 10451, 45, 376, 392, 98, 16053])).
% 3.43/3.60 tff(16230,plain,
% 3.43/3.60 (r(s(s(z)), z)),
% 3.43/3.60 inference(unit_resolution,[status(thm)],[186, 16229])).
% 3.43/3.60 tff(16231,plain,
% 3.43/3.60 ($false),
% 3.43/3.60 inference(unit_resolution,[status(thm)],[12271, 16230, 16228, 392, 117])).
% 3.43/3.60 tff(16232,plain,(b(s(z), s(s(s(elem!1)))) | (~r(s(s(z)), s(z))) | (~b(z, s(s(z)))) | (s(s(elem!1)) = s(s(s(elem!1)))) | (~b(s(z), s(s(elem!1)))) | (~b(s(z), z)) | (s(s(z)) = s(s(elem!1)))), inference(lemma,lemma(discharge,[]))).
% 3.43/3.60 tff(16233,plain,
% 3.43/3.60 (b(s(z), s(s(s(elem!1))))),
% 3.43/3.60 inference(unit_resolution,[status(thm)],[16232, 45, 10451, 4143, 376, 53, 16052])).
% 3.43/3.60 tff(16234,plain,
% 3.43/3.60 (~b(s(s(s(elem!1))), s(s(elem!1)))),
% 3.43/3.60 inference(unit_resolution,[status(thm)],[1366, 16233, 376, 16051])).
% 3.43/3.60 tff(16235,plain,
% 3.43/3.60 (r(s(s(s(elem!1))), s(s(elem!1)))),
% 3.43/3.60 inference(unit_resolution,[status(thm)],[889, 16234, 51])).
% 3.43/3.60 tff(16236,plain,
% 3.43/3.60 (~b(z, s(s(elem!1)))),
% 3.43/3.60 inference(unit_resolution,[status(thm)],[8791, 16051, 53, 376])).
% 3.43/3.60 tff(16237,plain,
% 3.43/3.60 (r(z, s(s(elem!1)))),
% 3.43/3.60 inference(unit_resolution,[status(thm)],[1795, 16236])).
% 3.43/3.60 tff(16238,plain,
% 3.43/3.60 (~r(s(s(s(elem!1))), z)),
% 3.43/3.60 inference(unit_resolution,[status(thm)],[1386, 377, 365, 905])).
% 3.43/3.60 tff(16239,plain,
% 3.43/3.60 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(elem!1)))) | (~r(s(s(elem!1)), s(s(s(elem!1))))) | (~r(s(s(z)), s(s(elem!1)))) | (~r(s(s(z)), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, s(s(elem!1)))) | (~r(s(s(elem!1)), s(s(s(elem!1))))) | (~r(s(s(z)), s(s(elem!1)))) | (~r(s(s(z)), z)))),
% 3.43/3.60 inference(rewrite,[status(thm)],[])).
% 3.43/3.60 tff(16240,plain,
% 3.43/3.60 (((~r(s(s(elem!1)), s(s(s(elem!1))))) | (~r(z, s(s(elem!1)))) | (~r(s(s(z)), s(s(elem!1)))) | (~r(s(s(z)), z))) <=> ((~r(z, s(s(elem!1)))) | (~r(s(s(elem!1)), s(s(s(elem!1))))) | (~r(s(s(z)), s(s(elem!1)))) | (~r(s(s(z)), z)))),
% 3.43/3.60 inference(rewrite,[status(thm)],[])).
% 3.43/3.60 tff(16241,plain,
% 3.43/3.60 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(elem!1)), s(s(s(elem!1))))) | (~r(z, s(s(elem!1)))) | (~r(s(s(z)), s(s(elem!1)))) | (~r(s(s(z)), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(elem!1)))) | (~r(s(s(elem!1)), s(s(s(elem!1))))) | (~r(s(s(z)), s(s(elem!1)))) | (~r(s(s(z)), z))))),
% 3.43/3.60 inference(monotonicity,[status(thm)],[16240])).
% 3.43/3.60 tff(16242,plain,
% 3.43/3.60 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(elem!1)), s(s(s(elem!1))))) | (~r(z, s(s(elem!1)))) | (~r(s(s(z)), s(s(elem!1)))) | (~r(s(s(z)), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, s(s(elem!1)))) | (~r(s(s(elem!1)), s(s(s(elem!1))))) | (~r(s(s(z)), s(s(elem!1)))) | (~r(s(s(z)), z)))),
% 3.43/3.60 inference(transitivity,[status(thm)],[16241, 16239])).
% 3.43/3.60 tff(16243,plain,
% 3.43/3.60 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(elem!1)), s(s(s(elem!1))))) | (~r(z, s(s(elem!1)))) | (~r(s(s(z)), s(s(elem!1)))) | (~r(s(s(z)), z)))),
% 3.43/3.60 inference(quant_inst,[status(thm)],[])).
% 3.43/3.60 tff(16244,plain,
% 3.43/3.60 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, s(s(elem!1)))) | (~r(s(s(elem!1)), s(s(s(elem!1))))) | (~r(s(s(z)), s(s(elem!1)))) | (~r(s(s(z)), z))),
% 3.43/3.60 inference(modus_ponens,[status(thm)],[16243, 16242])).
% 3.43/3.60 tff(16245,plain,
% 3.43/3.60 (~r(s(s(z)), z)),
% 3.43/3.60 inference(unit_resolution,[status(thm)],[16244, 197, 377, 12431, 365])).
% 3.43/3.60 tff(16246,plain,
% 3.43/3.60 (b(s(s(z)), z)),
% 3.43/3.60 inference(unit_resolution,[status(thm)],[186, 16245])).
% 3.43/3.60 tff(16247,plain,
% 3.43/3.60 ($false),
% 3.43/3.60 inference(unit_resolution,[status(thm)],[12445, 166, 241, 53, 10451, 121, 16246])).
% 3.43/3.60 tff(16248,plain,((~b(s(z), z)) | (~b(s(z), s(s(s(elem!1))))) | (~b(z, s(s(z)))) | (~b(s(s(s(elem!1))), z)) | (~r(s(s(elem!1)), s(s(s(elem!1))))) | (~r(z, s(s(elem!1)))) | (s(s(z)) = s(s(elem!1))) | (~b(s(z), s(s(elem!1))))), inference(lemma,lemma(discharge,[]))).
% 3.43/3.60 tff(16249,plain,
% 3.43/3.60 (~b(s(s(s(elem!1))), z)),
% 3.43/3.60 inference(unit_resolution,[status(thm)],[16248, 377, 10451, 365, 53, 241, 52, 376])).
% 3.43/3.60 tff(16250,plain,
% 3.43/3.60 ($false),
% 3.43/3.60 inference(unit_resolution,[status(thm)],[94, 16249, 16238])).
% 3.43/3.60 tff(16251,plain,((~r(s(s(elem!1)), s(s(s(elem!1))))) | (~b(z, s(s(z)))) | (~r(z, s(s(elem!1)))) | (~b(s(z), z)) | (~b(s(z), s(s(s(elem!1))))) | (s(s(z)) = s(s(elem!1))) | (~b(s(z), s(s(elem!1)))) | (~r(s(s(s(elem!1))), s(s(elem!1))))), inference(lemma,lemma(discharge,[]))).
% 3.43/3.60 tff(16252,plain,
% 3.43/3.60 (~r(s(s(elem!1)), s(s(s(elem!1))))),
% 3.43/3.60 inference(unit_resolution,[status(thm)],[16251, 16237, 10451, 53, 16233, 16052, 376, 16235])).
% 3.43/3.60 tff(16253,plain,
% 3.43/3.60 (b(s(s(elem!1)), s(s(s(elem!1))))),
% 3.43/3.60 inference(unit_resolution,[status(thm)],[461, 16252, 45])).
% 3.43/3.60 tff(16254,plain,
% 3.43/3.60 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(s(s(elem!1)), z)) | (~b(s(z), s(s(elem!1)))) | (~b(z, s(z))) | (~b(s(s(elem!1)), s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(s(s(elem!1)), z)) | (~b(s(z), s(s(elem!1)))) | (~b(z, s(z))) | (~b(s(s(elem!1)), s(z))))),
% 3.43/3.60 inference(rewrite,[status(thm)],[])).
% 3.43/3.60 tff(16255,plain,
% 3.43/3.60 (((~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(s(z), s(s(elem!1)))) | (~b(z, s(z))) | (~b(s(s(elem!1)), s(z))) | (~b(s(s(elem!1)), z))) <=> ((~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(s(s(elem!1)), z)) | (~b(s(z), s(s(elem!1)))) | (~b(z, s(z))) | (~b(s(s(elem!1)), s(z))))),
% 3.43/3.60 inference(rewrite,[status(thm)],[])).
% 3.43/3.60 tff(16256,plain,
% 3.43/3.60 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(s(z), s(s(elem!1)))) | (~b(z, s(z))) | (~b(s(s(elem!1)), s(z))) | (~b(s(s(elem!1)), z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(s(s(elem!1)), z)) | (~b(s(z), s(s(elem!1)))) | (~b(z, s(z))) | (~b(s(s(elem!1)), s(z)))))),
% 3.43/3.60 inference(monotonicity,[status(thm)],[16255])).
% 3.43/3.60 tff(16257,plain,
% 3.43/3.60 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(s(z), s(s(elem!1)))) | (~b(z, s(z))) | (~b(s(s(elem!1)), s(z))) | (~b(s(s(elem!1)), z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(s(s(elem!1)), z)) | (~b(s(z), s(s(elem!1)))) | (~b(z, s(z))) | (~b(s(s(elem!1)), s(z))))),
% 3.43/3.60 inference(transitivity,[status(thm)],[16256, 16254])).
% 3.43/3.60 tff(16258,plain,
% 3.43/3.60 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(s(z), s(s(elem!1)))) | (~b(z, s(z))) | (~b(s(s(elem!1)), s(z))) | (~b(s(s(elem!1)), z)))),
% 3.43/3.60 inference(quant_inst,[status(thm)],[])).
% 3.43/3.60 tff(16259,plain,
% 3.43/3.60 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(s(s(elem!1)), z)) | (~b(s(z), s(s(elem!1)))) | (~b(z, s(z))) | (~b(s(s(elem!1)), s(z)))),
% 3.43/3.60 inference(modus_ponens,[status(thm)],[16258, 16257])).
% 3.43/3.60 tff(16260,plain,
% 3.43/3.60 (~b(s(s(elem!1)), z)),
% 3.43/3.60 inference(unit_resolution,[status(thm)],[16259, 166, 376, 463, 118, 310])).
% 3.43/3.60 tff(16261,plain,
% 3.43/3.60 (r(s(s(elem!1)), z)),
% 3.43/3.60 inference(unit_resolution,[status(thm)],[608, 16260])).
% 3.43/3.60 tff(16262,plain,
% 3.43/3.60 (~b(z, s(s(elem!1)))),
% 3.43/3.60 inference(unit_resolution,[status(thm)],[8791, 310, 53, 376])).
% 3.43/3.60 tff(16263,plain,
% 3.43/3.60 (r(z, s(s(elem!1)))),
% 3.43/3.60 inference(unit_resolution,[status(thm)],[1795, 16262])).
% 3.43/3.60 tff(16264,plain,
% 3.43/3.60 (~b(s(s(s(elem!1))), z)),
% 3.43/3.60 inference(unit_resolution,[status(thm)],[7322, 118, 376, 53, 241])).
% 3.43/3.60 tff(16265,plain,
% 3.43/3.60 (r(s(s(s(elem!1))), z)),
% 3.43/3.60 inference(unit_resolution,[status(thm)],[94, 16264])).
% 3.43/3.60 tff(16266,plain,
% 3.43/3.60 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), z)) | (~r(s(s(s(elem!1))), s(s(elem!1)))) | (~r(z, s(s(elem!1)))) | (~r(s(s(elem!1)), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(elem!1))), z)) | (~r(s(s(s(elem!1))), s(s(elem!1)))) | (~r(z, s(s(elem!1)))) | (~r(s(s(elem!1)), z)))),
% 3.43/3.60 inference(rewrite,[status(thm)],[])).
% 3.43/3.60 tff(16267,plain,
% 3.43/3.60 (((~r(s(s(elem!1)), z)) | (~r(z, s(s(elem!1)))) | (~r(s(s(s(elem!1))), s(s(elem!1)))) | (~r(s(s(s(elem!1))), z))) <=> ((~r(s(s(s(elem!1))), z)) | (~r(s(s(s(elem!1))), s(s(elem!1)))) | (~r(z, s(s(elem!1)))) | (~r(s(s(elem!1)), z)))),
% 3.43/3.60 inference(rewrite,[status(thm)],[])).
% 3.43/3.60 tff(16268,plain,
% 3.43/3.60 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(elem!1)), z)) | (~r(z, s(s(elem!1)))) | (~r(s(s(s(elem!1))), s(s(elem!1)))) | (~r(s(s(s(elem!1))), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), z)) | (~r(s(s(s(elem!1))), s(s(elem!1)))) | (~r(z, s(s(elem!1)))) | (~r(s(s(elem!1)), z))))),
% 3.43/3.61 inference(monotonicity,[status(thm)],[16267])).
% 3.43/3.61 tff(16269,plain,
% 3.43/3.61 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(elem!1)), z)) | (~r(z, s(s(elem!1)))) | (~r(s(s(s(elem!1))), s(s(elem!1)))) | (~r(s(s(s(elem!1))), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(elem!1))), z)) | (~r(s(s(s(elem!1))), s(s(elem!1)))) | (~r(z, s(s(elem!1)))) | (~r(s(s(elem!1)), z)))),
% 3.43/3.61 inference(transitivity,[status(thm)],[16268, 16266])).
% 3.43/3.61 tff(16270,plain,
% 3.43/3.61 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(elem!1)), z)) | (~r(z, s(s(elem!1)))) | (~r(s(s(s(elem!1))), s(s(elem!1)))) | (~r(s(s(s(elem!1))), z)))),
% 3.43/3.61 inference(quant_inst,[status(thm)],[])).
% 3.43/3.61 tff(16271,plain,
% 3.43/3.61 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(elem!1))), z)) | (~r(s(s(s(elem!1))), s(s(elem!1)))) | (~r(z, s(s(elem!1)))) | (~r(s(s(elem!1)), z))),
% 3.43/3.61 inference(modus_ponens,[status(thm)],[16270, 16269])).
% 3.43/3.61 tff(16272,plain,
% 3.43/3.61 ($false),
% 3.43/3.61 inference(unit_resolution,[status(thm)],[16271, 197, 16265, 16263, 905, 16261])).
% 3.43/3.61 tff(16273,plain,((~b(z, s(z))) | (~r(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(z), s(s(elem!1)))) | (~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(s(s(elem!1)), s(z))) | (~b(s(z), z)) | (~b(s(z), s(s(s(elem!1)))))), inference(lemma,lemma(discharge,[]))).
% 3.43/3.61 tff(16274,plain,
% 3.43/3.61 (~b(z, s(z))),
% 3.43/3.61 inference(unit_resolution,[status(thm)],[16273, 16235, 376, 16253, 16051, 53, 16233])).
% 3.43/3.61 tff(16275,plain,
% 3.43/3.61 (r(z, s(z))),
% 3.43/3.61 inference(unit_resolution,[status(thm)],[321, 16274])).
% 3.43/3.61 tff(16276,plain,
% 3.43/3.61 (~b(s(s(s(elem!1))), s(z))),
% 3.43/3.61 inference(unit_resolution,[status(thm)],[1994, 16253, 16051, 16233])).
% 3.43/3.61 tff(16277,plain,
% 3.43/3.61 (r(s(s(s(elem!1))), s(z))),
% 3.43/3.61 inference(unit_resolution,[status(thm)],[1849, 16276])).
% 3.43/3.61 tff(16278,plain,
% 3.43/3.61 (~r(s(z), s(s(z)))),
% 3.43/3.61 inference(unit_resolution,[status(thm)],[14139, 323, 392, 866])).
% 3.43/3.61 tff(16279,plain,
% 3.43/3.61 (b(s(z), s(s(z)))),
% 3.43/3.61 inference(unit_resolution,[status(thm)],[427, 16278])).
% 3.43/3.61 tff(16280,plain,
% 3.43/3.61 (~b(s(s(z)), s(s(elem!1)))),
% 3.43/3.61 inference(unit_resolution,[status(thm)],[14016, 16279, 463, 53, 10451, 241])).
% 3.43/3.61 tff(16281,plain,
% 3.43/3.61 (r(s(s(z)), s(s(elem!1)))),
% 3.43/3.61 inference(unit_resolution,[status(thm)],[390, 16280, 52])).
% 3.43/3.61 tff(16282,plain,
% 3.43/3.61 ($false),
% 3.43/3.61 inference(unit_resolution,[status(thm)],[12437, 197, 393, 333, 365, 866])).
% 3.43/3.61 tff(16283,plain,((~r(s(s(elem!1)), s(s(z)))) | (~r(s(s(z)), s(s(elem!1)))) | (~r(z, s(s(elem!1)))) | (~r(s(s(z)), z))), inference(lemma,lemma(discharge,[]))).
% 3.43/3.61 tff(16284,plain,
% 3.43/3.61 (~r(s(s(elem!1)), s(s(z)))),
% 3.43/3.61 inference(unit_resolution,[status(thm)],[16283, 16281, 365, 866])).
% 3.43/3.61 tff(16285,plain,
% 3.43/3.61 (b(s(s(elem!1)), s(s(z)))),
% 3.43/3.61 inference(unit_resolution,[status(thm)],[441, 16284, 132])).
% 3.43/3.61 tff(16286,plain,
% 3.43/3.61 (~r(s(s(s(elem!1))), s(s(z)))),
% 3.43/3.61 inference(unit_resolution,[status(thm)],[14314, 154, 323, 866])).
% 3.43/3.61 tff(16287,plain,
% 3.43/3.61 (r(s(s(z)), s(s(s(elem!1))))),
% 3.43/3.61 inference(unit_resolution,[status(thm)],[501, 16286, 463, 405])).
% 3.43/3.61 tff(16288,plain,
% 3.43/3.61 ($false),
% 3.43/3.61 inference(unit_resolution,[status(thm)],[14322, 197, 154, 323, 16287, 866])).
% 3.43/3.61 tff(16289,plain,((~r(s(s(s(elem!1))), z)) | (~r(z, s(z))) | (~r(s(s(z)), z)) | (~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(s(s(elem!1)), s(s(z))))), inference(lemma,lemma(discharge,[]))).
% 3.43/3.61 tff(16290,plain,
% 3.43/3.61 (~r(s(s(s(elem!1))), z)),
% 3.43/3.61 inference(unit_resolution,[status(thm)],[16289, 323, 866, 463, 16285])).
% 3.43/3.61 tff(16291,plain,
% 3.43/3.61 (b(s(s(s(elem!1))), z)),
% 3.43/3.61 inference(unit_resolution,[status(thm)],[94, 16290])).
% 3.43/3.61 tff(16292,plain,
% 3.43/3.61 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(z, s(s(z)))) | (~b(s(z), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), z)) | (~b(s(s(elem!1)), s(s(z)))) | (~b(s(s(elem!1)), s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(z, s(s(z)))) | (~b(s(z), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), z)) | (~b(s(s(elem!1)), s(s(z)))) | (~b(s(s(elem!1)), s(z))))),
% 3.43/3.61 inference(rewrite,[status(thm)],[])).
% 3.43/3.61 tff(16293,plain,
% 3.43/3.61 (((~b(z, s(s(z)))) | (~b(s(s(elem!1)), s(s(z)))) | (~b(s(s(s(elem!1))), z)) | (~b(s(z), s(s(s(elem!1))))) | (~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(s(s(elem!1)), s(z)))) <=> ((~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(z, s(s(z)))) | (~b(s(z), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), z)) | (~b(s(s(elem!1)), s(s(z)))) | (~b(s(s(elem!1)), s(z))))),
% 3.43/3.61 inference(rewrite,[status(thm)],[])).
% 3.43/3.61 tff(16294,plain,
% 3.43/3.61 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(z)))) | (~b(s(s(elem!1)), s(s(z)))) | (~b(s(s(s(elem!1))), z)) | (~b(s(z), s(s(s(elem!1))))) | (~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(s(s(elem!1)), s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(z, s(s(z)))) | (~b(s(z), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), z)) | (~b(s(s(elem!1)), s(s(z)))) | (~b(s(s(elem!1)), s(z)))))),
% 3.43/3.61 inference(monotonicity,[status(thm)],[16293])).
% 3.43/3.61 tff(16295,plain,
% 3.43/3.61 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(z)))) | (~b(s(s(elem!1)), s(s(z)))) | (~b(s(s(s(elem!1))), z)) | (~b(s(z), s(s(s(elem!1))))) | (~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(s(s(elem!1)), s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(z, s(s(z)))) | (~b(s(z), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), z)) | (~b(s(s(elem!1)), s(s(z)))) | (~b(s(s(elem!1)), s(z))))),
% 3.43/3.61 inference(transitivity,[status(thm)],[16294, 16292])).
% 3.43/3.61 tff(16296,plain,
% 3.43/3.61 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(z)))) | (~b(s(s(elem!1)), s(s(z)))) | (~b(s(s(s(elem!1))), z)) | (~b(s(z), s(s(s(elem!1))))) | (~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(s(s(elem!1)), s(z))))),
% 3.43/3.61 inference(quant_inst,[status(thm)],[])).
% 3.43/3.61 tff(16297,plain,
% 3.43/3.61 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(z, s(s(z)))) | (~b(s(z), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), z)) | (~b(s(s(elem!1)), s(s(z)))) | (~b(s(s(elem!1)), s(z)))),
% 3.43/3.61 inference(modus_ponens,[status(thm)],[16296, 16295])).
% 3.43/3.61 tff(16298,plain,
% 3.43/3.61 ($false),
% 3.43/3.61 inference(unit_resolution,[status(thm)],[16297, 166, 463, 241, 16285, 10451, 310, 16291])).
% 3.43/3.61 tff(16299,plain,((~r(z, s(z))) | (~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(s(z), s(s(s(elem!1))))) | (~b(z, s(s(z)))) | (~b(s(s(elem!1)), s(z))) | (~r(s(s(z)), z)) | (~r(z, s(s(elem!1)))) | (s(s(z)) = s(s(elem!1))) | (~b(s(z), z)) | (~r(s(s(z)), s(z)))), inference(lemma,lemma(discharge,[]))).
% 3.43/3.61 tff(16300,plain,
% 3.43/3.61 (~r(s(s(z)), z)),
% 3.43/3.61 inference(unit_resolution,[status(thm)],[16299, 16275, 16233, 10451, 16051, 16253, 16237, 16052, 53, 4143])).
% 3.43/3.61 tff(16301,plain,
% 3.43/3.61 (b(s(s(z)), z)),
% 3.43/3.61 inference(unit_resolution,[status(thm)],[186, 16300])).
% 3.43/3.61 tff(16302,plain,
% 3.43/3.61 (~b(s(z), s(s(z)))),
% 3.43/3.61 inference(unit_resolution,[status(thm)],[12846, 16301, 53, 10451])).
% 3.43/3.61 tff(16303,plain,
% 3.43/3.61 (r(s(z), s(s(z)))),
% 3.43/3.61 inference(unit_resolution,[status(thm)],[427, 16302])).
% 3.43/3.61 tff(16304,plain,
% 3.43/3.61 (~b(s(s(s(elem!1))), z)),
% 3.43/3.61 inference(unit_resolution,[status(thm)],[10745, 16303, 10451, 16277, 16301])).
% 3.43/3.61 tff(16305,plain,
% 3.43/3.61 (r(s(s(s(elem!1))), z)),
% 3.43/3.61 inference(unit_resolution,[status(thm)],[94, 16304])).
% 3.43/3.61 tff(16306,plain,
% 3.43/3.61 ($false),
% 3.43/3.61 inference(unit_resolution,[status(thm)],[10031, 197, 16305, 16303, 16277, 16275])).
% 3.43/3.61 tff(16307,plain,((s(s(elem!1)) = s(s(s(elem!1)))) | (~b(z, s(s(z)))) | (~b(s(z), z)) | (~b(s(z), s(s(elem!1)))) | b(s(s(z)), s(z))), inference(lemma,lemma(discharge,[]))).
% 3.43/3.61 tff(16308,plain,
% 3.43/3.61 (s(s(elem!1)) = s(s(s(elem!1)))),
% 3.43/3.61 inference(unit_resolution,[status(thm)],[16307, 53, 10451, 376, 3936])).
% 3.43/3.61 tff(16309,plain,
% 3.43/3.61 (s(s(s(elem!1))) = s(elem!1)),
% 3.43/3.61 inference(unit_resolution,[status(thm)],[2594, 16308])).
% 3.43/3.61 tff(16310,plain,
% 3.43/3.61 (s(elem!1) = s(s(s(elem!1)))),
% 3.43/3.61 inference(symmetry,[status(thm)],[16309])).
% 3.43/3.61 tff(16311,plain,
% 3.43/3.61 (inj_0(s(elem!1)) = inj_0(s(s(s(elem!1))))),
% 3.43/3.61 inference(monotonicity,[status(thm)],[16310])).
% 3.43/3.61 tff(16312,plain,
% 3.43/3.61 (elem!1 = s(s(s(elem!1)))),
% 3.43/3.61 inference(transitivity,[status(thm)],[1170, 16311, 104, 16308])).
% 3.43/3.61 tff(16313,plain,
% 3.43/3.61 ((z = elem!1) <=> (z = s(s(s(elem!1))))),
% 3.43/3.61 inference(monotonicity,[status(thm)],[16312])).
% 3.43/3.61 tff(16314,plain,
% 3.43/3.61 ((z = elem!1) <=> (s(s(s(elem!1))) = z)),
% 3.43/3.61 inference(transitivity,[status(thm)],[16313, 7746])).
% 3.43/3.61 tff(16315,plain,
% 3.43/3.61 ((s(s(s(elem!1))) = z) <=> (z = elem!1)),
% 3.43/3.61 inference(symmetry,[status(thm)],[16314])).
% 3.43/3.61 tff(16316,plain,
% 3.43/3.61 ((~(s(s(s(elem!1))) = z)) <=> (~(z = elem!1))),
% 3.43/3.61 inference(monotonicity,[status(thm)],[16315])).
% 3.43/3.61 tff(16317,plain,
% 3.43/3.61 (~(z = elem!1)),
% 3.43/3.61 inference(modus_ponens,[status(thm)],[89, 16316])).
% 3.43/3.61 tff(16318,plain,
% 3.43/3.61 ((s(s(elem!1)) = elem!1) <=> (s(s(s(elem!1))) = elem!1)),
% 3.43/3.61 inference(monotonicity,[status(thm)],[16308])).
% 3.43/3.61 tff(16319,plain,
% 3.43/3.61 ((s(s(elem!1)) = elem!1) <=> (elem!1 = s(s(s(elem!1))))),
% 3.43/3.61 inference(transitivity,[status(thm)],[16318, 5406])).
% 3.43/3.61 tff(16320,plain,
% 3.43/3.61 (s(s(elem!1)) = elem!1),
% 3.43/3.61 inference(unit_resolution,[status(thm)],[10139, 16309])).
% 3.43/3.61 tff(16321,plain,
% 3.43/3.61 (elem!1 = s(s(s(elem!1)))),
% 3.43/3.61 inference(modus_ponens,[status(thm)],[16320, 16319])).
% 3.43/3.61 tff(16322,plain,
% 3.43/3.61 (~b(s(s(elem!1)), s(z))),
% 3.43/3.61 inference(unit_resolution,[status(thm)],[8791, 1820, 53, 376])).
% 3.43/3.61 tff(16323,plain,
% 3.43/3.61 (~b(s(s(s(elem!1))), s(z))),
% 3.43/3.61 inference(unit_resolution,[status(thm)],[4570, 16322, 334])).
% 3.43/3.61 tff(16324,plain,
% 3.43/3.61 (r(s(s(s(elem!1))), s(z))),
% 3.43/3.61 inference(unit_resolution,[status(thm)],[1849, 16323])).
% 3.43/3.61 tff(16325,plain,
% 3.43/3.61 (~b(z, s(z))),
% 3.43/3.61 inference(unit_resolution,[status(thm)],[15822, 16324, 10451, 376, 392, 16322])).
% 3.43/3.61 tff(16326,plain,
% 3.43/3.61 (r(z, s(z))),
% 3.43/3.61 inference(unit_resolution,[status(thm)],[321, 16325])).
% 3.43/3.61 tff(16327,plain,
% 3.43/3.61 (r(s(s(elem!1)), s(z))),
% 3.43/3.61 inference(unit_resolution,[status(thm)],[1912, 16322])).
% 3.43/3.61 tff(16328,plain,
% 3.43/3.61 ($false),
% 3.43/3.61 inference(unit_resolution,[status(thm)],[11138, 15837, 120, 10451, 4577, 350, 323, 1820])).
% 3.43/3.61 tff(16329,plain,((~r(s(z), s(s(z)))) | (~b(z, s(s(z)))) | (~r(s(s(elem!1)), s(z))) | (~r(s(s(s(elem!1))), s(z))) | (~r(z, s(z))) | (~b(z, s(s(elem!1)))) | (~r(s(s(z)), s(z)))), inference(lemma,lemma(discharge,[]))).
% 3.43/3.61 tff(16330,plain,
% 3.43/3.61 (~r(s(z), s(s(z)))),
% 3.43/3.61 inference(unit_resolution,[status(thm)],[16329, 16327, 10451, 16324, 16326, 1820, 392])).
% 3.43/3.61 tff(16331,plain,
% 3.43/3.61 (b(s(z), s(s(z)))),
% 3.43/3.61 inference(unit_resolution,[status(thm)],[427, 16330])).
% 3.43/3.61 tff(16332,plain,
% 3.43/3.61 (~b(s(s(z)), z)),
% 3.43/3.61 inference(unit_resolution,[status(thm)],[12846, 16331, 53, 10451])).
% 3.43/3.61 tff(16333,plain,
% 3.43/3.61 (r(s(s(z)), z)),
% 3.43/3.61 inference(unit_resolution,[status(thm)],[186, 16332])).
% 3.43/3.61 tff(16334,plain,
% 3.43/3.61 (~r(s(z), s(s(s(z))))),
% 3.43/3.61 inference(unit_resolution,[status(thm)],[1661, 16333, 392, 16326])).
% 3.43/3.61 tff(16335,plain,
% 3.43/3.61 (b(s(z), s(s(s(z))))),
% 3.43/3.61 inference(unit_resolution,[status(thm)],[1674, 16334])).
% 3.43/3.61 tff(16336,plain,
% 3.43/3.61 (~r(s(s(s(z))), z)),
% 3.43/3.61 inference(unit_resolution,[status(thm)],[8748, 16335, 16331, 16326, 16333])).
% 3.43/3.61 tff(16337,plain,
% 3.43/3.61 ((~b(s(s(s(elem!1))), z)) <=> (~b(s(s(elem!1)), z))),
% 3.43/3.61 inference(monotonicity,[status(thm)],[4323])).
% 3.43/3.61 tff(16338,plain,
% 3.43/3.61 (~b(z, s(z))),
% 3.43/3.61 inference(unit_resolution,[status(thm)],[7322, 121, 376, 53, 5555])).
% 3.43/3.61 tff(16339,plain,
% 3.43/3.61 (r(z, s(z))),
% 3.43/3.61 inference(unit_resolution,[status(thm)],[321, 16338])).
% 3.43/3.61 tff(16340,plain,
% 3.43/3.61 (~b(z, s(s(s(elem!1))))),
% 3.43/3.61 inference(unit_resolution,[status(thm)],[1470, 121, 53, 5555])).
% 3.43/3.61 tff(16341,plain,
% 3.43/3.61 (~b(z, s(s(elem!1)))),
% 3.43/3.61 inference(unit_resolution,[status(thm)],[8327, 16340, 4031])).
% 3.43/3.61 tff(16342,plain,
% 3.43/3.61 (r(z, s(s(elem!1)))),
% 3.43/3.61 inference(unit_resolution,[status(thm)],[1795, 16341])).
% 3.43/3.61 tff(16343,plain,
% 3.43/3.61 (~r(s(z), z)),
% 3.43/3.61 inference(unit_resolution,[status(thm)],[8426, 4577, 323, 365])).
% 3.43/3.61 tff(16344,plain,
% 3.43/3.61 (b(s(z), z)),
% 3.43/3.61 inference(unit_resolution,[status(thm)],[230, 16343])).
% 3.43/3.61 tff(16345,plain,
% 3.43/3.61 (~b(s(s(z)), s(s(elem!1)))),
% 3.43/3.61 inference(unit_resolution,[status(thm)],[12429, 16344, 241, 10451, 121, 376])).
% 3.43/3.61 tff(16346,plain,
% 3.43/3.61 (r(s(s(z)), s(s(elem!1)))),
% 3.43/3.61 inference(unit_resolution,[status(thm)],[390, 16345, 52])).
% 3.43/3.61 tff(16347,plain,
% 3.43/3.61 (~r(s(s(z)), z)),
% 3.43/3.61 inference(unit_resolution,[status(thm)],[15264, 16346, 365, 4577])).
% 3.43/3.61 tff(16348,plain,
% 3.43/3.61 (b(s(s(z)), z)),
% 3.43/3.61 inference(unit_resolution,[status(thm)],[186, 16347])).
% 3.43/3.61 tff(16349,plain,
% 3.43/3.61 ($false),
% 3.43/3.61 inference(unit_resolution,[status(thm)],[12445, 166, 241, 16344, 10451, 121, 16348])).
% 3.43/3.61 tff(16350,plain,((~r(s(s(elem!1)), s(z))) | (~b(s(z), s(s(s(elem!1))))) | (~b(z, s(s(z)))) | (~b(s(s(s(elem!1))), z)) | (~r(z, s(s(elem!1)))) | (s(s(z)) = s(s(elem!1))) | (~b(s(z), s(s(elem!1)))) | (~r(z, s(z)))), inference(lemma,lemma(discharge,[]))).
% 3.43/3.61 tff(16351,plain,
% 3.43/3.61 (~r(s(s(elem!1)), s(z))),
% 3.43/3.61 inference(unit_resolution,[status(thm)],[16350, 16342, 10451, 121, 16339, 6641, 376, 5555])).
% 3.43/3.61 tff(16352,plain,
% 3.43/3.61 (b(s(s(elem!1)), s(z))),
% 3.43/3.61 inference(unit_resolution,[status(thm)],[1912, 16351])).
% 3.43/3.61 tff(16353,plain,
% 3.43/3.61 (b(s(s(s(elem!1))), s(z))),
% 3.43/3.61 inference(unit_resolution,[status(thm)],[3849, 16352, 334])).
% 3.43/3.61 tff(16354,plain,
% 3.43/3.61 (b(s(s(elem!1)), s(s(z))) <=> b(s(s(s(elem!1))), s(s(z)))),
% 3.43/3.61 inference(monotonicity,[status(thm)],[334])).
% 3.43/3.61 tff(16355,plain,
% 3.43/3.61 (~r(s(s(elem!1)), s(s(z)))),
% 3.43/3.61 inference(unit_resolution,[status(thm)],[12447, 16342, 10451, 121, 53, 5555, 6641, 376])).
% 3.43/3.61 tff(16356,plain,
% 3.43/3.61 (b(s(s(elem!1)), s(s(z)))),
% 3.43/3.61 inference(unit_resolution,[status(thm)],[441, 16355, 13569])).
% 3.43/3.61 tff(16357,plain,
% 3.43/3.61 (b(s(s(s(elem!1))), s(s(z)))),
% 3.43/3.61 inference(modus_ponens,[status(thm)],[16356, 16354])).
% 3.43/3.61 tff(16358,plain,
% 3.43/3.61 (~b(s(s(z)), z)),
% 3.43/3.61 inference(unit_resolution,[status(thm)],[10459, 121, 10451, 16357])).
% 3.43/3.61 tff(16359,plain,
% 3.43/3.61 (r(s(s(z)), z)),
% 3.43/3.61 inference(unit_resolution,[status(thm)],[186, 16358])).
% 3.43/3.61 tff(16360,plain,
% 3.43/3.61 (~r(s(z), s(s(s(z))))),
% 3.43/3.61 inference(unit_resolution,[status(thm)],[1661, 16359, 392, 16339])).
% 3.43/3.61 tff(16361,plain,
% 3.43/3.61 (b(s(z), s(s(s(z))))),
% 3.43/3.61 inference(unit_resolution,[status(thm)],[1674, 16360])).
% 3.43/3.61 tff(16362,plain,
% 3.43/3.61 (~b(s(s(s(z))), s(s(s(elem!1))))),
% 3.43/3.61 inference(unit_resolution,[status(thm)],[8841, 16361, 16353, 5555])).
% 3.43/3.61 tff(16363,plain,
% 3.43/3.61 (~b(s(s(s(z))), elem!1)),
% 3.43/3.61 inference(unit_resolution,[status(thm)],[4078, 16362, 4031])).
% 3.43/3.61 tff(16364,plain,
% 3.43/3.61 (r(s(s(s(z))), elem!1)),
% 3.43/3.61 inference(unit_resolution,[status(thm)],[2826, 16363, 4027])).
% 3.43/3.61 tff(16365,plain,
% 3.43/3.61 (r(s(s(s(z))), s(s(elem!1)))),
% 3.43/3.61 inference(modus_ponens,[status(thm)],[16364, 4026])).
% 3.43/3.61 tff(16366,plain,
% 3.43/3.61 (r(s(s(s(z))), s(s(s(elem!1))))),
% 3.43/3.61 inference(modus_ponens,[status(thm)],[16365, 4024])).
% 3.43/3.61 tff(16367,plain,
% 3.43/3.61 (~b(s(s(z)), s(s(s(z))))),
% 3.43/3.61 inference(unit_resolution,[status(thm)],[16037, 16361, 10451, 53, 121, 5555])).
% 3.43/3.61 tff(16368,plain,
% 3.43/3.61 (r(s(s(z)), s(s(s(z))))),
% 3.43/3.61 inference(unit_resolution,[status(thm)],[1730, 16367])).
% 3.43/3.61 tff(16369,plain,
% 3.43/3.61 (~r(s(z), s(s(z)))),
% 3.43/3.61 inference(unit_resolution,[status(thm)],[14139, 16359, 392, 16339])).
% 3.43/3.61 tff(16370,plain,
% 3.43/3.61 (b(s(z), s(s(z)))),
% 3.43/3.61 inference(unit_resolution,[status(thm)],[427, 16369])).
% 3.43/3.61 tff(16371,plain,
% 3.43/3.61 (~r(s(s(s(z))), z)),
% 3.43/3.61 inference(unit_resolution,[status(thm)],[8748, 16370, 16361, 16339, 16359])).
% 3.43/3.61 tff(16372,plain,
% 3.43/3.61 (b(s(s(s(z))), z)),
% 3.43/3.61 inference(unit_resolution,[status(thm)],[1713, 16371])).
% 3.43/3.61 tff(16373,plain,
% 3.43/3.61 (~b(z, s(s(s(z))))),
% 3.43/3.61 inference(unit_resolution,[status(thm)],[1708, 16372, 53, 16361])).
% 3.43/3.61 tff(16374,plain,
% 3.43/3.61 (r(z, s(s(s(z))))),
% 3.43/3.61 inference(unit_resolution,[status(thm)],[1697, 16373])).
% 3.43/3.61 tff(16375,plain,
% 3.43/3.61 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(z))), s(s(s(elem!1))))) | (~r(z, s(s(s(z))))) | (~r(s(s(z)), z)) | (~r(s(s(z)), s(s(s(z))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(z))), s(s(s(elem!1))))) | (~r(z, s(s(s(z))))) | (~r(s(s(z)), z)) | (~r(s(s(z)), s(s(s(z))))))),
% 3.43/3.61 inference(rewrite,[status(thm)],[])).
% 3.43/3.61 tff(16376,plain,
% 3.43/3.61 (((~r(s(s(s(z))), s(s(s(elem!1))))) | (~r(z, s(s(s(z))))) | (~r(s(s(z)), s(s(s(z))))) | (~r(s(s(z)), z))) <=> ((~r(s(s(s(z))), s(s(s(elem!1))))) | (~r(z, s(s(s(z))))) | (~r(s(s(z)), z)) | (~r(s(s(z)), s(s(s(z))))))),
% 3.43/3.61 inference(rewrite,[status(thm)],[])).
% 3.43/3.61 tff(16377,plain,
% 3.43/3.61 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(z))), s(s(s(elem!1))))) | (~r(z, s(s(s(z))))) | (~r(s(s(z)), s(s(s(z))))) | (~r(s(s(z)), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(z))), s(s(s(elem!1))))) | (~r(z, s(s(s(z))))) | (~r(s(s(z)), z)) | (~r(s(s(z)), s(s(s(z)))))))),
% 3.43/3.61 inference(monotonicity,[status(thm)],[16376])).
% 3.43/3.61 tff(16378,plain,
% 3.43/3.61 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(z))), s(s(s(elem!1))))) | (~r(z, s(s(s(z))))) | (~r(s(s(z)), s(s(s(z))))) | (~r(s(s(z)), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(z))), s(s(s(elem!1))))) | (~r(z, s(s(s(z))))) | (~r(s(s(z)), z)) | (~r(s(s(z)), s(s(s(z))))))),
% 3.43/3.61 inference(transitivity,[status(thm)],[16377, 16375])).
% 3.43/3.61 tff(16379,plain,
% 3.43/3.61 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(z))), s(s(s(elem!1))))) | (~r(z, s(s(s(z))))) | (~r(s(s(z)), s(s(s(z))))) | (~r(s(s(z)), z)))),
% 3.43/3.61 inference(quant_inst,[status(thm)],[])).
% 3.43/3.61 tff(16380,plain,
% 3.43/3.61 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(z))), s(s(s(elem!1))))) | (~r(z, s(s(s(z))))) | (~r(s(s(z)), z)) | (~r(s(s(z)), s(s(s(z)))))),
% 3.43/3.61 inference(modus_ponens,[status(thm)],[16379, 16378])).
% 3.43/3.61 tff(16381,plain,
% 3.43/3.61 (~r(s(s(s(z))), s(s(s(elem!1))))),
% 3.43/3.61 inference(unit_resolution,[status(thm)],[16380, 197, 16359, 16374, 16368])).
% 3.43/3.61 tff(16382,plain,
% 3.43/3.61 ($false),
% 3.43/3.61 inference(unit_resolution,[status(thm)],[16381, 16366])).
% 3.43/3.61 tff(16383,plain,((~b(s(s(s(elem!1))), z)) | (~(s(s(elem!1)) = s(s(s(elem!1))))) | (~b(s(z), z)) | (~b(z, s(s(z)))) | (~r(s(s(z)), s(z))) | (~b(s(z), s(s(elem!1))))), inference(lemma,lemma(discharge,[]))).
% 3.43/3.61 tff(16384,plain,
% 3.43/3.61 (~b(s(s(s(elem!1))), z)),
% 3.43/3.61 inference(unit_resolution,[status(thm)],[16383, 334, 53, 10451, 392, 376])).
% 3.43/3.61 tff(16385,plain,
% 3.43/3.61 (~b(s(s(elem!1)), z)),
% 3.43/3.61 inference(modus_ponens,[status(thm)],[16384, 16337])).
% 3.43/3.61 tff(16386,plain,
% 3.43/3.61 (r(s(s(elem!1)), z)),
% 3.43/3.61 inference(unit_resolution,[status(thm)],[608, 16385])).
% 3.43/3.61 tff(16387,plain,
% 3.43/3.61 (~r(s(s(z)), s(s(elem!1)))),
% 3.43/3.61 inference(unit_resolution,[status(thm)],[9517, 16333, 16386, 16326])).
% 3.43/3.61 tff(16388,plain,
% 3.43/3.61 (b(s(s(z)), s(s(elem!1)))),
% 3.43/3.61 inference(unit_resolution,[status(thm)],[390, 16387, 6641])).
% 3.43/3.61 tff(16389,plain,
% 3.43/3.61 (~b(s(s(s(z))), z)),
% 3.43/3.61 inference(unit_resolution,[status(thm)],[15961, 16388, 53, 10451, 376, 16335])).
% 3.43/3.61 tff(16390,plain,
% 3.43/3.61 ($false),
% 3.43/3.61 inference(unit_resolution,[status(thm)],[1713, 16389, 16336])).
% 3.43/3.61 tff(16391,plain,((~b(z, s(s(elem!1)))) | (~b(s(z), z)) | (~b(z, s(s(z)))) | (~b(s(z), s(s(elem!1)))) | (~r(s(s(z)), s(z))) | (~(s(s(elem!1)) = s(s(s(elem!1)))))), inference(lemma,lemma(discharge,[]))).
% 3.43/3.61 tff(16392,plain,
% 3.43/3.61 (~b(z, s(s(elem!1)))),
% 3.43/3.61 inference(unit_resolution,[status(thm)],[16391, 53, 10451, 376, 4143, 16308])).
% 3.43/3.61 tff(16393,plain,
% 3.43/3.61 (~b(z, s(s(s(elem!1))))),
% 3.43/3.61 inference(unit_resolution,[status(thm)],[4345, 16392, 16308])).
% 3.43/3.61 tff(16394,plain,
% 3.43/3.61 (~b(z, elem!1)),
% 3.43/3.61 inference(unit_resolution,[status(thm)],[11488, 16393, 16321])).
% 3.43/3.61 tff(16395,plain,
% 3.43/3.61 (r(z, elem!1)),
% 3.43/3.61 inference(unit_resolution,[status(thm)],[2514, 16394, 16317])).
% 3.43/3.61 tff(16396,plain,
% 3.43/3.61 ((z = elem!1) <=> (elem!1 = z)),
% 3.43/3.61 inference(symmetry,[status(thm)],[1147])).
% 3.43/3.61 tff(16397,plain,
% 3.43/3.61 ((s(s(s(elem!1))) = z) <=> (elem!1 = z)),
% 3.43/3.61 inference(transitivity,[status(thm)],[16315, 16396])).
% 3.43/3.61 tff(16398,plain,
% 3.43/3.61 ((~(s(s(s(elem!1))) = z)) <=> (~(elem!1 = z))),
% 3.43/3.61 inference(monotonicity,[status(thm)],[16397])).
% 3.43/3.61 tff(16399,plain,
% 3.43/3.61 (~(elem!1 = z)),
% 3.43/3.61 inference(modus_ponens,[status(thm)],[89, 16398])).
% 3.43/3.61 tff(16400,plain,
% 3.43/3.61 (b(elem!1, z) <=> b(s(s(s(elem!1))), z)),
% 3.43/3.61 inference(monotonicity,[status(thm)],[16312])).
% 3.43/3.61 tff(16401,plain,
% 3.43/3.61 (b(s(s(s(elem!1))), z) <=> b(elem!1, z)),
% 3.43/3.61 inference(symmetry,[status(thm)],[16400])).
% 3.43/3.61 tff(16402,plain,
% 3.43/3.61 ((~b(s(s(s(elem!1))), z)) <=> (~b(elem!1, z))),
% 3.43/3.61 inference(monotonicity,[status(thm)],[16401])).
% 3.43/3.61 tff(16403,plain,
% 3.43/3.61 (~b(s(s(s(elem!1))), z)),
% 3.43/3.61 inference(unit_resolution,[status(thm)],[16383, 16308, 53, 10451, 4143, 376])).
% 3.43/3.61 tff(16404,plain,
% 3.43/3.61 (~b(elem!1, z)),
% 3.43/3.61 inference(modus_ponens,[status(thm)],[16403, 16402])).
% 3.43/3.61 tff(16405,plain,
% 3.43/3.61 (r(elem!1, z)),
% 3.43/3.61 inference(unit_resolution,[status(thm)],[1239, 16404, 16399])).
% 3.43/3.61 tff(16406,plain,
% 3.43/3.61 ((elem!1 = s(s(s(z)))) <=> (s(s(s(elem!1))) = s(s(s(z))))),
% 3.43/3.61 inference(monotonicity,[status(thm)],[6548])).
% 3.43/3.61 tff(16407,plain,
% 3.43/3.61 ((~(elem!1 = s(s(s(z))))) <=> (~(s(s(s(elem!1))) = s(s(s(z)))))),
% 3.43/3.61 inference(monotonicity,[status(thm)],[16406])).
% 3.43/3.61 tff(16408,plain,
% 3.43/3.61 (~(s(s(s(elem!1))) = s(s(s(z))))),
% 3.43/3.61 inference(modus_ponens,[status(thm)],[8222, 16407])).
% 3.43/3.61 tff(16409,plain,
% 3.43/3.61 (~b(s(z), s(s(z)))),
% 3.43/3.61 inference(unit_resolution,[status(thm)],[12846, 122, 53, 10451])).
% 3.43/3.61 tff(16410,plain,
% 3.43/3.61 (r(s(z), s(s(z)))),
% 3.43/3.61 inference(unit_resolution,[status(thm)],[427, 16409])).
% 3.43/3.61 tff(16411,plain,
% 3.43/3.61 (~b(s(s(s(z))), z)),
% 3.43/3.61 inference(unit_resolution,[status(thm)],[5078, 16410, 392, 53, 118, 122])).
% 3.43/3.61 tff(16412,plain,
% 3.43/3.61 (r(s(s(s(z))), z)),
% 3.43/3.61 inference(unit_resolution,[status(thm)],[1713, 16411])).
% 3.43/3.61 tff(16413,plain,
% 3.43/3.61 (~b(z, s(s(elem!1)))),
% 3.43/3.61 inference(unit_resolution,[status(thm)],[16391, 53, 10451, 376, 392, 334])).
% 3.43/3.61 tff(16414,plain,
% 3.43/3.61 (~b(z, s(s(s(elem!1))))),
% 3.43/3.61 inference(unit_resolution,[status(thm)],[4345, 16413, 334])).
% 3.43/3.61 tff(16415,plain,
% 3.43/3.61 (r(z, s(s(s(elem!1))))),
% 3.43/3.61 inference(unit_resolution,[status(thm)],[261, 16414])).
% 3.43/3.61 tff(16416,plain,
% 3.43/3.61 (r(s(s(s(elem!1))), z)),
% 3.43/3.61 inference(unit_resolution,[status(thm)],[94, 16384])).
% 3.43/3.61 tff(16417,plain,
% 3.43/3.61 (~r(s(s(s(elem!1))), s(s(s(z))))),
% 3.43/3.61 inference(unit_resolution,[status(thm)],[13638, 197, 16416, 16415, 16412])).
% 3.43/3.61 tff(16418,plain,
% 3.43/3.61 (b(s(s(s(elem!1))), s(s(s(z))))),
% 3.43/3.61 inference(unit_resolution,[status(thm)],[3574, 16417, 16408])).
% 3.43/3.61 tff(16419,plain,
% 3.43/3.61 (~r(s(s(s(z))), s(s(s(elem!1))))),
% 3.43/3.61 inference(unit_resolution,[status(thm)],[13628, 197, 16416, 16415, 16412])).
% 3.43/3.61 tff(16420,plain,
% 3.43/3.61 (~r(s(s(s(z))), elem!1)),
% 3.43/3.61 inference(modus_ponens,[status(thm)],[16419, 5509])).
% 3.43/3.61 tff(16421,plain,
% 3.43/3.61 (b(s(s(s(z))), elem!1)),
% 3.43/3.61 inference(unit_resolution,[status(thm)],[2826, 16420, 4027])).
% 3.43/3.61 tff(16422,plain,
% 3.43/3.61 (b(s(s(s(z))), s(s(s(elem!1))))),
% 3.43/3.61 inference(unit_resolution,[status(thm)],[4078, 16421, 4031])).
% 3.43/3.61 tff(16423,plain,
% 3.43/3.61 (~b(s(s(s(z))), s(z))),
% 3.43/3.61 inference(unit_resolution,[status(thm)],[5561, 166, 5555, 16422, 16418])).
% 3.43/3.61 tff(16424,plain,
% 3.43/3.61 (r(s(s(s(z))), s(z))),
% 3.43/3.61 inference(unit_resolution,[status(thm)],[1763, 16423])).
% 3.43/3.61 tff(16425,plain,
% 3.43/3.61 (~r(s(s(s(z))), s(s(z)))),
% 3.43/3.61 inference(unit_resolution,[status(thm)],[5076, 197, 16410, 392, 16424])).
% 3.43/3.61 tff(16426,plain,
% 3.43/3.61 (b(s(s(s(z))), s(s(z)))),
% 3.43/3.61 inference(unit_resolution,[status(thm)],[1010, 16425])).
% 3.43/3.61 tff(16427,plain,
% 3.43/3.61 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(z)))) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(s(z)), z)) | (~b(z, s(s(s(z))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(s(z)))) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(s(z)), z)) | (~b(z, s(s(s(z))))))),
% 3.43/3.61 inference(rewrite,[status(thm)],[])).
% 3.43/3.61 tff(16428,plain,
% 3.43/3.61 (((~b(z, s(s(z)))) | (~b(z, s(s(z)))) | (~b(s(s(z)), z)) | (~b(s(s(s(z))), s(s(z)))) | (~b(z, s(s(z)))) | (~b(z, s(s(s(z)))))) <=> ((~b(z, s(s(z)))) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(s(z)), z)) | (~b(z, s(s(s(z))))))),
% 3.43/3.61 inference(rewrite,[status(thm)],[])).
% 3.43/3.61 tff(16429,plain,
% 3.43/3.61 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(z)))) | (~b(z, s(s(z)))) | (~b(s(s(z)), z)) | (~b(s(s(s(z))), s(s(z)))) | (~b(z, s(s(z)))) | (~b(z, s(s(s(z))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(z)))) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(s(z)), z)) | (~b(z, s(s(s(z)))))))),
% 3.43/3.61 inference(monotonicity,[status(thm)],[16428])).
% 3.43/3.61 tff(16430,plain,
% 3.43/3.61 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(z)))) | (~b(z, s(s(z)))) | (~b(s(s(z)), z)) | (~b(s(s(s(z))), s(s(z)))) | (~b(z, s(s(z)))) | (~b(z, s(s(s(z))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(s(z)))) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(s(z)), z)) | (~b(z, s(s(s(z))))))),
% 3.43/3.61 inference(transitivity,[status(thm)],[16429, 16427])).
% 3.43/3.61 tff(16431,plain,
% 3.43/3.61 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(z)))) | (~b(z, s(s(z)))) | (~b(s(s(z)), z)) | (~b(s(s(s(z))), s(s(z)))) | (~b(z, s(s(z)))) | (~b(z, s(s(s(z))))))),
% 3.43/3.62 inference(quant_inst,[status(thm)],[])).
% 3.43/3.62 tff(16432,plain,
% 3.43/3.62 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(s(z)))) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(s(z)), z)) | (~b(z, s(s(s(z)))))),
% 3.43/3.62 inference(modus_ponens,[status(thm)],[16431, 16430])).
% 3.43/3.62 tff(16433,plain,
% 3.43/3.62 (~b(z, s(s(s(z))))),
% 3.43/3.62 inference(unit_resolution,[status(thm)],[16432, 166, 10451, 122, 16426])).
% 3.43/3.62 tff(16434,plain,
% 3.43/3.62 (r(z, s(s(s(z))))),
% 3.43/3.62 inference(unit_resolution,[status(thm)],[1697, 16433])).
% 3.43/3.62 tff(16435,plain,
% 3.43/3.62 ((elem!1 = s(s(s(z)))) <=> (s(s(s(z))) = s(s(elem!1)))),
% 3.43/3.62 inference(transitivity,[status(thm)],[16406, 5527])).
% 3.43/3.62 tff(16436,plain,
% 3.43/3.62 ((~(elem!1 = s(s(s(z))))) <=> (~(s(s(s(z))) = s(s(elem!1))))),
% 3.43/3.62 inference(monotonicity,[status(thm)],[16435])).
% 3.43/3.62 tff(16437,plain,
% 3.43/3.62 (~(s(s(s(z))) = s(s(elem!1)))),
% 3.43/3.62 inference(modus_ponens,[status(thm)],[8222, 16436])).
% 3.43/3.62 tff(16438,plain,
% 3.43/3.62 (~r(s(s(elem!1)), s(s(s(z))))),
% 3.43/3.62 inference(modus_ponens,[status(thm)],[16417, 5524])).
% 3.43/3.62 tff(16439,plain,
% 3.43/3.62 (~r(s(s(s(z))), s(s(elem!1)))),
% 3.43/3.62 inference(modus_ponens,[status(thm)],[16419, 5530])).
% 3.43/3.62 tff(16440,plain,
% 3.43/3.62 (~b(s(z), s(s(s(z))))),
% 3.43/3.62 inference(unit_resolution,[status(thm)],[5552, 16439, 376, 16438, 16437])).
% 3.43/3.62 tff(16441,plain,
% 3.43/3.62 (r(s(z), s(s(s(z))))),
% 3.43/3.62 inference(unit_resolution,[status(thm)],[1674, 16440])).
% 3.43/3.62 tff(16442,plain,
% 3.43/3.62 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(s(z))))) | (~r(s(s(s(z))), s(z))) | (~r(s(s(s(s(z)))), z)) | (~r(s(s(s(s(z)))), s(s(s(z))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, s(s(s(z))))) | (~r(s(s(s(z))), s(z))) | (~r(s(s(s(s(z)))), z)) | (~r(s(s(s(s(z)))), s(s(s(z))))))),
% 3.43/3.62 inference(rewrite,[status(thm)],[])).
% 3.43/3.62 tff(16443,plain,
% 3.43/3.62 (((~r(s(s(s(z))), s(z))) | (~r(z, s(s(s(z))))) | (~r(s(s(s(s(z)))), s(s(s(z))))) | (~r(s(s(s(s(z)))), z))) <=> ((~r(z, s(s(s(z))))) | (~r(s(s(s(z))), s(z))) | (~r(s(s(s(s(z)))), z)) | (~r(s(s(s(s(z)))), s(s(s(z))))))),
% 3.43/3.62 inference(rewrite,[status(thm)],[])).
% 3.43/3.62 tff(16444,plain,
% 3.43/3.62 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(z))), s(z))) | (~r(z, s(s(s(z))))) | (~r(s(s(s(s(z)))), s(s(s(z))))) | (~r(s(s(s(s(z)))), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(s(z))))) | (~r(s(s(s(z))), s(z))) | (~r(s(s(s(s(z)))), z)) | (~r(s(s(s(s(z)))), s(s(s(z)))))))),
% 3.43/3.62 inference(monotonicity,[status(thm)],[16443])).
% 3.43/3.62 tff(16445,plain,
% 3.43/3.62 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(z))), s(z))) | (~r(z, s(s(s(z))))) | (~r(s(s(s(s(z)))), s(s(s(z))))) | (~r(s(s(s(s(z)))), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, s(s(s(z))))) | (~r(s(s(s(z))), s(z))) | (~r(s(s(s(s(z)))), z)) | (~r(s(s(s(s(z)))), s(s(s(z))))))),
% 3.43/3.62 inference(transitivity,[status(thm)],[16444, 16442])).
% 3.43/3.62 tff(16446,plain,
% 3.43/3.62 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(z))), s(z))) | (~r(z, s(s(s(z))))) | (~r(s(s(s(s(z)))), s(s(s(z))))) | (~r(s(s(s(s(z)))), z)))),
% 3.43/3.62 inference(quant_inst,[status(thm)],[])).
% 3.43/3.62 tff(16447,plain,
% 3.43/3.62 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, s(s(s(z))))) | (~r(s(s(s(z))), s(z))) | (~r(s(s(s(s(z)))), z)) | (~r(s(s(s(s(z)))), s(s(s(z)))))),
% 3.43/3.62 inference(modus_ponens,[status(thm)],[16446, 16445])).
% 3.43/3.62 tff(16448,plain,
% 3.43/3.62 (~r(s(s(s(s(z)))), z)),
% 3.43/3.62 inference(unit_resolution,[status(thm)],[16447, 197, 1677, 4680, 1746])).
% 3.43/3.62 tff(16449,plain,
% 3.43/3.62 (b(s(s(s(s(z)))), z)),
% 3.43/3.62 inference(unit_resolution,[status(thm)],[3266, 16448])).
% 3.43/3.62 tff(16450,plain,
% 3.43/3.62 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(s(s(z))))) | (~r(s(s(s(z))), s(z))) | (~r(s(s(s(s(z)))), s(s(s(z))))) | (~r(s(z), s(s(s(s(z)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(z), s(s(s(z))))) | (~r(s(s(s(z))), s(z))) | (~r(s(s(s(s(z)))), s(s(s(z))))) | (~r(s(z), s(s(s(s(z)))))))),
% 3.43/3.62 inference(rewrite,[status(thm)],[])).
% 3.43/3.62 tff(16451,plain,
% 3.43/3.62 (((~r(s(s(s(z))), s(z))) | (~r(s(s(s(s(z)))), s(s(s(z))))) | (~r(s(z), s(s(s(z))))) | (~r(s(z), s(s(s(s(z))))))) <=> ((~r(s(z), s(s(s(z))))) | (~r(s(s(s(z))), s(z))) | (~r(s(s(s(s(z)))), s(s(s(z))))) | (~r(s(z), s(s(s(s(z)))))))),
% 3.43/3.62 inference(rewrite,[status(thm)],[])).
% 3.43/3.62 tff(16452,plain,
% 3.43/3.62 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(z))), s(z))) | (~r(s(s(s(s(z)))), s(s(s(z))))) | (~r(s(z), s(s(s(z))))) | (~r(s(z), s(s(s(s(z)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(s(s(z))))) | (~r(s(s(s(z))), s(z))) | (~r(s(s(s(s(z)))), s(s(s(z))))) | (~r(s(z), s(s(s(s(z))))))))),
% 3.43/3.62 inference(monotonicity,[status(thm)],[16451])).
% 3.43/3.62 tff(16453,plain,
% 3.43/3.62 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(z))), s(z))) | (~r(s(s(s(s(z)))), s(s(s(z))))) | (~r(s(z), s(s(s(z))))) | (~r(s(z), s(s(s(s(z)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(z), s(s(s(z))))) | (~r(s(s(s(z))), s(z))) | (~r(s(s(s(s(z)))), s(s(s(z))))) | (~r(s(z), s(s(s(s(z)))))))),
% 3.43/3.62 inference(transitivity,[status(thm)],[16452, 16450])).
% 3.43/3.62 tff(16454,plain,
% 3.43/3.62 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(z))), s(z))) | (~r(s(s(s(s(z)))), s(s(s(z))))) | (~r(s(z), s(s(s(z))))) | (~r(s(z), s(s(s(s(z)))))))),
% 3.43/3.62 inference(quant_inst,[status(thm)],[])).
% 3.43/3.62 tff(16455,plain,
% 3.43/3.62 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(z), s(s(s(z))))) | (~r(s(s(s(z))), s(z))) | (~r(s(s(s(s(z)))), s(s(s(z))))) | (~r(s(z), s(s(s(s(z))))))),
% 3.43/3.62 inference(modus_ponens,[status(thm)],[16454, 16453])).
% 3.43/3.62 tff(16456,plain,
% 3.43/3.62 (~r(s(z), s(s(s(s(z)))))),
% 3.43/3.62 inference(unit_resolution,[status(thm)],[16455, 197, 4680, 1746, 1653])).
% 3.43/3.62 tff(16457,plain,
% 3.43/3.62 (b(s(z), s(s(s(s(z)))))),
% 3.43/3.62 inference(unit_resolution,[status(thm)],[3302, 16456])).
% 3.43/3.62 tff(16458,plain,
% 3.43/3.62 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(z)))) | (~b(s(z), z)) | (~b(s(s(z)), z)) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(s(z)))) | (~b(s(z), z)) | (~b(s(s(z)), z)) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), z)))),
% 3.43/3.62 inference(rewrite,[status(thm)],[])).
% 3.43/3.62 tff(16459,plain,
% 3.43/3.62 (((~b(s(s(z)), z)) | (~b(s(z), z)) | (~b(z, s(s(z)))) | (~b(s(s(s(s(z)))), z)) | (~b(s(z), z)) | (~b(s(z), s(s(s(s(z))))))) <=> ((~b(z, s(s(z)))) | (~b(s(z), z)) | (~b(s(s(z)), z)) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), z)))),
% 3.43/3.62 inference(rewrite,[status(thm)],[])).
% 3.43/3.62 tff(16460,plain,
% 3.43/3.62 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), z)) | (~b(s(z), z)) | (~b(z, s(s(z)))) | (~b(s(s(s(s(z)))), z)) | (~b(s(z), z)) | (~b(s(z), s(s(s(s(z)))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(z)))) | (~b(s(z), z)) | (~b(s(s(z)), z)) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), z))))),
% 3.43/3.62 inference(monotonicity,[status(thm)],[16459])).
% 3.43/3.62 tff(16461,plain,
% 3.43/3.62 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), z)) | (~b(s(z), z)) | (~b(z, s(s(z)))) | (~b(s(s(s(s(z)))), z)) | (~b(s(z), z)) | (~b(s(z), s(s(s(s(z)))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(s(z)))) | (~b(s(z), z)) | (~b(s(s(z)), z)) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), z)))),
% 3.43/3.62 inference(transitivity,[status(thm)],[16460, 16458])).
% 3.43/3.62 tff(16462,plain,
% 3.43/3.62 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), z)) | (~b(s(z), z)) | (~b(z, s(s(z)))) | (~b(s(s(s(s(z)))), z)) | (~b(s(z), z)) | (~b(s(z), s(s(s(s(z)))))))),
% 3.43/3.62 inference(quant_inst,[status(thm)],[])).
% 3.43/3.62 tff(16463,plain,
% 3.43/3.62 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(s(z)))) | (~b(s(z), z)) | (~b(s(s(z)), z)) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), z))),
% 3.43/3.62 inference(modus_ponens,[status(thm)],[16462, 16461])).
% 3.43/3.62 tff(16464,plain,
% 3.43/3.62 ($false),
% 3.43/3.62 inference(unit_resolution,[status(thm)],[16463, 166, 53, 10451, 122, 16457, 16449])).
% 3.43/3.62 tff(16465,plain,((~r(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(z), z)) | (~b(z, s(s(z)))) | (~b(s(s(z)), z)) | (~r(s(s(s(z))), s(z))) | (~r(s(z), s(s(s(z))))) | (~r(z, s(s(s(z)))))), inference(lemma,lemma(discharge,[]))).
% 3.43/3.62 tff(16466,plain,
% 3.43/3.62 (~r(s(s(s(s(z)))), s(s(s(z))))),
% 3.43/3.62 inference(unit_resolution,[status(thm)],[16465, 122, 10451, 53, 16424, 16441, 16434])).
% 3.43/3.62 tff(16467,plain,
% 3.43/3.62 (b(s(s(s(s(z)))), s(s(s(z))))),
% 3.43/3.62 inference(unit_resolution,[status(thm)],[4662, 16466])).
% 3.43/3.62 tff(16468,plain,
% 3.43/3.62 (~r(s(s(z)), s(s(s(z))))),
% 3.43/3.62 inference(unit_resolution,[status(thm)],[5590, 197, 16410, 392, 16424])).
% 3.43/3.62 tff(16469,plain,
% 3.43/3.62 (b(s(s(z)), s(s(s(z))))),
% 3.43/3.62 inference(unit_resolution,[status(thm)],[1730, 16468])).
% 3.43/3.62 tff(16470,plain,
% 3.43/3.62 (~b(s(s(s(s(z)))), s(s(z)))),
% 3.43/3.62 inference(unit_resolution,[status(thm)],[5622, 166, 16469, 16426, 16467])).
% 3.43/3.62 tff(16471,plain,
% 3.43/3.62 (r(s(s(s(s(z)))), s(s(z)))),
% 3.43/3.62 inference(unit_resolution,[status(thm)],[5631, 16470])).
% 3.43/3.62 tff(16472,plain,
% 3.43/3.62 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), s(s(z)))) | (~b(s(s(s(z))), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(s(s(z))))) | (~b(s(s(z)), s(s(s(z))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(elem!1))), s(s(z)))) | (~b(s(s(s(z))), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(s(s(z))))) | (~b(s(s(z)), s(s(s(z))))))),
% 3.43/3.62 inference(rewrite,[status(thm)],[])).
% 3.43/3.62 tff(16473,plain,
% 3.43/3.62 (((~b(s(s(s(elem!1))), s(s(s(z))))) | (~b(s(s(s(elem!1))), s(s(s(z))))) | (~b(s(s(s(z))), s(s(s(elem!1))))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(s(elem!1))), s(s(s(z))))) | (~b(s(s(s(elem!1))), s(s(z))))) <=> ((~b(s(s(s(elem!1))), s(s(z)))) | (~b(s(s(s(z))), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(s(s(z))))) | (~b(s(s(z)), s(s(s(z))))))),
% 3.43/3.62 inference(rewrite,[status(thm)],[])).
% 3.43/3.62 tff(16474,plain,
% 3.43/3.62 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), s(s(s(z))))) | (~b(s(s(s(elem!1))), s(s(s(z))))) | (~b(s(s(s(z))), s(s(s(elem!1))))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(s(elem!1))), s(s(s(z))))) | (~b(s(s(s(elem!1))), s(s(z)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), s(s(z)))) | (~b(s(s(s(z))), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(s(s(z))))) | (~b(s(s(z)), s(s(s(z)))))))),
% 3.43/3.62 inference(monotonicity,[status(thm)],[16473])).
% 3.43/3.62 tff(16475,plain,
% 3.43/3.62 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), s(s(s(z))))) | (~b(s(s(s(elem!1))), s(s(s(z))))) | (~b(s(s(s(z))), s(s(s(elem!1))))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(s(elem!1))), s(s(s(z))))) | (~b(s(s(s(elem!1))), s(s(z)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(elem!1))), s(s(z)))) | (~b(s(s(s(z))), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(s(s(z))))) | (~b(s(s(z)), s(s(s(z))))))),
% 3.43/3.62 inference(transitivity,[status(thm)],[16474, 16472])).
% 3.43/3.62 tff(16476,plain,
% 3.43/3.62 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), s(s(s(z))))) | (~b(s(s(s(elem!1))), s(s(s(z))))) | (~b(s(s(s(z))), s(s(s(elem!1))))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(s(elem!1))), s(s(s(z))))) | (~b(s(s(s(elem!1))), s(s(z)))))),
% 3.43/3.62 inference(quant_inst,[status(thm)],[])).
% 3.43/3.62 tff(16477,plain,
% 3.43/3.62 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(elem!1))), s(s(z)))) | (~b(s(s(s(z))), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(s(s(z))))) | (~b(s(s(z)), s(s(s(z)))))),
% 3.43/3.62 inference(modus_ponens,[status(thm)],[16476, 16475])).
% 3.43/3.62 tff(16478,plain,
% 3.43/3.62 (~b(s(s(s(elem!1))), s(s(z)))),
% 3.43/3.62 inference(unit_resolution,[status(thm)],[16477, 166, 16422, 16469, 16418])).
% 3.43/3.62 tff(16479,plain,
% 3.43/3.62 (r(s(s(s(elem!1))), s(s(z)))),
% 3.43/3.62 inference(unit_resolution,[status(thm)],[218, 16478])).
% 3.43/3.62 tff(16480,plain,
% 3.43/3.62 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(z)), s(z))) | (~r(s(s(s(elem!1))), s(s(z)))) | (~r(s(s(s(s(z)))), s(s(z)))) | (~r(s(s(s(elem!1))), s(s(s(s(z)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(z)), s(z))) | (~r(s(s(s(elem!1))), s(s(z)))) | (~r(s(s(s(s(z)))), s(s(z)))) | (~r(s(s(s(elem!1))), s(s(s(s(z)))))))),
% 3.43/3.62 inference(rewrite,[status(thm)],[])).
% 3.43/3.62 tff(16481,plain,
% 3.43/3.62 (((~r(s(s(z)), s(z))) | (~r(s(s(s(s(z)))), s(s(z)))) | (~r(s(s(s(elem!1))), s(s(z)))) | (~r(s(s(s(elem!1))), s(s(s(s(z))))))) <=> ((~r(s(s(z)), s(z))) | (~r(s(s(s(elem!1))), s(s(z)))) | (~r(s(s(s(s(z)))), s(s(z)))) | (~r(s(s(s(elem!1))), s(s(s(s(z)))))))),
% 3.43/3.62 inference(rewrite,[status(thm)],[])).
% 3.43/3.62 tff(16482,plain,
% 3.43/3.62 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(z)), s(z))) | (~r(s(s(s(s(z)))), s(s(z)))) | (~r(s(s(s(elem!1))), s(s(z)))) | (~r(s(s(s(elem!1))), s(s(s(s(z)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(z)), s(z))) | (~r(s(s(s(elem!1))), s(s(z)))) | (~r(s(s(s(s(z)))), s(s(z)))) | (~r(s(s(s(elem!1))), s(s(s(s(z))))))))),
% 3.43/3.62 inference(monotonicity,[status(thm)],[16481])).
% 3.43/3.62 tff(16483,plain,
% 3.43/3.62 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(z)), s(z))) | (~r(s(s(s(s(z)))), s(s(z)))) | (~r(s(s(s(elem!1))), s(s(z)))) | (~r(s(s(s(elem!1))), s(s(s(s(z)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(z)), s(z))) | (~r(s(s(s(elem!1))), s(s(z)))) | (~r(s(s(s(s(z)))), s(s(z)))) | (~r(s(s(s(elem!1))), s(s(s(s(z)))))))),
% 3.43/3.62 inference(transitivity,[status(thm)],[16482, 16480])).
% 3.43/3.62 tff(16484,plain,
% 3.43/3.62 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(z)), s(z))) | (~r(s(s(s(s(z)))), s(s(z)))) | (~r(s(s(s(elem!1))), s(s(z)))) | (~r(s(s(s(elem!1))), s(s(s(s(z)))))))),
% 3.43/3.62 inference(quant_inst,[status(thm)],[])).
% 3.43/3.62 tff(16485,plain,
% 3.43/3.62 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(z)), s(z))) | (~r(s(s(s(elem!1))), s(s(z)))) | (~r(s(s(s(s(z)))), s(s(z)))) | (~r(s(s(s(elem!1))), s(s(s(s(z))))))),
% 3.43/3.62 inference(modus_ponens,[status(thm)],[16484, 16483])).
% 3.43/3.62 tff(16486,plain,
% 3.43/3.62 (~r(s(s(s(elem!1))), s(s(s(s(z)))))),
% 3.43/3.62 inference(unit_resolution,[status(thm)],[16485, 197, 392, 16479, 16471])).
% 3.43/3.62 tff(16487,plain,
% 3.43/3.62 (~r(s(s(s(elem!1))), s(z))),
% 3.43/3.62 inference(unit_resolution,[status(thm)],[483, 16479, 392, 16410])).
% 3.43/3.62 tff(16488,plain,
% 3.43/3.62 (b(s(s(s(elem!1))), s(z))),
% 3.43/3.62 inference(unit_resolution,[status(thm)],[1849, 16487])).
