%------------------------------------------------------------------------------
% File : Z3---4.15.1
% Problem : GRA172-1 : TPTP v9.3.0. Released v9.3.0.
% Transfm : none
% Format : tptp
% Command : run_E %s %d THM
% Computer : n027.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Tue May 5 06:34:23 PM UTC 2026
% Result : Unsatisfiable 0.40s 0.61s
% Output : Proof 0.75s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : GRA172-1 : TPTP v9.3.0. Released v9.3.0.
% 0.00/0.12 % Command : run_E %s %d THM
% 0.16/0.33 % Computer : n027.cluster.edu
% 0.16/0.33 % Model : x86_64 x86_64
% 0.16/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.16/0.33 % Memory : 8042.1875MB
% 0.16/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.16/0.33 % CPULimit : 300
% 0.16/0.33 % WCLimit : 300
% 0.16/0.33 % DateTime : Tue May 5 01:02:06 EDT 2026
% 0.16/0.33 % CPUTime :
% 0.40/0.61 % SZS status Unsatisfiable
% 0.40/0.61 % SZS output start Proof
% 0.40/0.61 tff(r_type, type, (
% 0.40/0.61 r: ( $i * $i ) > $o)).
% 0.40/0.61 tff(z_type, type, (
% 0.40/0.61 z: $i)).
% 0.40/0.61 tff(s_type, type, (
% 0.40/0.61 s: $i > $i)).
% 0.40/0.61 tff(elem_1_type, type, (
% 0.40/0.61 elem_1: $i)).
% 0.40/0.61 tff(b_type, type, (
% 0.40/0.61 b: ( $i * $i ) > $o)).
% 0.40/0.61 tff(inj_0_type, type, (
% 0.40/0.61 inj_0: $i > $i)).
% 0.40/0.61 tff(1,assumption,(b(s(s(z)), s(z))), introduced(assumption)).
% 0.40/0.61 tff(2,assumption,(r(z, s(z))), introduced(assumption)).
% 0.40/0.61 tff(3,assumption,(r(s(s(s(s(z)))), s(z))), introduced(assumption)).
% 0.40/0.61 tff(4,assumption,(r(z, s(s(s(s(z)))))), introduced(assumption)).
% 0.40/0.61 tff(5,plain,
% 0.40/0.61 (^[X0: $i, X2: $i, X1: $i] : refl(((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1))) <=> ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1))))),
% 0.40/0.61 inference(bind,[status(th)],[])).
% 0.40/0.61 tff(6,plain,
% 0.40/0.61 (![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1))) <=> ![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))),
% 0.40/0.61 inference(quant_intro,[status(thm)],[5])).
% 0.40/0.61 tff(7,plain,
% 0.40/0.61 (![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1))) <=> ![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))),
% 0.40/0.61 inference(rewrite,[status(thm)],[])).
% 0.40/0.61 tff(8,plain,
% 0.40/0.61 (^[X0: $i, X2: $i, X1: $i] : rewrite((((~r(X0, X1)) | (~r(X0, X2))) | (~r(X1, X2))) <=> ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1))))),
% 0.40/0.61 inference(bind,[status(th)],[])).
% 0.40/0.61 tff(9,plain,
% 0.40/0.61 (![X0: $i, X2: $i, X1: $i] : (((~r(X0, X1)) | (~r(X0, X2))) | (~r(X1, X2))) <=> ![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))),
% 0.40/0.61 inference(quant_intro,[status(thm)],[8])).
% 0.40/0.61 tff(10,axiom,(![X0: $i, X2: $i, X1: $i] : (((~r(X0, X1)) | (~r(X0, X2))) | (~r(X1, X2)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','axr')).
% 0.40/0.61 tff(11,plain,
% 0.40/0.61 (![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))),
% 0.40/0.61 inference(modus_ponens,[status(thm)],[10, 9])).
% 0.40/0.61 tff(12,plain,
% 0.40/0.61 (![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))),
% 0.40/0.61 inference(modus_ponens,[status(thm)],[11, 7])).
% 0.40/0.61 tff(13,plain,(
% 0.40/0.61 ![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))),
% 0.40/0.61 inference(skolemize,[status(sab)],[12])).
% 0.40/0.61 tff(14,plain,
% 0.40/0.61 (![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))),
% 0.40/0.61 inference(modus_ponens,[status(thm)],[13, 6])).
% 0.40/0.61 tff(15,plain,
% 0.40/0.61 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(z))) | (~r(z, s(s(s(s(z)))))) | (~r(s(s(s(s(z)))), s(z))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, s(z))) | (~r(z, s(s(s(s(z)))))) | (~r(s(s(s(s(z)))), s(z))))),
% 0.40/0.61 inference(rewrite,[status(thm)],[])).
% 0.40/0.61 tff(16,plain,
% 0.40/0.61 (((~r(s(s(s(s(z)))), s(z))) | (~r(z, s(z))) | (~r(z, s(s(s(s(z))))))) <=> ((~r(z, s(z))) | (~r(z, s(s(s(s(z)))))) | (~r(s(s(s(s(z)))), s(z))))),
% 0.40/0.61 inference(rewrite,[status(thm)],[])).
% 0.40/0.61 tff(17,plain,
% 0.40/0.61 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(z)))), s(z))) | (~r(z, s(z))) | (~r(z, s(s(s(s(z)))))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(z))) | (~r(z, s(s(s(s(z)))))) | (~r(s(s(s(s(z)))), s(z)))))),
% 0.40/0.61 inference(monotonicity,[status(thm)],[16])).
% 0.40/0.61 tff(18,plain,
% 0.40/0.61 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(z)))), s(z))) | (~r(z, s(z))) | (~r(z, s(s(s(s(z)))))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, s(z))) | (~r(z, s(s(s(s(z)))))) | (~r(s(s(s(s(z)))), s(z))))),
% 0.40/0.61 inference(transitivity,[status(thm)],[17, 15])).
% 0.40/0.61 tff(19,plain,
% 0.40/0.61 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(z)))), s(z))) | (~r(z, s(z))) | (~r(z, s(s(s(s(z)))))))),
% 0.40/0.61 inference(quant_inst,[status(thm)],[])).
% 0.40/0.61 tff(20,plain,
% 0.40/0.61 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, s(z))) | (~r(z, s(s(s(s(z)))))) | (~r(s(s(s(s(z)))), s(z)))),
% 0.40/0.61 inference(modus_ponens,[status(thm)],[19, 18])).
% 0.40/0.61 tff(21,plain,
% 0.40/0.61 ($false),
% 0.40/0.61 inference(unit_resolution,[status(thm)],[20, 14, 2, 4, 3])).
% 0.40/0.61 tff(22,plain,((~r(s(s(s(s(z)))), s(z))) | (~r(z, s(z))) | (~r(z, s(s(s(s(z))))))), inference(lemma,lemma(discharge,[]))).
% 0.40/0.61 tff(23,plain,
% 0.40/0.61 (~r(z, s(s(s(s(z)))))),
% 0.40/0.61 inference(unit_resolution,[status(thm)],[22, 3, 2])).
% 0.40/0.61 tff(24,plain,
% 0.40/0.61 ((z = s(s(s(s(z))))) <=> (s(s(s(s(z)))) = z)),
% 0.40/0.61 inference(commutativity,[status(thm)],[])).
% 0.40/0.61 tff(25,plain,
% 0.40/0.61 ((s(s(s(s(z)))) = z) <=> (z = s(s(s(s(z)))))),
% 0.40/0.61 inference(symmetry,[status(thm)],[24])).
% 0.40/0.61 tff(26,plain,
% 0.40/0.61 ((~(s(s(s(s(z)))) = z)) <=> (~(z = s(s(s(s(z))))))),
% 0.40/0.61 inference(monotonicity,[status(thm)],[25])).
% 0.40/0.61 tff(27,plain,
% 0.40/0.61 (^[X: $i] : refl((~(s(X) = z)) <=> (~(s(X) = z)))),
% 0.40/0.61 inference(bind,[status(th)],[])).
% 0.40/0.61 tff(28,plain,
% 0.40/0.61 (![X: $i] : (~(s(X) = z)) <=> ![X: $i] : (~(s(X) = z))),
% 0.40/0.61 inference(quant_intro,[status(thm)],[27])).
% 0.40/0.61 tff(29,plain,
% 0.40/0.61 (![X: $i] : (~(s(X) = z)) <=> ![X: $i] : (~(s(X) = z))),
% 0.40/0.61 inference(rewrite,[status(thm)],[])).
% 0.40/0.61 tff(30,axiom,(![X: $i] : (~(s(X) = z))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','snz')).
% 0.40/0.61 tff(31,plain,
% 0.40/0.61 (![X: $i] : (~(s(X) = z))),
% 0.40/0.61 inference(modus_ponens,[status(thm)],[30, 29])).
% 0.40/0.61 tff(32,plain,(
% 0.40/0.61 ![X: $i] : (~(s(X) = z))),
% 0.40/0.61 inference(skolemize,[status(sab)],[31])).
% 0.40/0.61 tff(33,plain,
% 0.40/0.61 (![X: $i] : (~(s(X) = z))),
% 0.40/0.61 inference(modus_ponens,[status(thm)],[32, 28])).
% 0.40/0.61 tff(34,plain,
% 0.40/0.61 ((~![X: $i] : (~(s(X) = z))) | (~(s(s(s(s(z)))) = z))),
% 0.40/0.61 inference(quant_inst,[status(thm)],[])).
% 0.40/0.61 tff(35,plain,
% 0.40/0.61 (~(s(s(s(s(z)))) = z)),
% 0.40/0.61 inference(unit_resolution,[status(thm)],[34, 33])).
% 0.40/0.61 tff(36,plain,
% 0.40/0.61 (~(z = s(s(s(s(z)))))),
% 0.40/0.61 inference(modus_ponens,[status(thm)],[35, 26])).
% 0.40/0.61 tff(37,plain,
% 0.40/0.61 (^[Y: $i, X: $i] : refl(((X = Y) | b(X, Y) | r(X, Y)) <=> ((X = Y) | b(X, Y) | r(X, Y)))),
% 0.40/0.61 inference(bind,[status(th)],[])).
% 0.40/0.61 tff(38,plain,
% 0.40/0.61 (![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y)) <=> ![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))),
% 0.40/0.61 inference(quant_intro,[status(thm)],[37])).
% 0.40/0.61 tff(39,plain,
% 0.40/0.61 (![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y)) <=> ![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))),
% 0.40/0.61 inference(rewrite,[status(thm)],[])).
% 0.40/0.61 tff(40,plain,
% 0.40/0.61 (^[Y: $i, X: $i] : rewrite((((X = Y) | r(X, Y)) | b(X, Y)) <=> ((X = Y) | b(X, Y) | r(X, Y)))),
% 0.40/0.61 inference(bind,[status(th)],[])).
% 0.40/0.61 tff(41,plain,
% 0.40/0.61 (![Y: $i, X: $i] : (((X = Y) | r(X, Y)) | b(X, Y)) <=> ![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))),
% 0.40/0.61 inference(quant_intro,[status(thm)],[40])).
% 0.40/0.61 tff(42,axiom,(![Y: $i, X: $i] : (((X = Y) | r(X, Y)) | b(X, Y))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','rb')).
% 0.40/0.61 tff(43,plain,
% 0.40/0.61 (![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))),
% 0.40/0.61 inference(modus_ponens,[status(thm)],[42, 41])).
% 0.40/0.61 tff(44,plain,
% 0.40/0.61 (![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))),
% 0.40/0.61 inference(modus_ponens,[status(thm)],[43, 39])).
% 0.40/0.61 tff(45,plain,(
% 0.40/0.61 ![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))),
% 0.40/0.61 inference(skolemize,[status(sab)],[44])).
% 0.40/0.61 tff(46,plain,
% 0.40/0.61 (![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))),
% 0.40/0.61 inference(modus_ponens,[status(thm)],[45, 38])).
% 0.40/0.61 tff(47,plain,
% 0.40/0.61 (((~![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))))))),
% 0.40/0.61 inference(rewrite,[status(thm)],[])).
% 0.40/0.61 tff(48,plain,
% 0.40/0.61 ((~![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))))))),
% 0.40/0.61 inference(quant_inst,[status(thm)],[])).
% 0.40/0.61 tff(49,plain,
% 0.40/0.61 ((~![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)))))),
% 0.40/0.61 inference(modus_ponens,[status(thm)],[48, 47])).
% 0.40/0.61 tff(50,plain,
% 0.40/0.61 ((z = s(s(s(s(z))))) | b(z, s(s(s(s(z))))) | r(z, s(s(s(s(z)))))),
% 0.40/0.61 inference(unit_resolution,[status(thm)],[49, 46])).
% 0.40/0.61 tff(51,plain,
% 0.40/0.61 (b(z, s(s(s(s(z))))) | r(z, s(s(s(s(z)))))),
% 0.40/0.61 inference(unit_resolution,[status(thm)],[50, 36])).
% 0.40/0.61 tff(52,plain,
% 0.40/0.61 (b(z, s(s(s(s(z)))))),
% 0.40/0.61 inference(unit_resolution,[status(thm)],[51, 23])).
% 0.40/0.62 tff(53,assumption,(r(s(s(z)), s(z))), introduced(assumption)).
% 0.40/0.62 tff(54,plain,
% 0.40/0.62 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(z))) | (~r(s(s(z)), s(z))) | (~r(s(s(z)), z)))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, s(z))) | (~r(s(s(z)), s(z))) | (~r(s(s(z)), z)))),
% 0.40/0.62 inference(rewrite,[status(thm)],[])).
% 0.40/0.62 tff(55,plain,
% 0.40/0.62 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(z))) | (~r(s(s(z)), s(z))) | (~r(s(s(z)), z)))),
% 0.40/0.62 inference(quant_inst,[status(thm)],[])).
% 0.40/0.62 tff(56,plain,
% 0.40/0.62 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, s(z))) | (~r(s(s(z)), s(z))) | (~r(s(s(z)), z))),
% 0.40/0.62 inference(modus_ponens,[status(thm)],[55, 54])).
% 0.40/0.62 tff(57,plain,
% 0.40/0.62 (~r(s(s(z)), z)),
% 0.40/0.62 inference(unit_resolution,[status(thm)],[56, 14, 2, 53])).
% 0.40/0.62 tff(58,plain,
% 0.40/0.62 ((~![X: $i] : (~(s(X) = z))) | (~(s(s(z)) = z))),
% 0.40/0.62 inference(quant_inst,[status(thm)],[])).
% 0.40/0.62 tff(59,plain,
% 0.40/0.62 (~(s(s(z)) = z)),
% 0.40/0.62 inference(unit_resolution,[status(thm)],[58, 33])).
% 0.40/0.62 tff(60,plain,
% 0.40/0.62 (((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((s(s(z)) = z) | b(s(s(z)), z) | r(s(s(z)), z))) <=> ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (s(s(z)) = z) | b(s(s(z)), z) | r(s(s(z)), z))),
% 0.40/0.62 inference(rewrite,[status(thm)],[])).
% 0.40/0.62 tff(61,plain,
% 0.40/0.62 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((s(s(z)) = z) | b(s(s(z)), z) | r(s(s(z)), z))),
% 0.40/0.62 inference(quant_inst,[status(thm)],[])).
% 0.40/0.62 tff(62,plain,
% 0.40/0.62 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (s(s(z)) = z) | b(s(s(z)), z) | r(s(s(z)), z)),
% 0.40/0.62 inference(modus_ponens,[status(thm)],[61, 60])).
% 0.40/0.62 tff(63,plain,
% 0.40/0.62 (b(s(s(z)), z)),
% 0.40/0.62 inference(unit_resolution,[status(thm)],[62, 46, 59, 57])).
% 0.40/0.62 tff(64,plain,
% 0.40/0.62 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(z)), s(z))) | (~r(s(s(s(s(z)))), s(z))) | (~r(s(s(z)), s(s(s(s(z)))))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(z)), s(z))) | (~r(s(s(s(s(z)))), s(z))) | (~r(s(s(z)), s(s(s(s(z)))))))),
% 0.40/0.62 inference(rewrite,[status(thm)],[])).
% 0.40/0.62 tff(65,plain,
% 0.40/0.62 (((~r(s(s(s(s(z)))), s(z))) | (~r(s(s(z)), s(z))) | (~r(s(s(z)), s(s(s(s(z))))))) <=> ((~r(s(s(z)), s(z))) | (~r(s(s(s(s(z)))), s(z))) | (~r(s(s(z)), s(s(s(s(z)))))))),
% 0.40/0.62 inference(rewrite,[status(thm)],[])).
% 0.40/0.62 tff(66,plain,
% 0.40/0.62 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(z)))), s(z))) | (~r(s(s(z)), s(z))) | (~r(s(s(z)), s(s(s(s(z)))))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(z)), s(z))) | (~r(s(s(s(s(z)))), s(z))) | (~r(s(s(z)), s(s(s(s(z))))))))),
% 0.40/0.62 inference(monotonicity,[status(thm)],[65])).
% 0.40/0.62 tff(67,plain,
% 0.40/0.62 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(z)))), s(z))) | (~r(s(s(z)), s(z))) | (~r(s(s(z)), s(s(s(s(z)))))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(z)), s(z))) | (~r(s(s(s(s(z)))), s(z))) | (~r(s(s(z)), s(s(s(s(z)))))))),
% 0.40/0.62 inference(transitivity,[status(thm)],[66, 64])).
% 0.40/0.62 tff(68,plain,
% 0.40/0.62 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(z)))), s(z))) | (~r(s(s(z)), s(z))) | (~r(s(s(z)), s(s(s(s(z)))))))),
% 0.40/0.62 inference(quant_inst,[status(thm)],[])).
% 0.40/0.62 tff(69,plain,
% 0.40/0.62 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(z)), s(z))) | (~r(s(s(s(s(z)))), s(z))) | (~r(s(s(z)), s(s(s(s(z))))))),
% 0.40/0.62 inference(modus_ponens,[status(thm)],[68, 67])).
% 0.40/0.62 tff(70,plain,
% 0.40/0.62 (~r(s(s(z)), s(s(s(s(z)))))),
% 0.40/0.62 inference(unit_resolution,[status(thm)],[69, 14, 3, 53])).
% 0.40/0.62 tff(71,plain,
% 0.40/0.62 ((s(s(s(s(z)))) = s(s(z))) <=> (s(s(z)) = s(s(s(s(z)))))),
% 0.40/0.62 inference(commutativity,[status(thm)],[])).
% 0.40/0.62 tff(72,plain,
% 0.40/0.62 ((~(s(s(s(s(z)))) = s(s(z)))) <=> (~(s(s(z)) = s(s(s(s(z))))))),
% 0.40/0.62 inference(monotonicity,[status(thm)],[71])).
% 0.40/0.62 tff(73,plain,
% 0.40/0.62 (![Xk!0: $i] : (inj_0(s(Xk!0)) = Xk!0) <=> ![Xk!0: $i] : (inj_0(s(Xk!0)) = Xk!0)),
% 0.40/0.62 inference(rewrite,[status(thm)],[])).
% 0.40/0.62 tff(74,plain,
% 0.40/0.62 (![Y: $i, X: $i] : ((~(s(X) = s(Y))) | (X = Y)) <=> ![Xk!0: $i] : (inj_0(s(Xk!0)) = Xk!0)),
% 0.40/0.62 inference(rewrite,[status(thm)],[])).
% 0.40/0.62 tff(75,plain,
% 0.40/0.62 (![Y: $i, X: $i] : ((~(s(X) = s(Y))) | (X = Y)) <=> ![Y: $i, X: $i] : ((~(s(X) = s(Y))) | (X = Y))),
% 0.40/0.62 inference(rewrite,[status(thm)],[])).
% 0.40/0.62 tff(76,axiom,(![Y: $i, X: $i] : ((~(s(X) = s(Y))) | (X = Y))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','sinj')).
% 0.40/0.62 tff(77,plain,
% 0.40/0.62 (![Y: $i, X: $i] : ((~(s(X) = s(Y))) | (X = Y))),
% 0.40/0.62 inference(modus_ponens,[status(thm)],[76, 75])).
% 0.40/0.62 tff(78,plain,(
% 0.40/0.62 ![Y: $i, X: $i] : ((~(s(X) = s(Y))) | (X = Y))),
% 0.40/0.62 inference(skolemize,[status(sab)],[77])).
% 0.40/0.62 tff(79,plain,
% 0.40/0.62 (![Xk!0: $i] : (inj_0(s(Xk!0)) = Xk!0)),
% 0.40/0.62 inference(modus_ponens,[status(thm)],[78, 74])).
% 0.40/0.62 tff(80,plain,
% 0.40/0.62 (![Xk!0: $i] : (inj_0(s(Xk!0)) = Xk!0)),
% 0.40/0.62 inference(modus_ponens,[status(thm)],[79, 73])).
% 0.40/0.62 tff(81,plain,
% 0.40/0.62 ((~![Xk!0: $i] : (inj_0(s(Xk!0)) = Xk!0)) | (inj_0(s(s(z))) = s(z))),
% 0.40/0.62 inference(quant_inst,[status(thm)],[])).
% 0.40/0.62 tff(82,plain,
% 0.40/0.62 (inj_0(s(s(z))) = s(z)),
% 0.40/0.62 inference(unit_resolution,[status(thm)],[81, 80])).
% 0.40/0.62 tff(83,assumption,(s(s(s(s(z)))) = s(s(z))), introduced(assumption)).
% 0.40/0.62 tff(84,plain,
% 0.40/0.62 (inj_0(s(s(s(s(z))))) = inj_0(s(s(z)))),
% 0.40/0.62 inference(monotonicity,[status(thm)],[83])).
% 0.40/0.62 tff(85,plain,
% 0.40/0.62 ((~![Xk!0: $i] : (inj_0(s(Xk!0)) = Xk!0)) | (inj_0(s(s(s(s(z))))) = s(s(s(z))))),
% 0.40/0.62 inference(quant_inst,[status(thm)],[])).
% 0.40/0.62 tff(86,plain,
% 0.40/0.62 (inj_0(s(s(s(s(z))))) = s(s(s(z)))),
% 0.40/0.62 inference(unit_resolution,[status(thm)],[85, 80])).
% 0.40/0.62 tff(87,plain,
% 0.40/0.62 (s(s(s(z))) = inj_0(s(s(s(s(z)))))),
% 0.40/0.62 inference(symmetry,[status(thm)],[86])).
% 0.40/0.62 tff(88,plain,
% 0.40/0.62 (s(s(s(z))) = s(z)),
% 0.40/0.62 inference(transitivity,[status(thm)],[87, 84, 82])).
% 0.40/0.62 tff(89,plain,
% 0.40/0.62 ((~![Xk!0: $i] : (inj_0(s(Xk!0)) = Xk!0)) | (inj_0(s(z)) = z)),
% 0.40/0.62 inference(quant_inst,[status(thm)],[])).
% 0.40/0.62 tff(90,plain,
% 0.40/0.62 (inj_0(s(z)) = z),
% 0.40/0.62 inference(unit_resolution,[status(thm)],[89, 80])).
% 0.40/0.62 tff(91,assumption,(s(s(s(z))) = s(z)), introduced(assumption)).
% 0.40/0.62 tff(92,plain,
% 0.40/0.62 (inj_0(s(s(s(z)))) = inj_0(s(z))),
% 0.40/0.62 inference(monotonicity,[status(thm)],[91])).
% 0.40/0.62 tff(93,plain,
% 0.40/0.62 ((~![Xk!0: $i] : (inj_0(s(Xk!0)) = Xk!0)) | (inj_0(s(s(s(z)))) = s(s(z)))),
% 0.40/0.62 inference(quant_inst,[status(thm)],[])).
% 0.40/0.62 tff(94,plain,
% 0.40/0.62 (inj_0(s(s(s(z)))) = s(s(z))),
% 0.40/0.62 inference(unit_resolution,[status(thm)],[93, 80])).
% 0.40/0.62 tff(95,plain,
% 0.40/0.62 (s(s(z)) = inj_0(s(s(s(z))))),
% 0.40/0.62 inference(symmetry,[status(thm)],[94])).
% 0.40/0.62 tff(96,plain,
% 0.40/0.62 (s(s(z)) = z),
% 0.40/0.62 inference(transitivity,[status(thm)],[95, 92, 90])).