% 3.43/3.62 tff(16489,plain,
% 3.43/3.62 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), s(z))) | (~b(s(s(s(z))), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(elem!1))), s(s(s(s(z)))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(s(s(z))), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(elem!1))), s(s(s(s(z)))))))),
% 3.43/3.62 inference(rewrite,[status(thm)],[])).
% 3.43/3.62 tff(16490,plain,
% 3.43/3.62 (((~b(s(s(s(elem!1))), s(z))) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(s(s(z))), s(s(s(elem!1))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(elem!1))), s(s(s(z))))) | (~b(s(s(s(elem!1))), s(s(s(s(z))))))) <=> ((~b(s(s(s(elem!1))), s(z))) | (~b(s(s(s(z))), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(elem!1))), s(s(s(s(z)))))))),
% 3.43/3.62 inference(rewrite,[status(thm)],[])).
% 3.43/3.62 tff(16491,plain,
% 3.43/3.62 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), s(z))) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(s(s(z))), s(s(s(elem!1))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(elem!1))), s(s(s(z))))) | (~b(s(s(s(elem!1))), s(s(s(s(z)))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), s(z))) | (~b(s(s(s(z))), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(elem!1))), s(s(s(s(z))))))))),
% 3.43/3.63 inference(monotonicity,[status(thm)],[16490])).
% 3.43/3.63 tff(16492,plain,
% 3.43/3.63 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), s(z))) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(s(s(z))), s(s(s(elem!1))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(elem!1))), s(s(s(z))))) | (~b(s(s(s(elem!1))), s(s(s(s(z)))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(s(s(z))), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(elem!1))), s(s(s(s(z)))))))),
% 3.43/3.63 inference(transitivity,[status(thm)],[16491, 16489])).
% 3.43/3.63 tff(16493,plain,
% 3.43/3.63 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), s(z))) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(s(s(z))), s(s(s(elem!1))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(elem!1))), s(s(s(z))))) | (~b(s(s(s(elem!1))), s(s(s(s(z)))))))),
% 3.43/3.63 inference(quant_inst,[status(thm)],[])).
% 3.43/3.63 tff(16494,plain,
% 3.43/3.63 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(s(s(z))), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(elem!1))), s(s(s(s(z))))))),
% 3.43/3.63 inference(modus_ponens,[status(thm)],[16493, 16492])).
% 3.43/3.63 tff(16495,plain,
% 3.43/3.63 (~b(s(s(s(elem!1))), s(s(s(s(z)))))),
% 3.43/3.63 inference(unit_resolution,[status(thm)],[16494, 166, 16488, 16422, 16467, 16418])).
% 3.43/3.63 tff(16496,plain,
% 3.43/3.63 (~b(elem!1, s(s(s(s(z)))))),
% 3.43/3.63 inference(modus_ponens,[status(thm)],[16495, 6551])).
% 3.43/3.63 tff(16497,plain,
% 3.43/3.63 (r(elem!1, s(s(s(s(z)))))),
% 3.43/3.63 inference(unit_resolution,[status(thm)],[1098, 16496, 6568])).
% 3.43/3.63 tff(16498,plain,
% 3.43/3.63 ($false),
% 3.43/3.63 inference(unit_resolution,[status(thm)],[5665, 16497, 16486, 334])).
% 3.43/3.63 tff(16499,plain,((~b(s(s(z)), z)) | (~(s(s(elem!1)) = s(s(s(elem!1))))) | (~r(s(s(z)), s(z))) | (~b(z, s(s(z)))) | (~b(s(z), z)) | (~b(s(z), s(s(elem!1)))) | (~b(z, s(z)))), inference(lemma,lemma(discharge,[]))).
% 3.43/3.63 tff(16500,plain,
% 3.43/3.63 (~b(s(s(z)), z)),
% 3.43/3.63 inference(unit_resolution,[status(thm)],[16499, 118, 392, 10451, 53, 376, 334])).
% 3.43/3.63 tff(16501,plain,
% 3.43/3.63 (r(s(s(z)), z)),
% 3.43/3.63 inference(unit_resolution,[status(thm)],[186, 16500])).
% 3.43/3.63 tff(16502,plain,
% 3.43/3.63 ((z = elem!1) <=> (z = s(s(s(elem!1))))),
% 3.43/3.63 inference(monotonicity,[status(thm)],[6548])).
% 3.43/3.63 tff(16503,plain,
% 3.43/3.63 ((z = elem!1) <=> (s(s(s(elem!1))) = z)),
% 3.43/3.63 inference(transitivity,[status(thm)],[16502, 7746])).
% 3.43/3.63 tff(16504,plain,
% 3.43/3.63 ((s(s(s(elem!1))) = z) <=> (z = elem!1)),
% 3.43/3.63 inference(symmetry,[status(thm)],[16503])).
% 3.43/3.63 tff(16505,plain,
% 3.43/3.63 ((~(s(s(s(elem!1))) = z)) <=> (~(z = elem!1))),
% 3.43/3.63 inference(monotonicity,[status(thm)],[16504])).
% 3.43/3.63 tff(16506,plain,
% 3.43/3.63 (~(z = elem!1)),
% 3.43/3.63 inference(modus_ponens,[status(thm)],[89, 16505])).
% 3.43/3.63 tff(16507,plain,
% 3.43/3.63 (~b(z, elem!1)),
% 3.43/3.63 inference(unit_resolution,[status(thm)],[11488, 16414, 11481])).
% 3.43/3.63 tff(16508,plain,
% 3.43/3.63 (r(z, elem!1)),
% 3.43/3.63 inference(unit_resolution,[status(thm)],[2514, 16507, 16506])).
% 3.43/3.63 tff(16509,plain,
% 3.43/3.63 ((s(s(s(elem!1))) = z) <=> (elem!1 = z)),
% 3.43/3.63 inference(transitivity,[status(thm)],[16504, 16396])).
% 3.43/3.63 tff(16510,plain,
% 3.43/3.63 ((~(s(s(s(elem!1))) = z)) <=> (~(elem!1 = z))),
% 3.43/3.63 inference(monotonicity,[status(thm)],[16509])).
% 3.43/3.63 tff(16511,plain,
% 3.43/3.63 (~(elem!1 = z)),
% 3.43/3.63 inference(modus_ponens,[status(thm)],[89, 16510])).
% 3.43/3.63 tff(16512,plain,
% 3.43/3.63 (b(elem!1, z) <=> b(s(s(s(elem!1))), z)),
% 3.43/3.63 inference(monotonicity,[status(thm)],[6548])).
% 3.43/3.63 tff(16513,plain,
% 3.43/3.63 (b(s(s(s(elem!1))), z) <=> b(elem!1, z)),
% 3.43/3.63 inference(symmetry,[status(thm)],[16512])).
% 3.43/3.63 tff(16514,plain,
% 3.43/3.63 ((~b(s(s(s(elem!1))), z)) <=> (~b(elem!1, z))),
% 3.43/3.63 inference(monotonicity,[status(thm)],[16513])).
% 3.43/3.63 tff(16515,plain,
% 3.43/3.63 (~b(elem!1, z)),
% 3.43/3.63 inference(modus_ponens,[status(thm)],[16384, 16514])).
% 3.43/3.63 tff(16516,plain,
% 3.43/3.63 (r(elem!1, z)),
% 3.43/3.63 inference(unit_resolution,[status(thm)],[1239, 16515, 16511])).
% 3.43/3.63 tff(16517,plain,
% 3.43/3.63 (~r(elem!1, s(s(z)))),
% 3.43/3.63 inference(unit_resolution,[status(thm)],[15494, 16501, 16516, 16508])).
% 3.43/3.63 tff(16518,plain,
% 3.43/3.63 (~r(s(s(elem!1)), s(s(z)))),
% 3.43/3.63 inference(unit_resolution,[status(thm)],[3656, 16517, 3115])).
% 3.43/3.63 tff(16519,plain,
% 3.43/3.63 (b(s(s(elem!1)), s(s(z)))),
% 3.43/3.63 inference(unit_resolution,[status(thm)],[441, 16518, 13569])).
% 3.43/3.63 tff(16520,plain,
% 3.43/3.63 (b(s(s(s(elem!1))), s(s(z)))),
% 3.43/3.63 inference(modus_ponens,[status(thm)],[16519, 16354])).
% 3.43/3.63 tff(16521,plain,
% 3.43/3.63 (~r(s(s(s(z))), z)),
% 3.43/3.63 inference(unit_resolution,[status(thm)],[13666, 16520, 334, 16416, 16415, 16501])).
% 3.43/3.63 tff(16522,plain,
% 3.43/3.63 (b(s(s(s(z))), z)),
% 3.43/3.63 inference(unit_resolution,[status(thm)],[1713, 16521])).
% 3.43/3.63 tff(16523,plain,
% 3.43/3.63 (~b(s(s(s(z))), s(z))),
% 3.43/3.63 inference(unit_resolution,[status(thm)],[4045, 166, 53, 118, 16522])).
% 3.43/3.63 tff(16524,plain,
% 3.43/3.63 (r(s(s(s(z))), s(z))),
% 3.43/3.63 inference(unit_resolution,[status(thm)],[1763, 16523])).
% 3.43/3.63 tff(16525,plain,
% 3.43/3.63 (~r(s(s(z)), s(s(s(elem!1))))),
% 3.43/3.63 inference(unit_resolution,[status(thm)],[13284, 16501, 16416, 16415])).
% 3.43/3.63 tff(16526,plain,
% 3.43/3.63 (~r(s(s(z)), s(s(elem!1)))),
% 3.43/3.63 inference(unit_resolution,[status(thm)],[338, 16525, 334])).
% 3.43/3.63 tff(16527,plain,
% 3.43/3.63 (~b(s(z), s(s(z)))),
% 3.43/3.63 inference(unit_resolution,[status(thm)],[5300, 16518, 376, 6641, 16526])).
% 3.43/3.63 tff(16528,plain,
% 3.43/3.63 (r(s(z), s(s(z)))),
% 3.43/3.63 inference(unit_resolution,[status(thm)],[427, 16527])).
% 3.43/3.63 tff(16529,plain,
% 3.43/3.63 (~r(s(s(s(z))), s(s(z)))),
% 3.43/3.63 inference(unit_resolution,[status(thm)],[5076, 197, 16528, 392, 16524])).
% 3.43/3.63 tff(16530,plain,
% 3.43/3.63 (b(s(s(s(z))), s(s(z)))),
% 3.43/3.63 inference(unit_resolution,[status(thm)],[1010, 16529])).
% 3.43/3.63 tff(16531,plain,
% 3.43/3.63 (~r(s(s(z)), s(s(s(z))))),
% 3.43/3.63 inference(unit_resolution,[status(thm)],[5590, 197, 16528, 392, 16524])).
% 3.43/3.63 tff(16532,plain,
% 3.43/3.63 (b(s(s(z)), s(s(s(z))))),
% 3.43/3.63 inference(unit_resolution,[status(thm)],[1730, 16531])).
% 3.43/3.63 tff(16533,plain,
% 3.43/3.63 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(z)))) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(s(s(z))), z)) | (~b(s(s(z)), s(s(s(z))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(s(z)))) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(s(s(z))), z)) | (~b(s(s(z)), s(s(s(z))))))),
% 3.43/3.63 inference(rewrite,[status(thm)],[])).
% 3.43/3.63 tff(16534,plain,
% 3.43/3.63 (((~b(s(s(s(z))), z)) | (~b(s(s(s(z))), z)) | (~b(s(s(z)), s(s(s(z))))) | (~b(z, s(s(z)))) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(s(s(z))), z))) <=> ((~b(z, s(s(z)))) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(s(s(z))), z)) | (~b(s(s(z)), s(s(s(z))))))),
% 3.43/3.63 inference(rewrite,[status(thm)],[])).
% 3.43/3.63 tff(16535,plain,
% 3.43/3.63 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), z)) | (~b(s(s(s(z))), z)) | (~b(s(s(z)), s(s(s(z))))) | (~b(z, s(s(z)))) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(s(s(z))), z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(z)))) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(s(s(z))), z)) | (~b(s(s(z)), s(s(s(z)))))))),
% 3.43/3.63 inference(monotonicity,[status(thm)],[16534])).
% 3.43/3.63 tff(16536,plain,
% 3.43/3.63 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), z)) | (~b(s(s(s(z))), z)) | (~b(s(s(z)), s(s(s(z))))) | (~b(z, s(s(z)))) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(s(s(z))), z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(s(z)))) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(s(s(z))), z)) | (~b(s(s(z)), s(s(s(z))))))),
% 3.43/3.63 inference(transitivity,[status(thm)],[16535, 16533])).
% 3.43/3.63 tff(16537,plain,
% 3.43/3.63 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), z)) | (~b(s(s(s(z))), z)) | (~b(s(s(z)), s(s(s(z))))) | (~b(z, s(s(z)))) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(s(s(z))), z)))),
% 3.43/3.63 inference(quant_inst,[status(thm)],[])).
% 3.43/3.63 tff(16538,plain,
% 3.43/3.63 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(s(z)))) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(s(s(z))), z)) | (~b(s(s(z)), s(s(s(z)))))),
% 3.43/3.63 inference(modus_ponens,[status(thm)],[16537, 16536])).
% 3.43/3.63 tff(16539,plain,
% 3.43/3.63 ($false),
% 3.43/3.63 inference(unit_resolution,[status(thm)],[16538, 166, 10451, 16532, 16530, 16522])).
% 3.43/3.63 tff(16540,plain,((~b(z, s(z))) | (~b(z, s(s(z)))) | (~r(s(s(z)), s(z))) | (~b(s(z), z)) | (~(s(s(elem!1)) = s(s(s(elem!1))))) | (~b(s(z), s(s(elem!1))))), inference(lemma,lemma(discharge,[]))).
% 3.43/3.63 tff(16541,plain,
% 3.43/3.63 (~b(z, s(z))),
% 3.43/3.63 inference(unit_resolution,[status(thm)],[16540, 53, 4143, 10451, 16308, 376])).
% 3.43/3.63 tff(16542,plain,
% 3.43/3.63 (r(z, s(z))),
% 3.43/3.63 inference(unit_resolution,[status(thm)],[321, 16541])).
% 3.43/3.63 tff(16543,plain,
% 3.43/3.63 (b(s(s(elem!1)), z) <=> b(s(s(s(elem!1))), z)),
% 3.43/3.63 inference(monotonicity,[status(thm)],[16308])).
% 3.43/3.63 tff(16544,plain,
% 3.43/3.63 (b(s(s(s(elem!1))), z) <=> b(s(s(elem!1)), z)),
% 3.43/3.63 inference(symmetry,[status(thm)],[16543])).
% 3.43/3.63 tff(16545,plain,
% 3.43/3.63 ((~b(s(s(s(elem!1))), z)) <=> (~b(s(s(elem!1)), z))),
% 3.43/3.63 inference(monotonicity,[status(thm)],[16544])).
% 3.43/3.63 tff(16546,plain,
% 3.43/3.63 (~b(s(s(elem!1)), z)),
% 3.43/3.63 inference(modus_ponens,[status(thm)],[16403, 16545])).
% 3.43/3.63 tff(16547,plain,
% 3.43/3.63 (r(s(s(elem!1)), z)),
% 3.43/3.63 inference(unit_resolution,[status(thm)],[608, 16546])).
% 3.43/3.63 tff(16548,plain,
% 3.43/3.63 ((s(s(elem!1)) = s(s(z))) <=> (s(s(s(elem!1))) = s(s(z)))),
% 3.43/3.63 inference(monotonicity,[status(thm)],[16308])).
% 3.43/3.63 tff(16549,plain,
% 3.43/3.63 ((s(s(elem!1)) = s(s(z))) <=> (s(s(z)) = s(s(s(elem!1))))),
% 3.43/3.63 inference(transitivity,[status(thm)],[16548, 487])).
% 3.43/3.63 tff(16550,plain,
% 3.43/3.63 ((s(s(z)) = s(s(s(elem!1)))) <=> (s(s(elem!1)) = s(s(z)))),
% 3.43/3.63 inference(symmetry,[status(thm)],[16549])).
% 3.43/3.63 tff(16551,plain,
% 3.43/3.63 ((s(s(z)) = s(s(s(elem!1)))) <=> (s(s(z)) = s(s(elem!1)))),
% 3.43/3.63 inference(transitivity,[status(thm)],[16550, 127])).
% 3.43/3.63 tff(16552,plain,
% 3.43/3.63 ((~(s(s(z)) = s(s(s(elem!1))))) <=> (~(s(s(z)) = s(s(elem!1))))),
% 3.43/3.63 inference(monotonicity,[status(thm)],[16551])).
% 3.43/3.63 tff(16553,plain,
% 3.43/3.63 (~(s(s(z)) = s(s(elem!1)))),
% 3.43/3.63 inference(modus_ponens,[status(thm)],[209, 16552])).
% 3.43/3.63 tff(16554,plain,
% 3.43/3.63 (~r(s(s(z)), s(s(elem!1)))),
% 3.43/3.63 inference(unit_resolution,[status(thm)],[9517, 866, 1970, 323])).
% 3.43/3.63 tff(16555,plain,
% 3.43/3.63 (~r(elem!1, s(s(z)))),
% 3.43/3.63 inference(unit_resolution,[status(thm)],[15494, 866, 9751, 2481])).
% 3.43/3.63 tff(16556,plain,
% 3.43/3.63 (~r(s(s(elem!1)), s(s(z)))),
% 3.43/3.63 inference(unit_resolution,[status(thm)],[3656, 16555, 1177])).
% 3.43/3.63 tff(16557,plain,
% 3.43/3.63 (~r(s(z), s(s(z)))),
% 3.43/3.63 inference(unit_resolution,[status(thm)],[14139, 866, 392, 323])).
% 3.43/3.63 tff(16558,plain,
% 3.43/3.63 (b(s(z), s(s(z)))),
% 3.43/3.63 inference(unit_resolution,[status(thm)],[427, 16557])).
% 3.43/3.63 tff(16559,plain,
% 3.43/3.63 ($false),
% 3.43/3.63 inference(unit_resolution,[status(thm)],[5300, 16558, 16556, 376, 52, 16554])).
% 3.43/3.63 tff(16560,plain,((~r(s(s(z)), z)) | (~b(s(z), s(s(elem!1)))) | (s(s(z)) = s(s(elem!1))) | (~(s(s(s(elem!1))) = s(elem!1))) | (~r(s(s(elem!1)), z)) | (~r(z, s(z))) | (~r(s(s(z)), s(z))) | (~r(elem!1, z)) | (~r(z, elem!1))), inference(lemma,lemma(discharge,[]))).
% 3.43/3.63 tff(16561,plain,
% 3.43/3.63 (~r(s(s(z)), z)),
% 3.43/3.63 inference(unit_resolution,[status(thm)],[16560, 16553, 376, 16309, 16547, 16542, 4143, 16405, 16395])).
% 3.43/3.63 tff(16562,plain,
% 3.43/3.63 (b(s(s(z)), z)),
% 3.43/3.63 inference(unit_resolution,[status(thm)],[186, 16561])).
% 3.43/3.63 tff(16563,plain,
% 3.43/3.63 (~b(s(z), s(s(z)))),
% 3.43/3.63 inference(unit_resolution,[status(thm)],[12846, 16562, 53, 10451])).
% 3.43/3.63 tff(16564,plain,
% 3.43/3.63 (r(s(z), s(s(z)))),
% 3.43/3.63 inference(unit_resolution,[status(thm)],[427, 16563])).
% 3.43/3.63 tff(16565,plain,
% 3.43/3.63 (r(s(s(s(elem!1))), z)),
% 3.43/3.63 inference(unit_resolution,[status(thm)],[94, 16403])).
% 3.43/3.63 tff(16566,plain,
% 3.43/3.63 (r(z, s(s(s(elem!1))))),
% 3.43/3.63 inference(unit_resolution,[status(thm)],[261, 16393])).
% 3.43/3.63 tff(16567,plain,
% 3.43/3.63 (~r(s(s(s(elem!1))), s(z))),
% 3.43/3.63 inference(unit_resolution,[status(thm)],[980, 16564, 16566, 16542])).
% 3.43/3.63 tff(16568,plain,
% 3.43/3.63 (b(s(s(s(elem!1))), s(z))),
% 3.43/3.63 inference(unit_resolution,[status(thm)],[1849, 16567])).
% 3.43/3.63 tff(16569,plain,
% 3.43/3.63 (b(s(z), s(s(s(elem!1))))),
% 3.43/3.63 inference(unit_resolution,[status(thm)],[5500, 16308, 376])).
% 3.43/3.63 tff(16570,plain,
% 3.43/3.63 ((elem!1 = s(s(s(z)))) <=> (s(s(s(elem!1))) = s(s(s(z))))),
% 3.43/3.63 inference(monotonicity,[status(thm)],[16312])).
% 3.43/3.63 tff(16571,plain,
% 3.43/3.63 ((~(elem!1 = s(s(s(z))))) <=> (~(s(s(s(elem!1))) = s(s(s(z)))))),
% 3.43/3.63 inference(monotonicity,[status(thm)],[16570])).
% 3.43/3.63 tff(16572,plain,
% 3.43/3.63 (~(s(s(s(z))) = elem!1)),
% 3.43/3.63 inference(unit_resolution,[status(thm)],[3122, 16308])).
% 3.43/3.63 tff(16573,plain,
% 3.43/3.63 (~(elem!1 = s(s(s(z))))),
% 3.43/3.63 inference(unit_resolution,[status(thm)],[1564, 16572])).
% 3.43/3.63 tff(16574,plain,
% 3.43/3.63 (~(s(s(s(elem!1))) = s(s(s(z))))),
% 3.43/3.63 inference(modus_ponens,[status(thm)],[16573, 16571])).
% 3.43/3.63 tff(16575,plain,
% 3.43/3.63 (~r(s(s(s(z))), z)),
% 3.43/3.63 inference(unit_resolution,[status(thm)],[13905, 16574, 16569, 16568, 16565, 16542, 16564])).
% 3.43/3.63 tff(16576,plain,
% 3.43/3.63 (b(s(s(s(z))), z)),
% 3.43/3.63 inference(unit_resolution,[status(thm)],[1713, 16575])).
% 3.43/3.63 tff(16577,plain,
% 3.43/3.63 (~b(s(s(z)), s(s(s(z))))),
% 3.43/3.63 inference(unit_resolution,[status(thm)],[13913, 166, 10451, 16562, 16576])).
% 3.43/3.63 tff(16578,plain,
% 3.43/3.63 (r(s(s(z)), s(s(s(z))))),
% 3.43/3.63 inference(unit_resolution,[status(thm)],[1730, 16577])).
% 3.43/3.63 tff(16579,plain,
% 3.43/3.63 (~b(s(z), s(s(s(z))))),
% 3.43/3.63 inference(unit_resolution,[status(thm)],[13921, 166, 53, 10451, 16562, 16576])).
% 3.43/3.63 tff(16580,plain,
% 3.43/3.63 (r(s(z), s(s(s(z))))),
% 3.43/3.63 inference(unit_resolution,[status(thm)],[1674, 16579])).
% 3.43/3.63 tff(16581,plain,
% 3.43/3.63 (~b(s(s(s(z))), s(z))),
% 3.43/3.63 inference(unit_resolution,[status(thm)],[13929, 166, 53, 10451, 16562, 16576])).
% 3.43/3.63 tff(16582,plain,
% 3.43/3.63 (r(s(s(s(z))), s(z))),
% 3.43/3.63 inference(unit_resolution,[status(thm)],[1763, 16581])).
% 3.43/3.63 tff(16583,plain,
% 3.43/3.63 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(s(z)))) | (~r(s(s(z)), s(s(s(z))))) | (~r(s(z), s(s(s(z))))) | (~r(s(s(s(z))), s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(z), s(s(z)))) | (~r(s(s(z)), s(s(s(z))))) | (~r(s(z), s(s(s(z))))) | (~r(s(s(s(z))), s(z))))),
% 3.43/3.63 inference(rewrite,[status(thm)],[])).
% 3.43/3.63 tff(16584,plain,
% 3.43/3.63 (((~r(s(s(s(z))), s(z))) | (~r(s(s(z)), s(s(s(z))))) | (~r(s(z), s(s(s(z))))) | (~r(s(z), s(s(z))))) <=> ((~r(s(z), s(s(z)))) | (~r(s(s(z)), s(s(s(z))))) | (~r(s(z), s(s(s(z))))) | (~r(s(s(s(z))), s(z))))),
% 3.43/3.63 inference(rewrite,[status(thm)],[])).
% 3.43/3.63 tff(16585,plain,
% 3.43/3.63 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(z))), s(z))) | (~r(s(s(z)), s(s(s(z))))) | (~r(s(z), s(s(s(z))))) | (~r(s(z), s(s(z)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(s(z)))) | (~r(s(s(z)), s(s(s(z))))) | (~r(s(z), s(s(s(z))))) | (~r(s(s(s(z))), s(z)))))),
% 3.43/3.63 inference(monotonicity,[status(thm)],[16584])).
% 3.43/3.63 tff(16586,plain,
% 3.43/3.63 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(z))), s(z))) | (~r(s(s(z)), s(s(s(z))))) | (~r(s(z), s(s(s(z))))) | (~r(s(z), s(s(z)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(z), s(s(z)))) | (~r(s(s(z)), s(s(s(z))))) | (~r(s(z), s(s(s(z))))) | (~r(s(s(s(z))), s(z))))),
% 3.43/3.63 inference(transitivity,[status(thm)],[16585, 16583])).
% 3.43/3.63 tff(16587,plain,
% 3.43/3.63 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(z))), s(z))) | (~r(s(s(z)), s(s(s(z))))) | (~r(s(z), s(s(s(z))))) | (~r(s(z), s(s(z)))))),
% 3.43/3.63 inference(quant_inst,[status(thm)],[])).
% 3.43/3.63 tff(16588,plain,
% 3.43/3.63 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(z), s(s(z)))) | (~r(s(s(z)), s(s(s(z))))) | (~r(s(z), s(s(s(z))))) | (~r(s(s(s(z))), s(z)))),
% 3.43/3.63 inference(modus_ponens,[status(thm)],[16587, 16586])).
% 3.43/3.63 tff(16589,plain,
% 3.43/3.63 ($false),
% 3.43/3.63 inference(unit_resolution,[status(thm)],[16588, 197, 16564, 16582, 16580, 16578])).
% 3.43/3.63 tff(16590,plain,((~b(s(z), z)) | (~b(z, s(s(z)))) | (~b(s(z), s(s(elem!1)))) | b(s(s(z)), s(z))), inference(lemma,lemma(discharge,[]))).
% 3.43/3.63 tff(16591,plain,
% 3.43/3.63 (~b(s(z), z)),
% 3.43/3.63 inference(unit_resolution,[status(thm)],[16590, 3936, 376, 10451])).
% 3.43/3.63 tff(16592,plain,
% 3.43/3.63 (r(s(z), z)),
% 3.43/3.63 inference(unit_resolution,[status(thm)],[230, 16591])).
% 3.43/3.63 tff(16593,plain,
% 3.43/3.63 (b(s(s(elem!1)), s(z))),
% 3.43/3.63 inference(unit_resolution,[status(thm)],[11986, 16592, 10451, 4143])).
% 3.43/3.63 tff(16594,plain,
% 3.43/3.63 (~(s(s(z)) = s(s(elem!1)))),
% 3.43/3.63 inference(unit_resolution,[status(thm)],[3938, 16593, 3936])).
% 3.43/3.63 tff(16595,plain,
% 3.43/3.63 (b(s(s(elem!1)), s(z))),
% 3.43/3.63 inference(unit_resolution,[status(thm)],[11986, 97, 10451, 392])).
% 3.43/3.63 tff(16596,plain,
% 3.43/3.63 (~b(z, s(s(elem!1)))),
% 3.43/3.63 inference(unit_resolution,[status(thm)],[5343, 118, 376, 16595])).
% 3.43/3.63 tff(16597,plain,
% 3.43/3.63 (r(z, s(s(elem!1)))),
% 3.43/3.63 inference(unit_resolution,[status(thm)],[1795, 16596])).
% 3.43/3.63 tff(16598,plain,
% 3.43/3.63 (~r(s(s(z)), z)),
% 3.43/3.63 inference(unit_resolution,[status(thm)],[11980, 16597, 392, 97])).
% 3.43/3.63 tff(16599,plain,
% 3.43/3.63 (b(s(s(z)), z)),
% 3.43/3.63 inference(unit_resolution,[status(thm)],[186, 16598])).
% 3.43/3.63 tff(16600,plain,
% 3.43/3.63 (~r(s(s(s(elem!1))), s(z))),
% 3.43/3.63 inference(unit_resolution,[status(thm)],[10745, 121, 10451, 13953, 122])).
% 3.43/3.63 tff(16601,plain,
% 3.43/3.63 (~b(s(s(s(elem!1))), s(z))),
% 3.43/3.63 inference(unit_resolution,[status(thm)],[7150, 121, 376, 118, 310])).
% 3.43/3.63 tff(16602,plain,
% 3.43/3.63 ($false),
% 3.43/3.63 inference(unit_resolution,[status(thm)],[1849, 16601, 16600])).
% 3.43/3.63 tff(16603,plain,((~b(s(s(s(elem!1))), z)) | (~b(s(z), s(s(elem!1)))) | (~b(z, s(z))) | (~b(s(s(elem!1)), s(z))) | (~b(z, s(s(z)))) | (~b(s(s(z)), z))), inference(lemma,lemma(discharge,[]))).
% 3.43/3.63 tff(16604,plain,
% 3.43/3.63 (~b(s(s(s(elem!1))), z)),
% 3.43/3.63 inference(unit_resolution,[status(thm)],[16603, 118, 376, 16595, 10451, 16599])).
% 3.43/3.63 tff(16605,plain,
% 3.43/3.63 (r(s(s(s(elem!1))), z)),
% 3.43/3.63 inference(unit_resolution,[status(thm)],[94, 16604])).
% 3.43/3.63 tff(16606,plain,
% 3.43/3.63 (~r(s(s(s(elem!1))), s(z))),
% 3.43/3.63 inference(unit_resolution,[status(thm)],[4466, 16605, 97, 16597])).
% 3.43/3.63 tff(16607,plain,
% 3.43/3.63 (b(s(s(s(elem!1))), s(z))),
% 3.43/3.63 inference(unit_resolution,[status(thm)],[1849, 16606])).
% 3.43/3.63 tff(16608,plain,
% 3.43/3.63 (~b(s(s(elem!1)), s(s(s(elem!1))))),
% 3.43/3.63 inference(unit_resolution,[status(thm)],[8544, 166, 376, 16607, 16595])).
% 3.43/3.63 tff(16609,plain,
% 3.43/3.63 (~b(s(s(elem!1)), z)),
% 3.43/3.63 inference(unit_resolution,[status(thm)],[7172, 166, 376, 118, 16595])).
% 3.43/3.63 tff(16610,plain,
% 3.43/3.63 (r(s(s(elem!1)), z)),
% 3.43/3.63 inference(unit_resolution,[status(thm)],[608, 16609])).
% 3.43/3.63 tff(16611,plain,
% 3.43/3.63 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(s(elem!1))))) | (~b(s(z), s(s(elem!1)))) | (~b(s(s(s(elem!1))), s(z))) | (~b(z, s(z))) | (~b(s(s(elem!1)), s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(s(s(elem!1))))) | (~b(s(z), s(s(elem!1)))) | (~b(s(s(s(elem!1))), s(z))) | (~b(z, s(z))) | (~b(s(s(elem!1)), s(z))))),
% 3.43/3.63 inference(rewrite,[status(thm)],[])).
% 3.43/3.63 tff(16612,plain,
% 3.43/3.63 (((~b(s(s(elem!1)), s(z))) | (~b(z, s(z))) | (~b(s(z), s(s(elem!1)))) | (~b(s(s(s(elem!1))), s(z))) | (~b(z, s(z))) | (~b(z, s(s(s(elem!1)))))) <=> ((~b(z, s(s(s(elem!1))))) | (~b(s(z), s(s(elem!1)))) | (~b(s(s(s(elem!1))), s(z))) | (~b(z, s(z))) | (~b(s(s(elem!1)), s(z))))),
% 3.43/3.63 inference(rewrite,[status(thm)],[])).
% 3.43/3.63 tff(16613,plain,
% 3.43/3.63 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), s(z))) | (~b(z, s(z))) | (~b(s(z), s(s(elem!1)))) | (~b(s(s(s(elem!1))), s(z))) | (~b(z, s(z))) | (~b(z, s(s(s(elem!1))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(s(elem!1))))) | (~b(s(z), s(s(elem!1)))) | (~b(s(s(s(elem!1))), s(z))) | (~b(z, s(z))) | (~b(s(s(elem!1)), s(z)))))),
% 3.43/3.63 inference(monotonicity,[status(thm)],[16612])).
% 3.43/3.63 tff(16614,plain,
% 3.43/3.63 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), s(z))) | (~b(z, s(z))) | (~b(s(z), s(s(elem!1)))) | (~b(s(s(s(elem!1))), s(z))) | (~b(z, s(z))) | (~b(z, s(s(s(elem!1))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(s(s(elem!1))))) | (~b(s(z), s(s(elem!1)))) | (~b(s(s(s(elem!1))), s(z))) | (~b(z, s(z))) | (~b(s(s(elem!1)), s(z))))),
% 3.43/3.63 inference(transitivity,[status(thm)],[16613, 16611])).
% 3.43/3.63 tff(16615,plain,
% 3.43/3.63 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), s(z))) | (~b(z, s(z))) | (~b(s(z), s(s(elem!1)))) | (~b(s(s(s(elem!1))), s(z))) | (~b(z, s(z))) | (~b(z, s(s(s(elem!1))))))),
% 3.43/3.63 inference(quant_inst,[status(thm)],[])).
% 3.43/3.63 tff(16616,plain,
% 3.43/3.63 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(s(s(elem!1))))) | (~b(s(z), s(s(elem!1)))) | (~b(s(s(s(elem!1))), s(z))) | (~b(z, s(z))) | (~b(s(s(elem!1)), s(z)))),
% 3.43/3.63 inference(modus_ponens,[status(thm)],[16615, 16614])).
% 3.43/3.63 tff(16617,plain,
% 3.43/3.63 (~b(z, s(s(s(elem!1))))),
% 3.43/3.63 inference(unit_resolution,[status(thm)],[16616, 166, 376, 16607, 118, 16595])).
% 3.43/3.63 tff(16618,plain,
% 3.43/3.63 (r(z, s(s(s(elem!1))))),
% 3.43/3.63 inference(unit_resolution,[status(thm)],[261, 16617])).
% 3.43/3.63 tff(16619,plain,
% 3.43/3.63 (~r(s(s(elem!1)), s(s(s(elem!1))))),
% 3.43/3.63 inference(unit_resolution,[status(thm)],[4018, 16618, 16605, 16610])).
% 3.43/3.63 tff(16620,plain,
% 3.43/3.63 (s(s(elem!1)) = s(s(s(elem!1)))),
% 3.43/3.63 inference(unit_resolution,[status(thm)],[461, 16619, 16608])).
% 3.43/3.63 tff(16621,plain,
% 3.43/3.63 (s(s(s(elem!1))) = s(s(elem!1))),
% 3.43/3.63 inference(symmetry,[status(thm)],[16620])).
% 3.43/3.63 tff(16622,plain,
% 3.43/3.63 (r(s(s(s(z))), s(s(s(elem!1)))) <=> r(s(s(s(z))), s(s(elem!1)))),
% 3.43/3.63 inference(monotonicity,[status(thm)],[16621])).
% 3.43/3.63 tff(16623,plain,
% 3.43/3.63 (r(s(s(s(z))), s(s(elem!1))) <=> r(s(s(s(z))), s(s(s(elem!1))))),
% 3.43/3.63 inference(symmetry,[status(thm)],[16622])).
% 3.43/3.63 tff(16624,plain,
% 3.43/3.63 (s(s(s(elem!1))) = s(elem!1)),
% 3.43/3.63 inference(unit_resolution,[status(thm)],[2594, 16620])).
% 3.43/3.63 tff(16625,plain,
% 3.43/3.63 (s(elem!1) = s(s(s(elem!1)))),
% 3.43/3.63 inference(symmetry,[status(thm)],[16624])).
% 3.43/3.63 tff(16626,plain,
% 3.43/3.63 (inj_0(s(elem!1)) = inj_0(s(s(s(elem!1))))),
% 3.43/3.63 inference(monotonicity,[status(thm)],[16625])).
% 3.43/3.63 tff(16627,plain,
% 3.43/3.63 (elem!1 = s(s(elem!1))),
% 3.43/3.63 inference(transitivity,[status(thm)],[1170, 16626, 104])).
% 3.43/3.63 tff(16628,plain,
% 3.43/3.63 (r(s(s(s(z))), elem!1) <=> r(s(s(s(z))), s(s(elem!1)))),
% 3.43/3.63 inference(monotonicity,[status(thm)],[16627])).
% 3.43/3.63 tff(16629,plain,
% 3.43/3.63 (~(s(s(s(z))) = elem!1)),
% 3.43/3.63 inference(unit_resolution,[status(thm)],[3122, 16620])).
% 3.43/3.63 tff(16630,plain,
% 3.43/3.63 (s(s(s(elem!1))) = s(s(elem!1))),
% 3.43/3.63 inference(unit_resolution,[status(thm)],[4030, 16620])).
% 3.43/3.63 tff(16631,plain,
% 3.43/3.63 (b(s(z), s(s(s(elem!1))))),
% 3.43/3.63 inference(unit_resolution,[status(thm)],[5500, 16620, 376])).
% 3.43/3.63 tff(16632,plain,
% 3.43/3.63 (~b(s(s(s(z))), z)),
% 3.43/3.63 inference(unit_resolution,[status(thm)],[13966, 16631, 16607, 118, 392, 10451, 16599])).
% 3.43/3.63 tff(16633,plain,
% 3.43/3.63 (r(s(s(s(z))), z)),
% 3.43/3.63 inference(unit_resolution,[status(thm)],[1713, 16632])).
% 3.43/3.63 tff(16634,plain,
% 3.43/3.63 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(s(elem!1))))) | (~r(s(z), z)) | (~r(s(s(s(z))), z)) | (~r(s(z), s(s(s(z))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, s(s(s(elem!1))))) | (~r(s(z), z)) | (~r(s(s(s(z))), z)) | (~r(s(z), s(s(s(z))))))),
% 3.43/3.63 inference(rewrite,[status(thm)],[])).
% 3.43/3.64 tff(16635,plain,
% 3.43/3.64 (((~r(z, s(s(s(elem!1))))) | (~r(s(s(s(z))), z)) | (~r(s(z), z)) | (~r(s(z), s(s(s(z)))))) <=> ((~r(z, s(s(s(elem!1))))) | (~r(s(z), z)) | (~r(s(s(s(z))), z)) | (~r(s(z), s(s(s(z))))))),
% 3.43/3.64 inference(rewrite,[status(thm)],[])).
% 3.43/3.64 tff(16636,plain,
% 3.43/3.64 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(s(elem!1))))) | (~r(s(s(s(z))), z)) | (~r(s(z), z)) | (~r(s(z), s(s(s(z))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(s(elem!1))))) | (~r(s(z), z)) | (~r(s(s(s(z))), z)) | (~r(s(z), s(s(s(z)))))))),
% 3.43/3.64 inference(monotonicity,[status(thm)],[16635])).
% 3.43/3.64 tff(16637,plain,
% 3.43/3.64 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(s(elem!1))))) | (~r(s(s(s(z))), z)) | (~r(s(z), z)) | (~r(s(z), s(s(s(z))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, s(s(s(elem!1))))) | (~r(s(z), z)) | (~r(s(s(s(z))), z)) | (~r(s(z), s(s(s(z))))))),
% 3.43/3.64 inference(transitivity,[status(thm)],[16636, 16634])).
% 3.43/3.64 tff(16638,plain,
% 3.43/3.64 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(s(elem!1))))) | (~r(s(s(s(z))), z)) | (~r(s(z), z)) | (~r(s(z), s(s(s(z))))))),
% 3.43/3.64 inference(quant_inst,[status(thm)],[])).
% 3.43/3.64 tff(16639,plain,
% 3.43/3.64 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, s(s(s(elem!1))))) | (~r(s(z), z)) | (~r(s(s(s(z))), z)) | (~r(s(z), s(s(s(z)))))),
% 3.43/3.64 inference(modus_ponens,[status(thm)],[16638, 16637])).
% 3.43/3.64 tff(16640,plain,
% 3.43/3.64 (~r(s(z), s(s(s(z))))),
% 3.43/3.64 inference(unit_resolution,[status(thm)],[16639, 197, 97, 16618, 16633])).
% 3.43/3.64 tff(16641,plain,
% 3.43/3.64 (b(s(z), s(s(s(z))))),
% 3.43/3.64 inference(unit_resolution,[status(thm)],[1674, 16640])).
% 3.43/3.64 tff(16642,plain,
% 3.43/3.64 (~b(s(s(s(z))), s(s(s(elem!1))))),
% 3.43/3.64 inference(unit_resolution,[status(thm)],[8841, 16641, 16607, 16631])).
% 3.43/3.64 tff(16643,plain,
% 3.43/3.64 (~b(s(s(s(z))), elem!1)),
% 3.43/3.64 inference(unit_resolution,[status(thm)],[4078, 16642, 16630])).
% 3.43/3.64 tff(16644,plain,
% 3.43/3.64 (r(s(s(s(z))), elem!1)),
% 3.43/3.64 inference(unit_resolution,[status(thm)],[2826, 16643, 16629])).
% 3.43/3.64 tff(16645,plain,
% 3.43/3.64 (r(s(s(s(z))), s(s(elem!1)))),
% 3.43/3.64 inference(modus_ponens,[status(thm)],[16644, 16628])).
% 3.43/3.64 tff(16646,plain,
% 3.43/3.64 (r(s(s(s(z))), s(s(s(elem!1))))),
% 3.43/3.64 inference(modus_ponens,[status(thm)],[16645, 16623])).
% 3.43/3.64 tff(16647,plain,
% 3.43/3.64 (~r(s(s(s(z))), s(s(s(elem!1))))),
% 3.43/3.64 inference(unit_resolution,[status(thm)],[13628, 197, 16605, 16618, 16633])).
% 3.43/3.64 tff(16648,plain,
% 3.43/3.64 ($false),
% 3.43/3.64 inference(unit_resolution,[status(thm)],[16647, 16646])).
% 3.43/3.64 tff(16649,plain,((~b(z, s(z))) | (~r(s(z), z)) | (~r(s(s(z)), s(z))) | (~b(z, s(s(z)))) | (~b(s(z), s(s(elem!1))))), inference(lemma,lemma(discharge,[]))).
% 3.43/3.64 tff(16650,plain,
% 3.43/3.64 (~b(z, s(z))),
% 3.43/3.64 inference(unit_resolution,[status(thm)],[16649, 97, 392, 10451, 376])).
% 3.43/3.64 tff(16651,plain,
% 3.43/3.64 (r(z, s(z))),
% 3.43/3.64 inference(unit_resolution,[status(thm)],[321, 16650])).
% 3.43/3.64 tff(16652,plain,
% 3.43/3.64 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), z)) | (~r(s(s(z)), s(z))) | (~r(s(s(s(elem!1))), s(z))) | (~r(s(s(s(elem!1))), s(s(z)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(z), z)) | (~r(s(s(z)), s(z))) | (~r(s(s(s(elem!1))), s(z))) | (~r(s(s(s(elem!1))), s(s(z)))))),
% 3.43/3.64 inference(rewrite,[status(thm)],[])).
% 3.43/3.64 tff(16653,plain,
% 3.43/3.64 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), z)) | (~r(s(s(z)), s(z))) | (~r(s(s(s(elem!1))), s(z))) | (~r(s(s(s(elem!1))), s(s(z)))))),
% 3.43/3.64 inference(quant_inst,[status(thm)],[])).
% 3.43/3.64 tff(16654,plain,
% 3.43/3.64 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(z), z)) | (~r(s(s(z)), s(z))) | (~r(s(s(s(elem!1))), s(z))) | (~r(s(s(s(elem!1))), s(s(z))))),
% 3.43/3.64 inference(modus_ponens,[status(thm)],[16653, 16652])).
% 3.43/3.64 tff(16655,plain,
% 3.43/3.64 (~r(s(s(s(elem!1))), s(s(z)))),
% 3.43/3.64 inference(unit_resolution,[status(thm)],[16654, 197, 350, 97, 392])).
% 3.43/3.64 tff(16656,plain,
% 3.43/3.64 (b(s(s(s(elem!1))), s(s(z)))),
% 3.43/3.64 inference(unit_resolution,[status(thm)],[218, 16655])).
% 3.43/3.64 tff(16657,plain,
% 3.43/3.64 ($false),
% 3.43/3.64 inference(unit_resolution,[status(thm)],[10459, 16656, 2661, 10451, 12378])).
% 3.43/3.64 tff(16658,plain,((~r(s(s(s(elem!1))), s(z))) | (~b(z, s(s(z)))) | (~r(s(z), z)) | (~r(s(s(z)), s(z))) | (~r(z, s(z)))), inference(lemma,lemma(discharge,[]))).
% 3.43/3.64 tff(16659,plain,
% 3.43/3.64 (~r(s(s(s(elem!1))), s(z))),
% 3.43/3.64 inference(unit_resolution,[status(thm)],[16658, 97, 10451, 392, 16651])).
% 3.43/3.64 tff(16660,plain,
% 3.43/3.64 (b(s(s(s(elem!1))), s(z))),
% 3.43/3.64 inference(unit_resolution,[status(thm)],[1849, 16659])).
% 3.43/3.64 tff(16661,plain,
% 3.43/3.64 (~b(s(s(s(elem!1))), s(s(elem!1)))),
% 3.43/3.64 inference(unit_resolution,[status(thm)],[1858, 16660, 376, 16595])).
% 3.43/3.64 tff(16662,plain,
% 3.43/3.64 (r(s(s(s(elem!1))), s(s(elem!1)))),
% 3.43/3.64 inference(unit_resolution,[status(thm)],[889, 51, 16661])).
% 3.43/3.64 tff(16663,plain,
% 3.43/3.64 (~b(s(s(elem!1)), s(s(s(elem!1))))),
% 3.43/3.64 inference(unit_resolution,[status(thm)],[8544, 166, 376, 16660, 16595])).
% 3.43/3.64 tff(16664,plain,
% 3.43/3.64 (r(s(s(elem!1)), s(s(s(elem!1))))),
% 3.43/3.64 inference(unit_resolution,[status(thm)],[461, 45, 16663])).
% 3.43/3.64 tff(16665,plain,
% 3.43/3.64 (~r(s(s(z)), z)),
% 3.43/3.64 inference(unit_resolution,[status(thm)],[12376, 197, 16651, 97, 392])).
% 3.43/3.64 tff(16666,plain,
% 3.43/3.64 (b(s(s(z)), z)),
% 3.43/3.64 inference(unit_resolution,[status(thm)],[186, 16665])).
% 3.43/3.64 tff(16667,plain,
% 3.43/3.64 (~b(s(s(s(elem!1))), s(s(z)))),
% 3.43/3.64 inference(unit_resolution,[status(thm)],[10459, 121, 10451, 16666])).
% 3.43/3.64 tff(16668,plain,
% 3.43/3.64 (r(s(s(s(elem!1))), s(s(z)))),
% 3.43/3.64 inference(unit_resolution,[status(thm)],[218, 16667])).
% 3.43/3.64 tff(16669,plain,
% 3.43/3.64 (~r(s(s(elem!1)), s(s(z)))),
% 3.43/3.64 inference(unit_resolution,[status(thm)],[4313, 464, 392, 905])).
% 3.43/3.64 tff(16670,plain,
% 3.43/3.64 (r(s(s(z)), s(s(elem!1)))),
% 3.43/3.64 inference(unit_resolution,[status(thm)],[5300, 16669, 376, 52, 556])).
% 3.43/3.64 tff(16671,plain,
% 3.43/3.64 ($false),
% 3.43/3.64 inference(unit_resolution,[status(thm)],[12620, 197, 377, 16670, 905, 464])).
% 3.43/3.64 tff(16672,plain,((~r(s(s(s(elem!1))), s(s(z)))) | (~r(s(s(elem!1)), s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(z), s(s(elem!1)))) | (s(s(z)) = s(s(elem!1))) | (~b(s(z), s(s(z)))) | (~r(s(s(z)), s(z)))), inference(lemma,lemma(discharge,[]))).
% 3.43/3.64 tff(16673,plain,
% 3.43/3.64 ($false),
% 3.43/3.64 inference(unit_resolution,[status(thm)],[16672, 12349, 12351, 464, 376, 52, 556, 392])).
% 3.43/3.64 tff(16674,plain,((s(s(elem!1)) = s(s(s(elem!1)))) | (~r(s(s(s(elem!1))), s(s(z)))) | (~b(s(z), s(s(elem!1)))) | (s(s(z)) = s(s(elem!1))) | (~b(s(z), s(s(z)))) | (~r(s(s(z)), s(z))) | b(s(s(s(elem!1))), s(s(elem!1))) | b(s(s(elem!1)), s(s(s(elem!1))))), inference(lemma,lemma(discharge,[]))).
% 3.43/3.64 tff(16675,plain,
% 3.43/3.64 (s(s(elem!1)) = s(s(s(elem!1)))),
% 3.43/3.64 inference(unit_resolution,[status(thm)],[16674, 556, 376, 52, 16668, 392, 16661, 16663])).
% 3.43/3.64 tff(16676,plain,
% 3.43/3.64 (s(s(s(elem!1))) = s(s(elem!1))),
% 3.43/3.64 inference(symmetry,[status(thm)],[16675])).
% 3.43/3.64 tff(16677,plain,
% 3.43/3.64 (r(s(s(s(z))), s(s(s(elem!1)))) <=> r(s(s(s(z))), s(s(elem!1)))),
% 3.43/3.64 inference(monotonicity,[status(thm)],[16676])).
% 3.43/3.64 tff(16678,plain,
% 3.43/3.64 (r(s(s(s(z))), s(s(elem!1))) <=> r(s(s(s(z))), s(s(s(elem!1))))),
% 3.43/3.64 inference(symmetry,[status(thm)],[16677])).
% 3.43/3.64 tff(16679,plain,
% 3.43/3.64 (s(s(s(elem!1))) = s(elem!1)),
% 3.43/3.64 inference(unit_resolution,[status(thm)],[2594, 16675])).
% 3.43/3.64 tff(16680,plain,
% 3.43/3.64 (s(elem!1) = s(s(s(elem!1)))),
% 3.43/3.64 inference(symmetry,[status(thm)],[16679])).
% 3.43/3.64 tff(16681,plain,
% 3.43/3.64 (inj_0(s(elem!1)) = inj_0(s(s(s(elem!1))))),
% 3.43/3.64 inference(monotonicity,[status(thm)],[16680])).
% 3.43/3.64 tff(16682,plain,
% 3.43/3.64 (elem!1 = s(s(elem!1))),
% 3.43/3.64 inference(transitivity,[status(thm)],[1170, 16681, 104])).
% 3.43/3.64 tff(16683,plain,
% 3.43/3.64 (r(s(s(s(z))), elem!1) <=> r(s(s(s(z))), s(s(elem!1)))),
% 3.43/3.64 inference(monotonicity,[status(thm)],[16682])).
% 3.43/3.64 tff(16684,plain,
% 3.43/3.64 (~(s(s(s(z))) = elem!1)),
% 3.43/3.64 inference(unit_resolution,[status(thm)],[3122, 16675])).
% 3.43/3.64 tff(16685,plain,
% 3.43/3.64 (s(s(s(elem!1))) = s(s(elem!1))),
% 3.43/3.64 inference(unit_resolution,[status(thm)],[4030, 16675])).
% 3.43/3.64 tff(16686,plain,
% 3.43/3.64 (~b(s(s(z)), s(s(s(elem!1))))),
% 3.43/3.64 inference(unit_resolution,[status(thm)],[10468, 166, 10451, 121, 16666])).
% 3.43/3.64 tff(16687,plain,
% 3.43/3.64 (r(s(s(z)), s(s(s(elem!1))))),
% 3.43/3.64 inference(unit_resolution,[status(thm)],[279, 16686])).
% 3.43/3.64 tff(16688,plain,
% 3.43/3.64 (b(s(z), s(s(s(elem!1))))),
% 3.43/3.64 inference(unit_resolution,[status(thm)],[15377, 16687, 376, 392, 16661])).
% 3.43/3.64 tff(16689,plain,
% 3.43/3.64 (~b(s(z), s(s(s(z))))),
% 3.43/3.64 inference(unit_resolution,[status(thm)],[8866, 556, 16687, 16668, 16675, 16660, 16688])).
% 3.43/3.64 tff(16690,plain,
% 3.43/3.64 (r(s(z), s(s(s(z))))),
% 3.43/3.64 inference(unit_resolution,[status(thm)],[1674, 16689])).
% 3.43/3.64 tff(16691,plain,
% 3.43/3.64 (~r(s(s(s(z))), z)),
% 3.43/3.64 inference(unit_resolution,[status(thm)],[8876, 16690, 97, 16651])).
% 3.43/3.64 tff(16692,plain,
% 3.43/3.64 (b(s(s(s(z))), z)),
% 3.43/3.64 inference(unit_resolution,[status(thm)],[1713, 16691])).
% 3.43/3.64 tff(16693,plain,
% 3.43/3.64 (~b(s(s(s(z))), s(s(s(elem!1))))),
% 3.43/3.64 inference(unit_resolution,[status(thm)],[12285, 166, 10451, 121, 16666, 16692])).
% 3.43/3.64 tff(16694,plain,
% 3.43/3.64 (~b(s(s(s(z))), elem!1)),
% 3.43/3.64 inference(unit_resolution,[status(thm)],[4078, 16693, 16685])).
% 3.43/3.64 tff(16695,plain,
% 3.43/3.64 (r(s(s(s(z))), elem!1)),
% 3.43/3.64 inference(unit_resolution,[status(thm)],[2826, 16694, 16684])).
% 3.43/3.64 tff(16696,plain,
% 3.43/3.64 (r(s(s(s(z))), s(s(elem!1)))),
% 3.43/3.64 inference(modus_ponens,[status(thm)],[16695, 16683])).
% 3.43/3.64 tff(16697,plain,
% 3.43/3.64 (r(s(s(s(z))), s(s(s(elem!1))))),
% 3.43/3.64 inference(modus_ponens,[status(thm)],[16696, 16678])).
% 3.43/3.64 tff(16698,plain,
% 3.43/3.64 (~b(s(s(z)), s(s(s(z))))),
% 3.43/3.64 inference(unit_resolution,[status(thm)],[13913, 166, 10451, 16666, 16692])).
% 3.43/3.64 tff(16699,plain,
% 3.43/3.64 (r(s(s(z)), s(s(s(z))))),
% 3.43/3.64 inference(unit_resolution,[status(thm)],[1730, 16698])).
% 3.43/3.64 tff(16700,plain,
% 3.43/3.64 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(z))), s(s(s(elem!1))))) | (~r(s(s(z)), s(z))) | (~r(s(s(z)), s(s(s(z))))) | (~r(s(z), s(s(s(z))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(z))), s(s(s(elem!1))))) | (~r(s(s(z)), s(z))) | (~r(s(s(z)), s(s(s(z))))) | (~r(s(z), s(s(s(z))))))),
% 3.43/3.64 inference(rewrite,[status(thm)],[])).
% 3.43/3.64 tff(16701,plain,
% 3.43/3.64 (((~r(s(s(s(z))), s(s(s(elem!1))))) | (~r(s(z), s(s(s(z))))) | (~r(s(s(z)), s(s(s(z))))) | (~r(s(s(z)), s(z)))) <=> ((~r(s(s(s(z))), s(s(s(elem!1))))) | (~r(s(s(z)), s(z))) | (~r(s(s(z)), s(s(s(z))))) | (~r(s(z), s(s(s(z))))))),
% 3.43/3.64 inference(rewrite,[status(thm)],[])).
% 3.43/3.64 tff(16702,plain,
% 3.43/3.64 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(z))), s(s(s(elem!1))))) | (~r(s(z), s(s(s(z))))) | (~r(s(s(z)), s(s(s(z))))) | (~r(s(s(z)), s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(z))), s(s(s(elem!1))))) | (~r(s(s(z)), s(z))) | (~r(s(s(z)), s(s(s(z))))) | (~r(s(z), s(s(s(z)))))))),
% 3.43/3.64 inference(monotonicity,[status(thm)],[16701])).
% 3.43/3.64 tff(16703,plain,
% 3.43/3.64 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(z))), s(s(s(elem!1))))) | (~r(s(z), s(s(s(z))))) | (~r(s(s(z)), s(s(s(z))))) | (~r(s(s(z)), s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(z))), s(s(s(elem!1))))) | (~r(s(s(z)), s(z))) | (~r(s(s(z)), s(s(s(z))))) | (~r(s(z), s(s(s(z))))))),
% 3.43/3.64 inference(transitivity,[status(thm)],[16702, 16700])).
% 3.43/3.64 tff(16704,plain,
% 3.43/3.64 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(z))), s(s(s(elem!1))))) | (~r(s(z), s(s(s(z))))) | (~r(s(s(z)), s(s(s(z))))) | (~r(s(s(z)), s(z))))),
% 3.43/3.64 inference(quant_inst,[status(thm)],[])).
% 3.43/3.64 tff(16705,plain,
% 3.43/3.64 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(z))), s(s(s(elem!1))))) | (~r(s(s(z)), s(z))) | (~r(s(s(z)), s(s(s(z))))) | (~r(s(z), s(s(s(z)))))),
% 3.43/3.64 inference(modus_ponens,[status(thm)],[16704, 16703])).
% 3.43/3.64 tff(16706,plain,
% 3.43/3.64 (~r(s(s(s(z))), s(s(s(elem!1))))),
% 3.43/3.64 inference(unit_resolution,[status(thm)],[16705, 197, 392, 16690, 16699])).
% 3.43/3.64 tff(16707,plain,
% 3.43/3.64 ($false),
% 3.43/3.64 inference(unit_resolution,[status(thm)],[16706, 16697])).
% 3.43/3.64 tff(16708,plain,((~b(s(z), s(s(z)))) | (~r(s(s(z)), s(z))) | (~b(z, s(s(z)))) | (~b(s(s(s(elem!1))), z)) | (~r(s(z), z)) | (~b(s(z), s(s(elem!1)))) | (s(s(z)) = s(s(elem!1)))), inference(lemma,lemma(discharge,[]))).
% 3.43/3.64 tff(16709,plain,
% 3.43/3.64 (~b(s(z), s(s(z)))),
% 3.43/3.64 inference(unit_resolution,[status(thm)],[16708, 121, 10451, 392, 97, 376, 52])).
% 3.43/3.64 tff(16710,plain,
% 3.43/3.64 (s(s(elem!1)) = s(s(s(elem!1)))),
% 3.43/3.64 inference(unit_resolution,[status(thm)],[12596, 121, 97, 16651, 10451, 16709, 132, 392, 16661, 16663])).
% 3.43/3.64 tff(16711,plain,
% 3.43/3.64 (s(s(s(elem!1))) = s(elem!1)),
% 3.43/3.64 inference(unit_resolution,[status(thm)],[2594, 16710])).
% 3.43/3.64 tff(16712,plain,
% 3.43/3.64 (s(elem!1) = s(s(s(elem!1)))),
% 3.43/3.64 inference(symmetry,[status(thm)],[16711])).
% 3.43/3.64 tff(16713,plain,
% 3.43/3.64 (inj_0(s(elem!1)) = inj_0(s(s(s(elem!1))))),
% 3.43/3.64 inference(monotonicity,[status(thm)],[16712])).
% 3.43/3.64 tff(16714,plain,
% 3.43/3.64 (elem!1 = s(s(s(elem!1)))),
% 3.43/3.64 inference(transitivity,[status(thm)],[1170, 16713, 104, 16710])).
% 3.43/3.64 tff(16715,plain,
% 3.43/3.64 (b(elem!1, s(s(s(s(z))))) <=> b(s(s(s(elem!1))), s(s(s(s(z)))))),
% 3.43/3.64 inference(monotonicity,[status(thm)],[16714])).
% 3.43/3.64 tff(16716,plain,
% 3.43/3.64 ((s(s(elem!1)) = s(s(s(s(elem!1))))) <=> (s(s(s(elem!1))) = s(s(s(s(elem!1)))))),
% 3.43/3.64 inference(monotonicity,[status(thm)],[16710])).
% 3.43/3.64 tff(16717,plain,
% 3.43/3.64 ((s(s(s(elem!1))) = s(s(s(s(elem!1))))) <=> (s(s(elem!1)) = s(s(s(s(elem!1)))))),
% 3.43/3.64 inference(symmetry,[status(thm)],[16716])).
% 3.43/3.64 tff(16718,plain,
% 3.43/3.64 (s(s(s(elem!1))) = s(s(elem!1))),
% 3.43/3.64 inference(symmetry,[status(thm)],[16710])).
% 3.43/3.64 tff(16719,plain,
% 3.43/3.64 (s(s(s(s(elem!1)))) = s(s(s(elem!1)))),
% 3.43/3.64 inference(monotonicity,[status(thm)],[16718])).
% 3.43/3.64 tff(16720,plain,
% 3.43/3.64 (s(s(s(elem!1))) = s(s(s(s(elem!1))))),
% 3.43/3.64 inference(symmetry,[status(thm)],[16719])).
% 3.43/3.64 tff(16721,plain,
% 3.43/3.64 (s(s(elem!1)) = s(s(s(s(elem!1))))),
% 3.43/3.64 inference(modus_ponens,[status(thm)],[16720, 16717])).
% 3.43/3.64 tff(16722,plain,
% 3.43/3.64 (~(elem!1 = s(s(s(s(z)))))),
% 3.43/3.64 inference(unit_resolution,[status(thm)],[5489, 16721])).
% 3.43/3.64 tff(16723,plain,
% 3.43/3.64 (r(s(z), s(s(z)))),
% 3.43/3.64 inference(unit_resolution,[status(thm)],[427, 16709])).
% 3.43/3.64 tff(16724,plain,
% 3.43/3.64 (~b(s(s(s(z))), z)),
% 3.43/3.64 inference(unit_resolution,[status(thm)],[12304, 16710, 10451, 16666, 121])).
% 3.43/3.64 tff(16725,plain,
% 3.43/3.64 (r(s(s(s(z))), z)),
% 3.43/3.64 inference(unit_resolution,[status(thm)],[1713, 16724])).
% 3.43/3.64 tff(16726,plain,
% 3.43/3.64 (~r(s(s(s(z))), s(z))),
% 3.43/3.64 inference(unit_resolution,[status(thm)],[3213, 16725, 16651, 16723])).
% 3.43/3.64 tff(16727,plain,
% 3.43/3.64 (b(s(s(s(z))), s(z))),
% 3.43/3.64 inference(unit_resolution,[status(thm)],[1763, 16726])).
% 3.43/3.64 tff(16728,plain,
% 3.43/3.64 (~r(s(z), s(s(s(z))))),
% 3.43/3.64 inference(unit_resolution,[status(thm)],[8876, 16725, 97, 16651])).
% 3.43/3.64 tff(16729,plain,
% 3.43/3.64 (b(s(z), s(s(s(z))))),
% 3.43/3.64 inference(unit_resolution,[status(thm)],[1674, 16728])).
% 3.43/3.64 tff(16730,plain,
% 3.43/3.64 (~b(s(s(s(elem!1))), s(s(s(z))))),
% 3.43/3.64 inference(unit_resolution,[status(thm)],[11932, 166, 16660, 16729, 16727])).
% 3.43/3.64 tff(16731,plain,
% 3.43/3.64 (r(s(s(s(elem!1))), s(s(s(z))))),
% 3.43/3.64 inference(unit_resolution,[status(thm)],[3574, 16730, 140])).
% 3.43/3.64 tff(16732,plain,
% 3.43/3.64 (r(s(s(s(z))), s(s(s(elem!1)))) <=> r(s(s(s(z))), s(s(elem!1)))),
% 3.43/3.64 inference(monotonicity,[status(thm)],[16718])).
% 3.43/3.64 tff(16733,plain,
% 3.43/3.64 (r(s(s(s(z))), s(s(elem!1))) <=> r(s(s(s(z))), s(s(s(elem!1))))),
% 3.43/3.64 inference(symmetry,[status(thm)],[16732])).
% 3.43/3.64 tff(16734,plain,
% 3.43/3.64 (elem!1 = s(s(elem!1))),
% 3.43/3.64 inference(transitivity,[status(thm)],[1170, 16713, 104])).
% 3.43/3.64 tff(16735,plain,
% 3.43/3.64 (r(s(s(s(z))), elem!1) <=> r(s(s(s(z))), s(s(elem!1)))),
% 3.43/3.64 inference(monotonicity,[status(thm)],[16734])).
% 3.43/3.64 tff(16736,plain,
% 3.43/3.64 (~(s(s(s(z))) = elem!1)),
% 3.43/3.64 inference(unit_resolution,[status(thm)],[3122, 16710])).
% 3.43/3.64 tff(16737,plain,
% 3.43/3.64 (s(s(s(elem!1))) = s(s(elem!1))),
% 3.43/3.64 inference(unit_resolution,[status(thm)],[4030, 16710])).
% 3.43/3.64 tff(16738,plain,
% 3.43/3.64 (~b(s(s(s(z))), s(s(s(elem!1))))),
% 3.43/3.64 inference(unit_resolution,[status(thm)],[8841, 16729, 16660, 16688])).
% 3.43/3.64 tff(16739,plain,
% 3.43/3.64 (~b(s(s(s(z))), elem!1)),
% 3.43/3.64 inference(unit_resolution,[status(thm)],[4078, 16738, 16737])).
% 3.43/3.64 tff(16740,plain,
% 3.43/3.64 (r(s(s(s(z))), elem!1)),
% 3.43/3.64 inference(unit_resolution,[status(thm)],[2826, 16739, 16736])).
% 3.43/3.64 tff(16741,plain,
% 3.43/3.64 (r(s(s(s(z))), s(s(elem!1)))),
% 3.43/3.64 inference(modus_ponens,[status(thm)],[16740, 16735])).
% 3.43/3.64 tff(16742,plain,
% 3.43/3.64 (r(s(s(s(z))), s(s(s(elem!1))))),
% 3.43/3.64 inference(modus_ponens,[status(thm)],[16741, 16733])).
% 3.43/3.64 tff(16743,plain,
% 3.43/3.64 ((~r(s(s(s(z))), s(s(s(elem!1))))) | (~r(s(s(s(z))), s(s(z))))),
% 3.43/3.64 inference(unit_resolution,[status(thm)],[8852, 197, 16687, 16668])).
% 3.43/3.64 tff(16744,plain,
% 3.43/3.64 (~r(s(s(s(z))), s(s(z)))),
% 3.43/3.64 inference(unit_resolution,[status(thm)],[16743, 16742])).
% 3.43/3.64 tff(16745,plain,
% 3.43/3.64 (b(s(s(s(z))), s(s(z)))),
% 3.43/3.64 inference(unit_resolution,[status(thm)],[1010, 16744])).
% 3.43/3.64 tff(16746,plain,
% 3.43/3.64 ((~r(s(s(s(z))), s(s(s(elem!1))))) | (~r(s(s(z)), s(s(s(z)))))),
% 3.43/3.64 inference(unit_resolution,[status(thm)],[8861, 197, 16687, 16668])).
% 3.43/3.64 tff(16747,plain,
% 3.43/3.64 (~r(s(s(z)), s(s(s(z))))),
% 3.43/3.64 inference(unit_resolution,[status(thm)],[16746, 16742])).
% 3.43/3.64 tff(16748,plain,
% 3.43/3.64 (b(s(s(z)), s(s(s(z))))),
% 3.43/3.64 inference(unit_resolution,[status(thm)],[1730, 16747])).
% 3.43/3.64 tff(16749,plain,
% 3.43/3.64 (~b(s(s(s(s(z)))), s(s(s(z))))),
% 3.43/3.64 inference(unit_resolution,[status(thm)],[4778, 16723, 16729, 16727, 16748, 16745])).
% 3.43/3.64 tff(16750,plain,
% 3.43/3.64 (r(s(s(s(s(z)))), s(s(s(z))))),
% 3.43/3.64 inference(unit_resolution,[status(thm)],[4662, 16749])).
% 3.43/3.64 tff(16751,plain,
% 3.43/3.64 (~r(s(s(s(elem!1))), s(s(s(s(z)))))),
% 3.43/3.64 inference(unit_resolution,[status(thm)],[8264, 197, 16750, 16725, 16731])).
% 3.43/3.64 tff(16752,plain,
% 3.43/3.64 (~r(elem!1, s(s(s(s(z)))))),
% 3.43/3.64 inference(unit_resolution,[status(thm)],[5665, 16751, 16710])).
% 3.43/3.64 tff(16753,plain,
% 3.43/3.64 (b(elem!1, s(s(s(s(z)))))),
% 3.43/3.64 inference(unit_resolution,[status(thm)],[1098, 16752, 16722])).
% 3.43/3.64 tff(16754,plain,
% 3.43/3.64 (b(s(s(s(elem!1))), s(s(s(s(z)))))),
% 3.43/3.64 inference(modus_ponens,[status(thm)],[16753, 16715])).
% 3.43/3.64 tff(16755,plain,
% 3.43/3.64 (~b(z, s(s(s(z))))),
% 3.43/3.64 inference(unit_resolution,[status(thm)],[16432, 166, 10451, 16666, 16745])).
% 3.43/3.64 tff(16756,plain,
% 3.43/3.64 (r(z, s(s(s(z))))),
% 3.43/3.64 inference(unit_resolution,[status(thm)],[1697, 16755])).
% 3.43/3.64 tff(16757,plain,
% 3.43/3.64 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(s(z))))) | (~r(s(s(s(z))), z)) | (~r(s(s(s(s(z)))), z)) | (~r(s(s(s(s(z)))), s(s(s(z))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, s(s(s(z))))) | (~r(s(s(s(z))), z)) | (~r(s(s(s(s(z)))), z)) | (~r(s(s(s(s(z)))), s(s(s(z))))))),
% 3.43/3.64 inference(rewrite,[status(thm)],[])).
% 3.43/3.64 tff(16758,plain,
% 3.43/3.64 (((~r(s(s(s(z))), z)) | (~r(z, s(s(s(z))))) | (~r(s(s(s(s(z)))), s(s(s(z))))) | (~r(s(s(s(s(z)))), z))) <=> ((~r(z, s(s(s(z))))) | (~r(s(s(s(z))), z)) | (~r(s(s(s(s(z)))), z)) | (~r(s(s(s(s(z)))), s(s(s(z))))))),
% 3.43/3.64 inference(rewrite,[status(thm)],[])).
% 3.43/3.64 tff(16759,plain,
% 3.43/3.64 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(z))), z)) | (~r(z, s(s(s(z))))) | (~r(s(s(s(s(z)))), s(s(s(z))))) | (~r(s(s(s(s(z)))), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(s(z))))) | (~r(s(s(s(z))), z)) | (~r(s(s(s(s(z)))), z)) | (~r(s(s(s(s(z)))), s(s(s(z)))))))),
% 3.43/3.64 inference(monotonicity,[status(thm)],[16758])).
% 3.43/3.64 tff(16760,plain,
% 3.43/3.64 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(z))), z)) | (~r(z, s(s(s(z))))) | (~r(s(s(s(s(z)))), s(s(s(z))))) | (~r(s(s(s(s(z)))), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, s(s(s(z))))) | (~r(s(s(s(z))), z)) | (~r(s(s(s(s(z)))), z)) | (~r(s(s(s(s(z)))), s(s(s(z))))))),
% 3.43/3.64 inference(transitivity,[status(thm)],[16759, 16757])).
% 3.43/3.64 tff(16761,plain,
% 3.43/3.64 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(z))), z)) | (~r(z, s(s(s(z))))) | (~r(s(s(s(s(z)))), s(s(s(z))))) | (~r(s(s(s(s(z)))), z)))),
% 3.43/3.64 inference(quant_inst,[status(thm)],[])).
% 3.43/3.64 tff(16762,plain,
% 3.43/3.64 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, s(s(s(z))))) | (~r(s(s(s(z))), z)) | (~r(s(s(s(s(z)))), z)) | (~r(s(s(s(s(z)))), s(s(s(z)))))),
% 3.43/3.64 inference(modus_ponens,[status(thm)],[16761, 16760])).
% 3.43/3.64 tff(16763,plain,
% 3.43/3.64 (~r(s(s(s(s(z)))), z)),
% 3.43/3.64 inference(unit_resolution,[status(thm)],[16762, 197, 16756, 16750, 16725])).
% 3.43/3.64 tff(16764,plain,
% 3.43/3.64 (b(s(s(s(s(z)))), z)),
% 3.43/3.64 inference(unit_resolution,[status(thm)],[3266, 16763])).
% 3.43/3.64 tff(16765,plain,
% 3.43/3.64 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), s(s(s(z))))) | (~r(z, s(s(s(elem!1))))) | (~r(z, s(s(s(z))))) | (~r(s(s(s(z))), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(elem!1))), s(s(s(z))))) | (~r(z, s(s(s(elem!1))))) | (~r(z, s(s(s(z))))) | (~r(s(s(s(z))), z)))),
% 3.43/3.64 inference(rewrite,[status(thm)],[])).
% 3.43/3.64 tff(16766,plain,
% 3.43/3.64 (((~r(s(s(s(z))), z)) | (~r(s(s(s(elem!1))), s(s(s(z))))) | (~r(z, s(s(s(z))))) | (~r(z, s(s(s(elem!1)))))) <=> ((~r(s(s(s(elem!1))), s(s(s(z))))) | (~r(z, s(s(s(elem!1))))) | (~r(z, s(s(s(z))))) | (~r(s(s(s(z))), z)))),
% 3.43/3.64 inference(rewrite,[status(thm)],[])).
% 3.43/3.64 tff(16767,plain,
% 3.43/3.64 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(z))), z)) | (~r(s(s(s(elem!1))), s(s(s(z))))) | (~r(z, s(s(s(z))))) | (~r(z, s(s(s(elem!1))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), s(s(s(z))))) | (~r(z, s(s(s(elem!1))))) | (~r(z, s(s(s(z))))) | (~r(s(s(s(z))), z))))),
% 3.43/3.64 inference(monotonicity,[status(thm)],[16766])).
% 3.43/3.64 tff(16768,plain,
% 3.43/3.64 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(z))), z)) | (~r(s(s(s(elem!1))), s(s(s(z))))) | (~r(z, s(s(s(z))))) | (~r(z, s(s(s(elem!1))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(elem!1))), s(s(s(z))))) | (~r(z, s(s(s(elem!1))))) | (~r(z, s(s(s(z))))) | (~r(s(s(s(z))), z)))),
% 3.43/3.64 inference(transitivity,[status(thm)],[16767, 16765])).
% 3.43/3.64 tff(16769,plain,
% 3.43/3.64 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(z))), z)) | (~r(s(s(s(elem!1))), s(s(s(z))))) | (~r(z, s(s(s(z))))) | (~r(z, s(s(s(elem!1))))))),
% 3.43/3.64 inference(quant_inst,[status(thm)],[])).