% 0.40/0.62 tff(97,plain,
% 0.40/0.62 ($false),
% 0.40/0.62 inference(unit_resolution,[status(thm)],[59, 96])).
% 0.40/0.62 tff(98,plain,(~(s(s(s(z))) = s(z))), inference(lemma,lemma(discharge,[]))).
% 0.40/0.62 tff(99,plain,
% 0.40/0.62 ($false),
% 0.40/0.62 inference(unit_resolution,[status(thm)],[98, 88])).
% 0.40/0.62 tff(100,plain,(~(s(s(s(s(z)))) = s(s(z)))), inference(lemma,lemma(discharge,[]))).
% 0.40/0.62 tff(101,plain,
% 0.40/0.62 (~(s(s(z)) = s(s(s(s(z)))))),
% 0.40/0.62 inference(modus_ponens,[status(thm)],[100, 72])).
% 0.40/0.62 tff(102,plain,
% 0.40/0.62 (((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((s(s(z)) = s(s(s(s(z))))) | b(s(s(z)), s(s(s(s(z))))) | r(s(s(z)), s(s(s(s(z))))))) <=> ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (s(s(z)) = s(s(s(s(z))))) | b(s(s(z)), s(s(s(s(z))))) | r(s(s(z)), s(s(s(s(z))))))),
% 0.40/0.62 inference(rewrite,[status(thm)],[])).
% 0.40/0.62 tff(103,plain,
% 0.40/0.62 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((s(s(z)) = s(s(s(s(z))))) | b(s(s(z)), s(s(s(s(z))))) | r(s(s(z)), s(s(s(s(z))))))),
% 0.40/0.62 inference(quant_inst,[status(thm)],[])).
% 0.40/0.62 tff(104,plain,
% 0.40/0.62 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (s(s(z)) = s(s(s(s(z))))) | b(s(s(z)), s(s(s(s(z))))) | r(s(s(z)), s(s(s(s(z)))))),
% 0.40/0.62 inference(modus_ponens,[status(thm)],[103, 102])).
% 0.40/0.62 tff(105,plain,
% 0.40/0.62 ((s(s(z)) = s(s(s(s(z))))) | b(s(s(z)), s(s(s(s(z))))) | r(s(s(z)), s(s(s(s(z)))))),
% 0.40/0.62 inference(unit_resolution,[status(thm)],[104, 46])).
% 0.40/0.62 tff(106,plain,
% 0.40/0.62 (b(s(s(z)), s(s(s(s(z))))) | r(s(s(z)), s(s(s(s(z)))))),
% 0.40/0.62 inference(unit_resolution,[status(thm)],[105, 101])).
% 0.40/0.62 tff(107,plain,
% 0.40/0.62 (b(s(s(z)), s(s(s(s(z)))))),
% 0.40/0.62 inference(unit_resolution,[status(thm)],[106, 70])).
% 0.40/0.62 tff(108,plain,
% 0.40/0.62 (^[X0: $i, X2: $i, X1: $i] : refl(((~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1))) <=> ((~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1))))),
% 0.40/0.62 inference(bind,[status(th)],[])).
% 0.40/0.62 tff(109,plain,
% 0.40/0.62 (![X0: $i, X2: $i, X1: $i] : ((~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1))) <=> ![X0: $i, X2: $i, X1: $i] : ((~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))),
% 0.40/0.62 inference(quant_intro,[status(thm)],[108])).
% 0.40/0.62 tff(110,plain,
% 0.40/0.62 (![X0: $i, X2: $i, X1: $i] : ((~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1))) <=> ![X0: $i, X2: $i, X1: $i] : ((~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))),
% 0.40/0.62 inference(rewrite,[status(thm)],[])).
% 0.40/0.62 tff(111,plain,
% 0.40/0.62 (^[X0: $i, X2: $i, X1: $i] : rewrite((((~b(X0, X1)) | (~b(X0, X2))) | (~b(X1, X2))) <=> ((~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1))))),
% 0.40/0.62 inference(bind,[status(th)],[])).
% 0.40/0.62 tff(112,plain,
% 0.40/0.62 (![X0: $i, X2: $i, X1: $i] : (((~b(X0, X1)) | (~b(X0, X2))) | (~b(X1, X2))) <=> ![X0: $i, X2: $i, X1: $i] : ((~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))),
% 0.40/0.62 inference(quant_intro,[status(thm)],[111])).
% 0.40/0.62 tff(113,axiom,(![X0: $i, X2: $i, X1: $i] : (((~b(X0, X1)) | (~b(X0, X2))) | (~b(X1, X2)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','axb')).
% 0.40/0.62 tff(114,plain,
% 0.40/0.62 (![X0: $i, X2: $i, X1: $i] : ((~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))),
% 0.40/0.62 inference(modus_ponens,[status(thm)],[113, 112])).
% 0.40/0.62 tff(115,plain,
% 0.40/0.62 (![X0: $i, X2: $i, X1: $i] : ((~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))),
% 0.40/0.62 inference(modus_ponens,[status(thm)],[114, 110])).
% 0.40/0.62 tff(116,plain,(
% 0.40/0.62 ![X0: $i, X2: $i, X1: $i] : ((~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))),
% 0.40/0.62 inference(skolemize,[status(sab)],[115])).
% 0.40/0.62 tff(117,plain,
% 0.40/0.62 (![X0: $i, X2: $i, X1: $i] : ((~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))),
% 0.40/0.62 inference(modus_ponens,[status(thm)],[116, 109])).
% 0.40/0.62 tff(118,plain,
% 0.40/0.62 (((~![X0: $i, X2: $i, X1: $i] : ((~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(s(s(z)))))) | (~b(s(s(z)), z)) | (~b(s(s(z)), s(s(s(s(z)))))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(s(s(s(z)))))) | (~b(s(s(z)), z)) | (~b(s(s(z)), s(s(s(s(z)))))))),
% 0.40/0.62 inference(rewrite,[status(thm)],[])).
% 0.40/0.62 tff(119,plain,
% 0.40/0.62 (((~b(z, s(s(s(s(z)))))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(z)), z))) <=> ((~b(z, s(s(s(s(z)))))) | (~b(s(s(z)), z)) | (~b(s(s(z)), s(s(s(s(z)))))))),
% 0.40/0.62 inference(rewrite,[status(thm)],[])).
% 0.40/0.62 tff(120,plain,
% 0.40/0.62 (((~![X0: $i, X2: $i, X1: $i] : ((~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(s(s(z)))))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(z)), z)))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(s(s(z)))))) | (~b(s(s(z)), z)) | (~b(s(s(z)), s(s(s(s(z))))))))),
% 0.40/0.62 inference(monotonicity,[status(thm)],[119])).
% 0.40/0.62 tff(121,plain,
% 0.40/0.62 (((~![X0: $i, X2: $i, X1: $i] : ((~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(s(s(z)))))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(z)), z)))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(s(s(s(z)))))) | (~b(s(s(z)), z)) | (~b(s(s(z)), s(s(s(s(z)))))))),
% 0.40/0.62 inference(transitivity,[status(thm)],[120, 118])).
% 0.40/0.62 tff(122,plain,
% 0.40/0.62 ((~![X0: $i, X2: $i, X1: $i] : ((~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(s(s(z)))))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(z)), z)))),
% 0.40/0.62 inference(quant_inst,[status(thm)],[])).
% 0.40/0.62 tff(123,plain,
% 0.40/0.62 ((~![X0: $i, X2: $i, X1: $i] : ((~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(s(s(s(z)))))) | (~b(s(s(z)), z)) | (~b(s(s(z)), s(s(s(s(z))))))),
% 0.40/0.62 inference(modus_ponens,[status(thm)],[122, 121])).
% 0.40/0.62 tff(124,plain,
% 0.40/0.62 ($false),
% 0.40/0.62 inference(unit_resolution,[status(thm)],[123, 117, 52, 107, 63])).
% 0.40/0.62 tff(125,plain,((~r(s(s(z)), s(z))) | (~r(s(s(s(s(z)))), s(z))) | (~r(z, s(z)))), inference(lemma,lemma(discharge,[]))).
% 0.40/0.62 tff(126,plain,
% 0.40/0.62 (~r(s(s(z)), s(z))),
% 0.40/0.62 inference(unit_resolution,[status(thm)],[125, 3, 2])).
% 0.40/0.62 tff(127,assumption,(s(s(z)) = s(z)), introduced(assumption)).
% 0.40/0.62 tff(128,plain,
% 0.40/0.62 (s(z) = s(s(z))),
% 0.40/0.62 inference(symmetry,[status(thm)],[127])).
% 0.40/0.62 tff(129,plain,
% 0.40/0.62 (inj_0(s(z)) = inj_0(s(s(z)))),
% 0.40/0.62 inference(monotonicity,[status(thm)],[128])).
% 0.40/0.62 tff(130,plain,
% 0.40/0.62 (inj_0(s(s(z))) = inj_0(s(z))),
% 0.40/0.62 inference(symmetry,[status(thm)],[129])).
% 0.40/0.62 tff(131,plain,
% 0.40/0.62 (s(z) = inj_0(s(s(z)))),
% 0.40/0.62 inference(symmetry,[status(thm)],[82])).
% 0.40/0.62 tff(132,plain,
% 0.40/0.62 (s(z) = z),
% 0.40/0.62 inference(transitivity,[status(thm)],[131, 130, 90])).
% 0.40/0.62 tff(133,plain,
% 0.40/0.62 ((~![X: $i] : (~(s(X) = z))) | (~(s(z) = z))),
% 0.40/0.62 inference(quant_inst,[status(thm)],[])).
% 0.40/0.62 tff(134,plain,
% 0.40/0.62 (~(s(z) = z)),
% 0.40/0.62 inference(unit_resolution,[status(thm)],[133, 33])).
% 0.40/0.62 tff(135,plain,
% 0.40/0.62 ($false),
% 0.40/0.62 inference(unit_resolution,[status(thm)],[134, 132])).
% 0.40/0.62 tff(136,plain,(~(s(s(z)) = s(z))), inference(lemma,lemma(discharge,[]))).
% 0.40/0.62 tff(137,plain,
% 0.40/0.62 (((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((s(s(z)) = s(z)) | b(s(s(z)), s(z)) | r(s(s(z)), s(z)))) <=> ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (s(s(z)) = s(z)) | b(s(s(z)), s(z)) | r(s(s(z)), s(z)))),
% 0.40/0.62 inference(rewrite,[status(thm)],[])).
% 0.40/0.62 tff(138,plain,
% 0.40/0.62 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((s(s(z)) = s(z)) | b(s(s(z)), s(z)) | r(s(s(z)), s(z)))),
% 0.40/0.62 inference(quant_inst,[status(thm)],[])).
% 0.40/0.62 tff(139,plain,
% 0.40/0.62 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (s(s(z)) = s(z)) | b(s(s(z)), s(z)) | r(s(s(z)), s(z))),
% 0.40/0.62 inference(modus_ponens,[status(thm)],[138, 137])).
% 0.40/0.62 tff(140,plain,
% 0.40/0.62 ((s(s(z)) = s(z)) | b(s(s(z)), s(z)) | r(s(s(z)), s(z))),
% 0.40/0.62 inference(unit_resolution,[status(thm)],[139, 46])).
% 0.40/0.62 tff(141,plain,
% 0.40/0.62 (b(s(s(z)), s(z)) | r(s(s(z)), s(z))),
% 0.40/0.62 inference(unit_resolution,[status(thm)],[140, 136])).
% 0.40/0.62 tff(142,plain,
% 0.40/0.62 (b(s(s(z)), s(z))),
% 0.40/0.62 inference(unit_resolution,[status(thm)],[141, 126])).
% 0.40/0.62 tff(143,plain,
% 0.40/0.62 ((~![Xk!0: $i] : (inj_0(s(Xk!0)) = Xk!0)) | (inj_0(s(s(s(s(elem!1))))) = s(s(s(elem!1))))),
% 0.40/0.62 inference(quant_inst,[status(thm)],[])).
% 0.40/0.62 tff(144,plain,
% 0.40/0.62 (inj_0(s(s(s(s(elem!1))))) = s(s(s(elem!1)))),
% 0.40/0.62 inference(unit_resolution,[status(thm)],[143, 80])).
% 0.40/0.62 tff(145,assumption,(~(s(s(elem!1)) = s(s(s(elem!1))))), introduced(assumption)).
% 0.40/0.62 tff(146,assumption,(~(s(s(s(s(elem!1)))) = s(s(elem!1)))), introduced(assumption)).
% 0.40/0.62 tff(147,assumption,(s(s(s(s(elem!1)))) = s(s(s(elem!1)))), introduced(assumption)).
% 0.40/0.62 tff(148,plain,
% 0.40/0.62 (s(s(s(elem!1))) = s(s(s(s(elem!1))))),
% 0.40/0.62 inference(symmetry,[status(thm)],[147])).
% 0.40/0.62 tff(149,plain,
% 0.40/0.62 (inj_0(s(s(s(elem!1)))) = inj_0(s(s(s(s(elem!1)))))),
% 0.40/0.62 inference(monotonicity,[status(thm)],[148])).
% 0.40/0.62 tff(150,plain,
% 0.40/0.62 ((~![Xk!0: $i] : (inj_0(s(Xk!0)) = Xk!0)) | (inj_0(s(s(s(elem!1)))) = s(s(elem!1)))),
% 0.40/0.62 inference(quant_inst,[status(thm)],[])).
% 0.40/0.62 tff(151,plain,
% 0.40/0.62 (inj_0(s(s(s(elem!1)))) = s(s(elem!1))),
% 0.40/0.62 inference(unit_resolution,[status(thm)],[150, 80])).
% 0.40/0.62 tff(152,plain,
% 0.40/0.62 (s(s(elem!1)) = inj_0(s(s(s(elem!1))))),
% 0.40/0.62 inference(symmetry,[status(thm)],[151])).
% 0.40/0.62 tff(153,plain,
% 0.40/0.62 (s(s(elem!1)) = s(s(s(elem!1)))),
% 0.40/0.62 inference(transitivity,[status(thm)],[152, 149, 144])).
% 0.40/0.62 tff(154,plain,
% 0.40/0.62 ($false),
% 0.40/0.62 inference(unit_resolution,[status(thm)],[145, 153])).
% 0.40/0.62 tff(155,plain,((~(s(s(s(s(elem!1)))) = s(s(s(elem!1))))) | (s(s(elem!1)) = s(s(s(elem!1))))), inference(lemma,lemma(discharge,[]))).
% 0.40/0.62 tff(156,plain,
% 0.40/0.62 (~(s(s(s(s(elem!1)))) = s(s(s(elem!1))))),
% 0.40/0.62 inference(unit_resolution,[status(thm)],[155, 145])).
% 0.40/0.62 tff(157,assumption,(b(s(s(s(elem!1))), z)), introduced(assumption)).
% 0.40/0.62 tff(158,assumption,(~b(s(s(elem!1)), s(z))), introduced(assumption)).
% 0.40/0.62 tff(159,plain,
% 0.40/0.62 ((s(s(elem!1)) = s(z)) <=> (s(z) = s(s(elem!1)))),
% 0.40/0.62 inference(commutativity,[status(thm)],[])).
% 0.40/0.62 tff(160,plain,
% 0.40/0.62 ((s(z) = s(s(elem!1))) <=> (s(s(elem!1)) = s(z))),
% 0.40/0.62 inference(symmetry,[status(thm)],[159])).
% 0.40/0.62 tff(161,plain,
% 0.40/0.62 ((~(s(z) = s(s(elem!1)))) <=> (~(s(s(elem!1)) = s(z)))),
% 0.40/0.62 inference(monotonicity,[status(thm)],[160])).
% 0.40/0.62 tff(162,assumption,(s(z) = s(s(elem!1))), introduced(assumption)).
% 0.40/0.62 tff(163,plain,
% 0.40/0.62 (inj_0(s(z)) = inj_0(s(s(elem!1)))),
% 0.40/0.62 inference(monotonicity,[status(thm)],[162])).
% 0.40/0.62 tff(164,plain,
% 0.40/0.62 (inj_0(s(s(elem!1))) = inj_0(s(z))),
% 0.40/0.62 inference(symmetry,[status(thm)],[163])).
% 0.40/0.62 tff(165,plain,
% 0.40/0.62 ((~![Xk!0: $i] : (inj_0(s(Xk!0)) = Xk!0)) | (inj_0(s(s(elem!1))) = s(elem!1))),
% 0.40/0.62 inference(quant_inst,[status(thm)],[])).
% 0.40/0.62 tff(166,plain,
% 0.40/0.62 (inj_0(s(s(elem!1))) = s(elem!1)),
% 0.40/0.62 inference(unit_resolution,[status(thm)],[165, 80])).
% 0.40/0.62 tff(167,plain,
% 0.40/0.62 (s(elem!1) = inj_0(s(s(elem!1)))),
% 0.40/0.62 inference(symmetry,[status(thm)],[166])).
% 0.40/0.62 tff(168,plain,
% 0.40/0.62 (s(elem!1) = z),
% 0.40/0.62 inference(transitivity,[status(thm)],[167, 164, 90])).
% 0.40/0.62 tff(169,plain,
% 0.40/0.62 ((~![X: $i] : (~(s(X) = z))) | (~(s(elem!1) = z))),
% 0.40/0.62 inference(quant_inst,[status(thm)],[])).
% 0.40/0.62 tff(170,plain,
% 0.40/0.62 (~(s(elem!1) = z)),
% 0.40/0.62 inference(unit_resolution,[status(thm)],[169, 33])).
% 0.40/0.62 tff(171,plain,
% 0.40/0.62 ($false),
% 0.40/0.62 inference(unit_resolution,[status(thm)],[170, 168])).
% 0.40/0.62 tff(172,plain,(~(s(z) = s(s(elem!1)))), inference(lemma,lemma(discharge,[]))).
% 0.40/0.62 tff(173,plain,
% 0.40/0.62 (~(s(s(elem!1)) = s(z))),
% 0.40/0.62 inference(modus_ponens,[status(thm)],[172, 161])).
% 0.40/0.62 tff(174,plain,
% 0.40/0.62 (((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((s(s(elem!1)) = s(z)) | b(s(s(elem!1)), s(z)) | r(s(s(elem!1)), s(z)))) <=> ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (s(s(elem!1)) = s(z)) | b(s(s(elem!1)), s(z)) | r(s(s(elem!1)), s(z)))),
% 0.40/0.62 inference(rewrite,[status(thm)],[])).
% 0.40/0.62 tff(175,plain,
% 0.40/0.62 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((s(s(elem!1)) = s(z)) | b(s(s(elem!1)), s(z)) | r(s(s(elem!1)), s(z)))),
% 0.40/0.62 inference(quant_inst,[status(thm)],[])).
% 0.40/0.62 tff(176,plain,
% 0.40/0.62 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (s(s(elem!1)) = s(z)) | b(s(s(elem!1)), s(z)) | r(s(s(elem!1)), s(z))),
% 0.40/0.62 inference(modus_ponens,[status(thm)],[175, 174])).
% 0.40/0.62 tff(177,plain,
% 0.40/0.62 ((s(s(elem!1)) = s(z)) | b(s(s(elem!1)), s(z)) | r(s(s(elem!1)), s(z))),
% 0.40/0.62 inference(unit_resolution,[status(thm)],[176, 46])).
% 0.40/0.62 tff(178,plain,
% 0.40/0.62 (b(s(s(elem!1)), s(z)) | r(s(s(elem!1)), s(z))),
% 0.40/0.62 inference(unit_resolution,[status(thm)],[177, 173])).
% 0.40/0.62 tff(179,plain,
% 0.40/0.62 (r(s(s(elem!1)), s(z))),
% 0.40/0.62 inference(unit_resolution,[status(thm)],[178, 158])).
% 0.40/0.62 tff(180,assumption,(r(s(s(s(z))), z)), introduced(assumption)).
% 0.40/0.62 tff(181,assumption,(r(s(s(elem!1)), s(z))), introduced(assumption)).
% 0.40/0.62 tff(182,assumption,(r(s(s(elem!1)), z)), introduced(assumption)).
% 0.40/0.62 tff(183,assumption,(r(s(z), z)), introduced(assumption)).
% 0.40/0.62 tff(184,plain,
% 0.40/0.62 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), z)) | (~r(s(s(elem!1)), z)) | (~r(s(s(elem!1)), s(z))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(z), z)) | (~r(s(s(elem!1)), z)) | (~r(s(s(elem!1)), s(z))))),
% 0.40/0.62 inference(rewrite,[status(thm)],[])).
% 0.40/0.62 tff(185,plain,
% 0.40/0.62 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), z)) | (~r(s(s(elem!1)), z)) | (~r(s(s(elem!1)), s(z))))),
% 0.40/0.62 inference(quant_inst,[status(thm)],[])).
% 0.40/0.62 tff(186,plain,
% 0.40/0.62 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(z), z)) | (~r(s(s(elem!1)), z)) | (~r(s(s(elem!1)), s(z)))),
% 0.40/0.62 inference(modus_ponens,[status(thm)],[185, 184])).
% 0.40/0.62 tff(187,plain,
% 0.40/0.62 ($false),
% 0.40/0.62 inference(unit_resolution,[status(thm)],[186, 14, 181, 182, 183])).
% 0.40/0.62 tff(188,plain,((~r(s(z), z)) | (~r(s(s(elem!1)), s(z))) | (~r(s(s(elem!1)), z))), inference(lemma,lemma(discharge,[]))).
% 0.40/0.62 tff(189,plain,
% 0.40/0.62 (~r(s(z), z)),
% 0.40/0.62 inference(unit_resolution,[status(thm)],[188, 182, 181])).
% 0.40/0.62 tff(190,plain,
% 0.40/0.62 (((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((s(z) = z) | b(s(z), z) | r(s(z), z))) <=> ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (s(z) = z) | b(s(z), z) | r(s(z), z))),
% 0.40/0.62 inference(rewrite,[status(thm)],[])).
% 0.40/0.62 tff(191,plain,
% 0.40/0.62 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((s(z) = z) | b(s(z), z) | r(s(z), z))),
% 0.40/0.62 inference(quant_inst,[status(thm)],[])).
% 0.40/0.62 tff(192,plain,
% 0.40/0.62 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (s(z) = z) | b(s(z), z) | r(s(z), z)),
% 0.40/0.62 inference(modus_ponens,[status(thm)],[191, 190])).
% 0.48/0.63 tff(193,plain,
% 0.48/0.63 (b(s(z), z) | r(s(z), z)),
% 0.48/0.63 inference(unit_resolution,[status(thm)],[192, 46, 134])).
% 0.48/0.63 tff(194,plain,
% 0.48/0.63 (b(s(z), z)),
% 0.48/0.63 inference(unit_resolution,[status(thm)],[193, 189])).
% 0.48/0.63 tff(195,assumption,(r(s(s(elem!1)), s(s(s(elem!1))))), introduced(assumption)).
% 0.48/0.63 tff(196,assumption,(r(s(s(s(elem!1))), z)), introduced(assumption)).
% 0.48/0.63 tff(197,plain,
% 0.48/0.63 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(elem!1)), z)) | (~r(s(s(s(elem!1))), z)) | (~r(s(s(elem!1)), s(s(s(elem!1))))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(elem!1)), z)) | (~r(s(s(s(elem!1))), z)) | (~r(s(s(elem!1)), s(s(s(elem!1))))))),
% 0.48/0.63 inference(rewrite,[status(thm)],[])).
% 0.48/0.63 tff(198,plain,
% 0.48/0.63 (((~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(elem!1)), z)) | (~r(s(s(s(elem!1))), z)) | (~r(s(s(elem!1)), s(s(s(elem!1))))))),
% 0.48/0.63 inference(rewrite,[status(thm)],[])).
% 0.48/0.63 tff(199,plain,
% 0.48/0.63 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), z)) | (~r(s(s(elem!1)), z)) | (~r(s(s(elem!1)), s(s(s(elem!1))))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(elem!1)), z)) | (~r(s(s(s(elem!1))), z)) | (~r(s(s(elem!1)), s(s(s(elem!1)))))))),
% 0.48/0.63 inference(monotonicity,[status(thm)],[198])).