% 3.43/3.64 tff(16770,plain,
% 3.43/3.64 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(elem!1))), s(s(s(z))))) | (~r(z, s(s(s(elem!1))))) | (~r(z, s(s(s(z))))) | (~r(s(s(s(z))), z))),
% 3.43/3.64 inference(modus_ponens,[status(thm)],[16769, 16768])).
% 3.43/3.64 tff(16771,plain,
% 3.43/3.64 (~r(z, s(s(s(elem!1))))),
% 3.43/3.64 inference(unit_resolution,[status(thm)],[16770, 197, 16756, 16725, 16731])).
% 3.43/3.64 tff(16772,plain,
% 3.43/3.64 (b(z, s(s(s(elem!1))))),
% 3.43/3.64 inference(unit_resolution,[status(thm)],[261, 16771])).
% 3.43/3.64 tff(16773,plain,
% 3.43/3.64 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), z)) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(elem!1))), s(s(s(s(z)))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), z)) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(elem!1))), s(s(s(s(z)))))))),
% 3.43/3.64 inference(rewrite,[status(thm)],[])).
% 3.43/3.64 tff(16774,plain,
% 3.43/3.64 (((~b(s(s(s(elem!1))), s(z))) | (~b(s(s(s(elem!1))), s(z))) | (~b(z, s(s(s(elem!1))))) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(elem!1))), z)) | (~b(s(s(s(elem!1))), s(s(s(s(z))))))) <=> ((~b(z, s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), z)) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(elem!1))), s(s(s(s(z)))))))),
% 3.43/3.65 inference(rewrite,[status(thm)],[])).
% 3.43/3.65 tff(16775,plain,
% 3.43/3.65 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), s(z))) | (~b(s(s(s(elem!1))), s(z))) | (~b(z, s(s(s(elem!1))))) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(elem!1))), z)) | (~b(s(s(s(elem!1))), s(s(s(s(z)))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), z)) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(elem!1))), s(s(s(s(z))))))))),
% 3.43/3.65 inference(monotonicity,[status(thm)],[16774])).
% 3.43/3.65 tff(16776,plain,
% 3.43/3.65 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), s(z))) | (~b(s(s(s(elem!1))), s(z))) | (~b(z, s(s(s(elem!1))))) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(elem!1))), z)) | (~b(s(s(s(elem!1))), s(s(s(s(z)))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), z)) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(elem!1))), s(s(s(s(z)))))))),
% 3.43/3.65 inference(transitivity,[status(thm)],[16775, 16773])).
% 3.43/3.65 tff(16777,plain,
% 3.43/3.65 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), s(z))) | (~b(s(s(s(elem!1))), s(z))) | (~b(z, s(s(s(elem!1))))) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(elem!1))), z)) | (~b(s(s(s(elem!1))), s(s(s(s(z)))))))),
% 3.43/3.65 inference(quant_inst,[status(thm)],[])).
% 3.43/3.65 tff(16778,plain,
% 3.43/3.65 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), z)) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(elem!1))), s(s(s(s(z))))))),
% 3.43/3.65 inference(modus_ponens,[status(thm)],[16777, 16776])).
% 3.43/3.65 tff(16779,plain,
% 3.43/3.65 ($false),
% 3.43/3.65 inference(unit_resolution,[status(thm)],[16778, 166, 16772, 16660, 121, 16764, 16754])).
% 3.43/3.65 tff(16780,plain,((~b(s(s(s(elem!1))), z)) | (~b(z, s(s(z)))) | (~r(s(z), z)) | (~r(s(s(z)), s(z))) | (~b(s(z), s(s(elem!1)))) | (s(s(z)) = s(s(elem!1)))), inference(lemma,lemma(discharge,[]))).
% 3.43/3.65 tff(16781,plain,
% 3.43/3.65 (~b(s(s(s(elem!1))), z)),
% 3.43/3.65 inference(unit_resolution,[status(thm)],[16780, 97, 10451, 392, 376, 52])).
% 3.43/3.65 tff(16782,plain,
% 3.43/3.65 (r(s(s(s(elem!1))), z)),
% 3.43/3.65 inference(unit_resolution,[status(thm)],[94, 16781])).
% 3.43/3.65 tff(16783,plain,
% 3.43/3.65 (~r(z, s(s(elem!1)))),
% 3.43/3.65 inference(unit_resolution,[status(thm)],[1386, 16662, 16782, 16664])).
% 3.43/3.65 tff(16784,plain,
% 3.43/3.65 (b(z, s(s(elem!1)))),
% 3.43/3.65 inference(unit_resolution,[status(thm)],[1795, 16783])).
% 3.43/3.65 tff(16785,plain,
% 3.43/3.65 (~r(s(z), s(s(s(elem!1))))),
% 3.43/3.65 inference(unit_resolution,[status(thm)],[14413, 197, 154, 16651, 97])).
% 3.43/3.65 tff(16786,plain,
% 3.43/3.65 (b(s(z), s(s(s(elem!1))))),
% 3.43/3.65 inference(unit_resolution,[status(thm)],[116, 16785])).
% 3.43/3.65 tff(16787,plain,
% 3.43/3.65 (~r(s(s(s(z))), z)),
% 3.43/3.65 inference(unit_resolution,[status(thm)],[13905, 120, 3567, 16651, 16660, 154, 16786])).
% 3.43/3.65 tff(16788,plain,
% 3.43/3.65 (b(s(s(s(z))), z)),
% 3.43/3.65 inference(unit_resolution,[status(thm)],[1713, 16787])).
% 3.43/3.65 tff(16789,plain,
% 3.43/3.65 (~b(s(s(s(z))), s(s(z)))),
% 3.43/3.65 inference(unit_resolution,[status(thm)],[12296, 166, 10451, 16666, 16788])).
% 3.43/3.65 tff(16790,plain,
% 3.43/3.65 (r(s(s(s(z))), s(s(z)))),
% 3.43/3.65 inference(unit_resolution,[status(thm)],[1010, 16789])).
% 3.43/3.65 tff(16791,plain,
% 3.43/3.65 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(z)), s(z))) | (~r(s(z), s(s(z)))) | (~r(s(z), s(s(s(z))))) | (~r(s(s(s(z))), s(s(z)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(z)), s(z))) | (~r(s(z), s(s(z)))) | (~r(s(z), s(s(s(z))))) | (~r(s(s(s(z))), s(s(z)))))),
% 3.43/3.65 inference(rewrite,[status(thm)],[])).
% 3.43/3.65 tff(16792,plain,
% 3.43/3.65 (((~r(s(s(z)), s(z))) | (~r(s(s(s(z))), s(s(z)))) | (~r(s(z), s(s(z)))) | (~r(s(z), s(s(s(z)))))) <=> ((~r(s(s(z)), s(z))) | (~r(s(z), s(s(z)))) | (~r(s(z), s(s(s(z))))) | (~r(s(s(s(z))), s(s(z)))))),
% 3.43/3.65 inference(rewrite,[status(thm)],[])).
% 3.43/3.65 tff(16793,plain,
% 3.43/3.65 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(z)), s(z))) | (~r(s(s(s(z))), s(s(z)))) | (~r(s(z), s(s(z)))) | (~r(s(z), s(s(s(z))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(z)), s(z))) | (~r(s(z), s(s(z)))) | (~r(s(z), s(s(s(z))))) | (~r(s(s(s(z))), s(s(z))))))),
% 3.43/3.65 inference(monotonicity,[status(thm)],[16792])).
% 3.43/3.65 tff(16794,plain,
% 3.43/3.65 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(z)), s(z))) | (~r(s(s(s(z))), s(s(z)))) | (~r(s(z), s(s(z)))) | (~r(s(z), s(s(s(z))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(z)), s(z))) | (~r(s(z), s(s(z)))) | (~r(s(z), s(s(s(z))))) | (~r(s(s(s(z))), s(s(z)))))),
% 3.43/3.65 inference(transitivity,[status(thm)],[16793, 16791])).
% 3.43/3.65 tff(16795,plain,
% 3.43/3.65 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(z)), s(z))) | (~r(s(s(s(z))), s(s(z)))) | (~r(s(z), s(s(z)))) | (~r(s(z), s(s(s(z))))))),
% 3.43/3.65 inference(quant_inst,[status(thm)],[])).
% 3.43/3.65 tff(16796,plain,
% 3.43/3.65 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(z)), s(z))) | (~r(s(z), s(s(z)))) | (~r(s(z), s(s(s(z))))) | (~r(s(s(s(z))), s(s(z))))),
% 3.43/3.65 inference(modus_ponens,[status(thm)],[16795, 16794])).
% 3.43/3.65 tff(16797,plain,
% 3.43/3.65 (~r(s(z), s(s(s(z))))),
% 3.43/3.65 inference(unit_resolution,[status(thm)],[16796, 197, 120, 392, 16790])).
% 3.43/3.65 tff(16798,plain,
% 3.43/3.65 (b(s(z), s(s(s(z))))),
% 3.43/3.65 inference(unit_resolution,[status(thm)],[1674, 16797])).
% 3.43/3.65 tff(16799,plain,
% 3.43/3.65 (~b(s(s(s(z))), s(s(s(elem!1))))),
% 3.43/3.65 inference(unit_resolution,[status(thm)],[8841, 16798, 16660, 16786])).
% 3.43/3.65 tff(16800,plain,
% 3.43/3.65 ((s(s(s(z))) = s(s(s(elem!1)))) | r(s(s(s(z))), s(s(s(elem!1))))),
% 3.43/3.65 inference(unit_resolution,[status(thm)],[10059, 79, 16799])).
% 3.43/3.65 tff(16801,plain,
% 3.43/3.65 (r(s(s(s(z))), s(s(s(elem!1))))),
% 3.43/3.65 inference(unit_resolution,[status(thm)],[16800, 10056])).
% 3.43/3.65 tff(16802,plain,
% 3.43/3.65 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(z))), s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), z)) | (~r(s(s(elem!1)), s(s(s(elem!1))))) | (~r(s(s(s(z))), s(s(elem!1)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(z))), s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), z)) | (~r(s(s(elem!1)), s(s(s(elem!1))))) | (~r(s(s(s(z))), s(s(elem!1)))))),
% 3.43/3.65 inference(rewrite,[status(thm)],[])).
% 3.43/3.65 tff(16803,plain,
% 3.43/3.65 (((~r(s(s(s(elem!1))), z)) | (~r(s(s(elem!1)), s(s(s(elem!1))))) | (~r(s(s(s(z))), s(s(s(elem!1))))) | (~r(s(s(s(z))), s(s(elem!1))))) <=> ((~r(s(s(s(z))), s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), z)) | (~r(s(s(elem!1)), s(s(s(elem!1))))) | (~r(s(s(s(z))), s(s(elem!1)))))),
% 3.43/3.65 inference(rewrite,[status(thm)],[])).
% 3.43/3.65 tff(16804,plain,
% 3.43/3.65 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), z)) | (~r(s(s(elem!1)), s(s(s(elem!1))))) | (~r(s(s(s(z))), s(s(s(elem!1))))) | (~r(s(s(s(z))), s(s(elem!1)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(z))), s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), z)) | (~r(s(s(elem!1)), s(s(s(elem!1))))) | (~r(s(s(s(z))), s(s(elem!1))))))),
% 3.43/3.65 inference(monotonicity,[status(thm)],[16803])).
% 3.43/3.65 tff(16805,plain,
% 3.43/3.65 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), z)) | (~r(s(s(elem!1)), s(s(s(elem!1))))) | (~r(s(s(s(z))), s(s(s(elem!1))))) | (~r(s(s(s(z))), s(s(elem!1)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(z))), s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), z)) | (~r(s(s(elem!1)), s(s(s(elem!1))))) | (~r(s(s(s(z))), s(s(elem!1)))))),
% 3.43/3.65 inference(transitivity,[status(thm)],[16804, 16802])).
% 3.43/3.65 tff(16806,plain,
% 3.43/3.65 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), z)) | (~r(s(s(elem!1)), s(s(s(elem!1))))) | (~r(s(s(s(z))), s(s(s(elem!1))))) | (~r(s(s(s(z))), s(s(elem!1)))))),
% 3.43/3.65 inference(quant_inst,[status(thm)],[])).
% 3.43/3.65 tff(16807,plain,
% 3.43/3.65 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(z))), s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), z)) | (~r(s(s(elem!1)), s(s(s(elem!1))))) | (~r(s(s(s(z))), s(s(elem!1))))),
% 3.43/3.65 inference(modus_ponens,[status(thm)],[16806, 16805])).
% 3.43/3.65 tff(16808,plain,
% 3.43/3.65 (~r(s(s(s(z))), s(s(elem!1)))),
% 3.43/3.65 inference(unit_resolution,[status(thm)],[16807, 197, 154, 377, 16801])).
% 3.43/3.65 tff(16809,plain,
% 3.43/3.65 (~r(s(s(s(z))), s(z))),
% 3.43/3.65 inference(unit_resolution,[status(thm)],[13956, 197, 120, 392, 16790])).
% 3.43/3.65 tff(16810,plain,
% 3.43/3.65 (b(s(s(s(z))), s(z))),
% 3.43/3.65 inference(unit_resolution,[status(thm)],[1763, 16809])).
% 3.43/3.65 tff(16811,plain,
% 3.43/3.65 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(s(elem!1)), s(z))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(z))), s(s(elem!1)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(s(elem!1)), s(z))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(z))), s(s(elem!1)))))),
% 3.43/3.65 inference(rewrite,[status(thm)],[])).
% 3.43/3.65 tff(16812,plain,
% 3.43/3.65 (((~b(s(s(s(elem!1))), s(z))) | (~b(s(s(s(z))), s(z))) | (~b(s(z), s(s(s(elem!1))))) | (~b(s(s(elem!1)), s(z))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(z))), s(s(elem!1))))) <=> ((~b(s(z), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(s(elem!1)), s(z))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(z))), s(s(elem!1)))))),
% 3.43/3.65 inference(rewrite,[status(thm)],[])).
% 3.43/3.65 tff(16813,plain,
% 3.43/3.65 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), s(z))) | (~b(s(s(s(z))), s(z))) | (~b(s(z), s(s(s(elem!1))))) | (~b(s(s(elem!1)), s(z))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(z))), s(s(elem!1)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(s(elem!1)), s(z))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(z))), s(s(elem!1))))))),
% 3.43/3.65 inference(monotonicity,[status(thm)],[16812])).
% 3.43/3.65 tff(16814,plain,
% 3.43/3.65 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), s(z))) | (~b(s(s(s(z))), s(z))) | (~b(s(z), s(s(s(elem!1))))) | (~b(s(s(elem!1)), s(z))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(z))), s(s(elem!1)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(s(elem!1)), s(z))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(z))), s(s(elem!1)))))),
% 3.43/3.65 inference(transitivity,[status(thm)],[16813, 16811])).
% 3.43/3.65 tff(16815,plain,
% 3.43/3.65 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), s(z))) | (~b(s(s(s(z))), s(z))) | (~b(s(z), s(s(s(elem!1))))) | (~b(s(s(elem!1)), s(z))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(z))), s(s(elem!1)))))),
% 3.43/3.65 inference(quant_inst,[status(thm)],[])).
% 3.43/3.65 tff(16816,plain,
% 3.43/3.65 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(s(elem!1)), s(z))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(z))), s(s(elem!1))))),
% 3.43/3.65 inference(modus_ponens,[status(thm)],[16815, 16814])).
% 3.43/3.65 tff(16817,plain,
% 3.43/3.65 (~b(s(s(s(z))), s(s(elem!1)))),
% 3.43/3.65 inference(unit_resolution,[status(thm)],[16816, 166, 16786, 16660, 16595, 16810])).
% 3.43/3.65 tff(16818,plain,
% 3.43/3.65 ((s(s(s(z))) = s(s(elem!1))) | r(s(s(s(z))), s(s(elem!1)))),
% 3.43/3.65 inference(unit_resolution,[status(thm)],[4523, 79, 16817])).
% 3.43/3.65 tff(16819,plain,
% 3.43/3.65 (s(s(s(z))) = s(s(elem!1))),
% 3.43/3.65 inference(unit_resolution,[status(thm)],[16818, 16808])).
% 3.43/3.65 tff(16820,plain,
% 3.43/3.65 (inj_0(s(s(s(z)))) = inj_0(s(s(elem!1)))),
% 3.43/3.65 inference(monotonicity,[status(thm)],[16819])).
% 3.43/3.65 tff(16821,plain,
% 3.43/3.65 (s(s(z)) = s(elem!1)),
% 3.43/3.65 inference(transitivity,[status(thm)],[1666, 16820, 38])).
% 3.43/3.65 tff(16822,plain,
% 3.43/3.65 (b(s(s(z)), s(s(s(elem!1)))) <=> b(s(elem!1), s(s(s(elem!1))))),
% 3.43/3.65 inference(monotonicity,[status(thm)],[16821])).
% 3.43/3.65 tff(16823,plain,
% 3.43/3.65 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(elem!1)))) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(s(elem!1)), s(z))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(elem!1))), s(s(s(z))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), s(s(elem!1)))) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(s(elem!1)), s(z))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(elem!1))), s(s(s(z))))))),
% 3.43/3.65 inference(rewrite,[status(thm)],[])).
% 3.43/3.65 tff(16824,plain,
% 3.43/3.65 (((~b(s(s(elem!1)), s(z))) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(z), s(s(elem!1)))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(s(s(elem!1))), s(s(s(z)))))) <=> ((~b(s(z), s(s(elem!1)))) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(s(elem!1)), s(z))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(elem!1))), s(s(s(z))))))),
% 3.43/3.65 inference(rewrite,[status(thm)],[])).
% 3.43/3.65 tff(16825,plain,
% 3.43/3.65 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), s(z))) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(z), s(s(elem!1)))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(s(s(elem!1))), s(s(s(z))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(elem!1)))) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(s(elem!1)), s(z))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(elem!1))), s(s(s(z)))))))),
% 3.43/3.65 inference(monotonicity,[status(thm)],[16824])).
% 3.43/3.65 tff(16826,plain,
% 3.43/3.65 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), s(z))) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(z), s(s(elem!1)))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(s(s(elem!1))), s(s(s(z))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), s(s(elem!1)))) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(s(elem!1)), s(z))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(elem!1))), s(s(s(z))))))),
% 3.43/3.65 inference(transitivity,[status(thm)],[16825, 16823])).
% 3.43/3.65 tff(16827,plain,
% 3.43/3.65 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), s(z))) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(z), s(s(elem!1)))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(s(s(elem!1))), s(s(s(z))))))),
% 3.43/3.65 inference(quant_inst,[status(thm)],[])).
% 3.43/3.65 tff(16828,plain,
% 3.43/3.65 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), s(s(elem!1)))) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(s(elem!1)), s(z))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(elem!1))), s(s(s(z)))))),
% 3.43/3.65 inference(modus_ponens,[status(thm)],[16827, 16826])).
% 3.43/3.65 tff(16829,plain,
% 3.43/3.65 (~b(s(s(s(elem!1))), s(s(s(z))))),
% 3.43/3.65 inference(unit_resolution,[status(thm)],[16828, 166, 376, 16660, 16595, 16810])).
% 3.43/3.65 tff(16830,plain,
% 3.43/3.65 (r(s(s(s(elem!1))), s(s(s(z))))),
% 3.43/3.65 inference(unit_resolution,[status(thm)],[3574, 16829, 3567])).
% 3.43/3.65 tff(16831,plain,
% 3.43/3.65 (~b(s(s(z)), s(s(s(z))))),
% 3.43/3.65 inference(unit_resolution,[status(thm)],[13913, 166, 10451, 16666, 16788])).
% 3.43/3.65 tff(16832,plain,
% 3.43/3.65 (r(s(s(z)), s(s(s(z))))),
% 3.43/3.65 inference(unit_resolution,[status(thm)],[1730, 16831])).
% 3.43/3.65 tff(16833,plain,
% 3.43/3.65 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), s(s(s(z))))) | (~r(s(s(z)), s(s(s(elem!1))))) | (~r(s(s(z)), s(s(s(z))))) | (~r(s(s(s(z))), s(s(z)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(elem!1))), s(s(s(z))))) | (~r(s(s(z)), s(s(s(elem!1))))) | (~r(s(s(z)), s(s(s(z))))) | (~r(s(s(s(z))), s(s(z)))))),
% 3.43/3.65 inference(rewrite,[status(thm)],[])).
% 3.43/3.65 tff(16834,plain,
% 3.43/3.65 (((~r(s(s(s(z))), s(s(z)))) | (~r(s(s(s(elem!1))), s(s(s(z))))) | (~r(s(s(z)), s(s(s(z))))) | (~r(s(s(z)), s(s(s(elem!1)))))) <=> ((~r(s(s(s(elem!1))), s(s(s(z))))) | (~r(s(s(z)), s(s(s(elem!1))))) | (~r(s(s(z)), s(s(s(z))))) | (~r(s(s(s(z))), s(s(z)))))),
% 3.43/3.65 inference(rewrite,[status(thm)],[])).
% 3.43/3.65 tff(16835,plain,
% 3.43/3.65 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(z))), s(s(z)))) | (~r(s(s(s(elem!1))), s(s(s(z))))) | (~r(s(s(z)), s(s(s(z))))) | (~r(s(s(z)), s(s(s(elem!1))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), s(s(s(z))))) | (~r(s(s(z)), s(s(s(elem!1))))) | (~r(s(s(z)), s(s(s(z))))) | (~r(s(s(s(z))), s(s(z))))))),
% 3.43/3.65 inference(monotonicity,[status(thm)],[16834])).
% 3.43/3.65 tff(16836,plain,
% 3.43/3.65 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(z))), s(s(z)))) | (~r(s(s(s(elem!1))), s(s(s(z))))) | (~r(s(s(z)), s(s(s(z))))) | (~r(s(s(z)), s(s(s(elem!1))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(elem!1))), s(s(s(z))))) | (~r(s(s(z)), s(s(s(elem!1))))) | (~r(s(s(z)), s(s(s(z))))) | (~r(s(s(s(z))), s(s(z)))))),
% 3.43/3.65 inference(transitivity,[status(thm)],[16835, 16833])).
% 3.43/3.65 tff(16837,plain,
% 3.43/3.65 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(z))), s(s(z)))) | (~r(s(s(s(elem!1))), s(s(s(z))))) | (~r(s(s(z)), s(s(s(z))))) | (~r(s(s(z)), s(s(s(elem!1))))))),
% 3.43/3.65 inference(quant_inst,[status(thm)],[])).
% 3.43/3.65 tff(16838,plain,
% 3.43/3.65 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(elem!1))), s(s(s(z))))) | (~r(s(s(z)), s(s(s(elem!1))))) | (~r(s(s(z)), s(s(s(z))))) | (~r(s(s(s(z))), s(s(z))))),
% 3.43/3.65 inference(modus_ponens,[status(thm)],[16837, 16836])).
% 3.43/3.65 tff(16839,plain,
% 3.43/3.65 (~r(s(s(z)), s(s(s(elem!1))))),
% 3.43/3.65 inference(unit_resolution,[status(thm)],[16838, 197, 16790, 16832, 16830])).
% 3.43/3.65 tff(16840,plain,
% 3.43/3.65 (b(s(s(z)), s(s(s(elem!1))))),
% 3.43/3.65 inference(unit_resolution,[status(thm)],[279, 16839])).
% 3.43/3.65 tff(16841,plain,
% 3.43/3.65 (b(s(elem!1), s(s(s(elem!1))))),
% 3.43/3.65 inference(modus_ponens,[status(thm)],[16840, 16822])).
% 3.43/3.65 tff(16842,plain,
% 3.43/3.65 (b(s(s(s(elem!1))), s(s(z))) <=> b(s(s(s(elem!1))), s(elem!1))),
% 3.43/3.65 inference(monotonicity,[status(thm)],[16821])).
% 3.43/3.65 tff(16843,plain,
% 3.43/3.65 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), s(s(s(z))))) | (~r(s(s(s(elem!1))), s(s(z)))) | (~r(s(s(z)), s(s(s(z))))) | (~r(s(s(s(z))), s(s(z)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(elem!1))), s(s(s(z))))) | (~r(s(s(s(elem!1))), s(s(z)))) | (~r(s(s(z)), s(s(s(z))))) | (~r(s(s(s(z))), s(s(z)))))),
% 3.43/3.66 inference(rewrite,[status(thm)],[])).
% 3.43/3.66 tff(16844,plain,
% 3.43/3.66 (((~r(s(s(s(z))), s(s(z)))) | (~r(s(s(z)), s(s(s(z))))) | (~r(s(s(s(elem!1))), s(s(s(z))))) | (~r(s(s(s(elem!1))), s(s(z))))) <=> ((~r(s(s(s(elem!1))), s(s(s(z))))) | (~r(s(s(s(elem!1))), s(s(z)))) | (~r(s(s(z)), s(s(s(z))))) | (~r(s(s(s(z))), s(s(z)))))),
% 3.43/3.66 inference(rewrite,[status(thm)],[])).
% 3.43/3.66 tff(16845,plain,
% 3.43/3.66 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(z))), s(s(z)))) | (~r(s(s(z)), s(s(s(z))))) | (~r(s(s(s(elem!1))), s(s(s(z))))) | (~r(s(s(s(elem!1))), s(s(z)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), s(s(s(z))))) | (~r(s(s(s(elem!1))), s(s(z)))) | (~r(s(s(z)), s(s(s(z))))) | (~r(s(s(s(z))), s(s(z))))))),
% 3.43/3.66 inference(monotonicity,[status(thm)],[16844])).
% 3.43/3.66 tff(16846,plain,
% 3.43/3.66 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(z))), s(s(z)))) | (~r(s(s(z)), s(s(s(z))))) | (~r(s(s(s(elem!1))), s(s(s(z))))) | (~r(s(s(s(elem!1))), s(s(z)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(elem!1))), s(s(s(z))))) | (~r(s(s(s(elem!1))), s(s(z)))) | (~r(s(s(z)), s(s(s(z))))) | (~r(s(s(s(z))), s(s(z)))))),
% 3.43/3.66 inference(transitivity,[status(thm)],[16845, 16843])).
% 3.43/3.66 tff(16847,plain,
% 3.43/3.66 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(z))), s(s(z)))) | (~r(s(s(z)), s(s(s(z))))) | (~r(s(s(s(elem!1))), s(s(s(z))))) | (~r(s(s(s(elem!1))), s(s(z)))))),
% 3.43/3.66 inference(quant_inst,[status(thm)],[])).
% 3.43/3.66 tff(16848,plain,
% 3.43/3.66 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(elem!1))), s(s(s(z))))) | (~r(s(s(s(elem!1))), s(s(z)))) | (~r(s(s(z)), s(s(s(z))))) | (~r(s(s(s(z))), s(s(z))))),
% 3.43/3.66 inference(modus_ponens,[status(thm)],[16847, 16846])).
% 3.43/3.66 tff(16849,plain,
% 3.43/3.66 (~r(s(s(s(elem!1))), s(s(z)))),
% 3.43/3.66 inference(unit_resolution,[status(thm)],[16848, 197, 16790, 16832, 16830])).
% 3.43/3.66 tff(16850,plain,
% 3.43/3.66 (b(s(s(s(elem!1))), s(s(z)))),
% 3.43/3.66 inference(unit_resolution,[status(thm)],[218, 16849])).
% 3.43/3.66 tff(16851,plain,
% 3.43/3.66 (b(s(s(s(elem!1))), s(elem!1))),
% 3.43/3.66 inference(modus_ponens,[status(thm)],[16850, 16842])).
% 3.43/3.66 tff(16852,plain,
% 3.43/3.66 (r(s(s(z)), s(z)) <=> r(s(elem!1), s(z))),
% 3.43/3.66 inference(monotonicity,[status(thm)],[16821])).
% 3.43/3.66 tff(16853,plain,
% 3.43/3.66 (r(s(elem!1), s(z))),
% 3.43/3.66 inference(modus_ponens,[status(thm)],[392, 16852])).
% 3.43/3.66 tff(16854,plain,
% 3.43/3.66 (r(s(s(s(s(elem!1)))), s(elem!1)) <=> r(s(s(s(s(elem!1)))), s(s(z)))),
% 3.43/3.66 inference(symmetry,[status(thm)],[14482])).
% 3.43/3.66 tff(16855,plain,
% 3.43/3.66 ((~r(s(s(s(s(elem!1)))), s(elem!1))) <=> (~r(s(s(s(s(elem!1)))), s(s(z))))),
% 3.43/3.66 inference(monotonicity,[status(thm)],[16854])).
% 3.43/3.66 tff(16856,assumption,(b(s(s(s(elem!1))), s(elem!1))), introduced(assumption)).
% 3.43/3.66 tff(16857,plain,
% 3.43/3.66 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), s(s(s(elem!1))))) | (~b(s(z), s(s(s(elem!1))))) | (~b(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(elem!1))) | (~b(s(s(s(s(elem!1)))), s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(elem!1), s(s(s(elem!1))))) | (~b(s(z), s(s(s(elem!1))))) | (~b(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(elem!1))) | (~b(s(s(s(s(elem!1)))), s(z))))),
% 3.43/3.66 inference(rewrite,[status(thm)],[])).
% 3.43/3.66 tff(16858,plain,
% 3.43/3.66 (((~b(s(elem!1), s(s(s(elem!1))))) | (~b(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(elem!1))) | (~b(s(z), s(s(s(elem!1))))) | (~b(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~b(s(s(s(s(elem!1)))), s(z)))) <=> ((~b(s(elem!1), s(s(s(elem!1))))) | (~b(s(z), s(s(s(elem!1))))) | (~b(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(elem!1))) | (~b(s(s(s(s(elem!1)))), s(z))))),
% 3.43/3.66 inference(rewrite,[status(thm)],[])).
% 3.43/3.66 tff(16859,plain,
% 3.43/3.66 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), s(s(s(elem!1))))) | (~b(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(elem!1))) | (~b(s(z), s(s(s(elem!1))))) | (~b(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~b(s(s(s(s(elem!1)))), s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), s(s(s(elem!1))))) | (~b(s(z), s(s(s(elem!1))))) | (~b(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(elem!1))) | (~b(s(s(s(s(elem!1)))), s(z)))))),
% 3.43/3.66 inference(monotonicity,[status(thm)],[16858])).
% 3.43/3.66 tff(16860,plain,
% 3.43/3.66 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), s(s(s(elem!1))))) | (~b(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(elem!1))) | (~b(s(z), s(s(s(elem!1))))) | (~b(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~b(s(s(s(s(elem!1)))), s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(elem!1), s(s(s(elem!1))))) | (~b(s(z), s(s(s(elem!1))))) | (~b(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(elem!1))) | (~b(s(s(s(s(elem!1)))), s(z))))),
% 3.43/3.66 inference(transitivity,[status(thm)],[16859, 16857])).
% 3.43/3.66 tff(16861,plain,
% 3.43/3.66 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), s(s(s(elem!1))))) | (~b(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(elem!1))) | (~b(s(z), s(s(s(elem!1))))) | (~b(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~b(s(s(s(s(elem!1)))), s(z))))),
% 3.43/3.66 inference(quant_inst,[status(thm)],[])).
% 3.43/3.66 tff(16862,plain,
% 3.43/3.66 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(elem!1), s(s(s(elem!1))))) | (~b(s(z), s(s(s(elem!1))))) | (~b(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(elem!1))) | (~b(s(s(s(s(elem!1)))), s(z)))),
% 3.43/3.66 inference(modus_ponens,[status(thm)],[16861, 16860])).
% 3.43/3.66 tff(16863,plain,
% 3.43/3.66 (~b(s(s(s(s(elem!1)))), s(z))),
% 3.43/3.66 inference(unit_resolution,[status(thm)],[16862, 166, 16856, 15689, 241, 1107])).
% 3.43/3.66 tff(16864,plain,
% 3.43/3.66 (r(s(s(s(s(elem!1)))), s(z))),
% 3.43/3.66 inference(unit_resolution,[status(thm)],[661, 16863])).
% 3.43/3.66 tff(16865,plain,
% 3.43/3.66 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), z)) | (~r(s(elem!1), s(z))) | (~r(s(s(s(s(elem!1)))), s(z))) | (~r(s(s(s(s(elem!1)))), s(elem!1))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(z), z)) | (~r(s(elem!1), s(z))) | (~r(s(s(s(s(elem!1)))), s(z))) | (~r(s(s(s(s(elem!1)))), s(elem!1))))),
% 3.43/3.66 inference(rewrite,[status(thm)],[])).
% 3.43/3.66 tff(16866,plain,
% 3.43/3.66 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), z)) | (~r(s(elem!1), s(z))) | (~r(s(s(s(s(elem!1)))), s(z))) | (~r(s(s(s(s(elem!1)))), s(elem!1))))),
% 3.43/3.66 inference(quant_inst,[status(thm)],[])).
% 3.43/3.66 tff(16867,plain,
% 3.43/3.66 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(z), z)) | (~r(s(elem!1), s(z))) | (~r(s(s(s(s(elem!1)))), s(z))) | (~r(s(s(s(s(elem!1)))), s(elem!1)))),
% 3.43/3.66 inference(modus_ponens,[status(thm)],[16866, 16865])).
% 3.43/3.66 tff(16868,plain,
% 3.43/3.66 (~r(s(s(s(s(elem!1)))), s(elem!1))),
% 3.43/3.66 inference(unit_resolution,[status(thm)],[16867, 197, 97, 2848, 16864])).
% 3.43/3.66 tff(16869,plain,
% 3.43/3.66 (~r(s(s(s(s(elem!1)))), s(s(z)))),
% 3.43/3.66 inference(modus_ponens,[status(thm)],[16868, 16855])).
% 3.43/3.66 tff(16870,plain,
% 3.43/3.66 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), s(s(s(elem!1))))) | (~b(s(s(s(s(elem!1)))), s(elem!1))) | (~b(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(elem!1))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(elem!1), s(s(s(elem!1))))) | (~b(s(s(s(s(elem!1)))), s(elem!1))) | (~b(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(elem!1))))),
% 3.43/3.66 inference(rewrite,[status(thm)],[])).
% 3.43/3.66 tff(16871,plain,
% 3.43/3.66 (((~b(s(elem!1), s(s(s(elem!1))))) | (~b(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(elem!1))) | (~b(s(elem!1), s(s(s(elem!1))))) | (~b(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~b(s(s(s(s(elem!1)))), s(elem!1)))) <=> ((~b(s(elem!1), s(s(s(elem!1))))) | (~b(s(s(s(s(elem!1)))), s(elem!1))) | (~b(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(elem!1))))),
% 3.43/3.66 inference(rewrite,[status(thm)],[])).
% 3.43/3.66 tff(16872,plain,
% 3.43/3.66 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), s(s(s(elem!1))))) | (~b(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(elem!1))) | (~b(s(elem!1), s(s(s(elem!1))))) | (~b(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~b(s(s(s(s(elem!1)))), s(elem!1))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), s(s(s(elem!1))))) | (~b(s(s(s(s(elem!1)))), s(elem!1))) | (~b(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(elem!1)))))),
% 3.43/3.66 inference(monotonicity,[status(thm)],[16871])).
% 3.43/3.66 tff(16873,plain,
% 3.43/3.66 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), s(s(s(elem!1))))) | (~b(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(elem!1))) | (~b(s(elem!1), s(s(s(elem!1))))) | (~b(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~b(s(s(s(s(elem!1)))), s(elem!1))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(elem!1), s(s(s(elem!1))))) | (~b(s(s(s(s(elem!1)))), s(elem!1))) | (~b(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(elem!1))))),
% 3.43/3.66 inference(transitivity,[status(thm)],[16872, 16870])).
% 3.43/3.66 tff(16874,plain,
% 3.43/3.66 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), s(s(s(elem!1))))) | (~b(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(elem!1))) | (~b(s(elem!1), s(s(s(elem!1))))) | (~b(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~b(s(s(s(s(elem!1)))), s(elem!1))))),
% 3.43/3.66 inference(quant_inst,[status(thm)],[])).
% 3.43/3.66 tff(16875,plain,
% 3.43/3.66 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(elem!1), s(s(s(elem!1))))) | (~b(s(s(s(s(elem!1)))), s(elem!1))) | (~b(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(elem!1)))),
% 3.43/3.66 inference(modus_ponens,[status(thm)],[16874, 16873])).
% 3.43/3.66 tff(16876,plain,
% 3.43/3.66 (~b(s(s(s(s(elem!1)))), s(elem!1))),
% 3.43/3.66 inference(unit_resolution,[status(thm)],[16875, 166, 16856, 15689, 1107])).
% 3.43/3.66 tff(16877,plain,
% 3.43/3.66 (~b(s(s(s(s(elem!1)))), s(s(z)))),
% 3.43/3.66 inference(modus_ponens,[status(thm)],[16876, 14485])).
% 3.43/3.66 tff(16878,plain,
% 3.43/3.66 (r(s(s(s(s(elem!1)))), s(s(z)))),
% 3.43/3.66 inference(unit_resolution,[status(thm)],[1299, 16877])).
% 3.43/3.66 tff(16879,plain,
% 3.43/3.66 ($false),
% 3.43/3.66 inference(unit_resolution,[status(thm)],[16878, 16869])).
% 3.43/3.66 tff(16880,plain,((~b(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~(s(s(s(z))) = s(s(elem!1)))) | (~r(s(z), z)) | (~r(s(elem!1), s(z))) | (~b(s(s(s(elem!1))), s(elem!1))) | (~b(s(elem!1), s(s(s(elem!1))))) | (~b(s(z), s(s(s(elem!1)))))), inference(lemma,lemma(discharge,[]))).
% 3.43/3.66 tff(16881,plain,
% 3.43/3.66 (~b(s(s(s(s(elem!1)))), s(s(s(elem!1))))),
% 3.43/3.66 inference(unit_resolution,[status(thm)],[16880, 16819, 97, 16853, 16851, 16841, 16786])).
% 3.43/3.66 tff(16882,plain,
% 3.43/3.66 (r(s(s(s(s(elem!1)))), s(s(s(elem!1))))),
% 3.43/3.66 inference(unit_resolution,[status(thm)],[1065, 16881, 1058])).
% 3.43/3.66 tff(16883,plain,
% 3.43/3.66 (b(z, s(s(z))) <=> b(z, s(elem!1))),
% 3.43/3.66 inference(monotonicity,[status(thm)],[16821])).
% 3.43/3.66 tff(16884,plain,
% 3.43/3.66 (b(z, s(elem!1))),
% 3.43/3.66 inference(modus_ponens,[status(thm)],[10451, 16883])).
% 3.43/3.66 tff(16885,plain,
% 3.43/3.66 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), s(s(s(elem!1))))) | (~b(z, s(s(s(elem!1))))) | (~b(z, s(elem!1))) | (~b(s(s(s(elem!1))), s(elem!1))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(elem!1), s(s(s(elem!1))))) | (~b(z, s(s(s(elem!1))))) | (~b(z, s(elem!1))) | (~b(s(s(s(elem!1))), s(elem!1))))),
% 3.43/3.66 inference(rewrite,[status(thm)],[])).
% 3.43/3.66 tff(16886,plain,
% 3.43/3.66 (((~b(s(s(s(elem!1))), s(elem!1))) | (~b(z, s(elem!1))) | (~b(s(elem!1), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(elem!1))) | (~b(z, s(elem!1))) | (~b(z, s(s(s(elem!1)))))) <=> ((~b(s(elem!1), s(s(s(elem!1))))) | (~b(z, s(s(s(elem!1))))) | (~b(z, s(elem!1))) | (~b(s(s(s(elem!1))), s(elem!1))))),
% 3.43/3.66 inference(rewrite,[status(thm)],[])).
% 3.43/3.66 tff(16887,plain,
% 3.43/3.66 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), s(elem!1))) | (~b(z, s(elem!1))) | (~b(s(elem!1), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(elem!1))) | (~b(z, s(elem!1))) | (~b(z, s(s(s(elem!1))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), s(s(s(elem!1))))) | (~b(z, s(s(s(elem!1))))) | (~b(z, s(elem!1))) | (~b(s(s(s(elem!1))), s(elem!1)))))),
% 3.43/3.66 inference(monotonicity,[status(thm)],[16886])).
% 3.43/3.66 tff(16888,plain,
% 3.43/3.66 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), s(elem!1))) | (~b(z, s(elem!1))) | (~b(s(elem!1), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(elem!1))) | (~b(z, s(elem!1))) | (~b(z, s(s(s(elem!1))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(elem!1), s(s(s(elem!1))))) | (~b(z, s(s(s(elem!1))))) | (~b(z, s(elem!1))) | (~b(s(s(s(elem!1))), s(elem!1))))),
% 3.43/3.66 inference(transitivity,[status(thm)],[16887, 16885])).
% 3.43/3.66 tff(16889,plain,
% 3.43/3.66 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), s(elem!1))) | (~b(z, s(elem!1))) | (~b(s(elem!1), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(elem!1))) | (~b(z, s(elem!1))) | (~b(z, s(s(s(elem!1))))))),
% 3.43/3.66 inference(quant_inst,[status(thm)],[])).
% 3.43/3.66 tff(16890,plain,
% 3.43/3.66 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(elem!1), s(s(s(elem!1))))) | (~b(z, s(s(s(elem!1))))) | (~b(z, s(elem!1))) | (~b(s(s(s(elem!1))), s(elem!1)))),
% 3.43/3.66 inference(modus_ponens,[status(thm)],[16889, 16888])).
% 3.43/3.66 tff(16891,plain,
% 3.43/3.66 (~b(z, s(s(s(elem!1))))),
% 3.43/3.66 inference(unit_resolution,[status(thm)],[16890, 166, 16851, 16841, 16884])).
% 3.43/3.66 tff(16892,plain,
% 3.43/3.66 (r(z, s(s(s(elem!1))))),
% 3.43/3.66 inference(unit_resolution,[status(thm)],[261, 16891])).
% 3.43/3.66 tff(16893,plain,
% 3.43/3.66 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), z)) | (~r(z, s(s(s(elem!1))))) | (~r(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~r(z, s(s(s(s(elem!1)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(elem!1))), z)) | (~r(z, s(s(s(elem!1))))) | (~r(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~r(z, s(s(s(s(elem!1)))))))),
% 3.43/3.66 inference(rewrite,[status(thm)],[])).
% 3.43/3.66 tff(16894,plain,
% 3.43/3.66 (((~r(s(s(s(elem!1))), z)) | (~r(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~r(z, s(s(s(elem!1))))) | (~r(z, s(s(s(s(elem!1))))))) <=> ((~r(s(s(s(elem!1))), z)) | (~r(z, s(s(s(elem!1))))) | (~r(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~r(z, s(s(s(s(elem!1)))))))),
% 3.43/3.66 inference(rewrite,[status(thm)],[])).
% 3.43/3.66 tff(16895,plain,
% 3.43/3.66 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), z)) | (~r(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~r(z, s(s(s(elem!1))))) | (~r(z, s(s(s(s(elem!1)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), z)) | (~r(z, s(s(s(elem!1))))) | (~r(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~r(z, s(s(s(s(elem!1))))))))),
% 3.43/3.66 inference(monotonicity,[status(thm)],[16894])).
% 3.43/3.66 tff(16896,plain,
% 3.43/3.66 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), z)) | (~r(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~r(z, s(s(s(elem!1))))) | (~r(z, s(s(s(s(elem!1)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(elem!1))), z)) | (~r(z, s(s(s(elem!1))))) | (~r(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~r(z, s(s(s(s(elem!1)))))))),
% 3.43/3.66 inference(transitivity,[status(thm)],[16895, 16893])).
% 3.43/3.66 tff(16897,plain,
% 3.43/3.66 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), z)) | (~r(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~r(z, s(s(s(elem!1))))) | (~r(z, s(s(s(s(elem!1)))))))),
% 3.43/3.66 inference(quant_inst,[status(thm)],[])).
% 3.43/3.66 tff(16898,plain,
% 3.43/3.66 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(elem!1))), z)) | (~r(z, s(s(s(elem!1))))) | (~r(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~r(z, s(s(s(s(elem!1))))))),
% 3.43/3.66 inference(modus_ponens,[status(thm)],[16897, 16896])).
% 3.43/3.66 tff(16899,plain,
% 3.43/3.66 (~r(z, s(s(s(s(elem!1)))))),
% 3.43/3.66 inference(unit_resolution,[status(thm)],[16898, 197, 154, 16892, 16882])).
% 3.43/3.66 tff(16900,assumption,(z = s(s(s(s(elem!1))))), introduced(assumption)).
% 3.43/3.66 tff(16901,plain,
% 3.43/3.66 (s(s(s(s(elem!1)))) = z),
% 3.43/3.66 inference(symmetry,[status(thm)],[16900])).
% 3.43/3.66 tff(16902,plain,
% 3.43/3.66 ($false),
% 3.43/3.66 inference(unit_resolution,[status(thm)],[626, 16901])).
% 3.43/3.66 tff(16903,plain,(~(z = s(s(s(s(elem!1)))))), inference(lemma,lemma(discharge,[]))).
% 3.43/3.66 tff(16904,plain,
% 3.43/3.66 (b(z, s(s(s(s(elem!1)))))),
% 3.43/3.66 inference(unit_resolution,[status(thm)],[1496, 79, 16903, 16899])).
% 3.43/3.66 tff(16905,plain,
% 3.43/3.66 ((s(elem!1) = s(s(s(elem!1)))) <=> (s(s(s(elem!1))) = s(elem!1))),
% 3.43/3.66 inference(commutativity,[status(thm)],[])).
% 3.43/3.66 tff(16906,plain,
% 3.43/3.66 ((s(s(z)) = s(s(s(elem!1)))) <=> (s(elem!1) = s(s(s(elem!1))))),
% 3.43/3.66 inference(monotonicity,[status(thm)],[16821])).
% 3.43/3.66 tff(16907,plain,
% 3.43/3.66 ((s(s(z)) = s(s(s(elem!1)))) <=> (s(s(s(elem!1))) = s(elem!1))),
% 3.43/3.66 inference(transitivity,[status(thm)],[16906, 16905])).
% 3.43/3.66 tff(16908,plain,
% 3.43/3.66 ((~(s(s(z)) = s(s(s(elem!1))))) <=> (~(s(s(s(elem!1))) = s(elem!1)))),
% 3.43/3.66 inference(monotonicity,[status(thm)],[16907])).
% 3.43/3.66 tff(16909,plain,
% 3.43/3.66 (~(s(s(s(elem!1))) = s(elem!1))),
% 3.43/3.66 inference(modus_ponens,[status(thm)],[209, 16908])).
% 3.43/3.66 tff(16910,plain,
% 3.43/3.66 (~(s(s(s(s(elem!1)))) = s(s(elem!1)))),
% 3.43/3.66 inference(unit_resolution,[status(thm)],[1166, 16909])).
% 3.43/3.66 tff(16911,plain,
% 3.43/3.66 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), z)) | (~r(s(s(elem!1)), s(s(s(elem!1))))) | (~r(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~r(s(s(s(s(elem!1)))), s(s(elem!1)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(elem!1))), z)) | (~r(s(s(elem!1)), s(s(s(elem!1))))) | (~r(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~r(s(s(s(s(elem!1)))), s(s(elem!1)))))),
% 3.43/3.67 inference(rewrite,[status(thm)],[])).
% 3.43/3.67 tff(16912,plain,
% 3.43/3.67 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), z)) | (~r(s(s(elem!1)), s(s(s(elem!1))))) | (~r(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~r(s(s(s(s(elem!1)))), s(s(elem!1)))))),
% 3.43/3.67 inference(quant_inst,[status(thm)],[])).
% 3.43/3.67 tff(16913,plain,
% 3.43/3.67 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(elem!1))), z)) | (~r(s(s(elem!1)), s(s(s(elem!1))))) | (~r(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~r(s(s(s(s(elem!1)))), s(s(elem!1))))),
% 3.43/3.67 inference(modus_ponens,[status(thm)],[16912, 16911])).
% 3.43/3.67 tff(16914,plain,
% 3.43/3.67 (~r(s(s(s(s(elem!1)))), s(s(elem!1)))),
% 3.43/3.67 inference(unit_resolution,[status(thm)],[16913, 197, 154, 377, 16882])).
% 3.43/3.67 tff(16915,plain,
% 3.43/3.67 (b(s(s(s(s(elem!1)))), s(s(elem!1)))),
% 3.43/3.67 inference(unit_resolution,[status(thm)],[813, 16914, 16910])).
% 3.43/3.67 tff(16916,plain,
% 3.43/3.67 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(elem!1)))) | (~b(s(s(s(s(elem!1)))), s(s(elem!1)))) | (~b(s(z), s(s(elem!1)))) | (~b(s(s(elem!1)), s(z))) | (~b(z, s(s(s(s(elem!1)))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(s(elem!1)))) | (~b(s(s(s(s(elem!1)))), s(s(elem!1)))) | (~b(s(z), s(s(elem!1)))) | (~b(s(s(elem!1)), s(z))) | (~b(z, s(s(s(s(elem!1)))))))),
% 3.43/3.67 inference(rewrite,[status(thm)],[])).
% 3.43/3.67 tff(16917,plain,
% 3.43/3.67 (((~b(s(z), s(s(elem!1)))) | (~b(z, s(s(elem!1)))) | (~b(s(s(elem!1)), s(z))) | (~b(s(s(s(s(elem!1)))), s(s(elem!1)))) | (~b(z, s(s(elem!1)))) | (~b(z, s(s(s(s(elem!1))))))) <=> ((~b(z, s(s(elem!1)))) | (~b(s(s(s(s(elem!1)))), s(s(elem!1)))) | (~b(s(z), s(s(elem!1)))) | (~b(s(s(elem!1)), s(z))) | (~b(z, s(s(s(s(elem!1)))))))),
% 3.43/3.67 inference(rewrite,[status(thm)],[])).
% 3.43/3.67 tff(16918,plain,
% 3.43/3.67 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(elem!1)))) | (~b(z, s(s(elem!1)))) | (~b(s(s(elem!1)), s(z))) | (~b(s(s(s(s(elem!1)))), s(s(elem!1)))) | (~b(z, s(s(elem!1)))) | (~b(z, s(s(s(s(elem!1)))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(elem!1)))) | (~b(s(s(s(s(elem!1)))), s(s(elem!1)))) | (~b(s(z), s(s(elem!1)))) | (~b(s(s(elem!1)), s(z))) | (~b(z, s(s(s(s(elem!1))))))))),
% 3.43/3.67 inference(monotonicity,[status(thm)],[16917])).
% 3.43/3.67 tff(16919,plain,
% 3.43/3.67 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(elem!1)))) | (~b(z, s(s(elem!1)))) | (~b(s(s(elem!1)), s(z))) | (~b(s(s(s(s(elem!1)))), s(s(elem!1)))) | (~b(z, s(s(elem!1)))) | (~b(z, s(s(s(s(elem!1)))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(s(elem!1)))) | (~b(s(s(s(s(elem!1)))), s(s(elem!1)))) | (~b(s(z), s(s(elem!1)))) | (~b(s(s(elem!1)), s(z))) | (~b(z, s(s(s(s(elem!1)))))))),
% 3.43/3.67 inference(transitivity,[status(thm)],[16918, 16916])).
% 3.43/3.67 tff(16920,plain,
% 3.43/3.67 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(elem!1)))) | (~b(z, s(s(elem!1)))) | (~b(s(s(elem!1)), s(z))) | (~b(s(s(s(s(elem!1)))), s(s(elem!1)))) | (~b(z, s(s(elem!1)))) | (~b(z, s(s(s(s(elem!1)))))))),
% 3.43/3.67 inference(quant_inst,[status(thm)],[])).
% 3.43/3.67 tff(16921,plain,
% 3.43/3.67 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(s(elem!1)))) | (~b(s(s(s(s(elem!1)))), s(s(elem!1)))) | (~b(s(z), s(s(elem!1)))) | (~b(s(s(elem!1)), s(z))) | (~b(z, s(s(s(s(elem!1))))))),
% 3.43/3.67 inference(modus_ponens,[status(thm)],[16920, 16919])).
% 3.43/3.67 tff(16922,plain,
% 3.43/3.67 ($false),
% 3.43/3.67 inference(unit_resolution,[status(thm)],[16921, 166, 376, 1820, 16595, 16915, 16904])).
% 3.43/3.67 tff(16923,plain,((~r(s(z), s(s(z)))) | (~b(s(z), s(s(elem!1)))) | (~b(z, s(s(elem!1)))) | (~r(s(s(s(elem!1))), z)) | (~r(s(s(elem!1)), s(s(s(elem!1))))) | (s(s(s(s(elem!1)))) = s(s(s(elem!1)))) | (~r(s(z), z)) | (~r(s(s(z)), s(z))) | (~b(z, s(s(z)))) | (s(s(s(elem!1))) = s(s(s(z))))), inference(lemma,lemma(discharge,[]))).
% 3.43/3.67 tff(16924,plain,
% 3.43/3.67 (~r(s(z), s(s(z)))),
% 3.43/3.67 inference(unit_resolution,[status(thm)],[16923, 16784, 376, 16782, 16664, 364, 97, 392, 10451, 140])).
% 3.43/3.67 tff(16925,plain,
% 3.43/3.67 (b(s(z), s(s(z)))),
% 3.43/3.67 inference(unit_resolution,[status(thm)],[427, 16924])).
% 3.43/3.67 tff(16926,plain,
% 3.43/3.67 (~r(s(s(s(elem!1))), s(s(z)))),
% 3.43/3.67 inference(unit_resolution,[status(thm)],[16674, 16925, 376, 52, 45, 392, 16661, 16663])).
% 3.43/3.67 tff(16927,plain,
% 3.43/3.67 (b(s(s(s(elem!1))), s(s(z)))),
% 3.43/3.67 inference(unit_resolution,[status(thm)],[218, 16926])).
% 3.43/3.67 tff(16928,plain,
% 3.43/3.67 (~b(s(s(z)), s(s(elem!1)))),
% 3.43/3.67 inference(unit_resolution,[status(thm)],[4226, 16927, 16595, 16925, 16660])).
% 3.43/3.67 tff(16929,plain,
% 3.43/3.67 (r(s(s(z)), s(s(elem!1)))),
% 3.43/3.67 inference(unit_resolution,[status(thm)],[390, 16928, 52])).
% 3.43/3.67 tff(16930,plain,
% 3.43/3.67 (((~r(s(s(elem!1)), s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), s(s(elem!1)))) | (~r(s(s(z)), s(s(elem!1)))) | (~r(s(s(z)), s(s(s(elem!1)))))) <=> ((~r(s(s(s(elem!1))), s(s(elem!1)))) | (~r(s(s(elem!1)), s(s(s(elem!1))))) | (~r(s(s(z)), s(s(elem!1)))) | (~r(s(s(z)), s(s(s(elem!1))))))),
% 3.43/3.67 inference(rewrite,[status(thm)],[])).
% 3.43/3.67 tff(16931,plain,
% 3.43/3.67 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(elem!1)), s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), s(s(elem!1)))) | (~r(s(s(z)), s(s(elem!1)))) | (~r(s(s(z)), s(s(s(elem!1))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), s(s(elem!1)))) | (~r(s(s(elem!1)), s(s(s(elem!1))))) | (~r(s(s(z)), s(s(elem!1)))) | (~r(s(s(z)), s(s(s(elem!1)))))))),
% 3.43/3.67 inference(monotonicity,[status(thm)],[16930])).
% 3.43/3.67 tff(16932,plain,
% 3.43/3.67 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(elem!1)), s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), s(s(elem!1)))) | (~r(s(s(z)), s(s(elem!1)))) | (~r(s(s(z)), s(s(s(elem!1))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(elem!1))), s(s(elem!1)))) | (~r(s(s(elem!1)), s(s(s(elem!1))))) | (~r(s(s(z)), s(s(elem!1)))) | (~r(s(s(z)), s(s(s(elem!1))))))),
% 3.43/3.67 inference(transitivity,[status(thm)],[16931, 12392])).
% 3.43/3.67 tff(16933,plain,
% 3.43/3.67 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(elem!1)), s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), s(s(elem!1)))) | (~r(s(s(z)), s(s(elem!1)))) | (~r(s(s(z)), s(s(s(elem!1))))))),
% 3.43/3.67 inference(quant_inst,[status(thm)],[])).
% 3.43/3.67 tff(16934,plain,
% 3.43/3.67 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(elem!1))), s(s(elem!1)))) | (~r(s(s(elem!1)), s(s(s(elem!1))))) | (~r(s(s(z)), s(s(elem!1)))) | (~r(s(s(z)), s(s(s(elem!1)))))),
% 3.43/3.67 inference(modus_ponens,[status(thm)],[16933, 16932])).
% 3.43/3.67 tff(16935,plain,
% 3.43/3.67 (~r(s(s(z)), s(s(s(elem!1))))),
% 3.43/3.67 inference(unit_resolution,[status(thm)],[16934, 197, 16664, 16929, 16662])).
% 3.43/3.67 tff(16936,plain,
% 3.43/3.67 (b(s(s(z)), s(s(s(elem!1))))),
% 3.43/3.67 inference(unit_resolution,[status(thm)],[279, 16935])).
% 3.43/3.67 tff(16937,plain,
% 3.43/3.67 (~r(s(z), s(s(s(elem!1))))),
% 3.43/3.67 inference(unit_resolution,[status(thm)],[14413, 197, 16782, 16651, 97])).
% 3.43/3.67 tff(16938,plain,
% 3.43/3.67 (b(s(z), s(s(s(elem!1))))),
% 3.43/3.67 inference(unit_resolution,[status(thm)],[116, 16937])).
% 3.43/3.67 tff(16939,plain,
% 3.43/3.67 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(s(elem!1))))) | (~b(s(z), s(s(elem!1)))) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(z), s(s(z)))) | (~b(s(s(z)), s(s(s(elem!1))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), s(s(s(elem!1))))) | (~b(s(z), s(s(elem!1)))) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(z), s(s(z)))) | (~b(s(s(z)), s(s(s(elem!1))))))),
% 3.43/3.67 inference(rewrite,[status(thm)],[])).
% 3.43/3.67 tff(16940,plain,
% 3.43/3.67 (((~b(s(z), s(s(elem!1)))) | (~b(s(z), s(s(elem!1)))) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(s(z)), s(s(s(elem!1))))) | (~b(s(z), s(s(s(elem!1))))) | (~b(s(z), s(s(z))))) <=> ((~b(s(z), s(s(s(elem!1))))) | (~b(s(z), s(s(elem!1)))) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(z), s(s(z)))) | (~b(s(s(z)), s(s(s(elem!1))))))),
% 3.43/3.67 inference(rewrite,[status(thm)],[])).
% 3.43/3.67 tff(16941,plain,
% 3.43/3.67 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(elem!1)))) | (~b(s(z), s(s(elem!1)))) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(s(z)), s(s(s(elem!1))))) | (~b(s(z), s(s(s(elem!1))))) | (~b(s(z), s(s(z)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(s(elem!1))))) | (~b(s(z), s(s(elem!1)))) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(z), s(s(z)))) | (~b(s(s(z)), s(s(s(elem!1)))))))),
% 3.43/3.67 inference(monotonicity,[status(thm)],[16940])).
% 3.43/3.67 tff(16942,plain,
% 3.43/3.67 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(elem!1)))) | (~b(s(z), s(s(elem!1)))) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(s(z)), s(s(s(elem!1))))) | (~b(s(z), s(s(s(elem!1))))) | (~b(s(z), s(s(z)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), s(s(s(elem!1))))) | (~b(s(z), s(s(elem!1)))) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(z), s(s(z)))) | (~b(s(s(z)), s(s(s(elem!1))))))),
% 3.43/3.67 inference(transitivity,[status(thm)],[16941, 16939])).
% 3.43/3.67 tff(16943,plain,
% 3.43/3.67 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(elem!1)))) | (~b(s(z), s(s(elem!1)))) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(s(z)), s(s(s(elem!1))))) | (~b(s(z), s(s(s(elem!1))))) | (~b(s(z), s(s(z)))))),
% 3.43/3.67 inference(quant_inst,[status(thm)],[])).
% 3.43/3.67 tff(16944,plain,
% 3.43/3.67 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), s(s(s(elem!1))))) | (~b(s(z), s(s(elem!1)))) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(z), s(s(z)))) | (~b(s(s(z)), s(s(s(elem!1)))))),
% 3.43/3.67 inference(modus_ponens,[status(thm)],[16943, 16942])).
% 3.43/3.67 tff(16945,plain,
% 3.43/3.67 ($false),
% 3.43/3.67 inference(unit_resolution,[status(thm)],[16944, 166, 376, 16938, 16925, 16660, 16936])).
% 3.43/3.67 tff(16946,plain,((s(s(elem!1)) = s(s(s(elem!1)))) | (~b(s(z), s(s(elem!1)))) | (s(s(z)) = s(s(elem!1))) | (~r(s(s(z)), s(z))) | (~r(s(z), z)) | (~b(z, s(s(z))))), inference(lemma,lemma(discharge,[]))).
% 3.43/3.67 tff(16947,plain,
% 3.43/3.67 (s(s(elem!1)) = s(s(s(elem!1)))),
% 3.43/3.67 inference(unit_resolution,[status(thm)],[16946, 16594, 376, 4143, 16592, 10451])).
% 3.43/3.67 tff(16948,plain,
% 3.43/3.67 (s(s(s(elem!1))) = s(elem!1)),
% 3.43/3.67 inference(unit_resolution,[status(thm)],[2594, 16947])).
% 3.43/3.67 tff(16949,plain,
% 3.43/3.67 (s(elem!1) = s(s(s(elem!1)))),
% 3.43/3.67 inference(symmetry,[status(thm)],[16948])).
% 3.43/3.67 tff(16950,plain,
% 3.43/3.67 (b(s(elem!1), s(z)) <=> b(s(s(s(elem!1))), s(z))),
% 3.43/3.67 inference(monotonicity,[status(thm)],[16949])).
% 3.43/3.67 tff(16951,plain,
% 3.43/3.67 (b(s(s(s(elem!1))), s(z)) <=> b(s(elem!1), s(z))),
% 3.43/3.67 inference(symmetry,[status(thm)],[16950])).
% 3.43/3.67 tff(16952,plain,
% 3.43/3.67 (~b(z, s(z))),
% 3.43/3.67 inference(unit_resolution,[status(thm)],[16649, 16592, 4143, 10451, 376])).
% 3.43/3.67 tff(16953,plain,
% 3.43/3.67 (r(z, s(z))),
% 3.43/3.67 inference(unit_resolution,[status(thm)],[321, 16952])).
% 3.43/3.67 tff(16954,plain,
% 3.43/3.67 (~r(s(s(s(elem!1))), s(z))),
% 3.43/3.67 inference(unit_resolution,[status(thm)],[16658, 16592, 10451, 4143, 16953])).
% 3.43/3.67 tff(16955,plain,
% 3.43/3.67 (b(s(s(s(elem!1))), s(z))),
% 3.43/3.67 inference(unit_resolution,[status(thm)],[1849, 16954])).
% 3.43/3.67 tff(16956,plain,
% 3.43/3.67 (b(s(elem!1), s(z))),
% 3.43/3.67 inference(modus_ponens,[status(thm)],[16955, 16951])).
% 3.43/3.67 tff(16957,plain,
% 3.43/3.67 (b(s(z), s(elem!1)) <=> b(s(z), s(s(s(elem!1))))),
% 3.43/3.67 inference(monotonicity,[status(thm)],[16949])).
% 3.43/3.67 tff(16958,plain,
% 3.43/3.67 (b(s(z), s(s(s(elem!1)))) <=> b(s(z), s(elem!1))),
% 3.43/3.67 inference(symmetry,[status(thm)],[16957])).
% 3.43/3.67 tff(16959,plain,
% 3.43/3.67 (~b(s(s(s(elem!1))), z)),
% 3.43/3.67 inference(unit_resolution,[status(thm)],[16780, 16592, 10451, 4143, 376, 16594])).
% 3.43/3.67 tff(16960,plain,
% 3.43/3.67 (r(s(s(s(elem!1))), z)),
% 3.43/3.67 inference(unit_resolution,[status(thm)],[94, 16959])).
% 3.43/3.67 tff(16961,plain,
% 3.43/3.67 (~r(s(z), s(s(s(elem!1))))),
% 3.43/3.67 inference(unit_resolution,[status(thm)],[14413, 197, 16960, 16953, 16592])).
% 3.43/3.67 tff(16962,plain,
% 3.43/3.67 (b(s(z), s(s(s(elem!1))))),
% 3.43/3.67 inference(unit_resolution,[status(thm)],[116, 16961])).
% 3.43/3.67 tff(16963,plain,
% 3.43/3.67 (b(s(z), s(elem!1))),
% 3.43/3.67 inference(modus_ponens,[status(thm)],[16962, 16958])).
% 3.43/3.67 tff(16964,plain,
% 3.43/3.67 (s(s(elem!1)) = elem!1),
% 3.43/3.67 inference(unit_resolution,[status(thm)],[10139, 16948])).
% 3.43/3.67 tff(16965,plain,
% 3.43/3.67 (~(s(s(s(z))) = elem!1)),
% 3.43/3.67 inference(unit_resolution,[status(thm)],[3122, 16947])).
% 3.43/3.67 tff(16966,plain,
% 3.43/3.67 (r(s(s(elem!1)), z) <=> r(s(s(s(elem!1))), z)),
% 3.43/3.67 inference(monotonicity,[status(thm)],[16947])).
% 3.43/3.67 tff(16967,plain,
% 3.43/3.67 (r(s(s(s(elem!1))), z) <=> r(s(s(elem!1)), z)),
% 3.43/3.67 inference(symmetry,[status(thm)],[16966])).
% 3.43/3.67 tff(16968,plain,
% 3.43/3.67 (r(s(s(elem!1)), z)),
% 3.43/3.67 inference(modus_ponens,[status(thm)],[16960, 16967])).
% 3.43/3.67 tff(16969,plain,
% 3.43/3.67 (~r(s(s(s(z))), z)),
% 3.43/3.67 inference(unit_resolution,[status(thm)],[12545, 16968, 16592, 16953, 16965, 16964, 16963, 16593, 16956])).
% 3.43/3.67 tff(16970,plain,
% 3.43/3.67 (b(s(s(s(z))), z)),
% 3.43/3.67 inference(unit_resolution,[status(thm)],[1713, 16969])).
% 3.43/3.67 tff(16971,plain,
% 3.43/3.67 (~r(s(s(z)), z)),
% 3.43/3.67 inference(unit_resolution,[status(thm)],[12376, 197, 16953, 16592, 4143])).
% 3.43/3.67 tff(16972,plain,
% 3.43/3.67 (b(s(s(z)), z)),
% 3.43/3.67 inference(unit_resolution,[status(thm)],[186, 16971])).
% 3.43/3.67 tff(16973,plain,
% 3.43/3.67 (~b(s(s(z)), s(s(s(z))))),
% 3.43/3.67 inference(unit_resolution,[status(thm)],[13913, 166, 10451, 16972, 16970])).
% 3.43/3.67 tff(16974,plain,
% 3.43/3.67 (r(s(s(z)), s(s(s(z))))),
% 3.43/3.67 inference(unit_resolution,[status(thm)],[1730, 16973])).
% 3.43/3.67 tff(16975,plain,
% 3.43/3.67 (r(s(s(elem!1)), s(s(s(z)))) <=> r(s(s(s(elem!1))), s(s(s(z))))),
% 3.43/3.67 inference(monotonicity,[status(thm)],[16947])).
% 3.43/3.67 tff(16976,plain,
% 3.43/3.67 (r(s(s(s(elem!1))), s(s(s(z)))) <=> r(s(s(elem!1)), s(s(s(z))))),
% 3.43/3.67 inference(symmetry,[status(thm)],[16975])).
% 3.43/3.67 tff(16977,plain,
% 3.43/3.67 ((~r(s(s(s(elem!1))), s(s(s(z))))) <=> (~r(s(s(elem!1)), s(s(s(z)))))),
% 3.43/3.67 inference(monotonicity,[status(thm)],[16976])).
% 3.43/3.67 tff(16978,plain,
% 3.43/3.67 (~b(s(s(s(z))), s(s(z)))),
% 3.43/3.67 inference(unit_resolution,[status(thm)],[12296, 166, 10451, 16972, 16970])).
% 3.43/3.67 tff(16979,plain,
% 3.43/3.67 (r(s(s(s(z))), s(s(z)))),
% 3.43/3.67 inference(unit_resolution,[status(thm)],[1010, 16978])).
% 3.43/3.67 tff(16980,plain,
% 3.43/3.67 (~(s(s(elem!1)) = s(s(z)))),
% 3.43/3.67 inference(unit_resolution,[status(thm)],[131, 16594])).
% 3.43/3.67 tff(16981,plain,
% 3.43/3.67 (~(s(s(s(elem!1))) = s(s(s(z))))),
% 3.43/3.67 inference(unit_resolution,[status(thm)],[139, 16980])).
% 3.43/3.67 tff(16982,plain,
% 3.43/3.67 (~b(s(s(z)), s(s(s(z))))),
% 3.43/3.67 inference(unit_resolution,[status(thm)],[13913, 166, 10451, 122, 1699])).
% 3.43/3.67 tff(16983,plain,
% 3.43/3.67 (r(s(s(z)), s(s(s(z))))),
% 3.43/3.67 inference(unit_resolution,[status(thm)],[1730, 16982])).
% 3.43/3.67 tff(16984,plain,
% 3.43/3.67 (~r(s(s(s(z))), s(z))),
% 3.43/3.67 inference(unit_resolution,[status(thm)],[13956, 197, 120, 392, 1676])).
% 3.43/3.67 tff(16985,plain,
% 3.43/3.67 (b(s(s(s(z))), s(z))),
% 3.43/3.67 inference(unit_resolution,[status(thm)],[1763, 16984])).
% 3.43/3.67 tff(16986,plain,
% 3.43/3.67 (~r(s(z), s(s(s(z))))),
% 3.43/3.67 inference(unit_resolution,[status(thm)],[16796, 197, 120, 392, 1676])).
% 3.43/3.67 tff(16987,plain,
% 3.43/3.67 (b(s(z), s(s(s(z))))),
% 3.43/3.67 inference(unit_resolution,[status(thm)],[1674, 16986])).
% 3.43/3.67 tff(16988,plain,
% 3.43/3.67 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(z)))) | (~b(s(s(s(elem!1))), s(s(z)))) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(s(s(z))), z)) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(elem!1))), s(s(s(z))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(s(z)))) | (~b(s(s(s(elem!1))), s(s(z)))) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(s(s(z))), z)) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(elem!1))), s(s(s(z))))))),
% 3.43/3.67 inference(rewrite,[status(thm)],[])).
% 3.43/3.67 tff(16989,plain,
% 3.43/3.67 (((~b(z, s(s(z)))) | (~b(s(s(s(elem!1))), s(s(z)))) | (~b(s(s(s(z))), z)) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(elem!1))), s(s(s(z))))) | (~b(s(s(s(elem!1))), s(z)))) <=> ((~b(z, s(s(z)))) | (~b(s(s(s(elem!1))), s(s(z)))) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(s(s(z))), z)) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(elem!1))), s(s(s(z))))))),
% 3.43/3.67 inference(rewrite,[status(thm)],[])).
% 3.43/3.67 tff(16990,plain,
% 3.43/3.67 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(z)))) | (~b(s(s(s(elem!1))), s(s(z)))) | (~b(s(s(s(z))), z)) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(elem!1))), s(s(s(z))))) | (~b(s(s(s(elem!1))), s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(z)))) | (~b(s(s(s(elem!1))), s(s(z)))) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(s(s(z))), z)) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(elem!1))), s(s(s(z)))))))),
% 3.43/3.67 inference(monotonicity,[status(thm)],[16989])).
% 3.43/3.67 tff(16991,plain,
% 3.43/3.67 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(z)))) | (~b(s(s(s(elem!1))), s(s(z)))) | (~b(s(s(s(z))), z)) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(elem!1))), s(s(s(z))))) | (~b(s(s(s(elem!1))), s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(s(z)))) | (~b(s(s(s(elem!1))), s(s(z)))) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(s(s(z))), z)) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(elem!1))), s(s(s(z))))))),
% 3.43/3.67 inference(transitivity,[status(thm)],[16990, 16988])).
% 3.43/3.67 tff(16992,plain,
% 3.43/3.67 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(z)))) | (~b(s(s(s(elem!1))), s(s(z)))) | (~b(s(s(s(z))), z)) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(elem!1))), s(s(s(z))))) | (~b(s(s(s(elem!1))), s(z))))),
% 3.43/3.67 inference(quant_inst,[status(thm)],[])).
% 3.43/3.67 tff(16993,plain,
% 3.43/3.67 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(s(z)))) | (~b(s(s(s(elem!1))), s(s(z)))) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(s(s(z))), z)) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(elem!1))), s(s(s(z)))))),
% 3.43/3.67 inference(modus_ponens,[status(thm)],[16992, 16991])).
% 3.43/3.67 tff(16994,plain,
% 3.43/3.67 (~b(s(s(s(elem!1))), s(s(s(z))))),
% 3.43/3.67 inference(unit_resolution,[status(thm)],[16993, 166, 10451, 96, 16987, 1699, 2060])).
% 3.43/3.67 tff(16995,plain,
% 3.43/3.67 (r(s(s(s(elem!1))), s(s(s(z))))),
% 3.43/3.67 inference(unit_resolution,[status(thm)],[3574, 16994, 3567])).
% 3.43/3.67 tff(16996,plain,
% 3.43/3.67 (~r(s(s(s(elem!1))), s(s(s(s(z)))))),
% 3.43/3.67 inference(unit_resolution,[status(thm)],[8152, 197, 1676, 4680, 3183])).
% 3.43/3.67 tff(16997,plain,
% 3.43/3.67 (~r(elem!1, s(s(s(s(z)))))),
% 3.43/3.67 inference(unit_resolution,[status(thm)],[5665, 16996, 334])).
% 3.43/3.67 tff(16998,plain,
% 3.43/3.67 (b(elem!1, s(s(s(s(z)))))),
% 3.43/3.67 inference(unit_resolution,[status(thm)],[1098, 16997, 6568])).
% 3.43/3.67 tff(16999,plain,
% 3.43/3.67 (b(s(s(s(elem!1))), s(s(s(s(z)))))),
% 3.43/3.67 inference(modus_ponens,[status(thm)],[16998, 6549])).
% 3.43/3.67 tff(17000,plain,
% 3.43/3.67 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(z)), s(s(s(z))))) | (~r(s(s(s(z))), s(s(z)))) | (~r(s(s(s(s(z)))), s(s(s(z))))) | (~r(s(s(s(s(z)))), s(s(z)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(z)), s(s(s(z))))) | (~r(s(s(s(z))), s(s(z)))) | (~r(s(s(s(s(z)))), s(s(s(z))))) | (~r(s(s(s(s(z)))), s(s(z)))))),
% 3.43/3.68 inference(rewrite,[status(thm)],[])).