% 0.48/0.63 tff(200,plain,
% 0.48/0.63 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), z)) | (~r(s(s(elem!1)), z)) | (~r(s(s(elem!1)), s(s(s(elem!1))))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(elem!1)), z)) | (~r(s(s(s(elem!1))), z)) | (~r(s(s(elem!1)), s(s(s(elem!1))))))),
% 0.48/0.63 inference(transitivity,[status(thm)],[199, 197])).
% 0.48/0.63 tff(201,plain,
% 0.48/0.63 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), z)) | (~r(s(s(elem!1)), z)) | (~r(s(s(elem!1)), s(s(s(elem!1))))))),
% 0.48/0.63 inference(quant_inst,[status(thm)],[])).
% 0.48/0.63 tff(202,plain,
% 0.48/0.63 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(elem!1)), z)) | (~r(s(s(s(elem!1))), z)) | (~r(s(s(elem!1)), s(s(s(elem!1)))))),
% 0.48/0.63 inference(modus_ponens,[status(thm)],[201, 200])).
% 0.48/0.63 tff(203,plain,
% 0.48/0.63 ($false),
% 0.48/0.63 inference(unit_resolution,[status(thm)],[202, 14, 196, 182, 195])).
% 0.48/0.63 tff(204,plain,((~r(s(s(s(elem!1))), z)) | (~r(s(s(elem!1)), z)) | (~r(s(s(elem!1)), s(s(s(elem!1)))))), inference(lemma,lemma(discharge,[]))).
% 0.48/0.63 tff(205,plain,
% 0.48/0.63 (~r(s(s(s(elem!1))), z)),
% 0.48/0.63 inference(unit_resolution,[status(thm)],[204, 195, 182])).
% 0.48/0.63 tff(206,plain,
% 0.48/0.63 ((~![X: $i] : (~(s(X) = z))) | (~(s(s(s(elem!1))) = z))),
% 0.48/0.63 inference(quant_inst,[status(thm)],[])).
% 0.48/0.63 tff(207,plain,
% 0.48/0.63 (~(s(s(s(elem!1))) = z)),
% 0.48/0.63 inference(unit_resolution,[status(thm)],[206, 33])).
% 0.48/0.63 tff(208,plain,
% 0.48/0.63 (((~![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))),
% 0.48/0.63 inference(rewrite,[status(thm)],[])).
% 0.48/0.63 tff(209,plain,
% 0.48/0.63 ((~![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))),
% 0.48/0.63 inference(quant_inst,[status(thm)],[])).
% 0.48/0.63 tff(210,plain,
% 0.48/0.63 ((~![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)),
% 0.48/0.63 inference(modus_ponens,[status(thm)],[209, 208])).
% 0.48/0.63 tff(211,plain,
% 0.48/0.63 (b(s(s(s(elem!1))), z) | r(s(s(s(elem!1))), z)),
% 0.48/0.63 inference(unit_resolution,[status(thm)],[210, 46, 207])).
% 0.48/0.63 tff(212,plain,
% 0.48/0.63 (b(s(s(s(elem!1))), z)),
% 0.48/0.63 inference(unit_resolution,[status(thm)],[211, 205])).
% 0.48/0.63 tff(213,assumption,(r(s(z), s(s(s(elem!1))))), introduced(assumption)).
% 0.48/0.63 tff(214,plain,
% 0.48/0.63 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~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))))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~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))))))),
% 0.48/0.63 inference(rewrite,[status(thm)],[])).
% 0.48/0.63 tff(215,plain,
% 0.48/0.63 (((~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(elem!1)), s(z))) | (~r(s(z), s(s(s(elem!1))))) | (~r(s(s(elem!1)), s(s(s(elem!1))))))),
% 0.48/0.63 inference(rewrite,[status(thm)],[])).
% 0.48/0.63 tff(216,plain,
% 0.48/0.63 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(s(s(elem!1))))) | (~r(s(s(elem!1)), s(s(s(elem!1))))) | (~r(s(s(elem!1)), s(z))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(elem!1)), s(z))) | (~r(s(z), s(s(s(elem!1))))) | (~r(s(s(elem!1)), s(s(s(elem!1)))))))),
% 0.48/0.63 inference(monotonicity,[status(thm)],[215])).
% 0.48/0.63 tff(217,plain,
% 0.48/0.63 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(s(s(elem!1))))) | (~r(s(s(elem!1)), s(s(s(elem!1))))) | (~r(s(s(elem!1)), s(z))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(elem!1)), s(z))) | (~r(s(z), s(s(s(elem!1))))) | (~r(s(s(elem!1)), s(s(s(elem!1))))))),
% 0.48/0.63 inference(transitivity,[status(thm)],[216, 214])).
% 0.48/0.63 tff(218,plain,
% 0.48/0.63 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(s(s(elem!1))))) | (~r(s(s(elem!1)), s(s(s(elem!1))))) | (~r(s(s(elem!1)), s(z))))),
% 0.48/0.63 inference(quant_inst,[status(thm)],[])).
% 0.48/0.63 tff(219,plain,
% 0.48/0.63 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(elem!1)), s(z))) | (~r(s(z), s(s(s(elem!1))))) | (~r(s(s(elem!1)), s(s(s(elem!1)))))),
% 0.48/0.63 inference(modus_ponens,[status(thm)],[218, 217])).
% 0.48/0.63 tff(220,plain,
% 0.48/0.63 ($false),
% 0.48/0.63 inference(unit_resolution,[status(thm)],[219, 14, 181, 195, 213])).
% 0.48/0.63 tff(221,plain,((~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)))))), inference(lemma,lemma(discharge,[]))).
% 0.48/0.63 tff(222,plain,
% 0.48/0.63 (~r(s(z), s(s(s(elem!1))))),
% 0.48/0.63 inference(unit_resolution,[status(thm)],[221, 195, 181])).
% 0.48/0.63 tff(223,assumption,(s(z) = s(s(s(elem!1)))), introduced(assumption)).
% 0.48/0.63 tff(224,plain,
% 0.48/0.63 (inj_0(s(z)) = inj_0(s(s(s(elem!1))))),
% 0.48/0.63 inference(monotonicity,[status(thm)],[223])).
% 0.48/0.63 tff(225,plain,
% 0.48/0.63 (inj_0(s(s(s(elem!1)))) = inj_0(s(z))),
% 0.48/0.63 inference(symmetry,[status(thm)],[224])).
% 0.48/0.63 tff(226,plain,
% 0.48/0.63 (s(s(elem!1)) = z),
% 0.48/0.63 inference(transitivity,[status(thm)],[152, 225, 90])).
% 0.48/0.63 tff(227,plain,
% 0.48/0.63 ((~![X: $i] : (~(s(X) = z))) | (~(s(s(elem!1)) = z))),
% 0.48/0.63 inference(quant_inst,[status(thm)],[])).
% 0.48/0.63 tff(228,plain,
% 0.48/0.63 (~(s(s(elem!1)) = z)),
% 0.48/0.63 inference(unit_resolution,[status(thm)],[227, 33])).
% 0.48/0.63 tff(229,plain,
% 0.48/0.63 ($false),
% 0.48/0.63 inference(unit_resolution,[status(thm)],[228, 226])).
% 0.48/0.63 tff(230,plain,(~(s(z) = s(s(s(elem!1))))), inference(lemma,lemma(discharge,[]))).
% 0.48/0.63 tff(231,plain,
% 0.48/0.63 (((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((s(z) = s(s(s(elem!1)))) | b(s(z), s(s(s(elem!1)))) | r(s(z), s(s(s(elem!1)))))) <=> ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (s(z) = s(s(s(elem!1)))) | b(s(z), s(s(s(elem!1)))) | r(s(z), s(s(s(elem!1)))))),
% 0.48/0.63 inference(rewrite,[status(thm)],[])).
% 0.48/0.63 tff(232,plain,
% 0.48/0.63 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((s(z) = s(s(s(elem!1)))) | b(s(z), s(s(s(elem!1)))) | r(s(z), s(s(s(elem!1)))))),
% 0.48/0.63 inference(quant_inst,[status(thm)],[])).
% 0.48/0.63 tff(233,plain,
% 0.48/0.63 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (s(z) = s(s(s(elem!1)))) | b(s(z), s(s(s(elem!1)))) | r(s(z), s(s(s(elem!1))))),
% 0.48/0.63 inference(modus_ponens,[status(thm)],[232, 231])).
% 0.48/0.63 tff(234,plain,
% 0.48/0.63 ((s(z) = s(s(s(elem!1)))) | b(s(z), s(s(s(elem!1)))) | r(s(z), s(s(s(elem!1))))),
% 0.48/0.63 inference(unit_resolution,[status(thm)],[233, 46])).
% 0.48/0.63 tff(235,plain,
% 0.48/0.63 (b(s(z), s(s(s(elem!1)))) | r(s(z), s(s(s(elem!1))))),
% 0.48/0.63 inference(unit_resolution,[status(thm)],[234, 230])).
% 0.48/0.63 tff(236,plain,
% 0.48/0.63 (b(s(z), s(s(s(elem!1))))),
% 0.48/0.63 inference(unit_resolution,[status(thm)],[235, 222])).
% 0.48/0.63 tff(237,assumption,(b(s(z), z)), introduced(assumption)).
% 0.48/0.63 tff(238,assumption,(b(s(z), s(s(s(elem!1))))), introduced(assumption)).
% 0.48/0.63 tff(239,plain,
% 0.48/0.63 (((~![X0: $i, X2: $i, X1: $i] : ((~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)))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~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)))),
% 0.48/0.63 inference(rewrite,[status(thm)],[])).
% 0.48/0.63 tff(240,plain,
% 0.48/0.63 (((~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)))),
% 0.48/0.63 inference(rewrite,[status(thm)],[])).
% 0.48/0.63 tff(241,plain,
% 0.48/0.63 (((~![X0: $i, X2: $i, X1: $i] : ((~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), z)) | (~b(s(z), z)) | (~b(s(z), s(s(s(elem!1))))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~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))))),
% 0.48/0.63 inference(monotonicity,[status(thm)],[240])).
% 0.48/0.63 tff(242,plain,
% 0.48/0.63 (((~![X0: $i, X2: $i, X1: $i] : ((~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), z)) | (~b(s(z), z)) | (~b(s(z), s(s(s(elem!1))))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~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)))),
% 0.48/0.63 inference(transitivity,[status(thm)],[241, 239])).
% 0.48/0.63 tff(243,plain,
% 0.48/0.63 ((~![X0: $i, X2: $i, X1: $i] : ((~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), z)) | (~b(s(z), z)) | (~b(s(z), s(s(s(elem!1))))))),
% 0.48/0.63 inference(quant_inst,[status(thm)],[])).
% 0.48/0.63 tff(244,plain,
% 0.48/0.63 ((~![X0: $i, X2: $i, X1: $i] : ((~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), z)) | (~b(s(z), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), z))),
% 0.48/0.63 inference(modus_ponens,[status(thm)],[243, 242])).
% 0.48/0.63 tff(245,plain,
% 0.48/0.63 ($false),
% 0.48/0.63 inference(unit_resolution,[status(thm)],[244, 117, 157, 238, 237])).
% 0.48/0.63 tff(246,plain,((~b(s(s(s(elem!1))), z)) | (~b(s(z), s(s(s(elem!1))))) | (~b(s(z), z))), inference(lemma,lemma(discharge,[]))).
% 0.48/0.63 tff(247,plain,
% 0.48/0.63 ($false),
% 0.48/0.63 inference(unit_resolution,[status(thm)],[246, 236, 212, 194])).
% 0.48/0.63 tff(248,plain,((~r(s(s(elem!1)), s(s(s(elem!1))))) | (~r(s(s(elem!1)), s(z))) | (~r(s(s(elem!1)), z))), inference(lemma,lemma(discharge,[]))).
% 0.48/0.63 tff(249,plain,
% 0.48/0.63 (~r(s(s(elem!1)), s(s(s(elem!1))))),
% 0.48/0.63 inference(unit_resolution,[status(thm)],[248, 182, 181])).
% 0.48/0.63 tff(250,plain,
% 0.48/0.63 (((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((s(s(elem!1)) = s(s(s(elem!1)))) | b(s(s(elem!1)), s(s(s(elem!1)))) | r(s(s(elem!1)), s(s(s(elem!1)))))) <=> ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (s(s(elem!1)) = s(s(s(elem!1)))) | b(s(s(elem!1)), s(s(s(elem!1)))) | r(s(s(elem!1)), s(s(s(elem!1)))))),
% 0.48/0.63 inference(rewrite,[status(thm)],[])).
% 0.48/0.63 tff(251,plain,
% 0.48/0.63 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((s(s(elem!1)) = s(s(s(elem!1)))) | b(s(s(elem!1)), s(s(s(elem!1)))) | r(s(s(elem!1)), s(s(s(elem!1)))))),
% 0.48/0.63 inference(quant_inst,[status(thm)],[])).
% 0.48/0.63 tff(252,plain,
% 0.48/0.63 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (s(s(elem!1)) = s(s(s(elem!1)))) | b(s(s(elem!1)), s(s(s(elem!1)))) | r(s(s(elem!1)), s(s(s(elem!1))))),
% 0.48/0.63 inference(modus_ponens,[status(thm)],[251, 250])).
% 0.48/0.63 tff(253,plain,
% 0.48/0.63 ((s(s(elem!1)) = s(s(s(elem!1)))) | b(s(s(elem!1)), s(s(s(elem!1)))) | r(s(s(elem!1)), s(s(s(elem!1))))),
% 0.48/0.63 inference(unit_resolution,[status(thm)],[252, 46])).
% 0.48/0.63 tff(254,plain,
% 0.48/0.63 (b(s(s(elem!1)), s(s(s(elem!1))))),
% 0.48/0.63 inference(unit_resolution,[status(thm)],[253, 249, 145])).
% 0.48/0.63 tff(255,assumption,(s(s(s(s(elem!1)))) = s(s(elem!1))), introduced(assumption)).
% 0.48/0.63 tff(256,plain,
% 0.48/0.63 ((~![Xk!0: $i] : (inj_0(s(Xk!0)) = Xk!0)) | (inj_0(s(elem!1)) = elem!1)),
% 0.48/0.63 inference(quant_inst,[status(thm)],[])).
% 0.48/0.63 tff(257,plain,
% 0.48/0.63 (inj_0(s(elem!1)) = elem!1),
% 0.48/0.63 inference(unit_resolution,[status(thm)],[256, 80])).
% 0.48/0.63 tff(258,plain,
% 0.48/0.63 (inj_0(s(s(s(s(elem!1))))) = inj_0(s(s(elem!1)))),
% 0.48/0.63 inference(monotonicity,[status(thm)],[255])).
% 0.48/0.63 tff(259,plain,
% 0.48/0.63 (inj_0(s(s(elem!1))) = inj_0(s(s(s(s(elem!1)))))),
% 0.48/0.63 inference(symmetry,[status(thm)],[258])).
% 0.48/0.63 tff(260,plain,
% 0.48/0.63 (s(elem!1) = s(s(s(elem!1)))),
% 0.48/0.63 inference(transitivity,[status(thm)],[167, 259, 144])).
% 0.48/0.63 tff(261,plain,
% 0.48/0.63 (inj_0(s(elem!1)) = inj_0(s(s(s(elem!1))))),
% 0.48/0.63 inference(monotonicity,[status(thm)],[260])).
% 0.48/0.63 tff(262,plain,
% 0.48/0.63 (inj_0(s(s(s(elem!1)))) = inj_0(s(elem!1))),
% 0.48/0.63 inference(symmetry,[status(thm)],[261])).
% 0.48/0.63 tff(263,plain,
% 0.48/0.63 (s(s(elem!1)) = elem!1),
% 0.48/0.63 inference(transitivity,[status(thm)],[152, 262, 257])).
% 0.48/0.63 tff(264,assumption,(~(s(s(elem!1)) = elem!1)), introduced(assumption)).
% 0.48/0.63 tff(265,plain,
% 0.48/0.63 ($false),
% 0.48/0.63 inference(unit_resolution,[status(thm)],[264, 263])).
% 0.48/0.63 tff(266,plain,((~(s(s(s(s(elem!1)))) = s(s(elem!1)))) | (s(s(elem!1)) = elem!1)), inference(lemma,lemma(discharge,[]))).
% 0.48/0.63 tff(267,plain,
% 0.48/0.63 (s(s(elem!1)) = elem!1),
% 0.48/0.63 inference(unit_resolution,[status(thm)],[266, 255])).
% 0.48/0.63 tff(268,plain,
% 0.48/0.63 (b(s(s(s(z))), s(s(elem!1))) <=> b(s(s(s(z))), elem!1)),
% 0.48/0.63 inference(monotonicity,[status(thm)],[267])).
% 0.48/0.63 tff(269,plain,
% 0.48/0.63 (b(s(s(s(z))), elem!1) <=> b(s(s(s(z))), s(s(elem!1)))),
% 0.48/0.63 inference(symmetry,[status(thm)],[268])).
% 0.48/0.63 tff(270,plain,
% 0.48/0.63 (s(s(s(s(elem!1)))) = elem!1),
% 0.48/0.63 inference(transitivity,[status(thm)],[255, 267])).
% 0.48/0.63 tff(271,plain,
% 0.48/0.63 ((s(s(s(z))) = s(s(s(s(elem!1))))) <=> (s(s(s(z))) = elem!1)),
% 0.48/0.63 inference(monotonicity,[status(thm)],[270])).
% 0.48/0.63 tff(272,plain,
% 0.48/0.63 ((~(s(s(s(z))) = s(s(s(s(elem!1)))))) <=> (~(s(s(s(z))) = elem!1))),
% 0.48/0.63 inference(monotonicity,[status(thm)],[271])).
% 0.48/0.63 tff(273,assumption,(s(s(s(z))) = s(s(s(s(elem!1))))), introduced(assumption)).
% 0.48/0.63 tff(274,plain,
% 0.48/0.63 (inj_0(s(s(s(z)))) = inj_0(s(s(s(s(elem!1)))))),
% 0.48/0.63 inference(monotonicity,[status(thm)],[273])).
% 0.48/0.63 tff(275,plain,
% 0.48/0.63 (s(s(z)) = s(s(s(elem!1)))),
% 0.48/0.63 inference(transitivity,[status(thm)],[95, 274, 144])).
% 0.48/0.63 tff(276,plain,
% 0.48/0.63 (inj_0(s(s(z))) = inj_0(s(s(s(elem!1))))),
% 0.48/0.63 inference(monotonicity,[status(thm)],[275])).
% 0.48/0.63 tff(277,plain,
% 0.48/0.63 (s(z) = s(s(elem!1))),
% 0.48/0.63 inference(transitivity,[status(thm)],[131, 276, 151])).
% 0.48/0.63 tff(278,plain,
% 0.48/0.63 ($false),
% 0.48/0.63 inference(unit_resolution,[status(thm)],[172, 277])).
% 0.48/0.63 tff(279,plain,(~(s(s(s(z))) = s(s(s(s(elem!1)))))), inference(lemma,lemma(discharge,[]))).
% 0.48/0.63 tff(280,plain,
% 0.48/0.63 (~(s(s(s(z))) = elem!1)),
% 0.48/0.63 inference(modus_ponens,[status(thm)],[279, 272])).
% 0.48/0.63 tff(281,plain,
% 0.48/0.63 (r(s(s(s(z))), s(s(elem!1))) <=> r(s(s(s(z))), elem!1)),
% 0.48/0.63 inference(monotonicity,[status(thm)],[267])).
% 0.48/0.63 tff(282,plain,
% 0.48/0.63 ((~r(s(s(s(z))), s(s(elem!1)))) <=> (~r(s(s(s(z))), elem!1))),
% 0.48/0.63 inference(monotonicity,[status(thm)],[281])).
% 0.48/0.63 tff(283,assumption,(r(s(s(s(z))), s(z))), introduced(assumption)).
% 0.48/0.63 tff(284,plain,
% 0.48/0.63 ((s(s(s(elem!1))) = s(s(s(s(elem!1))))) <=> (s(s(s(s(elem!1)))) = s(s(s(elem!1))))),
% 0.48/0.63 inference(commutativity,[status(thm)],[])).
% 0.48/0.63 tff(285,assumption,(s(s(s(elem!1))) = s(s(s(s(elem!1))))), introduced(assumption)).
% 0.48/0.63 tff(286,plain,
% 0.48/0.63 (s(s(s(s(elem!1)))) = s(s(s(elem!1)))),
% 0.48/0.63 inference(modus_ponens,[status(thm)],[285, 284])).
% 0.48/0.63 tff(287,assumption,(~(s(s(s(s(elem!1)))) = s(s(s(elem!1))))), introduced(assumption)).
% 0.48/0.63 tff(288,plain,
% 0.48/0.63 ($false),
% 0.48/0.63 inference(unit_resolution,[status(thm)],[287, 286])).
% 0.48/0.63 tff(289,plain,((~(s(s(s(elem!1))) = s(s(s(s(elem!1)))))) | (s(s(s(s(elem!1)))) = s(s(s(elem!1))))), inference(lemma,lemma(discharge,[]))).
% 0.48/0.63 tff(290,plain,
% 0.48/0.63 (~(s(s(s(elem!1))) = s(s(s(s(elem!1)))))),
% 0.48/0.63 inference(unit_resolution,[status(thm)],[289, 156])).
% 0.48/0.63 tff(291,plain,
% 0.48/0.63 (b(s(s(s(s(z)))), s(s(elem!1))) <=> b(s(s(s(s(z)))), elem!1)),
% 0.48/0.63 inference(monotonicity,[status(thm)],[267])).
% 0.48/0.63 tff(292,plain,
% 0.48/0.63 (b(s(s(s(s(z)))), elem!1) <=> b(s(s(s(s(z)))), s(s(elem!1)))),
% 0.48/0.63 inference(symmetry,[status(thm)],[291])).
% 0.48/0.63 tff(293,plain,
% 0.48/0.63 ((s(s(s(s(z)))) = elem!1) <=> (elem!1 = s(s(s(s(z)))))),
% 0.48/0.63 inference(commutativity,[status(thm)],[])).
% 0.48/0.63 tff(294,plain,
% 0.48/0.63 ((elem!1 = s(s(s(s(z))))) <=> (s(s(s(s(z)))) = elem!1)),
% 0.48/0.63 inference(symmetry,[status(thm)],[293])).
% 0.48/0.63 tff(295,plain,
% 0.48/0.63 (s(s(s(elem!1))) = inj_0(s(s(s(s(elem!1)))))),
% 0.48/0.63 inference(symmetry,[status(thm)],[144])).
% 0.48/0.63 tff(296,plain,
% 0.48/0.63 (s(s(s(s(s(elem!1))))) = s(s(s(elem!1)))),
% 0.48/0.63 inference(monotonicity,[status(thm)],[255])).
% 0.48/0.63 tff(297,plain,
% 0.48/0.63 (s(s(s(s(s(elem!1))))) = s(elem!1)),
% 0.48/0.63 inference(transitivity,[status(thm)],[296, 295, 258, 166])).
% 0.48/0.63 tff(298,plain,
% 0.48/0.63 (s(s(s(s(s(s(elem!1)))))) = s(s(elem!1))),
% 0.48/0.63 inference(monotonicity,[status(thm)],[297])).
% 0.48/0.63 tff(299,plain,
% 0.48/0.63 (s(s(s(s(s(s(elem!1)))))) = elem!1),
% 0.48/0.63 inference(transitivity,[status(thm)],[298, 267])).
% 0.48/0.63 tff(300,plain,
% 0.48/0.63 ((s(s(s(s(s(s(elem!1)))))) = s(s(s(s(z))))) <=> (elem!1 = s(s(s(s(z)))))),
% 0.48/0.63 inference(monotonicity,[status(thm)],[299])).
% 0.48/0.63 tff(301,plain,
% 0.48/0.63 ((s(s(s(s(s(s(elem!1)))))) = s(s(s(s(z))))) <=> (s(s(s(s(z)))) = elem!1)),
% 0.48/0.63 inference(transitivity,[status(thm)],[300, 294])).
% 0.48/0.63 tff(302,plain,
% 0.48/0.63 ((~(s(s(s(s(s(s(elem!1)))))) = s(s(s(s(z)))))) <=> (~(s(s(s(s(z)))) = elem!1))),
% 0.48/0.63 inference(monotonicity,[status(thm)],[301])).