% 3.43/3.68 tff(17001,plain,
% 3.43/3.68 (((~r(s(s(s(z))), s(s(z)))) | (~r(s(s(z)), s(s(s(z))))) | (~r(s(s(s(s(z)))), s(s(s(z))))) | (~r(s(s(s(s(z)))), s(s(z))))) <=> ((~r(s(s(z)), s(s(s(z))))) | (~r(s(s(s(z))), s(s(z)))) | (~r(s(s(s(s(z)))), s(s(s(z))))) | (~r(s(s(s(s(z)))), s(s(z)))))),
% 3.43/3.68 inference(rewrite,[status(thm)],[])).
% 3.43/3.68 tff(17002,plain,
% 3.43/3.68 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(z))), s(s(z)))) | (~r(s(s(z)), s(s(s(z))))) | (~r(s(s(s(s(z)))), s(s(s(z))))) | (~r(s(s(s(s(z)))), s(s(z)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(z)), s(s(s(z))))) | (~r(s(s(s(z))), s(s(z)))) | (~r(s(s(s(s(z)))), s(s(s(z))))) | (~r(s(s(s(s(z)))), s(s(z))))))),
% 3.43/3.68 inference(monotonicity,[status(thm)],[17001])).
% 3.43/3.68 tff(17003,plain,
% 3.43/3.68 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(z))), s(s(z)))) | (~r(s(s(z)), s(s(s(z))))) | (~r(s(s(s(s(z)))), s(s(s(z))))) | (~r(s(s(s(s(z)))), s(s(z)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(z)), s(s(s(z))))) | (~r(s(s(s(z))), s(s(z)))) | (~r(s(s(s(s(z)))), s(s(s(z))))) | (~r(s(s(s(s(z)))), s(s(z)))))),
% 3.43/3.68 inference(transitivity,[status(thm)],[17002, 17000])).
% 3.43/3.68 tff(17004,plain,
% 3.43/3.68 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(z))), s(s(z)))) | (~r(s(s(z)), s(s(s(z))))) | (~r(s(s(s(s(z)))), s(s(s(z))))) | (~r(s(s(s(s(z)))), s(s(z)))))),
% 3.43/3.68 inference(quant_inst,[status(thm)],[])).
% 3.43/3.68 tff(17005,plain,
% 3.43/3.68 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(z)), s(s(s(z))))) | (~r(s(s(s(z))), s(s(z)))) | (~r(s(s(s(s(z)))), s(s(s(z))))) | (~r(s(s(s(s(z)))), s(s(z))))),
% 3.43/3.68 inference(modus_ponens,[status(thm)],[17004, 17003])).
% 3.43/3.68 tff(17006,plain,
% 3.43/3.68 (~r(s(s(s(s(z)))), s(s(z)))),
% 3.43/3.68 inference(unit_resolution,[status(thm)],[17005, 197, 1676, 4680, 1732])).
% 3.43/3.68 tff(17007,plain,
% 3.43/3.68 (b(s(s(s(s(z)))), s(s(z)))),
% 3.43/3.68 inference(unit_resolution,[status(thm)],[5631, 17006])).
% 3.43/3.68 tff(17008,plain,
% 3.43/3.68 (~r(s(s(z)), s(s(s(elem!1))))),
% 3.43/3.68 inference(unit_resolution,[status(thm)],[16838, 197, 1676, 1732, 3183])).
% 3.43/3.68 tff(17009,plain,
% 3.43/3.68 (b(s(s(z)), s(s(s(elem!1))))),
% 3.43/3.68 inference(unit_resolution,[status(thm)],[279, 17008])).
% 3.43/3.68 tff(17010,plain,
% 3.43/3.68 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), s(s(z)))) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(s(z)), s(s(s(elem!1))))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(s(elem!1))), s(s(s(s(z)))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(elem!1))), s(s(z)))) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(s(z)), s(s(s(elem!1))))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(s(elem!1))), s(s(s(s(z)))))))),
% 3.43/3.68 inference(rewrite,[status(thm)],[])).
% 3.43/3.68 tff(17011,plain,
% 3.43/3.68 (((~b(s(s(s(elem!1))), s(z))) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(s(z)), s(s(s(elem!1))))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(s(elem!1))), s(s(z)))) | (~b(s(s(s(elem!1))), s(s(s(s(z))))))) <=> ((~b(s(s(s(elem!1))), s(s(z)))) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(s(z)), s(s(s(elem!1))))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(s(elem!1))), s(s(s(s(z)))))))),
% 3.43/3.68 inference(rewrite,[status(thm)],[])).
% 3.43/3.68 tff(17012,plain,
% 3.43/3.68 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), s(z))) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(s(z)), s(s(s(elem!1))))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(s(elem!1))), s(s(z)))) | (~b(s(s(s(elem!1))), s(s(s(s(z)))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), s(s(z)))) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(s(z)), s(s(s(elem!1))))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(s(elem!1))), s(s(s(s(z))))))))),
% 3.43/3.68 inference(monotonicity,[status(thm)],[17011])).
% 3.43/3.68 tff(17013,plain,
% 3.43/3.68 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), s(z))) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(s(z)), s(s(s(elem!1))))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(s(elem!1))), s(s(z)))) | (~b(s(s(s(elem!1))), s(s(s(s(z)))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(elem!1))), s(s(z)))) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(s(z)), s(s(s(elem!1))))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(s(elem!1))), s(s(s(s(z)))))))),
% 3.43/3.68 inference(transitivity,[status(thm)],[17012, 17010])).
% 3.43/3.68 tff(17014,plain,
% 3.43/3.68 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), s(z))) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(s(z)), s(s(s(elem!1))))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(s(elem!1))), s(s(z)))) | (~b(s(s(s(elem!1))), s(s(s(s(z)))))))),
% 3.43/3.68 inference(quant_inst,[status(thm)],[])).
% 3.43/3.68 tff(17015,plain,
% 3.43/3.68 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(elem!1))), s(s(z)))) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(s(z)), s(s(s(elem!1))))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(s(elem!1))), s(s(s(s(z))))))),
% 3.43/3.68 inference(modus_ponens,[status(thm)],[17014, 17013])).
% 3.43/3.68 tff(17016,plain,
% 3.43/3.68 ($false),
% 3.43/3.68 inference(unit_resolution,[status(thm)],[17015, 166, 96, 17009, 2060, 17007, 16999])).
% 3.43/3.68 tff(17017,plain,((~r(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(s(s(elem!1))), s(s(z)))) | (~(s(s(elem!1)) = s(s(s(elem!1))))) | (~r(s(s(s(z))), s(s(z)))) | (~r(s(s(s(elem!1))), s(s(s(z))))) | (~r(s(s(z)), s(s(s(z)))))), inference(lemma,lemma(discharge,[]))).
% 3.43/3.68 tff(17018,plain,
% 3.43/3.68 (~r(s(s(s(s(z)))), s(s(s(z))))),
% 3.43/3.68 inference(unit_resolution,[status(thm)],[17017, 16995, 2060, 334, 1676, 96, 1732])).
% 3.43/3.68 tff(17019,plain,
% 3.43/3.68 (b(s(s(s(s(z)))), s(s(s(z))))),
% 3.43/3.68 inference(unit_resolution,[status(thm)],[4662, 17018])).
% 3.43/3.68 tff(17020,plain,
% 3.43/3.68 (~r(s(s(s(s(z)))), s(z))),
% 3.43/3.68 inference(unit_resolution,[status(thm)],[12740, 17019, 323, 120, 1699])).
% 3.43/3.68 tff(17021,plain,
% 3.43/3.68 (b(s(s(s(s(z)))), s(z))),
% 3.43/3.68 inference(unit_resolution,[status(thm)],[3285, 17020])).
% 3.43/3.68 tff(17022,plain,
% 3.43/3.68 ($false),
% 3.43/3.68 inference(unit_resolution,[status(thm)],[4768, 166, 16987, 17019, 17021, 16985])).
% 3.43/3.68 tff(17023,plain,((~r(s(z), s(s(z)))) | (~r(z, s(z))) | (~b(s(s(s(z))), z)) | (~b(s(s(s(elem!1))), s(s(z)))) | (~(s(s(elem!1)) = s(s(s(elem!1))))) | (~r(s(s(s(z))), s(s(z)))) | (~b(s(s(s(elem!1))), s(z))) | (~r(s(s(z)), s(s(s(z))))) | (s(s(s(elem!1))) = s(s(s(z)))) | (~b(z, s(s(z)))) | (~r(s(s(z)), s(z)))), inference(lemma,lemma(discharge,[]))).
% 3.43/3.68 tff(17024,plain,
% 3.43/3.68 (~r(s(z), s(s(z)))),
% 3.43/3.68 inference(unit_resolution,[status(thm)],[17023, 2060, 1699, 323, 334, 12298, 96, 16983, 3567, 10451, 392])).
% 3.43/3.68 tff(17025,plain,
% 3.43/3.68 (b(s(z), s(s(z)))),
% 3.43/3.68 inference(unit_resolution,[status(thm)],[427, 17024])).
% 3.43/3.68 tff(17026,plain,
% 3.43/3.68 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(z)))) | (~b(s(s(s(elem!1))), s(s(z)))) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(z), s(s(z)))) | (~b(s(s(z)), z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(s(z)))) | (~b(s(s(s(elem!1))), s(s(z)))) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(z), s(s(z)))) | (~b(s(s(z)), z)))),
% 3.43/3.68 inference(rewrite,[status(thm)],[])).
% 3.43/3.68 tff(17027,plain,
% 3.43/3.68 (((~b(z, s(s(z)))) | (~b(s(s(s(elem!1))), s(s(z)))) | (~b(s(s(z)), z)) | (~b(s(z), s(s(z)))) | (~b(s(s(s(elem!1))), s(s(z)))) | (~b(s(s(s(elem!1))), s(z)))) <=> ((~b(z, s(s(z)))) | (~b(s(s(s(elem!1))), s(s(z)))) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(z), s(s(z)))) | (~b(s(s(z)), z)))),
% 3.43/3.68 inference(rewrite,[status(thm)],[])).
% 3.43/3.68 tff(17028,plain,
% 3.43/3.68 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(z)))) | (~b(s(s(s(elem!1))), s(s(z)))) | (~b(s(s(z)), z)) | (~b(s(z), s(s(z)))) | (~b(s(s(s(elem!1))), s(s(z)))) | (~b(s(s(s(elem!1))), s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(z)))) | (~b(s(s(s(elem!1))), s(s(z)))) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(z), s(s(z)))) | (~b(s(s(z)), z))))),
% 3.43/3.68 inference(monotonicity,[status(thm)],[17027])).
% 3.43/3.68 tff(17029,plain,
% 3.43/3.68 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(z)))) | (~b(s(s(s(elem!1))), s(s(z)))) | (~b(s(s(z)), z)) | (~b(s(z), s(s(z)))) | (~b(s(s(s(elem!1))), s(s(z)))) | (~b(s(s(s(elem!1))), s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(s(z)))) | (~b(s(s(s(elem!1))), s(s(z)))) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(z), s(s(z)))) | (~b(s(s(z)), z)))),
% 3.43/3.68 inference(transitivity,[status(thm)],[17028, 17026])).
% 3.43/3.68 tff(17030,plain,
% 3.43/3.68 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(z)))) | (~b(s(s(s(elem!1))), s(s(z)))) | (~b(s(s(z)), z)) | (~b(s(z), s(s(z)))) | (~b(s(s(s(elem!1))), s(s(z)))) | (~b(s(s(s(elem!1))), s(z))))),
% 3.43/3.68 inference(quant_inst,[status(thm)],[])).
% 3.43/3.68 tff(17031,plain,
% 3.43/3.68 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(s(z)))) | (~b(s(s(s(elem!1))), s(s(z)))) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(z), s(s(z)))) | (~b(s(s(z)), z))),
% 3.43/3.68 inference(modus_ponens,[status(thm)],[17030, 17029])).
% 3.43/3.68 tff(17032,plain,
% 3.43/3.68 ($false),
% 3.43/3.68 inference(unit_resolution,[status(thm)],[17031, 166, 17025, 10451, 96, 122, 2060])).
% 3.43/3.68 tff(17033,plain,((~b(s(s(s(elem!1))), s(s(z)))) | (~b(z, s(s(z)))) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(s(z)), z)) | (~b(s(s(s(z))), z)) | (~r(z, s(z))) | (~(s(s(elem!1)) = s(s(s(elem!1))))) | (s(s(s(elem!1))) = s(s(s(z)))) | (~r(s(s(z)), s(z)))), inference(lemma,lemma(discharge,[]))).
% 3.43/3.68 tff(17034,plain,
% 3.43/3.68 (~b(s(s(s(elem!1))), s(s(z)))),
% 3.43/3.68 inference(unit_resolution,[status(thm)],[17033, 16955, 10451, 16972, 16970, 16953, 16947, 16981, 4143])).
% 3.43/3.68 tff(17035,plain,
% 3.43/3.68 (r(s(s(s(elem!1))), s(s(z)))),
% 3.43/3.68 inference(unit_resolution,[status(thm)],[218, 17034])).
% 3.43/3.68 tff(17036,plain,
% 3.43/3.68 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), s(s(s(z))))) | (~r(s(s(z)), s(z))) | (~r(s(s(s(elem!1))), s(s(z)))) | (~r(s(s(s(z))), s(s(z)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(elem!1))), s(s(s(z))))) | (~r(s(s(z)), s(z))) | (~r(s(s(s(elem!1))), s(s(z)))) | (~r(s(s(s(z))), s(s(z)))))),
% 3.43/3.68 inference(rewrite,[status(thm)],[])).
% 3.43/3.68 tff(17037,plain,
% 3.43/3.68 (((~r(s(s(z)), s(z))) | (~r(s(s(s(z))), s(s(z)))) | (~r(s(s(s(elem!1))), s(s(z)))) | (~r(s(s(s(elem!1))), s(s(s(z)))))) <=> ((~r(s(s(s(elem!1))), s(s(s(z))))) | (~r(s(s(z)), s(z))) | (~r(s(s(s(elem!1))), s(s(z)))) | (~r(s(s(s(z))), s(s(z)))))),
% 3.43/3.68 inference(rewrite,[status(thm)],[])).
% 3.43/3.68 tff(17038,plain,
% 3.43/3.68 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(z)), s(z))) | (~r(s(s(s(z))), s(s(z)))) | (~r(s(s(s(elem!1))), s(s(z)))) | (~r(s(s(s(elem!1))), s(s(s(z))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), s(s(s(z))))) | (~r(s(s(z)), s(z))) | (~r(s(s(s(elem!1))), s(s(z)))) | (~r(s(s(s(z))), s(s(z))))))),
% 3.43/3.68 inference(monotonicity,[status(thm)],[17037])).
% 3.43/3.68 tff(17039,plain,
% 3.43/3.68 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(z)), s(z))) | (~r(s(s(s(z))), s(s(z)))) | (~r(s(s(s(elem!1))), s(s(z)))) | (~r(s(s(s(elem!1))), s(s(s(z))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(elem!1))), s(s(s(z))))) | (~r(s(s(z)), s(z))) | (~r(s(s(s(elem!1))), s(s(z)))) | (~r(s(s(s(z))), s(s(z)))))),
% 3.43/3.68 inference(transitivity,[status(thm)],[17038, 17036])).
% 3.43/3.68 tff(17040,plain,
% 3.43/3.68 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(z)), s(z))) | (~r(s(s(s(z))), s(s(z)))) | (~r(s(s(s(elem!1))), s(s(z)))) | (~r(s(s(s(elem!1))), s(s(s(z))))))),
% 3.43/3.68 inference(quant_inst,[status(thm)],[])).
% 3.43/3.68 tff(17041,plain,
% 3.43/3.68 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(elem!1))), s(s(s(z))))) | (~r(s(s(z)), s(z))) | (~r(s(s(s(elem!1))), s(s(z)))) | (~r(s(s(s(z))), s(s(z))))),
% 3.43/3.68 inference(modus_ponens,[status(thm)],[17040, 17039])).
% 3.43/3.68 tff(17042,plain,
% 3.43/3.68 (~r(s(s(s(elem!1))), s(s(s(z))))),
% 3.43/3.68 inference(unit_resolution,[status(thm)],[17041, 197, 4143, 17035, 16979])).
% 3.43/3.68 tff(17043,plain,
% 3.43/3.68 (~r(s(s(elem!1)), s(s(s(z))))),
% 3.43/3.68 inference(modus_ponens,[status(thm)],[17042, 16977])).
% 3.43/3.68 tff(17044,plain,
% 3.43/3.68 (s(s(s(elem!1))) = s(s(elem!1))),
% 3.43/3.68 inference(symmetry,[status(thm)],[16947])).
% 3.43/3.68 tff(17045,plain,
% 3.43/3.68 ((s(s(s(elem!1))) = s(s(s(z)))) <=> (s(s(elem!1)) = s(s(s(z))))),
% 3.43/3.68 inference(monotonicity,[status(thm)],[17044])).
% 3.43/3.68 tff(17046,plain,
% 3.43/3.68 ((s(s(s(elem!1))) = s(s(s(z)))) <=> (s(s(s(z))) = s(s(elem!1)))),
% 3.43/3.68 inference(transitivity,[status(thm)],[17045, 4437])).
% 3.43/3.68 tff(17047,plain,
% 3.43/3.68 ((~(s(s(s(elem!1))) = s(s(s(z))))) <=> (~(s(s(s(z))) = s(s(elem!1))))),
% 3.43/3.68 inference(monotonicity,[status(thm)],[17046])).
% 3.43/3.68 tff(17048,plain,
% 3.43/3.68 (~(s(s(s(z))) = s(s(elem!1)))),
% 3.43/3.68 inference(modus_ponens,[status(thm)],[16981, 17047])).
% 3.43/3.68 tff(17049,plain,
% 3.43/3.68 (r(s(s(s(z))), s(s(s(elem!1)))) <=> r(s(s(s(z))), s(s(elem!1)))),
% 3.43/3.68 inference(monotonicity,[status(thm)],[17044])).
% 3.43/3.68 tff(17050,plain,
% 3.43/3.68 ((~r(s(s(s(z))), s(s(s(elem!1))))) <=> (~r(s(s(s(z))), s(s(elem!1))))),
% 3.43/3.68 inference(monotonicity,[status(thm)],[17049])).
% 3.43/3.68 tff(17051,plain,
% 3.43/3.68 (~r(s(s(s(z))), s(s(s(elem!1))))),
% 3.43/3.68 inference(unit_resolution,[status(thm)],[15468, 197, 4143, 17035, 16979])).
% 3.43/3.68 tff(17052,plain,
% 3.43/3.68 (~r(s(s(s(z))), s(s(elem!1)))),
% 3.43/3.68 inference(modus_ponens,[status(thm)],[17051, 17050])).
% 3.43/3.68 tff(17053,plain,
% 3.43/3.68 (~b(s(z), s(s(s(z))))),
% 3.43/3.68 inference(unit_resolution,[status(thm)],[5552, 17052, 376, 17048, 17043])).
% 3.43/3.68 tff(17054,plain,
% 3.43/3.68 (r(s(z), s(s(s(z))))),
% 3.43/3.68 inference(unit_resolution,[status(thm)],[1674, 17053])).
% 3.43/3.68 tff(17055,plain,
% 3.43/3.68 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(z)), s(z))) | (~r(s(s(z)), s(s(s(z))))) | (~r(s(z), s(s(s(z))))) | (~r(s(s(s(z))), s(s(z)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(z)), s(z))) | (~r(s(s(z)), s(s(s(z))))) | (~r(s(z), s(s(s(z))))) | (~r(s(s(s(z))), s(s(z)))))),
% 3.43/3.68 inference(rewrite,[status(thm)],[])).
% 3.43/3.68 tff(17056,plain,
% 3.43/3.68 (((~r(s(s(s(z))), s(s(z)))) | (~r(s(z), s(s(s(z))))) | (~r(s(s(z)), s(s(s(z))))) | (~r(s(s(z)), s(z)))) <=> ((~r(s(s(z)), s(z))) | (~r(s(s(z)), s(s(s(z))))) | (~r(s(z), s(s(s(z))))) | (~r(s(s(s(z))), s(s(z)))))),
% 3.43/3.68 inference(rewrite,[status(thm)],[])).
% 3.43/3.68 tff(17057,plain,
% 3.43/3.68 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(z))), s(s(z)))) | (~r(s(z), s(s(s(z))))) | (~r(s(s(z)), s(s(s(z))))) | (~r(s(s(z)), s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(z)), s(z))) | (~r(s(s(z)), s(s(s(z))))) | (~r(s(z), s(s(s(z))))) | (~r(s(s(s(z))), s(s(z))))))),
% 3.43/3.69 inference(monotonicity,[status(thm)],[17056])).
% 3.43/3.69 tff(17058,plain,
% 3.43/3.69 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(z))), s(s(z)))) | (~r(s(z), s(s(s(z))))) | (~r(s(s(z)), s(s(s(z))))) | (~r(s(s(z)), s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(z)), s(z))) | (~r(s(s(z)), s(s(s(z))))) | (~r(s(z), s(s(s(z))))) | (~r(s(s(s(z))), s(s(z)))))),
% 3.43/3.69 inference(transitivity,[status(thm)],[17057, 17055])).
% 3.43/3.69 tff(17059,plain,
% 3.43/3.69 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(z))), s(s(z)))) | (~r(s(z), s(s(s(z))))) | (~r(s(s(z)), s(s(s(z))))) | (~r(s(s(z)), s(z))))),
% 3.43/3.69 inference(quant_inst,[status(thm)],[])).
% 3.43/3.69 tff(17060,plain,
% 3.43/3.69 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(z)), s(z))) | (~r(s(s(z)), s(s(s(z))))) | (~r(s(z), s(s(s(z))))) | (~r(s(s(s(z))), s(s(z))))),
% 3.43/3.69 inference(modus_ponens,[status(thm)],[17059, 17058])).
% 3.43/3.69 tff(17061,plain,
% 3.43/3.69 ($false),
% 3.43/3.69 inference(unit_resolution,[status(thm)],[17060, 197, 4143, 16979, 17054, 16974])).
% 3.43/3.69 tff(17062,plain,(b(s(s(z)), s(z)) | (~b(s(z), s(s(elem!1)))) | (~b(z, s(s(z))))), inference(lemma,lemma(discharge,[]))).
% 3.43/3.69 tff(17063,plain,
% 3.43/3.69 (b(s(s(z)), s(z)) | (~b(s(z), s(s(elem!1))))),
% 3.43/3.69 inference(unit_resolution,[status(thm)],[17062, 10450])).
% 3.43/3.69 tff(17064,plain,
% 3.43/3.69 (b(s(s(z)), s(z))),
% 3.43/3.69 inference(unit_resolution,[status(thm)],[17063, 15211])).
% 3.43/3.69 tff(17065,plain,
% 3.43/3.69 ((~b(s(z), z)) | (~b(z, s(z)))),
% 3.43/3.69 inference(unit_resolution,[status(thm)],[14305, 17064])).
% 3.43/3.69 tff(17066,plain,
% 3.43/3.69 (~b(z, s(z))),
% 3.43/3.69 inference(unit_resolution,[status(thm)],[17065, 53])).
% 3.43/3.69 tff(17067,plain,
% 3.43/3.69 (r(z, s(z))),
% 3.43/3.69 inference(unit_resolution,[status(thm)],[321, 17066])).
% 3.43/3.69 tff(17068,plain,
% 3.43/3.69 (~b(s(s(z)), z)),
% 3.43/3.69 inference(unit_resolution,[status(thm)],[12884, 166, 53, 10450, 17064])).
% 3.43/3.69 tff(17069,plain,
% 3.43/3.69 (r(s(s(z)), z)),
% 3.43/3.69 inference(unit_resolution,[status(thm)],[186, 17068])).
% 3.43/3.69 tff(17070,plain,
% 3.43/3.69 (b(s(s(elem!1)), s(z))),
% 3.43/3.69 inference(unit_resolution,[status(thm)],[15928, 118, 10451, 376, 350])).
% 3.43/3.69 tff(17071,plain,
% 3.43/3.69 (~b(z, s(s(elem!1)))),
% 3.43/3.69 inference(unit_resolution,[status(thm)],[5343, 17070, 376, 118])).
% 3.43/3.69 tff(17072,plain,
% 3.43/3.69 (r(z, s(s(elem!1)))),
% 3.43/3.69 inference(unit_resolution,[status(thm)],[1795, 17071])).
% 3.43/3.69 tff(17073,plain,
% 3.43/3.69 (b(s(s(z)), s(z))),
% 3.43/3.69 inference(unit_resolution,[status(thm)],[17062, 376, 10451])).
% 3.43/3.69 tff(17074,plain,
% 3.43/3.69 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(elem!1)))) | (~b(z, s(z))) | (~b(s(s(elem!1)), s(z))) | (~b(s(s(z)), z)) | (~b(s(s(z)), s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), s(s(elem!1)))) | (~b(z, s(z))) | (~b(s(s(elem!1)), s(z))) | (~b(s(s(z)), z)) | (~b(s(s(z)), s(z))))),
% 3.43/3.69 inference(rewrite,[status(thm)],[])).
% 3.43/3.69 tff(17075,plain,
% 3.43/3.69 (((~b(s(s(elem!1)), s(z))) | (~b(s(s(z)), s(z))) | (~b(s(z), s(s(elem!1)))) | (~b(z, s(z))) | (~b(s(s(z)), s(z))) | (~b(s(s(z)), z))) <=> ((~b(s(z), s(s(elem!1)))) | (~b(z, s(z))) | (~b(s(s(elem!1)), s(z))) | (~b(s(s(z)), z)) | (~b(s(s(z)), s(z))))),
% 3.43/3.69 inference(rewrite,[status(thm)],[])).
% 3.43/3.69 tff(17076,plain,
% 3.43/3.69 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), s(z))) | (~b(s(s(z)), s(z))) | (~b(s(z), s(s(elem!1)))) | (~b(z, s(z))) | (~b(s(s(z)), s(z))) | (~b(s(s(z)), z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(elem!1)))) | (~b(z, s(z))) | (~b(s(s(elem!1)), s(z))) | (~b(s(s(z)), z)) | (~b(s(s(z)), s(z)))))),
% 3.43/3.69 inference(monotonicity,[status(thm)],[17075])).
% 3.43/3.69 tff(17077,plain,
% 3.43/3.69 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), s(z))) | (~b(s(s(z)), s(z))) | (~b(s(z), s(s(elem!1)))) | (~b(z, s(z))) | (~b(s(s(z)), s(z))) | (~b(s(s(z)), z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), s(s(elem!1)))) | (~b(z, s(z))) | (~b(s(s(elem!1)), s(z))) | (~b(s(s(z)), z)) | (~b(s(s(z)), s(z))))),
% 3.43/3.69 inference(transitivity,[status(thm)],[17076, 17074])).
% 3.43/3.69 tff(17078,plain,
% 3.43/3.69 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), s(z))) | (~b(s(s(z)), s(z))) | (~b(s(z), s(s(elem!1)))) | (~b(z, s(z))) | (~b(s(s(z)), s(z))) | (~b(s(s(z)), z)))),
% 3.43/3.69 inference(quant_inst,[status(thm)],[])).
% 3.43/3.69 tff(17079,plain,
% 3.43/3.69 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), s(s(elem!1)))) | (~b(z, s(z))) | (~b(s(s(elem!1)), s(z))) | (~b(s(s(z)), z)) | (~b(s(s(z)), s(z)))),
% 3.43/3.69 inference(modus_ponens,[status(thm)],[17078, 17077])).
% 3.43/3.69 tff(17080,plain,
% 3.43/3.69 ($false),
% 3.43/3.69 inference(unit_resolution,[status(thm)],[17079, 166, 376, 118, 310, 156, 122])).
% 3.43/3.69 tff(17081,plain,((~b(s(z), s(s(elem!1)))) | (~b(z, s(z))) | (~b(s(s(elem!1)), s(z))) | (~b(s(s(z)), s(z))) | (~b(s(s(z)), z))), inference(lemma,lemma(discharge,[]))).
% 3.43/3.69 tff(17082,plain,
% 3.43/3.69 (~b(s(s(z)), z)),
% 3.43/3.69 inference(unit_resolution,[status(thm)],[17081, 17070, 376, 17073, 118])).
% 3.43/3.69 tff(17083,plain,
% 3.43/3.69 (r(s(s(z)), z)),
% 3.43/3.69 inference(unit_resolution,[status(thm)],[186, 17082])).
% 3.43/3.69 tff(17084,plain,
% 3.43/3.69 (~b(s(s(z)), s(s(elem!1)))),
% 3.43/3.69 inference(unit_resolution,[status(thm)],[454, 17070, 376, 17073])).
% 3.43/3.69 tff(17085,plain,
% 3.43/3.69 (~(s(s(z)) = s(s(elem!1)))),
% 3.43/3.69 inference(unit_resolution,[status(thm)],[10937, 17071, 10451])).
% 3.43/3.69 tff(17086,plain,
% 3.43/3.69 (r(s(s(z)), s(s(elem!1)))),
% 3.43/3.69 inference(unit_resolution,[status(thm)],[390, 17085, 17084])).
% 3.43/3.69 tff(17087,plain,
% 3.43/3.69 (~b(s(s(elem!1)), s(s(z)))),
% 3.43/3.69 inference(unit_resolution,[status(thm)],[15908, 118, 10451, 376, 17073])).
% 3.43/3.69 tff(17088,plain,
% 3.43/3.69 (~(s(s(elem!1)) = s(s(z)))),
% 3.43/3.69 inference(unit_resolution,[status(thm)],[131, 17085])).
% 3.43/3.69 tff(17089,plain,
% 3.43/3.69 (r(s(s(elem!1)), s(s(z)))),
% 3.43/3.69 inference(unit_resolution,[status(thm)],[441, 17088, 17087])).
% 3.43/3.69 tff(17090,plain,
% 3.43/3.69 ($false),
% 3.43/3.69 inference(unit_resolution,[status(thm)],[16283, 17089, 17086, 17083, 17072])).
% 3.43/3.69 tff(17091,plain,((~b(z, s(z))) | (~b(z, s(s(z)))) | (~b(s(z), s(s(elem!1)))) | (~r(s(s(s(elem!1))), s(z)))), inference(lemma,lemma(discharge,[]))).
% 3.43/3.69 tff(17092,plain,
% 3.43/3.69 (~b(z, s(z))),
% 3.43/3.69 inference(unit_resolution,[status(thm)],[17091, 350, 376, 10451])).
% 3.43/3.69 tff(17093,plain,
% 3.43/3.69 (r(z, s(z))),
% 3.43/3.69 inference(unit_resolution,[status(thm)],[321, 17092])).
% 3.43/3.69 tff(17094,plain,
% 3.43/3.69 (~r(s(z), s(s(z)))),
% 3.43/3.69 inference(unit_resolution,[status(thm)],[10033, 154, 350, 17093])).
% 3.43/3.69 tff(17095,plain,
% 3.43/3.69 (b(s(z), s(s(z)))),
% 3.43/3.69 inference(unit_resolution,[status(thm)],[427, 17094])).
% 3.43/3.69 tff(17096,plain,
% 3.43/3.69 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(z)))) | (~b(s(z), z)) | (~b(s(z), s(s(elem!1)))) | (~b(s(z), s(s(z)))) | (~b(s(s(z)), s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(s(z)))) | (~b(s(z), z)) | (~b(s(z), s(s(elem!1)))) | (~b(s(z), s(s(z)))) | (~b(s(s(z)), s(z))))),
% 3.43/3.69 inference(rewrite,[status(thm)],[])).
% 3.43/3.69 tff(17097,plain,
% 3.43/3.69 (((~b(s(z), s(s(elem!1)))) | (~b(s(z), s(s(elem!1)))) | (~b(s(s(z)), s(z))) | (~b(z, s(s(z)))) | (~b(s(z), s(s(z)))) | (~b(s(z), z))) <=> ((~b(z, s(s(z)))) | (~b(s(z), z)) | (~b(s(z), s(s(elem!1)))) | (~b(s(z), s(s(z)))) | (~b(s(s(z)), s(z))))),
% 3.43/3.69 inference(rewrite,[status(thm)],[])).
% 3.43/3.69 tff(17098,plain,
% 3.43/3.69 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(elem!1)))) | (~b(s(z), s(s(elem!1)))) | (~b(s(s(z)), s(z))) | (~b(z, s(s(z)))) | (~b(s(z), s(s(z)))) | (~b(s(z), z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(z)))) | (~b(s(z), z)) | (~b(s(z), s(s(elem!1)))) | (~b(s(z), s(s(z)))) | (~b(s(s(z)), s(z)))))),
% 3.43/3.69 inference(monotonicity,[status(thm)],[17097])).
% 3.43/3.69 tff(17099,plain,
% 3.43/3.69 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(elem!1)))) | (~b(s(z), s(s(elem!1)))) | (~b(s(s(z)), s(z))) | (~b(z, s(s(z)))) | (~b(s(z), s(s(z)))) | (~b(s(z), z)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(s(z)))) | (~b(s(z), z)) | (~b(s(z), s(s(elem!1)))) | (~b(s(z), s(s(z)))) | (~b(s(s(z)), s(z))))),
% 3.43/3.69 inference(transitivity,[status(thm)],[17098, 17096])).
% 3.43/3.69 tff(17100,plain,
% 3.43/3.69 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(elem!1)))) | (~b(s(z), s(s(elem!1)))) | (~b(s(s(z)), s(z))) | (~b(z, s(s(z)))) | (~b(s(z), s(s(z)))) | (~b(s(z), z)))),
% 3.43/3.69 inference(quant_inst,[status(thm)],[])).
% 3.43/3.69 tff(17101,plain,
% 3.43/3.69 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(s(z)))) | (~b(s(z), z)) | (~b(s(z), s(s(elem!1)))) | (~b(s(z), s(s(z)))) | (~b(s(s(z)), s(z)))),
% 3.43/3.69 inference(modus_ponens,[status(thm)],[17100, 17099])).
% 3.43/3.69 tff(17102,plain,
% 3.43/3.69 ((~b(s(z), z)) | (~b(s(z), s(s(z))))),
% 3.43/3.69 inference(unit_resolution,[status(thm)],[17101, 166, 376, 10451, 17073])).
% 3.43/3.69 tff(17103,plain,
% 3.43/3.69 (~b(s(z), z)),
% 3.43/3.69 inference(unit_resolution,[status(thm)],[17102, 17095])).
% 3.43/3.69 tff(17104,plain,
% 3.43/3.69 (r(s(z), z)),
% 3.43/3.69 inference(unit_resolution,[status(thm)],[230, 17103])).
% 3.43/3.69 tff(17105,plain,
% 3.43/3.69 ($false),
% 3.43/3.69 inference(unit_resolution,[status(thm)],[2659, 197, 154, 350, 17093, 17104])).
% 3.43/3.69 tff(17106,plain,((~r(s(s(s(elem!1))), z)) | (~r(s(s(s(elem!1))), s(z))) | (~b(s(z), s(s(elem!1)))) | (~b(z, s(s(z))))), inference(lemma,lemma(discharge,[]))).
% 3.43/3.69 tff(17107,plain,
% 3.43/3.69 (~r(s(s(s(elem!1))), z)),
% 3.43/3.69 inference(unit_resolution,[status(thm)],[17106, 350, 376, 10451])).
% 3.43/3.69 tff(17108,plain,
% 3.43/3.69 (b(s(s(s(elem!1))), z)),
% 3.43/3.69 inference(unit_resolution,[status(thm)],[94, 17107])).
% 3.43/3.69 tff(17109,plain,
% 3.43/3.69 (~b(s(z), s(s(z)))),
% 3.43/3.69 inference(unit_resolution,[status(thm)],[17102, 53])).
% 3.43/3.69 tff(17110,plain,
% 3.43/3.69 (r(s(z), s(s(z)))),
% 3.43/3.69 inference(unit_resolution,[status(thm)],[427, 17109])).
% 3.43/3.69 tff(17111,plain,
% 3.43/3.69 (~b(s(s(z)), z)),
% 3.43/3.69 inference(unit_resolution,[status(thm)],[10745, 17110, 10451, 350, 17108])).
% 3.43/3.69 tff(17112,plain,
% 3.43/3.69 (~b(s(s(s(elem!1))), s(s(z)))),
% 3.43/3.69 inference(unit_resolution,[status(thm)],[12875, 53, 10451, 17073, 17108])).
% 3.43/3.69 tff(17113,plain,
% 3.43/3.69 (r(s(s(s(elem!1))), s(s(z)))),
% 3.43/3.69 inference(unit_resolution,[status(thm)],[218, 17112])).
% 3.43/3.69 tff(17114,plain,
% 3.43/3.69 (~r(s(s(z)), z)),
% 3.43/3.69 inference(unit_resolution,[status(thm)],[874, 17113, 350, 17110])).
% 3.43/3.69 tff(17115,plain,
% 3.43/3.69 ($false),
% 3.43/3.69 inference(unit_resolution,[status(thm)],[186, 17114, 17111])).
% 3.43/3.69 tff(17116,plain,((~b(s(z), z)) | (~r(s(s(s(elem!1))), s(z))) | (~b(z, s(s(z)))) | (~b(s(z), s(s(elem!1))))), inference(lemma,lemma(discharge,[]))).
% 3.43/3.69 tff(17117,plain,
% 3.43/3.69 ((~b(s(z), z)) | (~r(s(s(s(elem!1))), s(z))) | (~b(s(z), s(s(elem!1))))),
% 3.43/3.69 inference(unit_resolution,[status(thm)],[17116, 10450])).
% 3.43/3.69 tff(17118,plain,
% 3.43/3.69 (~r(s(s(s(elem!1))), s(z))),
% 3.43/3.69 inference(unit_resolution,[status(thm)],[17117, 53, 15211])).
% 3.43/3.69 tff(17119,plain,
% 3.43/3.69 (~b(s(s(s(elem!1))), s(z))),
% 3.43/3.69 inference(unit_resolution,[status(thm)],[12830, 53, 121, 17064])).
% 3.43/3.69 tff(17120,plain,
% 3.43/3.69 ($false),
% 3.43/3.69 inference(unit_resolution,[status(thm)],[1849, 17119, 17118])).
% 3.43/3.69 tff(17121,plain,((~b(s(z), z)) | (~b(s(s(s(elem!1))), z))), inference(lemma,lemma(discharge,[]))).
% 3.43/3.69 tff(17122,plain,
% 3.43/3.69 (~b(s(z), z)),
% 3.43/3.69 inference(unit_resolution,[status(thm)],[17121, 121])).
% 3.43/3.69 tff(17123,plain,
% 3.43/3.69 (r(s(z), z)),
% 3.43/3.69 inference(unit_resolution,[status(thm)],[230, 17122])).
% 3.43/3.69 tff(17124,plain,
% 3.43/3.69 ((~b(z, s(z))) | (~b(s(z), s(s(elem!1)))) | (~r(s(s(s(elem!1))), s(z)))),
% 3.43/3.69 inference(unit_resolution,[status(thm)],[17091, 10450])).
% 3.43/3.69 tff(17125,plain,
% 3.43/3.69 (~b(z, s(z))),
% 3.43/3.69 inference(unit_resolution,[status(thm)],[17124, 350, 15211])).
% 3.43/3.69 tff(17126,plain,
% 3.43/3.69 (r(z, s(z))),
% 3.43/3.69 inference(unit_resolution,[status(thm)],[321, 17125])).
% 3.43/3.69 tff(17127,plain,
% 3.43/3.69 (~r(z, s(s(s(elem!1))))),
% 3.43/3.69 inference(unit_resolution,[status(thm)],[2613, 17126, 17123, 350])).
% 3.43/3.69 tff(17128,plain,
% 3.43/3.69 (b(z, s(s(s(elem!1))))),
% 3.43/3.69 inference(unit_resolution,[status(thm)],[261, 17127])).
% 3.43/3.69 tff(17129,plain,
% 3.43/3.69 (~(s(s(elem!1)) = s(s(s(elem!1))))),
% 3.43/3.69 inference(unit_resolution,[status(thm)],[5500, 98, 15211])).
% 3.43/3.69 tff(17130,plain,
% 3.43/3.69 (~r(s(s(elem!1)), s(z))),
% 3.43/3.69 inference(unit_resolution,[status(thm)],[10127, 17129, 17123, 350, 17126, 121, 17128])).
% 3.43/3.69 tff(17131,plain,
% 3.43/3.69 (b(s(s(elem!1)), s(z))),
% 3.43/3.69 inference(unit_resolution,[status(thm)],[1912, 17130])).
% 3.43/3.69 tff(17132,plain,
% 3.43/3.69 (~b(s(z), z)),
% 3.43/3.69 inference(unit_resolution,[status(thm)],[17116, 350, 10451, 376])).
% 3.43/3.69 tff(17133,plain,
% 3.43/3.69 (r(s(z), z)),
% 3.43/3.69 inference(unit_resolution,[status(thm)],[230, 17132])).
% 3.43/3.69 tff(17134,plain,
% 3.43/3.69 (~r(z, s(s(s(elem!1))))),
% 3.43/3.69 inference(unit_resolution,[status(thm)],[2613, 17133, 350, 17093])).
% 3.43/3.69 tff(17135,plain,
% 3.43/3.69 (b(z, s(s(s(elem!1))))),
% 3.43/3.69 inference(unit_resolution,[status(thm)],[261, 17134])).
% 3.43/3.69 tff(17136,plain,
% 3.43/3.69 (~r(s(s(elem!1)), s(z))),
% 3.43/3.69 inference(unit_resolution,[status(thm)],[10127, 17135, 350, 45, 17108, 17093, 17133])).
% 3.43/3.69 tff(17137,plain,
% 3.43/3.69 (b(s(s(elem!1)), s(z))),
% 3.43/3.69 inference(unit_resolution,[status(thm)],[1912, 17136])).
% 3.43/3.69 tff(17138,plain,
% 3.43/3.69 (~b(s(s(z)), s(s(elem!1)))),
% 3.43/3.69 inference(unit_resolution,[status(thm)],[454, 17137, 376, 17073])).
% 3.43/3.69 tff(17139,plain,
% 3.43/3.69 (~b(s(s(elem!1)), s(s(z)))),
% 3.43/3.69 inference(unit_resolution,[status(thm)],[2690, 166, 376, 17137, 17073])).
% 3.43/3.69 tff(17140,plain,
% 3.43/3.69 (~r(s(s(s(s(elem!1)))), s(z))),
% 3.43/3.69 inference(unit_resolution,[status(thm)],[2669, 17133, 350, 17093, 364])).
% 3.43/3.69 tff(17141,plain,
% 3.43/3.69 (b(s(s(s(s(elem!1)))), s(z))),
% 3.43/3.69 inference(unit_resolution,[status(thm)],[661, 17140])).
% 3.43/3.69 tff(17142,plain,
% 3.43/3.69 (~b(s(s(s(s(elem!1)))), s(s(z)))),
% 3.43/3.69 inference(unit_resolution,[status(thm)],[2698, 166, 376, 17137, 17073, 17141])).
% 3.43/3.69 tff(17143,plain,
% 3.43/3.69 (r(s(s(s(s(elem!1)))), s(s(z)))),
% 3.43/3.69 inference(unit_resolution,[status(thm)],[1299, 17142])).
% 3.43/3.69 tff(17144,plain,
% 3.43/3.69 (~b(s(s(elem!1)), s(s(s(s(elem!1)))))),
% 3.43/3.69 inference(unit_resolution,[status(thm)],[822, 166, 376, 17137, 17141])).
% 3.43/3.69 tff(17145,plain,
% 3.43/3.69 (~b(s(s(s(s(elem!1)))), s(s(elem!1)))),
% 3.43/3.69 inference(unit_resolution,[status(thm)],[804, 166, 376, 17137, 17141])).
% 3.43/3.69 tff(17146,plain,
% 3.43/3.69 (~b(s(s(z)), z)),
% 3.43/3.69 inference(unit_resolution,[status(thm)],[10745, 12399, 10451, 350, 17108])).
% 3.43/3.69 tff(17147,plain,
% 3.43/3.69 (r(s(s(z)), z)),
% 3.43/3.69 inference(unit_resolution,[status(thm)],[186, 17146])).
% 3.43/3.69 tff(17148,plain,
% 3.43/3.69 (~r(s(s(s(s(elem!1)))), s(s(elem!1)))),
% 3.43/3.69 inference(unit_resolution,[status(thm)],[2706, 197, 2168, 2077, 2073])).
% 3.43/3.69 tff(17149,plain,
% 3.43/3.69 (s(s(s(s(elem!1)))) = s(s(elem!1))),
% 3.43/3.69 inference(unit_resolution,[status(thm)],[813, 17148, 807])).
% 3.43/3.69 tff(17150,plain,
% 3.43/3.69 (s(s(s(elem!1))) = s(elem!1)),
% 3.43/3.69 inference(unit_resolution,[status(thm)],[1166, 17149])).
% 3.43/3.69 tff(17151,plain,
% 3.43/3.69 (r(s(s(s(elem!1))), s(z)) <=> r(s(elem!1), s(z))),
% 3.43/3.69 inference(monotonicity,[status(thm)],[17150])).
% 3.43/3.69 tff(17152,plain,
% 3.43/3.69 (r(s(elem!1), s(z))),
% 3.43/3.69 inference(modus_ponens,[status(thm)],[350, 17151])).
% 3.43/3.69 tff(17153,plain,
% 3.43/3.69 (b(z, s(s(s(elem!1)))) <=> b(z, s(elem!1))),
% 3.43/3.69 inference(monotonicity,[status(thm)],[17150])).
% 3.43/3.69 tff(17154,plain,
% 3.43/3.69 (b(z, s(elem!1))),
% 3.43/3.69 inference(modus_ponens,[status(thm)],[240, 17153])).
% 3.43/3.69 tff(17155,plain,
% 3.43/3.69 (b(s(s(s(elem!1))), z) <=> b(s(elem!1), z)),
% 3.43/3.69 inference(monotonicity,[status(thm)],[17150])).
% 3.43/3.69 tff(17156,plain,
% 3.43/3.69 (b(s(elem!1), z)),
% 3.43/3.69 inference(modus_ponens,[status(thm)],[121, 17155])).
% 3.43/3.69 tff(17157,assumption,(~b(s(s(elem!1)), s(s(s(s(elem!1)))))), introduced(assumption)).
% 3.43/3.69 tff(17158,plain,
% 3.43/3.69 (~r(s(s(elem!1)), s(s(s(s(elem!1)))))),
% 3.43/3.69 inference(unit_resolution,[status(thm)],[2721, 197, 2168, 2077, 2073])).
% 3.43/3.69 tff(17159,plain,
% 3.43/3.69 (s(s(elem!1)) = s(s(s(s(elem!1))))),
% 3.43/3.69 inference(unit_resolution,[status(thm)],[827, 17158, 17157])).
% 3.43/3.69 tff(17160,plain,
% 3.43/3.69 (b(s(s(elem!1)), z) <=> b(s(s(s(s(elem!1)))), z)),
% 3.43/3.69 inference(monotonicity,[status(thm)],[17159])).
% 3.43/3.69 tff(17161,plain,
% 3.43/3.69 (~r(s(s(elem!1)), z)),
% 3.43/3.69 inference(unit_resolution,[status(thm)],[9517, 2073, 323, 866])).
% 3.43/3.69 tff(17162,plain,
% 3.43/3.69 (b(s(s(elem!1)), z)),
% 3.43/3.69 inference(unit_resolution,[status(thm)],[608, 17161])).
% 3.43/3.69 tff(17163,plain,
% 3.43/3.69 (b(s(s(s(s(elem!1)))), z)),
% 3.43/3.69 inference(modus_ponens,[status(thm)],[17162, 17160])).
% 3.43/3.69 tff(17164,plain,
% 3.43/3.69 (r(s(s(s(s(elem!1)))), s(s(s(elem!1)))) <=> r(s(s(s(s(elem!1)))), s(elem!1))),
% 3.43/3.69 inference(monotonicity,[status(thm)],[17150])).
% 3.43/3.69 tff(17165,plain,
% 3.43/3.69 (r(s(s(elem!1)), s(s(s(elem!1)))) <=> r(s(s(s(s(elem!1)))), s(s(s(elem!1))))),
% 3.43/3.69 inference(monotonicity,[status(thm)],[17159])).
% 3.43/3.69 tff(17166,plain,
% 3.43/3.69 (~r(z, s(s(elem!1)))),
% 3.43/3.69 inference(unit_resolution,[status(thm)],[16283, 2077, 866, 2073])).
% 3.43/3.69 tff(17167,plain,
% 3.43/3.69 (b(z, s(s(elem!1)))),
% 3.43/3.69 inference(unit_resolution,[status(thm)],[1795, 17166])).
% 3.43/3.69 tff(17168,plain,
% 3.43/3.69 (~b(s(s(elem!1)), s(s(s(elem!1))))),
% 3.43/3.69 inference(unit_resolution,[status(thm)],[3593, 17162, 17167, 121])).
% 3.43/3.69 tff(17169,plain,
% 3.43/3.69 (r(s(s(elem!1)), s(s(s(elem!1))))),
% 3.43/3.69 inference(unit_resolution,[status(thm)],[461, 17168, 45])).
% 3.43/3.69 tff(17170,plain,
% 3.43/3.69 (r(s(s(s(s(elem!1)))), s(s(s(elem!1))))),
% 3.43/3.69 inference(modus_ponens,[status(thm)],[17169, 17165])).
% 3.43/3.69 tff(17171,plain,
% 3.43/3.69 (r(s(s(s(s(elem!1)))), s(elem!1))),
% 3.43/3.69 inference(modus_ponens,[status(thm)],[17170, 17164])).
% 3.43/3.69 tff(17172,plain,
% 3.43/3.69 ($false),
% 3.43/3.69 inference(unit_resolution,[status(thm)],[2856, 17171, 17163, 1699, 17159, 17150, 17156, 17154, 17152])).
% 3.43/3.69 tff(17173,plain,((s(s(z)) = s(s(elem!1))) | (~b(s(s(s(z))), z)) | (~b(s(s(s(elem!1))), z)) | (~r(s(s(s(elem!1))), s(z))) | (~b(z, s(s(s(elem!1))))) | b(s(s(s(s(elem!1)))), s(s(elem!1))) | b(s(s(elem!1)), s(s(s(s(elem!1))))) | (~r(s(s(s(s(elem!1)))), s(s(z)))) | (s(s(elem!1)) = s(s(s(elem!1)))) | (~r(s(s(z)), z)) | (~r(z, s(z))) | b(s(s(elem!1)), s(s(z))) | b(s(s(z)), s(s(elem!1)))), inference(lemma,lemma(discharge,[]))).
% 3.43/3.69 tff(17174,plain,
% 3.43/3.69 (~b(s(s(s(z))), z)),
% 3.43/3.69 inference(unit_resolution,[status(thm)],[17173, 17147, 17108, 350, 17135, 17145, 17144, 17143, 45, 15212, 17093, 17139, 17138])).
% 3.43/3.69 tff(17175,plain,
% 3.43/3.69 (r(s(s(s(z))), z)),
% 3.43/3.69 inference(unit_resolution,[status(thm)],[1713, 17174])).
% 3.43/3.69 tff(17176,plain,
% 3.43/3.69 (~r(s(s(s(z))), s(z))),
% 3.43/3.69 inference(unit_resolution,[status(thm)],[3213, 17175, 17093, 12399])).
% 3.43/3.69 tff(17177,plain,
% 3.43/3.69 (b(s(s(s(z))), s(z))),
% 3.43/3.69 inference(unit_resolution,[status(thm)],[1763, 17176])).
% 3.43/3.69 tff(17178,plain,
% 3.43/3.69 (~r(s(z), s(s(s(z))))),
% 3.43/3.69 inference(unit_resolution,[status(thm)],[8876, 17175, 17133, 17093])).
% 3.43/3.69 tff(17179,plain,
% 3.43/3.69 (b(s(z), s(s(s(z))))),
% 3.43/3.69 inference(unit_resolution,[status(thm)],[1674, 17178])).
% 3.43/3.69 tff(17180,plain,
% 3.43/3.69 (~b(s(s(z)), s(s(s(z))))),
% 3.43/3.69 inference(unit_resolution,[status(thm)],[3248, 17179, 17073, 17177])).
% 3.43/3.69 tff(17181,plain,
% 3.43/3.69 (r(s(s(z)), s(s(s(z))))),
% 3.43/3.69 inference(unit_resolution,[status(thm)],[1730, 17180])).
% 3.43/3.69 tff(17182,plain,
% 3.43/3.69 ($false),
% 3.43/3.69 inference(unit_resolution,[status(thm)],[8744, 197, 17093, 17147, 17175, 17181])).
% 3.43/3.69 tff(17183,plain,(b(s(z), s(s(z))) | (~r(s(s(s(elem!1))), s(z))) | (s(s(elem!1)) = s(s(s(elem!1)))) | (~b(z, s(s(z)))) | (~b(s(z), s(s(elem!1))))), inference(lemma,lemma(discharge,[]))).
% 3.43/3.69 tff(17184,plain,
% 3.43/3.69 (b(s(z), s(s(z))) | (~r(s(s(s(elem!1))), s(z))) | (s(s(elem!1)) = s(s(s(elem!1)))) | (~b(s(z), s(s(elem!1))))),
% 3.43/3.69 inference(unit_resolution,[status(thm)],[17183, 10450])).
% 3.43/3.69 tff(17185,plain,
% 3.43/3.69 (b(s(z), s(s(z)))),
% 3.43/3.69 inference(unit_resolution,[status(thm)],[17184, 17129, 15211, 350])).
% 3.43/3.69 tff(17186,plain,
% 3.43/3.69 (r(s(s(s(z))), elem!1) <=> r(s(s(s(z))), s(s(s(elem!1))))),
% 3.43/3.69 inference(monotonicity,[status(thm)],[6548])).
% 3.43/3.69 tff(17187,plain,
% 3.43/3.69 (b(s(z), s(s(s(elem!1))))),
% 3.43/3.69 inference(unit_resolution,[status(thm)],[5500, 334, 15211])).
% 3.43/3.69 tff(17188,plain,
% 3.43/3.69 ((~r(s(s(elem!1)), s(z))) | (~b(s(z), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), z)) | (~r(z, s(s(elem!1)))) | (s(s(z)) = s(s(elem!1))) | (~b(s(z), s(s(elem!1)))) | (~r(z, s(z)))),
% 3.43/3.69 inference(unit_resolution,[status(thm)],[16350, 10450])).
% 3.43/3.69 tff(17189,plain,
% 3.43/3.69 (~r(s(s(elem!1)), s(z))),
% 3.43/3.69 inference(unit_resolution,[status(thm)],[17188, 17187, 15211, 121, 44, 4458, 323])).
% 3.43/3.69 tff(17190,plain,
% 3.43/3.69 (b(s(s(elem!1)), s(z))),
% 3.43/3.69 inference(unit_resolution,[status(thm)],[1912, 17189])).
% 3.43/3.69 tff(17191,plain,
% 3.43/3.69 (b(s(s(s(elem!1))), s(z))),
% 3.43/3.69 inference(unit_resolution,[status(thm)],[3849, 17190, 334])).
% 3.43/3.69 tff(17192,plain,
% 3.43/3.69 (~b(s(z), z)),
% 3.43/3.69 inference(unit_resolution,[status(thm)],[12830, 17191, 121, 17064])).
% 3.43/3.69 tff(17193,plain,
% 3.43/3.69 (r(s(z), z)),
% 3.43/3.69 inference(unit_resolution,[status(thm)],[230, 17192])).
% 3.43/3.69 tff(17194,plain,
% 3.43/3.69 (~b(s(s(z)), s(s(elem!1)))),
% 3.43/3.69 inference(unit_resolution,[status(thm)],[454, 17190, 15211, 17064])).
% 3.43/3.69 tff(17195,plain,
% 3.43/3.69 (r(s(s(z)), s(s(elem!1)))),
% 3.43/3.69 inference(unit_resolution,[status(thm)],[390, 17194, 44])).
% 3.43/3.69 tff(17196,plain,
% 3.43/3.69 (b(s(s(s(elem!1))), s(s(z))) <=> b(s(s(elem!1)), s(s(z)))),
% 3.43/3.69 inference(symmetry,[status(thm)],[16354])).
% 3.43/3.69 tff(17197,plain,
% 3.43/3.69 ((~b(s(s(s(elem!1))), s(s(z)))) <=> (~b(s(s(elem!1)), s(s(z))))),
% 3.43/3.69 inference(monotonicity,[status(thm)],[17196])).
% 3.43/3.69 tff(17198,plain,
% 3.43/3.69 (~b(s(s(s(elem!1))), s(s(z)))),
% 3.43/3.69 inference(unit_resolution,[status(thm)],[9072, 166, 17187, 17191, 17064])).
% 3.43/3.69 tff(17199,plain,
% 3.43/3.69 (~b(s(s(elem!1)), s(s(z)))),
% 3.43/3.69 inference(modus_ponens,[status(thm)],[17198, 17197])).
% 3.43/3.69 tff(17200,plain,
% 3.43/3.69 (r(s(s(elem!1)), s(s(z)))),
% 3.43/3.69 inference(unit_resolution,[status(thm)],[441, 17199, 11])).
% 3.43/3.69 tff(17201,plain,
% 3.43/3.69 (~r(s(s(z)), z)),
% 3.43/3.69 inference(unit_resolution,[status(thm)],[16283, 17200, 4458, 17195])).
% 3.43/3.69 tff(17202,plain,
% 3.43/3.69 (b(s(s(z)), z)),
% 3.43/3.69 inference(unit_resolution,[status(thm)],[186, 17201])).
% 3.43/3.69 tff(17203,plain,
% 3.43/3.69 (~b(s(s(s(z))), z)),
% 3.43/3.69 inference(unit_resolution,[status(thm)],[12305, 17202, 121, 334])).
% 3.43/3.69 tff(17204,plain,
% 3.43/3.69 (r(s(s(s(z))), z)),
% 3.43/3.69 inference(unit_resolution,[status(thm)],[1713, 17203])).
% 3.43/3.69 tff(17205,plain,
% 3.43/3.69 (~r(s(z), s(s(s(z))))),
% 3.43/3.69 inference(unit_resolution,[status(thm)],[8876, 17204, 323, 17193])).
% 3.43/3.69 tff(17206,plain,
% 3.43/3.69 (b(s(z), s(s(s(z))))),
% 3.43/3.69 inference(unit_resolution,[status(thm)],[1674, 17205])).
% 3.43/3.69 tff(17207,plain,
% 3.43/3.69 (~b(s(s(s(z))), s(s(s(elem!1))))),
% 3.43/3.69 inference(unit_resolution,[status(thm)],[8841, 17206, 17187, 17191])).
% 3.43/3.69 tff(17208,plain,
% 3.43/3.69 (~b(s(s(s(z))), elem!1)),
% 3.43/3.69 inference(unit_resolution,[status(thm)],[4078, 17207, 4031])).
% 3.43/3.69 tff(17209,plain,
% 3.43/3.69 (r(s(s(s(z))), elem!1)),
% 3.43/3.69 inference(unit_resolution,[status(thm)],[2826, 17208, 4027])).
% 3.43/3.69 tff(17210,plain,
% 3.43/3.69 (r(s(s(s(z))), s(s(s(elem!1))))),
% 3.43/3.69 inference(modus_ponens,[status(thm)],[17209, 17186])).
% 3.43/3.69 tff(17211,plain,
% 3.43/3.69 (r(s(s(s(elem!1))), s(s(z)))),
% 3.43/3.69 inference(unit_resolution,[status(thm)],[218, 17198])).
% 3.43/3.69 tff(17212,plain,
% 3.43/3.69 (~b(z, s(s(s(elem!1))))),
% 3.43/3.69 inference(unit_resolution,[status(thm)],[4345, 334, 1790])).
% 3.43/3.69 tff(17213,plain,
% 3.43/3.69 (r(z, s(s(s(elem!1))))),
% 3.43/3.69 inference(unit_resolution,[status(thm)],[261, 17212])).
% 3.43/3.69 tff(17214,plain,
% 3.43/3.69 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(z))), s(s(s(elem!1))))) | (~r(z, s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), s(s(z)))) | (~r(s(s(s(z))), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(z))), s(s(s(elem!1))))) | (~r(z, s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), s(s(z)))) | (~r(s(s(s(z))), z)))),
% 3.43/3.69 inference(rewrite,[status(thm)],[])).
% 3.43/3.69 tff(17215,plain,
% 3.43/3.69 (((~r(s(s(s(elem!1))), s(s(z)))) | (~r(z, s(s(s(elem!1))))) | (~r(s(s(s(z))), s(s(s(elem!1))))) | (~r(s(s(s(z))), z))) <=> ((~r(s(s(s(z))), s(s(s(elem!1))))) | (~r(z, s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), s(s(z)))) | (~r(s(s(s(z))), z)))),
% 3.43/3.69 inference(rewrite,[status(thm)],[])).
% 3.43/3.69 tff(17216,plain,
% 3.43/3.69 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), s(s(z)))) | (~r(z, s(s(s(elem!1))))) | (~r(s(s(s(z))), s(s(s(elem!1))))) | (~r(s(s(s(z))), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(z))), s(s(s(elem!1))))) | (~r(z, s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), s(s(z)))) | (~r(s(s(s(z))), z))))),
% 3.43/3.69 inference(monotonicity,[status(thm)],[17215])).
% 3.43/3.69 tff(17217,plain,
% 3.43/3.69 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), s(s(z)))) | (~r(z, s(s(s(elem!1))))) | (~r(s(s(s(z))), s(s(s(elem!1))))) | (~r(s(s(s(z))), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(z))), s(s(s(elem!1))))) | (~r(z, s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), s(s(z)))) | (~r(s(s(s(z))), z)))),
% 3.43/3.69 inference(transitivity,[status(thm)],[17216, 17214])).
% 3.43/3.69 tff(17218,plain,
% 3.43/3.69 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), s(s(z)))) | (~r(z, s(s(s(elem!1))))) | (~r(s(s(s(z))), s(s(s(elem!1))))) | (~r(s(s(s(z))), z)))),
% 3.43/3.69 inference(quant_inst,[status(thm)],[])).
% 3.43/3.69 tff(17219,plain,
% 3.43/3.69 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(z))), s(s(s(elem!1))))) | (~r(z, s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), s(s(z)))) | (~r(s(s(s(z))), z))),
% 3.43/3.69 inference(modus_ponens,[status(thm)],[17218, 17217])).
% 3.43/3.69 tff(17220,plain,
% 3.43/3.69 ($false),
% 3.43/3.69 inference(unit_resolution,[status(thm)],[17219, 197, 17213, 17211, 17204, 17210])).
% 3.43/3.69 tff(17221,plain,((~(s(s(elem!1)) = s(s(s(elem!1))))) | (~r(z, s(z))) | (~b(s(s(s(elem!1))), z)) | (s(s(elem!1)) = s(s(z))) | b(z, s(s(elem!1)))), inference(lemma,lemma(discharge,[]))).
% 3.43/3.69 tff(17222,plain,
% 3.43/3.69 (~(s(s(elem!1)) = s(s(s(elem!1))))),
% 3.43/3.69 inference(unit_resolution,[status(thm)],[17221, 323, 121, 11, 1790])).
% 3.43/3.69 tff(17223,plain,
% 3.43/3.69 (~(s(s(s(elem!1))) = s(s(elem!1)))),
% 3.43/3.69 inference(unit_resolution,[status(thm)],[50, 17222])).
% 3.43/3.69 tff(17224,plain,
% 3.43/3.69 (~b(s(z), z)),
% 3.43/3.69 inference(unit_resolution,[status(thm)],[12830, 96, 121, 17064])).
% 3.43/3.69 tff(17225,plain,
% 3.43/3.69 (r(s(z), z)),
% 3.43/3.69 inference(unit_resolution,[status(thm)],[230, 17224])).
% 3.43/3.69 tff(17226,plain,
% 3.43/3.69 (~r(s(s(elem!1)), s(z))),
% 3.43/3.69 inference(unit_resolution,[status(thm)],[8426, 17225, 323, 365])).
% 3.43/3.69 tff(17227,plain,
% 3.43/3.69 (b(s(s(elem!1)), s(z))),
% 3.43/3.69 inference(unit_resolution,[status(thm)],[1912, 17226])).
% 3.43/3.69 tff(17228,plain,
% 3.43/3.69 (~b(s(s(z)), s(s(elem!1)))),
% 3.43/3.69 inference(unit_resolution,[status(thm)],[454, 17227, 15211, 17064])).
% 3.43/3.69 tff(17229,plain,
% 3.43/3.69 (r(s(s(z)), s(s(elem!1)))),
% 3.43/3.69 inference(unit_resolution,[status(thm)],[390, 17228, 44])).
% 3.43/3.69 tff(17230,plain,
% 3.43/3.69 (~b(s(s(z)), s(s(s(elem!1))))),
% 3.43/3.69 inference(unit_resolution,[status(thm)],[12136, 17225, 17064, 121, 96, 323])).
% 3.43/3.69 tff(17231,plain,
% 3.43/3.69 (r(s(s(z)), s(s(s(elem!1))))),
% 3.43/3.69 inference(unit_resolution,[status(thm)],[279, 17230])).
% 3.43/3.69 tff(17232,plain,
% 3.43/3.69 (~b(s(s(s(elem!1))), s(s(elem!1)))),
% 3.43/3.69 inference(unit_resolution,[status(thm)],[1858, 17227, 15211, 96])).
% 3.43/3.69 tff(17233,plain,
% 3.43/3.69 (r(s(s(s(elem!1))), s(s(elem!1)))),
% 3.43/3.69 inference(unit_resolution,[status(thm)],[889, 17232, 1863])).
% 3.43/3.69 tff(17234,plain,
% 3.43/3.69 (~r(s(s(elem!1)), s(s(z)))),
% 3.43/3.69 inference(unit_resolution,[status(thm)],[4513, 17233, 17231, 17229])).
% 3.43/3.69 tff(17235,plain,
% 3.43/3.69 (b(s(s(elem!1)), s(s(z)))),
% 3.43/3.69 inference(unit_resolution,[status(thm)],[441, 17234, 11])).
% 3.43/3.69 tff(17236,plain,
% 3.43/3.69 (~r(s(z), s(s(s(elem!1))))),
% 3.43/3.69 inference(unit_resolution,[status(thm)],[3618, 17235, 17231, 17233, 17227])).
% 3.43/3.69 tff(17237,plain,
% 3.43/3.69 (b(s(z), s(s(s(elem!1))))),
% 3.43/3.69 inference(unit_resolution,[status(thm)],[116, 17236])).
% 3.43/3.69 tff(17238,plain,
% 3.43/3.69 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(s(elem!1))))) | (~b(s(s(elem!1)), s(s(z)))) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(s(elem!1)), s(z))) | (~b(s(s(z)), s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), s(s(s(elem!1))))) | (~b(s(s(elem!1)), s(s(z)))) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(s(elem!1)), s(z))) | (~b(s(s(z)), s(z))))),
% 3.53/3.70 inference(rewrite,[status(thm)],[])).
% 3.53/3.70 tff(17239,plain,
% 3.53/3.70 (((~b(s(s(s(elem!1))), s(z))) | (~b(s(s(elem!1)), s(z))) | (~b(s(z), s(s(s(elem!1))))) | (~b(s(s(z)), s(z))) | (~b(s(s(elem!1)), s(z))) | (~b(s(s(elem!1)), s(s(z))))) <=> ((~b(s(z), s(s(s(elem!1))))) | (~b(s(s(elem!1)), s(s(z)))) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(s(elem!1)), s(z))) | (~b(s(s(z)), s(z))))),
% 3.53/3.70 inference(rewrite,[status(thm)],[])).
% 3.53/3.70 tff(17240,plain,
% 3.53/3.70 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), s(z))) | (~b(s(s(elem!1)), s(z))) | (~b(s(z), s(s(s(elem!1))))) | (~b(s(s(z)), s(z))) | (~b(s(s(elem!1)), s(z))) | (~b(s(s(elem!1)), s(s(z)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(s(elem!1))))) | (~b(s(s(elem!1)), s(s(z)))) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(s(elem!1)), s(z))) | (~b(s(s(z)), s(z)))))),
% 3.53/3.70 inference(monotonicity,[status(thm)],[17239])).
% 3.53/3.70 tff(17241,plain,
% 3.53/3.70 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), s(z))) | (~b(s(s(elem!1)), s(z))) | (~b(s(z), s(s(s(elem!1))))) | (~b(s(s(z)), s(z))) | (~b(s(s(elem!1)), s(z))) | (~b(s(s(elem!1)), s(s(z)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), s(s(s(elem!1))))) | (~b(s(s(elem!1)), s(s(z)))) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(s(elem!1)), s(z))) | (~b(s(s(z)), s(z))))),
% 3.53/3.70 inference(transitivity,[status(thm)],[17240, 17238])).
% 3.53/3.70 tff(17242,plain,
% 3.53/3.70 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), s(z))) | (~b(s(s(elem!1)), s(z))) | (~b(s(z), s(s(s(elem!1))))) | (~b(s(s(z)), s(z))) | (~b(s(s(elem!1)), s(z))) | (~b(s(s(elem!1)), s(s(z)))))),
% 3.53/3.70 inference(quant_inst,[status(thm)],[])).
% 3.53/3.70 tff(17243,plain,
% 3.53/3.70 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), s(s(s(elem!1))))) | (~b(s(s(elem!1)), s(s(z)))) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(s(elem!1)), s(z))) | (~b(s(s(z)), s(z)))),
% 3.53/3.70 inference(modus_ponens,[status(thm)],[17242, 17241])).
% 3.53/3.70 tff(17244,plain,
% 3.53/3.70 ($false),
% 3.53/3.70 inference(unit_resolution,[status(thm)],[17243, 166, 17237, 17235, 96, 17227, 17064])).
% 3.53/3.70 tff(17245,plain,((~b(s(s(s(elem!1))), s(z))) | (s(s(elem!1)) = s(s(z))) | (s(s(s(elem!1))) = s(s(elem!1))) | (~r(z, s(z))) | (~r(z, s(s(elem!1)))) | (~b(s(s(s(elem!1))), z))), inference(lemma,lemma(discharge,[]))).
% 3.53/3.70 tff(17246,plain,
% 3.53/3.70 (~b(s(s(s(elem!1))), s(z))),
% 3.53/3.70 inference(unit_resolution,[status(thm)],[17245, 17223, 11, 323, 4458, 121])).
% 3.53/3.70 tff(17247,plain,
% 3.53/3.70 (r(s(s(s(elem!1))), s(z))),
% 3.53/3.70 inference(unit_resolution,[status(thm)],[1849, 17246])).
% 3.53/3.70 tff(17248,plain,
% 3.53/3.70 (b(s(z), s(s(z)))),
% 3.53/3.70 inference(unit_resolution,[status(thm)],[17184, 17247, 15211, 17222])).
% 3.53/3.70 tff(17249,plain,
% 3.53/3.70 (~b(s(z), z)),
% 3.53/3.70 inference(unit_resolution,[status(thm)],[17117, 17247, 15211])).
% 3.53/3.70 tff(17250,plain,
% 3.53/3.70 (r(s(z), z)),
% 3.53/3.70 inference(unit_resolution,[status(thm)],[230, 17249])).
% 3.53/3.70 tff(17251,plain,
% 3.53/3.70 (~r(z, s(s(s(elem!1))))),
% 3.53/3.70 inference(unit_resolution,[status(thm)],[2613, 17250, 323, 17247])).
% 3.53/3.70 tff(17252,plain,
% 3.53/3.70 (b(z, s(s(s(elem!1))))),
% 3.53/3.70 inference(unit_resolution,[status(thm)],[261, 17251])).
% 3.53/3.70 tff(17253,plain,
% 3.53/3.70 (~b(s(z), z)),
% 3.53/3.70 inference(unit_resolution,[status(thm)],[17102, 556])).
% 3.53/3.70 tff(17254,plain,
% 3.53/3.70 (r(s(z), z)),
% 3.53/3.70 inference(unit_resolution,[status(thm)],[230, 17253])).
% 3.53/3.70 tff(17255,plain,
% 3.53/3.70 (~r(s(s(elem!1)), s(z))),
% 3.53/3.70 inference(unit_resolution,[status(thm)],[10127, 17254, 350, 45, 121, 17093, 240])).
% 3.53/3.70 tff(17256,plain,
% 3.53/3.70 (b(s(s(elem!1)), s(z))),
% 3.53/3.70 inference(unit_resolution,[status(thm)],[1912, 17255])).
% 3.53/3.70 tff(17257,plain,
% 3.53/3.70 (~b(s(s(z)), s(s(elem!1)))),
% 3.53/3.70 inference(unit_resolution,[status(thm)],[454, 17256, 376, 17073])).
% 3.53/3.70 tff(17258,plain,
% 3.53/3.70 (~b(s(s(elem!1)), s(s(z)))),
% 3.53/3.70 inference(unit_resolution,[status(thm)],[2690, 166, 376, 17256, 17073])).
% 3.53/3.70 tff(17259,plain,
% 3.53/3.70 (~r(s(s(s(s(elem!1)))), s(z))),
% 3.53/3.70 inference(unit_resolution,[status(thm)],[2669, 17254, 350, 17093, 364])).
% 3.53/3.70 tff(17260,plain,
% 3.53/3.70 (b(s(s(s(s(elem!1)))), s(z))),
% 3.53/3.70 inference(unit_resolution,[status(thm)],[661, 17259])).
% 3.53/3.70 tff(17261,plain,
% 3.53/3.70 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(z)))) | (~b(s(s(z)), s(z))) | (~b(s(s(s(s(elem!1)))), s(z))) | (~b(s(s(s(s(elem!1)))), s(s(z)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), s(s(z)))) | (~b(s(s(z)), s(z))) | (~b(s(s(s(s(elem!1)))), s(z))) | (~b(s(s(s(s(elem!1)))), s(s(z)))))),
% 3.53/3.70 inference(rewrite,[status(thm)],[])).
% 3.53/3.70 tff(17262,plain,
% 3.53/3.70 (((~b(s(s(z)), s(z))) | (~b(s(s(s(s(elem!1)))), s(z))) | (~b(s(z), s(s(z)))) | (~b(s(s(z)), s(z))) | (~b(s(s(s(s(elem!1)))), s(z))) | (~b(s(s(s(s(elem!1)))), s(s(z))))) <=> ((~b(s(z), s(s(z)))) | (~b(s(s(z)), s(z))) | (~b(s(s(s(s(elem!1)))), s(z))) | (~b(s(s(s(s(elem!1)))), s(s(z)))))),
% 3.53/3.70 inference(rewrite,[status(thm)],[])).
% 3.53/3.70 tff(17263,plain,
% 3.53/3.70 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), s(z))) | (~b(s(s(s(s(elem!1)))), s(z))) | (~b(s(z), s(s(z)))) | (~b(s(s(z)), s(z))) | (~b(s(s(s(s(elem!1)))), s(z))) | (~b(s(s(s(s(elem!1)))), s(s(z)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(z)))) | (~b(s(s(z)), s(z))) | (~b(s(s(s(s(elem!1)))), s(z))) | (~b(s(s(s(s(elem!1)))), s(s(z))))))),
% 3.53/3.70 inference(monotonicity,[status(thm)],[17262])).