% 0.48/0.63 tff(303,plain,
% 0.48/0.63 ((~![Xk!0: $i] : (inj_0(s(Xk!0)) = Xk!0)) | (inj_0(s(s(s(s(s(s(elem!1))))))) = s(s(s(s(s(elem!1))))))),
% 0.48/0.63 inference(quant_inst,[status(thm)],[])).
% 0.48/0.63 tff(304,plain,
% 0.48/0.63 (inj_0(s(s(s(s(s(s(elem!1))))))) = s(s(s(s(s(elem!1)))))),
% 0.48/0.63 inference(unit_resolution,[status(thm)],[303, 80])).
% 0.48/0.63 tff(305,assumption,(s(s(s(s(s(s(elem!1)))))) = s(s(s(s(z))))), introduced(assumption)).
% 0.48/0.63 tff(306,plain,
% 0.48/0.63 (inj_0(s(s(s(s(s(s(elem!1))))))) = inj_0(s(s(s(s(z)))))),
% 0.48/0.63 inference(monotonicity,[status(thm)],[305])).
% 0.48/0.63 tff(307,plain,
% 0.48/0.63 (inj_0(s(s(s(s(z))))) = inj_0(s(s(s(s(s(s(elem!1)))))))),
% 0.48/0.63 inference(symmetry,[status(thm)],[306])).
% 0.48/0.63 tff(308,plain,
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% 0.48/0.63 inference(transitivity,[status(thm)],[87, 307, 304])).
% 0.48/0.63 tff(309,plain,
% 0.48/0.63 ((~![Xk!0: $i] : (inj_0(s(Xk!0)) = Xk!0)) | (inj_0(s(s(s(s(s(elem!1)))))) = s(s(s(s(elem!1)))))),
% 0.48/0.63 inference(quant_inst,[status(thm)],[])).
% 0.48/0.63 tff(310,plain,
% 0.48/0.63 (inj_0(s(s(s(s(s(elem!1)))))) = s(s(s(s(elem!1))))),
% 0.48/0.63 inference(unit_resolution,[status(thm)],[309, 80])).
% 0.48/0.63 tff(311,assumption,(s(s(s(z))) = s(s(s(s(s(elem!1)))))), introduced(assumption)).
% 0.48/0.63 tff(312,plain,
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% 0.48/0.63 inference(monotonicity,[status(thm)],[311])).
% 0.48/0.63 tff(313,plain,
% 0.48/0.63 (s(s(z)) = s(s(s(s(elem!1))))),
% 0.48/0.63 inference(transitivity,[status(thm)],[95, 312, 310])).
% 0.48/0.63 tff(314,plain,
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% 0.48/0.63 inference(monotonicity,[status(thm)],[313])).
% 0.48/0.63 tff(315,plain,
% 0.48/0.63 (s(z) = s(s(s(elem!1)))),
% 0.48/0.63 inference(transitivity,[status(thm)],[131, 314, 144])).
% 0.48/0.63 tff(316,plain,
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% 0.48/0.63 inference(unit_resolution,[status(thm)],[230, 315])).
% 0.48/0.63 tff(317,plain,(~(s(s(s(z))) = s(s(s(s(s(elem!1))))))), inference(lemma,lemma(discharge,[]))).
% 0.48/0.63 tff(318,plain,
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% 0.48/0.63 inference(unit_resolution,[status(thm)],[317, 308])).
% 0.48/0.63 tff(319,plain,(~(s(s(s(s(s(s(elem!1)))))) = s(s(s(s(z)))))), inference(lemma,lemma(discharge,[]))).
% 0.48/0.63 tff(320,plain,
% 0.48/0.63 (~(s(s(s(s(z)))) = elem!1)),
% 0.48/0.63 inference(modus_ponens,[status(thm)],[319, 302])).
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% 0.48/0.63 (r(s(s(s(s(z)))), s(s(elem!1))) <=> r(s(s(s(s(z)))), elem!1)),
% 0.48/0.63 inference(monotonicity,[status(thm)],[267])).
% 0.48/0.63 tff(322,plain,
% 0.48/0.63 ((~r(s(s(s(s(z)))), s(s(elem!1)))) <=> (~r(s(s(s(s(z)))), elem!1))),
% 0.48/0.63 inference(monotonicity,[status(thm)],[321])).
% 0.48/0.63 tff(323,assumption,(~(s(s(s(elem!1))) = s(s(s(s(elem!1)))))), introduced(assumption)).
% 0.48/0.63 tff(324,assumption,(b(s(s(elem!1)), s(s(s(elem!1))))), introduced(assumption)).
% 0.48/0.63 tff(325,plain,
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% 0.48/0.63 inference(commutativity,[status(thm)],[])).
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% 0.48/0.63 ((s(s(elem!1)) = z) <=> (z = s(s(elem!1)))),
% 0.48/0.63 inference(symmetry,[status(thm)],[325])).
% 0.48/0.63 tff(327,plain,
% 0.48/0.63 ((~(s(s(elem!1)) = z)) <=> (~(z = s(s(elem!1))))),
% 0.48/0.63 inference(monotonicity,[status(thm)],[326])).
% 0.48/0.63 tff(328,plain,
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% 0.48/0.63 inference(modus_ponens,[status(thm)],[228, 327])).
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% 0.48/0.63 (b(s(s(elem!1)), s(s(s(z)))) <=> b(elem!1, s(s(s(z))))),
% 0.48/0.63 inference(monotonicity,[status(thm)],[267])).
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% 0.48/0.63 (b(elem!1, s(s(s(z)))) <=> b(s(s(elem!1)), s(s(s(z))))),
% 0.48/0.63 inference(symmetry,[status(thm)],[329])).
% 0.48/0.63 tff(331,plain,
% 0.48/0.63 ((elem!1 = s(s(s(z)))) <=> (s(s(s(z))) = elem!1)),
% 0.48/0.63 inference(commutativity,[status(thm)],[])).
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% 0.48/0.63 ((s(s(s(z))) = elem!1) <=> (elem!1 = s(s(s(z))))),
% 0.48/0.63 inference(symmetry,[status(thm)],[331])).
% 0.48/0.63 tff(333,plain,
% 0.48/0.63 ((s(s(s(z))) = s(s(s(s(elem!1))))) <=> (elem!1 = s(s(s(z))))),
% 0.48/0.63 inference(transitivity,[status(thm)],[271, 332])).
% 0.48/0.63 tff(334,plain,
% 0.48/0.63 ((~(s(s(s(z))) = s(s(s(s(elem!1)))))) <=> (~(elem!1 = s(s(s(z)))))),
% 0.48/0.63 inference(monotonicity,[status(thm)],[333])).
% 0.48/0.63 tff(335,plain,
% 0.48/0.63 (~(elem!1 = s(s(s(z))))),
% 0.48/0.63 inference(modus_ponens,[status(thm)],[279, 334])).
% 0.48/0.63 tff(336,plain,
% 0.48/0.63 (r(s(s(elem!1)), s(s(s(z)))) <=> r(elem!1, s(s(s(z))))),
% 0.48/0.63 inference(monotonicity,[status(thm)],[267])).
% 0.48/0.63 tff(337,plain,
% 0.48/0.63 ((~r(s(s(elem!1)), s(s(s(z))))) <=> (~r(elem!1, s(s(s(z)))))),
% 0.48/0.63 inference(monotonicity,[status(thm)],[336])).
% 0.48/0.63 tff(338,assumption,(b(s(s(s(z))), z)), introduced(assumption)).
% 0.48/0.63 tff(339,plain,
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% 0.48/0.64 inference(rewrite,[status(thm)],[])).
% 0.48/0.64 tff(340,plain,
% 0.48/0.64 ((~![X0: $i, X2: $i, X1: $i] : ((~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), z)) | (~b(s(s(s(z))), z)) | (~b(s(s(s(z))), s(z))))),
% 0.48/0.64 inference(quant_inst,[status(thm)],[])).
% 0.48/0.64 tff(341,plain,
% 0.48/0.64 ((~![X0: $i, X2: $i, X1: $i] : ((~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), z)) | (~b(s(s(s(z))), z)) | (~b(s(s(s(z))), s(z)))),
% 0.48/0.64 inference(modus_ponens,[status(thm)],[340, 339])).
% 0.48/0.64 tff(342,plain,
% 0.48/0.64 (~b(s(s(s(z))), s(z))),
% 0.48/0.64 inference(unit_resolution,[status(thm)],[341, 117, 237, 338])).
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% 0.48/0.64 (((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((s(s(s(z))) = s(z)) | b(s(s(s(z))), s(z)) | r(s(s(s(z))), s(z)))) <=> ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (s(s(s(z))) = s(z)) | b(s(s(s(z))), s(z)) | r(s(s(s(z))), s(z)))),
% 0.48/0.64 inference(rewrite,[status(thm)],[])).
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% 0.48/0.64 inference(quant_inst,[status(thm)],[])).
% 0.48/0.64 tff(345,plain,
% 0.48/0.64 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (s(s(s(z))) = s(z)) | b(s(s(s(z))), s(z)) | r(s(s(s(z))), s(z))),
% 0.48/0.64 inference(modus_ponens,[status(thm)],[344, 343])).
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% 0.48/0.64 ((s(s(s(z))) = s(z)) | b(s(s(s(z))), s(z)) | r(s(s(s(z))), s(z))),
% 0.48/0.64 inference(unit_resolution,[status(thm)],[345, 46])).
% 0.48/0.64 tff(347,plain,
% 0.48/0.64 (b(s(s(s(z))), s(z)) | r(s(s(s(z))), s(z))),
% 0.48/0.64 inference(unit_resolution,[status(thm)],[346, 98])).
% 0.48/0.64 tff(348,plain,
% 0.48/0.64 (r(s(s(s(z))), s(z))),
% 0.48/0.64 inference(unit_resolution,[status(thm)],[347, 342])).
% 0.48/0.64 tff(349,plain,
% 0.48/0.64 (elem!1 = s(s(elem!1))),
% 0.48/0.64 inference(symmetry,[status(thm)],[267])).
% 0.48/0.64 tff(350,plain,
% 0.48/0.64 (r(elem!1, s(z)) <=> r(s(s(elem!1)), s(z))),
% 0.48/0.64 inference(monotonicity,[status(thm)],[349])).
% 0.48/0.64 tff(351,plain,
% 0.48/0.64 ((elem!1 = s(z)) <=> (s(z) = elem!1)),
% 0.48/0.64 inference(commutativity,[status(thm)],[])).
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% 0.48/0.64 ((s(z) = elem!1) <=> (elem!1 = s(z))),
% 0.48/0.64 inference(symmetry,[status(thm)],[351])).
% 0.48/0.64 tff(353,plain,
% 0.48/0.64 ((s(z) = elem!1) <=> (s(z) = s(s(elem!1)))),
% 0.48/0.64 inference(monotonicity,[status(thm)],[349])).
% 0.48/0.64 tff(354,plain,
% 0.48/0.64 ((s(z) = s(s(elem!1))) <=> (s(z) = elem!1)),
% 0.48/0.64 inference(symmetry,[status(thm)],[353])).
% 0.48/0.64 tff(355,plain,
% 0.48/0.64 ((s(z) = s(s(elem!1))) <=> (elem!1 = s(z))),
% 0.48/0.64 inference(transitivity,[status(thm)],[354, 352])).
% 0.48/0.64 tff(356,plain,
% 0.48/0.64 ((~(s(z) = s(s(elem!1)))) <=> (~(elem!1 = s(z)))),
% 0.48/0.64 inference(monotonicity,[status(thm)],[355])).
% 0.48/0.64 tff(357,plain,
% 0.48/0.64 (~(elem!1 = s(z))),
% 0.48/0.64 inference(modus_ponens,[status(thm)],[172, 356])).
% 0.48/0.64 tff(358,plain,
% 0.48/0.64 (b(elem!1, s(s(s(elem!1)))) <=> b(s(s(elem!1)), s(s(s(elem!1))))),
% 0.48/0.64 inference(monotonicity,[status(thm)],[349])).
% 0.48/0.64 tff(359,plain,
% 0.48/0.64 (b(s(s(elem!1)), s(s(s(elem!1)))) <=> b(elem!1, s(s(s(elem!1))))),
% 0.48/0.64 inference(symmetry,[status(thm)],[358])).
% 0.48/0.64 tff(360,plain,
% 0.48/0.64 (b(elem!1, s(s(s(elem!1))))),
% 0.48/0.64 inference(modus_ponens,[status(thm)],[324, 359])).
% 0.48/0.64 tff(361,plain,
% 0.48/0.64 (((~![X0: $i, X2: $i, X1: $i] : ((~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), z)) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(z))), z)))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), z)) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(z))), z)))),
% 0.48/0.64 inference(rewrite,[status(thm)],[])).
% 0.48/0.64 tff(362,plain,
% 0.48/0.64 (((~b(s(s(s(z))), z)) | (~b(s(z), z)) | (~b(s(z), s(s(s(z)))))) <=> ((~b(s(z), z)) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(z))), z)))),
% 0.48/0.64 inference(rewrite,[status(thm)],[])).
% 0.48/0.64 tff(363,plain,
% 0.48/0.64 (((~![X0: $i, X2: $i, X1: $i] : ((~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), z)) | (~b(s(z), z)) | (~b(s(z), s(s(s(z))))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), z)) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(z))), z))))),
% 0.48/0.64 inference(monotonicity,[status(thm)],[362])).
% 0.48/0.64 tff(364,plain,
% 0.48/0.64 (((~![X0: $i, X2: $i, X1: $i] : ((~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), z)) | (~b(s(z), z)) | (~b(s(z), s(s(s(z))))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), z)) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(z))), z)))),
% 0.48/0.64 inference(transitivity,[status(thm)],[363, 361])).
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% 0.48/0.64 ((~![X0: $i, X2: $i, X1: $i] : ((~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), z)) | (~b(s(z), z)) | (~b(s(z), s(s(s(z))))))),
% 0.48/0.64 inference(quant_inst,[status(thm)],[])).
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% 0.48/0.64 ((~![X0: $i, X2: $i, X1: $i] : ((~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), z)) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(z))), z))),
% 0.48/0.64 inference(modus_ponens,[status(thm)],[365, 364])).
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% 0.48/0.64 inference(unit_resolution,[status(thm)],[366, 117, 237, 338])).
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% 0.48/0.64 ((s(z) = s(s(s(z)))) <=> (s(s(s(z))) = s(z))),
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% 0.48/0.64 ((s(s(s(z))) = s(z)) <=> (s(z) = s(s(s(z))))),
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% 0.48/0.64 tff(370,plain,
% 0.48/0.64 ((~(s(s(s(z))) = s(z))) <=> (~(s(z) = s(s(s(z)))))),
% 0.48/0.64 inference(monotonicity,[status(thm)],[369])).
% 0.48/0.64 tff(371,plain,
% 0.48/0.64 (~(s(z) = s(s(s(z))))),
% 0.48/0.64 inference(modus_ponens,[status(thm)],[98, 370])).
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% 0.48/0.64 (((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((s(z) = s(s(s(z)))) | b(s(z), s(s(s(z)))) | r(s(z), s(s(s(z)))))) <=> ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (s(z) = s(s(s(z)))) | b(s(z), s(s(s(z)))) | r(s(z), s(s(s(z)))))),
% 0.48/0.64 inference(rewrite,[status(thm)],[])).
% 0.48/0.64 tff(373,plain,
% 0.48/0.64 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((s(z) = s(s(s(z)))) | b(s(z), s(s(s(z)))) | r(s(z), s(s(s(z)))))),
% 0.48/0.64 inference(quant_inst,[status(thm)],[])).
% 0.48/0.64 tff(374,plain,
% 0.48/0.64 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (s(z) = s(s(s(z)))) | b(s(z), s(s(s(z)))) | r(s(z), s(s(s(z))))),
% 0.48/0.64 inference(modus_ponens,[status(thm)],[373, 372])).
% 0.48/0.64 tff(375,plain,
% 0.48/0.64 ((s(z) = s(s(s(z)))) | b(s(z), s(s(s(z)))) | r(s(z), s(s(s(z))))),
% 0.48/0.64 inference(unit_resolution,[status(thm)],[374, 46])).
% 0.48/0.64 tff(376,plain,
% 0.48/0.64 (b(s(z), s(s(s(z)))) | r(s(z), s(s(s(z))))),
% 0.48/0.64 inference(unit_resolution,[status(thm)],[375, 371])).
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% 0.48/0.64 (r(s(z), s(s(s(z))))),
% 0.48/0.64 inference(unit_resolution,[status(thm)],[376, 367])).
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% 0.48/0.64 (b(s(elem!1), z) <=> b(s(s(s(elem!1))), z)),
% 0.48/0.64 inference(monotonicity,[status(thm)],[260])).
% 0.48/0.64 tff(379,plain,
% 0.48/0.64 (b(s(s(s(elem!1))), z) <=> b(s(elem!1), z)),
% 0.48/0.64 inference(symmetry,[status(thm)],[378])).
% 0.48/0.64 tff(380,plain,
% 0.48/0.64 (r(s(elem!1), z) <=> r(s(s(s(elem!1))), z)),
% 0.48/0.64 inference(monotonicity,[status(thm)],[260])).
% 0.48/0.64 tff(381,plain,
% 0.48/0.64 ((~r(s(elem!1), z)) <=> (~r(s(s(s(elem!1))), z))),
% 0.48/0.64 inference(monotonicity,[status(thm)],[380])).
% 0.48/0.64 tff(382,plain,
% 0.48/0.64 (r(elem!1, s(s(s(z)))) <=> r(s(s(elem!1)), s(s(s(z))))),
% 0.48/0.64 inference(symmetry,[status(thm)],[336])).
% 0.48/0.64 tff(383,plain,
% 0.48/0.64 ((~b(s(s(elem!1)), s(s(s(z))))) <=> (~b(elem!1, s(s(s(z)))))),
% 0.48/0.64 inference(monotonicity,[status(thm)],[329])).
% 0.48/0.64 tff(384,plain,
% 0.48/0.64 (b(s(s(elem!1)), s(elem!1)) <=> b(s(s(elem!1)), s(s(s(elem!1))))),
% 0.48/0.64 inference(monotonicity,[status(thm)],[260])).
% 0.48/0.64 tff(385,plain,
% 0.48/0.64 (b(s(s(elem!1)), s(s(s(elem!1)))) <=> b(s(s(elem!1)), s(elem!1))),
% 0.48/0.64 inference(symmetry,[status(thm)],[384])).
% 0.48/0.64 tff(386,plain,
% 0.48/0.64 (b(s(s(elem!1)), s(elem!1))),
% 0.48/0.64 inference(modus_ponens,[status(thm)],[324, 385])).
% 0.48/0.64 tff(387,assumption,(b(s(s(s(z))), s(elem!1))), introduced(assumption)).
% 0.48/0.64 tff(388,plain,
% 0.48/0.64 (((~![X0: $i, X2: $i, X1: $i] : ((~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), s(elem!1))) | (~b(s(s(elem!1)), s(s(s(z))))) | (~b(s(s(s(z))), s(elem!1))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(elem!1)), s(elem!1))) | (~b(s(s(elem!1)), s(s(s(z))))) | (~b(s(s(s(z))), s(elem!1))))),
% 0.48/0.64 inference(rewrite,[status(thm)],[])).
% 0.48/0.64 tff(389,plain,
% 0.48/0.64 (((~b(s(s(s(z))), s(elem!1))) | (~b(s(s(elem!1)), s(elem!1))) | (~b(s(s(elem!1)), s(s(s(z)))))) <=> ((~b(s(s(elem!1)), s(elem!1))) | (~b(s(s(elem!1)), s(s(s(z))))) | (~b(s(s(s(z))), s(elem!1))))),
% 0.48/0.64 inference(rewrite,[status(thm)],[])).
% 0.48/0.64 tff(390,plain,
% 0.48/0.64 (((~![X0: $i, X2: $i, X1: $i] : ((~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), s(elem!1))) | (~b(s(s(elem!1)), s(elem!1))) | (~b(s(s(elem!1)), s(s(s(z))))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), s(elem!1))) | (~b(s(s(elem!1)), s(s(s(z))))) | (~b(s(s(s(z))), s(elem!1)))))),
% 0.48/0.64 inference(monotonicity,[status(thm)],[389])).
% 0.48/0.64 tff(391,plain,
% 0.48/0.64 (((~![X0: $i, X2: $i, X1: $i] : ((~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), s(elem!1))) | (~b(s(s(elem!1)), s(elem!1))) | (~b(s(s(elem!1)), s(s(s(z))))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(elem!1)), s(elem!1))) | (~b(s(s(elem!1)), s(s(s(z))))) | (~b(s(s(s(z))), s(elem!1))))),
% 0.48/0.64 inference(transitivity,[status(thm)],[390, 388])).
% 0.48/0.64 tff(392,plain,
% 0.48/0.64 ((~![X0: $i, X2: $i, X1: $i] : ((~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), s(elem!1))) | (~b(s(s(elem!1)), s(elem!1))) | (~b(s(s(elem!1)), s(s(s(z))))))),
% 0.48/0.64 inference(quant_inst,[status(thm)],[])).
% 0.48/0.64 tff(393,plain,
% 0.48/0.64 ((~![X0: $i, X2: $i, X1: $i] : ((~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(elem!1)), s(elem!1))) | (~b(s(s(elem!1)), s(s(s(z))))) | (~b(s(s(s(z))), s(elem!1)))),
% 0.48/0.64 inference(modus_ponens,[status(thm)],[392, 391])).
% 0.48/0.64 tff(394,plain,
% 0.48/0.64 ((~b(s(s(elem!1)), s(elem!1))) | (~b(s(s(elem!1)), s(s(s(z)))))),
% 0.48/0.64 inference(unit_resolution,[status(thm)],[393, 117, 387])).
% 0.48/0.64 tff(395,plain,
% 0.48/0.64 (~b(s(s(elem!1)), s(s(s(z))))),
% 0.48/0.64 inference(unit_resolution,[status(thm)],[394, 386])).
% 0.48/0.64 tff(396,plain,
% 0.48/0.64 (~b(elem!1, s(s(s(z))))),
% 0.48/0.64 inference(modus_ponens,[status(thm)],[395, 383])).
% 0.48/0.64 tff(397,plain,
% 0.48/0.64 (((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((elem!1 = s(s(s(z)))) | b(elem!1, s(s(s(z)))) | r(elem!1, s(s(s(z)))))) <=> ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (elem!1 = s(s(s(z)))) | b(elem!1, s(s(s(z)))) | r(elem!1, s(s(s(z)))))),
% 0.48/0.64 inference(rewrite,[status(thm)],[])).
% 0.48/0.64 tff(398,plain,
% 0.48/0.64 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((elem!1 = s(s(s(z)))) | b(elem!1, s(s(s(z)))) | r(elem!1, s(s(s(z)))))),
% 0.48/0.64 inference(quant_inst,[status(thm)],[])).
% 0.48/0.64 tff(399,plain,
% 0.48/0.64 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (elem!1 = s(s(s(z)))) | b(elem!1, s(s(s(z)))) | r(elem!1, s(s(s(z))))),
% 0.48/0.64 inference(modus_ponens,[status(thm)],[398, 397])).
% 0.48/0.64 tff(400,plain,
% 0.48/0.64 ((elem!1 = s(s(s(z)))) | b(elem!1, s(s(s(z)))) | r(elem!1, s(s(s(z))))),
% 0.48/0.64 inference(unit_resolution,[status(thm)],[399, 46])).
% 0.48/0.64 tff(401,plain,
% 0.48/0.64 (r(elem!1, s(s(s(z))))),
% 0.48/0.64 inference(unit_resolution,[status(thm)],[400, 396, 335])).
% 0.48/0.64 tff(402,plain,
% 0.48/0.64 (r(s(s(elem!1)), s(s(s(z))))),
% 0.48/0.64 inference(modus_ponens,[status(thm)],[401, 382])).
% 0.48/0.64 tff(403,assumption,(r(s(z), s(s(s(z))))), introduced(assumption)).
% 0.48/0.64 tff(404,plain,
% 0.48/0.64 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(s(elem!1)))) | (~r(s(z), s(s(s(z))))) | (~r(s(s(elem!1)), s(s(s(z))))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(z), s(s(elem!1)))) | (~r(s(z), s(s(s(z))))) | (~r(s(s(elem!1)), s(s(s(z))))))),
% 0.48/0.64 inference(rewrite,[status(thm)],[])).