% 3.53/3.70 tff(17264,plain,
% 3.53/3.70 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), s(z))) | (~b(s(s(s(s(elem!1)))), s(z))) | (~b(s(z), s(s(z)))) | (~b(s(s(z)), s(z))) | (~b(s(s(s(s(elem!1)))), s(z))) | (~b(s(s(s(s(elem!1)))), s(s(z)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), s(s(z)))) | (~b(s(s(z)), s(z))) | (~b(s(s(s(s(elem!1)))), s(z))) | (~b(s(s(s(s(elem!1)))), s(s(z)))))),
% 3.53/3.70 inference(transitivity,[status(thm)],[17263, 17261])).
% 3.53/3.70 tff(17265,plain,
% 3.53/3.70 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), s(z))) | (~b(s(s(s(s(elem!1)))), s(z))) | (~b(s(z), s(s(z)))) | (~b(s(s(z)), s(z))) | (~b(s(s(s(s(elem!1)))), s(z))) | (~b(s(s(s(s(elem!1)))), s(s(z)))))),
% 3.53/3.70 inference(quant_inst,[status(thm)],[])).
% 3.53/3.70 tff(17266,plain,
% 3.53/3.70 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), s(s(z)))) | (~b(s(s(z)), s(z))) | (~b(s(s(s(s(elem!1)))), s(z))) | (~b(s(s(s(s(elem!1)))), s(s(z))))),
% 3.53/3.70 inference(modus_ponens,[status(thm)],[17265, 17264])).
% 3.53/3.70 tff(17267,plain,
% 3.53/3.70 (~b(s(s(s(s(elem!1)))), s(s(z)))),
% 3.53/3.70 inference(unit_resolution,[status(thm)],[17266, 166, 556, 17073, 17260])).
% 3.53/3.70 tff(17268,plain,
% 3.53/3.70 (r(s(s(s(s(elem!1)))), s(s(z)))),
% 3.53/3.70 inference(unit_resolution,[status(thm)],[1299, 17267])).
% 3.53/3.70 tff(17269,plain,
% 3.53/3.70 (~b(s(s(elem!1)), s(s(s(s(elem!1)))))),
% 3.53/3.70 inference(unit_resolution,[status(thm)],[822, 166, 376, 17256, 17260])).
% 3.53/3.70 tff(17270,plain,
% 3.53/3.70 (~b(s(s(s(s(elem!1)))), s(s(elem!1)))),
% 3.53/3.70 inference(unit_resolution,[status(thm)],[804, 166, 376, 17256, 17260])).
% 3.53/3.70 tff(17271,plain,
% 3.53/3.70 (~r(s(s(s(z))), z)),
% 3.53/3.70 inference(unit_resolution,[status(thm)],[13007, 556, 17093, 866, 17254])).
% 3.53/3.70 tff(17272,plain,
% 3.53/3.70 (b(s(s(s(z))), z)),
% 3.53/3.70 inference(unit_resolution,[status(thm)],[1713, 17271])).
% 3.53/3.70 tff(17273,plain,
% 3.53/3.70 (s(s(z)) = s(s(elem!1))),
% 3.53/3.70 inference(unit_resolution,[status(thm)],[17173, 17272, 121, 350, 240, 17270, 17269, 17268, 45, 866, 17093, 17258, 17257])).
% 3.53/3.70 tff(17274,plain,
% 3.53/3.70 (s(elem!1) = s(z)),
% 3.53/3.70 inference(unit_resolution,[status(thm)],[43, 17273])).
% 3.53/3.70 tff(17275,plain,
% 3.53/3.70 (z = elem!1),
% 3.53/3.70 inference(unit_resolution,[status(thm)],[30, 17274])).
% 3.53/3.70 tff(17276,plain,
% 3.53/3.70 ((s(s(s(s(elem!1)))) = z) <=> (s(s(s(s(elem!1)))) = elem!1)),
% 3.53/3.70 inference(monotonicity,[status(thm)],[17275])).
% 3.53/3.70 tff(17277,plain,
% 3.53/3.70 ((~(s(s(s(s(elem!1)))) = z)) <=> (~(s(s(s(s(elem!1)))) = elem!1))),
% 3.53/3.70 inference(monotonicity,[status(thm)],[17276])).
% 3.53/3.70 tff(17278,plain,
% 3.53/3.70 (~(s(s(s(s(elem!1)))) = elem!1)),
% 3.53/3.70 inference(modus_ponens,[status(thm)],[626, 17277])).
% 3.53/3.70 tff(17279,plain,
% 3.53/3.70 (r(elem!1, s(z))),
% 3.53/3.70 inference(unit_resolution,[status(thm)],[741, 17275, 17093])).
% 3.53/3.70 tff(17280,plain,
% 3.53/3.70 (r(s(s(z)), s(s(s(s(elem!1))))) <=> r(s(s(elem!1)), s(s(s(s(elem!1)))))),
% 3.53/3.70 inference(monotonicity,[status(thm)],[17273])).
% 3.53/3.70 tff(17281,plain,
% 3.53/3.70 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(z)))) | (~b(s(s(z)), s(z))) | (~b(s(s(s(s(elem!1)))), s(z))) | (~b(s(s(z)), s(s(s(s(elem!1)))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), s(s(z)))) | (~b(s(s(z)), s(z))) | (~b(s(s(s(s(elem!1)))), s(z))) | (~b(s(s(z)), s(s(s(s(elem!1)))))))),
% 3.53/3.70 inference(rewrite,[status(thm)],[])).
% 3.53/3.70 tff(17282,plain,
% 3.53/3.70 (((~b(s(s(z)), s(z))) | (~b(s(s(z)), s(z))) | (~b(s(z), s(s(z)))) | (~b(s(s(s(s(elem!1)))), s(z))) | (~b(s(s(z)), s(z))) | (~b(s(s(z)), s(s(s(s(elem!1))))))) <=> ((~b(s(z), s(s(z)))) | (~b(s(s(z)), s(z))) | (~b(s(s(s(s(elem!1)))), s(z))) | (~b(s(s(z)), s(s(s(s(elem!1)))))))),
% 3.53/3.70 inference(rewrite,[status(thm)],[])).
% 3.53/3.70 tff(17283,plain,
% 3.53/3.70 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), s(z))) | (~b(s(s(z)), s(z))) | (~b(s(z), s(s(z)))) | (~b(s(s(s(s(elem!1)))), s(z))) | (~b(s(s(z)), s(z))) | (~b(s(s(z)), s(s(s(s(elem!1)))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(z)))) | (~b(s(s(z)), s(z))) | (~b(s(s(s(s(elem!1)))), s(z))) | (~b(s(s(z)), s(s(s(s(elem!1))))))))),
% 3.53/3.70 inference(monotonicity,[status(thm)],[17282])).
% 3.53/3.70 tff(17284,plain,
% 3.53/3.70 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), s(z))) | (~b(s(s(z)), s(z))) | (~b(s(z), s(s(z)))) | (~b(s(s(s(s(elem!1)))), s(z))) | (~b(s(s(z)), s(z))) | (~b(s(s(z)), s(s(s(s(elem!1)))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), s(s(z)))) | (~b(s(s(z)), s(z))) | (~b(s(s(s(s(elem!1)))), s(z))) | (~b(s(s(z)), s(s(s(s(elem!1)))))))),
% 3.53/3.70 inference(transitivity,[status(thm)],[17283, 17281])).
% 3.53/3.70 tff(17285,plain,
% 3.53/3.70 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), s(z))) | (~b(s(s(z)), s(z))) | (~b(s(z), s(s(z)))) | (~b(s(s(s(s(elem!1)))), s(z))) | (~b(s(s(z)), s(z))) | (~b(s(s(z)), s(s(s(s(elem!1)))))))),
% 3.53/3.70 inference(quant_inst,[status(thm)],[])).
% 3.53/3.70 tff(17286,plain,
% 3.53/3.70 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), s(s(z)))) | (~b(s(s(z)), s(z))) | (~b(s(s(s(s(elem!1)))), s(z))) | (~b(s(s(z)), s(s(s(s(elem!1))))))),
% 3.53/3.70 inference(modus_ponens,[status(thm)],[17285, 17284])).
% 3.53/3.70 tff(17287,plain,
% 3.53/3.70 (~b(s(s(z)), s(s(s(s(elem!1)))))),
% 3.53/3.70 inference(unit_resolution,[status(thm)],[17286, 166, 556, 17073, 17260])).
% 3.53/3.70 tff(17288,plain,
% 3.53/3.70 ((s(s(z)) = s(s(s(s(elem!1))))) | r(s(s(z)), s(s(s(s(elem!1)))))),
% 3.53/3.70 inference(unit_resolution,[status(thm)],[1288, 79, 17287])).
% 3.53/3.70 tff(17289,plain,
% 3.53/3.70 (r(s(s(z)), s(s(s(s(elem!1)))))),
% 3.53/3.70 inference(unit_resolution,[status(thm)],[17288, 1278])).
% 3.53/3.70 tff(17290,plain,
% 3.53/3.70 (r(s(s(elem!1)), s(s(s(s(elem!1)))))),
% 3.53/3.70 inference(modus_ponens,[status(thm)],[17289, 17280])).
% 3.53/3.70 tff(17291,plain,
% 3.53/3.70 (r(s(s(elem!1)), z) <=> r(s(s(elem!1)), elem!1)),
% 3.53/3.70 inference(monotonicity,[status(thm)],[17275])).
% 3.53/3.70 tff(17292,plain,
% 3.53/3.70 (r(s(s(z)), z) <=> r(s(s(elem!1)), z)),
% 3.53/3.70 inference(monotonicity,[status(thm)],[17273])).
% 3.53/3.70 tff(17293,plain,
% 3.53/3.70 (r(s(s(elem!1)), z)),
% 3.53/3.70 inference(modus_ponens,[status(thm)],[866, 17292])).
% 3.53/3.70 tff(17294,plain,
% 3.53/3.70 (r(s(s(elem!1)), elem!1)),
% 3.53/3.70 inference(modus_ponens,[status(thm)],[17293, 17291])).
% 3.53/3.70 tff(17295,plain,
% 3.53/3.70 (~r(s(s(s(s(elem!1)))), elem!1)),
% 3.53/3.70 inference(unit_resolution,[status(thm)],[9687, 17294, 17290, 17279])).
% 3.53/3.70 tff(17296,plain,
% 3.53/3.70 (b(s(s(s(s(elem!1)))), elem!1)),
% 3.53/3.70 inference(unit_resolution,[status(thm)],[719, 17295, 17278])).
% 3.53/3.70 tff(17297,plain,
% 3.53/3.70 (b(s(s(s(elem!1))), elem!1)),
% 3.53/3.70 inference(unit_resolution,[status(thm)],[634, 17275, 121])).
% 3.53/3.70 tff(17298,plain,
% 3.53/3.70 (elem!1 = z),
% 3.53/3.70 inference(symmetry,[status(thm)],[17275])).
% 3.53/3.70 tff(17299,plain,
% 3.53/3.70 (b(elem!1, s(s(elem!1))) <=> b(z, s(s(elem!1)))),
% 3.53/3.70 inference(monotonicity,[status(thm)],[17298])).
% 3.53/3.70 tff(17300,plain,
% 3.53/3.70 (b(z, s(s(elem!1))) <=> b(elem!1, s(s(elem!1)))),
% 3.53/3.70 inference(symmetry,[status(thm)],[17299])).
% 3.53/3.70 tff(17301,plain,
% 3.53/3.70 (b(z, s(s(elem!1)))),
% 3.53/3.70 inference(unit_resolution,[status(thm)],[10937, 17273, 10451])).
% 3.53/3.70 tff(17302,plain,
% 3.53/3.70 (b(elem!1, s(s(elem!1)))),
% 3.53/3.70 inference(modus_ponens,[status(thm)],[17301, 17300])).
% 3.53/3.70 tff(17303,plain,
% 3.53/3.70 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(s(elem!1)))) | (~b(s(s(elem!1)), s(z))) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(s(s(s(elem!1)))), elem!1)) | (~b(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~b(s(s(s(s(elem!1)))), s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(s(elem!1)))) | (~b(s(s(elem!1)), s(z))) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(s(s(s(elem!1)))), elem!1)) | (~b(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~b(s(s(s(s(elem!1)))), s(z))))),
% 3.53/3.70 inference(rewrite,[status(thm)],[])).
% 3.53/3.70 tff(17304,plain,
% 3.53/3.70 (((~b(s(s(elem!1)), s(z))) | (~b(s(s(s(s(elem!1)))), s(z))) | (~b(elem!1, s(s(elem!1)))) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(s(s(s(elem!1)))), elem!1)) | (~b(s(s(s(s(elem!1)))), s(s(s(elem!1)))))) <=> ((~b(elem!1, s(s(elem!1)))) | (~b(s(s(elem!1)), s(z))) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(s(s(s(elem!1)))), elem!1)) | (~b(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~b(s(s(s(s(elem!1)))), s(z))))),
% 3.53/3.70 inference(rewrite,[status(thm)],[])).
% 3.53/3.70 tff(17305,plain,
% 3.53/3.70 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), s(z))) | (~b(s(s(s(s(elem!1)))), s(z))) | (~b(elem!1, s(s(elem!1)))) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(s(s(s(elem!1)))), elem!1)) | (~b(s(s(s(s(elem!1)))), s(s(s(elem!1))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(s(elem!1)))) | (~b(s(s(elem!1)), s(z))) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(s(s(s(elem!1)))), elem!1)) | (~b(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~b(s(s(s(s(elem!1)))), s(z)))))),
% 3.53/3.70 inference(monotonicity,[status(thm)],[17304])).
% 3.53/3.70 tff(17306,plain,
% 3.53/3.70 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), s(z))) | (~b(s(s(s(s(elem!1)))), s(z))) | (~b(elem!1, s(s(elem!1)))) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(s(s(s(elem!1)))), elem!1)) | (~b(s(s(s(s(elem!1)))), s(s(s(elem!1))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(s(elem!1)))) | (~b(s(s(elem!1)), s(z))) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(s(s(s(elem!1)))), elem!1)) | (~b(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~b(s(s(s(s(elem!1)))), s(z))))),
% 3.53/3.70 inference(transitivity,[status(thm)],[17305, 17303])).
% 3.53/3.70 tff(17307,plain,
% 3.53/3.70 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), s(z))) | (~b(s(s(s(s(elem!1)))), s(z))) | (~b(elem!1, s(s(elem!1)))) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(s(s(s(elem!1)))), elem!1)) | (~b(s(s(s(s(elem!1)))), s(s(s(elem!1))))))),
% 3.53/3.70 inference(quant_inst,[status(thm)],[])).
% 3.53/3.70 tff(17308,plain,
% 3.53/3.70 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(s(elem!1)))) | (~b(s(s(elem!1)), s(z))) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(s(s(s(elem!1)))), elem!1)) | (~b(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~b(s(s(s(s(elem!1)))), s(z)))),
% 3.53/3.70 inference(modus_ponens,[status(thm)],[17307, 17306])).
% 3.53/3.70 tff(17309,plain,
% 3.53/3.70 ((~b(s(s(s(s(elem!1)))), elem!1)) | (~b(s(s(s(s(elem!1)))), s(s(s(elem!1)))))),
% 3.53/3.70 inference(unit_resolution,[status(thm)],[17308, 166, 17256, 17260, 17302, 17297])).
% 3.53/3.70 tff(17310,plain,
% 3.53/3.70 (~b(s(s(s(s(elem!1)))), s(s(s(elem!1))))),
% 3.53/3.70 inference(unit_resolution,[status(thm)],[17309, 17296])).
% 3.53/3.70 tff(17311,plain,
% 3.53/3.70 (r(s(s(s(s(elem!1)))), s(s(s(elem!1))))),
% 3.53/3.70 inference(unit_resolution,[status(thm)],[1065, 17310, 364])).
% 3.53/3.70 tff(17312,plain,
% 3.53/3.70 (r(s(s(s(s(elem!1)))), s(s(elem!1)))),
% 3.53/3.70 inference(unit_resolution,[status(thm)],[4866, 17273, 17268])).
% 3.53/3.70 tff(17313,plain,
% 3.53/3.70 (b(z, s(s(s(elem!1)))) <=> b(elem!1, s(s(s(elem!1))))),
% 3.53/3.70 inference(monotonicity,[status(thm)],[17275])).
% 3.53/3.70 tff(17314,plain,
% 3.53/3.70 (b(elem!1, s(s(s(elem!1))))),
% 3.53/3.70 inference(modus_ponens,[status(thm)],[240, 17313])).
% 3.53/3.70 tff(17315,plain,
% 3.53/3.70 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(elem!1, s(s(s(elem!1))))) | (~b(elem!1, s(s(elem!1)))) | (~b(s(z), s(s(elem!1)))) | (~b(s(s(elem!1)), s(z))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(elem!1, s(s(s(elem!1))))) | (~b(elem!1, s(s(elem!1)))) | (~b(s(z), s(s(elem!1)))) | (~b(s(s(elem!1)), s(z))))),
% 3.53/3.70 inference(rewrite,[status(thm)],[])).
% 3.53/3.70 tff(17316,plain,
% 3.53/3.70 (((~b(s(z), s(s(elem!1)))) | (~b(elem!1, s(s(elem!1)))) | (~b(s(s(elem!1)), s(z))) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(elem!1, s(s(elem!1)))) | (~b(elem!1, s(s(s(elem!1)))))) <=> ((~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(elem!1, s(s(s(elem!1))))) | (~b(elem!1, s(s(elem!1)))) | (~b(s(z), s(s(elem!1)))) | (~b(s(s(elem!1)), s(z))))),
% 3.53/3.70 inference(rewrite,[status(thm)],[])).
% 3.53/3.70 tff(17317,plain,
% 3.53/3.70 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(elem!1)))) | (~b(elem!1, s(s(elem!1)))) | (~b(s(s(elem!1)), s(z))) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(elem!1, s(s(elem!1)))) | (~b(elem!1, s(s(s(elem!1))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(elem!1, s(s(s(elem!1))))) | (~b(elem!1, s(s(elem!1)))) | (~b(s(z), s(s(elem!1)))) | (~b(s(s(elem!1)), s(z)))))),
% 3.53/3.71 inference(monotonicity,[status(thm)],[17316])).
% 3.53/3.71 tff(17318,plain,
% 3.53/3.71 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(elem!1)))) | (~b(elem!1, s(s(elem!1)))) | (~b(s(s(elem!1)), s(z))) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(elem!1, s(s(elem!1)))) | (~b(elem!1, s(s(s(elem!1))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(elem!1, s(s(s(elem!1))))) | (~b(elem!1, s(s(elem!1)))) | (~b(s(z), s(s(elem!1)))) | (~b(s(s(elem!1)), s(z))))),
% 3.53/3.71 inference(transitivity,[status(thm)],[17317, 17315])).
% 3.53/3.71 tff(17319,plain,
% 3.53/3.71 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(elem!1)))) | (~b(elem!1, s(s(elem!1)))) | (~b(s(s(elem!1)), s(z))) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(elem!1, s(s(elem!1)))) | (~b(elem!1, s(s(s(elem!1))))))),
% 3.53/3.71 inference(quant_inst,[status(thm)],[])).
% 3.53/3.71 tff(17320,plain,
% 3.53/3.71 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(elem!1, s(s(s(elem!1))))) | (~b(elem!1, s(s(elem!1)))) | (~b(s(z), s(s(elem!1)))) | (~b(s(s(elem!1)), s(z)))),
% 3.53/3.71 inference(modus_ponens,[status(thm)],[17319, 17318])).
% 3.53/3.71 tff(17321,plain,
% 3.53/3.71 ((~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(elem!1, s(s(s(elem!1))))) | (~b(elem!1, s(s(elem!1)))) | (~b(s(z), s(s(elem!1)))) | (~b(s(s(elem!1)), s(z)))),
% 3.53/3.71 inference(unit_resolution,[status(thm)],[17320, 166])).
% 3.53/3.71 tff(17322,plain,
% 3.53/3.71 (~b(s(s(s(elem!1))), s(s(elem!1)))),
% 3.53/3.71 inference(unit_resolution,[status(thm)],[17321, 17302, 17256, 17314, 376])).
% 3.53/3.71 tff(17323,plain,
% 3.53/3.71 (r(s(s(s(elem!1))), s(s(elem!1)))),
% 3.53/3.71 inference(unit_resolution,[status(thm)],[889, 17322, 51])).
% 3.53/3.71 tff(17324,plain,
% 3.53/3.71 ($false),
% 3.53/3.71 inference(unit_resolution,[status(thm)],[15685, 197, 17294, 17323, 17312, 17311])).
% 3.53/3.71 tff(17325,plain,((~b(s(z), s(s(z)))) | (~b(s(z), s(s(elem!1)))) | (~b(z, s(s(s(elem!1))))) | (~r(s(s(z)), z)) | (~b(s(s(s(elem!1))), z)) | (~b(z, s(s(z)))) | (~r(s(s(s(elem!1))), s(z))) | (s(s(elem!1)) = s(s(s(elem!1))))), inference(lemma,lemma(discharge,[]))).
% 3.53/3.71 tff(17326,plain,
% 3.53/3.71 ((~b(s(z), s(s(z)))) | (~b(s(z), s(s(elem!1)))) | (~b(z, s(s(s(elem!1))))) | (~r(s(s(z)), z)) | (~b(s(s(s(elem!1))), z)) | (~r(s(s(s(elem!1))), s(z))) | (s(s(elem!1)) = s(s(s(elem!1))))),
% 3.53/3.71 inference(unit_resolution,[status(thm)],[17325, 10450])).
% 3.53/3.71 tff(17327,plain,
% 3.53/3.71 (~r(s(s(z)), z)),
% 3.53/3.71 inference(unit_resolution,[status(thm)],[17326, 17252, 15211, 121, 17248, 17247, 17222])).
% 3.53/3.71 tff(17328,plain,
% 3.53/3.71 (b(s(s(z)), z)),
% 3.53/3.71 inference(unit_resolution,[status(thm)],[186, 17327])).
% 3.53/3.71 tff(17329,plain,
% 3.53/3.71 (~(s(s(s(elem!1))) = s(s(s(s(elem!1)))))),
% 3.53/3.71 inference(unit_resolution,[status(thm)],[357, 17222])).
% 3.53/3.71 tff(17330,plain,
% 3.53/3.71 (~b(s(s(s(elem!1))), s(z))),
% 3.53/3.71 inference(unit_resolution,[status(thm)],[17245, 51, 11, 323, 365, 121])).
% 3.53/3.71 tff(17331,plain,
% 3.53/3.71 (r(s(s(s(elem!1))), s(z))),
% 3.53/3.71 inference(unit_resolution,[status(thm)],[1849, 17330])).
% 3.53/3.71 tff(17332,plain,
% 3.53/3.71 (b(s(z), s(s(z)))),
% 3.53/3.71 inference(unit_resolution,[status(thm)],[17184, 17331, 15211, 45])).
% 3.53/3.71 tff(17333,plain,
% 3.53/3.71 (~r(z, s(s(s(elem!1))))),
% 3.53/3.71 inference(unit_resolution,[status(thm)],[933, 17331, 365, 12351])).
% 3.53/3.71 tff(17334,plain,
% 3.53/3.71 (b(z, s(s(s(elem!1))))),
% 3.53/3.71 inference(unit_resolution,[status(thm)],[261, 17333])).
% 3.53/3.71 tff(17335,plain,
% 3.53/3.71 (~r(s(s(z)), z)),
% 3.53/3.71 inference(unit_resolution,[status(thm)],[17326, 17334, 15211, 121, 17332, 17331, 45])).
% 3.53/3.71 tff(17336,plain,
% 3.53/3.71 (b(s(s(z)), z)),
% 3.53/3.71 inference(unit_resolution,[status(thm)],[186, 17335])).
% 3.53/3.71 tff(17337,plain,
% 3.53/3.71 ((~b(s(s(z)), z)) | (~b(s(s(z)), s(s(s(elem!1)))))),
% 3.53/3.71 inference(unit_resolution,[status(thm)],[12123, 166, 10450, 121, 17064])).
% 3.53/3.71 tff(17338,plain,
% 3.53/3.71 (~b(s(s(z)), s(s(s(elem!1))))),
% 3.53/3.71 inference(unit_resolution,[status(thm)],[17337, 17336])).
% 3.53/3.71 tff(17339,plain,
% 3.53/3.71 (r(s(s(z)), s(s(s(elem!1))))),
% 3.53/3.71 inference(unit_resolution,[status(thm)],[279, 17338])).
% 3.53/3.71 tff(17340,plain,
% 3.53/3.71 (~b(s(z), z)),
% 3.53/3.71 inference(unit_resolution,[status(thm)],[17117, 17331, 15211])).
% 3.53/3.71 tff(17341,plain,
% 3.53/3.71 (r(s(z), z)),
% 3.53/3.71 inference(unit_resolution,[status(thm)],[230, 17340])).
% 3.53/3.71 tff(17342,plain,
% 3.53/3.71 (~r(s(s(elem!1)), s(z))),
% 3.53/3.71 inference(unit_resolution,[status(thm)],[8426, 17341, 323, 365])).
% 3.53/3.71 tff(17343,plain,
% 3.53/3.71 (b(s(s(elem!1)), s(z))),
% 3.53/3.71 inference(unit_resolution,[status(thm)],[1912, 17342])).
% 3.53/3.71 tff(17344,plain,
% 3.53/3.71 (~b(s(s(z)), s(s(elem!1)))),
% 3.53/3.71 inference(unit_resolution,[status(thm)],[454, 17343, 15211, 17064])).
% 3.53/3.71 tff(17345,plain,
% 3.53/3.71 (r(s(s(z)), s(s(elem!1)))),
% 3.53/3.71 inference(unit_resolution,[status(thm)],[390, 17344, 44])).
% 3.53/3.71 tff(17346,plain,
% 3.53/3.71 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), s(z))) | (~r(s(s(elem!1)), s(s(s(elem!1))))) | (~r(s(s(z)), s(s(elem!1)))) | (~r(s(s(z)), s(s(s(elem!1))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(elem!1))), s(z))) | (~r(s(s(elem!1)), s(s(s(elem!1))))) | (~r(s(s(z)), s(s(elem!1)))) | (~r(s(s(z)), s(s(s(elem!1))))))),
% 3.53/3.71 inference(rewrite,[status(thm)],[])).
% 3.53/3.71 tff(17347,plain,
% 3.53/3.71 (((~r(s(s(s(elem!1))), s(z))) | (~r(s(s(elem!1)), s(s(s(elem!1))))) | (~r(s(s(z)), s(s(s(elem!1))))) | (~r(s(s(z)), s(s(elem!1))))) <=> ((~r(s(s(s(elem!1))), s(z))) | (~r(s(s(elem!1)), s(s(s(elem!1))))) | (~r(s(s(z)), s(s(elem!1)))) | (~r(s(s(z)), s(s(s(elem!1))))))),
% 3.53/3.71 inference(rewrite,[status(thm)],[])).
% 3.53/3.71 tff(17348,plain,
% 3.53/3.71 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), s(z))) | (~r(s(s(elem!1)), s(s(s(elem!1))))) | (~r(s(s(z)), s(s(s(elem!1))))) | (~r(s(s(z)), s(s(elem!1)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), s(z))) | (~r(s(s(elem!1)), s(s(s(elem!1))))) | (~r(s(s(z)), s(s(elem!1)))) | (~r(s(s(z)), s(s(s(elem!1)))))))),
% 3.53/3.71 inference(monotonicity,[status(thm)],[17347])).
% 3.53/3.71 tff(17349,plain,
% 3.53/3.71 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), s(z))) | (~r(s(s(elem!1)), s(s(s(elem!1))))) | (~r(s(s(z)), s(s(s(elem!1))))) | (~r(s(s(z)), s(s(elem!1)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(elem!1))), s(z))) | (~r(s(s(elem!1)), s(s(s(elem!1))))) | (~r(s(s(z)), s(s(elem!1)))) | (~r(s(s(z)), s(s(s(elem!1))))))),
% 3.53/3.71 inference(transitivity,[status(thm)],[17348, 17346])).
% 3.53/3.71 tff(17350,plain,
% 3.53/3.71 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), s(z))) | (~r(s(s(elem!1)), s(s(s(elem!1))))) | (~r(s(s(z)), s(s(s(elem!1))))) | (~r(s(s(z)), s(s(elem!1)))))),
% 3.53/3.71 inference(quant_inst,[status(thm)],[])).
% 3.53/3.71 tff(17351,plain,
% 3.53/3.71 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(elem!1))), s(z))) | (~r(s(s(elem!1)), s(s(s(elem!1))))) | (~r(s(s(z)), s(s(elem!1)))) | (~r(s(s(z)), s(s(s(elem!1)))))),
% 3.53/3.71 inference(modus_ponens,[status(thm)],[17350, 17349])).
% 3.53/3.71 tff(17352,plain,
% 3.53/3.71 ($false),
% 3.53/3.71 inference(unit_resolution,[status(thm)],[17351, 197, 17331, 12351, 17345, 17339])).
% 3.53/3.71 tff(17353,plain,((s(s(elem!1)) = s(s(s(elem!1)))) | (~b(s(s(s(elem!1))), z)) | (~r(z, s(z))) | (~r(z, s(s(elem!1)))) | (s(s(elem!1)) = s(s(z))) | b(s(s(elem!1)), s(s(s(elem!1))))), inference(lemma,lemma(discharge,[]))).
% 3.53/3.71 tff(17354,plain,
% 3.53/3.71 (b(s(s(elem!1)), s(s(s(elem!1))))),
% 3.53/3.71 inference(unit_resolution,[status(thm)],[17353, 17222, 323, 4458, 11, 121])).
% 3.53/3.71 tff(17355,plain,
% 3.53/3.71 (~r(s(s(elem!1)), s(z))),
% 3.53/3.71 inference(unit_resolution,[status(thm)],[8426, 17250, 323, 4458])).
% 3.53/3.71 tff(17356,plain,
% 3.53/3.71 (b(s(s(elem!1)), s(z))),
% 3.53/3.71 inference(unit_resolution,[status(thm)],[1912, 17355])).
% 3.53/3.71 tff(17357,plain,
% 3.53/3.71 (~b(s(s(z)), s(s(elem!1)))),
% 3.53/3.71 inference(unit_resolution,[status(thm)],[454, 17356, 15211, 17064])).
% 3.53/3.71 tff(17358,plain,
% 3.53/3.71 (r(s(s(z)), s(s(elem!1)))),
% 3.53/3.71 inference(unit_resolution,[status(thm)],[390, 17357, 44])).
% 3.53/3.71 tff(17359,plain,
% 3.53/3.71 (~b(s(s(elem!1)), s(s(z)))),
% 3.53/3.71 inference(unit_resolution,[status(thm)],[549, 17356, 15211, 17354, 17064])).
% 3.53/3.71 tff(17360,plain,
% 3.53/3.71 (r(s(s(elem!1)), s(s(z)))),
% 3.53/3.71 inference(unit_resolution,[status(thm)],[441, 17359, 11])).
% 3.53/3.71 tff(17361,plain,
% 3.53/3.71 (~b(s(s(z)), s(s(s(elem!1))))),
% 3.53/3.71 inference(unit_resolution,[status(thm)],[17337, 17328])).
% 3.53/3.71 tff(17362,plain,
% 3.53/3.71 (r(s(s(z)), s(s(s(elem!1))))),
% 3.53/3.71 inference(unit_resolution,[status(thm)],[279, 17361])).
% 3.53/3.71 tff(17363,plain,
% 3.53/3.71 (~r(s(s(s(elem!1))), s(s(elem!1)))),
% 3.53/3.71 inference(unit_resolution,[status(thm)],[4513, 17362, 17360, 17358])).
% 3.53/3.71 tff(17364,plain,
% 3.53/3.71 (b(s(s(s(elem!1))), s(s(elem!1)))),
% 3.53/3.71 inference(unit_resolution,[status(thm)],[889, 17363, 17223])).
% 3.53/3.71 tff(17365,plain,
% 3.53/3.71 (~b(s(z), s(s(s(elem!1))))),
% 3.53/3.71 inference(unit_resolution,[status(thm)],[6038, 17364, 15211, 17354])).
% 3.53/3.71 tff(17366,plain,
% 3.53/3.71 (r(s(z), s(s(s(elem!1))))),
% 3.53/3.71 inference(unit_resolution,[status(thm)],[116, 17365])).
% 3.53/3.71 tff(17367,plain,
% 3.53/3.71 (~b(s(s(s(s(elem!1)))), s(s(elem!1)))),
% 3.53/3.71 inference(unit_resolution,[status(thm)],[7907, 17366, 15211, 17356, 17364, 17354, 17329])).
% 3.53/3.71 tff(17368,plain,
% 3.53/3.71 (~(s(s(s(s(elem!1)))) = s(s(s(elem!1))))),
% 3.53/3.71 inference(unit_resolution,[status(thm)],[363, 17329])).
% 3.53/3.71 tff(17369,plain,
% 3.53/3.71 (~r(s(s(s(s(elem!1)))), s(z))),
% 3.53/3.71 inference(unit_resolution,[status(thm)],[2669, 17250, 323, 17247, 17368])).
% 3.53/3.71 tff(17370,plain,
% 3.53/3.71 (b(s(s(s(s(elem!1)))), s(z))),
% 3.53/3.71 inference(unit_resolution,[status(thm)],[661, 17369])).
% 3.53/3.71 tff(17371,plain,
% 3.53/3.71 (~b(s(s(s(s(elem!1)))), s(s(z)))),
% 3.53/3.71 inference(unit_resolution,[status(thm)],[17266, 166, 17248, 17064, 17370])).
% 3.53/3.71 tff(17372,plain,
% 3.53/3.71 (r(s(s(s(s(elem!1)))), s(s(z)))),
% 3.53/3.71 inference(unit_resolution,[status(thm)],[1299, 17371])).
% 3.53/3.71 tff(17373,plain,
% 3.53/3.71 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(elem!1)), s(s(z)))) | (~r(s(s(z)), s(s(s(elem!1))))) | (~r(s(s(s(s(elem!1)))), s(s(elem!1)))) | (~r(s(s(s(s(elem!1)))), s(s(z)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(elem!1)), s(s(z)))) | (~r(s(s(z)), s(s(s(elem!1))))) | (~r(s(s(s(s(elem!1)))), s(s(elem!1)))) | (~r(s(s(s(s(elem!1)))), s(s(z)))))),
% 3.53/3.71 inference(rewrite,[status(thm)],[])).
% 3.53/3.71 tff(17374,plain,
% 3.53/3.71 (((~r(s(s(z)), s(s(s(elem!1))))) | (~r(s(s(elem!1)), s(s(z)))) | (~r(s(s(s(s(elem!1)))), s(s(z)))) | (~r(s(s(s(s(elem!1)))), s(s(elem!1))))) <=> ((~r(s(s(elem!1)), s(s(z)))) | (~r(s(s(z)), s(s(s(elem!1))))) | (~r(s(s(s(s(elem!1)))), s(s(elem!1)))) | (~r(s(s(s(s(elem!1)))), s(s(z)))))),
% 3.53/3.71 inference(rewrite,[status(thm)],[])).
% 3.53/3.71 tff(17375,plain,
% 3.53/3.71 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(z)), s(s(s(elem!1))))) | (~r(s(s(elem!1)), s(s(z)))) | (~r(s(s(s(s(elem!1)))), s(s(z)))) | (~r(s(s(s(s(elem!1)))), s(s(elem!1)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(elem!1)), s(s(z)))) | (~r(s(s(z)), s(s(s(elem!1))))) | (~r(s(s(s(s(elem!1)))), s(s(elem!1)))) | (~r(s(s(s(s(elem!1)))), s(s(z))))))),
% 3.53/3.71 inference(monotonicity,[status(thm)],[17374])).
% 3.53/3.71 tff(17376,plain,
% 3.53/3.71 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(z)), s(s(s(elem!1))))) | (~r(s(s(elem!1)), s(s(z)))) | (~r(s(s(s(s(elem!1)))), s(s(z)))) | (~r(s(s(s(s(elem!1)))), s(s(elem!1)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(elem!1)), s(s(z)))) | (~r(s(s(z)), s(s(s(elem!1))))) | (~r(s(s(s(s(elem!1)))), s(s(elem!1)))) | (~r(s(s(s(s(elem!1)))), s(s(z)))))),
% 3.53/3.71 inference(transitivity,[status(thm)],[17375, 17373])).
% 3.53/3.71 tff(17377,plain,
% 3.53/3.71 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(z)), s(s(s(elem!1))))) | (~r(s(s(elem!1)), s(s(z)))) | (~r(s(s(s(s(elem!1)))), s(s(z)))) | (~r(s(s(s(s(elem!1)))), s(s(elem!1)))))),
% 3.53/3.71 inference(quant_inst,[status(thm)],[])).
% 3.53/3.71 tff(17378,plain,
% 3.53/3.71 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(elem!1)), s(s(z)))) | (~r(s(s(z)), s(s(s(elem!1))))) | (~r(s(s(s(s(elem!1)))), s(s(elem!1)))) | (~r(s(s(s(s(elem!1)))), s(s(z))))),
% 3.53/3.71 inference(modus_ponens,[status(thm)],[17377, 17376])).
% 3.53/3.71 tff(17379,plain,
% 3.53/3.71 (~r(s(s(s(s(elem!1)))), s(s(elem!1)))),
% 3.53/3.71 inference(unit_resolution,[status(thm)],[17378, 197, 17372, 17360, 17362])).
% 3.53/3.71 tff(17380,plain,
% 3.53/3.71 (s(s(s(s(elem!1)))) = s(s(elem!1))),
% 3.53/3.71 inference(unit_resolution,[status(thm)],[813, 17379, 17367])).
% 3.53/3.71 tff(17381,plain,
% 3.53/3.71 (s(s(s(elem!1))) = s(elem!1)),
% 3.53/3.71 inference(unit_resolution,[status(thm)],[1166, 17380])).
% 3.53/3.71 tff(17382,plain,
% 3.53/3.71 (b(z, s(s(s(elem!1)))) <=> b(z, s(elem!1))),
% 3.53/3.71 inference(monotonicity,[status(thm)],[17381])).
% 3.53/3.71 tff(17383,plain,
% 3.53/3.71 (b(z, s(elem!1))),
% 3.53/3.71 inference(modus_ponens,[status(thm)],[17252, 17382])).
% 3.53/3.71 tff(17384,plain,
% 3.53/3.71 (b(s(s(s(elem!1))), z) <=> b(s(elem!1), z)),
% 3.53/3.71 inference(monotonicity,[status(thm)],[17381])).
% 3.53/3.71 tff(17385,plain,
% 3.53/3.71 (b(s(elem!1), z)),
% 3.53/3.71 inference(modus_ponens,[status(thm)],[121, 17384])).
% 3.53/3.71 tff(17386,plain,
% 3.53/3.71 (~b(s(s(elem!1)), s(s(s(s(elem!1)))))),
% 3.53/3.71 inference(unit_resolution,[status(thm)],[1410, 17356, 15211, 17354, 17370])).
% 3.53/3.71 tff(17387,plain,
% 3.53/3.71 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(elem!1)), s(s(z)))) | (~r(s(s(z)), s(s(s(elem!1))))) | (~r(s(s(elem!1)), s(s(s(s(elem!1)))))) | (~r(s(s(s(s(elem!1)))), s(s(z)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(elem!1)), s(s(z)))) | (~r(s(s(z)), s(s(s(elem!1))))) | (~r(s(s(elem!1)), s(s(s(s(elem!1)))))) | (~r(s(s(s(s(elem!1)))), s(s(z)))))),
% 3.53/3.71 inference(rewrite,[status(thm)],[])).
% 3.53/3.71 tff(17388,plain,
% 3.53/3.71 (((~r(s(s(z)), s(s(s(elem!1))))) | (~r(s(s(s(s(elem!1)))), s(s(z)))) | (~r(s(s(elem!1)), s(s(z)))) | (~r(s(s(elem!1)), s(s(s(s(elem!1))))))) <=> ((~r(s(s(elem!1)), s(s(z)))) | (~r(s(s(z)), s(s(s(elem!1))))) | (~r(s(s(elem!1)), s(s(s(s(elem!1)))))) | (~r(s(s(s(s(elem!1)))), s(s(z)))))),
% 3.53/3.71 inference(rewrite,[status(thm)],[])).
% 3.53/3.71 tff(17389,plain,
% 3.53/3.71 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(z)), s(s(s(elem!1))))) | (~r(s(s(s(s(elem!1)))), s(s(z)))) | (~r(s(s(elem!1)), s(s(z)))) | (~r(s(s(elem!1)), s(s(s(s(elem!1)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(elem!1)), s(s(z)))) | (~r(s(s(z)), s(s(s(elem!1))))) | (~r(s(s(elem!1)), s(s(s(s(elem!1)))))) | (~r(s(s(s(s(elem!1)))), s(s(z))))))),
% 3.53/3.71 inference(monotonicity,[status(thm)],[17388])).
% 3.53/3.71 tff(17390,plain,
% 3.53/3.71 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(z)), s(s(s(elem!1))))) | (~r(s(s(s(s(elem!1)))), s(s(z)))) | (~r(s(s(elem!1)), s(s(z)))) | (~r(s(s(elem!1)), s(s(s(s(elem!1)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(elem!1)), s(s(z)))) | (~r(s(s(z)), s(s(s(elem!1))))) | (~r(s(s(elem!1)), s(s(s(s(elem!1)))))) | (~r(s(s(s(s(elem!1)))), s(s(z)))))),
% 3.53/3.71 inference(transitivity,[status(thm)],[17389, 17387])).
% 3.53/3.71 tff(17391,plain,
% 3.53/3.71 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(z)), s(s(s(elem!1))))) | (~r(s(s(s(s(elem!1)))), s(s(z)))) | (~r(s(s(elem!1)), s(s(z)))) | (~r(s(s(elem!1)), s(s(s(s(elem!1)))))))),
% 3.53/3.71 inference(quant_inst,[status(thm)],[])).
% 3.53/3.71 tff(17392,plain,
% 3.53/3.71 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(elem!1)), s(s(z)))) | (~r(s(s(z)), s(s(s(elem!1))))) | (~r(s(s(elem!1)), s(s(s(s(elem!1)))))) | (~r(s(s(s(s(elem!1)))), s(s(z))))),
% 3.53/3.71 inference(modus_ponens,[status(thm)],[17391, 17390])).
% 3.53/3.71 tff(17393,plain,
% 3.53/3.71 (~r(s(s(elem!1)), s(s(s(s(elem!1)))))),
% 3.53/3.71 inference(unit_resolution,[status(thm)],[17392, 197, 17372, 17360, 17362])).
% 3.53/3.71 tff(17394,plain,
% 3.53/3.71 (s(s(elem!1)) = s(s(s(s(elem!1))))),
% 3.53/3.71 inference(unit_resolution,[status(thm)],[827, 17393, 17386])).
% 3.53/3.71 tff(17395,plain,
% 3.53/3.71 (~(s(s(s(z))) = s(elem!1))),
% 3.53/3.71 inference(unit_resolution,[status(thm)],[2841, 17381, 17394])).
% 3.53/3.71 tff(17396,plain,
% 3.53/3.71 (r(s(s(z)), s(s(s(elem!1)))) <=> r(s(s(z)), s(elem!1))),
% 3.53/3.71 inference(monotonicity,[status(thm)],[17381])).
% 3.53/3.71 tff(17397,plain,
% 3.53/3.71 (r(s(s(z)), s(elem!1))),
% 3.53/3.71 inference(modus_ponens,[status(thm)],[17362, 17396])).
% 3.53/3.71 tff(17398,plain,
% 3.53/3.71 (r(s(s(s(elem!1))), s(s(z))) <=> r(s(elem!1), s(s(z)))),
% 3.53/3.71 inference(monotonicity,[status(thm)],[17381])).
% 3.53/3.71 tff(17399,plain,
% 3.53/3.71 (~b(s(s(s(elem!1))), s(s(z)))),
% 3.53/3.71 inference(unit_resolution,[status(thm)],[10460, 17328, 121])).
% 3.53/3.71 tff(17400,plain,
% 3.53/3.71 (r(s(s(s(elem!1))), s(s(z)))),
% 3.53/3.71 inference(unit_resolution,[status(thm)],[218, 17399])).
% 3.53/3.71 tff(17401,plain,
% 3.53/3.71 (r(s(elem!1), s(s(z)))),
% 3.53/3.71 inference(modus_ponens,[status(thm)],[17400, 17398])).
% 3.53/3.71 tff(17402,assumption,(~(s(s(s(z))) = s(elem!1))), introduced(assumption)).
% 3.53/3.71 tff(17403,plain,
% 3.53/3.71 (r(s(s(s(z))), s(elem!1))),
% 3.53/3.71 inference(unit_resolution,[status(thm)],[2845, 79, 17402, 2835])).
% 3.53/3.71 tff(17404,plain,
% 3.53/3.71 (~b(s(s(s(z))), s(s(z)))),
% 3.53/3.71 inference(unit_resolution,[status(thm)],[12562, 166, 2747, 2814, 122, 1699])).
% 3.53/3.71 tff(17405,plain,
% 3.53/3.71 (r(s(s(s(z))), s(s(z)))),
% 3.53/3.71 inference(unit_resolution,[status(thm)],[1010, 17404])).
% 3.53/3.71 tff(17406,assumption,(r(s(s(z)), s(elem!1))), introduced(assumption)).
% 3.53/3.71 tff(17407,plain,
% 3.53/3.71 ($false),
% 3.53/3.71 inference(unit_resolution,[status(thm)],[12571, 197, 1247, 17406, 17405, 17403])).
% 3.53/3.71 tff(17408,plain,((~b(s(s(s(z))), z)) | (~r(s(elem!1), s(s(z)))) | (~r(s(s(z)), s(elem!1))) | (s(s(s(z))) = s(elem!1)) | (~b(s(elem!1), z)) | (~b(z, s(elem!1))) | (~b(s(s(z)), z))), inference(lemma,lemma(discharge,[]))).
% 3.53/3.71 tff(17409,plain,
% 3.53/3.71 (~b(s(s(s(z))), z)),
% 3.53/3.71 inference(unit_resolution,[status(thm)],[17408, 17401, 17397, 17395, 17385, 17383, 17328])).
% 3.53/3.71 tff(17410,plain,
% 3.53/3.71 (r(s(s(s(z))), z)),
% 3.53/3.71 inference(unit_resolution,[status(thm)],[1713, 17409])).
% 3.53/3.71 tff(17411,plain,
% 3.53/3.71 (r(s(s(elem!1)), z) <=> r(s(s(s(s(elem!1)))), z)),
% 3.53/3.71 inference(monotonicity,[status(thm)],[17394])).
% 3.53/3.71 tff(17412,plain,
% 3.53/3.71 (~b(s(s(elem!1)), z)),
% 3.53/3.71 inference(unit_resolution,[status(thm)],[600, 17252, 121, 17354])).
% 3.53/3.71 tff(17413,plain,
% 3.53/3.71 (r(s(s(elem!1)), z)),
% 3.53/3.71 inference(unit_resolution,[status(thm)],[608, 17412])).
% 3.53/3.71 tff(17414,plain,
% 3.53/3.71 (r(s(s(s(s(elem!1)))), z)),
% 3.53/3.71 inference(modus_ponens,[status(thm)],[17413, 17411])).
% 3.53/3.71 tff(17415,plain,
% 3.53/3.71 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(z))) | (~r(s(s(s(z))), z)) | (~r(s(s(s(s(elem!1)))), z)) | (~r(s(s(s(s(elem!1)))), s(s(s(z))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, s(z))) | (~r(s(s(s(z))), z)) | (~r(s(s(s(s(elem!1)))), z)) | (~r(s(s(s(s(elem!1)))), s(s(s(z))))))),
% 3.53/3.71 inference(rewrite,[status(thm)],[])).
% 3.53/3.71 tff(17416,plain,
% 3.53/3.71 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(z))) | (~r(s(s(s(z))), z)) | (~r(s(s(s(s(elem!1)))), z)) | (~r(s(s(s(s(elem!1)))), s(s(s(z))))))),
% 3.53/3.71 inference(quant_inst,[status(thm)],[])).
% 3.53/3.71 tff(17417,plain,
% 3.53/3.71 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, s(z))) | (~r(s(s(s(z))), z)) | (~r(s(s(s(s(elem!1)))), z)) | (~r(s(s(s(s(elem!1)))), s(s(s(z)))))),
% 3.53/3.71 inference(modus_ponens,[status(thm)],[17416, 17415])).
% 3.53/3.71 tff(17418,plain,
% 3.53/3.71 (~r(s(s(s(s(elem!1)))), s(s(s(z))))),
% 3.53/3.71 inference(unit_resolution,[status(thm)],[17417, 197, 323, 17414, 17410])).
% 3.53/3.71 tff(17419,plain,
% 3.53/3.71 (((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((s(s(s(s(elem!1)))) = s(s(s(z)))) | b(s(s(s(s(elem!1)))), s(s(s(z)))) | r(s(s(s(s(elem!1)))), s(s(s(z)))))) <=> ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (s(s(s(s(elem!1)))) = s(s(s(z)))) | b(s(s(s(s(elem!1)))), s(s(s(z)))) | r(s(s(s(s(elem!1)))), s(s(s(z)))))),
% 3.53/3.72 inference(rewrite,[status(thm)],[])).
% 3.53/3.72 tff(17420,plain,
% 3.53/3.72 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((s(s(s(s(elem!1)))) = s(s(s(z)))) | b(s(s(s(s(elem!1)))), s(s(s(z)))) | r(s(s(s(s(elem!1)))), s(s(s(z)))))),
% 3.53/3.72 inference(quant_inst,[status(thm)],[])).
% 3.53/3.72 tff(17421,plain,
% 3.53/3.72 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (s(s(s(s(elem!1)))) = s(s(s(z)))) | b(s(s(s(s(elem!1)))), s(s(s(z)))) | r(s(s(s(s(elem!1)))), s(s(s(z))))),
% 3.53/3.72 inference(modus_ponens,[status(thm)],[17420, 17419])).
% 3.53/3.72 tff(17422,plain,
% 3.53/3.72 (b(s(s(s(s(elem!1)))), s(s(s(z))))),
% 3.53/3.72 inference(unit_resolution,[status(thm)],[17421, 79, 5112, 17418])).
% 3.53/3.72 tff(17423,plain,
% 3.53/3.72 (~r(s(s(s(z))), s(z))),
% 3.53/3.72 inference(unit_resolution,[status(thm)],[12220, 197, 323, 17250, 17410])).
% 3.53/3.72 tff(17424,plain,
% 3.53/3.72 (b(s(s(s(z))), s(z))),
% 3.53/3.72 inference(unit_resolution,[status(thm)],[1763, 17423])).
% 3.53/3.72 tff(17425,plain,
% 3.53/3.72 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(z)))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(z)), s(z))) | (~b(s(s(s(s(elem!1)))), s(z))) | (~b(s(s(s(s(elem!1)))), s(s(s(z))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), s(s(z)))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(z)), s(z))) | (~b(s(s(s(s(elem!1)))), s(z))) | (~b(s(s(s(s(elem!1)))), s(s(s(z))))))),
% 3.53/3.72 inference(rewrite,[status(thm)],[])).
% 3.53/3.72 tff(17426,plain,
% 3.53/3.72 (((~b(s(s(z)), s(z))) | (~b(s(s(s(s(elem!1)))), s(z))) | (~b(s(z), s(s(z)))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(s(elem!1)))), s(z))) | (~b(s(s(s(s(elem!1)))), s(s(s(z)))))) <=> ((~b(s(z), s(s(z)))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(z)), s(z))) | (~b(s(s(s(s(elem!1)))), s(z))) | (~b(s(s(s(s(elem!1)))), s(s(s(z))))))),
% 3.53/3.72 inference(rewrite,[status(thm)],[])).
% 3.53/3.72 tff(17427,plain,
% 3.53/3.72 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), s(z))) | (~b(s(s(s(s(elem!1)))), s(z))) | (~b(s(z), s(s(z)))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(s(elem!1)))), s(z))) | (~b(s(s(s(s(elem!1)))), s(s(s(z))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(z)))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(z)), s(z))) | (~b(s(s(s(s(elem!1)))), s(z))) | (~b(s(s(s(s(elem!1)))), s(s(s(z)))))))),
% 3.53/3.72 inference(monotonicity,[status(thm)],[17426])).
% 3.53/3.72 tff(17428,plain,
% 3.53/3.72 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), s(z))) | (~b(s(s(s(s(elem!1)))), s(z))) | (~b(s(z), s(s(z)))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(s(elem!1)))), s(z))) | (~b(s(s(s(s(elem!1)))), s(s(s(z))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), s(s(z)))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(z)), s(z))) | (~b(s(s(s(s(elem!1)))), s(z))) | (~b(s(s(s(s(elem!1)))), s(s(s(z))))))),
% 3.53/3.72 inference(transitivity,[status(thm)],[17427, 17425])).
% 3.53/3.72 tff(17429,plain,
% 3.53/3.72 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), s(z))) | (~b(s(s(s(s(elem!1)))), s(z))) | (~b(s(z), s(s(z)))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(s(elem!1)))), s(z))) | (~b(s(s(s(s(elem!1)))), s(s(s(z))))))),
% 3.53/3.72 inference(quant_inst,[status(thm)],[])).
% 3.53/3.72 tff(17430,plain,
% 3.53/3.72 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), s(s(z)))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(z)), s(z))) | (~b(s(s(s(s(elem!1)))), s(z))) | (~b(s(s(s(s(elem!1)))), s(s(s(z)))))),
% 3.53/3.72 inference(modus_ponens,[status(thm)],[17429, 17428])).
% 3.53/3.72 tff(17431,plain,
% 3.53/3.72 ($false),
% 3.53/3.72 inference(unit_resolution,[status(thm)],[17430, 166, 17248, 17064, 17370, 17424, 17422])).
% 3.53/3.72 tff(17432,plain,((~r(z, s(z))) | (~b(s(s(s(elem!1))), z)) | (s(s(elem!1)) = s(s(z))) | b(z, s(s(elem!1)))), inference(lemma,lemma(discharge,[]))).
% 3.53/3.72 tff(17433,plain,
% 3.53/3.72 (~r(z, s(z))),
% 3.53/3.72 inference(unit_resolution,[status(thm)],[17432, 1790, 11, 121])).
% 3.53/3.72 tff(17434,plain,
% 3.53/3.72 (b(z, s(z))),
% 3.53/3.72 inference(unit_resolution,[status(thm)],[321, 17433])).
% 3.53/3.72 tff(17435,plain,
% 3.53/3.72 (~b(s(z), s(s(z)))),
% 3.53/3.72 inference(unit_resolution,[status(thm)],[14336, 17434, 17064])).
% 3.53/3.72 tff(17436,plain,
% 3.53/3.72 (r(s(z), s(s(z)))),
% 3.53/3.72 inference(unit_resolution,[status(thm)],[427, 17435])).
% 3.53/3.72 tff(17437,plain,
% 3.53/3.72 (~r(s(s(s(elem!1))), s(z))),
% 3.53/3.72 inference(unit_resolution,[status(thm)],[17124, 17434, 15211])).
% 3.53/3.72 tff(17438,plain,
% 3.53/3.72 (b(s(s(s(elem!1))), s(z))),
% 3.53/3.72 inference(unit_resolution,[status(thm)],[1849, 17437])).
% 3.53/3.72 tff(17439,plain,
% 3.53/3.72 (~b(s(z), s(s(s(elem!1))))),
% 3.53/3.72 inference(unit_resolution,[status(thm)],[12629, 17438, 17064, 17434])).
% 3.53/3.72 tff(17440,plain,
% 3.53/3.72 (r(s(z), s(s(s(elem!1))))),
% 3.53/3.72 inference(unit_resolution,[status(thm)],[116, 17439])).
% 3.53/3.72 tff(17441,plain,
% 3.53/3.72 (~b(s(z), z)),
% 3.53/3.72 inference(unit_resolution,[status(thm)],[14305, 17434, 17064])).
% 3.53/3.72 tff(17442,plain,
% 3.53/3.72 (r(s(z), z)),
% 3.53/3.72 inference(unit_resolution,[status(thm)],[230, 17441])).
% 3.53/3.72 tff(17443,plain,
% 3.53/3.72 (~r(s(s(z)), z)),
% 3.53/3.72 inference(unit_resolution,[status(thm)],[2359, 17436, 4458, 17442])).
% 3.53/3.72 tff(17444,plain,
% 3.53/3.72 (b(s(s(z)), z)),
% 3.53/3.72 inference(unit_resolution,[status(thm)],[186, 17443])).
% 3.53/3.72 tff(17445,plain,
% 3.53/3.72 ($false),
% 3.53/3.72 inference(unit_resolution,[status(thm)],[10477, 17444, 17440, 121, 17436])).
% 3.53/3.72 tff(17446,plain,(b(z, s(s(elem!1))) | (~b(s(s(s(elem!1))), z)) | (s(s(elem!1)) = s(s(z)))), inference(lemma,lemma(discharge,[]))).
% 3.53/3.72 tff(17447,plain,
% 3.53/3.72 (b(z, s(s(elem!1)))),
% 3.53/3.72 inference(unit_resolution,[status(thm)],[17446, 11, 121])).
% 3.53/3.72 tff(17448,plain,
% 3.53/3.72 (~(s(s(s(elem!1))) = s(s(elem!1)))),
% 3.53/3.72 inference(unit_resolution,[status(thm)],[50, 17129])).
% 3.53/3.72 tff(17449,plain,
% 3.53/3.72 (~b(s(s(z)), s(s(elem!1)))),
% 3.53/3.72 inference(unit_resolution,[status(thm)],[454, 17131, 15211, 17064])).
% 3.53/3.72 tff(17450,plain,
% 3.53/3.72 (r(s(s(z)), s(s(elem!1)))),
% 3.53/3.72 inference(unit_resolution,[status(thm)],[390, 17449, 44])).
% 3.53/3.72 tff(17451,plain,
% 3.53/3.72 (~r(s(s(s(elem!1))), z)),
% 3.53/3.72 inference(unit_resolution,[status(thm)],[577, 197, 350, 17093, 119])).
% 3.53/3.72 tff(17452,plain,
% 3.53/3.72 (b(s(s(s(elem!1))), z)),
% 3.53/3.72 inference(unit_resolution,[status(thm)],[94, 17451])).
% 3.53/3.72 tff(17453,plain,
% 3.53/3.72 (~r(z, s(s(s(elem!1))))),
% 3.53/3.72 inference(unit_resolution,[status(thm)],[587, 119, 350, 17093])).
% 3.53/3.72 tff(17454,plain,
% 3.53/3.72 (b(z, s(s(s(elem!1))))),
% 3.53/3.72 inference(unit_resolution,[status(thm)],[261, 17453])).
% 3.53/3.72 tff(17455,plain,
% 3.53/3.72 (~b(s(z), s(s(z)))),
% 3.53/3.72 inference(unit_resolution,[status(thm)],[17325, 17454, 376, 866, 17452, 10451, 350, 45])).
% 3.53/3.72 tff(17456,plain,
% 3.53/3.72 (r(s(z), s(s(z)))),
% 3.53/3.72 inference(unit_resolution,[status(thm)],[427, 17455])).
% 3.53/3.72 tff(17457,plain,
% 3.53/3.72 (~r(s(s(s(elem!1))), s(s(z)))),
% 3.53/3.72 inference(unit_resolution,[status(thm)],[874, 17456, 350, 866])).
% 3.53/3.72 tff(17458,plain,
% 3.53/3.72 (b(s(s(s(elem!1))), s(s(z)))),
% 3.53/3.72 inference(unit_resolution,[status(thm)],[218, 17457])).
% 3.53/3.72 tff(17459,plain,
% 3.53/3.72 (~b(s(z), z)),
% 3.53/3.72 inference(unit_resolution,[status(thm)],[12875, 17452, 10451, 17073, 17458])).
% 3.53/3.72 tff(17460,plain,
% 3.53/3.72 (r(s(z), z)),
% 3.53/3.72 inference(unit_resolution,[status(thm)],[230, 17459])).
% 3.53/3.72 tff(17461,plain,
% 3.53/3.72 ($false),
% 3.53/3.72 inference(unit_resolution,[status(thm)],[12132, 197, 17456, 17093, 17460, 866])).
% 3.53/3.72 tff(17462,plain,((~r(s(z), s(s(s(elem!1))))) | (~r(s(s(z)), z)) | (~b(z, s(s(z)))) | (~r(s(s(s(elem!1))), s(z))) | (~b(s(z), s(s(elem!1)))) | (s(s(elem!1)) = s(s(s(elem!1))))), inference(lemma,lemma(discharge,[]))).
% 3.53/3.72 tff(17463,plain,
% 3.53/3.72 ((~r(s(z), s(s(s(elem!1))))) | (~r(s(s(z)), z)) | (~r(s(s(s(elem!1))), s(z))) | (~b(s(z), s(s(elem!1)))) | (s(s(elem!1)) = s(s(s(elem!1))))),
% 3.53/3.72 inference(unit_resolution,[status(thm)],[17462, 10450])).
% 3.53/3.72 tff(17464,plain,
% 3.53/3.72 (~r(s(s(z)), z)),
% 3.53/3.72 inference(unit_resolution,[status(thm)],[17463, 117, 15211, 350, 17129])).
% 3.53/3.72 tff(17465,plain,
% 3.53/3.72 (b(s(s(z)), z)),
% 3.53/3.72 inference(unit_resolution,[status(thm)],[186, 17464])).
% 3.53/3.72 tff(17466,plain,
% 3.53/3.72 (~b(s(s(z)), s(s(s(elem!1))))),
% 3.53/3.72 inference(unit_resolution,[status(thm)],[17337, 17465])).
% 3.53/3.72 tff(17467,plain,
% 3.53/3.72 (r(s(s(z)), s(s(s(elem!1))))),
% 3.53/3.72 inference(unit_resolution,[status(thm)],[279, 17466])).
% 3.53/3.72 tff(17468,plain,
% 3.53/3.72 (~b(s(s(elem!1)), s(s(z)))),
% 3.53/3.72 inference(unit_resolution,[status(thm)],[4405, 166, 17185, 17131, 17064])).
% 3.53/3.72 tff(17469,plain,
% 3.53/3.72 (r(s(s(elem!1)), s(s(z)))),
% 3.53/3.72 inference(unit_resolution,[status(thm)],[441, 17468, 11])).
% 3.53/3.72 tff(17470,plain,
% 3.53/3.72 (~r(s(s(s(elem!1))), s(s(elem!1)))),
% 3.53/3.72 inference(unit_resolution,[status(thm)],[4513, 17469, 17467, 17450])).
% 3.53/3.72 tff(17471,plain,
% 3.53/3.72 (b(s(s(s(elem!1))), s(s(elem!1)))),
% 3.53/3.72 inference(unit_resolution,[status(thm)],[889, 17470, 17448])).
% 3.53/3.72 tff(17472,plain,
% 3.53/3.72 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(z, s(s(z)))) | (~b(z, s(s(s(elem!1))))) | (~b(z, s(s(elem!1)))) | (~b(s(s(elem!1)), s(z))) | (~b(s(z), s(s(z)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(z, s(s(z)))) | (~b(z, s(s(s(elem!1))))) | (~b(z, s(s(elem!1)))) | (~b(s(s(elem!1)), s(z))) | (~b(s(z), s(s(z)))))),
% 3.53/3.72 inference(rewrite,[status(thm)],[])).
% 3.53/3.72 tff(17473,plain,
% 3.53/3.72 (((~b(s(z), s(s(z)))) | (~b(z, s(s(z)))) | (~b(s(s(elem!1)), s(z))) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(z, s(s(elem!1)))) | (~b(z, s(s(s(elem!1)))))) <=> ((~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(z, s(s(z)))) | (~b(z, s(s(s(elem!1))))) | (~b(z, s(s(elem!1)))) | (~b(s(s(elem!1)), s(z))) | (~b(s(z), s(s(z)))))),
% 3.53/3.72 inference(rewrite,[status(thm)],[])).
% 3.53/3.72 tff(17474,plain,
% 3.53/3.72 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(z)))) | (~b(z, s(s(z)))) | (~b(s(s(elem!1)), s(z))) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(z, s(s(elem!1)))) | (~b(z, s(s(s(elem!1))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(z, s(s(z)))) | (~b(z, s(s(s(elem!1))))) | (~b(z, s(s(elem!1)))) | (~b(s(s(elem!1)), s(z))) | (~b(s(z), s(s(z))))))),
% 3.53/3.72 inference(monotonicity,[status(thm)],[17473])).
% 3.53/3.72 tff(17475,plain,
% 3.53/3.72 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(z)))) | (~b(z, s(s(z)))) | (~b(s(s(elem!1)), s(z))) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(z, s(s(elem!1)))) | (~b(z, s(s(s(elem!1))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(z, s(s(z)))) | (~b(z, s(s(s(elem!1))))) | (~b(z, s(s(elem!1)))) | (~b(s(s(elem!1)), s(z))) | (~b(s(z), s(s(z)))))),
% 3.53/3.72 inference(transitivity,[status(thm)],[17474, 17472])).
% 3.53/3.72 tff(17476,plain,
% 3.53/3.72 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(z)))) | (~b(z, s(s(z)))) | (~b(s(s(elem!1)), s(z))) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(z, s(s(elem!1)))) | (~b(z, s(s(s(elem!1))))))),
% 3.53/3.72 inference(quant_inst,[status(thm)],[])).
% 3.53/3.72 tff(17477,plain,
% 3.53/3.72 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(z, s(s(z)))) | (~b(z, s(s(s(elem!1))))) | (~b(z, s(s(elem!1)))) | (~b(s(s(elem!1)), s(z))) | (~b(s(z), s(s(z))))),
% 3.53/3.72 inference(modus_ponens,[status(thm)],[17476, 17475])).
% 3.53/3.72 tff(17478,plain,
% 3.53/3.72 ($false),
% 3.53/3.72 inference(unit_resolution,[status(thm)],[17477, 166, 17471, 17128, 17447, 17185, 10450, 17131])).
% 3.53/3.72 tff(17479,plain,(b(s(z), s(s(s(elem!1)))) | (s(s(elem!1)) = s(s(z))) | (~b(s(s(s(elem!1))), z)) | (~r(s(s(s(elem!1))), s(z)))), inference(lemma,lemma(discharge,[]))).
% 3.53/3.72 tff(17480,plain,
% 3.53/3.72 (b(s(z), s(s(s(elem!1))))),
% 3.53/3.72 inference(unit_resolution,[status(thm)],[17479, 3953, 121, 11])).
% 3.53/3.72 tff(17481,plain,
% 3.53/3.72 (s(s(elem!1)) = s(s(s(elem!1)))),
% 3.53/3.72 inference(unit_resolution,[status(thm)],[10127, 10521, 17123, 350, 17126, 121, 17128])).
% 3.53/3.72 tff(17482,plain,
% 3.53/3.72 (r(s(s(z)), s(s(elem!1)))),
% 3.53/3.72 inference(unit_resolution,[status(thm)],[11731, 4568, 17123])).
% 3.53/3.72 tff(17483,plain,
% 3.53/3.72 (r(s(s(z)), s(s(s(elem!1))))),
% 3.53/3.72 inference(unit_resolution,[status(thm)],[338, 17481, 17482])).
% 3.53/3.72 tff(17484,plain,
% 3.53/3.72 (r(s(s(elem!1)), s(s(z))) <=> r(s(s(s(elem!1))), s(s(z)))),
% 3.53/3.72 inference(monotonicity,[status(thm)],[17481])).
% 3.53/3.72 tff(17485,plain,
% 3.53/3.72 (r(s(s(s(elem!1))), s(s(z))) <=> r(s(s(elem!1)), s(s(z)))),
% 3.53/3.72 inference(symmetry,[status(thm)],[17484])).
% 3.53/3.72 tff(17486,plain,
% 3.53/3.72 (s(s(s(elem!1))) = s(elem!1)),
% 3.53/3.72 inference(unit_resolution,[status(thm)],[2594, 17481])).
% 3.53/3.72 tff(17487,plain,
% 3.53/3.72 (s(elem!1) = s(s(s(elem!1)))),
% 3.53/3.72 inference(symmetry,[status(thm)],[17486])).
% 3.53/3.72 tff(17488,plain,
% 3.53/3.72 ((s(elem!1) = s(s(z))) <=> (s(s(s(elem!1))) = s(s(z)))),
% 3.53/3.72 inference(monotonicity,[status(thm)],[17487])).
% 3.53/3.72 tff(17489,plain,
% 3.53/3.72 ((s(elem!1) = s(s(z))) <=> (s(s(z)) = s(s(s(elem!1))))),
% 3.53/3.72 inference(transitivity,[status(thm)],[17488, 487])).
% 3.53/3.72 tff(17490,plain,
% 3.53/3.72 ((s(s(z)) = s(s(s(elem!1)))) <=> (s(elem!1) = s(s(z)))),
% 3.53/3.72 inference(symmetry,[status(thm)],[17489])).
% 3.53/3.72 tff(17491,plain,
% 3.53/3.72 ((~(s(s(z)) = s(s(s(elem!1))))) <=> (~(s(elem!1) = s(s(z))))),
% 3.53/3.72 inference(monotonicity,[status(thm)],[17490])).
% 3.53/3.72 tff(17492,plain,
% 3.53/3.72 (~(s(elem!1) = s(s(z)))),
% 3.53/3.72 inference(modus_ponens,[status(thm)],[209, 17491])).
% 3.53/3.72 tff(17493,plain,
% 3.53/3.72 (b(z, s(elem!1)) <=> b(z, s(s(s(elem!1))))),
% 3.53/3.72 inference(monotonicity,[status(thm)],[17487])).
% 3.53/3.72 tff(17494,plain,
% 3.53/3.72 (b(z, s(s(s(elem!1)))) <=> b(z, s(elem!1))),
% 3.53/3.72 inference(symmetry,[status(thm)],[17493])).
% 3.53/3.72 tff(17495,plain,
% 3.53/3.72 (b(z, s(elem!1))),
% 3.53/3.72 inference(modus_ponens,[status(thm)],[17128, 17494])).
% 3.53/3.72 tff(17496,plain,
% 3.53/3.72 (b(s(z), elem!1)),
% 3.53/3.72 inference(unit_resolution,[status(thm)],[9915, 17486, 15211])).
% 3.53/3.72 tff(17497,plain,
% 3.53/3.72 (inj_0(s(elem!1)) = inj_0(s(s(s(elem!1))))),
% 3.53/3.72 inference(monotonicity,[status(thm)],[17487])).
% 3.53/3.72 tff(17498,plain,
% 3.53/3.72 (elem!1 = s(s(s(elem!1)))),
% 3.53/3.72 inference(transitivity,[status(thm)],[1170, 17497, 104, 17481])).
% 3.53/3.72 tff(17499,plain,
% 3.53/3.72 (b(z, elem!1) <=> b(z, s(s(s(elem!1))))),
% 3.53/3.72 inference(monotonicity,[status(thm)],[17498])).
% 3.53/3.72 tff(17500,plain,
% 3.53/3.72 (b(z, s(s(s(elem!1)))) <=> b(z, elem!1)),
% 3.53/3.72 inference(symmetry,[status(thm)],[17499])).
% 3.53/3.72 tff(17501,plain,
% 3.53/3.72 (b(z, elem!1)),
% 3.53/3.72 inference(modus_ponens,[status(thm)],[17128, 17500])).
% 3.53/3.72 tff(17502,plain,
% 3.53/3.72 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(z)))) | (~b(s(z), elem!1)) | (~b(z, elem!1)) | (~b(z, s(elem!1))) | (~b(s(s(z)), s(z))) | (~b(s(elem!1), s(s(z)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(s(z)))) | (~b(s(z), elem!1)) | (~b(z, elem!1)) | (~b(z, s(elem!1))) | (~b(s(s(z)), s(z))) | (~b(s(elem!1), s(s(z)))))),
% 3.53/3.72 inference(rewrite,[status(thm)],[])).
% 3.53/3.72 tff(17503,plain,
% 3.53/3.72 (((~b(s(z), elem!1)) | (~b(z, elem!1)) | (~b(s(s(z)), s(z))) | (~b(s(elem!1), s(s(z)))) | (~b(z, s(s(z)))) | (~b(z, s(elem!1)))) <=> ((~b(z, s(s(z)))) | (~b(s(z), elem!1)) | (~b(z, elem!1)) | (~b(z, s(elem!1))) | (~b(s(s(z)), s(z))) | (~b(s(elem!1), s(s(z)))))),
% 3.53/3.72 inference(rewrite,[status(thm)],[])).
% 3.53/3.72 tff(17504,plain,
% 3.53/3.72 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), elem!1)) | (~b(z, elem!1)) | (~b(s(s(z)), s(z))) | (~b(s(elem!1), s(s(z)))) | (~b(z, s(s(z)))) | (~b(z, s(elem!1))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(z)))) | (~b(s(z), elem!1)) | (~b(z, elem!1)) | (~b(z, s(elem!1))) | (~b(s(s(z)), s(z))) | (~b(s(elem!1), s(s(z))))))),
% 3.53/3.72 inference(monotonicity,[status(thm)],[17503])).
% 3.53/3.72 tff(17505,plain,
% 3.53/3.72 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), elem!1)) | (~b(z, elem!1)) | (~b(s(s(z)), s(z))) | (~b(s(elem!1), s(s(z)))) | (~b(z, s(s(z)))) | (~b(z, s(elem!1))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(s(z)))) | (~b(s(z), elem!1)) | (~b(z, elem!1)) | (~b(z, s(elem!1))) | (~b(s(s(z)), s(z))) | (~b(s(elem!1), s(s(z)))))),
% 3.53/3.72 inference(transitivity,[status(thm)],[17504, 17502])).
% 3.53/3.72 tff(17506,plain,
% 3.53/3.72 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), elem!1)) | (~b(z, elem!1)) | (~b(s(s(z)), s(z))) | (~b(s(elem!1), s(s(z)))) | (~b(z, s(s(z)))) | (~b(z, s(elem!1))))),
% 3.53/3.72 inference(quant_inst,[status(thm)],[])).
% 3.53/3.72 tff(17507,plain,
% 3.53/3.72 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(s(z)))) | (~b(s(z), elem!1)) | (~b(z, elem!1)) | (~b(z, s(elem!1))) | (~b(s(s(z)), s(z))) | (~b(s(elem!1), s(s(z))))),
% 3.53/3.72 inference(modus_ponens,[status(thm)],[17506, 17505])).
% 3.53/3.72 tff(17508,plain,
% 3.53/3.72 ($false),
% 3.53/3.72 inference(unit_resolution,[status(thm)],[17507, 166, 2517, 1642, 10451, 642, 156, 2814])).