% 0.48/0.64 tff(405,plain,
% 0.48/0.64 (((~r(s(s(elem!1)), s(s(s(z))))) | (~r(s(z), s(s(s(z))))) | (~r(s(z), s(s(elem!1))))) <=> ((~r(s(z), s(s(elem!1)))) | (~r(s(z), s(s(s(z))))) | (~r(s(s(elem!1)), s(s(s(z))))))),
% 0.48/0.64 inference(rewrite,[status(thm)],[])).
% 0.48/0.64 tff(406,plain,
% 0.48/0.64 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(elem!1)), s(s(s(z))))) | (~r(s(z), s(s(s(z))))) | (~r(s(z), s(s(elem!1)))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(s(elem!1)))) | (~r(s(z), s(s(s(z))))) | (~r(s(s(elem!1)), s(s(s(z)))))))),
% 0.48/0.64 inference(monotonicity,[status(thm)],[405])).
% 0.48/0.64 tff(407,plain,
% 0.48/0.64 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(elem!1)), s(s(s(z))))) | (~r(s(z), s(s(s(z))))) | (~r(s(z), s(s(elem!1)))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(z), s(s(elem!1)))) | (~r(s(z), s(s(s(z))))) | (~r(s(s(elem!1)), s(s(s(z))))))),
% 0.48/0.64 inference(transitivity,[status(thm)],[406, 404])).
% 0.48/0.64 tff(408,plain,
% 0.48/0.64 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(elem!1)), s(s(s(z))))) | (~r(s(z), s(s(s(z))))) | (~r(s(z), s(s(elem!1)))))),
% 0.48/0.64 inference(quant_inst,[status(thm)],[])).
% 0.48/0.64 tff(409,plain,
% 0.48/0.64 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(z), s(s(elem!1)))) | (~r(s(z), s(s(s(z))))) | (~r(s(s(elem!1)), s(s(s(z)))))),
% 0.48/0.64 inference(modus_ponens,[status(thm)],[408, 407])).
% 0.48/0.64 tff(410,plain,
% 0.48/0.64 ((~r(s(z), s(s(elem!1)))) | (~r(s(s(elem!1)), s(s(s(z)))))),
% 0.48/0.64 inference(unit_resolution,[status(thm)],[409, 14, 403])).
% 0.48/0.64 tff(411,plain,
% 0.48/0.64 (~r(s(z), s(s(elem!1)))),
% 0.48/0.64 inference(unit_resolution,[status(thm)],[410, 402])).
% 0.48/0.64 tff(412,plain,
% 0.48/0.64 (((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((s(z) = s(s(elem!1))) | b(s(z), s(s(elem!1))) | r(s(z), s(s(elem!1))))) <=> ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (s(z) = s(s(elem!1))) | b(s(z), s(s(elem!1))) | r(s(z), s(s(elem!1))))),
% 0.48/0.64 inference(rewrite,[status(thm)],[])).
% 0.48/0.64 tff(413,plain,
% 0.48/0.64 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((s(z) = s(s(elem!1))) | b(s(z), s(s(elem!1))) | r(s(z), s(s(elem!1))))),
% 0.48/0.64 inference(quant_inst,[status(thm)],[])).
% 0.48/0.64 tff(414,plain,
% 0.48/0.64 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (s(z) = s(s(elem!1))) | b(s(z), s(s(elem!1))) | r(s(z), s(s(elem!1)))),
% 0.48/0.64 inference(modus_ponens,[status(thm)],[413, 412])).
% 0.48/0.64 tff(415,plain,
% 0.48/0.64 ((s(z) = s(s(elem!1))) | b(s(z), s(s(elem!1))) | r(s(z), s(s(elem!1)))),
% 0.48/0.64 inference(unit_resolution,[status(thm)],[414, 46])).
% 0.48/0.64 tff(416,plain,
% 0.48/0.64 (b(s(z), s(s(elem!1))) | r(s(z), s(s(elem!1)))),
% 0.48/0.64 inference(unit_resolution,[status(thm)],[415, 172])).
% 0.48/0.64 tff(417,plain,
% 0.48/0.64 (b(s(z), s(s(elem!1)))),
% 0.48/0.64 inference(unit_resolution,[status(thm)],[416, 411])).
% 0.48/0.64 tff(418,plain,
% 0.48/0.64 (((~![X0: $i, X2: $i, X1: $i] : ((~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(elem!1)), s(s(s(z))))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(elem!1)), s(z))) | (~r(s(z), s(s(s(z))))) | (~r(s(s(elem!1)), s(s(s(z))))))),
% 0.48/0.64 inference(rewrite,[status(thm)],[])).
% 0.48/0.64 tff(419,plain,
% 0.48/0.64 (((~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(z), s(s(s(z))))) | (~r(s(s(elem!1)), s(s(s(z))))))),
% 0.48/0.64 inference(rewrite,[status(thm)],[])).
% 0.48/0.64 tff(420,plain,
% 0.48/0.64 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(s(s(z))))) | (~r(s(s(elem!1)), s(s(s(z))))) | (~r(s(s(elem!1)), s(z))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(elem!1)), s(z))) | (~r(s(z), s(s(s(z))))) | (~r(s(s(elem!1)), s(s(s(z)))))))),
% 0.48/0.64 inference(monotonicity,[status(thm)],[419])).
% 0.48/0.64 tff(421,plain,
% 0.48/0.64 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(s(s(z))))) | (~r(s(s(elem!1)), s(s(s(z))))) | (~r(s(s(elem!1)), s(z))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(elem!1)), s(z))) | (~r(s(z), s(s(s(z))))) | (~r(s(s(elem!1)), s(s(s(z))))))),
% 0.48/0.64 inference(transitivity,[status(thm)],[420, 418])).
% 0.48/0.64 tff(422,plain,
% 0.48/0.64 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(s(s(z))))) | (~r(s(s(elem!1)), s(s(s(z))))) | (~r(s(s(elem!1)), s(z))))),
% 0.48/0.64 inference(quant_inst,[status(thm)],[])).
% 0.48/0.64 tff(423,plain,
% 0.48/0.64 ((~![X0: $i, X2: $i, X1: $i] : ((~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(elem!1)), s(s(s(z)))))),
% 0.48/0.64 inference(modus_ponens,[status(thm)],[422, 421])).
% 0.48/0.64 tff(424,plain,
% 0.48/0.64 ((~r(s(s(elem!1)), s(z))) | (~r(s(s(elem!1)), s(s(s(z)))))),
% 0.48/0.64 inference(unit_resolution,[status(thm)],[423, 14, 403])).
% 0.48/0.64 tff(425,plain,
% 0.48/0.64 (~r(s(s(elem!1)), s(z))),
% 0.48/0.64 inference(unit_resolution,[status(thm)],[424, 402])).
% 0.48/0.64 tff(426,plain,
% 0.48/0.64 (b(s(s(elem!1)), s(z))),
% 0.48/0.64 inference(unit_resolution,[status(thm)],[178, 425])).
% 0.48/0.64 tff(427,plain,
% 0.48/0.64 (r(s(elem!1), s(z)) <=> r(s(s(s(elem!1))), s(z))),
% 0.48/0.64 inference(monotonicity,[status(thm)],[260])).
% 0.48/0.64 tff(428,plain,
% 0.48/0.64 (r(s(s(s(elem!1))), s(z)) <=> r(s(elem!1), s(z))),
% 0.48/0.64 inference(symmetry,[status(thm)],[427])).
% 0.48/0.64 tff(429,plain,
% 0.48/0.64 (b(s(elem!1), s(z)) <=> b(s(s(s(elem!1))), s(z))),
% 0.48/0.64 inference(monotonicity,[status(thm)],[260])).
% 0.48/0.64 tff(430,plain,
% 0.48/0.64 ((~b(s(elem!1), s(z))) <=> (~b(s(s(s(elem!1))), s(z)))),
% 0.48/0.64 inference(monotonicity,[status(thm)],[429])).
% 0.48/0.64 tff(431,plain,
% 0.48/0.64 (b(s(elem!1), s(s(elem!1))) <=> b(s(s(s(elem!1))), s(s(elem!1)))),
% 0.48/0.64 inference(monotonicity,[status(thm)],[260])).
% 0.48/0.64 tff(432,plain,
% 0.48/0.64 (b(s(s(s(elem!1))), s(s(elem!1))) <=> b(s(elem!1), s(s(elem!1)))),
% 0.48/0.64 inference(symmetry,[status(thm)],[431])).
% 0.48/0.64 tff(433,plain,
% 0.48/0.64 (b(s(s(s(elem!1))), s(s(s(s(elem!1))))) <=> b(s(s(s(elem!1))), s(s(elem!1)))),
% 0.48/0.64 inference(monotonicity,[status(thm)],[255])).
% 0.48/0.64 tff(434,plain,
% 0.48/0.64 (r(s(s(s(elem!1))), s(s(s(s(elem!1))))) <=> r(s(s(s(elem!1))), s(s(elem!1)))),
% 0.48/0.64 inference(monotonicity,[status(thm)],[255])).
% 0.48/0.64 tff(435,plain,
% 0.48/0.64 (r(s(s(s(elem!1))), s(s(elem!1))) <=> r(s(s(s(elem!1))), s(s(s(s(elem!1)))))),
% 0.48/0.64 inference(symmetry,[status(thm)],[434])).
% 0.48/0.64 tff(436,plain,
% 0.48/0.64 (r(s(elem!1), s(s(elem!1))) <=> r(s(s(s(elem!1))), s(s(elem!1)))),
% 0.48/0.64 inference(monotonicity,[status(thm)],[260])).
% 0.48/0.64 tff(437,plain,
% 0.48/0.64 (r(s(elem!1), s(s(elem!1))) <=> r(s(s(s(elem!1))), s(s(s(s(elem!1)))))),
% 0.48/0.64 inference(transitivity,[status(thm)],[436, 435])).
% 0.48/0.64 tff(438,plain,
% 0.48/0.64 ((~r(s(elem!1), s(s(elem!1)))) <=> (~r(s(s(s(elem!1))), s(s(s(s(elem!1))))))),
% 0.48/0.64 inference(monotonicity,[status(thm)],[437])).
% 0.48/0.64 tff(439,assumption,(r(s(elem!1), z)), introduced(assumption)).
% 0.48/0.64 tff(440,plain,
% 0.48/0.64 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(elem!1)), z)) | (~r(s(elem!1), z)) | (~r(s(elem!1), s(s(elem!1)))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(elem!1)), z)) | (~r(s(elem!1), z)) | (~r(s(elem!1), s(s(elem!1)))))),
% 0.48/0.64 inference(rewrite,[status(thm)],[])).
% 0.48/0.64 tff(441,plain,
% 0.48/0.64 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(elem!1)), z)) | (~r(s(elem!1), z)) | (~r(s(elem!1), s(s(elem!1)))))),
% 0.48/0.64 inference(quant_inst,[status(thm)],[])).
% 0.48/0.64 tff(442,plain,
% 0.48/0.64 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(elem!1)), z)) | (~r(s(elem!1), z)) | (~r(s(elem!1), s(s(elem!1))))),
% 0.48/0.64 inference(modus_ponens,[status(thm)],[441, 440])).
% 0.48/0.64 tff(443,plain,
% 0.48/0.64 (~r(s(elem!1), s(s(elem!1)))),
% 0.48/0.64 inference(unit_resolution,[status(thm)],[442, 14, 182, 439])).
% 0.48/0.64 tff(444,plain,
% 0.48/0.64 (~r(s(s(s(elem!1))), s(s(s(s(elem!1)))))),
% 0.48/0.64 inference(modus_ponens,[status(thm)],[443, 438])).
% 0.48/0.64 tff(445,plain,
% 0.48/0.65 (((~![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))))))),
% 0.48/0.65 inference(rewrite,[status(thm)],[])).
% 0.48/0.65 tff(446,plain,
% 0.48/0.65 ((~![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))))))),
% 0.48/0.65 inference(quant_inst,[status(thm)],[])).
% 0.48/0.65 tff(447,plain,
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% 0.48/0.65 inference(modus_ponens,[status(thm)],[446, 445])).
% 0.48/0.65 tff(448,plain,
% 0.48/0.65 ((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)))))),
% 0.48/0.65 inference(unit_resolution,[status(thm)],[447, 46])).
% 0.48/0.65 tff(449,plain,
% 0.48/0.65 (b(s(s(s(elem!1))), s(s(s(s(elem!1)))))),
% 0.48/0.65 inference(unit_resolution,[status(thm)],[448, 444, 323])).
% 0.48/0.65 tff(450,plain,
% 0.48/0.65 (b(s(s(s(elem!1))), s(s(elem!1)))),
% 0.48/0.65 inference(modus_ponens,[status(thm)],[449, 433])).
% 0.48/0.65 tff(451,plain,
% 0.48/0.65 (b(s(elem!1), s(s(elem!1)))),
% 0.48/0.65 inference(modus_ponens,[status(thm)],[450, 432])).
% 0.48/0.65 tff(452,assumption,(b(s(z), s(s(elem!1)))), introduced(assumption)).
% 0.48/0.65 tff(453,plain,
% 0.48/0.65 (((~![X0: $i, X2: $i, X1: $i] : ((~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(elem!1)))) | (~b(s(elem!1), s(s(elem!1)))) | (~b(s(elem!1), s(z))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), s(s(elem!1)))) | (~b(s(elem!1), s(s(elem!1)))) | (~b(s(elem!1), s(z))))),
% 0.48/0.65 inference(rewrite,[status(thm)],[])).
% 0.48/0.65 tff(454,plain,
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% 0.48/0.65 inference(quant_inst,[status(thm)],[])).
% 0.48/0.65 tff(455,plain,
% 0.48/0.65 ((~![X0: $i, X2: $i, X1: $i] : ((~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), s(s(elem!1)))) | (~b(s(elem!1), s(s(elem!1)))) | (~b(s(elem!1), s(z)))),
% 0.48/0.65 inference(modus_ponens,[status(thm)],[454, 453])).
% 0.48/0.65 tff(456,plain,
% 0.48/0.65 ((~b(s(elem!1), s(s(elem!1)))) | (~b(s(elem!1), s(z)))),
% 0.48/0.65 inference(unit_resolution,[status(thm)],[455, 117, 452])).
% 0.48/0.65 tff(457,plain,
% 0.48/0.65 (~b(s(elem!1), s(z))),
% 0.48/0.65 inference(unit_resolution,[status(thm)],[456, 451])).
% 0.48/0.65 tff(458,plain,
% 0.48/0.65 (~b(s(s(s(elem!1))), s(z))),
% 0.48/0.65 inference(modus_ponens,[status(thm)],[457, 430])).
% 0.48/0.65 tff(459,plain,
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% 0.48/0.65 inference(commutativity,[status(thm)],[])).
% 0.48/0.65 tff(460,plain,
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% 0.48/0.65 tff(461,plain,
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% 0.48/0.65 inference(modus_ponens,[status(thm)],[230, 461])).
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% 0.48/0.65 inference(rewrite,[status(thm)],[])).
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% 0.48/0.65 inference(quant_inst,[status(thm)],[])).
% 0.48/0.65 tff(465,plain,
% 0.48/0.65 ((~![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))),
% 0.48/0.65 inference(modus_ponens,[status(thm)],[464, 463])).
% 0.48/0.65 tff(466,plain,
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% 0.48/0.65 inference(unit_resolution,[status(thm)],[465, 46])).
% 0.48/0.65 tff(467,plain,
% 0.48/0.65 (b(s(s(s(elem!1))), s(z)) | r(s(s(s(elem!1))), s(z))),
% 0.48/0.65 inference(unit_resolution,[status(thm)],[466, 462])).
% 0.48/0.65 tff(468,plain,
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% 0.48/0.65 inference(unit_resolution,[status(thm)],[467, 458])).
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% 0.48/0.65 inference(modus_ponens,[status(thm)],[468, 428])).
% 0.48/0.65 tff(470,assumption,(b(s(s(elem!1)), s(z))), introduced(assumption)).
% 0.48/0.65 tff(471,plain,
% 0.48/0.65 (s(s(elem!1)) = s(s(s(s(elem!1))))),
% 0.48/0.65 inference(symmetry,[status(thm)],[255])).
% 0.48/0.65 tff(472,assumption,(s(s(s(s(z)))) = s(elem!1)), introduced(assumption)).
% 0.48/0.65 tff(473,plain,
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% 0.48/0.65 inference(monotonicity,[status(thm)],[472])).
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% 0.48/0.65 inference(transitivity,[status(thm)],[87, 473, 257, 349, 471])).
% 0.48/0.65 tff(475,plain,
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% 0.48/0.65 inference(unit_resolution,[status(thm)],[279, 474])).
% 0.48/0.65 tff(476,plain,((~(s(s(s(s(z)))) = s(elem!1))) | (~(s(s(s(s(elem!1)))) = s(s(elem!1))))), inference(lemma,lemma(discharge,[]))).
% 0.48/0.65 tff(477,plain,
% 0.48/0.65 (~(s(s(s(s(z)))) = s(elem!1))),
% 0.48/0.65 inference(unit_resolution,[status(thm)],[476, 255])).
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% 0.48/0.65 ((s(s(s(s(s(elem!1))))) = s(s(s(z)))) <=> (s(s(s(z))) = s(s(s(s(s(elem!1))))))),
% 0.48/0.65 inference(commutativity,[status(thm)],[])).
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% 0.48/0.65 inference(symmetry,[status(thm)],[296])).
% 0.48/0.65 tff(480,plain,
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% 0.48/0.65 inference(transitivity,[status(thm)],[167, 259, 144, 479])).
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% 0.48/0.65 ((s(elem!1) = s(s(s(z)))) <=> (s(s(s(s(s(elem!1))))) = s(s(s(z))))),
% 0.48/0.65 inference(monotonicity,[status(thm)],[480])).
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% 0.48/0.65 inference(transitivity,[status(thm)],[481, 478])).
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% 0.48/0.65 inference(symmetry,[status(thm)],[482])).
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% 0.48/0.65 ((~(s(s(s(z))) = s(s(s(s(s(elem!1))))))) <=> (~(s(elem!1) = s(s(s(z)))))),
% 0.48/0.65 inference(monotonicity,[status(thm)],[483])).
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% 0.48/0.65 inference(rewrite,[status(thm)],[])).
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% 0.48/0.65 inference(quant_inst,[status(thm)],[])).
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% 0.48/0.65 inference(modus_ponens,[status(thm)],[487, 486])).
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% 0.48/0.65 inference(unit_resolution,[status(thm)],[488, 14, 283])).
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% 0.48/0.65 inference(rewrite,[status(thm)],[])).
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% 0.48/0.65 inference(quant_inst,[status(thm)],[])).
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% 0.48/0.65 inference(modus_ponens,[status(thm)],[492, 491])).
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% 0.48/0.65 inference(quant_inst,[status(thm)],[])).
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% 0.48/0.65 inference(modus_ponens,[status(thm)],[498, 497])).
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% 0.48/0.65 inference(unit_resolution,[status(thm)],[499, 14, 3, 496])).
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% 0.48/0.65 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((s(s(s(s(z)))) = s(elem!1)) | b(s(s(s(s(z)))), s(elem!1)) | r(s(s(s(s(z)))), s(elem!1)))),
% 0.48/0.65 inference(quant_inst,[status(thm)],[])).
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% 0.48/0.65 inference(quant_inst,[status(thm)],[])).
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% 0.48/0.65 inference(quant_inst,[status(thm)],[])).
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% 0.48/0.65 inference(quant_inst,[status(thm)],[])).
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% 0.48/0.65 inference(unit_resolution,[status(thm)],[527, 46])).
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% 0.48/0.65 inference(unit_resolution,[status(thm)],[528, 524])).
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% 0.48/0.65 inference(symmetry,[status(thm)],[557])).
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% 0.48/0.66 tff(587,plain,
% 0.48/0.66 (~r(s(s(s(s(z)))), s(s(elem!1)))),
% 0.48/0.66 inference(unit_resolution,[status(thm)],[586, 14, 182, 583])).
% 0.48/0.66 tff(588,plain,
% 0.48/0.66 ($false),
% 0.48/0.66 inference(unit_resolution,[status(thm)],[587, 573])).
% 0.48/0.66 tff(589,plain,((~b(s(s(s(s(z)))), s(z))) | (~(s(s(elem!1)) = elem!1)) | (s(s(s(s(z)))) = elem!1) | (~r(s(s(elem!1)), z)) | (~b(z, s(z))) | (~b(s(s(elem!1)), s(z)))), inference(lemma,lemma(discharge,[]))).
% 0.48/0.66 tff(590,plain,
% 0.48/0.66 (~b(z, s(z))),
% 0.48/0.66 inference(unit_resolution,[status(thm)],[589, 555, 320, 182, 267, 470])).
% 0.48/0.66 tff(591,plain,
% 0.48/0.66 ((z = s(z)) <=> (s(z) = z)),
% 0.48/0.66 inference(commutativity,[status(thm)],[])).
% 0.48/0.66 tff(592,plain,
% 0.48/0.66 ((s(z) = z) <=> (z = s(z))),
% 0.48/0.66 inference(symmetry,[status(thm)],[591])).
% 0.48/0.66 tff(593,plain,
% 0.48/0.66 ((~(s(z) = z)) <=> (~(z = s(z)))),
% 0.48/0.66 inference(monotonicity,[status(thm)],[592])).
% 0.48/0.66 tff(594,plain,
% 0.48/0.66 (~(z = s(z))),
% 0.48/0.66 inference(modus_ponens,[status(thm)],[134, 593])).
% 0.48/0.66 tff(595,plain,
% 0.48/0.66 (((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((z = s(z)) | b(z, s(z)) | r(z, s(z)))) <=> ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (z = s(z)) | b(z, s(z)) | r(z, s(z)))),
% 0.48/0.66 inference(rewrite,[status(thm)],[])).
% 0.48/0.66 tff(596,plain,
% 0.48/0.66 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((z = s(z)) | b(z, s(z)) | r(z, s(z)))),
% 0.48/0.66 inference(quant_inst,[status(thm)],[])).
% 0.48/0.66 tff(597,plain,
% 0.48/0.66 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (z = s(z)) | b(z, s(z)) | r(z, s(z))),
% 0.48/0.66 inference(modus_ponens,[status(thm)],[596, 595])).
% 0.48/0.66 tff(598,plain,
% 0.48/0.66 ((z = s(z)) | b(z, s(z)) | r(z, s(z))),
% 0.48/0.66 inference(unit_resolution,[status(thm)],[597, 46])).
% 0.48/0.66 tff(599,plain,
% 0.48/0.66 (b(z, s(z)) | r(z, s(z))),
% 0.48/0.66 inference(unit_resolution,[status(thm)],[598, 594])).
% 0.48/0.66 tff(600,plain,
% 0.48/0.66 (r(z, s(z))),
% 0.48/0.66 inference(unit_resolution,[status(thm)],[599, 590])).
% 0.48/0.66 tff(601,plain,
% 0.48/0.66 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(z))) | (~r(s(elem!1), z)) | (~r(s(elem!1), s(z))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, s(z))) | (~r(s(elem!1), z)) | (~r(s(elem!1), s(z))))),
% 0.48/0.66 inference(rewrite,[status(thm)],[])).
% 0.48/0.66 tff(602,plain,
% 0.48/0.66 (((~r(z, s(z))) | (~r(s(elem!1), s(z))) | (~r(s(elem!1), z))) <=> ((~r(z, s(z))) | (~r(s(elem!1), z)) | (~r(s(elem!1), s(z))))),
% 0.48/0.66 inference(rewrite,[status(thm)],[])).
% 0.48/0.66 tff(603,plain,
% 0.48/0.66 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(z))) | (~r(s(elem!1), s(z))) | (~r(s(elem!1), z)))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(z))) | (~r(s(elem!1), z)) | (~r(s(elem!1), s(z)))))),
% 0.48/0.66 inference(monotonicity,[status(thm)],[602])).
% 0.48/0.66 tff(604,plain,
% 0.48/0.66 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(z))) | (~r(s(elem!1), s(z))) | (~r(s(elem!1), z)))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, s(z))) | (~r(s(elem!1), z)) | (~r(s(elem!1), s(z))))),
% 0.48/0.66 inference(transitivity,[status(thm)],[603, 601])).