% 3.53/3.72 tff(17509,plain,((~b(s(s(z)), s(z))) | (~b(z, elem!1)) | (~b(s(elem!1), s(s(z)))) | (~b(z, s(s(z)))) | (~b(s(z), elem!1)) | (~b(z, s(elem!1)))), inference(lemma,lemma(discharge,[]))).
% 3.53/3.72 tff(17510,plain,
% 3.53/3.72 ((~b(s(s(z)), s(z))) | (~b(z, elem!1)) | (~b(s(elem!1), s(s(z)))) | (~b(s(z), elem!1)) | (~b(z, s(elem!1)))),
% 3.53/3.72 inference(unit_resolution,[status(thm)],[17509, 10450])).
% 3.53/3.72 tff(17511,plain,
% 3.53/3.72 (~b(s(elem!1), s(s(z)))),
% 3.53/3.72 inference(unit_resolution,[status(thm)],[17510, 17501, 17064, 17496, 17495])).
% 3.53/3.72 tff(17512,plain,
% 3.53/3.72 (r(s(elem!1), s(s(z)))),
% 3.53/3.72 inference(unit_resolution,[status(thm)],[1260, 17511, 17492])).
% 3.53/3.72 tff(17513,plain,
% 3.53/3.72 (r(s(s(s(elem!1))), s(s(z)))),
% 3.53/3.72 inference(unit_resolution,[status(thm)],[1250, 17512, 17486])).
% 3.53/3.72 tff(17514,plain,
% 3.53/3.72 (r(s(s(elem!1)), s(s(z)))),
% 3.53/3.72 inference(modus_ponens,[status(thm)],[17513, 17485])).
% 3.53/3.72 tff(17515,plain,
% 3.53/3.72 (~r(s(z), s(s(z)))),
% 3.53/3.72 inference(unit_resolution,[status(thm)],[7518, 17514, 10521, 17482])).
% 3.53/3.72 tff(17516,plain,
% 3.53/3.72 (b(s(z), s(s(z)))),
% 3.53/3.72 inference(unit_resolution,[status(thm)],[427, 17515])).
% 3.53/3.72 tff(17517,plain,
% 3.53/3.72 (~b(s(s(s(z))), s(s(s(elem!1))))),
% 3.53/3.72 inference(unit_resolution,[status(thm)],[12175, 166, 17128, 121, 1699])).
% 3.53/3.72 tff(17518,plain,
% 3.53/3.72 (~b(s(s(s(z))), elem!1)),
% 3.53/3.72 inference(unit_resolution,[status(thm)],[4078, 17517, 4031])).
% 3.53/3.72 tff(17519,plain,
% 3.53/3.72 (r(s(s(s(z))), elem!1)),
% 3.53/3.72 inference(unit_resolution,[status(thm)],[2826, 17518, 4027])).
% 3.53/3.72 tff(17520,plain,
% 3.53/3.72 (~r(s(s(z)), s(s(s(z))))),
% 3.53/3.72 inference(unit_resolution,[status(thm)],[8084, 17519, 350, 281, 334])).
% 3.53/3.72 tff(17521,plain,
% 3.53/3.72 (b(s(s(z)), s(s(s(z))))),
% 3.53/3.72 inference(unit_resolution,[status(thm)],[1730, 17520])).
% 3.53/3.72 tff(17522,plain,
% 3.53/3.72 (~b(s(s(s(z))), s(s(z)))),
% 3.53/3.72 inference(unit_resolution,[status(thm)],[16538, 166, 10451, 986, 1699])).
% 3.53/3.72 tff(17523,plain,
% 3.53/3.72 (r(s(s(s(z))), s(s(z)))),
% 3.53/3.72 inference(unit_resolution,[status(thm)],[1010, 17522])).
% 3.53/3.72 tff(17524,plain,
% 3.53/3.72 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(z)))) | (~b(z, s(s(s(elem!1))))) | (~b(s(s(s(z))), z)) | (~b(z, s(s(s(z))))) | (~b(s(s(z)), s(s(s(z))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(s(z)))) | (~b(z, s(s(s(elem!1))))) | (~b(s(s(s(z))), z)) | (~b(z, s(s(s(z))))) | (~b(s(s(z)), s(s(s(z))))))),
% 3.53/3.73 inference(rewrite,[status(thm)],[])).
% 3.53/3.73 tff(17525,plain,
% 3.53/3.73 (((~b(z, s(s(s(elem!1))))) | (~b(z, s(s(s(elem!1))))) | (~b(s(s(s(z))), z)) | (~b(s(s(z)), s(s(s(z))))) | (~b(z, s(s(s(z))))) | (~b(z, s(s(z))))) <=> ((~b(z, s(s(z)))) | (~b(z, s(s(s(elem!1))))) | (~b(s(s(s(z))), z)) | (~b(z, s(s(s(z))))) | (~b(s(s(z)), s(s(s(z))))))),
% 3.53/3.73 inference(rewrite,[status(thm)],[])).
% 3.53/3.73 tff(17526,plain,
% 3.53/3.73 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(s(elem!1))))) | (~b(z, s(s(s(elem!1))))) | (~b(s(s(s(z))), z)) | (~b(s(s(z)), s(s(s(z))))) | (~b(z, s(s(s(z))))) | (~b(z, s(s(z)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(z)))) | (~b(z, s(s(s(elem!1))))) | (~b(s(s(s(z))), z)) | (~b(z, s(s(s(z))))) | (~b(s(s(z)), s(s(s(z)))))))),
% 3.53/3.73 inference(monotonicity,[status(thm)],[17525])).
% 3.53/3.73 tff(17527,plain,
% 3.53/3.73 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(s(elem!1))))) | (~b(z, s(s(s(elem!1))))) | (~b(s(s(s(z))), z)) | (~b(s(s(z)), s(s(s(z))))) | (~b(z, s(s(s(z))))) | (~b(z, s(s(z)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(s(z)))) | (~b(z, s(s(s(elem!1))))) | (~b(s(s(s(z))), z)) | (~b(z, s(s(s(z))))) | (~b(s(s(z)), s(s(s(z))))))),
% 3.53/3.73 inference(transitivity,[status(thm)],[17526, 17524])).
% 3.53/3.73 tff(17528,plain,
% 3.53/3.73 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(s(elem!1))))) | (~b(z, s(s(s(elem!1))))) | (~b(s(s(s(z))), z)) | (~b(s(s(z)), s(s(s(z))))) | (~b(z, s(s(s(z))))) | (~b(z, s(s(z)))))),
% 3.53/3.73 inference(quant_inst,[status(thm)],[])).
% 3.53/3.73 tff(17529,plain,
% 3.53/3.73 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(s(z)))) | (~b(z, s(s(s(elem!1))))) | (~b(s(s(s(z))), z)) | (~b(z, s(s(s(z))))) | (~b(s(s(z)), s(s(s(z)))))),
% 3.53/3.73 inference(modus_ponens,[status(thm)],[17528, 17527])).
% 3.53/3.73 tff(17530,plain,
% 3.53/3.73 (~b(z, s(s(s(z))))),
% 3.53/3.73 inference(unit_resolution,[status(thm)],[17529, 166, 240, 10451, 986, 1699])).
% 3.53/3.73 tff(17531,plain,
% 3.53/3.73 (r(z, s(s(s(z))))),
% 3.53/3.73 inference(unit_resolution,[status(thm)],[1697, 17530])).
% 3.53/3.73 tff(17532,plain,
% 3.53/3.73 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(s(z))))) | (~r(s(z), z)) | (~r(s(z), s(s(s(z))))) | (~r(s(s(s(z))), s(s(z)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, s(s(s(z))))) | (~r(s(z), z)) | (~r(s(z), s(s(s(z))))) | (~r(s(s(s(z))), s(s(z)))))),
% 3.53/3.73 inference(rewrite,[status(thm)],[])).
% 3.53/3.73 tff(17533,plain,
% 3.53/3.73 (((~r(s(s(s(z))), s(s(z)))) | (~r(z, s(s(s(z))))) | (~r(s(z), s(s(s(z))))) | (~r(s(z), z))) <=> ((~r(z, s(s(s(z))))) | (~r(s(z), z)) | (~r(s(z), s(s(s(z))))) | (~r(s(s(s(z))), s(s(z)))))),
% 3.53/3.73 inference(rewrite,[status(thm)],[])).
% 3.53/3.73 tff(17534,plain,
% 3.53/3.73 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(z))), s(s(z)))) | (~r(z, s(s(s(z))))) | (~r(s(z), s(s(s(z))))) | (~r(s(z), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(s(z))))) | (~r(s(z), z)) | (~r(s(z), s(s(s(z))))) | (~r(s(s(s(z))), s(s(z))))))),
% 3.53/3.73 inference(monotonicity,[status(thm)],[17533])).
% 3.53/3.73 tff(17535,plain,
% 3.53/3.73 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(z))), s(s(z)))) | (~r(z, s(s(s(z))))) | (~r(s(z), s(s(s(z))))) | (~r(s(z), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, s(s(s(z))))) | (~r(s(z), z)) | (~r(s(z), s(s(s(z))))) | (~r(s(s(s(z))), s(s(z)))))),
% 3.53/3.73 inference(transitivity,[status(thm)],[17534, 17532])).
% 3.53/3.73 tff(17536,plain,
% 3.53/3.73 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(z))), s(s(z)))) | (~r(z, s(s(s(z))))) | (~r(s(z), s(s(s(z))))) | (~r(s(z), z)))),
% 3.53/3.73 inference(quant_inst,[status(thm)],[])).
% 3.53/3.73 tff(17537,plain,
% 3.53/3.73 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, s(s(s(z))))) | (~r(s(z), z)) | (~r(s(z), s(s(s(z))))) | (~r(s(s(s(z))), s(s(z))))),
% 3.53/3.73 inference(modus_ponens,[status(thm)],[17536, 17535])).
% 3.53/3.73 tff(17538,plain,
% 3.53/3.73 ($false),
% 3.53/3.73 inference(unit_resolution,[status(thm)],[17537, 197, 97, 17531, 17523, 1653])).
% 3.53/3.73 tff(17539,plain,((~b(s(s(z)), s(s(s(z))))) | (~r(s(z), z)) | (~r(s(z), s(s(s(z))))) | (~b(z, s(s(z)))) | (~b(s(s(s(z))), z)) | (~b(z, s(s(s(elem!1)))))), inference(lemma,lemma(discharge,[]))).
% 3.53/3.73 tff(17540,plain,
% 3.53/3.73 ((~b(s(s(z)), s(s(s(z))))) | (~r(s(z), z)) | (~r(s(z), s(s(s(z))))) | (~b(s(s(s(z))), z)) | (~b(z, s(s(s(elem!1)))))),
% 3.53/3.73 inference(unit_resolution,[status(thm)],[17539, 10450])).
% 3.53/3.73 tff(17541,plain,
% 3.53/3.73 (~r(s(z), s(s(s(z))))),
% 3.53/3.73 inference(unit_resolution,[status(thm)],[17540, 17521, 17123, 17128, 1699])).
% 3.53/3.73 tff(17542,plain,
% 3.53/3.73 (b(z, elem!1) <=> b(z, s(s(s(elem!1))))),
% 3.53/3.73 inference(monotonicity,[status(thm)],[6548])).
% 3.53/3.73 tff(17543,plain,
% 3.53/3.73 (b(z, s(s(s(elem!1)))) <=> b(z, elem!1)),
% 3.53/3.73 inference(symmetry,[status(thm)],[17542])).
% 3.53/3.73 tff(17544,plain,
% 3.53/3.73 (b(z, elem!1)),
% 3.53/3.73 inference(modus_ponens,[status(thm)],[17128, 17543])).
% 3.53/3.73 tff(17545,plain,
% 3.53/3.73 (b(s(z), elem!1)),
% 3.53/3.73 inference(unit_resolution,[status(thm)],[9915, 3115, 15211])).
% 3.53/3.73 tff(17546,plain,
% 3.53/3.73 (~b(s(z), s(s(s(z))))),
% 3.53/3.73 inference(unit_resolution,[status(thm)],[9924, 17521, 17545, 17544, 556, 1699])).
% 3.53/3.73 tff(17547,plain,
% 3.53/3.73 ($false),
% 3.53/3.73 inference(unit_resolution,[status(thm)],[1674, 17546, 17541])).
% 3.53/3.73 tff(17548,plain,((~b(s(s(s(z))), z)) | (~b(s(z), s(s(z)))) | (~r(s(s(s(elem!1))), s(z))) | (~r(s(s(z)), s(s(s(elem!1))))) | (~(s(s(elem!1)) = s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), z))), inference(lemma,lemma(discharge,[]))).
% 3.53/3.73 tff(17549,plain,
% 3.53/3.73 (~b(s(s(s(z))), z)),
% 3.53/3.73 inference(unit_resolution,[status(thm)],[17548, 17516, 350, 17483, 17481, 121])).
% 3.53/3.73 tff(17550,plain,
% 3.53/3.73 (r(s(s(s(z))), z)),
% 3.53/3.73 inference(unit_resolution,[status(thm)],[1713, 17549])).
% 3.53/3.73 tff(17551,plain,
% 3.53/3.73 (~r(s(z), s(s(s(z))))),
% 3.53/3.73 inference(unit_resolution,[status(thm)],[8876, 17550, 17126, 17123])).
% 3.53/3.73 tff(17552,plain,
% 3.53/3.73 (b(s(z), s(s(s(z))))),
% 3.53/3.73 inference(unit_resolution,[status(thm)],[1674, 17551])).
% 3.53/3.73 tff(17553,plain,
% 3.53/3.73 (s(s(s(elem!1))) = s(s(elem!1))),
% 3.53/3.73 inference(unit_resolution,[status(thm)],[4030, 17481])).
% 3.53/3.73 tff(17554,plain,
% 3.53/3.73 (~(s(s(s(z))) = elem!1)),
% 3.53/3.73 inference(unit_resolution,[status(thm)],[3122, 17481])).
% 3.53/3.73 tff(17555,plain,
% 3.53/3.73 (~r(s(s(s(z))), s(z))),
% 3.53/3.73 inference(unit_resolution,[status(thm)],[12220, 197, 17126, 17123, 17550])).
% 3.53/3.73 tff(17556,plain,
% 3.53/3.73 (b(s(s(s(z))), s(z))),
% 3.53/3.73 inference(unit_resolution,[status(thm)],[1763, 17555])).
% 3.53/3.73 tff(17557,plain,
% 3.53/3.73 (~b(s(s(z)), s(s(s(z))))),
% 3.53/3.73 inference(unit_resolution,[status(thm)],[3248, 17556, 17064, 17552])).
% 3.53/3.73 tff(17558,plain,
% 3.53/3.73 (r(s(s(z)), s(s(s(z))))),
% 3.53/3.73 inference(unit_resolution,[status(thm)],[1730, 17557])).
% 3.53/3.73 tff(17559,plain,
% 3.53/3.73 (~r(s(s(s(z))), elem!1)),
% 3.53/3.73 inference(unit_resolution,[status(thm)],[8084, 17558, 350, 17483, 17481])).
% 3.53/3.73 tff(17560,plain,
% 3.53/3.73 (b(s(s(s(z))), elem!1)),
% 3.53/3.73 inference(unit_resolution,[status(thm)],[2826, 17559, 17554])).
% 3.53/3.73 tff(17561,plain,
% 3.53/3.73 (b(s(s(s(z))), s(s(s(elem!1))))),
% 3.53/3.73 inference(unit_resolution,[status(thm)],[4078, 17560, 17553])).
% 3.53/3.73 tff(17562,plain,
% 3.53/3.73 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(s(elem!1))))) | (~b(s(z), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), z)) | (~b(s(s(s(z))), s(s(s(elem!1))))) | (~b(s(z), s(s(s(z))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(s(s(elem!1))))) | (~b(s(z), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), z)) | (~b(s(s(s(z))), s(s(s(elem!1))))) | (~b(s(z), s(s(s(z))))))),
% 3.53/3.73 inference(rewrite,[status(thm)],[])).
% 3.53/3.73 tff(17563,plain,
% 3.53/3.73 (((~b(z, s(s(s(elem!1))))) | (~b(s(z), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), z)) | (~b(s(s(s(z))), s(s(s(elem!1))))) | (~b(s(z), s(s(s(elem!1))))) | (~b(s(z), s(s(s(z)))))) <=> ((~b(z, s(s(s(elem!1))))) | (~b(s(z), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), z)) | (~b(s(s(s(z))), s(s(s(elem!1))))) | (~b(s(z), s(s(s(z))))))),
% 3.53/3.73 inference(rewrite,[status(thm)],[])).
% 3.53/3.73 tff(17564,plain,
% 3.53/3.73 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(s(elem!1))))) | (~b(s(z), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), z)) | (~b(s(s(s(z))), s(s(s(elem!1))))) | (~b(s(z), s(s(s(elem!1))))) | (~b(s(z), s(s(s(z))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(s(elem!1))))) | (~b(s(z), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), z)) | (~b(s(s(s(z))), s(s(s(elem!1))))) | (~b(s(z), s(s(s(z)))))))),
% 3.53/3.73 inference(monotonicity,[status(thm)],[17563])).
% 3.53/3.73 tff(17565,plain,
% 3.53/3.73 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(s(elem!1))))) | (~b(s(z), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), z)) | (~b(s(s(s(z))), s(s(s(elem!1))))) | (~b(s(z), s(s(s(elem!1))))) | (~b(s(z), s(s(s(z))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(s(s(elem!1))))) | (~b(s(z), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), z)) | (~b(s(s(s(z))), s(s(s(elem!1))))) | (~b(s(z), s(s(s(z))))))),
% 3.53/3.73 inference(transitivity,[status(thm)],[17564, 17562])).
% 3.53/3.73 tff(17566,plain,
% 3.53/3.73 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(s(elem!1))))) | (~b(s(z), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), z)) | (~b(s(s(s(z))), s(s(s(elem!1))))) | (~b(s(z), s(s(s(elem!1))))) | (~b(s(z), s(s(s(z))))))),
% 3.53/3.73 inference(quant_inst,[status(thm)],[])).
% 3.53/3.73 tff(17567,plain,
% 3.53/3.73 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(s(s(elem!1))))) | (~b(s(z), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), z)) | (~b(s(s(s(z))), s(s(s(elem!1))))) | (~b(s(z), s(s(s(z)))))),
% 3.53/3.73 inference(modus_ponens,[status(thm)],[17566, 17565])).
% 3.53/3.73 tff(17568,plain,
% 3.53/3.73 ($false),
% 3.53/3.73 inference(unit_resolution,[status(thm)],[17567, 166, 241, 17128, 121, 17561, 17552])).
% 3.53/3.73 tff(17569,plain,(b(s(s(elem!1)), s(z)) | (~b(s(z), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), z)) | (~r(s(s(s(elem!1))), s(z)))), inference(lemma,lemma(discharge,[]))).
% 3.53/3.73 tff(17570,plain,
% 3.53/3.73 (b(s(s(elem!1)), s(z))),
% 3.53/3.73 inference(unit_resolution,[status(thm)],[17569, 17480, 121, 3953])).
% 3.53/3.73 tff(17571,plain,
% 3.53/3.73 (~b(s(s(z)), s(s(elem!1)))),
% 3.53/3.73 inference(unit_resolution,[status(thm)],[454, 17570, 15211, 17064])).
% 3.53/3.73 tff(17572,plain,
% 3.53/3.73 (r(s(s(z)), s(s(elem!1)))),
% 3.53/3.73 inference(unit_resolution,[status(thm)],[390, 17571, 44])).
% 3.53/3.73 tff(17573,plain,
% 3.53/3.73 (~b(s(s(s(elem!1))), s(s(elem!1)))),
% 3.53/3.73 inference(unit_resolution,[status(thm)],[1366, 17570, 15211, 17480])).
% 3.53/3.73 tff(17574,plain,
% 3.53/3.73 (~(s(s(elem!1)) = s(s(s(elem!1))))),
% 3.53/3.73 inference(unit_resolution,[status(thm)],[3849, 17570, 3846])).
% 3.53/3.73 tff(17575,plain,
% 3.53/3.73 (~(s(s(s(elem!1))) = s(s(elem!1)))),
% 3.53/3.73 inference(unit_resolution,[status(thm)],[50, 17574])).
% 3.53/3.73 tff(17576,plain,
% 3.53/3.73 (r(s(s(s(elem!1))), s(s(elem!1)))),
% 3.53/3.73 inference(unit_resolution,[status(thm)],[889, 17575, 17573])).
% 3.53/3.73 tff(17577,plain,
% 3.53/3.73 (b(s(z), s(s(z)))),
% 3.53/3.73 inference(unit_resolution,[status(thm)],[17184, 17574, 15211, 3953])).
% 3.53/3.73 tff(17578,plain,
% 3.53/3.73 (~b(z, s(z))),
% 3.53/3.73 inference(unit_resolution,[status(thm)],[17124, 3953, 15211])).
% 3.53/3.73 tff(17579,plain,
% 3.53/3.73 (r(z, s(z))),
% 3.53/3.73 inference(unit_resolution,[status(thm)],[321, 17578])).
% 3.53/3.73 tff(17580,plain,
% 3.53/3.73 (~r(z, s(s(s(elem!1))))),
% 3.53/3.73 inference(unit_resolution,[status(thm)],[2613, 17579, 17123, 3953])).
% 3.53/3.73 tff(17581,plain,
% 3.53/3.73 (b(z, s(s(s(elem!1))))),
% 3.53/3.73 inference(unit_resolution,[status(thm)],[261, 17580])).
% 3.53/3.73 tff(17582,plain,
% 3.53/3.73 (~r(s(s(z)), z)),
% 3.53/3.73 inference(unit_resolution,[status(thm)],[17326, 17574, 15211, 121, 17581, 3953, 17577])).
% 3.53/3.73 tff(17583,plain,
% 3.53/3.73 (b(s(s(z)), z)),
% 3.53/3.73 inference(unit_resolution,[status(thm)],[186, 17582])).
% 3.53/3.73 tff(17584,plain,
% 3.53/3.73 (~b(s(s(z)), s(s(s(elem!1))))),
% 3.53/3.73 inference(unit_resolution,[status(thm)],[17337, 17583])).
% 3.53/3.73 tff(17585,plain,
% 3.53/3.73 (r(s(s(z)), s(s(s(elem!1))))),
% 3.53/3.73 inference(unit_resolution,[status(thm)],[279, 17584])).
% 3.53/3.73 tff(17586,plain,
% 3.53/3.73 (~r(s(s(elem!1)), s(s(z)))),
% 3.53/3.73 inference(unit_resolution,[status(thm)],[4513, 17585, 17576, 17572])).
% 3.53/3.73 tff(17587,plain,
% 3.53/3.73 (b(s(s(elem!1)), s(s(z)))),
% 3.53/3.73 inference(unit_resolution,[status(thm)],[441, 17586, 11])).
% 3.53/3.73 tff(17588,plain,
% 3.53/3.73 ($false),
% 3.53/3.73 inference(unit_resolution,[status(thm)],[2690, 166, 15211, 17587, 17570, 17064])).
% 3.53/3.73 tff(17589,plain,(b(s(s(s(elem!1))), s(z)) | (s(s(elem!1)) = s(s(z))) | (~b(s(s(s(elem!1))), z))), inference(lemma,lemma(discharge,[]))).
% 3.53/3.73 tff(17590,plain,
% 3.53/3.73 (b(s(s(s(elem!1))), s(z))),
% 3.53/3.73 inference(unit_resolution,[status(thm)],[17589, 11, 95])).
% 3.53/3.73 tff(17591,plain,
% 3.53/3.73 (b(z, s(s(elem!1)))),
% 3.53/3.73 inference(unit_resolution,[status(thm)],[17446, 11, 95])).
% 3.53/3.73 tff(17592,plain,
% 3.53/3.73 (~b(s(z), z)),
% 3.53/3.73 inference(unit_resolution,[status(thm)],[17121, 95])).
% 3.53/3.73 tff(17593,plain,
% 3.53/3.73 (r(s(z), z)),
% 3.53/3.73 inference(unit_resolution,[status(thm)],[230, 17592])).
% 3.53/3.73 tff(17594,plain,
% 3.53/3.73 (~b(s(s(elem!1)), s(z))),
% 3.53/3.73 inference(unit_resolution,[status(thm)],[5343, 118, 15211, 1820])).
% 3.53/3.73 tff(17595,plain,
% 3.53/3.73 (r(s(s(z)), s(s(elem!1)))),
% 3.53/3.73 inference(unit_resolution,[status(thm)],[11731, 17594, 97])).
% 3.53/3.73 tff(17596,plain,
% 3.53/3.73 (r(s(s(elem!1)), s(z))),
% 3.53/3.73 inference(unit_resolution,[status(thm)],[1912, 17594])).
% 3.53/3.73 tff(17597,plain,
% 3.53/3.73 ((~b(s(s(elem!1)), s(s(z)))) | (~b(s(z), s(s(elem!1)))) | (~b(z, s(z))) | (~b(s(s(z)), s(z)))),
% 3.53/3.73 inference(unit_resolution,[status(thm)],[15908, 10450])).
% 3.53/3.73 tff(17598,plain,
% 3.53/3.73 (~b(s(s(elem!1)), s(s(z)))),
% 3.53/3.73 inference(unit_resolution,[status(thm)],[17597, 118, 15211, 17064])).
% 3.53/3.73 tff(17599,plain,
% 3.53/3.73 (r(s(s(elem!1)), s(s(z)))),
% 3.53/3.73 inference(unit_resolution,[status(thm)],[441, 17598, 11])).
% 3.53/3.73 tff(17600,plain,
% 3.53/3.73 (~b(s(z), s(s(z)))),
% 3.53/3.73 inference(unit_resolution,[status(thm)],[14336, 118, 17064])).
% 3.53/3.73 tff(17601,plain,
% 3.53/3.73 (r(s(z), s(s(z)))),
% 3.53/3.73 inference(unit_resolution,[status(thm)],[427, 17600])).
% 3.53/3.73 tff(17602,plain,
% 3.53/3.73 ($false),
% 3.53/3.73 inference(unit_resolution,[status(thm)],[7518, 17601, 17599, 17596, 17595])).
% 3.53/3.73 tff(17603,plain,((~b(z, s(z))) | (~r(s(z), z)) | (s(s(elem!1)) = s(s(z))) | (~b(z, s(s(elem!1))))), inference(lemma,lemma(discharge,[]))).
% 3.53/3.73 tff(17604,plain,
% 3.53/3.73 (~b(z, s(z))),
% 3.53/3.73 inference(unit_resolution,[status(thm)],[17603, 11, 17593, 17591])).
% 3.53/3.73 tff(17605,plain,
% 3.53/3.73 (r(z, s(z))),
% 3.53/3.73 inference(unit_resolution,[status(thm)],[321, 17604])).
% 3.53/3.73 tff(17606,plain,
% 3.53/3.73 (~r(s(s(elem!1)), z)),
% 3.53/3.73 inference(unit_resolution,[status(thm)],[8490, 10521, 17123, 323])).
% 3.53/3.73 tff(17607,plain,
% 3.53/3.73 (b(s(s(elem!1)), z)),
% 3.53/3.73 inference(unit_resolution,[status(thm)],[608, 17606])).
% 3.53/3.73 tff(17608,plain,
% 3.53/3.73 (~(s(s(elem!1)) = s(s(s(elem!1))))),
% 3.53/3.73 inference(unit_resolution,[status(thm)],[4570, 4568, 96])).
% 3.53/3.73 tff(17609,plain,
% 3.53/3.73 (~(s(s(s(elem!1))) = s(s(elem!1)))),
% 3.53/3.73 inference(unit_resolution,[status(thm)],[50, 17608])).
% 3.53/3.73 tff(17610,plain,
% 3.53/3.73 (~b(s(s(z)), s(s(s(elem!1))))),
% 3.53/3.73 inference(unit_resolution,[status(thm)],[12136, 323, 17064, 121, 17123, 96])).
% 3.53/3.73 tff(17611,plain,
% 3.53/3.73 (r(s(s(z)), s(s(s(elem!1))))),
% 3.53/3.73 inference(unit_resolution,[status(thm)],[279, 17610])).
% 3.53/3.73 tff(17612,plain,
% 3.53/3.73 (~r(s(s(s(elem!1))), s(s(elem!1)))),
% 3.53/3.73 inference(unit_resolution,[status(thm)],[8677, 10521, 17611, 17482])).
% 3.53/3.73 tff(17613,plain,
% 3.53/3.73 (b(s(s(s(elem!1))), s(s(elem!1)))),
% 3.53/3.73 inference(unit_resolution,[status(thm)],[889, 17612, 17609])).
% 3.53/3.73 tff(17614,plain,
% 3.53/3.73 ($false),
% 3.53/3.73 inference(unit_resolution,[status(thm)],[9275, 166, 17613, 1820, 121, 17607])).
% 3.53/3.73 tff(17615,plain,(b(s(s(elem!1)), s(z)) | (~b(z, s(s(elem!1)))) | (~b(s(s(s(elem!1))), z)) | (~r(z, s(z))) | (~b(s(s(s(elem!1))), s(z)))), inference(lemma,lemma(discharge,[]))).
% 3.53/3.73 tff(17616,plain,
% 3.53/3.73 (b(s(s(elem!1)), s(z))),
% 3.53/3.73 inference(unit_resolution,[status(thm)],[17615, 17591, 95, 17605, 17590])).
% 3.53/3.73 tff(17617,plain,
% 3.53/3.73 (~b(s(s(s(elem!1))), s(s(elem!1)))),
% 3.53/3.73 inference(unit_resolution,[status(thm)],[1858, 17616, 15211, 17590])).
% 3.53/3.73 tff(17618,plain,
% 3.53/3.73 (~b(s(s(z)), s(s(elem!1)))),
% 3.53/3.73 inference(unit_resolution,[status(thm)],[454, 17616, 15211, 17064])).
% 3.53/3.73 tff(17619,plain,
% 3.53/3.73 (r(s(s(z)), s(s(elem!1)))),
% 3.53/3.73 inference(unit_resolution,[status(thm)],[390, 17618, 44])).
% 3.53/3.73 tff(17620,plain,
% 3.53/3.73 (~b(s(s(z)), s(s(s(elem!1))))),
% 3.53/3.73 inference(unit_resolution,[status(thm)],[12136, 17605, 17064, 95, 17593, 17590])).
% 3.53/3.73 tff(17621,plain,
% 3.53/3.73 (r(s(s(z)), s(s(s(elem!1))))),
% 3.53/3.73 inference(unit_resolution,[status(thm)],[279, 17620])).
% 3.53/3.73 tff(17622,plain,
% 3.53/3.73 (~b(s(s(elem!1)), s(s(z)))),
% 3.53/3.73 inference(unit_resolution,[status(thm)],[2690, 166, 15211, 17616, 17064])).
% 3.53/3.73 tff(17623,plain,
% 3.53/3.73 (r(s(s(elem!1)), s(s(z)))),
% 3.53/3.73 inference(unit_resolution,[status(thm)],[441, 17622, 11])).
% 3.53/3.73 tff(17624,plain,
% 3.53/3.73 (~r(s(s(s(elem!1))), s(s(elem!1)))),
% 3.53/3.73 inference(unit_resolution,[status(thm)],[4513, 17623, 17621, 17619])).
% 3.53/3.73 tff(17625,plain,
% 3.53/3.73 (s(s(s(elem!1))) = s(s(elem!1))),
% 3.53/3.73 inference(unit_resolution,[status(thm)],[889, 17624, 17617])).
% 3.53/3.73 tff(17626,plain,
% 3.53/3.73 ((s(s(s(elem!1))) = s(s(s(z)))) <=> (s(s(elem!1)) = s(s(s(z))))),
% 3.53/3.73 inference(monotonicity,[status(thm)],[17625])).
% 3.53/3.73 tff(17627,plain,
% 3.53/3.73 ((s(s(s(elem!1))) = s(s(s(z)))) <=> (s(s(s(z))) = s(s(elem!1)))),
% 3.53/3.73 inference(transitivity,[status(thm)],[17626, 4437])).
% 3.53/3.73 tff(17628,plain,
% 3.53/3.73 ((~(s(s(s(elem!1))) = s(s(s(z))))) <=> (~(s(s(s(z))) = s(s(elem!1))))),
% 3.53/3.73 inference(monotonicity,[status(thm)],[17627])).
% 3.53/3.73 tff(17629,plain,
% 3.53/3.73 (~(s(s(s(z))) = s(s(elem!1)))),
% 3.53/3.73 inference(modus_ponens,[status(thm)],[3537, 17628])).
% 3.53/3.73 tff(17630,plain,
% 3.53/3.73 (~b(s(s(s(elem!1))), s(s(z)))),
% 3.53/3.73 inference(unit_resolution,[status(thm)],[8478, 166, 15211, 17590, 17616, 17064])).
% 3.53/3.73 tff(17631,plain,
% 3.53/3.73 (r(s(s(s(elem!1))), s(s(z)))),
% 3.53/3.73 inference(unit_resolution,[status(thm)],[218, 17630])).
% 3.53/3.73 tff(17632,plain,
% 3.53/3.73 (s(s(elem!1)) = s(s(s(elem!1)))),
% 3.53/3.73 inference(unit_resolution,[status(thm)],[50, 17625])).
% 3.53/3.73 tff(17633,plain,
% 3.53/3.73 (b(s(z), s(s(s(elem!1))))),
% 3.53/3.73 inference(unit_resolution,[status(thm)],[5500, 17632, 15211])).
% 3.53/3.73 tff(17634,plain,
% 3.53/3.73 (b(s(z), s(s(s(elem!1))))),
% 3.53/3.73 inference(unit_resolution,[status(thm)],[5500, 4066, 15211])).
% 3.53/3.73 tff(17635,plain,
% 3.53/3.73 ($false),
% 3.53/3.73 inference(unit_resolution,[status(thm)],[12132, 197, 120, 323, 97, 866])).
% 3.53/3.73 tff(17636,plain,((~r(s(s(z)), z)) | (~r(s(z), s(s(z)))) | (~r(z, s(z))) | (~r(s(z), z))), inference(lemma,lemma(discharge,[]))).
% 3.53/3.73 tff(17637,plain,
% 3.53/3.73 (~r(s(s(z)), z)),
% 3.53/3.73 inference(unit_resolution,[status(thm)],[17636, 120, 323, 17123])).
% 3.53/3.73 tff(17638,plain,
% 3.53/3.73 (b(s(s(z)), z)),
% 3.53/3.73 inference(unit_resolution,[status(thm)],[186, 17637])).
% 3.53/3.73 tff(17639,plain,
% 3.53/3.73 (~b(s(s(s(z))), z)),
% 3.53/3.73 inference(unit_resolution,[status(thm)],[12305, 17638, 121, 4066])).
% 3.53/3.73 tff(17640,plain,
% 3.53/3.73 (r(s(s(s(z))), z)),
% 3.53/3.73 inference(unit_resolution,[status(thm)],[1713, 17639])).
% 3.53/3.73 tff(17641,plain,
% 3.53/3.73 (~r(s(z), s(s(s(z))))),
% 3.53/3.73 inference(unit_resolution,[status(thm)],[8876, 17640, 323, 17123])).
% 3.53/3.73 tff(17642,plain,
% 3.53/3.73 (b(s(z), s(s(s(z))))),
% 3.53/3.73 inference(unit_resolution,[status(thm)],[1674, 17641])).
% 3.53/3.73 tff(17643,plain,
% 3.53/3.73 (~b(s(s(s(z))), s(s(s(elem!1))))),
% 3.53/3.73 inference(unit_resolution,[status(thm)],[8841, 17642, 96, 17634])).
% 3.53/3.73 tff(17644,plain,
% 3.53/3.73 (~b(s(s(s(z))), elem!1)),
% 3.53/3.73 inference(unit_resolution,[status(thm)],[4078, 17643, 47])).
% 3.53/3.73 tff(17645,plain,
% 3.53/3.73 (r(s(s(s(z))), elem!1)),
% 3.53/3.73 inference(unit_resolution,[status(thm)],[2826, 17644, 10809])).
% 3.53/3.73 tff(17646,plain,
% 3.53/3.73 (r(s(s(s(z))), elem!1) <=> r(s(s(s(z))), s(s(elem!1)))),
% 3.53/3.73 inference(monotonicity,[status(thm)],[2808])).
% 3.53/3.73 tff(17647,plain,
% 3.53/3.73 (r(s(s(s(z))), s(s(elem!1)))),
% 3.53/3.73 inference(modus_ponens,[status(thm)],[8074, 17646])).
% 3.53/3.73 tff(17648,plain,
% 3.53/3.73 ($false),
% 3.53/3.73 inference(unit_resolution,[status(thm)],[5536, 17647])).
% 3.53/3.73 tff(17649,plain,((~r(s(s(s(z))), elem!1)) | r(s(s(s(z))), s(s(elem!1))) | (~(s(s(s(elem!1))) = s(elem!1)))), inference(lemma,lemma(discharge,[]))).
% 3.53/3.73 tff(17650,plain,
% 3.53/3.73 (r(s(s(s(z))), s(s(elem!1)))),
% 3.53/3.73 inference(unit_resolution,[status(thm)],[17649, 17645, 4067])).
% 3.53/3.73 tff(17651,plain,
% 3.53/3.73 (~r(s(s(s(z))), s(z))),
% 3.53/3.73 inference(unit_resolution,[status(thm)],[3213, 17640, 323, 120])).
% 3.53/3.73 tff(17652,plain,
% 3.53/3.73 (b(s(s(s(z))), s(z))),
% 3.53/3.73 inference(unit_resolution,[status(thm)],[1763, 17651])).
% 3.53/3.73 tff(17653,plain,
% 3.53/3.73 (~b(s(s(z)), s(s(s(z))))),
% 3.53/3.73 inference(unit_resolution,[status(thm)],[3248, 17652, 17064, 17642])).
% 3.53/3.73 tff(17654,plain,
% 3.53/3.73 (r(s(s(z)), s(s(s(z))))),
% 3.53/3.73 inference(unit_resolution,[status(thm)],[1730, 17653])).
% 3.53/3.73 tff(17655,plain,
% 3.53/3.73 ($false),
% 3.53/3.73 inference(unit_resolution,[status(thm)],[4415, 197, 393, 333, 17654, 17650])).
% 3.53/3.73 tff(17656,plain,((~r(s(z), s(s(z)))) | (~r(s(s(elem!1)), s(s(z)))) | (~r(s(s(z)), s(s(elem!1)))) | (~(s(s(s(elem!1))) = s(s(elem!1)))) | (~b(s(s(s(elem!1))), s(z))) | (~r(z, s(z))) | (~b(s(s(s(elem!1))), z))), inference(lemma,lemma(discharge,[]))).
% 3.53/3.73 tff(17657,plain,
% 3.53/3.73 (~r(s(z), s(s(z)))),
% 3.53/3.73 inference(unit_resolution,[status(thm)],[17656, 17623, 17619, 17625, 17590, 17605, 95])).
% 3.53/3.73 tff(17658,plain,
% 3.53/3.73 (b(s(z), s(s(z)))),
% 3.53/3.73 inference(unit_resolution,[status(thm)],[427, 17657])).
% 3.53/3.73 tff(17659,plain,
% 3.53/3.73 (~b(s(z), s(s(s(z))))),
% 3.53/3.73 inference(unit_resolution,[status(thm)],[8866, 17658, 17590, 17632, 17633, 17621, 17631])).
% 3.53/3.73 tff(17660,plain,
% 3.53/3.73 (r(s(z), s(s(s(z))))),
% 3.53/3.73 inference(unit_resolution,[status(thm)],[1674, 17659])).
% 3.53/3.73 tff(17661,plain,
% 3.53/3.73 (~r(s(s(s(z))), z)),
% 3.53/3.73 inference(unit_resolution,[status(thm)],[8876, 17660, 17605, 17593])).
% 3.53/3.73 tff(17662,plain,
% 3.53/3.73 (b(s(s(s(z))), z)),
% 3.53/3.73 inference(unit_resolution,[status(thm)],[1713, 17661])).
% 3.53/3.73 tff(17663,plain,
% 3.53/3.73 (~r(s(s(elem!1)), z)),
% 3.53/3.73 inference(unit_resolution,[status(thm)],[2974, 17632, 86])).
% 3.53/3.73 tff(17664,plain,
% 3.53/3.73 (b(s(s(elem!1)), z)),
% 3.53/3.73 inference(unit_resolution,[status(thm)],[608, 17663])).
% 3.53/3.73 tff(17665,plain,
% 3.53/3.73 (~b(s(s(s(z))), s(s(elem!1)))),
% 3.53/3.73 inference(unit_resolution,[status(thm)],[8902, 166, 17591, 17664, 17662])).
% 3.53/3.73 tff(17666,plain,
% 3.53/3.73 (r(s(s(s(z))), s(s(elem!1)))),
% 3.53/3.73 inference(unit_resolution,[status(thm)],[14510, 17665, 17629])).
% 3.53/3.73 tff(17667,plain,
% 3.53/3.73 (b(z, s(s(s(elem!1))))),
% 3.53/3.73 inference(unit_resolution,[status(thm)],[8327, 17625, 17591])).
% 3.53/3.73 tff(17668,plain,
% 3.53/3.73 (~b(s(s(z)), s(s(s(z))))),
% 3.53/3.73 inference(unit_resolution,[status(thm)],[17540, 17662, 17593, 17667, 17660])).
% 3.53/3.73 tff(17669,plain,
% 3.53/3.73 (r(s(s(z)), s(s(s(z))))),
% 3.53/3.73 inference(unit_resolution,[status(thm)],[1730, 17668])).
% 3.53/3.73 tff(17670,plain,
% 3.53/3.73 ($false),
% 3.53/3.73 inference(unit_resolution,[status(thm)],[4415, 197, 17623, 17619, 17669, 17666])).
% 3.53/3.73 tff(17671,plain,((s(s(elem!1)) = s(s(z))) | r(s(s(s(elem!1))), z)), inference(lemma,lemma(discharge,[]))).
% 3.53/3.73 tff(17672,plain,
% 3.53/3.73 (s(s(elem!1)) = s(s(z))),
% 3.53/3.73 inference(unit_resolution,[status(thm)],[17671, 86])).
% 3.53/3.73 tff(17673,plain,
% 3.53/3.73 (s(s(z)) = s(s(elem!1))),
% 3.53/3.73 inference(symmetry,[status(thm)],[17672])).
% 3.53/3.73 tff(17674,plain,
% 3.53/3.73 (b(elem!1, s(s(z))) <=> b(elem!1, s(s(elem!1)))),
% 3.53/3.73 inference(monotonicity,[status(thm)],[17673])).
% 3.53/3.73 tff(17675,plain,
% 3.53/3.73 (b(elem!1, s(s(elem!1))) <=> b(elem!1, s(s(z)))),
% 3.53/3.73 inference(symmetry,[status(thm)],[17674])).
% 3.53/3.73 tff(17676,plain,
% 3.53/3.73 (s(s(z)) = s(s(elem!1))),
% 3.53/3.73 inference(unit_resolution,[status(thm)],[131, 17672])).
% 3.53/3.73 tff(17677,plain,
% 3.53/3.73 (s(elem!1) = s(z)),
% 3.53/3.73 inference(unit_resolution,[status(thm)],[43, 17676])).
% 3.53/3.73 tff(17678,plain,
% 3.53/3.73 (z = elem!1),
% 3.53/3.73 inference(unit_resolution,[status(thm)],[30, 17677])).
% 3.53/3.73 tff(17679,plain,
% 3.53/3.73 (elem!1 = z),
% 3.53/3.73 inference(symmetry,[status(thm)],[17678])).
% 3.53/3.73 tff(17680,plain,
% 3.53/3.73 (b(elem!1, s(s(elem!1))) <=> b(z, s(s(z)))),
% 3.53/3.73 inference(monotonicity,[status(thm)],[17679, 17672])).
% 3.53/3.73 tff(17681,plain,
% 3.53/3.73 (b(z, s(s(z))) <=> b(elem!1, s(s(elem!1)))),
% 3.53/3.73 inference(symmetry,[status(thm)],[17680])).
% 3.53/3.73 tff(17682,plain,
% 3.53/3.73 (b(elem!1, s(s(elem!1)))),
% 3.53/3.73 inference(modus_ponens,[status(thm)],[10450, 17681])).
% 3.53/3.73 tff(17683,plain,
% 3.53/3.73 (b(elem!1, s(s(z)))),
% 3.53/3.73 inference(modus_ponens,[status(thm)],[17682, 17675])).
% 3.53/3.73 tff(17684,plain,
% 3.53/3.73 (s(s(s(elem!1))) = s(s(s(z)))),
% 3.53/3.73 inference(monotonicity,[status(thm)],[17672])).
% 3.53/3.73 tff(17685,plain,
% 3.53/3.73 (r(s(s(z)), s(s(s(elem!1)))) <=> r(s(s(z)), s(s(s(z))))),
% 3.53/3.73 inference(monotonicity,[status(thm)],[17684])).
% 3.53/3.73 tff(17686,plain,
% 3.53/3.73 (r(s(s(elem!1)), s(s(s(elem!1)))) <=> r(s(s(z)), s(s(s(elem!1))))),
% 3.53/3.73 inference(monotonicity,[status(thm)],[17672])).
% 3.53/3.73 tff(17687,plain,
% 3.53/3.73 (r(s(s(elem!1)), s(s(s(elem!1)))) <=> r(s(s(z)), s(s(s(z))))),
% 3.53/3.73 inference(transitivity,[status(thm)],[17686, 17685])).
% 3.53/3.73 tff(17688,plain,
% 3.53/3.73 ((s(s(elem!1)) = s(s(s(elem!1)))) <=> (s(s(z)) = s(s(s(elem!1))))),
% 3.53/3.73 inference(monotonicity,[status(thm)],[17672])).
% 3.53/3.73 tff(17689,plain,
% 3.53/3.73 ((s(s(z)) = s(s(s(elem!1)))) <=> (s(s(elem!1)) = s(s(s(elem!1))))),
% 3.53/3.73 inference(symmetry,[status(thm)],[17688])).
% 3.53/3.73 tff(17690,plain,
% 3.53/3.73 ((~(s(s(z)) = s(s(s(elem!1))))) <=> (~(s(s(elem!1)) = s(s(s(elem!1)))))),
% 3.53/3.73 inference(monotonicity,[status(thm)],[17689])).
% 3.53/3.73 tff(17691,plain,
% 3.53/3.73 (~(s(s(elem!1)) = s(s(s(elem!1))))),
% 3.53/3.73 inference(modus_ponens,[status(thm)],[209, 17690])).
% 3.53/3.73 tff(17692,plain,
% 3.53/3.73 ((s(s(z)) = s(s(s(elem!1)))) <=> (s(s(s(elem!1))) = s(s(elem!1)))),
% 3.53/3.73 inference(transitivity,[status(thm)],[17689, 3341])).
% 3.53/3.73 tff(17693,plain,
% 3.53/3.73 ((~(s(s(z)) = s(s(s(elem!1))))) <=> (~(s(s(s(elem!1))) = s(s(elem!1))))),
% 3.53/3.73 inference(monotonicity,[status(thm)],[17692])).
% 3.53/3.73 tff(17694,plain,
% 3.53/3.73 (~(s(s(s(elem!1))) = s(s(elem!1)))),
% 3.53/3.73 inference(modus_ponens,[status(thm)],[209, 17693])).
% 3.53/3.73 tff(17695,plain,
% 3.53/3.73 ((s(s(elem!1)) = s(s(s(s(s(s(elem!1))))))) <=> (s(s(s(s(s(s(elem!1)))))) = s(s(elem!1)))),
% 3.53/3.73 inference(commutativity,[status(thm)],[])).
% 3.53/3.73 tff(17696,plain,
% 3.53/3.73 ((s(s(z)) = s(s(s(s(s(s(elem!1))))))) <=> (s(s(elem!1)) = s(s(s(s(s(s(elem!1)))))))),
% 3.53/3.73 inference(monotonicity,[status(thm)],[4988])).
% 3.53/3.73 tff(17697,plain,
% 3.53/3.73 ((s(s(z)) = s(s(s(s(s(s(elem!1))))))) <=> (s(s(s(s(s(s(elem!1)))))) = s(s(elem!1)))),
% 3.53/3.73 inference(transitivity,[status(thm)],[17696, 17695])).
% 3.53/3.73 tff(17698,plain,
% 3.53/3.73 ((s(s(s(s(s(s(elem!1)))))) = s(s(elem!1))) <=> (s(s(z)) = s(s(s(s(s(s(elem!1)))))))),
% 3.53/3.73 inference(symmetry,[status(thm)],[17697])).
% 3.53/3.73 tff(17699,plain,
% 3.53/3.73 ((~(s(s(s(s(s(s(elem!1)))))) = s(s(elem!1)))) <=> (~(s(s(z)) = s(s(s(s(s(s(elem!1))))))))),
% 3.53/3.73 inference(monotonicity,[status(thm)],[17698])).
% 3.53/3.73 tff(17700,plain,
% 3.53/3.73 (~(s(s(s(s(s(s(elem!1)))))) = s(s(elem!1)))),
% 3.53/3.73 inference(unit_resolution,[status(thm)],[4986, 14761])).
% 3.53/3.73 tff(17701,plain,
% 3.53/3.73 (~(s(s(z)) = s(s(s(s(s(s(elem!1)))))))),
% 3.53/3.73 inference(modus_ponens,[status(thm)],[17700, 17699])).
% 3.53/3.73 tff(17702,plain,
% 3.53/3.73 (b(elem!1, s(s(elem!1)))),
% 3.53/3.73 inference(modus_ponens,[status(thm)],[10450, 14930])).
% 3.53/3.73 tff(17703,plain,
% 3.53/3.73 (b(elem!1, s(s(z)))),
% 3.53/3.73 inference(modus_ponens,[status(thm)],[17702, 14770])).
% 3.53/3.73 tff(17704,plain,
% 3.53/3.73 (~(s(s(s(s(s(s(elem!1)))))) = elem!1)),
% 3.53/3.73 inference(unit_resolution,[status(thm)],[4897, 14762])).
% 3.53/3.73 tff(17705,plain,
% 3.53/3.73 (b(s(z), s(s(z)))),
% 3.53/3.73 inference(unit_resolution,[status(thm)],[5435, 14760, 15211])).
% 3.53/3.73 tff(17706,plain,
% 3.53/3.73 (~b(z, s(z))),
% 3.53/3.73 inference(unit_resolution,[status(thm)],[14336, 17705, 17064])).
% 3.53/3.73 tff(17707,plain,
% 3.53/3.73 (r(z, s(z))),
% 3.53/3.73 inference(unit_resolution,[status(thm)],[321, 17706])).
% 3.53/3.73 tff(17708,plain,
% 3.53/3.73 ((s(s(s(z))) = s(s(s(s(elem!1))))) <=> (s(s(s(s(elem!1)))) = s(s(s(z))))),
% 3.53/3.73 inference(commutativity,[status(thm)],[])).
% 3.53/3.73 tff(17709,plain,
% 3.53/3.73 ((s(s(s(elem!1))) = s(s(s(s(elem!1))))) <=> (s(s(s(z))) = s(s(s(s(elem!1)))))),
% 3.53/3.73 inference(monotonicity,[status(thm)],[2195])).
% 3.53/3.73 tff(17710,plain,
% 3.53/3.73 ((s(s(s(elem!1))) = s(s(s(s(elem!1))))) <=> (s(s(s(s(elem!1)))) = s(s(s(z))))),
% 3.53/3.73 inference(transitivity,[status(thm)],[17709, 17708])).
% 3.53/3.73 tff(17711,plain,
% 3.53/3.73 ((s(s(s(s(elem!1)))) = s(s(s(z)))) <=> (s(s(s(elem!1))) = s(s(s(s(elem!1)))))),
% 3.53/3.73 inference(symmetry,[status(thm)],[17710])).
% 3.53/3.73 tff(17712,plain,
% 3.53/3.73 ((s(s(s(s(elem!1)))) = s(s(s(z)))) <=> (s(s(s(s(elem!1)))) = s(s(s(elem!1))))),
% 3.53/3.73 inference(transitivity,[status(thm)],[17711, 3797])).
% 3.53/3.73 tff(17713,plain,
% 3.53/3.73 ((~(s(s(s(s(elem!1)))) = s(s(s(z))))) <=> (~(s(s(s(s(elem!1)))) = s(s(s(elem!1)))))),
% 3.53/3.73 inference(monotonicity,[status(thm)],[17712])).
% 3.53/3.73 tff(17714,plain,
% 3.53/3.73 (~(s(s(s(s(elem!1)))) = s(s(s(elem!1))))),
% 3.53/3.73 inference(modus_ponens,[status(thm)],[5112, 17713])).
% 3.53/3.73 tff(17715,plain,
% 3.53/3.73 (~r(s(s(s(s(elem!1)))), s(z))),
% 3.53/3.73 inference(unit_resolution,[status(thm)],[2669, 350, 17123, 17714, 17707])).
% 3.53/3.73 tff(17716,plain,
% 3.53/3.73 (b(s(s(s(s(elem!1)))), s(z))),
% 3.53/3.73 inference(unit_resolution,[status(thm)],[661, 17715])).
% 3.53/3.73 tff(17717,plain,
% 3.53/3.73 (r(s(z), elem!1)),
% 3.53/3.73 inference(modus_ponens,[status(thm)],[17123, 14946])).
% 3.53/3.73 tff(17718,plain,
% 3.53/3.73 ((s(s(s(s(elem!1)))) = s(s(z))) <=> (s(s(s(s(elem!1)))) = s(s(elem!1)))),
% 3.53/3.73 inference(monotonicity,[status(thm)],[4988])).
% 3.53/3.73 tff(17719,plain,
% 3.53/3.73 ((s(s(s(s(elem!1)))) = s(s(z))) <=> (s(s(elem!1)) = s(s(s(s(elem!1)))))),
% 3.53/3.73 inference(transitivity,[status(thm)],[17718, 123])).
% 3.53/3.73 tff(17720,plain,
% 3.53/3.73 ((~(s(s(s(s(elem!1)))) = s(s(z)))) <=> (~(s(s(elem!1)) = s(s(s(s(elem!1))))))),
% 3.53/3.73 inference(monotonicity,[status(thm)],[17719])).
% 3.53/3.73 tff(17721,plain,
% 3.53/3.73 (~(s(s(elem!1)) = s(s(s(s(elem!1)))))),
% 3.53/3.73 inference(modus_ponens,[status(thm)],[733, 17720])).
% 3.53/3.73 tff(17722,plain,
% 3.53/3.73 (~(s(s(s(s(elem!1)))) = s(s(s(s(s(s(elem!1)))))))),
% 3.53/3.73 inference(unit_resolution,[status(thm)],[9243, 17721])).
% 3.53/3.73 tff(17723,plain,
% 3.53/3.73 (r(elem!1, s(z))),
% 3.53/3.73 inference(unit_resolution,[status(thm)],[741, 17707, 14762])).
% 3.53/3.73 tff(17724,plain,
% 3.53/3.73 (r(s(s(s(s(elem!1)))), elem!1) <=> r(s(s(s(s(z)))), elem!1)),
% 3.53/3.73 inference(monotonicity,[status(thm)],[2196])).
% 3.53/3.73 tff(17725,plain,
% 3.53/3.73 (r(s(s(s(s(z)))), elem!1) <=> r(s(s(s(s(elem!1)))), elem!1)),
% 3.53/3.73 inference(symmetry,[status(thm)],[17724])).
% 3.53/3.73 tff(17726,plain,
% 3.53/3.73 ((s(s(s(s(z)))) = z) <=> (s(s(s(s(z)))) = elem!1)),
% 3.53/3.73 inference(monotonicity,[status(thm)],[14762])).
% 3.53/3.73 tff(17727,plain,
% 3.53/3.73 ((s(s(s(s(z)))) = z) <=> (elem!1 = s(s(s(s(z)))))),
% 3.53/3.73 inference(transitivity,[status(thm)],[17726, 1039])).
% 3.53/3.73 tff(17728,plain,
% 3.53/3.73 ((s(s(s(s(z)))) = z) <=> (s(s(s(s(z)))) = elem!1)),
% 3.53/3.73 inference(transitivity,[status(thm)],[17727, 6181])).
% 3.53/3.73 tff(17729,plain,
% 3.53/3.73 ((~(s(s(s(s(z)))) = z)) <=> (~(s(s(s(s(z)))) = elem!1))),
% 3.53/3.73 inference(monotonicity,[status(thm)],[17728])).
% 3.53/3.73 tff(17730,plain,
% 3.53/3.73 (~(s(s(s(s(z)))) = elem!1)),
% 3.53/3.73 inference(modus_ponens,[status(thm)],[1044, 17729])).
% 3.53/3.73 tff(17731,plain,
% 3.53/3.73 ((s(s(s(s(elem!1)))) = z) <=> (s(s(s(s(elem!1)))) = elem!1)),
% 3.53/3.73 inference(monotonicity,[status(thm)],[14762])).
% 3.53/3.73 tff(17732,plain,
% 3.53/3.73 ((s(s(s(s(elem!1)))) = z) <=> (elem!1 = s(s(s(s(elem!1)))))),
% 3.53/3.73 inference(transitivity,[status(thm)],[17731, 2287])).
% 3.53/3.73 tff(17733,plain,
% 3.53/3.73 ((~(s(s(s(s(elem!1)))) = z)) <=> (~(elem!1 = s(s(s(s(elem!1))))))),
% 3.53/3.73 inference(monotonicity,[status(thm)],[17732])).
% 3.53/3.73 tff(17734,plain,
% 3.53/3.73 (~(elem!1 = s(s(s(s(elem!1)))))),
% 3.53/3.73 inference(modus_ponens,[status(thm)],[626, 17733])).
% 3.53/3.73 tff(17735,plain,
% 3.53/3.73 ((~(s(s(s(s(elem!1)))) = z)) <=> (~(s(s(s(s(elem!1)))) = elem!1))),
% 3.53/3.73 inference(monotonicity,[status(thm)],[17731])).
% 3.53/3.73 tff(17736,plain,
% 3.53/3.73 (~(s(s(s(s(elem!1)))) = elem!1)),
% 3.53/3.73 inference(modus_ponens,[status(thm)],[626, 17735])).
% 3.53/3.73 tff(17737,plain,
% 3.53/3.73 ((s(s(elem!1)) = s(s(s(elem!1)))) <=> (s(s(z)) = s(s(s(elem!1))))),
% 3.53/3.73 inference(monotonicity,[status(thm)],[128])).
% 3.53/3.73 tff(17738,plain,
% 3.53/3.73 ((s(s(z)) = s(s(s(elem!1)))) <=> (s(s(elem!1)) = s(s(s(elem!1))))),
% 3.53/3.73 inference(symmetry,[status(thm)],[17737])).
% 3.53/3.73 tff(17739,plain,
% 3.53/3.73 ((~(s(s(z)) = s(s(s(elem!1))))) <=> (~(s(s(elem!1)) = s(s(s(elem!1)))))),
% 3.53/3.73 inference(monotonicity,[status(thm)],[17738])).
% 3.53/3.73 tff(17740,plain,
% 3.53/3.73 (~(s(s(elem!1)) = s(s(s(elem!1))))),
% 3.53/3.73 inference(modus_ponens,[status(thm)],[209, 17739])).
% 3.53/3.73 tff(17741,plain,
% 3.53/3.73 (~r(z, s(s(s(elem!1))))),
% 3.53/3.73 inference(unit_resolution,[status(thm)],[2613, 350, 17123, 17707])).
% 3.53/3.73 tff(17742,plain,
% 3.53/3.73 (b(z, s(s(s(elem!1))))),
% 3.53/3.73 inference(unit_resolution,[status(thm)],[261, 17741])).
% 3.53/3.73 tff(17743,plain,
% 3.53/3.73 (~r(s(s(z)), z)),
% 3.53/3.73 inference(unit_resolution,[status(thm)],[17326, 17742, 15211, 121, 17740, 350, 17705])).
% 3.53/3.73 tff(17744,plain,
% 3.53/3.73 (b(s(s(z)), z)),
% 3.53/3.74 inference(unit_resolution,[status(thm)],[186, 17743])).
% 3.53/3.74 tff(17745,plain,
% 3.53/3.74 (b(s(s(elem!1)), elem!1)),
% 3.53/3.74 inference(unit_resolution,[status(thm)],[8754, 17744, 14760])).
% 3.53/3.74 tff(17746,plain,
% 3.53/3.74 (~b(s(s(s(s(elem!1)))), s(s(elem!1)))),
% 3.53/3.74 inference(unit_resolution,[status(thm)],[11698, 17745, 15211, 17702, 17736, 17717, 17734])).
% 3.53/3.74 tff(17747,plain,
% 3.53/3.74 (b(s(s(s(s(elem!1)))), s(s(elem!1)))),
% 3.53/3.74 inference(modus_ponens,[status(thm)],[3039, 2154])).
% 3.53/3.74 tff(17748,plain,
% 3.53/3.74 ($false),
% 3.53/3.74 inference(unit_resolution,[status(thm)],[807, 17747])).
% 3.53/3.74 tff(17749,plain,((~b(s(s(s(s(elem!1)))), s(s(z)))) | b(s(s(s(s(elem!1)))), s(s(elem!1))) | (~(s(s(z)) = s(s(elem!1))))), inference(lemma,lemma(discharge,[]))).
% 3.53/3.74 tff(17750,plain,
% 3.53/3.74 (~b(s(s(s(s(elem!1)))), s(s(z)))),
% 3.53/3.74 inference(unit_resolution,[status(thm)],[17749, 17746, 14760])).
% 3.53/3.74 tff(17751,plain,
% 3.53/3.74 (r(s(s(s(s(elem!1)))), s(s(z)))),
% 3.53/3.74 inference(unit_resolution,[status(thm)],[1299, 17750])).
% 3.53/3.74 tff(17752,plain,
% 3.53/3.74 (r(s(s(s(s(z)))), s(s(z)))),
% 3.53/3.74 inference(modus_ponens,[status(thm)],[17751, 2206])).
% 3.53/3.74 tff(17753,plain,
% 3.53/3.74 (b(s(s(z)), elem!1)),
% 3.53/3.74 inference(unit_resolution,[status(thm)],[14685, 17745, 128])).
% 3.53/3.74 tff(17754,plain,
% 3.53/3.74 (b(s(s(s(elem!1))), elem!1) <=> b(s(s(s(z))), elem!1)),
% 3.53/3.74 inference(monotonicity,[status(thm)],[2195])).
% 3.53/3.74 tff(17755,plain,
% 3.53/3.74 (b(s(s(s(elem!1))), elem!1)),
% 3.53/3.74 inference(unit_resolution,[status(thm)],[634, 14762, 121])).
% 3.53/3.74 tff(17756,plain,
% 3.53/3.74 (b(s(s(s(z))), elem!1)),
% 3.53/3.74 inference(modus_ponens,[status(thm)],[17755, 17754])).
% 3.53/3.74 tff(17757,plain,
% 3.53/3.74 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), elem!1)) | (~b(elem!1, s(s(z)))) | (~b(s(s(z)), s(z))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(s(z))), elem!1)))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(z)), elem!1)) | (~b(elem!1, s(s(z)))) | (~b(s(s(z)), s(z))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(s(z))), elem!1)))),
% 3.53/3.74 inference(rewrite,[status(thm)],[])).
% 3.53/3.74 tff(17758,plain,
% 3.53/3.74 (((~b(s(s(z)), s(z))) | (~b(s(s(z)), s(z))) | (~b(elem!1, s(s(z)))) | (~b(s(s(s(z))), elem!1)) | (~b(s(s(z)), elem!1)) | (~b(s(s(z)), s(s(s(z)))))) <=> ((~b(s(s(z)), elem!1)) | (~b(elem!1, s(s(z)))) | (~b(s(s(z)), s(z))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(s(z))), elem!1)))),
% 3.53/3.74 inference(rewrite,[status(thm)],[])).
% 3.53/3.74 tff(17759,plain,
% 3.53/3.74 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), s(z))) | (~b(s(s(z)), s(z))) | (~b(elem!1, s(s(z)))) | (~b(s(s(s(z))), elem!1)) | (~b(s(s(z)), elem!1)) | (~b(s(s(z)), s(s(s(z))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), elem!1)) | (~b(elem!1, s(s(z)))) | (~b(s(s(z)), s(z))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(s(z))), elem!1))))),
% 3.53/3.74 inference(monotonicity,[status(thm)],[17758])).
% 3.53/3.74 tff(17760,plain,
% 3.53/3.74 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), s(z))) | (~b(s(s(z)), s(z))) | (~b(elem!1, s(s(z)))) | (~b(s(s(s(z))), elem!1)) | (~b(s(s(z)), elem!1)) | (~b(s(s(z)), s(s(s(z))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(z)), elem!1)) | (~b(elem!1, s(s(z)))) | (~b(s(s(z)), s(z))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(s(z))), elem!1)))),
% 3.53/3.74 inference(transitivity,[status(thm)],[17759, 17757])).
% 3.53/3.74 tff(17761,plain,
% 3.53/3.74 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), s(z))) | (~b(s(s(z)), s(z))) | (~b(elem!1, s(s(z)))) | (~b(s(s(s(z))), elem!1)) | (~b(s(s(z)), elem!1)) | (~b(s(s(z)), s(s(s(z))))))),
% 3.53/3.74 inference(quant_inst,[status(thm)],[])).
% 3.53/3.74 tff(17762,plain,
% 3.53/3.74 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(z)), elem!1)) | (~b(elem!1, s(s(z)))) | (~b(s(s(z)), s(z))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(s(z))), elem!1))),
% 3.53/3.74 inference(modus_ponens,[status(thm)],[17761, 17760])).
% 3.53/3.74 tff(17763,plain,
% 3.53/3.74 ((~b(s(s(z)), elem!1)) | (~b(elem!1, s(s(z)))) | (~b(s(s(z)), s(s(s(z)))))),
% 3.53/3.74 inference(unit_resolution,[status(thm)],[17762, 166, 17064, 17756])).
% 3.53/3.74 tff(17764,plain,
% 3.53/3.74 (~b(s(s(z)), s(s(s(z))))),
% 3.53/3.74 inference(unit_resolution,[status(thm)],[17763, 17753, 17703])).
% 3.53/3.74 tff(17765,plain,
% 3.53/3.74 (r(s(s(z)), s(s(s(z))))),
% 3.53/3.74 inference(unit_resolution,[status(thm)],[1730, 17764])).
% 3.53/3.74 tff(17766,plain,
% 3.53/3.74 (r(s(s(s(elem!1))), s(s(z))) <=> r(s(s(s(z))), s(s(z)))),
% 3.53/3.74 inference(monotonicity,[status(thm)],[2195])).
% 3.53/3.74 tff(17767,plain,
% 3.53/3.74 (r(s(s(s(elem!1))), s(s(elem!1))) <=> r(s(s(s(z))), s(s(z)))),
% 3.53/3.74 inference(transitivity,[status(thm)],[15027, 17766])).
% 3.53/3.74 tff(17768,plain,
% 3.53/3.74 ((s(s(z)) = s(s(s(elem!1)))) <=> (s(s(s(elem!1))) = s(s(elem!1)))),
% 3.53/3.74 inference(transitivity,[status(thm)],[17738, 3341])).
% 3.53/3.74 tff(17769,plain,
% 3.53/3.74 ((~(s(s(z)) = s(s(s(elem!1))))) <=> (~(s(s(s(elem!1))) = s(s(elem!1))))),
% 3.53/3.74 inference(monotonicity,[status(thm)],[17768])).
% 3.53/3.74 tff(17770,plain,
% 3.53/3.74 (~(s(s(s(elem!1))) = s(s(elem!1)))),
% 3.53/3.74 inference(modus_ponens,[status(thm)],[209, 17769])).
% 3.53/3.74 tff(17771,plain,
% 3.53/3.74 (b(s(s(z)), s(z)) <=> b(s(s(elem!1)), s(z))),
% 3.53/3.74 inference(symmetry,[status(thm)],[15032])).
% 3.53/3.74 tff(17772,plain,
% 3.53/3.74 (b(s(s(elem!1)), s(z))),
% 3.53/3.74 inference(modus_ponens,[status(thm)],[17064, 17771])).
% 3.53/3.74 tff(17773,plain,
% 3.53/3.74 ((s(s(s(elem!1))) = z) <=> (s(s(s(elem!1))) = elem!1)),
% 3.53/3.74 inference(monotonicity,[status(thm)],[14762])).
% 3.53/3.74 tff(17774,plain,
% 3.53/3.74 ((s(s(s(elem!1))) = z) <=> (elem!1 = s(s(s(elem!1))))),
% 3.53/3.74 inference(transitivity,[status(thm)],[17773, 5406])).
% 3.53/3.74 tff(17775,plain,
% 3.53/3.74 ((~(s(s(s(elem!1))) = z)) <=> (~(elem!1 = s(s(s(elem!1)))))),
% 3.53/3.74 inference(monotonicity,[status(thm)],[17774])).
% 3.53/3.74 tff(17776,plain,
% 3.53/3.74 (~(elem!1 = s(s(s(elem!1))))),
% 3.53/3.74 inference(modus_ponens,[status(thm)],[89, 17775])).
% 3.53/3.74 tff(17777,plain,
% 3.53/3.74 (~r(elem!1, s(s(s(elem!1))))),
% 3.53/3.74 inference(unit_resolution,[status(thm)],[5446, 17741, 14762])).
% 3.53/3.74 tff(17778,plain,
% 3.53/3.74 (b(elem!1, s(s(s(elem!1))))),
% 3.53/3.74 inference(unit_resolution,[status(thm)],[5451, 17777, 17776])).
% 3.53/3.74 tff(17779,plain,
% 3.53/3.74 (~b(s(s(s(elem!1))), s(s(elem!1)))),
% 3.53/3.74 inference(unit_resolution,[status(thm)],[17321, 17778, 15211, 17772, 17702])).
% 3.53/3.74 tff(17780,plain,
% 3.53/3.74 (r(s(s(s(elem!1))), s(s(elem!1)))),
% 3.53/3.74 inference(unit_resolution,[status(thm)],[889, 17779, 17770])).
% 3.53/3.74 tff(17781,plain,
% 3.53/3.74 (r(s(s(s(z))), s(s(z)))),
% 3.53/3.74 inference(modus_ponens,[status(thm)],[17780, 17767])).
% 3.53/3.74 tff(17782,plain,
% 3.53/3.74 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(z)), s(s(s(z))))) | (~r(s(s(s(z))), s(s(z)))) | (~r(s(s(s(s(z)))), s(s(z)))) | (~r(s(s(s(s(z)))), s(s(s(z))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(z)), 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(s(z)))), s(s(s(z))))))),
% 3.53/3.74 inference(rewrite,[status(thm)],[])).
% 3.53/3.74 tff(17783,plain,
% 3.53/3.74 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(z)), s(s(s(z))))) | (~r(s(s(s(z))), s(s(z)))) | (~r(s(s(s(s(z)))), s(s(z)))) | (~r(s(s(s(s(z)))), s(s(s(z))))))),
% 3.53/3.74 inference(quant_inst,[status(thm)],[])).
% 3.53/3.74 tff(17784,plain,
% 3.53/3.74 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(z)), s(s(s(z))))) | (~r(s(s(s(z))), s(s(z)))) | (~r(s(s(s(s(z)))), s(s(z)))) | (~r(s(s(s(s(z)))), s(s(s(z)))))),
% 3.53/3.74 inference(modus_ponens,[status(thm)],[17783, 17782])).
% 3.53/3.74 tff(17785,plain,
% 3.53/3.74 (~r(s(s(s(s(z)))), s(s(s(z))))),
% 3.53/3.74 inference(unit_resolution,[status(thm)],[17784, 197, 17781, 17765, 17752])).
% 3.53/3.74 tff(17786,plain,
% 3.53/3.74 (b(s(s(s(s(z)))), s(s(s(z))))),
% 3.53/3.74 inference(unit_resolution,[status(thm)],[4662, 17785])).
% 3.53/3.74 tff(17787,plain,
% 3.53/3.74 (b(s(s(s(s(z)))), s(z))),
% 3.53/3.74 inference(modus_ponens,[status(thm)],[17716, 14790])).
% 3.53/3.74 tff(17788,plain,
% 3.53/3.74 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(s(z)))) | (~b(s(s(z)), s(z))) | (~b(s(s(s(z))), elem!1)) | (~b(s(s(s(s(z)))), elem!1)) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(s(z)))), s(s(s(z))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(s(z)))) | (~b(s(s(z)), s(z))) | (~b(s(s(s(z))), elem!1)) | (~b(s(s(s(s(z)))), elem!1)) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(s(z)))), s(s(s(z))))))),
% 3.53/3.74 inference(rewrite,[status(thm)],[])).
% 3.53/3.74 tff(17789,plain,
% 3.53/3.74 (((~b(s(s(z)), s(z))) | (~b(s(s(s(s(z)))), s(z))) | (~b(elem!1, s(s(z)))) | (~b(s(s(s(z))), elem!1)) | (~b(s(s(s(s(z)))), elem!1)) | (~b(s(s(s(s(z)))), s(s(s(z)))))) <=> ((~b(elem!1, s(s(z)))) | (~b(s(s(z)), s(z))) | (~b(s(s(s(z))), elem!1)) | (~b(s(s(s(s(z)))), elem!1)) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(s(z)))), s(s(s(z))))))),
% 3.53/3.74 inference(rewrite,[status(thm)],[])).
% 3.53/3.74 tff(17790,plain,
% 3.53/3.74 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), s(z))) | (~b(s(s(s(s(z)))), s(z))) | (~b(elem!1, s(s(z)))) | (~b(s(s(s(z))), elem!1)) | (~b(s(s(s(s(z)))), elem!1)) | (~b(s(s(s(s(z)))), s(s(s(z))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(s(z)))) | (~b(s(s(z)), s(z))) | (~b(s(s(s(z))), elem!1)) | (~b(s(s(s(s(z)))), elem!1)) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(s(z)))), s(s(s(z)))))))),
% 3.53/3.74 inference(monotonicity,[status(thm)],[17789])).
% 3.53/3.74 tff(17791,plain,
% 3.53/3.74 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), s(z))) | (~b(s(s(s(s(z)))), s(z))) | (~b(elem!1, s(s(z)))) | (~b(s(s(s(z))), elem!1)) | (~b(s(s(s(s(z)))), elem!1)) | (~b(s(s(s(s(z)))), s(s(s(z))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(s(z)))) | (~b(s(s(z)), s(z))) | (~b(s(s(s(z))), elem!1)) | (~b(s(s(s(s(z)))), elem!1)) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(s(z)))), s(s(s(z))))))),
% 3.53/3.74 inference(transitivity,[status(thm)],[17790, 17788])).
% 3.53/3.74 tff(17792,plain,
% 3.53/3.74 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), s(z))) | (~b(s(s(s(s(z)))), s(z))) | (~b(elem!1, s(s(z)))) | (~b(s(s(s(z))), elem!1)) | (~b(s(s(s(s(z)))), elem!1)) | (~b(s(s(s(s(z)))), s(s(s(z))))))),
% 3.53/3.74 inference(quant_inst,[status(thm)],[])).
% 3.53/3.74 tff(17793,plain,
% 3.53/3.74 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(s(z)))) | (~b(s(s(z)), s(z))) | (~b(s(s(s(z))), elem!1)) | (~b(s(s(s(s(z)))), elem!1)) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(s(z)))), s(s(s(z)))))),
% 3.53/3.74 inference(modus_ponens,[status(thm)],[17792, 17791])).
% 3.53/3.74 tff(17794,plain,
% 3.53/3.74 ((~b(s(s(s(s(z)))), elem!1)) | (~b(s(s(s(s(z)))), s(s(s(z)))))),
% 3.53/3.74 inference(unit_resolution,[status(thm)],[17793, 166, 17064, 17756, 17787, 17703])).
% 3.53/3.74 tff(17795,plain,
% 3.53/3.74 (~b(s(s(s(s(z)))), elem!1)),
% 3.53/3.74 inference(unit_resolution,[status(thm)],[17794, 17786])).
% 3.53/3.74 tff(17796,plain,
% 3.53/3.74 (r(s(s(s(s(z)))), elem!1)),
% 3.53/3.74 inference(unit_resolution,[status(thm)],[6190, 17795, 17730])).
% 3.53/3.74 tff(17797,plain,
% 3.53/3.74 (r(s(s(s(s(elem!1)))), elem!1)),
% 3.53/3.74 inference(modus_ponens,[status(thm)],[17796, 17725])).
% 3.53/3.74 tff(17798,plain,
% 3.53/3.74 (~r(s(s(s(s(s(s(elem!1)))))), elem!1)),
% 3.53/3.74 inference(unit_resolution,[status(thm)],[11362, 17797, 17723, 17722, 17717, 17716])).
% 3.53/3.74 tff(17799,plain,
% 3.53/3.74 (b(s(s(s(s(s(s(elem!1)))))), elem!1)),
% 3.53/3.74 inference(unit_resolution,[status(thm)],[9214, 17798, 17704])).
% 3.53/3.74 tff(17800,plain,
% 3.53/3.74 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), elem!1)) | (~b(elem!1, s(s(z)))) | (~b(s(s(s(s(s(s(elem!1)))))), elem!1)) | (~b(s(s(z)), s(s(s(s(s(s(elem!1)))))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(z)), elem!1)) | (~b(elem!1, s(s(z)))) | (~b(s(s(s(s(s(s(elem!1)))))), elem!1)) | (~b(s(s(z)), s(s(s(s(s(s(elem!1)))))))))),
% 3.53/3.74 inference(rewrite,[status(thm)],[])).
% 3.53/3.74 tff(17801,plain,
% 3.53/3.74 (((~b(s(s(z)), elem!1)) | (~b(s(s(z)), elem!1)) | (~b(elem!1, s(s(z)))) | (~b(s(s(s(s(s(s(elem!1)))))), elem!1)) | (~b(s(s(z)), elem!1)) | (~b(s(s(z)), s(s(s(s(s(s(elem!1))))))))) <=> ((~b(s(s(z)), elem!1)) | (~b(elem!1, s(s(z)))) | (~b(s(s(s(s(s(s(elem!1)))))), elem!1)) | (~b(s(s(z)), s(s(s(s(s(s(elem!1)))))))))),
% 3.53/3.74 inference(rewrite,[status(thm)],[])).
% 3.53/3.74 tff(17802,plain,
% 3.53/3.74 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), elem!1)) | (~b(s(s(z)), elem!1)) | (~b(elem!1, s(s(z)))) | (~b(s(s(s(s(s(s(elem!1)))))), elem!1)) | (~b(s(s(z)), elem!1)) | (~b(s(s(z)), s(s(s(s(s(s(elem!1)))))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), elem!1)) | (~b(elem!1, s(s(z)))) | (~b(s(s(s(s(s(s(elem!1)))))), elem!1)) | (~b(s(s(z)), s(s(s(s(s(s(elem!1))))))))))),
% 3.53/3.74 inference(monotonicity,[status(thm)],[17801])).
% 3.53/3.74 tff(17803,plain,
% 3.53/3.74 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), elem!1)) | (~b(s(s(z)), elem!1)) | (~b(elem!1, s(s(z)))) | (~b(s(s(s(s(s(s(elem!1)))))), elem!1)) | (~b(s(s(z)), elem!1)) | (~b(s(s(z)), s(s(s(s(s(s(elem!1)))))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(z)), elem!1)) | (~b(elem!1, s(s(z)))) | (~b(s(s(s(s(s(s(elem!1)))))), elem!1)) | (~b(s(s(z)), s(s(s(s(s(s(elem!1)))))))))),
% 3.53/3.74 inference(transitivity,[status(thm)],[17802, 17800])).
% 3.53/3.74 tff(17804,plain,
% 3.53/3.74 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), elem!1)) | (~b(s(s(z)), elem!1)) | (~b(elem!1, s(s(z)))) | (~b(s(s(s(s(s(s(elem!1)))))), elem!1)) | (~b(s(s(z)), elem!1)) | (~b(s(s(z)), s(s(s(s(s(s(elem!1)))))))))),
% 3.53/3.74 inference(quant_inst,[status(thm)],[])).
% 3.53/3.74 tff(17805,plain,
% 3.53/3.74 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(z)), elem!1)) | (~b(elem!1, s(s(z)))) | (~b(s(s(s(s(s(s(elem!1)))))), elem!1)) | (~b(s(s(z)), s(s(s(s(s(s(elem!1))))))))),
% 3.53/3.74 inference(modus_ponens,[status(thm)],[17804, 17803])).
% 3.53/3.74 tff(17806,plain,
% 3.53/3.74 (~b(s(s(z)), s(s(s(s(s(s(elem!1)))))))),
% 3.53/3.74 inference(unit_resolution,[status(thm)],[17805, 166, 17753, 17799, 17703])).
% 3.53/3.74 tff(17807,plain,
% 3.53/3.74 (((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((s(s(z)) = s(s(s(s(s(s(elem!1))))))) | b(s(s(z)), s(s(s(s(s(s(elem!1))))))) | r(s(s(z)), s(s(s(s(s(s(elem!1))))))))) <=> ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (s(s(z)) = s(s(s(s(s(s(elem!1))))))) | b(s(s(z)), s(s(s(s(s(s(elem!1))))))) | r(s(s(z)), s(s(s(s(s(s(elem!1))))))))),
% 3.53/3.74 inference(rewrite,[status(thm)],[])).
% 3.53/3.74 tff(17808,plain,
% 3.53/3.74 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((s(s(z)) = s(s(s(s(s(s(elem!1))))))) | b(s(s(z)), s(s(s(s(s(s(elem!1))))))) | r(s(s(z)), s(s(s(s(s(s(elem!1))))))))),
% 3.53/3.74 inference(quant_inst,[status(thm)],[])).
% 3.53/3.74 tff(17809,plain,
% 3.53/3.74 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (s(s(z)) = s(s(s(s(s(s(elem!1))))))) | b(s(s(z)), s(s(s(s(s(s(elem!1))))))) | r(s(s(z)), s(s(s(s(s(s(elem!1)))))))),
% 3.53/3.74 inference(modus_ponens,[status(thm)],[17808, 17807])).
% 3.53/3.74 tff(17810,plain,
% 3.53/3.74 ((s(s(z)) = s(s(s(s(s(s(elem!1))))))) | r(s(s(z)), s(s(s(s(s(s(elem!1)))))))),
% 3.53/3.74 inference(unit_resolution,[status(thm)],[17809, 79, 17806])).
% 3.53/3.74 tff(17811,plain,
% 3.53/3.74 (r(s(s(z)), s(s(s(s(s(s(elem!1)))))))),
% 3.53/3.74 inference(unit_resolution,[status(thm)],[17810, 17701])).
% 3.53/3.74 tff(17812,plain,
% 3.53/3.74 ((s(s(s(s(s(s(elem!1)))))) = s(s(z))) <=> (s(s(s(s(s(s(elem!1)))))) = s(s(elem!1)))),
% 3.53/3.74 inference(monotonicity,[status(thm)],[4988])).
% 3.53/3.74 tff(17813,plain,
% 3.53/3.74 ((s(s(s(s(s(s(elem!1)))))) = s(s(elem!1))) <=> (s(s(s(s(s(s(elem!1)))))) = s(s(z)))),
% 3.53/3.74 inference(symmetry,[status(thm)],[17812])).
% 3.53/3.74 tff(17814,plain,
% 3.53/3.74 ((~(s(s(s(s(s(s(elem!1)))))) = s(s(elem!1)))) <=> (~(s(s(s(s(s(s(elem!1)))))) = s(s(z))))),
% 3.53/3.74 inference(monotonicity,[status(thm)],[17813])).
% 3.53/3.74 tff(17815,plain,
% 3.53/3.74 (~(s(s(s(s(s(s(elem!1)))))) = s(s(z)))),
% 3.53/3.74 inference(modus_ponens,[status(thm)],[17700, 17814])).
% 3.53/3.74 tff(17816,plain,
% 3.53/3.74 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), elem!1)) | (~b(elem!1, s(s(z)))) | (~b(s(s(s(s(s(s(elem!1)))))), elem!1)) | (~b(s(s(s(s(s(s(elem!1)))))), s(s(z)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(z)), elem!1)) | (~b(elem!1, s(s(z)))) | (~b(s(s(s(s(s(s(elem!1)))))), elem!1)) | (~b(s(s(s(s(s(s(elem!1)))))), s(s(z)))))),
% 3.53/3.74 inference(rewrite,[status(thm)],[])).
% 3.53/3.74 tff(17817,plain,
% 3.53/3.74 (((~b(s(s(z)), elem!1)) | (~b(s(s(s(s(s(s(elem!1)))))), elem!1)) | (~b(elem!1, s(s(z)))) | (~b(s(s(z)), elem!1)) | (~b(s(s(s(s(s(s(elem!1)))))), elem!1)) | (~b(s(s(s(s(s(s(elem!1)))))), s(s(z))))) <=> ((~b(s(s(z)), elem!1)) | (~b(elem!1, s(s(z)))) | (~b(s(s(s(s(s(s(elem!1)))))), elem!1)) | (~b(s(s(s(s(s(s(elem!1)))))), s(s(z)))))),
% 3.53/3.74 inference(rewrite,[status(thm)],[])).
% 3.53/3.74 tff(17818,plain,
% 3.53/3.74 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), elem!1)) | (~b(s(s(s(s(s(s(elem!1)))))), elem!1)) | (~b(elem!1, s(s(z)))) | (~b(s(s(z)), elem!1)) | (~b(s(s(s(s(s(s(elem!1)))))), elem!1)) | (~b(s(s(s(s(s(s(elem!1)))))), s(s(z)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), elem!1)) | (~b(elem!1, s(s(z)))) | (~b(s(s(s(s(s(s(elem!1)))))), elem!1)) | (~b(s(s(s(s(s(s(elem!1)))))), s(s(z))))))),
% 3.53/3.74 inference(monotonicity,[status(thm)],[17817])).
% 3.53/3.74 tff(17819,plain,
% 3.53/3.74 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), elem!1)) | (~b(s(s(s(s(s(s(elem!1)))))), elem!1)) | (~b(elem!1, s(s(z)))) | (~b(s(s(z)), elem!1)) | (~b(s(s(s(s(s(s(elem!1)))))), elem!1)) | (~b(s(s(s(s(s(s(elem!1)))))), s(s(z)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(z)), elem!1)) | (~b(elem!1, s(s(z)))) | (~b(s(s(s(s(s(s(elem!1)))))), elem!1)) | (~b(s(s(s(s(s(s(elem!1)))))), s(s(z)))))),
% 3.53/3.74 inference(transitivity,[status(thm)],[17818, 17816])).
% 3.53/3.74 tff(17820,plain,
% 3.53/3.74 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), elem!1)) | (~b(s(s(s(s(s(s(elem!1)))))), elem!1)) | (~b(elem!1, s(s(z)))) | (~b(s(s(z)), elem!1)) | (~b(s(s(s(s(s(s(elem!1)))))), elem!1)) | (~b(s(s(s(s(s(s(elem!1)))))), s(s(z)))))),
% 3.53/3.74 inference(quant_inst,[status(thm)],[])).
% 3.53/3.74 tff(17821,plain,
% 3.53/3.74 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(z)), elem!1)) | (~b(elem!1, s(s(z)))) | (~b(s(s(s(s(s(s(elem!1)))))), elem!1)) | (~b(s(s(s(s(s(s(elem!1)))))), s(s(z))))),
% 3.53/3.74 inference(modus_ponens,[status(thm)],[17820, 17819])).
% 3.53/3.75 tff(17822,plain,
% 3.53/3.75 (~b(s(s(s(s(s(s(elem!1)))))), s(s(z)))),
% 3.53/3.75 inference(unit_resolution,[status(thm)],[17821, 166, 17753, 17799, 17703])).
% 3.53/3.75 tff(17823,plain,
% 3.53/3.75 (((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((s(s(s(s(s(s(elem!1)))))) = s(s(z))) | b(s(s(s(s(s(s(elem!1)))))), s(s(z))) | r(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(elem!1)))))) = s(s(z))) | b(s(s(s(s(s(s(elem!1)))))), s(s(z))) | r(s(s(s(s(s(s(elem!1)))))), s(s(z))))),
% 3.53/3.75 inference(rewrite,[status(thm)],[])).
% 3.53/3.75 tff(17824,plain,
% 3.53/3.75 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((s(s(s(s(s(s(elem!1)))))) = s(s(z))) | b(s(s(s(s(s(s(elem!1)))))), s(s(z))) | r(s(s(s(s(s(s(elem!1)))))), s(s(z))))),
% 3.53/3.75 inference(quant_inst,[status(thm)],[])).
% 3.53/3.75 tff(17825,plain,
% 3.53/3.75 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (s(s(s(s(s(s(elem!1)))))) = s(s(z))) | b(s(s(s(s(s(s(elem!1)))))), s(s(z))) | r(s(s(s(s(s(s(elem!1)))))), s(s(z)))),
% 3.53/3.75 inference(modus_ponens,[status(thm)],[17824, 17823])).
% 3.53/3.75 tff(17826,plain,
% 3.53/3.75 ((s(s(s(s(s(s(elem!1)))))) = s(s(z))) | r(s(s(s(s(s(s(elem!1)))))), s(s(z)))),
% 3.53/3.75 inference(unit_resolution,[status(thm)],[17825, 79, 17822])).
% 3.53/3.75 tff(17827,plain,
% 3.53/3.75 (r(s(s(s(s(s(s(elem!1)))))), s(s(z)))),
% 3.53/3.75 inference(unit_resolution,[status(thm)],[17826, 17815])).
% 3.53/3.75 tff(17828,plain,
% 3.53/3.75 ((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))))),
% 3.53/3.75 inference(commutativity,[status(thm)],[])).
% 3.53/3.75 tff(17829,plain,
% 3.53/3.75 ((s(s(s(z))) = s(s(s(s(s(s(elem!1))))))) <=> (s(s(s(elem!1))) = s(s(s(s(s(s(elem!1)))))))),
% 3.53/3.75 inference(monotonicity,[status(thm)],[2201])).
% 3.53/3.75 tff(17830,plain,
% 3.53/3.75 ((s(s(s(z))) = s(s(s(s(s(s(elem!1))))))) <=> (s(s(s(s(s(s(elem!1)))))) = s(s(s(elem!1))))),
% 3.53/3.75 inference(transitivity,[status(thm)],[17829, 17828])).
% 3.53/3.75 tff(17831,plain,
% 3.53/3.75 ((s(s(s(s(s(s(elem!1)))))) = s(s(s(elem!1)))) <=> (s(s(s(z))) = s(s(s(s(s(s(elem!1)))))))),
% 3.53/3.75 inference(symmetry,[status(thm)],[17830])).
% 3.53/3.75 tff(17832,plain,
% 3.53/3.75 ((~(s(s(s(s(s(s(elem!1)))))) = s(s(s(elem!1))))) <=> (~(s(s(s(z))) = s(s(s(s(s(s(elem!1))))))))),
% 3.53/3.75 inference(monotonicity,[status(thm)],[17831])).
% 3.53/3.75 tff(17833,plain,
% 3.53/3.75 (~(s(s(s(s(s(s(elem!1)))))) = s(s(s(elem!1))))),
% 3.53/3.75 inference(unit_resolution,[status(thm)],[4922, 14761])).
% 3.53/3.75 tff(17834,plain,
% 3.53/3.75 (~(s(s(s(z))) = s(s(s(s(s(s(elem!1)))))))),
% 3.53/3.75 inference(modus_ponens,[status(thm)],[17833, 17832])).
% 3.53/3.75 tff(17835,plain,
% 3.53/3.75 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), elem!1)) | (~b(elem!1, s(s(z)))) | (~b(s(s(s(z))), elem!1)) | (~b(s(s(s(s(s(s(elem!1)))))), elem!1)) | (~b(s(s(s(z))), s(s(s(s(s(s(elem!1)))))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(z)), elem!1)) | (~b(elem!1, s(s(z)))) | (~b(s(s(s(z))), elem!1)) | (~b(s(s(s(s(s(s(elem!1)))))), elem!1)) | (~b(s(s(s(z))), s(s(s(s(s(s(elem!1)))))))))),
% 3.53/3.75 inference(rewrite,[status(thm)],[])).
% 3.53/3.75 tff(17836,plain,
% 3.53/3.75 (((~b(s(s(z)), elem!1)) | (~b(s(s(s(z))), elem!1)) | (~b(elem!1, s(s(z)))) | (~b(s(s(s(s(s(s(elem!1)))))), elem!1)) | (~b(s(s(s(z))), elem!1)) | (~b(s(s(s(z))), s(s(s(s(s(s(elem!1))))))))) <=> ((~b(s(s(z)), elem!1)) | (~b(elem!1, s(s(z)))) | (~b(s(s(s(z))), elem!1)) | (~b(s(s(s(s(s(s(elem!1)))))), elem!1)) | (~b(s(s(s(z))), s(s(s(s(s(s(elem!1)))))))))),
% 3.53/3.75 inference(rewrite,[status(thm)],[])).
% 3.53/3.75 tff(17837,plain,
% 3.53/3.75 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), elem!1)) | (~b(s(s(s(z))), elem!1)) | (~b(elem!1, s(s(z)))) | (~b(s(s(s(s(s(s(elem!1)))))), elem!1)) | (~b(s(s(s(z))), elem!1)) | (~b(s(s(s(z))), s(s(s(s(s(s(elem!1)))))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), elem!1)) | (~b(elem!1, s(s(z)))) | (~b(s(s(s(z))), elem!1)) | (~b(s(s(s(s(s(s(elem!1)))))), elem!1)) | (~b(s(s(s(z))), s(s(s(s(s(s(elem!1))))))))))),
% 3.53/3.75 inference(monotonicity,[status(thm)],[17836])).
% 3.53/3.75 tff(17838,plain,
% 3.53/3.75 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), elem!1)) | (~b(s(s(s(z))), elem!1)) | (~b(elem!1, s(s(z)))) | (~b(s(s(s(s(s(s(elem!1)))))), elem!1)) | (~b(s(s(s(z))), elem!1)) | (~b(s(s(s(z))), s(s(s(s(s(s(elem!1)))))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(z)), elem!1)) | (~b(elem!1, s(s(z)))) | (~b(s(s(s(z))), elem!1)) | (~b(s(s(s(s(s(s(elem!1)))))), elem!1)) | (~b(s(s(s(z))), s(s(s(s(s(s(elem!1)))))))))),
% 3.53/3.75 inference(transitivity,[status(thm)],[17837, 17835])).
% 3.53/3.75 tff(17839,plain,
% 3.53/3.75 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), elem!1)) | (~b(s(s(s(z))), elem!1)) | (~b(elem!1, s(s(z)))) | (~b(s(s(s(s(s(s(elem!1)))))), elem!1)) | (~b(s(s(s(z))), elem!1)) | (~b(s(s(s(z))), s(s(s(s(s(s(elem!1)))))))))),
% 3.53/3.75 inference(quant_inst,[status(thm)],[])).
% 3.53/3.75 tff(17840,plain,
% 3.53/3.75 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(z)), elem!1)) | (~b(elem!1, s(s(z)))) | (~b(s(s(s(z))), elem!1)) | (~b(s(s(s(s(s(s(elem!1)))))), elem!1)) | (~b(s(s(s(z))), s(s(s(s(s(s(elem!1))))))))),
% 3.53/3.75 inference(modus_ponens,[status(thm)],[17839, 17838])).
% 3.53/3.75 tff(17841,plain,
% 3.53/3.75 (~b(s(s(s(z))), s(s(s(s(s(s(elem!1)))))))),
% 3.53/3.75 inference(unit_resolution,[status(thm)],[17840, 166, 17753, 17756, 17799, 17703])).
% 3.53/3.75 tff(17842,plain,
% 3.53/3.75 (((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((s(s(s(z))) = s(s(s(s(s(s(elem!1))))))) | b(s(s(s(z))), s(s(s(s(s(s(elem!1))))))) | r(s(s(s(z))), s(s(s(s(s(s(elem!1))))))))) <=> ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (s(s(s(z))) = s(s(s(s(s(s(elem!1))))))) | b(s(s(s(z))), s(s(s(s(s(s(elem!1))))))) | r(s(s(s(z))), s(s(s(s(s(s(elem!1))))))))),
% 3.53/3.75 inference(rewrite,[status(thm)],[])).
% 3.53/3.75 tff(17843,plain,
% 3.53/3.75 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((s(s(s(z))) = s(s(s(s(s(s(elem!1))))))) | b(s(s(s(z))), s(s(s(s(s(s(elem!1))))))) | r(s(s(s(z))), s(s(s(s(s(s(elem!1))))))))),
% 3.53/3.75 inference(quant_inst,[status(thm)],[])).
% 3.53/3.75 tff(17844,plain,
% 3.53/3.75 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (s(s(s(z))) = s(s(s(s(s(s(elem!1))))))) | b(s(s(s(z))), s(s(s(s(s(s(elem!1))))))) | r(s(s(s(z))), s(s(s(s(s(s(elem!1)))))))),
% 3.53/3.75 inference(modus_ponens,[status(thm)],[17843, 17842])).
% 3.53/3.75 tff(17845,plain,
% 3.53/3.75 ((s(s(s(z))) = s(s(s(s(s(s(elem!1))))))) | r(s(s(s(z))), s(s(s(s(s(s(elem!1)))))))),
% 3.53/3.75 inference(unit_resolution,[status(thm)],[17844, 79, 17841])).
% 3.53/3.75 tff(17846,plain,
% 3.53/3.75 (r(s(s(s(z))), s(s(s(s(s(s(elem!1)))))))),
% 3.53/3.75 inference(unit_resolution,[status(thm)],[17845, 17834])).
% 3.53/3.75 tff(17847,plain,
% 3.53/3.75 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(z))), s(s(z)))) | (~r(s(s(s(s(s(s(elem!1)))))), s(s(z)))) | (~r(s(s(z)), s(s(s(s(s(s(elem!1)))))))) | (~r(s(s(s(z))), s(s(s(s(s(s(elem!1)))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(z))), s(s(z)))) | (~r(s(s(s(s(s(s(elem!1)))))), s(s(z)))) | (~r(s(s(z)), s(s(s(s(s(s(elem!1)))))))) | (~r(s(s(s(z))), s(s(s(s(s(s(elem!1)))))))))),
% 3.53/3.75 inference(rewrite,[status(thm)],[])).
% 3.53/3.75 tff(17848,plain,
% 3.53/3.75 (((~r(s(s(s(s(s(s(elem!1)))))), s(s(z)))) | (~r(s(s(z)), s(s(s(s(s(s(elem!1)))))))) | (~r(s(s(s(z))), s(s(s(s(s(s(elem!1)))))))) | (~r(s(s(s(z))), s(s(z))))) <=> ((~r(s(s(s(z))), s(s(z)))) | (~r(s(s(s(s(s(s(elem!1)))))), s(s(z)))) | (~r(s(s(z)), s(s(s(s(s(s(elem!1)))))))) | (~r(s(s(s(z))), s(s(s(s(s(s(elem!1)))))))))),
% 3.53/3.75 inference(rewrite,[status(thm)],[])).
% 3.53/3.75 tff(17849,plain,
% 3.53/3.75 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(s(s(elem!1)))))), s(s(z)))) | (~r(s(s(z)), s(s(s(s(s(s(elem!1)))))))) | (~r(s(s(s(z))), s(s(s(s(s(s(elem!1)))))))) | (~r(s(s(s(z))), s(s(z)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(z))), s(s(z)))) | (~r(s(s(s(s(s(s(elem!1)))))), s(s(z)))) | (~r(s(s(z)), s(s(s(s(s(s(elem!1)))))))) | (~r(s(s(s(z))), s(s(s(s(s(s(elem!1))))))))))),
% 3.53/3.75 inference(monotonicity,[status(thm)],[17848])).
% 3.53/3.75 tff(17850,plain,
% 3.53/3.75 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(s(s(elem!1)))))), s(s(z)))) | (~r(s(s(z)), s(s(s(s(s(s(elem!1)))))))) | (~r(s(s(s(z))), s(s(s(s(s(s(elem!1)))))))) | (~r(s(s(s(z))), s(s(z)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(z))), s(s(z)))) | (~r(s(s(s(s(s(s(elem!1)))))), s(s(z)))) | (~r(s(s(z)), s(s(s(s(s(s(elem!1)))))))) | (~r(s(s(s(z))), s(s(s(s(s(s(elem!1)))))))))),
% 3.53/3.75 inference(transitivity,[status(thm)],[17849, 17847])).
% 3.53/3.75 tff(17851,plain,
% 3.53/3.75 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(s(s(elem!1)))))), s(s(z)))) | (~r(s(s(z)), s(s(s(s(s(s(elem!1)))))))) | (~r(s(s(s(z))), s(s(s(s(s(s(elem!1)))))))) | (~r(s(s(s(z))), s(s(z)))))),
% 3.53/3.75 inference(quant_inst,[status(thm)],[])).
% 3.53/3.75 tff(17852,plain,
% 3.53/3.75 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(z))), s(s(z)))) | (~r(s(s(s(s(s(s(elem!1)))))), s(s(z)))) | (~r(s(s(z)), s(s(s(s(s(s(elem!1)))))))) | (~r(s(s(s(z))), s(s(s(s(s(s(elem!1))))))))),
% 3.53/3.75 inference(modus_ponens,[status(thm)],[17851, 17850])).
% 3.53/3.75 tff(17853,plain,
% 3.53/3.75 ($false),
% 3.53/3.75 inference(unit_resolution,[status(thm)],[17852, 197, 17781, 17846, 17827, 17811])).
% 3.53/3.75 tff(17854,plain,((~r(s(s(s(elem!1))), s(z))) | (~(s(s(elem!1)) = s(s(z)))) | (~b(s(s(s(elem!1))), z))), inference(lemma,lemma(discharge,[]))).
% 3.53/3.75 tff(17855,plain,
% 3.53/3.75 (~r(s(s(s(elem!1))), s(z))),
% 3.53/3.75 inference(unit_resolution,[status(thm)],[17854, 17672, 95])).
% 3.53/3.75 tff(17856,plain,
% 3.53/3.75 (b(s(s(s(elem!1))), s(z))),
% 3.53/3.75 inference(unit_resolution,[status(thm)],[1849, 17855])).
% 3.53/3.75 tff(17857,plain,
% 3.53/3.75 (~b(s(s(elem!1)), s(s(s(elem!1))))),
% 3.53/3.75 inference(unit_resolution,[status(thm)],[7367, 17856, 15211, 95, 17694])).
% 3.53/3.75 tff(17858,plain,
% 3.53/3.75 (r(s(s(elem!1)), s(s(s(elem!1))))),
% 3.53/3.75 inference(unit_resolution,[status(thm)],[461, 17857, 17691])).
% 3.53/3.75 tff(17859,plain,
% 3.53/3.75 (r(s(s(z)), s(s(s(z))))),
% 3.53/3.75 inference(modus_ponens,[status(thm)],[17858, 17687])).
% 3.53/3.75 tff(17860,plain,
% 3.53/3.75 ((s(s(s(s(z)))) = z) <=> (s(s(s(s(z)))) = elem!1)),
% 3.53/3.75 inference(monotonicity,[status(thm)],[17678])).
% 3.53/3.75 tff(17861,plain,
% 3.53/3.75 ((s(s(s(s(z)))) = z) <=> (elem!1 = s(s(s(s(z)))))),
% 3.53/3.75 inference(transitivity,[status(thm)],[17860, 1039])).
% 3.53/3.75 tff(17862,plain,
% 3.53/3.75 ((s(s(s(s(z)))) = z) <=> (s(s(s(s(z)))) = elem!1)),
% 3.53/3.75 inference(transitivity,[status(thm)],[17861, 6181])).
% 3.53/3.75 tff(17863,plain,
% 3.53/3.75 ((~(s(s(s(s(z)))) = z)) <=> (~(s(s(s(s(z)))) = elem!1))),
% 3.53/3.75 inference(monotonicity,[status(thm)],[17862])).
% 3.53/3.75 tff(17864,plain,
% 3.53/3.75 (~(s(s(s(s(z)))) = elem!1)),
% 3.53/3.75 inference(modus_ponens,[status(thm)],[1044, 17863])).
% 3.53/3.75 tff(17865,plain,
% 3.53/3.75 (s(s(s(s(elem!1)))) = s(s(s(s(z))))),
% 3.53/3.75 inference(monotonicity,[status(thm)],[17684])).
% 3.53/3.75 tff(17866,plain,
% 3.53/3.75 (s(s(s(s(z)))) = s(s(s(s(elem!1))))),
% 3.53/3.75 inference(symmetry,[status(thm)],[17865])).
% 3.53/3.75 tff(17867,plain,
% 3.53/3.75 (r(s(s(s(s(z)))), s(z)) <=> r(s(s(s(s(elem!1)))), s(z))),
% 3.53/3.75 inference(monotonicity,[status(thm)],[17866])).
% 3.53/3.75 tff(17868,plain,
% 3.53/3.75 (r(s(s(s(s(elem!1)))), s(z)) <=> r(s(s(s(s(z)))), s(z))),
% 3.53/3.75 inference(symmetry,[status(thm)],[17867])).
% 3.53/3.75 tff(17869,plain,
% 3.53/3.75 ((s(s(s(s(elem!1)))) = s(s(z))) <=> (s(s(s(s(elem!1)))) = s(s(elem!1)))),
% 3.53/3.75 inference(monotonicity,[status(thm)],[17673])).
% 3.53/3.75 tff(17870,plain,
% 3.53/3.75 ((s(s(s(s(elem!1)))) = s(s(z))) <=> (s(s(elem!1)) = s(s(s(s(elem!1)))))),
% 3.53/3.75 inference(transitivity,[status(thm)],[17869, 123])).
% 3.53/3.75 tff(17871,plain,
% 3.53/3.75 ((s(s(s(s(elem!1)))) = s(s(z))) <=> (s(s(s(s(elem!1)))) = s(s(elem!1)))),
% 3.53/3.75 inference(transitivity,[status(thm)],[17870, 124])).
% 3.53/3.75 tff(17872,plain,
% 3.53/3.75 ((~(s(s(s(s(elem!1)))) = s(s(z)))) <=> (~(s(s(s(s(elem!1)))) = s(s(elem!1))))),
% 3.53/3.75 inference(monotonicity,[status(thm)],[17871])).
% 3.53/3.75 tff(17873,plain,
% 3.53/3.75 (~(s(s(s(s(elem!1)))) = s(s(elem!1)))),
% 3.53/3.75 inference(modus_ponens,[status(thm)],[733, 17872])).
% 3.53/3.75 tff(17874,plain,
% 3.53/3.75 (b(s(s(elem!1)), s(z)) <=> b(s(s(z)), s(z))),
% 3.53/3.75 inference(monotonicity,[status(thm)],[17672])).
% 3.53/3.75 tff(17875,plain,
% 3.53/3.75 (b(s(s(z)), s(z)) <=> b(s(s(elem!1)), s(z))),
% 3.53/3.75 inference(symmetry,[status(thm)],[17874])).
% 3.53/3.75 tff(17876,plain,
% 3.53/3.75 (b(s(s(elem!1)), s(z))),
% 3.53/3.75 inference(modus_ponens,[status(thm)],[17064, 17875])).
% 3.53/3.75 tff(17877,plain,
% 3.53/3.75 ((s(s(s(elem!1))) = s(s(s(s(elem!1))))) <=> (s(s(s(z))) = s(s(s(s(elem!1)))))),
% 3.53/3.75 inference(monotonicity,[status(thm)],[17684])).
% 3.53/3.75 tff(17878,plain,
% 3.53/3.75 ((s(s(s(elem!1))) = s(s(s(s(elem!1))))) <=> (s(s(s(s(elem!1)))) = s(s(s(z))))),
% 3.53/3.75 inference(transitivity,[status(thm)],[17877, 17708])).
% 3.53/3.75 tff(17879,plain,
% 3.53/3.75 ((s(s(s(s(elem!1)))) = s(s(s(z)))) <=> (s(s(s(elem!1))) = s(s(s(s(elem!1)))))),
% 3.53/3.75 inference(symmetry,[status(thm)],[17878])).
% 3.53/3.75 tff(17880,plain,
% 3.53/3.75 ((~(s(s(s(s(elem!1)))) = s(s(s(z))))) <=> (~(s(s(s(elem!1))) = s(s(s(s(elem!1))))))),
% 3.53/3.75 inference(monotonicity,[status(thm)],[17879])).
% 3.53/3.75 tff(17881,plain,
% 3.53/3.75 (~(s(s(s(elem!1))) = s(s(s(s(elem!1)))))),
% 3.53/3.75 inference(modus_ponens,[status(thm)],[5112, 17880])).
% 3.53/3.75 tff(17882,plain,
% 3.53/3.75 ((~(s(s(s(s(elem!1)))) = s(s(z)))) <=> (~(s(s(elem!1)) = s(s(s(s(elem!1))))))),
% 3.53/3.75 inference(monotonicity,[status(thm)],[17870])).
% 3.53/3.75 tff(17883,plain,
% 3.53/3.75 (~(s(s(elem!1)) = s(s(s(s(elem!1)))))),
% 3.53/3.75 inference(modus_ponens,[status(thm)],[733, 17882])).
% 3.53/3.75 tff(17884,plain,
% 3.53/3.75 (~b(s(s(s(elem!1))), s(s(elem!1)))),
% 3.53/3.75 inference(unit_resolution,[status(thm)],[1858, 17856, 15211, 17876])).
% 3.53/3.75 tff(17885,plain,
% 3.53/3.75 (r(s(s(s(elem!1))), s(s(elem!1)))),
% 3.53/3.75 inference(unit_resolution,[status(thm)],[889, 17884, 17694])).
% 3.53/3.75 tff(17886,plain,
% 3.53/3.75 (~b(s(s(s(s(elem!1)))), s(z))),
% 3.53/3.75 inference(unit_resolution,[status(thm)],[9124, 17885, 15211, 17883, 17881, 17876, 17873, 17856])).
% 3.53/3.75 tff(17887,plain,
% 3.53/3.75 (r(s(s(s(s(elem!1)))), s(z))),
% 3.53/3.75 inference(unit_resolution,[status(thm)],[661, 17886])).
% 3.53/3.75 tff(17888,plain,
% 3.53/3.75 (r(s(s(s(s(z)))), s(z))),
% 3.53/3.75 inference(modus_ponens,[status(thm)],[17887, 17868])).
% 3.53/3.75 tff(17889,plain,
% 3.53/3.75 (r(s(z), z) <=> r(s(z), elem!1)),
% 3.53/3.75 inference(monotonicity,[status(thm)],[17678])).
% 3.53/3.75 tff(17890,plain,
% 3.53/3.75 (r(s(z), elem!1)),
% 3.53/3.75 inference(modus_ponens,[status(thm)],[17593, 17889])).
% 3.53/3.75 tff(17891,plain,
% 3.53/3.75 (b(s(z), s(s(z)))),
% 3.53/3.75 inference(unit_resolution,[status(thm)],[5435, 17676, 15211])).
% 3.53/3.75 tff(17892,plain,
% 3.53/3.75 (~b(z, s(z))),
% 3.53/3.75 inference(unit_resolution,[status(thm)],[14336, 17891, 17064])).
% 3.53/3.75 tff(17893,plain,
% 3.53/3.75 (r(z, s(z))),
% 3.53/3.75 inference(unit_resolution,[status(thm)],[321, 17892])).
% 3.53/3.75 tff(17894,plain,
% 3.53/3.75 (r(elem!1, s(z))),
% 3.53/3.75 inference(unit_resolution,[status(thm)],[741, 17893, 17678])).
% 3.53/3.75 tff(17895,plain,
% 3.53/3.75 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), elem!1)) | (~r(elem!1, s(z))) | (~r(s(s(s(s(z)))), elem!1)) | (~r(s(s(s(s(z)))), s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(z), elem!1)) | (~r(elem!1, s(z))) | (~r(s(s(s(s(z)))), elem!1)) | (~r(s(s(s(s(z)))), s(z))))),
% 3.53/3.75 inference(rewrite,[status(thm)],[])).
% 3.53/3.75 tff(17896,plain,
% 3.53/3.75 (((~r(s(z), elem!1)) | (~r(elem!1, s(z))) | (~r(s(s(s(s(z)))), s(z))) | (~r(s(s(s(s(z)))), elem!1))) <=> ((~r(s(z), elem!1)) | (~r(elem!1, s(z))) | (~r(s(s(s(s(z)))), elem!1)) | (~r(s(s(s(s(z)))), s(z))))),
% 3.53/3.75 inference(rewrite,[status(thm)],[])).
% 3.53/3.75 tff(17897,plain,
% 3.53/3.75 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), elem!1)) | (~r(elem!1, s(z))) | (~r(s(s(s(s(z)))), s(z))) | (~r(s(s(s(s(z)))), elem!1)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), elem!1)) | (~r(elem!1, s(z))) | (~r(s(s(s(s(z)))), elem!1)) | (~r(s(s(s(s(z)))), s(z)))))),
% 3.53/3.75 inference(monotonicity,[status(thm)],[17896])).
% 3.53/3.75 tff(17898,plain,
% 3.53/3.75 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), elem!1)) | (~r(elem!1, s(z))) | (~r(s(s(s(s(z)))), s(z))) | (~r(s(s(s(s(z)))), elem!1)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(z), elem!1)) | (~r(elem!1, s(z))) | (~r(s(s(s(s(z)))), elem!1)) | (~r(s(s(s(s(z)))), s(z))))),
% 3.53/3.75 inference(transitivity,[status(thm)],[17897, 17895])).
% 3.53/3.75 tff(17899,plain,
% 3.53/3.75 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), elem!1)) | (~r(elem!1, s(z))) | (~r(s(s(s(s(z)))), s(z))) | (~r(s(s(s(s(z)))), elem!1)))),
% 3.53/3.75 inference(quant_inst,[status(thm)],[])).
% 3.53/3.75 tff(17900,plain,
% 3.53/3.75 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(z), elem!1)) | (~r(elem!1, s(z))) | (~r(s(s(s(s(z)))), elem!1)) | (~r(s(s(s(s(z)))), s(z)))),
% 3.53/3.75 inference(modus_ponens,[status(thm)],[17899, 17898])).
% 3.53/3.75 tff(17901,plain,
% 3.53/3.75 (~r(s(s(s(s(z)))), elem!1)),
% 3.53/3.75 inference(unit_resolution,[status(thm)],[17900, 197, 17894, 17890, 17888])).
% 3.53/3.75 tff(17902,plain,
% 3.53/3.75 (b(s(s(s(s(z)))), elem!1)),
% 3.53/3.75 inference(unit_resolution,[status(thm)],[6190, 17901, 17864])).
% 3.53/3.75 tff(17903,plain,
% 3.53/3.75 ((~(s(s(s(s(z)))) = z)) <=> (~(elem!1 = s(s(s(s(z))))))),
% 3.53/3.75 inference(monotonicity,[status(thm)],[17861])).
% 3.53/3.75 tff(17904,plain,
% 3.53/3.75 (~(elem!1 = s(s(s(s(z)))))),
% 3.53/3.75 inference(modus_ponens,[status(thm)],[1044, 17903])).
% 3.53/3.75 tff(17905,plain,
% 3.53/3.75 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), elem!1)) | (~r(elem!1, s(z))) | (~r(elem!1, s(s(s(s(z)))))) | (~r(s(s(s(s(z)))), s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(z), elem!1)) | (~r(elem!1, s(z))) | (~r(elem!1, s(s(s(s(z)))))) | (~r(s(s(s(s(z)))), s(z))))),
% 3.53/3.75 inference(rewrite,[status(thm)],[])).
% 3.53/3.75 tff(17906,plain,
% 3.53/3.75 (((~r(s(z), elem!1)) | (~r(s(s(s(s(z)))), s(z))) | (~r(elem!1, s(z))) | (~r(elem!1, s(s(s(s(z))))))) <=> ((~r(s(z), elem!1)) | (~r(elem!1, s(z))) | (~r(elem!1, s(s(s(s(z)))))) | (~r(s(s(s(s(z)))), s(z))))),
% 3.53/3.75 inference(rewrite,[status(thm)],[])).
% 3.53/3.75 tff(17907,plain,
% 3.53/3.75 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), elem!1)) | (~r(s(s(s(s(z)))), s(z))) | (~r(elem!1, s(z))) | (~r(elem!1, s(s(s(s(z)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), elem!1)) | (~r(elem!1, s(z))) | (~r(elem!1, s(s(s(s(z)))))) | (~r(s(s(s(s(z)))), s(z)))))),
% 3.53/3.75 inference(monotonicity,[status(thm)],[17906])).
% 3.53/3.75 tff(17908,plain,
% 3.53/3.75 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), elem!1)) | (~r(s(s(s(s(z)))), s(z))) | (~r(elem!1, s(z))) | (~r(elem!1, s(s(s(s(z)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(z), elem!1)) | (~r(elem!1, s(z))) | (~r(elem!1, s(s(s(s(z)))))) | (~r(s(s(s(s(z)))), s(z))))),
% 3.53/3.75 inference(transitivity,[status(thm)],[17907, 17905])).
% 3.53/3.75 tff(17909,plain,
% 3.53/3.75 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), elem!1)) | (~r(s(s(s(s(z)))), s(z))) | (~r(elem!1, s(z))) | (~r(elem!1, s(s(s(s(z)))))))),
% 3.53/3.75 inference(quant_inst,[status(thm)],[])).
% 3.53/3.75 tff(17910,plain,
% 3.53/3.75 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(z), elem!1)) | (~r(elem!1, s(z))) | (~r(elem!1, s(s(s(s(z)))))) | (~r(s(s(s(s(z)))), s(z)))),
% 3.53/3.75 inference(modus_ponens,[status(thm)],[17909, 17908])).
% 3.53/3.75 tff(17911,plain,
% 3.53/3.75 (~r(elem!1, s(s(s(s(z)))))),
% 3.53/3.75 inference(unit_resolution,[status(thm)],[17910, 197, 17894, 17890, 17888])).
% 3.53/3.75 tff(17912,plain,
% 3.53/3.75 (b(elem!1, s(s(s(s(z)))))),
% 3.53/3.75 inference(unit_resolution,[status(thm)],[1098, 17911, 17904])).
% 3.53/3.76 tff(17913,plain,
% 3.53/3.76 (b(s(s(s(elem!1))), elem!1) <=> b(s(s(s(z))), elem!1)),
% 3.53/3.76 inference(monotonicity,[status(thm)],[17684])).
% 3.53/3.76 tff(17914,plain,
% 3.53/3.76 (b(s(s(s(elem!1))), elem!1)),
% 3.53/3.76 inference(unit_resolution,[status(thm)],[634, 17678, 95])).
% 3.53/3.76 tff(17915,plain,
% 3.53/3.76 (b(s(s(s(z))), elem!1)),
% 3.53/3.76 inference(modus_ponens,[status(thm)],[17914, 17913])).
% 3.53/3.76 tff(17916,plain,
% 3.53/3.76 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), elem!1)) | (~b(s(s(s(s(z)))), elem!1)) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(elem!1, s(s(s(s(z)))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(z))), elem!1)) | (~b(s(s(s(s(z)))), elem!1)) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(elem!1, s(s(s(s(z)))))))),
% 3.53/3.76 inference(rewrite,[status(thm)],[])).
% 3.53/3.76 tff(17917,plain,
% 3.53/3.76 (((~b(s(s(s(s(z)))), elem!1)) | (~b(s(s(s(s(z)))), elem!1)) | (~b(elem!1, s(s(s(s(z)))))) | (~b(s(s(s(z))), elem!1)) | (~b(s(s(s(s(z)))), elem!1)) | (~b(s(s(s(s(z)))), s(s(s(z)))))) <=> ((~b(s(s(s(z))), elem!1)) | (~b(s(s(s(s(z)))), elem!1)) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(elem!1, s(s(s(s(z)))))))),
% 3.53/3.76 inference(rewrite,[status(thm)],[])).
% 3.53/3.76 tff(17918,plain,
% 3.53/3.76 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(z)))), elem!1)) | (~b(s(s(s(s(z)))), elem!1)) | (~b(elem!1, s(s(s(s(z)))))) | (~b(s(s(s(z))), elem!1)) | (~b(s(s(s(s(z)))), elem!1)) | (~b(s(s(s(s(z)))), s(s(s(z))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), elem!1)) | (~b(s(s(s(s(z)))), elem!1)) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(elem!1, s(s(s(s(z))))))))),
% 3.53/3.76 inference(monotonicity,[status(thm)],[17917])).
% 3.53/3.76 tff(17919,plain,
% 3.53/3.76 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(z)))), elem!1)) | (~b(s(s(s(s(z)))), elem!1)) | (~b(elem!1, s(s(s(s(z)))))) | (~b(s(s(s(z))), elem!1)) | (~b(s(s(s(s(z)))), elem!1)) | (~b(s(s(s(s(z)))), s(s(s(z))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(z))), elem!1)) | (~b(s(s(s(s(z)))), elem!1)) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(elem!1, s(s(s(s(z)))))))),
% 3.53/3.76 inference(transitivity,[status(thm)],[17918, 17916])).
% 3.53/3.76 tff(17920,plain,
% 3.53/3.76 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(z)))), elem!1)) | (~b(s(s(s(s(z)))), elem!1)) | (~b(elem!1, s(s(s(s(z)))))) | (~b(s(s(s(z))), elem!1)) | (~b(s(s(s(s(z)))), elem!1)) | (~b(s(s(s(s(z)))), s(s(s(z))))))),
% 3.53/3.76 inference(quant_inst,[status(thm)],[])).
% 3.53/3.76 tff(17921,plain,
% 3.53/3.76 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(z))), elem!1)) | (~b(s(s(s(s(z)))), elem!1)) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(elem!1, s(s(s(s(z))))))),
% 3.53/3.76 inference(modus_ponens,[status(thm)],[17920, 17919])).
% 3.53/3.76 tff(17922,plain,
% 3.53/3.76 (~b(s(s(s(s(z)))), s(s(s(z))))),
% 3.53/3.76 inference(unit_resolution,[status(thm)],[17921, 166, 17915, 17912, 17902])).
% 3.53/3.76 tff(17923,plain,
% 3.53/3.76 (r(s(s(s(s(z)))), s(s(s(z))))),
% 3.53/3.76 inference(unit_resolution,[status(thm)],[4662, 17922])).
% 3.53/3.76 tff(17924,plain,
% 3.53/3.76 (s(s(s(z))) = s(s(s(elem!1)))),
% 3.53/3.76 inference(symmetry,[status(thm)],[17684])).
% 3.53/3.76 tff(17925,plain,
% 3.53/3.76 (b(s(s(s(z))), s(z)) <=> b(s(s(s(elem!1))), s(z))),
% 3.53/3.76 inference(monotonicity,[status(thm)],[17924])).
% 3.53/3.76 tff(17926,plain,
% 3.53/3.76 (b(s(s(s(elem!1))), s(z)) <=> b(s(s(s(z))), s(z))),
% 3.53/3.76 inference(symmetry,[status(thm)],[17925])).
% 3.53/3.76 tff(17927,plain,
% 3.53/3.76 (b(s(s(s(z))), s(z))),
% 3.53/3.76 inference(modus_ponens,[status(thm)],[17856, 17926])).
% 3.53/3.76 tff(17928,plain,
% 3.53/3.76 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(s(z)))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(z)), s(z))) | (~b(s(s(s(z))), elem!1)) | (~b(s(s(s(s(z)))), elem!1)) | (~b(s(s(s(z))), s(s(s(s(z)))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(s(z)))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(z)), s(z))) | (~b(s(s(s(z))), elem!1)) | (~b(s(s(s(s(z)))), elem!1)) | (~b(s(s(s(z))), s(s(s(s(z)))))))),
% 3.53/3.76 inference(rewrite,[status(thm)],[])).
% 3.53/3.76 tff(17929,plain,
% 3.53/3.76 (((~b(s(s(z)), s(z))) | (~b(s(s(s(z))), s(z))) | (~b(elem!1, s(s(z)))) | (~b(s(s(s(s(z)))), elem!1)) | (~b(s(s(s(z))), elem!1)) | (~b(s(s(s(z))), s(s(s(s(z))))))) <=> ((~b(elem!1, s(s(z)))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(z)), s(z))) | (~b(s(s(s(z))), elem!1)) | (~b(s(s(s(s(z)))), elem!1)) | (~b(s(s(s(z))), s(s(s(s(z)))))))),
% 3.53/3.76 inference(rewrite,[status(thm)],[])).
% 3.53/3.76 tff(17930,plain,
% 3.53/3.76 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), s(z))) | (~b(s(s(s(z))), s(z))) | (~b(elem!1, s(s(z)))) | (~b(s(s(s(s(z)))), elem!1)) | (~b(s(s(s(z))), elem!1)) | (~b(s(s(s(z))), s(s(s(s(z)))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(s(z)))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(z)), s(z))) | (~b(s(s(s(z))), elem!1)) | (~b(s(s(s(s(z)))), elem!1)) | (~b(s(s(s(z))), s(s(s(s(z))))))))),
% 3.53/3.76 inference(monotonicity,[status(thm)],[17929])).
% 3.53/3.76 tff(17931,plain,
% 3.53/3.76 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), s(z))) | (~b(s(s(s(z))), s(z))) | (~b(elem!1, s(s(z)))) | (~b(s(s(s(s(z)))), elem!1)) | (~b(s(s(s(z))), elem!1)) | (~b(s(s(s(z))), s(s(s(s(z)))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(s(z)))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(z)), s(z))) | (~b(s(s(s(z))), elem!1)) | (~b(s(s(s(s(z)))), elem!1)) | (~b(s(s(s(z))), s(s(s(s(z)))))))),
% 3.53/3.76 inference(transitivity,[status(thm)],[17930, 17928])).
% 3.53/3.76 tff(17932,plain,
% 3.53/3.76 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), s(z))) | (~b(s(s(s(z))), s(z))) | (~b(elem!1, s(s(z)))) | (~b(s(s(s(s(z)))), elem!1)) | (~b(s(s(s(z))), elem!1)) | (~b(s(s(s(z))), s(s(s(s(z)))))))),
% 3.53/3.76 inference(quant_inst,[status(thm)],[])).
% 3.53/3.76 tff(17933,plain,
% 3.53/3.76 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(s(z)))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(z)), s(z))) | (~b(s(s(s(z))), elem!1)) | (~b(s(s(s(s(z)))), elem!1)) | (~b(s(s(s(z))), s(s(s(s(z))))))),
% 3.53/3.76 inference(modus_ponens,[status(thm)],[17932, 17931])).
% 3.53/3.76 tff(17934,plain,
% 3.53/3.76 (~b(s(s(s(z))), s(s(s(s(z)))))),
% 3.53/3.76 inference(unit_resolution,[status(thm)],[17933, 166, 17064, 17915, 17927, 17902, 17683])).
% 3.53/3.76 tff(17935,plain,
% 3.53/3.76 (r(s(s(s(z))), s(s(s(s(z)))))),
% 3.53/3.76 inference(unit_resolution,[status(thm)],[2233, 17934])).
% 3.53/3.76 tff(17936,plain,
% 3.53/3.76 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(z)), s(s(s(z))))) | (~r(s(s(s(s(z)))), s(s(s(z))))) | (~r(s(s(s(z))), s(s(s(s(z)))))) | (~r(s(s(z)), s(s(s(s(z)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(z)), s(s(s(z))))) | (~r(s(s(s(s(z)))), s(s(s(z))))) | (~r(s(s(s(z))), s(s(s(s(z)))))) | (~r(s(s(z)), s(s(s(s(z)))))))),
% 3.53/3.76 inference(rewrite,[status(thm)],[])).
% 3.53/3.76 tff(17937,plain,
% 3.53/3.76 (((~r(s(s(s(z))), s(s(s(s(z)))))) | (~r(s(s(s(s(z)))), s(s(s(z))))) | (~r(s(s(z)), s(s(s(z))))) | (~r(s(s(z)), s(s(s(s(z))))))) <=> ((~r(s(s(z)), s(s(s(z))))) | (~r(s(s(s(s(z)))), s(s(s(z))))) | (~r(s(s(s(z))), s(s(s(s(z)))))) | (~r(s(s(z)), s(s(s(s(z)))))))),
% 3.53/3.76 inference(rewrite,[status(thm)],[])).
% 3.53/3.76 tff(17938,plain,
% 3.53/3.76 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(z))), s(s(s(s(z)))))) | (~r(s(s(s(s(z)))), s(s(s(z))))) | (~r(s(s(z)), s(s(s(z))))) | (~r(s(s(z)), s(s(s(s(z)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(z)), s(s(s(z))))) | (~r(s(s(s(s(z)))), s(s(s(z))))) | (~r(s(s(s(z))), s(s(s(s(z)))))) | (~r(s(s(z)), s(s(s(s(z))))))))),
% 3.53/3.76 inference(monotonicity,[status(thm)],[17937])).
% 3.53/3.76 tff(17939,plain,
% 3.53/3.76 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(z))), s(s(s(s(z)))))) | (~r(s(s(s(s(z)))), s(s(s(z))))) | (~r(s(s(z)), s(s(s(z))))) | (~r(s(s(z)), s(s(s(s(z)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(z)), s(s(s(z))))) | (~r(s(s(s(s(z)))), s(s(s(z))))) | (~r(s(s(s(z))), s(s(s(s(z)))))) | (~r(s(s(z)), s(s(s(s(z)))))))),
% 3.53/3.76 inference(transitivity,[status(thm)],[17938, 17936])).
% 3.53/3.76 tff(17940,plain,
% 3.53/3.76 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(z))), s(s(s(s(z)))))) | (~r(s(s(s(s(z)))), s(s(s(z))))) | (~r(s(s(z)), s(s(s(z))))) | (~r(s(s(z)), s(s(s(s(z)))))))),
% 3.53/3.76 inference(quant_inst,[status(thm)],[])).
% 3.53/3.76 tff(17941,plain,
% 3.53/3.76 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(z)), s(s(s(z))))) | (~r(s(s(s(s(z)))), s(s(s(z))))) | (~r(s(s(s(z))), s(s(s(s(z)))))) | (~r(s(s(z)), s(s(s(s(z))))))),
% 3.53/3.76 inference(modus_ponens,[status(thm)],[17940, 17939])).
% 3.53/3.76 tff(17942,plain,
% 3.53/3.76 (~r(s(s(z)), s(s(s(s(z)))))),
% 3.53/3.76 inference(unit_resolution,[status(thm)],[17941, 197, 17935, 17923, 17859])).
% 3.53/3.76 tff(17943,plain,
% 3.53/3.76 (b(s(s(z)), s(s(s(s(z)))))),
% 3.53/3.76 inference(unit_resolution,[status(thm)],[4753, 17942])).
% 3.53/3.76 tff(17944,plain,
% 3.53/3.76 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(s(z)))) | (~b(s(s(s(s(z)))), elem!1)) | (~b(elem!1, s(s(s(s(z)))))) | (~b(s(s(z)), s(s(s(s(z)))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(s(z)))) | (~b(s(s(s(s(z)))), elem!1)) | (~b(elem!1, s(s(s(s(z)))))) | (~b(s(s(z)), s(s(s(s(z)))))))),
% 3.53/3.76 inference(rewrite,[status(thm)],[])).
% 3.53/3.76 tff(17945,plain,
% 3.53/3.76 (((~b(elem!1, s(s(z)))) | (~b(elem!1, s(s(z)))) | (~b(s(s(s(s(z)))), elem!1)) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(elem!1, s(s(s(s(z)))))) | (~b(elem!1, s(s(z))))) <=> ((~b(elem!1, s(s(z)))) | (~b(s(s(s(s(z)))), elem!1)) | (~b(elem!1, s(s(s(s(z)))))) | (~b(s(s(z)), s(s(s(s(z)))))))),
% 3.53/3.76 inference(rewrite,[status(thm)],[])).
% 3.53/3.76 tff(17946,plain,
% 3.53/3.76 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(s(z)))) | (~b(elem!1, s(s(z)))) | (~b(s(s(s(s(z)))), elem!1)) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(elem!1, s(s(s(s(z)))))) | (~b(elem!1, s(s(z)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(s(z)))) | (~b(s(s(s(s(z)))), elem!1)) | (~b(elem!1, s(s(s(s(z)))))) | (~b(s(s(z)), s(s(s(s(z))))))))),
% 3.53/3.76 inference(monotonicity,[status(thm)],[17945])).
% 3.53/3.76 tff(17947,plain,
% 3.53/3.76 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(s(z)))) | (~b(elem!1, s(s(z)))) | (~b(s(s(s(s(z)))), elem!1)) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(elem!1, s(s(s(s(z)))))) | (~b(elem!1, s(s(z)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(s(z)))) | (~b(s(s(s(s(z)))), elem!1)) | (~b(elem!1, s(s(s(s(z)))))) | (~b(s(s(z)), s(s(s(s(z)))))))),
% 3.53/3.76 inference(transitivity,[status(thm)],[17946, 17944])).
% 3.53/3.76 tff(17948,plain,
% 3.53/3.76 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(s(z)))) | (~b(elem!1, s(s(z)))) | (~b(s(s(s(s(z)))), elem!1)) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(elem!1, s(s(s(s(z)))))) | (~b(elem!1, s(s(z)))))),
% 3.53/3.76 inference(quant_inst,[status(thm)],[])).
% 3.53/3.76 tff(17949,plain,
% 3.53/3.76 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(s(z)))) | (~b(s(s(s(s(z)))), elem!1)) | (~b(elem!1, s(s(s(s(z)))))) | (~b(s(s(z)), s(s(s(s(z))))))),
% 3.53/3.76 inference(modus_ponens,[status(thm)],[17948, 17947])).
% 3.53/3.76 tff(17950,plain,
% 3.53/3.76 ($false),
% 3.53/3.76 inference(unit_resolution,[status(thm)],[17949, 166, 17912, 17902, 17943, 17683])).
% 3.53/3.76 tff(17951,plain,(r(s(s(s(elem!1))), z)), inference(lemma,lemma(discharge,[]))).
% 3.53/3.76 tff(17952,plain,
% 3.53/3.76 ((~r(s(s(s(elem!1))), s(s(z)))) | (~r(z, s(z))) | (~r(s(s(z)), z))),
% 3.53/3.76 inference(unit_resolution,[status(thm)],[14314, 17951])).
% 3.53/3.76 tff(17953,plain,
% 3.53/3.76 (~r(s(s(s(elem!1))), s(s(z)))),
% 3.53/3.76 inference(unit_resolution,[status(thm)],[17952, 17069, 17067])).
% 3.53/3.76 tff(17954,plain,
% 3.53/3.76 (b(s(s(s(elem!1))), s(s(z)))),
% 3.53/3.76 inference(unit_resolution,[status(thm)],[218, 17953])).
% 3.53/3.76 tff(17955,plain,
% 3.53/3.76 (~r(s(s(z)), s(s(s(elem!1))))),
% 3.53/3.76 inference(unit_resolution,[status(thm)],[14322, 197, 17951, 17067, 17069])).
% 3.53/3.76 tff(17956,plain,
% 3.53/3.76 (b(s(s(z)), s(s(s(elem!1))))),
% 3.53/3.76 inference(unit_resolution,[status(thm)],[279, 17955])).
% 3.53/3.76 tff(17957,plain,
% 3.53/3.76 ((~r(s(s(s(elem!1))), z)) | (~r(s(s(s(elem!1))), s(z))) | (~b(s(z), s(s(elem!1))))),
% 3.53/3.76 inference(unit_resolution,[status(thm)],[17106, 10450])).
% 3.53/3.76 tff(17958,plain,
% 3.53/3.76 (~r(s(s(s(elem!1))), s(z))),
% 3.53/3.76 inference(unit_resolution,[status(thm)],[17957, 17951, 15211])).
% 3.53/3.76 tff(17959,plain,
% 3.53/3.76 (b(s(s(s(elem!1))), s(z))),
% 3.53/3.76 inference(unit_resolution,[status(thm)],[1849, 17958])).
% 3.53/3.76 tff(17960,plain,
% 3.53/3.76 ((~b(s(z), s(s(s(elem!1))))) | (~b(s(s(z)), s(s(s(elem!1)))))),
% 3.53/3.76 inference(unit_resolution,[status(thm)],[271, 17064, 17959])).
% 3.53/3.76 tff(17961,plain,
% 3.53/3.76 (~b(s(z), s(s(s(elem!1))))),
% 3.53/3.76 inference(unit_resolution,[status(thm)],[17960, 17956])).
% 3.53/3.76 tff(17962,plain,
% 3.53/3.76 (r(s(z), s(s(s(elem!1))))),
% 3.53/3.76 inference(unit_resolution,[status(thm)],[116, 17961])).
% 3.53/3.76 tff(17963,plain,
% 3.53/3.76 ((~r(z, s(s(s(elem!1))))) | (~r(z, s(z))) | (~r(s(z), s(s(s(elem!1)))))),
% 3.53/3.76 inference(unit_resolution,[status(thm)],[13506, 17951])).
% 3.53/3.76 tff(17964,plain,
% 3.53/3.76 (~r(z, s(s(s(elem!1))))),
% 3.53/3.76 inference(unit_resolution,[status(thm)],[17963, 17962, 17067])).
% 3.53/3.76 tff(17965,plain,
% 3.53/3.76 (b(z, s(s(s(elem!1))))),
% 3.53/3.76 inference(unit_resolution,[status(thm)],[261, 17964])).
% 3.53/3.76 tff(17966,plain,
% 3.53/3.76 ($false),
% 3.53/3.76 inference(unit_resolution,[status(thm)],[10577, 166, 17965, 10450, 17956, 17954])).
% 3.53/3.76 tff(17967,plain,(~b(s(z), z)), inference(lemma,lemma(discharge,[]))).
% 3.53/3.76 tff(17968,plain,
% 3.53/3.76 (r(s(z), z)),
% 3.53/3.76 inference(unit_resolution,[status(thm)],[230, 17967])).
% 3.53/3.76 tff(17969,plain,
% 3.53/3.76 ((~b(s(z), s(s(s(elem!1))))) | (~b(z, s(z)))),
% 3.53/3.76 inference(unit_resolution,[status(thm)],[12629, 17064, 17959])).
% 3.53/3.76 tff(17970,plain,
% 3.53/3.76 (~b(s(z), s(s(s(elem!1))))),
% 3.53/3.76 inference(unit_resolution,[status(thm)],[17969, 118])).
% 3.53/3.76 tff(17971,plain,
% 3.53/3.76 (r(s(z), s(s(s(elem!1))))),
% 3.53/3.76 inference(unit_resolution,[status(thm)],[116, 17970])).
% 3.53/3.76 tff(17972,plain,
% 3.53/3.76 ((~r(z, s(s(elem!1)))) | (~r(s(z), z)) | (~r(s(z), s(s(s(elem!1)))))),
% 3.53/3.76 inference(unit_resolution,[status(thm)],[14558, 17951])).
% 3.53/3.76 tff(17973,plain,
% 3.53/3.76 (~r(z, s(s(elem!1)))),
% 3.53/3.76 inference(unit_resolution,[status(thm)],[17972, 17971, 17968])).
% 3.53/3.76 tff(17974,plain,
% 3.53/3.76 ((~b(s(z), s(s(z)))) | (~b(z, s(z)))),
% 3.53/3.76 inference(unit_resolution,[status(thm)],[14336, 17064])).
% 3.53/3.76 tff(17975,plain,
% 3.53/3.76 (~b(s(z), s(s(z)))),
% 3.53/3.76 inference(unit_resolution,[status(thm)],[17974, 118])).
% 3.53/3.76 tff(17976,plain,
% 3.53/3.76 ((~(s(s(z)) = s(s(elem!1)))) | b(s(z), s(s(z)))),
% 3.53/3.76 inference(unit_resolution,[status(thm)],[5435, 15211])).
% 3.53/3.76 tff(17977,plain,
% 3.53/3.76 (~(s(s(z)) = s(s(elem!1)))),
% 3.53/3.76 inference(unit_resolution,[status(thm)],[17976, 17975])).
% 3.53/3.76 tff(17978,plain,
% 3.53/3.76 (~(s(s(elem!1)) = s(s(z)))),
% 3.53/3.76 inference(unit_resolution,[status(thm)],[131, 17977])).
% 3.53/3.76 tff(17979,plain,
% 3.53/3.76 (~b(z, s(s(elem!1)))),
% 3.53/3.76 inference(unit_resolution,[status(thm)],[17603, 17978, 17968, 118])).
% 3.53/3.76 tff(17980,plain,
% 3.53/3.76 ($false),
% 3.53/3.76 inference(unit_resolution,[status(thm)],[1795, 17979, 17973])).
% 3.53/3.76 tff(17981,plain,(~b(z, s(z))), inference(lemma,lemma(discharge,[]))).
% 3.53/3.76 tff(17982,plain,
% 3.53/3.76 (r(z, s(z))),
% 3.53/3.76 inference(unit_resolution,[status(thm)],[321, 17981])).
% 3.53/3.76 tff(17983,plain,
% 3.53/3.76 ((~r(z, s(z))) | (~r(s(z), z)) | (~r(s(z), s(s(s(elem!1)))))),
% 3.53/3.76 inference(unit_resolution,[status(thm)],[15103, 17951])).
% 3.53/3.76 tff(17984,plain,
% 3.53/3.76 (~r(s(z), s(s(s(elem!1))))),
% 3.53/3.76 inference(unit_resolution,[status(thm)],[17983, 17982, 17968])).
% 3.53/3.76 tff(17985,plain,
% 3.53/3.76 (b(s(z), s(s(s(elem!1))))),
% 3.53/3.76 inference(unit_resolution,[status(thm)],[116, 17984])).
% 3.53/3.76 tff(17986,plain,
% 3.53/3.76 (~b(s(s(z)), s(s(s(elem!1))))),
% 3.53/3.76 inference(unit_resolution,[status(thm)],[17960, 17985])).
% 3.53/3.76 tff(17987,plain,
% 3.53/3.76 (r(s(s(z)), s(s(s(elem!1))))),
% 3.53/3.76 inference(unit_resolution,[status(thm)],[279, 17986])).
% 3.53/3.76 tff(17988,plain,
% 3.53/3.76 (~r(z, s(s(elem!1)))),
% 3.53/3.76 inference(unit_resolution,[status(thm)],[8426, 10521, 17968, 17982])).
% 3.53/3.76 tff(17989,plain,
% 3.53/3.76 (b(z, s(s(elem!1)))),
% 3.53/3.76 inference(unit_resolution,[status(thm)],[1795, 17988])).
% 3.53/3.76 tff(17990,plain,
% 3.53/3.76 (r(s(s(z)), s(s(elem!1)))),
% 3.53/3.76 inference(unit_resolution,[status(thm)],[11731, 4568, 17968])).
% 3.53/3.76 tff(17991,plain,
% 3.53/3.76 (~r(s(s(s(elem!1))), s(s(elem!1)))),
% 3.53/3.76 inference(unit_resolution,[status(thm)],[8677, 17990, 17987, 10521])).
% 3.53/3.76 tff(17992,plain,
% 3.53/3.76 ((s(s(s(elem!1))) = s(s(elem!1))) | (~b(s(z), s(s(s(elem!1))))) | r(s(s(elem!1)), s(s(s(elem!1)))) | r(s(s(s(elem!1))), s(s(elem!1)))),
% 3.53/3.76 inference(unit_resolution,[status(thm)],[6040, 15211])).
% 3.53/3.76 tff(17993,plain,
% 3.53/3.76 (r(s(s(elem!1)), s(s(s(elem!1))))),
% 3.53/3.76 inference(unit_resolution,[status(thm)],[17992, 17991, 1863, 17985])).
% 3.53/3.76 tff(17994,plain,
% 3.53/3.76 ((~r(s(s(elem!1)), s(s(s(elem!1))))) | (~b(z, s(s(elem!1)))) | (s(s(z)) = s(s(elem!1))) | (~r(s(s(z)), s(s(s(elem!1)))))),
% 3.53/3.76 inference(unit_resolution,[status(thm)],[14443, 17951])).
% 3.53/3.76 tff(17995,plain,
% 3.53/3.76 ($false),
% 3.53/3.76 inference(unit_resolution,[status(thm)],[17994, 17993, 17989, 17987, 52])).
% 3.53/3.76 tff(17996,plain,(b(s(s(elem!1)), s(z)) | (s(s(z)) = s(s(elem!1))) | (s(s(s(elem!1))) = s(s(elem!1)))), inference(lemma,lemma(discharge,[]))).
% 3.53/3.76 tff(17997,plain,
% 3.53/3.76 (b(s(s(elem!1)), s(z))),
% 3.53/3.76 inference(unit_resolution,[status(thm)],[17996, 51, 52])).
% 3.53/3.76 tff(17998,plain,
% 3.53/3.76 ((~b(s(s(elem!1)), s(z))) | (~b(s(s(s(elem!1))), s(s(elem!1))))),
% 3.53/3.76 inference(unit_resolution,[status(thm)],[1858, 15211, 17959])).
% 3.53/3.76 tff(17999,plain,
% 3.53/3.76 (~b(s(s(s(elem!1))), s(s(elem!1)))),
% 3.53/3.76 inference(unit_resolution,[status(thm)],[17998, 17997])).
% 3.53/3.76 tff(18000,plain,
% 3.53/3.76 (r(s(s(s(elem!1))), s(s(elem!1)))),
% 3.53/3.76 inference(unit_resolution,[status(thm)],[889, 17999, 51])).
% 3.53/3.76 tff(18001,plain,
% 3.53/3.76 ((~b(s(z), s(s(s(elem!1))))) | (~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(s(s(elem!1)), s(z)))),
% 3.53/3.76 inference(unit_resolution,[status(thm)],[1994, 17959])).
% 3.53/3.76 tff(18002,plain,
% 3.53/3.76 (~b(s(s(elem!1)), s(s(s(elem!1))))),
% 3.53/3.76 inference(unit_resolution,[status(thm)],[18001, 17997, 17985])).
% 3.53/3.76 tff(18003,plain,
% 3.53/3.76 (r(s(s(elem!1)), s(s(s(elem!1))))),
% 3.53/3.76 inference(unit_resolution,[status(thm)],[461, 18002, 45])).
% 3.53/3.76 tff(18004,plain,
% 3.53/3.76 ((~r(s(s(s(elem!1))), s(s(elem!1)))) | (~r(s(s(elem!1)), s(s(s(elem!1))))) | (~r(z, s(s(elem!1))))),
% 3.53/3.76 inference(unit_resolution,[status(thm)],[1386, 17951])).
% 3.53/3.76 tff(18005,plain,
% 3.53/3.76 (~r(z, s(s(elem!1)))),
% 3.53/3.76 inference(unit_resolution,[status(thm)],[18004, 18003, 18000])).
% 3.53/3.76 tff(18006,plain,
% 3.53/3.76 (~b(z, s(s(elem!1)))),
% 3.53/3.76 inference(unit_resolution,[status(thm)],[17994, 18003, 17987, 52])).
% 3.53/3.76 tff(18007,plain,
% 3.53/3.76 ($false),
% 3.53/3.76 inference(unit_resolution,[status(thm)],[1795, 18006, 18005])).
% 3.53/3.76 tff(18008,plain,((s(s(elem!1)) = s(s(s(elem!1)))) | (s(s(z)) = s(s(elem!1)))), inference(lemma,lemma(discharge,[]))).
% 3.53/3.77 tff(18009,plain,
% 3.53/3.77 (s(s(elem!1)) = s(s(s(elem!1)))),
% 3.53/3.77 inference(unit_resolution,[status(thm)],[18008, 44])).
% 3.53/3.77 tff(18010,plain,
% 3.53/3.77 (s(s(s(elem!1))) = s(elem!1)),
% 3.53/3.77 inference(unit_resolution,[status(thm)],[2594, 18009])).
% 3.53/3.77 tff(18011,plain,
% 3.53/3.77 (s(elem!1) = s(s(s(elem!1)))),
% 3.53/3.77 inference(symmetry,[status(thm)],[18010])).
% 3.53/3.77 tff(18012,plain,
% 3.53/3.77 (b(s(elem!1), s(z)) <=> b(s(s(s(elem!1))), s(z))),
% 3.53/3.77 inference(monotonicity,[status(thm)],[18011])).
% 3.53/3.77 tff(18013,plain,
% 3.53/3.77 (b(s(s(s(elem!1))), s(z)) <=> b(s(elem!1), s(z))),
% 3.53/3.77 inference(symmetry,[status(thm)],[18012])).
% 3.53/3.77 tff(18014,plain,
% 3.53/3.77 (b(s(elem!1), s(z))),
% 3.53/3.77 inference(modus_ponens,[status(thm)],[17959, 18013])).
% 3.53/3.77 tff(18015,plain,
% 3.53/3.77 ((~(s(s(elem!1)) = s(s(s(elem!1))))) | b(s(s(elem!1)), s(z))),
% 3.53/3.77 inference(unit_resolution,[status(thm)],[4570, 17959])).
% 3.53/3.77 tff(18016,plain,
% 3.53/3.77 (b(s(s(elem!1)), s(z))),
% 3.53/3.77 inference(unit_resolution,[status(thm)],[18015, 18009])).
% 3.53/3.77 tff(18017,plain,
% 3.53/3.77 (s(s(elem!1)) = elem!1),
% 3.53/3.77 inference(unit_resolution,[status(thm)],[10139, 18010])).
% 3.53/3.77 tff(18018,plain,
% 3.53/3.77 (~(s(s(s(z))) = elem!1)),
% 3.53/3.77 inference(unit_resolution,[status(thm)],[3122, 18009])).
% 3.53/3.77 tff(18019,plain,
% 3.53/3.77 (b(s(z), s(elem!1)) <=> b(s(z), s(s(s(elem!1))))),
% 3.53/3.77 inference(monotonicity,[status(thm)],[18011])).