% 0.48/0.66 tff(605,plain,
% 0.48/0.66 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(z))) | (~r(s(elem!1), s(z))) | (~r(s(elem!1), z)))),
% 0.48/0.66 inference(quant_inst,[status(thm)],[])).
% 0.48/0.66 tff(606,plain,
% 0.48/0.66 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, s(z))) | (~r(s(elem!1), z)) | (~r(s(elem!1), s(z)))),
% 0.48/0.66 inference(modus_ponens,[status(thm)],[605, 604])).
% 0.48/0.66 tff(607,plain,
% 0.48/0.66 ($false),
% 0.48/0.66 inference(unit_resolution,[status(thm)],[606, 14, 600, 439, 469])).
% 0.48/0.66 tff(608,plain,((~r(s(elem!1), z)) | (~r(s(s(elem!1)), z)) | (~b(s(s(elem!1)), s(z))) | (~r(s(s(s(z))), s(z))) | (~(s(s(s(s(elem!1)))) = s(s(elem!1)))) | (~b(s(z), s(s(elem!1)))) | (s(s(s(elem!1))) = s(s(s(s(elem!1)))))), inference(lemma,lemma(discharge,[]))).
% 0.48/0.66 tff(609,plain,
% 0.48/0.66 (~r(s(elem!1), z)),
% 0.48/0.66 inference(unit_resolution,[status(thm)],[608, 426, 182, 283, 255, 417, 323])).
% 0.48/0.66 tff(610,plain,
% 0.48/0.66 (~r(s(s(s(elem!1))), z)),
% 0.48/0.66 inference(modus_ponens,[status(thm)],[609, 381])).
% 0.48/0.66 tff(611,plain,
% 0.48/0.66 (b(s(s(s(elem!1))), z)),
% 0.48/0.66 inference(unit_resolution,[status(thm)],[211, 610])).
% 0.48/0.66 tff(612,plain,
% 0.48/0.66 (b(s(elem!1), z)),
% 0.48/0.66 inference(modus_ponens,[status(thm)],[611, 379])).
% 0.48/0.66 tff(613,plain,
% 0.48/0.66 (((~![X0: $i, X2: $i, X1: $i] : ((~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), z)) | (~b(s(s(s(z))), z)) | (~b(s(s(s(z))), s(elem!1))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(elem!1), z)) | (~b(s(s(s(z))), z)) | (~b(s(s(s(z))), s(elem!1))))),
% 0.48/0.66 inference(rewrite,[status(thm)],[])).
% 0.48/0.66 tff(614,plain,
% 0.48/0.66 ((~![X0: $i, X2: $i, X1: $i] : ((~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), z)) | (~b(s(s(s(z))), z)) | (~b(s(s(s(z))), s(elem!1))))),
% 0.48/0.66 inference(quant_inst,[status(thm)],[])).
% 0.48/0.66 tff(615,plain,
% 0.48/0.66 ((~![X0: $i, X2: $i, X1: $i] : ((~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(elem!1), z)) | (~b(s(s(s(z))), z)) | (~b(s(s(s(z))), s(elem!1)))),
% 0.48/0.66 inference(modus_ponens,[status(thm)],[614, 613])).
% 0.48/0.66 tff(616,plain,
% 0.48/0.66 (~b(s(elem!1), z)),
% 0.48/0.66 inference(unit_resolution,[status(thm)],[615, 117, 338, 387])).
% 0.48/0.66 tff(617,plain,
% 0.48/0.66 ($false),
% 0.48/0.66 inference(unit_resolution,[status(thm)],[616, 612])).
% 0.48/0.66 tff(618,plain,((~b(s(s(s(z))), s(elem!1))) | (~(s(s(s(s(elem!1)))) = s(s(elem!1)))) | (~b(s(s(s(z))), z)) | (~r(s(s(elem!1)), z)) | (~r(s(s(s(z))), s(z))) | (s(s(s(elem!1))) = s(s(s(s(elem!1))))) | (~r(s(z), s(s(s(z))))) | (~b(s(s(elem!1)), s(s(s(elem!1)))))), inference(lemma,lemma(discharge,[]))).
% 0.48/0.66 tff(619,plain,
% 0.48/0.66 (~b(s(s(s(z))), s(elem!1))),
% 0.48/0.66 inference(unit_resolution,[status(thm)],[618, 338, 255, 182, 348, 323, 377, 324])).
% 0.48/0.66 tff(620,assumption,(s(s(s(z))) = s(elem!1)), introduced(assumption)).
% 0.48/0.66 tff(621,plain,
% 0.48/0.66 (s(s(s(z))) = s(s(s(s(s(elem!1)))))),
% 0.48/0.66 inference(transitivity,[status(thm)],[620, 167, 259, 144, 479])).
% 0.48/0.66 tff(622,plain,
% 0.48/0.66 ($false),
% 0.48/0.66 inference(unit_resolution,[status(thm)],[317, 621])).
% 0.48/0.66 tff(623,plain,((~(s(s(s(z))) = s(elem!1))) | (~(s(s(s(s(elem!1)))) = s(s(elem!1))))), inference(lemma,lemma(discharge,[]))).
% 0.48/0.66 tff(624,plain,
% 0.48/0.66 (~(s(s(s(z))) = s(elem!1))),
% 0.48/0.66 inference(unit_resolution,[status(thm)],[623, 255])).
% 0.48/0.66 tff(625,plain,
% 0.48/0.66 (((~![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)))),
% 0.48/0.66 inference(rewrite,[status(thm)],[])).
% 0.48/0.66 tff(626,plain,
% 0.48/0.66 ((~![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)))),
% 0.48/0.66 inference(quant_inst,[status(thm)],[])).
% 0.48/0.66 tff(627,plain,
% 0.48/0.66 ((~![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))),
% 0.48/0.66 inference(modus_ponens,[status(thm)],[626, 625])).
% 0.48/0.66 tff(628,plain,
% 0.48/0.66 (r(s(s(s(z))), s(elem!1))),
% 0.48/0.66 inference(unit_resolution,[status(thm)],[627, 46, 624, 619])).
% 0.48/0.66 tff(629,assumption,(r(s(s(s(z))), s(elem!1))), introduced(assumption)).
% 0.48/0.66 tff(630,assumption,(r(s(z), s(elem!1))), introduced(assumption)).
% 0.48/0.66 tff(631,plain,
% 0.48/0.66 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(elem!1))) | (~r(s(s(s(z))), s(elem!1))) | (~r(s(s(s(z))), s(z))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(z), s(elem!1))) | (~r(s(s(s(z))), s(elem!1))) | (~r(s(s(s(z))), s(z))))),
% 0.48/0.66 inference(rewrite,[status(thm)],[])).
% 0.48/0.66 tff(632,plain,
% 0.48/0.66 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(elem!1))) | (~r(s(s(s(z))), s(elem!1))) | (~r(s(s(s(z))), s(z))))),
% 0.48/0.66 inference(quant_inst,[status(thm)],[])).
% 0.48/0.66 tff(633,plain,
% 0.48/0.66 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(z), s(elem!1))) | (~r(s(s(s(z))), s(elem!1))) | (~r(s(s(s(z))), s(z)))),
% 0.48/0.66 inference(modus_ponens,[status(thm)],[632, 631])).
% 0.48/0.66 tff(634,plain,
% 0.48/0.66 ($false),
% 0.48/0.66 inference(unit_resolution,[status(thm)],[633, 14, 283, 630, 629])).
% 0.48/0.66 tff(635,plain,((~r(s(s(s(z))), s(elem!1))) | (~r(s(s(s(z))), s(z))) | (~r(s(z), s(elem!1)))), inference(lemma,lemma(discharge,[]))).
% 0.48/0.66 tff(636,plain,
% 0.48/0.66 (~r(s(z), s(elem!1))),
% 0.48/0.66 inference(unit_resolution,[status(thm)],[635, 628, 348])).
% 0.48/0.66 tff(637,plain,
% 0.48/0.66 (r(s(z), s(elem!1)) <=> r(s(z), s(s(s(elem!1))))),
% 0.48/0.66 inference(monotonicity,[status(thm)],[260])).
% 0.48/0.66 tff(638,plain,
% 0.48/0.66 (r(s(z), s(s(s(elem!1)))) <=> r(s(z), s(elem!1))),
% 0.48/0.66 inference(symmetry,[status(thm)],[637])).
% 0.48/0.66 tff(639,plain,
% 0.48/0.66 (r(s(z), s(elem!1))),
% 0.48/0.66 inference(modus_ponens,[status(thm)],[213, 638])).
% 0.48/0.66 tff(640,assumption,(~r(s(z), s(elem!1))), introduced(assumption)).
% 0.48/0.66 tff(641,plain,
% 0.48/0.66 ($false),
% 0.48/0.66 inference(unit_resolution,[status(thm)],[640, 639])).
% 0.48/0.66 tff(642,plain,(r(s(z), s(elem!1)) | (~r(s(z), s(s(s(elem!1))))) | (~(s(s(s(s(elem!1)))) = s(s(elem!1))))), inference(lemma,lemma(discharge,[]))).
% 0.48/0.66 tff(643,plain,
% 0.48/0.66 (~r(s(z), s(s(s(elem!1))))),
% 0.48/0.66 inference(unit_resolution,[status(thm)],[642, 636, 255])).
% 0.48/0.66 tff(644,plain,
% 0.48/0.66 (b(s(z), s(s(s(elem!1))))),
% 0.48/0.66 inference(unit_resolution,[status(thm)],[235, 643])).
% 0.48/0.66 tff(645,assumption,(b(elem!1, s(s(s(elem!1))))), introduced(assumption)).
% 0.48/0.66 tff(646,assumption,(b(elem!1, s(z))), introduced(assumption)).
% 0.48/0.66 tff(647,plain,
% 0.48/0.66 (((~![X0: $i, X2: $i, X1: $i] : ((~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))))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~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))))))),
% 0.48/0.66 inference(rewrite,[status(thm)],[])).
% 0.48/0.66 tff(648,plain,
% 0.48/0.66 (((~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))))))),
% 0.48/0.66 inference(rewrite,[status(thm)],[])).
% 0.48/0.66 tff(649,plain,
% 0.48/0.66 (((~![X0: $i, X2: $i, X1: $i] : ((~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(z))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~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)))))))),
% 0.48/0.66 inference(monotonicity,[status(thm)],[648])).
% 0.48/0.66 tff(650,plain,
% 0.48/0.66 (((~![X0: $i, X2: $i, X1: $i] : ((~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(z))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~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))))))),
% 0.48/0.66 inference(transitivity,[status(thm)],[649, 647])).
% 0.48/0.66 tff(651,plain,
% 0.48/0.66 ((~![X0: $i, X2: $i, X1: $i] : ((~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(z))))),
% 0.48/0.66 inference(quant_inst,[status(thm)],[])).
% 0.48/0.66 tff(652,plain,
% 0.48/0.66 ((~![X0: $i, X2: $i, X1: $i] : ((~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(z))) | (~b(s(z), s(s(s(elem!1))))) | (~b(elem!1, s(s(s(elem!1)))))),
% 0.48/0.66 inference(modus_ponens,[status(thm)],[651, 650])).
% 0.48/0.66 tff(653,plain,
% 0.48/0.66 ($false),
% 0.48/0.66 inference(unit_resolution,[status(thm)],[652, 117, 646, 238, 645])).
% 0.48/0.66 tff(654,plain,((~b(elem!1, s(s(s(elem!1))))) | (~b(elem!1, s(z))) | (~b(s(z), s(s(s(elem!1)))))), inference(lemma,lemma(discharge,[]))).
% 0.48/0.66 tff(655,plain,
% 0.48/0.66 (~b(elem!1, s(z))),
% 0.48/0.66 inference(unit_resolution,[status(thm)],[654, 644, 360])).
% 0.48/0.66 tff(656,plain,
% 0.48/0.66 (((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((elem!1 = s(z)) | b(elem!1, s(z)) | r(elem!1, s(z)))) <=> ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (elem!1 = s(z)) | b(elem!1, s(z)) | r(elem!1, s(z)))),
% 0.48/0.66 inference(rewrite,[status(thm)],[])).
% 0.48/0.66 tff(657,plain,
% 0.48/0.66 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((elem!1 = s(z)) | b(elem!1, s(z)) | r(elem!1, s(z)))),
% 0.48/0.66 inference(quant_inst,[status(thm)],[])).
% 0.48/0.66 tff(658,plain,
% 0.48/0.66 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (elem!1 = s(z)) | b(elem!1, s(z)) | r(elem!1, s(z))),
% 0.48/0.66 inference(modus_ponens,[status(thm)],[657, 656])).
% 0.48/0.66 tff(659,plain,
% 0.48/0.66 ((elem!1 = s(z)) | b(elem!1, s(z)) | r(elem!1, s(z))),
% 0.48/0.66 inference(unit_resolution,[status(thm)],[658, 46])).
% 0.48/0.66 tff(660,plain,
% 0.48/0.66 (r(elem!1, s(z))),
% 0.48/0.66 inference(unit_resolution,[status(thm)],[659, 655, 357])).
% 0.48/0.66 tff(661,plain,
% 0.48/0.66 (r(s(s(elem!1)), s(z))),
% 0.48/0.66 inference(modus_ponens,[status(thm)],[660, 350])).
% 0.48/0.66 tff(662,plain,
% 0.48/0.66 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(elem!1)), s(z))) | (~r(s(s(s(z))), s(z))) | (~r(s(s(elem!1)), s(s(s(z))))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(elem!1)), s(z))) | (~r(s(s(s(z))), s(z))) | (~r(s(s(elem!1)), s(s(s(z))))))),
% 0.48/0.66 inference(rewrite,[status(thm)],[])).
% 0.48/0.66 tff(663,plain,
% 0.48/0.66 (((~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(s(s(z))), s(z))) | (~r(s(s(elem!1)), s(s(s(z))))))),
% 0.48/0.66 inference(rewrite,[status(thm)],[])).
% 0.48/0.66 tff(664,plain,
% 0.48/0.66 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(z))), s(z))) | (~r(s(s(elem!1)), s(z))) | (~r(s(s(elem!1)), s(s(s(z))))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(elem!1)), s(z))) | (~r(s(s(s(z))), s(z))) | (~r(s(s(elem!1)), s(s(s(z)))))))),
% 0.48/0.66 inference(monotonicity,[status(thm)],[663])).
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% 0.48/0.66 inference(transitivity,[status(thm)],[664, 662])).
% 0.48/0.66 tff(666,plain,
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% 0.48/0.66 inference(quant_inst,[status(thm)],[])).
% 0.48/0.66 tff(667,plain,
% 0.48/0.66 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(elem!1)), s(z))) | (~r(s(s(s(z))), s(z))) | (~r(s(s(elem!1)), s(s(s(z)))))),
% 0.48/0.66 inference(modus_ponens,[status(thm)],[666, 665])).
% 0.48/0.66 tff(668,plain,
% 0.48/0.66 (~r(s(s(elem!1)), s(s(s(z))))),
% 0.48/0.66 inference(unit_resolution,[status(thm)],[667, 14, 661, 348])).
% 0.48/0.66 tff(669,plain,
% 0.48/0.66 (~r(elem!1, s(s(s(z))))),
% 0.48/0.66 inference(modus_ponens,[status(thm)],[668, 337])).
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% 0.48/0.66 (b(elem!1, s(s(s(z))))),
% 0.48/0.66 inference(unit_resolution,[status(thm)],[400, 669, 335])).
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% 0.48/0.66 (b(s(s(elem!1)), s(s(s(z))))),
% 0.48/0.66 inference(modus_ponens,[status(thm)],[670, 330])).
% 0.48/0.66 tff(672,plain,
% 0.48/0.66 (r(z, s(elem!1)) <=> r(z, s(s(s(elem!1))))),
% 0.48/0.66 inference(monotonicity,[status(thm)],[260])).
% 0.48/0.66 tff(673,plain,
% 0.48/0.66 (r(z, s(s(s(elem!1)))) <=> r(z, s(elem!1))),
% 0.48/0.66 inference(symmetry,[status(thm)],[672])).
% 0.48/0.66 tff(674,assumption,(b(z, s(s(s(elem!1))))), introduced(assumption)).
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% 0.48/0.66 inference(rewrite,[status(thm)],[])).
% 0.48/0.66 tff(676,plain,
% 0.48/0.66 (((~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))))))),
% 0.48/0.66 inference(rewrite,[status(thm)],[])).
% 0.48/0.66 tff(677,plain,
% 0.48/0.66 (((~![X0: $i, X2: $i, X1: $i] : ((~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(z), z)))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(s(elem!1))))) | (~b(s(z), z)) | (~b(s(z), s(s(s(elem!1)))))))),
% 0.48/0.66 inference(monotonicity,[status(thm)],[676])).
% 0.48/0.66 tff(678,plain,
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% 0.48/0.66 inference(transitivity,[status(thm)],[677, 675])).
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% 0.48/0.67 inference(quant_inst,[status(thm)],[])).
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% 0.48/0.67 inference(modus_ponens,[status(thm)],[679, 678])).
% 0.48/0.67 tff(681,plain,
% 0.48/0.67 ($false),
% 0.48/0.67 inference(unit_resolution,[status(thm)],[680, 117, 674, 238, 237])).
% 0.48/0.67 tff(682,plain,((~b(z, s(s(s(elem!1))))) | (~b(s(z), s(s(s(elem!1))))) | (~b(s(z), z))), inference(lemma,lemma(discharge,[]))).
% 0.48/0.67 tff(683,plain,
% 0.48/0.67 (~b(z, s(s(s(elem!1))))),
% 0.48/0.67 inference(unit_resolution,[status(thm)],[682, 644, 237])).
% 0.48/0.67 tff(684,plain,
% 0.48/0.67 ((z = s(s(s(elem!1)))) <=> (s(s(s(elem!1))) = z)),
% 0.48/0.67 inference(commutativity,[status(thm)],[])).
% 0.48/0.67 tff(685,plain,
% 0.48/0.67 ((s(s(s(elem!1))) = z) <=> (z = s(s(s(elem!1))))),
% 0.48/0.67 inference(symmetry,[status(thm)],[684])).
% 0.48/0.67 tff(686,plain,
% 0.48/0.67 ((~(s(s(s(elem!1))) = z)) <=> (~(z = s(s(s(elem!1)))))),
% 0.48/0.67 inference(monotonicity,[status(thm)],[685])).
% 0.48/0.67 tff(687,plain,
% 0.48/0.67 (~(z = s(s(s(elem!1))))),
% 0.48/0.67 inference(modus_ponens,[status(thm)],[207, 686])).
% 0.48/0.67 tff(688,plain,
% 0.48/0.67 (((~![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)))))),
% 0.48/0.67 inference(rewrite,[status(thm)],[])).
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% 0.48/0.67 ((~![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)))))),
% 0.48/0.67 inference(quant_inst,[status(thm)],[])).
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% 0.48/0.67 inference(modus_ponens,[status(thm)],[689, 688])).
% 0.48/0.67 tff(691,plain,
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% 0.48/0.67 inference(unit_resolution,[status(thm)],[690, 46])).
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% 0.48/0.67 inference(unit_resolution,[status(thm)],[692, 683])).
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% 0.48/0.67 inference(rewrite,[status(thm)],[])).
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% 0.48/0.67 inference(rewrite,[status(thm)],[])).
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% 0.48/0.67 inference(monotonicity,[status(thm)],[696])).
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% 0.48/0.67 inference(quant_inst,[status(thm)],[])).
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% 0.48/0.67 inference(modus_ponens,[status(thm)],[699, 698])).
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% 0.48/0.67 inference(unit_resolution,[status(thm)],[700, 14, 628])).
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% 0.48/0.67 inference(commutativity,[status(thm)],[])).
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% 0.48/0.67 inference(symmetry,[status(thm)],[703])).
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% 0.48/0.67 ((~(s(s(s(z))) = z)) <=> (~(z = s(s(s(z)))))),
% 0.48/0.67 inference(monotonicity,[status(thm)],[704])).
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% 0.48/0.67 inference(rewrite,[status(thm)],[])).
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% 0.48/0.67 inference(quant_inst,[status(thm)],[])).
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% 0.48/0.67 inference(modus_ponens,[status(thm)],[708, 707])).
% 0.48/0.67 tff(710,plain,
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% 0.48/0.67 inference(unit_resolution,[status(thm)],[709, 46])).
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% 0.48/0.67 inference(unit_resolution,[status(thm)],[710, 706])).
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% 0.48/0.67 inference(rewrite,[status(thm)],[])).
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% 0.48/0.67 (((~b(s(s(elem!1)), s(s(s(z))))) | (~b(z, s(s(s(z))))) | (~b(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(z))))))),
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% 0.48/0.67 (((~![X0: $i, X2: $i, X1: $i] : ((~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), s(s(s(z))))) | (~b(z, s(s(s(z))))) | (~b(z, s(s(elem!1)))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~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)))))))),
% 0.48/0.67 inference(monotonicity,[status(thm)],[714])).
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% 0.48/0.67 inference(transitivity,[status(thm)],[715, 713])).
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% 0.48/0.67 inference(quant_inst,[status(thm)],[])).
% 0.48/0.67 tff(718,plain,
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% 0.48/0.67 inference(modus_ponens,[status(thm)],[717, 716])).
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% 0.48/0.67 inference(unit_resolution,[status(thm)],[718, 117, 712])).
% 0.48/0.67 tff(720,plain,
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% 0.48/0.67 inference(unit_resolution,[status(thm)],[719, 671])).
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% 0.48/0.67 inference(rewrite,[status(thm)],[])).
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% 0.48/0.67 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((z = s(s(elem!1))) | b(z, s(s(elem!1))) | r(z, s(s(elem!1))))),
% 0.48/0.67 inference(quant_inst,[status(thm)],[])).
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% 0.48/0.67 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (z = s(s(elem!1))) | b(z, s(s(elem!1))) | r(z, s(s(elem!1)))),
% 0.48/0.67 inference(modus_ponens,[status(thm)],[722, 721])).
% 0.48/0.67 tff(724,plain,
% 0.48/0.67 ((z = s(s(elem!1))) | r(z, s(s(elem!1)))),
% 0.48/0.67 inference(unit_resolution,[status(thm)],[723, 46, 720])).
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% 0.48/0.67 inference(unit_resolution,[status(thm)],[724, 328])).
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% 0.48/0.67 (b(s(z), s(elem!1)) <=> b(s(z), s(s(s(elem!1))))),
% 0.48/0.67 inference(monotonicity,[status(thm)],[260])).
% 0.48/0.67 tff(727,plain,
% 0.48/0.67 (b(s(z), s(s(s(elem!1)))) <=> b(s(z), s(elem!1))),
% 0.48/0.67 inference(symmetry,[status(thm)],[726])).
% 0.48/0.67 tff(728,plain,
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% 0.48/0.67 inference(modus_ponens,[status(thm)],[644, 727])).
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% 0.48/0.67 inference(rewrite,[status(thm)],[])).
% 0.48/0.67 tff(730,plain,
% 0.48/0.67 (((~b(s(s(elem!1)), s(elem!1))) | (~b(s(z), s(elem!1))) | (~b(s(z), s(s(elem!1))))) <=> ((~b(s(z), s(s(elem!1)))) | (~b(s(s(elem!1)), s(elem!1))) | (~b(s(z), s(elem!1))))),
% 0.48/0.67 inference(rewrite,[status(thm)],[])).
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% 0.48/0.67 inference(monotonicity,[status(thm)],[730])).
% 0.48/0.67 tff(732,plain,
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% 0.48/0.67 inference(transitivity,[status(thm)],[731, 729])).
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% 0.48/0.67 inference(quant_inst,[status(thm)],[])).
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% 0.48/0.67 inference(modus_ponens,[status(thm)],[733, 732])).
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% 0.48/0.67 inference(unit_resolution,[status(thm)],[734, 117])).
% 0.48/0.67 tff(736,plain,
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% 0.48/0.67 inference(unit_resolution,[status(thm)],[735, 386, 728])).
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% 0.48/0.67 inference(unit_resolution,[status(thm)],[416, 736])).
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% 0.48/0.67 inference(rewrite,[status(thm)],[])).
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% 0.48/0.67 (((~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(z))) | (~r(z, s(s(elem!1)))))),
% 0.48/0.67 inference(rewrite,[status(thm)],[])).
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% 0.48/0.67 inference(monotonicity,[status(thm)],[739])).
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% 0.48/0.67 inference(transitivity,[status(thm)],[740, 738])).
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% 0.48/0.67 inference(quant_inst,[status(thm)],[])).
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% 0.48/0.67 inference(modus_ponens,[status(thm)],[742, 741])).
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% 0.48/0.67 inference(unit_resolution,[status(thm)],[743, 14, 737, 725])).
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% 0.48/0.67 (b(s(s(s(elem!1))), s(z)) <=> b(s(elem!1), s(z))),
% 0.48/0.67 inference(symmetry,[status(thm)],[429])).
% 0.48/0.67 tff(747,plain,
% 0.48/0.67 ((~r(s(elem!1), s(z))) <=> (~r(s(s(s(elem!1))), s(z)))),
% 0.48/0.67 inference(monotonicity,[status(thm)],[427])).
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% 0.48/0.67 inference(rewrite,[status(thm)],[])).
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% 0.48/0.67 inference(quant_inst,[status(thm)],[])).
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% 0.48/0.67 inference(modus_ponens,[status(thm)],[749, 748])).
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% 0.48/0.67 inference(unit_resolution,[status(thm)],[750, 14, 661, 348])).
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% 0.48/0.67 inference(modus_ponens,[status(thm)],[751, 282])).
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% 0.48/0.67 inference(rewrite,[status(thm)],[])).
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% 0.48/0.67 inference(quant_inst,[status(thm)],[])).
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% 0.48/0.67 inference(modus_ponens,[status(thm)],[754, 753])).
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% 0.48/0.67 inference(rewrite,[status(thm)],[])).
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% 0.48/0.67 inference(monotonicity,[status(thm)],[769])).
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% 0.48/0.67 inference(transitivity,[status(thm)],[770, 768])).
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% 0.48/0.67 inference(unit_resolution,[status(thm)],[773, 117])).
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% 0.48/0.67 ((s(elem!1) = s(s(s(z)))) | r(s(elem!1), s(s(s(z))))),
% 0.48/0.67 inference(unit_resolution,[status(thm)],[493, 46, 775])).
% 0.48/0.67 tff(777,plain,
% 0.48/0.67 (r(s(elem!1), s(s(s(z))))),
% 0.48/0.67 inference(unit_resolution,[status(thm)],[776, 485])).
% 0.48/0.67 tff(778,plain,
% 0.48/0.67 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(elem!1), s(z))) | (~r(s(z), s(s(s(z))))) | (~r(s(elem!1), s(s(s(z))))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(elem!1), s(z))) | (~r(s(z), s(s(s(z))))) | (~r(s(elem!1), s(s(s(z))))))),
% 0.48/0.68 inference(rewrite,[status(thm)],[])).
% 0.48/0.68 tff(779,plain,
% 0.48/0.68 (((~r(s(z), s(s(s(z))))) | (~r(s(elem!1), s(s(s(z))))) | (~r(s(elem!1), s(z)))) <=> ((~r(s(elem!1), s(z))) | (~r(s(z), s(s(s(z))))) | (~r(s(elem!1), s(s(s(z))))))),
% 0.48/0.68 inference(rewrite,[status(thm)],[])).
% 0.48/0.68 tff(780,plain,
% 0.48/0.68 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(s(s(z))))) | (~r(s(elem!1), s(s(s(z))))) | (~r(s(elem!1), s(z))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(elem!1), s(z))) | (~r(s(z), s(s(s(z))))) | (~r(s(elem!1), s(s(s(z)))))))),
% 0.48/0.68 inference(monotonicity,[status(thm)],[779])).
% 0.48/0.68 tff(781,plain,
% 0.48/0.68 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(s(s(z))))) | (~r(s(elem!1), s(s(s(z))))) | (~r(s(elem!1), s(z))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(elem!1), s(z))) | (~r(s(z), s(s(s(z))))) | (~r(s(elem!1), s(s(s(z))))))),
% 0.48/0.68 inference(transitivity,[status(thm)],[780, 778])).
% 0.48/0.68 tff(782,plain,
% 0.48/0.68 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(s(s(z))))) | (~r(s(elem!1), s(s(s(z))))) | (~r(s(elem!1), s(z))))),
% 0.48/0.68 inference(quant_inst,[status(thm)],[])).
% 0.48/0.68 tff(783,plain,
% 0.48/0.68 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(elem!1), s(z))) | (~r(s(z), s(s(s(z))))) | (~r(s(elem!1), s(s(s(z)))))),
% 0.48/0.68 inference(modus_ponens,[status(thm)],[782, 781])).
% 0.48/0.68 tff(784,plain,
% 0.48/0.68 (~r(s(elem!1), s(z))),
% 0.48/0.68 inference(unit_resolution,[status(thm)],[783, 14, 377, 777])).
% 0.48/0.68 tff(785,plain,
% 0.48/0.68 (~r(s(s(s(elem!1))), s(z))),
% 0.48/0.68 inference(modus_ponens,[status(thm)],[784, 747])).
% 0.48/0.68 tff(786,plain,
% 0.48/0.68 (b(s(s(s(elem!1))), s(z))),
% 0.48/0.68 inference(unit_resolution,[status(thm)],[467, 785])).
% 0.48/0.68 tff(787,plain,
% 0.48/0.68 (b(s(elem!1), s(z))),
% 0.48/0.68 inference(modus_ponens,[status(thm)],[786, 746])).
% 0.48/0.68 tff(788,assumption,(b(s(elem!1), s(z))), introduced(assumption)).
% 0.48/0.68 tff(789,plain,
% 0.48/0.68 (((~![X0: $i, X2: $i, X1: $i] : ((~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), s(z))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(s(z)))), s(elem!1))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(elem!1), s(z))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(s(z)))), s(elem!1))))),
% 0.48/0.68 inference(rewrite,[status(thm)],[])).
% 0.48/0.68 tff(790,plain,
% 0.48/0.68 ((~![X0: $i, X2: $i, X1: $i] : ((~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), s(z))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(s(z)))), s(elem!1))))),
% 0.48/0.68 inference(quant_inst,[status(thm)],[])).
% 0.48/0.68 tff(791,plain,
% 0.48/0.68 ((~![X0: $i, X2: $i, X1: $i] : ((~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(elem!1), s(z))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(s(z)))), s(elem!1)))),
% 0.48/0.68 inference(modus_ponens,[status(thm)],[790, 789])).
% 0.48/0.68 tff(792,plain,
% 0.48/0.68 (~b(s(s(s(s(z)))), s(elem!1))),
% 0.48/0.68 inference(unit_resolution,[status(thm)],[791, 117, 562, 788])).
% 0.48/0.68 tff(793,plain,
% 0.48/0.68 (r(s(s(s(s(z)))), s(elem!1))),
% 0.48/0.68 inference(unit_resolution,[status(thm)],[504, 46, 501, 792])).
% 0.48/0.68 tff(794,plain,
% 0.48/0.68 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(elem!1), z)) | (~r(s(s(s(s(z)))), z)) | (~r(s(s(s(s(z)))), s(elem!1))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(elem!1), z)) | (~r(s(s(s(s(z)))), z)) | (~r(s(s(s(s(z)))), s(elem!1))))),
% 0.48/0.68 inference(rewrite,[status(thm)],[])).
% 0.48/0.68 tff(795,plain,
% 0.48/0.68 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(elem!1), z)) | (~r(s(s(s(s(z)))), z)) | (~r(s(s(s(s(z)))), s(elem!1))))),
% 0.48/0.68 inference(quant_inst,[status(thm)],[])).
% 0.48/0.68 tff(796,plain,
% 0.48/0.68 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(elem!1), z)) | (~r(s(s(s(s(z)))), z)) | (~r(s(s(s(s(z)))), s(elem!1)))),
% 0.48/0.68 inference(modus_ponens,[status(thm)],[795, 794])).
% 0.48/0.68 tff(797,plain,
% 0.48/0.68 ($false),
% 0.48/0.68 inference(unit_resolution,[status(thm)],[796, 14, 583, 439, 793])).
% 0.48/0.68 tff(798,plain,((~b(s(s(s(s(z)))), s(z))) | (~r(s(elem!1), z)) | (s(s(s(s(z)))) = s(elem!1)) | (~b(s(elem!1), s(z))) | (~b(z, s(z)))), inference(lemma,lemma(discharge,[]))).
% 0.48/0.68 tff(799,plain,
% 0.48/0.68 (~b(s(s(s(s(z)))), s(z))),
% 0.48/0.68 inference(unit_resolution,[status(thm)],[798, 762, 477, 787, 745])).
% 0.48/0.68 tff(800,plain,
% 0.48/0.68 (r(s(s(s(s(z)))), s(z))),
% 0.48/0.68 inference(unit_resolution,[status(thm)],[554, 799])).
% 0.48/0.68 tff(801,plain,
% 0.48/0.68 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(elem!1)), s(z))) | (~r(s(s(s(s(z)))), s(z))) | (~r(s(s(s(s(z)))), s(s(elem!1)))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(elem!1)), s(z))) | (~r(s(s(s(s(z)))), s(z))) | (~r(s(s(s(s(z)))), s(s(elem!1)))))),
% 0.48/0.68 inference(rewrite,[status(thm)],[])).
% 0.48/0.68 tff(802,plain,
% 0.48/0.68 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(elem!1)), s(z))) | (~r(s(s(s(s(z)))), s(z))) | (~r(s(s(s(s(z)))), s(s(elem!1)))))),
% 0.48/0.68 inference(quant_inst,[status(thm)],[])).
% 0.48/0.68 tff(803,plain,
% 0.48/0.68 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(elem!1)), s(z))) | (~r(s(s(s(s(z)))), s(z))) | (~r(s(s(s(s(z)))), s(s(elem!1))))),
% 0.48/0.68 inference(modus_ponens,[status(thm)],[802, 801])).
% 0.48/0.68 tff(804,plain,
% 0.48/0.68 (~r(s(s(s(s(z)))), s(s(elem!1)))),
% 0.48/0.68 inference(unit_resolution,[status(thm)],[803, 14, 661, 800])).
% 0.48/0.68 tff(805,plain,
% 0.48/0.68 (~r(s(s(s(s(z)))), elem!1)),
% 0.48/0.68 inference(modus_ponens,[status(thm)],[804, 322])).
% 0.48/0.68 tff(806,plain,
% 0.48/0.68 (b(s(s(s(s(z)))), elem!1)),
% 0.48/0.68 inference(unit_resolution,[status(thm)],[571, 805, 320])).
% 0.48/0.68 tff(807,plain,
% 0.48/0.68 (b(s(s(s(s(z)))), s(s(elem!1)))),
% 0.48/0.68 inference(modus_ponens,[status(thm)],[806, 292])).
% 0.48/0.68 tff(808,plain,
% 0.48/0.68 (~r(s(s(s(s(z)))), s(s(s(z))))),
% 0.48/0.68 inference(unit_resolution,[status(thm)],[509, 14, 800, 348])).
% 0.48/0.68 tff(809,plain,
% 0.48/0.68 (b(s(s(s(s(z)))), s(s(s(z))))),
% 0.48/0.68 inference(unit_resolution,[status(thm)],[529, 808])).
% 0.48/0.68 tff(810,plain,
% 0.48/0.68 (((~![X0: $i, X2: $i, X1: $i] : ((~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(elem!1)), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(elem!1)))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(elem!1)), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(elem!1)))))),
% 0.48/0.68 inference(rewrite,[status(thm)],[])).
% 0.48/0.68 tff(811,plain,
% 0.48/0.68 (((~b(s(s(elem!1)), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(elem!1))))) <=> ((~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(elem!1)), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(elem!1)))))),
% 0.48/0.68 inference(rewrite,[status(thm)],[])).
% 0.48/0.68 tff(812,plain,
% 0.48/0.68 (((~![X0: $i, X2: $i, X1: $i] : ((~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(elem!1)))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(elem!1)), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(elem!1))))))),
% 0.48/0.68 inference(monotonicity,[status(thm)],[811])).
% 0.48/0.68 tff(813,plain,
% 0.48/0.68 (((~![X0: $i, X2: $i, X1: $i] : ((~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(elem!1)))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(elem!1)), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(elem!1)))))),
% 0.48/0.68 inference(transitivity,[status(thm)],[812, 810])).
% 0.48/0.68 tff(814,plain,
% 0.48/0.68 ((~![X0: $i, X2: $i, X1: $i] : ((~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(elem!1)))))),
% 0.48/0.68 inference(quant_inst,[status(thm)],[])).
% 0.48/0.68 tff(815,plain,
% 0.48/0.68 ((~![X0: $i, X2: $i, X1: $i] : ((~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(elem!1)), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(elem!1))))),
% 0.48/0.68 inference(modus_ponens,[status(thm)],[814, 813])).
% 0.48/0.68 tff(816,plain,
% 0.48/0.68 (~b(s(s(s(s(z)))), s(s(elem!1)))),
% 0.48/0.68 inference(unit_resolution,[status(thm)],[815, 117, 809, 671])).
% 0.48/0.68 tff(817,plain,
% 0.48/0.68 ($false),
% 0.48/0.68 inference(unit_resolution,[status(thm)],[816, 807])).
% 0.48/0.68 tff(818,plain,((~b(s(s(s(z))), z)) | (~(s(s(s(s(elem!1)))) = s(s(elem!1)))) | (s(s(s(elem!1))) = s(s(s(s(elem!1))))) | (~b(s(s(elem!1)), s(s(s(elem!1))))) | (~r(s(s(elem!1)), z)) | (~b(s(z), z))), inference(lemma,lemma(discharge,[]))).
% 0.48/0.68 tff(819,plain,
% 0.48/0.68 (~b(s(s(s(z))), z)),
% 0.48/0.68 inference(unit_resolution,[status(thm)],[818, 324, 323, 255, 182, 237])).
% 0.48/0.68 tff(820,plain,
% 0.48/0.68 (((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((s(s(s(z))) = z) | b(s(s(s(z))), z) | r(s(s(s(z))), z))) <=> ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (s(s(s(z))) = z) | b(s(s(s(z))), z) | r(s(s(s(z))), z))),
% 0.48/0.68 inference(rewrite,[status(thm)],[])).
% 0.48/0.68 tff(821,plain,
% 0.48/0.68 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((s(s(s(z))) = z) | b(s(s(s(z))), z) | r(s(s(s(z))), z))),
% 0.48/0.68 inference(quant_inst,[status(thm)],[])).
% 0.48/0.68 tff(822,plain,
% 0.48/0.68 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (s(s(s(z))) = z) | b(s(s(s(z))), z) | r(s(s(s(z))), z)),
% 0.48/0.68 inference(modus_ponens,[status(thm)],[821, 820])).
% 0.48/0.68 tff(823,plain,
% 0.48/0.68 (b(s(s(s(z))), z) | r(s(s(s(z))), z)),
% 0.48/0.68 inference(unit_resolution,[status(thm)],[822, 46, 522])).
% 0.48/0.68 tff(824,plain,
% 0.48/0.68 (r(s(s(s(z))), z)),
% 0.48/0.68 inference(unit_resolution,[status(thm)],[823, 819])).
% 0.48/0.68 tff(825,plain,
% 0.48/0.68 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(elem!1)), z)) | (~r(s(s(s(z))), z)) | (~r(s(s(s(z))), s(s(elem!1)))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(elem!1)), z)) | (~r(s(s(s(z))), z)) | (~r(s(s(s(z))), s(s(elem!1)))))),
% 0.48/0.68 inference(rewrite,[status(thm)],[])).
% 0.48/0.68 tff(826,plain,
% 0.48/0.68 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(elem!1)), z)) | (~r(s(s(s(z))), z)) | (~r(s(s(s(z))), s(s(elem!1)))))),
% 0.48/0.68 inference(quant_inst,[status(thm)],[])).
% 0.48/0.68 tff(827,plain,
% 0.48/0.68 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(elem!1)), z)) | (~r(s(s(s(z))), z)) | (~r(s(s(s(z))), s(s(elem!1))))),
% 0.48/0.68 inference(modus_ponens,[status(thm)],[826, 825])).
% 0.48/0.68 tff(828,plain,
% 0.48/0.68 (~r(s(s(s(z))), s(s(elem!1)))),
% 0.48/0.68 inference(unit_resolution,[status(thm)],[827, 14, 182, 824])).
% 0.48/0.68 tff(829,plain,
% 0.48/0.68 (~r(s(s(s(z))), elem!1)),
% 0.48/0.68 inference(modus_ponens,[status(thm)],[828, 282])).
% 0.48/0.68 tff(830,plain,
% 0.48/0.68 (b(s(s(s(z))), elem!1)),
% 0.48/0.68 inference(unit_resolution,[status(thm)],[756, 829, 280])).
% 0.48/0.68 tff(831,plain,
% 0.48/0.68 (b(s(s(s(z))), s(s(elem!1)))),
% 0.48/0.68 inference(modus_ponens,[status(thm)],[830, 269])).
% 0.48/0.68 tff(832,assumption,(~b(s(s(elem!1)), s(elem!1))), introduced(assumption)).
% 0.48/0.68 tff(833,plain,
% 0.48/0.68 ($false),
% 0.48/0.68 inference(unit_resolution,[status(thm)],[832, 386])).
% 0.48/0.68 tff(834,plain,(b(s(s(elem!1)), s(elem!1)) | (~b(s(s(elem!1)), s(s(s(elem!1))))) | (~(s(s(s(s(elem!1)))) = s(s(elem!1))))), inference(lemma,lemma(discharge,[]))).
% 0.48/0.68 tff(835,plain,
% 0.48/0.68 (b(s(s(elem!1)), s(elem!1))),
% 0.48/0.68 inference(unit_resolution,[status(thm)],[834, 324, 255])).
% 0.48/0.68 tff(836,assumption,(b(s(s(elem!1)), s(elem!1))), introduced(assumption)).
% 0.48/0.68 tff(837,assumption,(b(s(s(s(z))), s(s(elem!1)))), introduced(assumption)).
% 0.48/0.68 tff(838,plain,
% 0.48/0.68 (((~![X0: $i, X2: $i, X1: $i] : ((~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), s(elem!1))) | (~b(s(s(s(z))), s(elem!1))) | (~b(s(s(s(z))), s(s(elem!1)))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(elem!1)), s(elem!1))) | (~b(s(s(s(z))), s(elem!1))) | (~b(s(s(s(z))), s(s(elem!1)))))),
% 0.48/0.68 inference(rewrite,[status(thm)],[])).
% 0.48/0.68 tff(839,plain,
% 0.48/0.68 ((~![X0: $i, X2: $i, X1: $i] : ((~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), s(elem!1))) | (~b(s(s(s(z))), s(elem!1))) | (~b(s(s(s(z))), s(s(elem!1)))))),
% 0.48/0.68 inference(quant_inst,[status(thm)],[])).
% 0.48/0.68 tff(840,plain,
% 0.48/0.68 ((~![X0: $i, X2: $i, X1: $i] : ((~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(elem!1)), s(elem!1))) | (~b(s(s(s(z))), s(elem!1))) | (~b(s(s(s(z))), s(s(elem!1))))),
% 0.48/0.68 inference(modus_ponens,[status(thm)],[839, 838])).
% 0.48/0.68 tff(841,plain,
% 0.48/0.68 ($false),
% 0.48/0.68 inference(unit_resolution,[status(thm)],[840, 117, 387, 837, 836])).
% 0.48/0.68 tff(842,plain,((~b(s(s(s(z))), s(elem!1))) | (~b(s(s(s(z))), s(s(elem!1)))) | (~b(s(s(elem!1)), s(elem!1)))), inference(lemma,lemma(discharge,[]))).
% 0.48/0.68 tff(843,plain,
% 0.48/0.68 (~b(s(s(s(z))), s(elem!1))),
% 0.48/0.68 inference(unit_resolution,[status(thm)],[842, 831, 835])).
% 0.48/0.68 tff(844,plain,
% 0.48/0.68 (r(s(s(s(z))), s(elem!1))),
% 0.48/0.68 inference(unit_resolution,[status(thm)],[627, 46, 624, 843])).
% 0.48/0.68 tff(845,plain,
% 0.48/0.68 (b(elem!1, s(z)) <=> b(s(s(elem!1)), s(z))),
% 0.48/0.68 inference(monotonicity,[status(thm)],[349])).
% 0.48/0.68 tff(846,plain,
% 0.48/0.68 (b(s(s(elem!1)), s(z)) <=> b(elem!1, s(z))),
% 0.48/0.68 inference(symmetry,[status(thm)],[845])).
% 0.48/0.68 tff(847,plain,
% 0.48/0.68 (b(elem!1, s(z))),
% 0.48/0.68 inference(modus_ponens,[status(thm)],[470, 846])).
% 0.48/0.68 tff(848,assumption,(b(s(s(s(z))), s(z))), introduced(assumption)).
% 0.48/0.68 tff(849,plain,
% 0.48/0.68 (((~![X0: $i, X2: $i, X1: $i] : ((~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~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, X2: $i, X1: $i] : ((~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(elem!1)), s(z))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(z))), s(s(elem!1)))))),
% 0.48/0.68 inference(rewrite,[status(thm)],[])).
% 0.48/0.68 tff(850,plain,
% 0.48/0.68 ((~![X0: $i, X2: $i, X1: $i] : ((~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), s(z))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(z))), s(s(elem!1)))))),
% 0.48/0.68 inference(quant_inst,[status(thm)],[])).
% 0.48/0.68 tff(851,plain,
% 0.48/0.68 ((~![X0: $i, X2: $i, X1: $i] : ((~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(elem!1)), s(z))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(z))), s(s(elem!1))))),
% 0.48/0.68 inference(modus_ponens,[status(thm)],[850, 849])).
% 0.48/0.68 tff(852,plain,
% 0.48/0.68 ($false),
% 0.48/0.68 inference(unit_resolution,[status(thm)],[851, 117, 470, 848, 837])).
% 0.48/0.68 tff(853,plain,((~b(s(s(elem!1)), s(z))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(z))), s(s(elem!1))))), inference(lemma,lemma(discharge,[]))).
% 0.48/0.68 tff(854,plain,
% 0.48/0.68 (~b(s(s(s(z))), s(z))),
% 0.48/0.68 inference(unit_resolution,[status(thm)],[853, 470, 837])).
% 0.48/0.68 tff(855,plain,
% 0.48/0.68 (r(s(s(s(z))), s(z))),
% 0.48/0.68 inference(unit_resolution,[status(thm)],[347, 854])).
% 0.48/0.68 tff(856,plain,
% 0.48/0.68 (~r(s(z), s(elem!1))),
% 0.48/0.68 inference(unit_resolution,[status(thm)],[635, 855, 629])).
% 0.48/0.68 tff(857,plain,
% 0.48/0.68 (~r(s(z), s(s(s(elem!1))))),
% 0.48/0.68 inference(unit_resolution,[status(thm)],[642, 856, 255])).
% 0.48/0.68 tff(858,plain,
% 0.48/0.68 (b(s(z), s(s(s(elem!1))))),
% 0.48/0.68 inference(unit_resolution,[status(thm)],[235, 857])).
% 0.48/0.68 tff(859,plain,
% 0.48/0.68 (~b(elem!1, s(z))),
% 0.48/0.68 inference(unit_resolution,[status(thm)],[654, 858, 645])).
% 0.48/0.68 tff(860,plain,
% 0.48/0.68 ($false),
% 0.48/0.68 inference(unit_resolution,[status(thm)],[859, 847])).
% 0.48/0.68 tff(861,plain,((~b(s(s(elem!1)), s(z))) | (~b(elem!1, s(s(s(elem!1))))) | (~(s(s(s(s(elem!1)))) = s(s(elem!1)))) | (~r(s(s(s(z))), s(elem!1))) | (~b(s(s(s(z))), s(s(elem!1))))), inference(lemma,lemma(discharge,[]))).
% 0.48/0.68 tff(862,plain,
% 0.48/0.68 (~b(s(s(elem!1)), s(z))),
% 0.48/0.68 inference(unit_resolution,[status(thm)],[861, 360, 255, 844, 831])).