% 3.53/3.77 tff(18020,plain,
% 3.53/3.77 (b(s(z), s(s(s(elem!1)))) <=> b(s(z), s(elem!1))),
% 3.53/3.77 inference(symmetry,[status(thm)],[18019])).
% 3.53/3.77 tff(18021,plain,
% 3.53/3.77 (b(s(z), s(elem!1))),
% 3.53/3.77 inference(modus_ponens,[status(thm)],[17985, 18020])).
% 3.53/3.77 tff(18022,plain,
% 3.53/3.77 (r(s(s(elem!1)), z) <=> r(s(s(s(elem!1))), z)),
% 3.53/3.77 inference(monotonicity,[status(thm)],[18009])).
% 3.53/3.77 tff(18023,plain,
% 3.53/3.77 (r(s(s(s(elem!1))), z) <=> r(s(s(elem!1)), z)),
% 3.53/3.77 inference(symmetry,[status(thm)],[18022])).
% 3.53/3.77 tff(18024,plain,
% 3.53/3.77 (r(s(s(elem!1)), z)),
% 3.53/3.77 inference(modus_ponens,[status(thm)],[17951, 18023])).
% 3.53/3.77 tff(18025,plain,
% 3.53/3.77 (~r(s(s(s(z))), z)),
% 3.53/3.77 inference(unit_resolution,[status(thm)],[12545, 18024, 17982, 18021, 17968, 18018, 18017, 18016, 18014])).
% 3.53/3.77 tff(18026,plain,
% 3.53/3.77 (b(s(s(s(z))), z)),
% 3.53/3.77 inference(unit_resolution,[status(thm)],[1713, 18025])).
% 3.53/3.77 tff(18027,plain,
% 3.53/3.77 (~b(s(s(s(elem!1))), s(s(z)))),
% 3.53/3.77 inference(unit_resolution,[status(thm)],[9072, 166, 17985, 17959, 17064])).
% 3.53/3.77 tff(18028,plain,
% 3.53/3.77 (r(s(s(s(elem!1))), s(s(z)))),
% 3.53/3.77 inference(unit_resolution,[status(thm)],[218, 18027])).
% 3.53/3.77 tff(18029,plain,
% 3.53/3.77 (~r(s(s(z)), z)),
% 3.53/3.77 inference(unit_resolution,[status(thm)],[17952, 18028, 17982])).
% 3.53/3.77 tff(18030,plain,
% 3.53/3.77 (b(s(s(z)), z)),
% 3.53/3.77 inference(unit_resolution,[status(thm)],[186, 18029])).
% 3.53/3.77 tff(18031,plain,
% 3.53/3.77 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(z)))) | (~b(s(s(z)), z)) | (~b(s(s(z)), s(z))) | (~b(s(s(s(z))), z)) | (~b(s(s(z)), s(s(s(z))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(s(z)))) | (~b(s(s(z)), z)) | (~b(s(s(z)), s(z))) | (~b(s(s(s(z))), z)) | (~b(s(s(z)), s(s(s(z))))))),
% 3.53/3.77 inference(rewrite,[status(thm)],[])).
% 3.53/3.77 tff(18032,plain,
% 3.53/3.77 (((~b(s(s(z)), s(z))) | (~b(s(s(z)), s(z))) | (~b(z, s(s(z)))) | (~b(s(s(s(z))), z)) | (~b(s(s(z)), z)) | (~b(s(s(z)), s(s(s(z)))))) <=> ((~b(z, s(s(z)))) | (~b(s(s(z)), z)) | (~b(s(s(z)), s(z))) | (~b(s(s(s(z))), z)) | (~b(s(s(z)), s(s(s(z))))))),
% 3.53/3.77 inference(rewrite,[status(thm)],[])).
% 3.53/3.77 tff(18033,plain,
% 3.53/3.77 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), s(z))) | (~b(s(s(z)), s(z))) | (~b(z, s(s(z)))) | (~b(s(s(s(z))), z)) | (~b(s(s(z)), z)) | (~b(s(s(z)), s(s(s(z))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(z)))) | (~b(s(s(z)), z)) | (~b(s(s(z)), s(z))) | (~b(s(s(s(z))), z)) | (~b(s(s(z)), s(s(s(z)))))))),
% 3.53/3.77 inference(monotonicity,[status(thm)],[18032])).
% 3.53/3.77 tff(18034,plain,
% 3.53/3.77 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), s(z))) | (~b(s(s(z)), s(z))) | (~b(z, s(s(z)))) | (~b(s(s(s(z))), z)) | (~b(s(s(z)), z)) | (~b(s(s(z)), s(s(s(z))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(s(z)))) | (~b(s(s(z)), z)) | (~b(s(s(z)), s(z))) | (~b(s(s(s(z))), z)) | (~b(s(s(z)), s(s(s(z))))))),
% 3.53/3.77 inference(transitivity,[status(thm)],[18033, 18031])).
% 3.53/3.77 tff(18035,plain,
% 3.53/3.77 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), s(z))) | (~b(s(s(z)), s(z))) | (~b(z, s(s(z)))) | (~b(s(s(s(z))), z)) | (~b(s(s(z)), z)) | (~b(s(s(z)), s(s(s(z))))))),
% 3.53/3.77 inference(quant_inst,[status(thm)],[])).
% 3.53/3.77 tff(18036,plain,
% 3.53/3.77 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(s(z)))) | (~b(s(s(z)), z)) | (~b(s(s(z)), s(z))) | (~b(s(s(s(z))), z)) | (~b(s(s(z)), s(s(s(z)))))),
% 3.53/3.77 inference(modus_ponens,[status(thm)],[18035, 18034])).
% 3.53/3.77 tff(18037,plain,
% 3.53/3.77 (~b(s(s(z)), s(s(s(z))))),
% 3.53/3.77 inference(unit_resolution,[status(thm)],[18036, 166, 10450, 17064, 18030, 18026])).
% 3.53/3.77 tff(18038,plain,
% 3.53/3.77 (r(s(s(z)), s(s(s(z))))),
% 3.53/3.77 inference(unit_resolution,[status(thm)],[1730, 18037])).
% 3.53/3.77 tff(18039,plain,
% 3.53/3.77 (~b(s(s(s(z))), s(s(z)))),
% 3.53/3.77 inference(unit_resolution,[status(thm)],[12296, 166, 10450, 18030, 18026])).
% 3.53/3.77 tff(18040,plain,
% 3.53/3.77 (r(s(s(s(z))), s(s(z)))),
% 3.53/3.77 inference(unit_resolution,[status(thm)],[1010, 18039])).
% 3.53/3.77 tff(18041,plain,
% 3.53/3.77 (~r(s(s(s(elem!1))), s(s(s(z))))),
% 3.53/3.77 inference(unit_resolution,[status(thm)],[12937, 197, 17987, 18028, 18040])).
% 3.53/3.77 tff(18042,plain,
% 3.53/3.77 (b(s(s(s(elem!1))), s(s(s(z))))),
% 3.53/3.77 inference(unit_resolution,[status(thm)],[3574, 18041, 3537])).
% 3.53/3.77 tff(18043,plain,
% 3.53/3.77 (s(s(s(elem!1))) = s(s(elem!1))),
% 3.53/3.77 inference(symmetry,[status(thm)],[18009])).
% 3.53/3.77 tff(18044,plain,
% 3.53/3.77 ((s(s(s(elem!1))) = s(s(s(z)))) <=> (s(s(elem!1)) = s(s(s(z))))),
% 3.53/3.77 inference(monotonicity,[status(thm)],[18043])).
% 3.53/3.77 tff(18045,plain,
% 3.53/3.77 ((s(s(s(elem!1))) = s(s(s(z)))) <=> (s(s(s(z))) = s(s(elem!1)))),
% 3.53/3.77 inference(transitivity,[status(thm)],[18044, 4437])).
% 3.53/3.77 tff(18046,plain,
% 3.53/3.77 ((~(s(s(s(elem!1))) = s(s(s(z))))) <=> (~(s(s(s(z))) = s(s(elem!1))))),
% 3.53/3.77 inference(monotonicity,[status(thm)],[18045])).
% 3.53/3.77 tff(18047,plain,
% 3.53/3.77 (~(s(s(s(z))) = s(s(elem!1)))),
% 3.53/3.77 inference(modus_ponens,[status(thm)],[3537, 18046])).
% 3.53/3.77 tff(18048,plain,
% 3.53/3.77 (r(s(s(s(z))), s(s(elem!1))) <=> r(s(s(s(z))), s(s(s(elem!1))))),
% 3.53/3.77 inference(monotonicity,[status(thm)],[18009])).
% 3.53/3.77 tff(18049,plain,
% 3.53/3.77 (r(s(s(s(z))), s(s(s(elem!1)))) <=> r(s(s(s(z))), s(s(elem!1)))),
% 3.53/3.77 inference(symmetry,[status(thm)],[18048])).
% 3.53/3.77 tff(18050,plain,
% 3.53/3.77 ((~r(s(s(s(z))), s(s(s(elem!1))))) <=> (~r(s(s(s(z))), s(s(elem!1))))),
% 3.53/3.77 inference(monotonicity,[status(thm)],[18049])).
% 3.53/3.77 tff(18051,plain,
% 3.53/3.77 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(z)), s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), s(s(z)))) | (~r(s(s(s(z))), s(s(z)))) | (~r(s(s(s(z))), s(s(s(elem!1))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(z)), s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), s(s(z)))) | (~r(s(s(s(z))), s(s(z)))) | (~r(s(s(s(z))), s(s(s(elem!1))))))),
% 3.53/3.77 inference(rewrite,[status(thm)],[])).
% 3.53/3.77 tff(18052,plain,
% 3.53/3.77 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(z)), s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), s(s(z)))) | (~r(s(s(s(z))), s(s(z)))) | (~r(s(s(s(z))), s(s(s(elem!1))))))),
% 3.53/3.77 inference(quant_inst,[status(thm)],[])).
% 3.53/3.77 tff(18053,plain,
% 3.53/3.77 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(z)), s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), s(s(z)))) | (~r(s(s(s(z))), s(s(z)))) | (~r(s(s(s(z))), s(s(s(elem!1)))))),
% 3.53/3.77 inference(modus_ponens,[status(thm)],[18052, 18051])).
% 3.53/3.77 tff(18054,plain,
% 3.53/3.77 (~r(s(s(s(z))), s(s(s(elem!1))))),
% 3.53/3.77 inference(unit_resolution,[status(thm)],[18053, 197, 17987, 18028, 18040])).
% 3.53/3.77 tff(18055,plain,
% 3.53/3.77 (~r(s(s(s(z))), s(s(elem!1)))),
% 3.53/3.77 inference(modus_ponens,[status(thm)],[18054, 18050])).
% 3.53/3.77 tff(18056,plain,
% 3.53/3.77 (r(s(s(elem!1)), s(s(s(z)))) <=> r(s(s(s(elem!1))), s(s(s(z))))),
% 3.53/3.77 inference(monotonicity,[status(thm)],[18009])).
% 3.53/3.77 tff(18057,plain,
% 3.53/3.77 (r(s(s(s(elem!1))), s(s(s(z)))) <=> r(s(s(elem!1)), s(s(s(z))))),
% 3.53/3.77 inference(symmetry,[status(thm)],[18056])).
% 3.53/3.77 tff(18058,plain,
% 3.53/3.77 ((~r(s(s(s(elem!1))), s(s(s(z))))) <=> (~r(s(s(elem!1)), s(s(s(z)))))),
% 3.53/3.77 inference(monotonicity,[status(thm)],[18057])).
% 3.53/3.77 tff(18059,plain,
% 3.53/3.77 (~r(s(s(elem!1)), s(s(s(z))))),
% 3.53/3.77 inference(modus_ponens,[status(thm)],[18041, 18058])).
% 3.53/3.77 tff(18060,plain,
% 3.53/3.77 ((s(s(s(z))) = s(s(elem!1))) | r(s(s(elem!1)), s(s(s(z)))) | (~b(s(z), s(s(s(z))))) | r(s(s(s(z))), s(s(elem!1)))),
% 3.53/3.77 inference(unit_resolution,[status(thm)],[5552, 15211])).
% 3.53/3.77 tff(18061,plain,
% 3.53/3.77 (~b(s(z), s(s(s(z))))),
% 3.53/3.77 inference(unit_resolution,[status(thm)],[18060, 18059, 18055, 18047])).
% 3.53/3.77 tff(18062,plain,
% 3.53/3.77 (r(s(z), s(s(s(z))))),
% 3.53/3.77 inference(unit_resolution,[status(thm)],[1674, 18061])).
% 3.53/3.77 tff(18063,plain,
% 3.53/3.77 (s(s(s(elem!1))) = s(s(elem!1))),
% 3.53/3.77 inference(unit_resolution,[status(thm)],[4030, 18009])).
% 3.53/3.77 tff(18064,plain,
% 3.53/3.77 (inj_0(s(elem!1)) = inj_0(s(s(s(elem!1))))),
% 3.53/3.77 inference(monotonicity,[status(thm)],[18011])).
% 3.53/3.77 tff(18065,plain,
% 3.53/3.77 (elem!1 = s(s(s(elem!1)))),
% 3.53/3.77 inference(transitivity,[status(thm)],[1170, 18064, 104, 18009])).
% 3.53/3.77 tff(18066,plain,
% 3.53/3.77 (r(s(s(s(z))), elem!1) <=> r(s(s(s(z))), s(s(s(elem!1))))),
% 3.53/3.77 inference(monotonicity,[status(thm)],[18065])).
% 3.53/3.77 tff(18067,plain,
% 3.53/3.77 (r(s(s(s(z))), s(s(s(elem!1)))) <=> r(s(s(s(z))), elem!1)),
% 3.53/3.77 inference(symmetry,[status(thm)],[18066])).
% 3.53/3.77 tff(18068,plain,
% 3.53/3.77 ((~r(s(s(s(z))), s(s(s(elem!1))))) <=> (~r(s(s(s(z))), elem!1))),
% 3.53/3.77 inference(monotonicity,[status(thm)],[18067])).
% 3.53/3.77 tff(18069,plain,
% 3.53/3.77 (~r(s(s(s(z))), elem!1)),
% 3.53/3.77 inference(modus_ponens,[status(thm)],[18054, 18068])).
% 3.53/3.77 tff(18070,plain,
% 3.53/3.77 (b(s(s(s(z))), elem!1)),
% 3.53/3.77 inference(unit_resolution,[status(thm)],[2826, 18069, 18018])).
% 3.53/3.77 tff(18071,plain,
% 3.53/3.77 (b(s(s(s(z))), s(s(s(elem!1))))),
% 3.53/3.77 inference(unit_resolution,[status(thm)],[4078, 18070, 18063])).
% 3.53/3.77 tff(18072,plain,
% 3.53/3.77 (~b(s(s(s(z))), s(z))),
% 3.53/3.77 inference(unit_resolution,[status(thm)],[5561, 166, 17985, 18071, 18042])).
% 3.53/3.77 tff(18073,plain,
% 3.53/3.77 (r(s(s(s(z))), s(z))),
% 3.53/3.77 inference(unit_resolution,[status(thm)],[1763, 18072])).
% 3.53/3.77 tff(18074,plain,
% 3.53/3.77 (~r(z, s(s(s(z))))),
% 3.53/3.77 inference(unit_resolution,[status(thm)],[11904, 18073, 17968, 18062])).
% 3.53/3.77 tff(18075,plain,
% 3.53/3.77 (b(z, s(s(s(z))))),
% 3.53/3.77 inference(unit_resolution,[status(thm)],[1697, 18074])).
% 3.53/3.77 tff(18076,plain,
% 3.53/3.77 (b(s(elem!1), s(z))),
% 3.53/3.77 inference(modus_ponens,[status(thm)],[17959, 4328])).
% 3.53/3.77 tff(18077,plain,
% 3.53/3.77 (b(s(s(elem!1)), s(z))),
% 3.53/3.77 inference(unit_resolution,[status(thm)],[18015, 334])).
% 3.53/3.77 tff(18078,plain,
% 3.53/3.77 (b(s(z), s(elem!1))),
% 3.53/3.77 inference(modus_ponens,[status(thm)],[17985, 8998])).
% 3.53/3.77 tff(18079,plain,
% 3.53/3.77 (r(s(s(s(elem!1))), z) <=> r(s(s(elem!1)), z)),
% 3.53/3.77 inference(symmetry,[status(thm)],[2971])).
% 3.53/3.77 tff(18080,plain,
% 3.53/3.77 (r(s(s(elem!1)), z)),
% 3.53/3.77 inference(modus_ponens,[status(thm)],[17951, 18079])).
% 3.53/3.77 tff(18081,plain,
% 3.53/3.77 (~r(s(s(s(z))), z)),
% 3.53/3.77 inference(unit_resolution,[status(thm)],[12545, 18080, 17982, 18078, 17968, 4027, 10150, 18077, 18076])).
% 3.53/3.77 tff(18082,plain,
% 3.53/3.77 (b(s(s(s(z))), z)),
% 3.53/3.77 inference(unit_resolution,[status(thm)],[1713, 18081])).
% 3.53/3.77 tff(18083,plain,
% 3.53/3.77 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(z)))) | (~b(z, s(s(s(elem!1))))) | (~b(s(s(s(z))), z)) | (~b(z, s(s(s(z))))) | (~b(s(s(s(elem!1))), s(s(s(z))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(s(z)))) | (~b(z, s(s(s(elem!1))))) | (~b(s(s(s(z))), z)) | (~b(z, s(s(s(z))))) | (~b(s(s(s(elem!1))), s(s(s(z))))))),
% 3.53/3.77 inference(rewrite,[status(thm)],[])).
% 3.53/3.77 tff(18084,plain,
% 3.53/3.77 (((~b(z, s(s(z)))) | (~b(z, s(s(z)))) | (~b(s(s(s(z))), z)) | (~b(s(s(s(elem!1))), s(s(s(z))))) | (~b(z, s(s(s(z))))) | (~b(z, s(s(s(elem!1)))))) <=> ((~b(z, s(s(z)))) | (~b(z, s(s(s(elem!1))))) | (~b(s(s(s(z))), z)) | (~b(z, s(s(s(z))))) | (~b(s(s(s(elem!1))), s(s(s(z))))))),
% 3.53/3.77 inference(rewrite,[status(thm)],[])).
% 3.53/3.77 tff(18085,plain,
% 3.53/3.77 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(z)))) | (~b(z, s(s(z)))) | (~b(s(s(s(z))), z)) | (~b(s(s(s(elem!1))), s(s(s(z))))) | (~b(z, s(s(s(z))))) | (~b(z, s(s(s(elem!1))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(z)))) | (~b(z, s(s(s(elem!1))))) | (~b(s(s(s(z))), z)) | (~b(z, s(s(s(z))))) | (~b(s(s(s(elem!1))), s(s(s(z)))))))),
% 3.53/3.77 inference(monotonicity,[status(thm)],[18084])).
% 3.53/3.77 tff(18086,plain,
% 3.53/3.77 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(z)))) | (~b(z, s(s(z)))) | (~b(s(s(s(z))), z)) | (~b(s(s(s(elem!1))), s(s(s(z))))) | (~b(z, s(s(s(z))))) | (~b(z, s(s(s(elem!1))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(s(z)))) | (~b(z, s(s(s(elem!1))))) | (~b(s(s(s(z))), z)) | (~b(z, s(s(s(z))))) | (~b(s(s(s(elem!1))), s(s(s(z))))))),
% 3.53/3.77 inference(transitivity,[status(thm)],[18085, 18083])).
% 3.53/3.77 tff(18087,plain,
% 3.53/3.77 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(z)))) | (~b(z, s(s(z)))) | (~b(s(s(s(z))), z)) | (~b(s(s(s(elem!1))), s(s(s(z))))) | (~b(z, s(s(s(z))))) | (~b(z, s(s(s(elem!1))))))),
% 3.53/3.77 inference(quant_inst,[status(thm)],[])).
% 3.53/3.77 tff(18088,plain,
% 3.53/3.77 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(s(z)))) | (~b(z, s(s(s(elem!1))))) | (~b(s(s(s(z))), z)) | (~b(z, s(s(s(z))))) | (~b(s(s(s(elem!1))), s(s(s(z)))))),
% 3.53/3.77 inference(modus_ponens,[status(thm)],[18087, 18086])).
% 3.53/3.77 tff(18089,plain,
% 3.53/3.77 ((~b(z, s(s(s(elem!1))))) | (~b(z, s(s(s(z)))))),
% 3.53/3.77 inference(unit_resolution,[status(thm)],[18088, 166, 10450, 18082, 3251])).
% 3.53/3.77 tff(18090,plain,
% 3.53/3.77 (~b(z, s(s(s(elem!1))))),
% 3.53/3.77 inference(unit_resolution,[status(thm)],[18089, 1700])).
% 3.53/3.77 tff(18091,plain,
% 3.53/3.77 (r(z, s(s(s(elem!1))))),
% 3.53/3.77 inference(unit_resolution,[status(thm)],[261, 18090])).
% 3.53/3.77 tff(18092,plain,
% 3.53/3.77 (~b(s(s(s(s(z)))), z)),
% 3.53/3.77 inference(unit_resolution,[status(thm)],[6574, 166, 18082, 1700, 4732])).
% 3.53/3.77 tff(18093,plain,
% 3.53/3.77 (r(s(s(s(s(z)))), z)),
% 3.53/3.77 inference(unit_resolution,[status(thm)],[3266, 18092])).
% 3.53/3.77 tff(18094,plain,
% 3.53/3.77 ((~r(s(s(s(s(z)))), z)) | (~r(z, s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), s(s(s(s(z))))))),
% 3.53/3.77 inference(unit_resolution,[status(thm)],[6585, 17951])).
% 3.53/3.77 tff(18095,plain,
% 3.53/3.77 (~r(s(s(s(elem!1))), s(s(s(s(z)))))),
% 3.53/3.77 inference(unit_resolution,[status(thm)],[18094, 18093, 18091])).
% 3.53/3.77 tff(18096,plain,
% 3.53/3.77 (r(s(s(s(z))), s(s(s(elem!1)))) <=> r(s(s(s(z))), elem!1)),
% 3.53/3.77 inference(symmetry,[status(thm)],[17186])).
% 3.53/3.77 tff(18097,plain,
% 3.53/3.77 ((~r(s(s(s(z))), s(s(s(elem!1))))) <=> (~r(s(s(s(z))), elem!1))),
% 3.53/3.77 inference(monotonicity,[status(thm)],[18096])).
% 3.53/3.77 tff(18098,plain,
% 3.53/3.77 (~b(s(s(s(z))), s(s(z)))),
% 3.53/3.77 inference(unit_resolution,[status(thm)],[12296, 166, 10450, 18030, 18082])).
% 3.53/3.77 tff(18099,plain,
% 3.53/3.77 (r(s(s(s(z))), s(s(z)))),
% 3.53/3.77 inference(unit_resolution,[status(thm)],[1010, 18098])).
% 3.53/3.77 tff(18100,plain,
% 3.53/3.77 (~r(s(s(s(z))), s(s(s(elem!1))))),
% 3.53/3.77 inference(unit_resolution,[status(thm)],[18053, 197, 17987, 18028, 18099])).
% 3.53/3.77 tff(18101,plain,
% 3.53/3.77 (~r(s(s(s(z))), elem!1)),
% 3.53/3.77 inference(modus_ponens,[status(thm)],[18100, 18097])).
% 3.53/3.77 tff(18102,plain,
% 3.53/3.77 (b(s(s(s(z))), elem!1)),
% 3.53/3.77 inference(unit_resolution,[status(thm)],[2826, 18101, 4027])).
% 3.53/3.77 tff(18103,plain,
% 3.53/3.77 (b(s(s(s(z))), s(s(s(elem!1))))),
% 3.53/3.77 inference(unit_resolution,[status(thm)],[4078, 18102, 4031])).
% 3.53/3.77 tff(18104,plain,
% 3.53/3.77 (~b(s(s(s(elem!1))), s(s(s(s(z)))))),
% 3.53/3.77 inference(unit_resolution,[status(thm)],[16494, 166, 17959, 18103, 4732, 3251])).
% 3.53/3.77 tff(18105,plain,
% 3.53/3.77 (~b(s(s(s(s(elem!1)))), s(s(s(s(z)))))),
% 3.53/3.77 inference(unit_resolution,[status(thm)],[12962, 18104, 334])).
% 3.53/3.77 tff(18106,plain,
% 3.53/3.77 (~b(elem!1, s(s(s(s(z)))))),
% 3.53/3.77 inference(unit_resolution,[status(thm)],[12970, 18105, 334])).
% 3.53/3.77 tff(18107,plain,
% 3.53/3.77 (r(elem!1, s(s(s(s(z)))))),
% 3.53/3.77 inference(unit_resolution,[status(thm)],[1098, 18106, 6568])).
% 3.53/3.77 tff(18108,plain,
% 3.53/3.77 ($false),
% 3.53/3.77 inference(unit_resolution,[status(thm)],[5665, 18107, 18095, 334])).
% 3.53/3.77 tff(18109,plain,((~b(s(s(s(s(z)))), s(s(s(z))))) | (~(s(s(elem!1)) = s(s(s(elem!1))))) | (~b(z, s(s(s(z))))) | (~b(s(s(s(elem!1))), s(s(s(z)))))), inference(lemma,lemma(discharge,[]))).
% 3.53/3.77 tff(18110,plain,
% 3.53/3.77 (~b(s(s(s(s(z)))), s(s(s(z))))),
% 3.53/3.77 inference(unit_resolution,[status(thm)],[18109, 18009, 18075, 18042])).
% 3.53/3.77 tff(18111,plain,
% 3.53/3.77 (r(s(s(s(s(z)))), s(s(s(z))))),
% 3.53/3.77 inference(unit_resolution,[status(thm)],[4662, 18110])).
% 3.53/3.77 tff(18112,plain,
% 3.53/3.77 (~r(s(s(z)), s(s(s(s(z)))))),
% 3.53/3.77 inference(unit_resolution,[status(thm)],[6600, 197, 18040, 18111, 18038])).
% 3.53/3.77 tff(18113,plain,
% 3.53/3.77 (b(s(s(z)), s(s(s(s(z)))))),
% 3.53/3.77 inference(unit_resolution,[status(thm)],[4753, 18112])).
% 3.53/3.77 tff(18114,plain,
% 3.53/3.77 (~r(s(s(s(s(z)))), s(z))),
% 3.53/3.77 inference(unit_resolution,[status(thm)],[6608, 197, 18040, 18111, 18062])).
% 3.53/3.77 tff(18115,plain,
% 3.53/3.77 (b(s(s(s(s(z)))), s(z))),
% 3.53/3.77 inference(unit_resolution,[status(thm)],[3285, 18114])).
% 3.53/3.77 tff(18116,plain,
% 3.53/3.77 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(s(z)), s(z))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(z)), s(s(s(s(z)))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(s(z)), s(z))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(z)), s(s(s(s(z)))))))),
% 3.53/3.77 inference(rewrite,[status(thm)],[])).
% 3.53/3.77 tff(18117,plain,
% 3.53/3.77 (((~b(s(s(s(elem!1))), s(z))) | (~b(s(s(z)), s(z))) | (~b(s(z), s(s(s(elem!1))))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(z)), s(z))) | (~b(s(s(z)), s(s(s(s(z))))))) <=> ((~b(s(z), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(s(z)), s(z))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(z)), s(s(s(s(z)))))))),
% 3.53/3.77 inference(rewrite,[status(thm)],[])).
% 3.53/3.77 tff(18118,plain,
% 3.53/3.77 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), s(z))) | (~b(s(s(z)), s(z))) | (~b(s(z), s(s(s(elem!1))))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(z)), s(z))) | (~b(s(s(z)), s(s(s(s(z)))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(s(z)), s(z))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(z)), s(s(s(s(z))))))))),
% 3.53/3.77 inference(monotonicity,[status(thm)],[18117])).
% 3.53/3.77 tff(18119,plain,
% 3.53/3.77 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), s(z))) | (~b(s(s(z)), s(z))) | (~b(s(z), s(s(s(elem!1))))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(z)), s(z))) | (~b(s(s(z)), s(s(s(s(z)))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(s(z)), s(z))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(z)), s(s(s(s(z)))))))),
% 3.53/3.77 inference(transitivity,[status(thm)],[18118, 18116])).
% 3.53/3.77 tff(18120,plain,
% 3.53/3.77 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), s(z))) | (~b(s(s(z)), s(z))) | (~b(s(z), s(s(s(elem!1))))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(z)), s(z))) | (~b(s(s(z)), s(s(s(s(z)))))))),
% 3.53/3.77 inference(quant_inst,[status(thm)],[])).
% 3.53/3.77 tff(18121,plain,
% 3.53/3.77 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(s(z)), s(z))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(z)), s(s(s(s(z))))))),
% 3.53/3.77 inference(modus_ponens,[status(thm)],[18120, 18119])).
% 3.53/3.77 tff(18122,plain,
% 3.53/3.77 ($false),
% 3.53/3.77 inference(unit_resolution,[status(thm)],[18121, 166, 17985, 17959, 17064, 18115, 18113])).
% 3.53/3.77 tff(18123,plain,(s(s(elem!1)) = s(s(z))), inference(lemma,lemma(discharge,[]))).
% 3.53/3.77 tff(18124,plain,
% 3.53/3.77 (s(s(z)) = s(s(elem!1))),
% 3.53/3.77 inference(symmetry,[status(thm)],[18123])).
% 3.53/3.77 tff(18125,plain,
% 3.53/3.77 ((s(s(s(s(s(s(s(s(elem!1)))))))) = s(s(z))) <=> (s(s(s(s(s(s(s(s(elem!1)))))))) = s(s(elem!1)))),
% 3.53/3.77 inference(monotonicity,[status(thm)],[18124])).
% 3.53/3.77 tff(18126,plain,
% 3.53/3.77 ((s(s(s(s(s(s(s(s(elem!1)))))))) = s(s(elem!1))) <=> (s(s(s(s(s(s(s(s(elem!1)))))))) = s(s(z)))),
% 3.53/3.77 inference(symmetry,[status(thm)],[18125])).
% 3.53/3.77 tff(18127,plain,
% 3.53/3.77 ((~(s(s(s(s(s(s(s(s(elem!1)))))))) = s(s(elem!1)))) <=> (~(s(s(s(s(s(s(s(s(elem!1)))))))) = s(s(z))))),
% 3.53/3.77 inference(monotonicity,[status(thm)],[18126])).
% 3.53/3.77 tff(18128,plain,
% 3.53/3.77 (s(s(z)) = s(s(elem!1))),
% 3.53/3.77 inference(unit_resolution,[status(thm)],[131, 18123])).
% 3.53/3.77 tff(18129,plain,
% 3.53/3.77 (s(elem!1) = s(z)),
% 3.53/3.77 inference(unit_resolution,[status(thm)],[43, 18128])).
% 3.53/3.77 tff(18130,plain,
% 3.53/3.77 (~(s(s(s(s(s(s(s(s(elem!1)))))))) = s(s(elem!1)))),
% 3.53/3.77 inference(unit_resolution,[status(thm)],[13189, 18129])).
% 3.53/3.77 tff(18131,plain,
% 3.53/3.77 (~(s(s(s(s(s(s(s(s(elem!1)))))))) = s(s(z)))),
% 3.53/3.77 inference(modus_ponens,[status(thm)],[18130, 18127])).
% 3.53/3.77 tff(18132,plain,
% 3.53/3.77 (b(elem!1, s(s(z))) <=> b(elem!1, s(s(elem!1)))),
% 3.53/3.77 inference(monotonicity,[status(thm)],[18124])).
% 3.53/3.77 tff(18133,plain,
% 3.53/3.77 (b(elem!1, s(s(elem!1))) <=> b(elem!1, s(s(z)))),
% 3.53/3.77 inference(symmetry,[status(thm)],[18132])).
% 3.53/3.77 tff(18134,plain,
% 3.53/3.77 (z = elem!1),
% 3.53/3.77 inference(unit_resolution,[status(thm)],[30, 18129])).
% 3.53/3.77 tff(18135,plain,
% 3.53/3.77 (elem!1 = z),
% 3.53/3.77 inference(symmetry,[status(thm)],[18134])).
% 3.53/3.77 tff(18136,plain,
% 3.53/3.77 (b(elem!1, s(s(elem!1))) <=> b(z, s(s(z)))),
% 3.53/3.77 inference(monotonicity,[status(thm)],[18135, 18123])).
% 3.53/3.77 tff(18137,plain,
% 3.53/3.77 (b(z, s(s(z))) <=> b(elem!1, s(s(elem!1)))),
% 3.53/3.77 inference(symmetry,[status(thm)],[18136])).
% 3.53/3.77 tff(18138,plain,
% 3.53/3.77 (b(elem!1, s(s(elem!1)))),
% 3.53/3.77 inference(modus_ponens,[status(thm)],[10450, 18137])).
% 3.53/3.77 tff(18139,plain,
% 3.53/3.77 (b(elem!1, s(s(z)))),
% 3.53/3.77 inference(modus_ponens,[status(thm)],[18138, 18133])).
% 3.53/3.77 tff(18140,plain,
% 3.53/3.77 ((s(s(s(s(s(s(s(s(elem!1)))))))) = z) <=> (s(s(s(s(s(s(s(s(elem!1)))))))) = elem!1)),
% 3.53/3.77 inference(monotonicity,[status(thm)],[18134])).
% 3.53/3.77 tff(18141,plain,
% 3.53/3.77 ((~(s(s(s(s(s(s(s(s(elem!1)))))))) = z)) <=> (~(s(s(s(s(s(s(s(s(elem!1)))))))) = elem!1))),
% 3.53/3.77 inference(monotonicity,[status(thm)],[18140])).
% 3.53/3.77 tff(18142,plain,
% 3.53/3.77 (~(s(s(s(s(s(s(s(s(elem!1)))))))) = elem!1)),
% 3.53/3.77 inference(modus_ponens,[status(thm)],[13119, 18141])).
% 3.53/3.77 tff(18143,plain,
% 3.53/3.77 (s(s(s(elem!1))) = s(s(s(z)))),
% 3.53/3.77 inference(monotonicity,[status(thm)],[18123])).
% 3.53/3.77 tff(18144,plain,
% 3.53/3.77 (s(s(s(z))) = s(s(s(elem!1)))),
% 3.53/3.77 inference(symmetry,[status(thm)],[18143])).
% 3.53/3.77 tff(18145,plain,
% 3.53/3.77 ((s(s(s(s(s(s(s(s(elem!1)))))))) = s(s(s(z)))) <=> (s(s(s(s(s(s(s(s(elem!1)))))))) = s(s(s(elem!1))))),
% 3.53/3.77 inference(monotonicity,[status(thm)],[18144])).
% 3.53/3.77 tff(18146,plain,
% 3.53/3.77 ((s(s(s(s(s(s(s(s(elem!1)))))))) = s(s(s(z)))) <=> (s(s(s(elem!1))) = s(s(s(s(s(s(s(s(elem!1)))))))))),
% 3.53/3.77 inference(transitivity,[status(thm)],[18145, 13360])).
% 3.53/3.77 tff(18147,plain,
% 3.53/3.77 ((s(s(s(elem!1))) = s(s(s(s(s(s(s(s(elem!1))))))))) <=> (s(s(s(s(s(s(s(s(elem!1)))))))) = s(s(s(z))))),
% 3.53/3.77 inference(symmetry,[status(thm)],[18146])).
% 3.53/3.78 tff(18148,plain,
% 3.53/3.78 ((~(s(s(s(elem!1))) = s(s(s(s(s(s(s(s(elem!1)))))))))) <=> (~(s(s(s(s(s(s(s(s(elem!1)))))))) = s(s(s(z)))))),
% 3.53/3.78 inference(monotonicity,[status(thm)],[18147])).
% 3.53/3.78 tff(18149,plain,
% 3.53/3.78 (~(s(s(s(elem!1))) = s(s(s(s(s(s(s(s(elem!1)))))))))),
% 3.53/3.78 inference(unit_resolution,[status(thm)],[13110, 18128])).
% 3.53/3.78 tff(18150,plain,
% 3.53/3.78 (~(s(s(s(s(s(s(s(s(elem!1)))))))) = s(s(s(z))))),
% 3.53/3.78 inference(modus_ponens,[status(thm)],[18149, 18148])).
% 3.53/3.78 tff(18151,plain,
% 3.53/3.78 (r(s(z), z) <=> r(s(z), elem!1)),
% 3.53/3.78 inference(monotonicity,[status(thm)],[18134])).
% 3.53/3.78 tff(18152,plain,
% 3.53/3.78 (r(s(z), elem!1)),
% 3.53/3.78 inference(modus_ponens,[status(thm)],[17968, 18151])).
% 3.53/3.78 tff(18153,plain,
% 3.53/3.78 (r(elem!1, s(z))),
% 3.53/3.78 inference(unit_resolution,[status(thm)],[741, 18134, 17982])).
% 3.53/3.78 tff(18154,plain,
% 3.53/3.78 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(z))) | (~r(s(z), elem!1)) | (~r(s(s(s(s(s(s(s(s(elem!1)))))))), elem!1)) | (~r(s(s(s(s(s(s(s(s(elem!1)))))))), s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(elem!1, s(z))) | (~r(s(z), elem!1)) | (~r(s(s(s(s(s(s(s(s(elem!1)))))))), elem!1)) | (~r(s(s(s(s(s(s(s(s(elem!1)))))))), s(z))))),
% 3.53/3.78 inference(rewrite,[status(thm)],[])).
% 3.53/3.78 tff(18155,plain,
% 3.53/3.78 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(z))) | (~r(s(z), elem!1)) | (~r(s(s(s(s(s(s(s(s(elem!1)))))))), elem!1)) | (~r(s(s(s(s(s(s(s(s(elem!1)))))))), s(z))))),
% 3.53/3.78 inference(quant_inst,[status(thm)],[])).
% 3.53/3.78 tff(18156,plain,
% 3.53/3.78 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(elem!1, s(z))) | (~r(s(z), elem!1)) | (~r(s(s(s(s(s(s(s(s(elem!1)))))))), elem!1)) | (~r(s(s(s(s(s(s(s(s(elem!1)))))))), s(z)))),
% 3.53/3.78 inference(modus_ponens,[status(thm)],[18155, 18154])).
% 3.53/3.78 tff(18157,plain,
% 3.53/3.78 (~r(s(s(s(s(s(s(s(s(elem!1)))))))), s(z))),
% 3.53/3.78 inference(unit_resolution,[status(thm)],[18156, 197, 18153, 18152, 13347])).
% 3.53/3.78 tff(18158,plain,
% 3.53/3.78 (~(s(s(s(s(s(s(s(s(elem!1)))))))) = s(z))),
% 3.53/3.78 inference(unit_resolution,[status(thm)],[13196, 18134])).
% 3.53/3.78 tff(18159,plain,
% 3.53/3.78 (b(s(s(s(s(s(s(s(s(elem!1)))))))), s(z))),
% 3.53/3.78 inference(unit_resolution,[status(thm)],[13209, 79, 18158, 18157])).
% 3.53/3.78 tff(18160,plain,
% 3.53/3.78 (b(s(s(s(z))), s(z)) <=> b(s(s(s(elem!1))), s(z))),
% 3.53/3.78 inference(monotonicity,[status(thm)],[18144])).
% 3.53/3.78 tff(18161,plain,
% 3.53/3.78 (b(s(s(s(elem!1))), s(z)) <=> b(s(s(s(z))), s(z))),
% 3.53/3.78 inference(symmetry,[status(thm)],[18160])).
% 3.53/3.78 tff(18162,plain,
% 3.53/3.78 (b(s(s(s(z))), s(z))),
% 3.53/3.78 inference(modus_ponens,[status(thm)],[17959, 18161])).
% 3.53/3.78 tff(18163,plain,
% 3.53/3.78 (b(s(z), s(s(z)))),
% 3.53/3.78 inference(unit_resolution,[status(thm)],[17976, 18128])).
% 3.53/3.78 tff(18164,plain,
% 3.53/3.78 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(z)))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(z)), s(z))) | (~b(s(s(s(s(s(s(s(s(elem!1)))))))), s(z))) | (~b(s(s(s(s(s(s(s(s(elem!1)))))))), s(s(s(z))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), s(s(z)))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(z)), s(z))) | (~b(s(s(s(s(s(s(s(s(elem!1)))))))), s(z))) | (~b(s(s(s(s(s(s(s(s(elem!1)))))))), s(s(s(z))))))),
% 3.53/3.78 inference(rewrite,[status(thm)],[])).
% 3.53/3.78 tff(18165,plain,
% 3.53/3.78 (((~b(s(s(z)), s(z))) | (~b(s(s(s(s(s(s(s(s(elem!1)))))))), s(z))) | (~b(s(z), s(s(z)))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(s(s(s(s(s(elem!1)))))))), s(z))) | (~b(s(s(s(s(s(s(s(s(elem!1)))))))), s(s(s(z)))))) <=> ((~b(s(z), s(s(z)))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(z)), s(z))) | (~b(s(s(s(s(s(s(s(s(elem!1)))))))), s(z))) | (~b(s(s(s(s(s(s(s(s(elem!1)))))))), s(s(s(z))))))),
% 3.53/3.78 inference(rewrite,[status(thm)],[])).
% 3.53/3.78 tff(18166,plain,
% 3.53/3.78 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), s(z))) | (~b(s(s(s(s(s(s(s(s(elem!1)))))))), s(z))) | (~b(s(z), s(s(z)))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(s(s(s(s(s(elem!1)))))))), s(z))) | (~b(s(s(s(s(s(s(s(s(elem!1)))))))), s(s(s(z))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(z)))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(z)), s(z))) | (~b(s(s(s(s(s(s(s(s(elem!1)))))))), s(z))) | (~b(s(s(s(s(s(s(s(s(elem!1)))))))), s(s(s(z)))))))),
% 3.53/3.78 inference(monotonicity,[status(thm)],[18165])).
% 3.53/3.78 tff(18167,plain,
% 3.53/3.78 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), s(z))) | (~b(s(s(s(s(s(s(s(s(elem!1)))))))), s(z))) | (~b(s(z), s(s(z)))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(s(s(s(s(s(elem!1)))))))), s(z))) | (~b(s(s(s(s(s(s(s(s(elem!1)))))))), s(s(s(z))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), s(s(z)))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(z)), s(z))) | (~b(s(s(s(s(s(s(s(s(elem!1)))))))), s(z))) | (~b(s(s(s(s(s(s(s(s(elem!1)))))))), s(s(s(z))))))),
% 3.53/3.78 inference(transitivity,[status(thm)],[18166, 18164])).
% 3.53/3.78 tff(18168,plain,
% 3.53/3.78 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), s(z))) | (~b(s(s(s(s(s(s(s(s(elem!1)))))))), s(z))) | (~b(s(z), s(s(z)))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(s(s(s(s(s(elem!1)))))))), s(z))) | (~b(s(s(s(s(s(s(s(s(elem!1)))))))), s(s(s(z))))))),
% 3.53/3.78 inference(quant_inst,[status(thm)],[])).
% 3.53/3.78 tff(18169,plain,
% 3.53/3.78 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), s(s(z)))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(z)), s(z))) | (~b(s(s(s(s(s(s(s(s(elem!1)))))))), s(z))) | (~b(s(s(s(s(s(s(s(s(elem!1)))))))), s(s(s(z)))))),
% 3.53/3.78 inference(modus_ponens,[status(thm)],[18168, 18167])).
% 3.53/3.78 tff(18170,plain,
% 3.53/3.78 (~b(s(s(s(s(s(s(s(s(elem!1)))))))), s(s(s(z))))),
% 3.53/3.78 inference(unit_resolution,[status(thm)],[18169, 166, 18163, 17064, 18162, 18159])).
% 3.53/3.78 tff(18171,plain,
% 3.53/3.78 (r(s(s(s(elem!1))), elem!1) <=> r(s(s(s(z))), elem!1)),
% 3.53/3.78 inference(monotonicity,[status(thm)],[18143])).
% 3.53/3.78 tff(18172,plain,
% 3.53/3.78 (r(s(s(s(elem!1))), elem!1) | (~(z = elem!1))),
% 3.53/3.78 inference(unit_resolution,[status(thm)],[966, 17951])).
% 3.53/3.78 tff(18173,plain,
% 3.53/3.78 (r(s(s(s(elem!1))), elem!1)),
% 3.53/3.78 inference(unit_resolution,[status(thm)],[18172, 18134])).
% 3.53/3.78 tff(18174,plain,
% 3.53/3.78 (r(s(s(s(z))), elem!1)),
% 3.53/3.78 inference(modus_ponens,[status(thm)],[18173, 18171])).
% 3.53/3.78 tff(18175,plain,
% 3.53/3.78 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(z))) | (~r(s(s(s(z))), elem!1)) | (~r(s(s(s(s(s(s(s(s(elem!1)))))))), elem!1)) | (~r(s(s(s(s(s(s(s(s(elem!1)))))))), s(s(s(z))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(elem!1, s(z))) | (~r(s(s(s(z))), elem!1)) | (~r(s(s(s(s(s(s(s(s(elem!1)))))))), elem!1)) | (~r(s(s(s(s(s(s(s(s(elem!1)))))))), s(s(s(z))))))),
% 3.53/3.78 inference(rewrite,[status(thm)],[])).
% 3.53/3.78 tff(18176,plain,
% 3.53/3.78 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(z))) | (~r(s(s(s(z))), elem!1)) | (~r(s(s(s(s(s(s(s(s(elem!1)))))))), elem!1)) | (~r(s(s(s(s(s(s(s(s(elem!1)))))))), s(s(s(z))))))),
% 3.53/3.78 inference(quant_inst,[status(thm)],[])).
% 3.53/3.78 tff(18177,plain,
% 3.53/3.78 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(elem!1, s(z))) | (~r(s(s(s(z))), elem!1)) | (~r(s(s(s(s(s(s(s(s(elem!1)))))))), elem!1)) | (~r(s(s(s(s(s(s(s(s(elem!1)))))))), s(s(s(z)))))),
% 3.53/3.78 inference(modus_ponens,[status(thm)],[18176, 18175])).
% 3.53/3.78 tff(18178,plain,
% 3.53/3.78 (~r(s(s(s(s(s(s(s(s(elem!1)))))))), s(s(s(z))))),
% 3.53/3.78 inference(unit_resolution,[status(thm)],[18177, 197, 18153, 13347, 18174])).
% 3.53/3.78 tff(18179,plain,
% 3.53/3.78 (((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((s(s(s(s(s(s(s(s(elem!1)))))))) = s(s(s(z)))) | b(s(s(s(s(s(s(s(s(elem!1)))))))), s(s(s(z)))) | r(s(s(s(s(s(s(s(s(elem!1)))))))), s(s(s(z)))))) <=> ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (s(s(s(s(s(s(s(s(elem!1)))))))) = s(s(s(z)))) | b(s(s(s(s(s(s(s(s(elem!1)))))))), s(s(s(z)))) | r(s(s(s(s(s(s(s(s(elem!1)))))))), s(s(s(z)))))),
% 3.53/3.78 inference(rewrite,[status(thm)],[])).
% 3.53/3.78 tff(18180,plain,
% 3.53/3.78 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((s(s(s(s(s(s(s(s(elem!1)))))))) = s(s(s(z)))) | b(s(s(s(s(s(s(s(s(elem!1)))))))), s(s(s(z)))) | r(s(s(s(s(s(s(s(s(elem!1)))))))), s(s(s(z)))))),
% 3.53/3.78 inference(quant_inst,[status(thm)],[])).
% 3.53/3.78 tff(18181,plain,
% 3.53/3.78 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (s(s(s(s(s(s(s(s(elem!1)))))))) = s(s(s(z)))) | b(s(s(s(s(s(s(s(s(elem!1)))))))), s(s(s(z)))) | r(s(s(s(s(s(s(s(s(elem!1)))))))), s(s(s(z))))),
% 3.53/3.78 inference(modus_ponens,[status(thm)],[18180, 18179])).
% 3.53/3.78 tff(18182,plain,
% 3.53/3.78 ((s(s(s(s(s(s(s(s(elem!1)))))))) = s(s(s(z)))) | b(s(s(s(s(s(s(s(s(elem!1)))))))), s(s(s(z))))),
% 3.53/3.78 inference(unit_resolution,[status(thm)],[18181, 79, 18178])).
% 3.53/3.78 tff(18183,plain,
% 3.53/3.78 ($false),
% 3.53/3.78 inference(unit_resolution,[status(thm)],[18182, 18170, 18150])).
% 3.53/3.78 tff(18184,plain,(~r(s(s(s(s(s(s(s(s(elem!1)))))))), elem!1)), inference(lemma,lemma(discharge,[]))).
% 3.53/3.78 tff(18185,plain,
% 3.53/3.78 (b(s(s(s(s(s(s(s(s(elem!1)))))))), elem!1)),
% 3.53/3.78 inference(unit_resolution,[status(thm)],[13235, 18184, 18142])).
% 3.53/3.78 tff(18186,plain,
% 3.53/3.78 (b(s(s(elem!1)), elem!1)),
% 3.53/3.78 inference(unit_resolution,[status(thm)],[8754, 18128, 18030])).
% 3.53/3.78 tff(18187,plain,
% 3.53/3.78 (b(s(s(z)), elem!1)),
% 3.53/3.78 inference(unit_resolution,[status(thm)],[14685, 18186, 18123])).
% 3.53/3.78 tff(18188,plain,
% 3.53/3.78 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), elem!1)) | (~b(elem!1, s(s(z)))) | (~b(s(s(s(s(s(s(s(s(elem!1)))))))), elem!1)) | (~b(s(s(s(s(s(s(s(s(elem!1)))))))), s(s(z)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(z)), elem!1)) | (~b(elem!1, s(s(z)))) | (~b(s(s(s(s(s(s(s(s(elem!1)))))))), elem!1)) | (~b(s(s(s(s(s(s(s(s(elem!1)))))))), s(s(z)))))),
% 3.53/3.78 inference(rewrite,[status(thm)],[])).
% 3.53/3.78 tff(18189,plain,
% 3.53/3.78 (((~b(s(s(z)), elem!1)) | (~b(s(s(s(s(s(s(s(s(elem!1)))))))), elem!1)) | (~b(elem!1, s(s(z)))) | (~b(s(s(z)), elem!1)) | (~b(s(s(s(s(s(s(s(s(elem!1)))))))), elem!1)) | (~b(s(s(s(s(s(s(s(s(elem!1)))))))), s(s(z))))) <=> ((~b(s(s(z)), elem!1)) | (~b(elem!1, s(s(z)))) | (~b(s(s(s(s(s(s(s(s(elem!1)))))))), elem!1)) | (~b(s(s(s(s(s(s(s(s(elem!1)))))))), s(s(z)))))),
% 3.53/3.78 inference(rewrite,[status(thm)],[])).
% 3.53/3.78 tff(18190,plain,
% 3.53/3.78 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), elem!1)) | (~b(s(s(s(s(s(s(s(s(elem!1)))))))), elem!1)) | (~b(elem!1, s(s(z)))) | (~b(s(s(z)), elem!1)) | (~b(s(s(s(s(s(s(s(s(elem!1)))))))), elem!1)) | (~b(s(s(s(s(s(s(s(s(elem!1)))))))), s(s(z)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), elem!1)) | (~b(elem!1, s(s(z)))) | (~b(s(s(s(s(s(s(s(s(elem!1)))))))), elem!1)) | (~b(s(s(s(s(s(s(s(s(elem!1)))))))), s(s(z))))))),
% 3.53/3.78 inference(monotonicity,[status(thm)],[18189])).
% 3.53/3.78 tff(18191,plain,
% 3.53/3.78 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), elem!1)) | (~b(s(s(s(s(s(s(s(s(elem!1)))))))), elem!1)) | (~b(elem!1, s(s(z)))) | (~b(s(s(z)), elem!1)) | (~b(s(s(s(s(s(s(s(s(elem!1)))))))), elem!1)) | (~b(s(s(s(s(s(s(s(s(elem!1)))))))), s(s(z)))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(z)), elem!1)) | (~b(elem!1, s(s(z)))) | (~b(s(s(s(s(s(s(s(s(elem!1)))))))), elem!1)) | (~b(s(s(s(s(s(s(s(s(elem!1)))))))), s(s(z)))))),
% 3.53/3.78 inference(transitivity,[status(thm)],[18190, 18188])).
% 3.53/3.78 tff(18192,plain,
% 3.53/3.78 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), elem!1)) | (~b(s(s(s(s(s(s(s(s(elem!1)))))))), elem!1)) | (~b(elem!1, s(s(z)))) | (~b(s(s(z)), elem!1)) | (~b(s(s(s(s(s(s(s(s(elem!1)))))))), elem!1)) | (~b(s(s(s(s(s(s(s(s(elem!1)))))))), s(s(z)))))),
% 3.53/3.78 inference(quant_inst,[status(thm)],[])).
% 3.53/3.78 tff(18193,plain,
% 3.53/3.78 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(z)), elem!1)) | (~b(elem!1, s(s(z)))) | (~b(s(s(s(s(s(s(s(s(elem!1)))))))), elem!1)) | (~b(s(s(s(s(s(s(s(s(elem!1)))))))), s(s(z))))),
% 3.53/3.78 inference(modus_ponens,[status(thm)],[18192, 18191])).
% 3.53/3.78 tff(18194,plain,
% 3.53/3.78 (~b(s(s(s(s(s(s(s(s(elem!1)))))))), s(s(z)))),
% 3.53/3.78 inference(unit_resolution,[status(thm)],[18193, 166, 18187, 18185, 18139])).
% 3.53/3.78 tff(18195,plain,
% 3.53/3.78 (((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((s(s(s(s(s(s(s(s(elem!1)))))))) = s(s(z))) | b(s(s(s(s(s(s(s(s(elem!1)))))))), s(s(z))) | r(s(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(s(elem!1)))))))) = s(s(z))) | b(s(s(s(s(s(s(s(s(elem!1)))))))), s(s(z))) | r(s(s(s(s(s(s(s(s(elem!1)))))))), s(s(z))))),
% 3.53/3.78 inference(rewrite,[status(thm)],[])).
% 3.53/3.78 tff(18196,plain,
% 3.53/3.78 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((s(s(s(s(s(s(s(s(elem!1)))))))) = s(s(z))) | b(s(s(s(s(s(s(s(s(elem!1)))))))), s(s(z))) | r(s(s(s(s(s(s(s(s(elem!1)))))))), s(s(z))))),
% 3.53/3.78 inference(quant_inst,[status(thm)],[])).
% 3.53/3.78 tff(18197,plain,
% 3.53/3.78 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (s(s(s(s(s(s(s(s(elem!1)))))))) = s(s(z))) | b(s(s(s(s(s(s(s(s(elem!1)))))))), s(s(z))) | r(s(s(s(s(s(s(s(s(elem!1)))))))), s(s(z)))),
% 3.53/3.78 inference(modus_ponens,[status(thm)],[18196, 18195])).
% 3.53/3.78 tff(18198,plain,
% 3.53/3.78 ((s(s(s(s(s(s(s(s(elem!1)))))))) = s(s(z))) | r(s(s(s(s(s(s(s(s(elem!1)))))))), s(s(z)))),
% 3.53/3.78 inference(unit_resolution,[status(thm)],[18197, 79, 18194])).
% 3.53/3.78 tff(18199,plain,
% 3.53/3.78 (r(s(s(s(s(s(s(s(s(elem!1)))))))), s(s(z)))),
% 3.53/3.78 inference(unit_resolution,[status(thm)],[18198, 18131])).
% 3.53/3.78 tff(18200,plain,
% 3.53/3.78 (s(s(s(s(elem!1)))) = s(s(s(s(z))))),
% 3.53/3.78 inference(monotonicity,[status(thm)],[18143])).
% 3.53/3.78 tff(18201,plain,
% 3.53/3.78 (s(s(s(s(z)))) = s(s(s(s(elem!1))))),
% 3.53/3.78 inference(symmetry,[status(thm)],[18200])).
% 3.53/3.78 tff(18202,plain,
% 3.53/3.78 (r(s(s(s(s(z)))), s(s(z))) <=> r(s(s(s(s(elem!1)))), s(s(z)))),
% 3.53/3.78 inference(monotonicity,[status(thm)],[18201])).
% 3.53/3.78 tff(18203,plain,
% 3.53/3.78 (r(s(s(s(s(elem!1)))), s(s(z))) <=> r(s(s(s(s(z)))), s(s(z)))),
% 3.53/3.78 inference(symmetry,[status(thm)],[18202])).
% 3.53/3.78 tff(18204,plain,
% 3.53/3.78 ((s(s(s(s(elem!1)))) = z) <=> (s(s(s(s(elem!1)))) = elem!1)),
% 3.53/3.78 inference(monotonicity,[status(thm)],[18134])).
% 3.53/3.78 tff(18205,plain,
% 3.53/3.78 ((s(s(s(s(elem!1)))) = z) <=> (elem!1 = s(s(s(s(elem!1)))))),
% 3.53/3.78 inference(transitivity,[status(thm)],[18204, 2287])).
% 3.53/3.78 tff(18206,plain,
% 3.53/3.78 ((~(s(s(s(s(elem!1)))) = z)) <=> (~(elem!1 = s(s(s(s(elem!1))))))),
% 3.53/3.78 inference(monotonicity,[status(thm)],[18205])).
% 3.53/3.78 tff(18207,plain,
% 3.53/3.78 (~(elem!1 = s(s(s(s(elem!1)))))),
% 3.53/3.78 inference(modus_ponens,[status(thm)],[626, 18206])).
% 3.53/3.78 tff(18208,plain,
% 3.53/3.78 ((~(s(s(s(s(elem!1)))) = z)) <=> (~(s(s(s(s(elem!1)))) = elem!1))),
% 3.53/3.78 inference(monotonicity,[status(thm)],[18204])).
% 3.53/3.78 tff(18209,plain,
% 3.53/3.78 (~(s(s(s(s(elem!1)))) = elem!1)),
% 3.53/3.78 inference(modus_ponens,[status(thm)],[626, 18208])).
% 3.53/3.78 tff(18210,plain,
% 3.53/3.78 ((~b(s(s(s(s(elem!1)))), s(s(elem!1)))) | (elem!1 = s(s(s(s(elem!1))))) | (~r(s(z), elem!1)) | (s(s(s(s(elem!1)))) = elem!1) | (~b(s(s(elem!1)), elem!1)) | (~b(elem!1, s(s(elem!1))))),
% 3.53/3.78 inference(unit_resolution,[status(thm)],[11698, 15211])).
% 3.53/3.78 tff(18211,plain,
% 3.53/3.78 (~b(s(s(s(s(elem!1)))), s(s(elem!1)))),
% 3.53/3.78 inference(unit_resolution,[status(thm)],[18210, 18138, 18186, 18209, 18152, 18207])).
% 3.53/3.78 tff(18212,plain,
% 3.53/3.78 (~b(s(s(s(s(elem!1)))), s(s(z)))),
% 3.53/3.78 inference(unit_resolution,[status(thm)],[17749, 18211, 18128])).
% 3.53/3.78 tff(18213,plain,
% 3.53/3.78 (r(s(s(s(s(elem!1)))), s(s(z)))),
% 3.53/3.78 inference(unit_resolution,[status(thm)],[1299, 18212])).
% 3.53/3.78 tff(18214,plain,
% 3.53/3.78 (r(s(s(s(s(z)))), s(s(z)))),
% 3.53/3.78 inference(modus_ponens,[status(thm)],[18213, 18203])).
% 3.53/3.78 tff(18215,plain,
% 3.53/3.78 (r(s(s(z)), s(s(s(elem!1)))) <=> r(s(s(z)), s(s(s(z))))),
% 3.53/3.78 inference(monotonicity,[status(thm)],[18143])).
% 3.53/3.78 tff(18216,plain,
% 3.53/3.78 (r(s(s(z)), s(s(s(z))))),
% 3.53/3.78 inference(modus_ponens,[status(thm)],[17987, 18215])).
% 3.53/3.78 tff(18217,plain,
% 3.53/3.78 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(z)), s(s(s(z))))) | (~r(s(s(s(s(z)))), s(s(z)))) | (~r(s(s(s(s(s(s(s(s(elem!1)))))))), s(s(z)))) | (~r(s(s(s(s(s(s(s(s(elem!1)))))))), s(s(s(s(z)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(z)), s(s(s(z))))) | (~r(s(s(s(s(z)))), s(s(z)))) | (~r(s(s(s(s(s(s(s(s(elem!1)))))))), s(s(z)))) | (~r(s(s(s(s(s(s(s(s(elem!1)))))))), s(s(s(s(z)))))))),
% 3.53/3.78 inference(rewrite,[status(thm)],[])).
% 3.53/3.78 tff(18218,plain,
% 3.53/3.78 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(z)), s(s(s(z))))) | (~r(s(s(s(s(z)))), s(s(z)))) | (~r(s(s(s(s(s(s(s(s(elem!1)))))))), s(s(z)))) | (~r(s(s(s(s(s(s(s(s(elem!1)))))))), s(s(s(s(z)))))))),
% 3.53/3.78 inference(quant_inst,[status(thm)],[])).
% 3.53/3.78 tff(18219,plain,
% 3.53/3.78 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X2, X3)) | (~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(z)), s(s(s(z))))) | (~r(s(s(s(s(z)))), s(s(z)))) | (~r(s(s(s(s(s(s(s(s(elem!1)))))))), s(s(z)))) | (~r(s(s(s(s(s(s(s(s(elem!1)))))))), s(s(s(s(z))))))),
% 3.53/3.78 inference(modus_ponens,[status(thm)],[18218, 18217])).
% 3.53/3.78 tff(18220,plain,
% 3.53/3.78 (~r(s(s(s(s(s(s(s(s(elem!1)))))))), s(s(s(s(z)))))),
% 3.53/3.78 inference(unit_resolution,[status(thm)],[18219, 197, 18216, 18214, 18199])).
% 3.53/3.78 tff(18221,plain,
% 3.53/3.78 ((s(s(s(s(z)))) = z) <=> (s(s(s(s(z)))) = elem!1)),
% 3.53/3.78 inference(monotonicity,[status(thm)],[18134])).
% 3.53/3.78 tff(18222,plain,
% 3.53/3.78 ((s(s(s(s(z)))) = z) <=> (elem!1 = s(s(s(s(z)))))),
% 3.53/3.78 inference(transitivity,[status(thm)],[18221, 1039])).
% 3.53/3.78 tff(18223,plain,
% 3.53/3.78 ((s(s(s(s(z)))) = z) <=> (s(s(s(s(z)))) = elem!1)),
% 3.53/3.78 inference(transitivity,[status(thm)],[18222, 6181])).
% 3.53/3.78 tff(18224,plain,
% 3.53/3.78 ((~(s(s(s(s(z)))) = z)) <=> (~(s(s(s(s(z)))) = elem!1))),
% 3.53/3.78 inference(monotonicity,[status(thm)],[18223])).
% 3.53/3.78 tff(18225,plain,
% 3.53/3.78 (~(s(s(s(s(z)))) = elem!1)),
% 3.53/3.78 inference(modus_ponens,[status(thm)],[1044, 18224])).
% 3.53/3.78 tff(18226,plain,
% 3.53/3.78 (r(s(s(s(s(elem!1)))), elem!1) <=> r(s(s(s(s(z)))), elem!1)),
% 3.53/3.78 inference(monotonicity,[status(thm)],[18200])).
% 3.53/3.78 tff(18227,plain,
% 3.53/3.78 ((~r(s(s(s(s(elem!1)))), elem!1)) <=> (~r(s(s(s(s(z)))), elem!1))),
% 3.53/3.78 inference(monotonicity,[status(thm)],[18226])).
% 3.53/3.78 tff(18228,plain,
% 3.53/3.78 ((s(s(s(elem!1))) = s(s(s(s(elem!1))))) <=> (s(s(s(z))) = s(s(s(s(elem!1)))))),
% 3.53/3.78 inference(monotonicity,[status(thm)],[18143])).
% 3.53/3.78 tff(18229,plain,
% 3.53/3.78 ((s(s(s(elem!1))) = s(s(s(s(elem!1))))) <=> (s(s(s(s(elem!1)))) = s(s(s(z))))),
% 3.53/3.78 inference(transitivity,[status(thm)],[18228, 17708])).
% 3.53/3.78 tff(18230,plain,
% 3.53/3.78 ((s(s(s(s(elem!1)))) = s(s(s(z)))) <=> (s(s(s(elem!1))) = s(s(s(s(elem!1)))))),
% 3.53/3.78 inference(symmetry,[status(thm)],[18229])).
% 3.53/3.78 tff(18231,plain,
% 3.53/3.78 ((~(s(s(s(s(elem!1)))) = s(s(s(z))))) <=> (~(s(s(s(elem!1))) = s(s(s(s(elem!1))))))),
% 3.53/3.78 inference(monotonicity,[status(thm)],[18230])).
% 3.53/3.78 tff(18232,plain,
% 3.53/3.78 (~(s(s(s(elem!1))) = s(s(s(s(elem!1)))))),
% 3.53/3.78 inference(modus_ponens,[status(thm)],[5112, 18231])).
% 3.53/3.78 tff(18233,plain,
% 3.53/3.78 ((~r(s(s(s(s(elem!1)))), elem!1)) | (~b(s(z), s(s(s(elem!1))))) | (s(s(s(elem!1))) = s(s(s(s(elem!1))))) | (~r(elem!1, s(z))) | (~r(s(s(s(elem!1))), elem!1)) | (~r(s(z), elem!1))),
% 3.53/3.78 inference(unit_resolution,[status(thm)],[11173, 17959])).
% 3.53/3.78 tff(18234,plain,
% 3.53/3.78 (~r(s(s(s(s(elem!1)))), elem!1)),
% 3.53/3.78 inference(unit_resolution,[status(thm)],[18233, 18152, 17985, 18173, 18232, 18153])).
% 3.53/3.78 tff(18235,plain,
% 3.53/3.79 (~r(s(s(s(s(z)))), elem!1)),
% 3.53/3.79 inference(modus_ponens,[status(thm)],[18234, 18227])).
% 3.53/3.79 tff(18236,plain,
% 3.53/3.79 (b(s(s(s(s(z)))), elem!1)),
% 3.53/3.79 inference(unit_resolution,[status(thm)],[6190, 18235, 18225])).
% 3.53/3.79 tff(18237,plain,
% 3.53/3.79 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), elem!1)) | (~b(elem!1, s(s(z)))) | (~b(s(s(s(s(z)))), elem!1)) | (~b(s(s(s(s(s(s(s(s(elem!1)))))))), elem!1)) | (~b(s(s(s(s(s(s(s(s(elem!1)))))))), s(s(s(s(z)))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(z)), elem!1)) | (~b(elem!1, s(s(z)))) | (~b(s(s(s(s(z)))), elem!1)) | (~b(s(s(s(s(s(s(s(s(elem!1)))))))), elem!1)) | (~b(s(s(s(s(s(s(s(s(elem!1)))))))), s(s(s(s(z)))))))),
% 3.53/3.79 inference(rewrite,[status(thm)],[])).
% 3.53/3.79 tff(18238,plain,
% 3.53/3.79 (((~b(s(s(z)), elem!1)) | (~b(s(s(s(s(s(s(s(s(elem!1)))))))), elem!1)) | (~b(elem!1, s(s(z)))) | (~b(s(s(s(s(z)))), elem!1)) | (~b(s(s(s(s(s(s(s(s(elem!1)))))))), elem!1)) | (~b(s(s(s(s(s(s(s(s(elem!1)))))))), s(s(s(s(z))))))) <=> ((~b(s(s(z)), elem!1)) | (~b(elem!1, s(s(z)))) | (~b(s(s(s(s(z)))), elem!1)) | (~b(s(s(s(s(s(s(s(s(elem!1)))))))), elem!1)) | (~b(s(s(s(s(s(s(s(s(elem!1)))))))), s(s(s(s(z)))))))),
% 3.53/3.79 inference(rewrite,[status(thm)],[])).
% 3.53/3.79 tff(18239,plain,
% 3.53/3.79 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), elem!1)) | (~b(s(s(s(s(s(s(s(s(elem!1)))))))), elem!1)) | (~b(elem!1, s(s(z)))) | (~b(s(s(s(s(z)))), elem!1)) | (~b(s(s(s(s(s(s(s(s(elem!1)))))))), elem!1)) | (~b(s(s(s(s(s(s(s(s(elem!1)))))))), s(s(s(s(z)))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), elem!1)) | (~b(elem!1, s(s(z)))) | (~b(s(s(s(s(z)))), elem!1)) | (~b(s(s(s(s(s(s(s(s(elem!1)))))))), elem!1)) | (~b(s(s(s(s(s(s(s(s(elem!1)))))))), s(s(s(s(z))))))))),
% 3.53/3.79 inference(monotonicity,[status(thm)],[18238])).
% 3.53/3.79 tff(18240,plain,
% 3.53/3.79 (((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), elem!1)) | (~b(s(s(s(s(s(s(s(s(elem!1)))))))), elem!1)) | (~b(elem!1, s(s(z)))) | (~b(s(s(s(s(z)))), elem!1)) | (~b(s(s(s(s(s(s(s(s(elem!1)))))))), elem!1)) | (~b(s(s(s(s(s(s(s(s(elem!1)))))))), s(s(s(s(z)))))))) <=> ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(z)), elem!1)) | (~b(elem!1, s(s(z)))) | (~b(s(s(s(s(z)))), elem!1)) | (~b(s(s(s(s(s(s(s(s(elem!1)))))))), elem!1)) | (~b(s(s(s(s(s(s(s(s(elem!1)))))))), s(s(s(s(z)))))))),
% 3.53/3.79 inference(transitivity,[status(thm)],[18239, 18237])).
% 3.53/3.79 tff(18241,plain,
% 3.53/3.79 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), elem!1)) | (~b(s(s(s(s(s(s(s(s(elem!1)))))))), elem!1)) | (~b(elem!1, s(s(z)))) | (~b(s(s(s(s(z)))), elem!1)) | (~b(s(s(s(s(s(s(s(s(elem!1)))))))), elem!1)) | (~b(s(s(s(s(s(s(s(s(elem!1)))))))), s(s(s(s(z)))))))),
% 3.53/3.79 inference(quant_inst,[status(thm)],[])).
% 3.53/3.79 tff(18242,plain,
% 3.53/3.79 ((~![X0: $i, X4: $i, X3: $i, X2: $i, X1: $i] : ((~b(X3, X4)) | (~b(X0, X4)) | (~b(X2, X3)) | (~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(z)), elem!1)) | (~b(elem!1, s(s(z)))) | (~b(s(s(s(s(z)))), elem!1)) | (~b(s(s(s(s(s(s(s(s(elem!1)))))))), elem!1)) | (~b(s(s(s(s(s(s(s(s(elem!1)))))))), s(s(s(s(z))))))),
% 3.53/3.79 inference(modus_ponens,[status(thm)],[18241, 18240])).
% 3.53/3.79 tff(18243,plain,
% 3.53/3.79 (~b(s(s(s(s(s(s(s(s(elem!1)))))))), s(s(s(s(z)))))),
% 3.53/3.79 inference(unit_resolution,[status(thm)],[18242, 166, 18187, 18185, 18236, 18139])).
% 3.53/3.79 tff(18244,plain,
% 3.53/3.79 (((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((s(s(s(s(s(s(s(s(elem!1)))))))) = s(s(s(s(z))))) | b(s(s(s(s(s(s(s(s(elem!1)))))))), s(s(s(s(z))))) | r(s(s(s(s(s(s(s(s(elem!1)))))))), s(s(s(s(z))))))) <=> ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (s(s(s(s(s(s(s(s(elem!1)))))))) = s(s(s(s(z))))) | b(s(s(s(s(s(s(s(s(elem!1)))))))), s(s(s(s(z))))) | r(s(s(s(s(s(s(s(s(elem!1)))))))), s(s(s(s(z))))))),
% 3.53/3.79 inference(rewrite,[status(thm)],[])).
% 3.53/3.79 tff(18245,plain,
% 3.53/3.79 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((s(s(s(s(s(s(s(s(elem!1)))))))) = s(s(s(s(z))))) | b(s(s(s(s(s(s(s(s(elem!1)))))))), s(s(s(s(z))))) | r(s(s(s(s(s(s(s(s(elem!1)))))))), s(s(s(s(z))))))),
% 3.53/3.79 inference(quant_inst,[status(thm)],[])).
% 3.53/3.79 tff(18246,plain,
% 3.53/3.79 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (s(s(s(s(s(s(s(s(elem!1)))))))) = s(s(s(s(z))))) | b(s(s(s(s(s(s(s(s(elem!1)))))))), s(s(s(s(z))))) | r(s(s(s(s(s(s(s(s(elem!1)))))))), s(s(s(s(z)))))),
% 3.53/3.79 inference(modus_ponens,[status(thm)],[18245, 18244])).
% 3.53/3.79 tff(18247,plain,
% 3.53/3.79 ((s(s(s(s(s(s(s(s(elem!1)))))))) = s(s(s(s(z))))) | r(s(s(s(s(s(s(s(s(elem!1)))))))), s(s(s(s(z)))))),
% 3.53/3.79 inference(unit_resolution,[status(thm)],[18246, 79, 18243])).
% 3.53/3.79 tff(18248,plain,
% 3.53/3.79 (s(s(s(s(s(s(s(s(elem!1)))))))) = s(s(s(s(z))))),
% 3.53/3.79 inference(unit_resolution,[status(thm)],[18247, 18220])).
% 3.53/3.79 tff(18249,plain,
% 3.53/3.79 (inj_0(s(s(s(s(s(s(s(s(elem!1))))))))) = inj_0(s(s(s(s(z)))))),
% 3.53/3.79 inference(monotonicity,[status(thm)],[18248])).
% 3.53/3.79 tff(18250,plain,
% 3.53/3.79 (inj_0(s(s(s(s(z))))) = inj_0(s(s(s(s(s(s(s(s(elem!1)))))))))),
% 3.53/3.79 inference(symmetry,[status(thm)],[18249])).
% 3.53/3.79 tff(18251,plain,
% 3.53/3.79 (s(s(s(z))) = s(s(s(s(s(s(s(elem!1)))))))),
% 3.53/3.79 inference(transitivity,[status(thm)],[3277, 18250, 10])).
% 3.53/3.79 tff(18252,plain,
% 3.53/3.79 (~(s(s(s(s(s(s(elem!1)))))) = s(s(elem!1)))),
% 3.53/3.79 inference(unit_resolution,[status(thm)],[4986, 18129])).
% 3.53/3.79 tff(18253,plain,
% 3.53/3.79 (~(s(s(s(z))) = s(s(s(s(s(s(s(elem!1))))))))),
% 3.53/3.79 inference(unit_resolution,[status(thm)],[4995, 18252, 18123])).
% 3.53/3.79 tff(18254,plain,
% 3.53/3.79 ($false),
% 3.53/3.79 inference(unit_resolution,[status(thm)],[18253, 18251])).
% 3.53/3.79 % SZS output end Proof
% 0.09/3.80 % E exiting
%------------------------------------------------------------------------------