% 0.48/0.68 tff(863,plain,
% 0.48/0.68 (r(s(s(elem!1)), s(z))),
% 0.48/0.68 inference(unit_resolution,[status(thm)],[178, 862])).
% 0.48/0.68 tff(864,plain,
% 0.48/0.68 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(z))) | (~r(s(s(elem!1)), s(z))) | (~r(s(s(elem!1)), z)))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, s(z))) | (~r(s(s(elem!1)), s(z))) | (~r(s(s(elem!1)), z)))),
% 0.48/0.68 inference(rewrite,[status(thm)],[])).
% 0.48/0.68 tff(865,plain,
% 0.48/0.68 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(z))) | (~r(s(s(elem!1)), s(z))) | (~r(s(s(elem!1)), z)))),
% 0.48/0.68 inference(quant_inst,[status(thm)],[])).
% 0.48/0.68 tff(866,plain,
% 0.48/0.68 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, s(z))) | (~r(s(s(elem!1)), s(z))) | (~r(s(s(elem!1)), z))),
% 0.48/0.68 inference(modus_ponens,[status(thm)],[865, 864])).
% 0.48/0.68 tff(867,plain,
% 0.48/0.68 ($false),
% 0.48/0.68 inference(unit_resolution,[status(thm)],[866, 14, 181, 182, 2])).
% 0.48/0.68 tff(868,plain,((~r(s(s(elem!1)), s(z))) | (~r(s(s(elem!1)), z)) | (~r(z, s(z)))), inference(lemma,lemma(discharge,[]))).
% 0.48/0.68 tff(869,plain,
% 0.48/0.68 (~r(z, s(z))),
% 0.48/0.68 inference(unit_resolution,[status(thm)],[868, 863, 182])).
% 0.48/0.68 tff(870,plain,
% 0.48/0.68 (b(z, s(z))),
% 0.48/0.68 inference(unit_resolution,[status(thm)],[599, 869])).
% 0.48/0.68 tff(871,plain,
% 0.48/0.68 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(elem!1), z)) | (~r(s(s(s(z))), z)) | (~r(s(s(s(z))), s(elem!1))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(elem!1), z)) | (~r(s(s(s(z))), z)) | (~r(s(s(s(z))), s(elem!1))))),
% 0.48/0.68 inference(rewrite,[status(thm)],[])).
% 0.48/0.68 tff(872,plain,
% 0.48/0.68 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(elem!1), z)) | (~r(s(s(s(z))), z)) | (~r(s(s(s(z))), s(elem!1))))),
% 0.48/0.68 inference(quant_inst,[status(thm)],[])).
% 0.48/0.68 tff(873,plain,
% 0.48/0.68 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(elem!1), z)) | (~r(s(s(s(z))), z)) | (~r(s(s(s(z))), s(elem!1)))),
% 0.48/0.68 inference(modus_ponens,[status(thm)],[872, 871])).
% 0.48/0.68 tff(874,plain,
% 0.48/0.68 ($false),
% 0.48/0.68 inference(unit_resolution,[status(thm)],[873, 14, 180, 439, 629])).
% 0.48/0.68 tff(875,plain,((~r(s(elem!1), z)) | (~r(s(s(s(z))), z)) | (~r(s(s(s(z))), s(elem!1)))), inference(lemma,lemma(discharge,[]))).
% 0.48/0.68 tff(876,plain,
% 0.48/0.68 (~r(s(elem!1), z)),
% 0.48/0.68 inference(unit_resolution,[status(thm)],[875, 824, 844])).
% 0.48/0.68 tff(877,plain,
% 0.48/0.68 (r(s(elem!1), z)),
% 0.48/0.68 inference(modus_ponens,[status(thm)],[196, 759])).
% 0.48/0.68 tff(878,assumption,(~r(s(elem!1), z)), introduced(assumption)).
% 0.48/0.68 tff(879,plain,
% 0.48/0.68 ($false),
% 0.48/0.68 inference(unit_resolution,[status(thm)],[878, 877])).
% 0.48/0.68 tff(880,plain,((~r(s(s(s(elem!1))), z)) | r(s(elem!1), z) | (~(s(s(s(s(elem!1)))) = s(s(elem!1))))), inference(lemma,lemma(discharge,[]))).
% 0.48/0.68 tff(881,plain,
% 0.48/0.68 (~r(s(s(s(elem!1))), z)),
% 0.48/0.68 inference(unit_resolution,[status(thm)],[880, 876, 255])).
% 0.48/0.68 tff(882,plain,
% 0.48/0.68 (b(s(s(s(elem!1))), z)),
% 0.48/0.68 inference(unit_resolution,[status(thm)],[211, 881])).
% 0.48/0.68 tff(883,plain,
% 0.48/0.68 (~b(s(z), s(s(s(elem!1))))),
% 0.48/0.68 inference(unit_resolution,[status(thm)],[246, 882, 237])).
% 0.48/0.68 tff(884,plain,
% 0.48/0.68 (r(s(z), s(s(s(elem!1))))),
% 0.48/0.68 inference(unit_resolution,[status(thm)],[235, 883])).
% 0.48/0.68 tff(885,plain,
% 0.48/0.68 (r(s(z), s(elem!1))),
% 0.48/0.68 inference(unit_resolution,[status(thm)],[642, 884, 255])).
% 0.48/0.68 tff(886,plain,
% 0.48/0.68 (~r(s(s(s(z))), s(z))),
% 0.48/0.68 inference(unit_resolution,[status(thm)],[635, 885, 844])).
% 0.48/0.68 tff(887,plain,
% 0.48/0.68 (b(s(s(s(z))), s(z))),
% 0.48/0.68 inference(unit_resolution,[status(thm)],[347, 886])).
% 0.48/0.68 tff(888,plain,
% 0.48/0.68 (((~![X0: $i, X2: $i, X1: $i] : ((~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), s(z))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(s(z)))), s(s(s(z))))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(s(z)))), s(s(s(z))))))),
% 0.48/0.68 inference(rewrite,[status(thm)],[])).
% 0.48/0.68 tff(889,plain,
% 0.48/0.68 ((~![X0: $i, X2: $i, X1: $i] : ((~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), s(z))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(s(z)))), s(s(s(z))))))),
% 0.48/0.68 inference(quant_inst,[status(thm)],[])).
% 0.48/0.68 tff(890,plain,
% 0.48/0.68 ((~![X0: $i, X2: $i, X1: $i] : ((~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(s(z)))), s(s(s(z)))))),
% 0.48/0.68 inference(modus_ponens,[status(thm)],[889, 888])).
% 0.48/0.68 tff(891,plain,
% 0.48/0.68 (~b(s(s(s(s(z)))), s(s(s(z))))),
% 0.48/0.68 inference(unit_resolution,[status(thm)],[890, 117, 562, 848])).
% 0.48/0.68 tff(892,plain,
% 0.48/0.68 (r(s(s(s(s(z)))), s(s(s(z))))),
% 0.48/0.68 inference(unit_resolution,[status(thm)],[529, 891])).
% 0.48/0.68 tff(893,plain,
% 0.48/0.68 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(z))), z)) | (~r(s(s(s(s(z)))), z)) | (~r(s(s(s(s(z)))), s(s(s(z))))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(z))), z)) | (~r(s(s(s(s(z)))), z)) | (~r(s(s(s(s(z)))), s(s(s(z))))))),
% 0.48/0.68 inference(rewrite,[status(thm)],[])).
% 0.48/0.68 tff(894,plain,
% 0.48/0.68 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(z))), z)) | (~r(s(s(s(s(z)))), z)) | (~r(s(s(s(s(z)))), s(s(s(z))))))),
% 0.48/0.68 inference(quant_inst,[status(thm)],[])).
% 0.48/0.68 tff(895,plain,
% 0.48/0.68 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(z))), z)) | (~r(s(s(s(s(z)))), z)) | (~r(s(s(s(s(z)))), s(s(s(z)))))),
% 0.48/0.68 inference(modus_ponens,[status(thm)],[894, 893])).
% 0.48/0.68 tff(896,plain,
% 0.48/0.68 ($false),
% 0.48/0.68 inference(unit_resolution,[status(thm)],[895, 14, 892, 180, 583])).
% 0.48/0.68 tff(897,plain,((~b(s(s(s(s(z)))), s(z))) | (~r(s(s(s(z))), z)) | (~b(s(s(s(z))), s(z))) | (~b(z, s(z)))), inference(lemma,lemma(discharge,[]))).
% 0.48/0.68 tff(898,plain,
% 0.48/0.68 (~b(s(s(s(s(z)))), s(z))),
% 0.48/0.68 inference(unit_resolution,[status(thm)],[897, 887, 824, 870])).
% 0.48/0.68 tff(899,plain,
% 0.48/0.68 (r(s(s(s(s(z)))), s(z))),
% 0.48/0.68 inference(unit_resolution,[status(thm)],[554, 898])).
% 0.48/0.68 tff(900,plain,
% 0.48/0.68 (~r(s(s(s(s(z)))), s(s(elem!1)))),
% 0.48/0.68 inference(unit_resolution,[status(thm)],[803, 14, 863, 899])).
% 0.48/0.69 tff(901,plain,
% 0.48/0.69 (~r(s(s(s(s(z)))), elem!1)),
% 0.48/0.69 inference(modus_ponens,[status(thm)],[900, 322])).
% 0.48/0.69 tff(902,plain,
% 0.48/0.69 (b(s(s(s(s(z)))), elem!1)),
% 0.48/0.69 inference(unit_resolution,[status(thm)],[571, 901, 320])).
% 0.48/0.69 tff(903,plain,
% 0.48/0.69 (b(s(s(s(s(z)))), s(s(elem!1)))),
% 0.48/0.69 inference(modus_ponens,[status(thm)],[902, 292])).
% 0.48/0.69 tff(904,plain,
% 0.48/0.69 (b(s(elem!1), z)),
% 0.48/0.69 inference(modus_ponens,[status(thm)],[157, 379])).
% 0.48/0.69 tff(905,assumption,(b(s(s(s(s(z)))), z)), introduced(assumption)).
% 0.48/0.69 tff(906,plain,
% 0.48/0.69 (((~![X0: $i, X2: $i, X1: $i] : ((~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), z)) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(s(z)))), s(elem!1))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(elem!1), z)) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(s(z)))), s(elem!1))))),
% 0.48/0.69 inference(rewrite,[status(thm)],[])).
% 0.48/0.69 tff(907,plain,
% 0.48/0.69 ((~![X0: $i, X2: $i, X1: $i] : ((~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), z)) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(s(z)))), s(elem!1))))),
% 0.48/0.69 inference(quant_inst,[status(thm)],[])).
% 0.48/0.69 tff(908,plain,
% 0.48/0.69 ((~![X0: $i, X2: $i, X1: $i] : ((~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(elem!1), z)) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(s(z)))), s(elem!1)))),
% 0.48/0.69 inference(modus_ponens,[status(thm)],[907, 906])).
% 0.48/0.69 tff(909,plain,
% 0.48/0.69 ((~b(s(elem!1), z)) | (~b(s(s(s(s(z)))), s(elem!1)))),
% 0.48/0.69 inference(unit_resolution,[status(thm)],[908, 117, 905])).
% 0.48/0.69 tff(910,plain,
% 0.48/0.69 (~b(s(s(s(s(z)))), s(elem!1))),
% 0.48/0.69 inference(unit_resolution,[status(thm)],[909, 904])).
% 0.48/0.69 tff(911,plain,
% 0.48/0.69 (r(s(s(s(s(z)))), s(elem!1))),
% 0.48/0.69 inference(unit_resolution,[status(thm)],[504, 46, 477, 910])).
% 0.48/0.69 tff(912,plain,
% 0.48/0.69 (~b(s(z), s(s(s(elem!1))))),
% 0.48/0.69 inference(unit_resolution,[status(thm)],[246, 157, 237])).
% 0.48/0.69 tff(913,plain,
% 0.48/0.69 (r(s(z), s(s(s(elem!1))))),
% 0.48/0.69 inference(unit_resolution,[status(thm)],[235, 912])).
% 0.48/0.69 tff(914,plain,
% 0.48/0.69 (r(s(z), s(elem!1))),
% 0.48/0.69 inference(unit_resolution,[status(thm)],[642, 913, 255])).
% 0.48/0.69 tff(915,plain,
% 0.48/0.69 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(elem!1))) | (~r(s(s(s(s(z)))), s(elem!1))) | (~r(s(s(s(s(z)))), s(z))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(z), s(elem!1))) | (~r(s(s(s(s(z)))), s(elem!1))) | (~r(s(s(s(s(z)))), s(z))))),
% 0.48/0.69 inference(rewrite,[status(thm)],[])).
% 0.48/0.69 tff(916,plain,
% 0.48/0.69 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(elem!1))) | (~r(s(s(s(s(z)))), s(elem!1))) | (~r(s(s(s(s(z)))), s(z))))),
% 0.48/0.69 inference(quant_inst,[status(thm)],[])).
% 0.48/0.69 tff(917,plain,
% 0.48/0.69 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(z), s(elem!1))) | (~r(s(s(s(s(z)))), s(elem!1))) | (~r(s(s(s(s(z)))), s(z)))),
% 0.48/0.69 inference(modus_ponens,[status(thm)],[916, 915])).
% 0.48/0.69 tff(918,plain,
% 0.48/0.69 ($false),
% 0.48/0.69 inference(unit_resolution,[status(thm)],[917, 14, 3, 914, 911])).
% 0.48/0.69 tff(919,plain,((~b(s(s(s(elem!1))), z)) | (~r(s(s(s(s(z)))), s(z))) | (~b(s(s(s(s(z)))), z)) | (~(s(s(s(s(elem!1)))) = s(s(elem!1)))) | (~b(s(z), z))), inference(lemma,lemma(discharge,[]))).
% 0.48/0.69 tff(920,plain,
% 0.48/0.69 (~b(s(s(s(s(z)))), z)),
% 0.48/0.69 inference(unit_resolution,[status(thm)],[919, 899, 882, 255, 237])).
% 0.48/0.69 tff(921,plain,
% 0.48/0.69 (r(s(s(s(s(z)))), z)),
% 0.48/0.69 inference(unit_resolution,[status(thm)],[582, 920])).
% 0.48/0.69 tff(922,plain,
% 0.48/0.69 (~r(s(s(s(s(z)))), s(s(s(z))))),
% 0.48/0.69 inference(unit_resolution,[status(thm)],[895, 14, 824, 921])).
% 0.48/0.69 tff(923,plain,
% 0.48/0.69 (b(s(s(s(s(z)))), s(s(s(z))))),
% 0.48/0.69 inference(unit_resolution,[status(thm)],[529, 922])).
% 0.48/0.69 tff(924,plain,
% 0.48/0.69 (((~![X0: $i, X2: $i, X1: $i] : ((~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), s(s(elem!1)))) | (~b(s(s(s(s(z)))), s(s(elem!1)))) | (~b(s(s(s(s(z)))), s(s(s(z))))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(z))), s(s(elem!1)))) | (~b(s(s(s(s(z)))), s(s(elem!1)))) | (~b(s(s(s(s(z)))), s(s(s(z))))))),
% 0.48/0.69 inference(rewrite,[status(thm)],[])).
% 0.48/0.69 tff(925,plain,
% 0.48/0.69 ((~![X0: $i, X2: $i, X1: $i] : ((~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), s(s(elem!1)))) | (~b(s(s(s(s(z)))), s(s(elem!1)))) | (~b(s(s(s(s(z)))), s(s(s(z))))))),
% 0.48/0.69 inference(quant_inst,[status(thm)],[])).
% 0.48/0.69 tff(926,plain,
% 0.48/0.69 ((~![X0: $i, X2: $i, X1: $i] : ((~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(z))), s(s(elem!1)))) | (~b(s(s(s(s(z)))), s(s(elem!1)))) | (~b(s(s(s(s(z)))), s(s(s(z)))))),
% 0.48/0.69 inference(modus_ponens,[status(thm)],[925, 924])).
% 0.48/0.69 tff(927,plain,
% 0.48/0.69 ($false),
% 0.48/0.69 inference(unit_resolution,[status(thm)],[926, 117, 923, 831, 903])).
% 0.48/0.69 tff(928,plain,((~b(s(s(elem!1)), s(s(s(elem!1))))) | (~(s(s(s(s(elem!1)))) = s(s(elem!1)))) | (~b(s(z), z)) | (~r(s(s(elem!1)), z)) | (s(s(s(elem!1))) = s(s(s(s(elem!1)))))), inference(lemma,lemma(discharge,[]))).
% 0.48/0.69 tff(929,plain,
% 0.48/0.69 (~b(s(s(elem!1)), s(s(s(elem!1))))),
% 0.48/0.69 inference(unit_resolution,[status(thm)],[928, 182, 237, 255, 290])).
% 0.48/0.69 tff(930,plain,
% 0.48/0.69 (r(s(s(elem!1)), s(s(s(elem!1))))),
% 0.48/0.69 inference(unit_resolution,[status(thm)],[253, 929, 145])).
% 0.48/0.69 tff(931,plain,
% 0.48/0.69 (~r(s(s(s(elem!1))), z)),
% 0.48/0.69 inference(unit_resolution,[status(thm)],[204, 930, 182])).
% 0.48/0.69 tff(932,plain,
% 0.48/0.69 (b(s(s(s(elem!1))), z)),
% 0.48/0.69 inference(unit_resolution,[status(thm)],[211, 931])).
% 0.48/0.69 tff(933,plain,
% 0.48/0.69 (~b(s(z), s(s(s(elem!1))))),
% 0.48/0.69 inference(unit_resolution,[status(thm)],[246, 932, 237])).
% 0.48/0.69 tff(934,plain,
% 0.48/0.69 (r(s(z), s(s(s(elem!1))))),
% 0.48/0.69 inference(unit_resolution,[status(thm)],[235, 933])).
% 0.48/0.69 tff(935,plain,
% 0.48/0.69 (~r(s(s(elem!1)), s(z))),
% 0.48/0.69 inference(unit_resolution,[status(thm)],[221, 934, 930])).
% 0.48/0.69 tff(936,plain,
% 0.48/0.69 (b(s(s(elem!1)), s(z))),
% 0.48/0.69 inference(unit_resolution,[status(thm)],[178, 935])).
% 0.48/0.69 tff(937,plain,
% 0.48/0.69 (r(s(s(s(z))), elem!1) <=> r(s(s(s(z))), s(s(elem!1)))),
% 0.48/0.69 inference(symmetry,[status(thm)],[281])).
% 0.48/0.69 tff(938,plain,
% 0.48/0.69 ((~b(s(s(s(z))), s(s(elem!1)))) <=> (~b(s(s(s(z))), elem!1))),
% 0.48/0.69 inference(monotonicity,[status(thm)],[268])).
% 0.48/0.69 tff(939,plain,
% 0.48/0.69 (~b(s(s(s(z))), s(s(elem!1)))),
% 0.48/0.69 inference(unit_resolution,[status(thm)],[853, 848, 470])).
% 0.48/0.69 tff(940,plain,
% 0.48/0.69 (~b(s(s(s(z))), elem!1)),
% 0.48/0.69 inference(modus_ponens,[status(thm)],[939, 938])).
% 0.48/0.69 tff(941,plain,
% 0.48/0.69 (r(s(s(s(z))), elem!1)),
% 0.48/0.69 inference(unit_resolution,[status(thm)],[756, 940, 280])).
% 0.48/0.69 tff(942,plain,
% 0.48/0.69 (r(s(s(s(z))), s(s(elem!1)))),
% 0.48/0.69 inference(modus_ponens,[status(thm)],[941, 937])).
% 0.48/0.69 tff(943,assumption,(r(s(s(s(z))), s(s(elem!1)))), introduced(assumption)).
% 0.48/0.69 tff(944,plain,
% 0.48/0.69 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(z))), s(s(elem!1)))) | (~r(s(s(s(s(z)))), s(s(elem!1)))) | (~r(s(s(s(s(z)))), s(s(s(z))))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(z))), s(s(elem!1)))) | (~r(s(s(s(s(z)))), s(s(elem!1)))) | (~r(s(s(s(s(z)))), s(s(s(z))))))),
% 0.48/0.69 inference(rewrite,[status(thm)],[])).
% 0.48/0.69 tff(945,plain,
% 0.48/0.69 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(z))), s(s(elem!1)))) | (~r(s(s(s(s(z)))), s(s(elem!1)))) | (~r(s(s(s(s(z)))), s(s(s(z))))))),
% 0.48/0.69 inference(quant_inst,[status(thm)],[])).
% 0.48/0.69 tff(946,plain,
% 0.48/0.69 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(z))), s(s(elem!1)))) | (~r(s(s(s(s(z)))), s(s(elem!1)))) | (~r(s(s(s(s(z)))), s(s(s(z)))))),
% 0.48/0.69 inference(modus_ponens,[status(thm)],[945, 944])).
% 0.48/0.69 tff(947,plain,
% 0.48/0.69 ($false),
% 0.48/0.69 inference(unit_resolution,[status(thm)],[946, 14, 892, 943, 573])).
% 0.48/0.69 tff(948,plain,((~b(s(s(s(s(z)))), s(z))) | (~r(s(s(s(z))), s(s(elem!1)))) | (~(s(s(elem!1)) = elem!1)) | (s(s(s(s(z)))) = elem!1) | (~b(s(s(s(z))), s(z))) | (~b(s(s(elem!1)), s(z)))), inference(lemma,lemma(discharge,[]))).
% 0.48/0.69 tff(949,plain,
% 0.48/0.69 (~b(s(s(s(s(z)))), s(z))),
% 0.48/0.69 inference(unit_resolution,[status(thm)],[948, 942, 267, 320, 848, 470])).
% 0.48/0.69 tff(950,plain,
% 0.48/0.69 (r(s(s(s(s(z)))), s(z))),
% 0.48/0.69 inference(unit_resolution,[status(thm)],[554, 949])).
% 0.48/0.69 tff(951,plain,
% 0.48/0.69 (~b(s(s(s(s(z)))), z)),
% 0.48/0.69 inference(unit_resolution,[status(thm)],[919, 3, 157, 255, 237])).
% 0.48/0.69 tff(952,plain,
% 0.48/0.69 (r(s(s(s(s(z)))), z)),
% 0.48/0.69 inference(unit_resolution,[status(thm)],[582, 951])).
% 0.48/0.69 tff(953,plain,
% 0.48/0.69 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(z))) | (~r(s(s(s(s(z)))), z)) | (~r(s(s(s(s(z)))), s(z))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, s(z))) | (~r(s(s(s(s(z)))), z)) | (~r(s(s(s(s(z)))), s(z))))),
% 0.48/0.69 inference(rewrite,[status(thm)],[])).
% 0.48/0.69 tff(954,plain,
% 0.48/0.69 (((~r(z, s(z))) | (~r(s(s(s(s(z)))), s(z))) | (~r(s(s(s(s(z)))), z))) <=> ((~r(z, s(z))) | (~r(s(s(s(s(z)))), z)) | (~r(s(s(s(s(z)))), s(z))))),
% 0.48/0.69 inference(rewrite,[status(thm)],[])).
% 0.48/0.69 tff(955,plain,
% 0.48/0.69 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(z))) | (~r(s(s(s(s(z)))), s(z))) | (~r(s(s(s(s(z)))), z)))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(z))) | (~r(s(s(s(s(z)))), z)) | (~r(s(s(s(s(z)))), s(z)))))),
% 0.48/0.69 inference(monotonicity,[status(thm)],[954])).
% 0.48/0.69 tff(956,plain,
% 0.48/0.69 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(z))) | (~r(s(s(s(s(z)))), s(z))) | (~r(s(s(s(s(z)))), z)))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, s(z))) | (~r(s(s(s(s(z)))), z)) | (~r(s(s(s(s(z)))), s(z))))),
% 0.48/0.69 inference(transitivity,[status(thm)],[955, 953])).
% 0.48/0.69 tff(957,plain,
% 0.48/0.69 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(z))) | (~r(s(s(s(s(z)))), s(z))) | (~r(s(s(s(s(z)))), z)))),
% 0.48/0.69 inference(quant_inst,[status(thm)],[])).
% 0.48/0.69 tff(958,plain,
% 0.48/0.69 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, s(z))) | (~r(s(s(s(s(z)))), z)) | (~r(s(s(s(s(z)))), s(z)))),
% 0.48/0.69 inference(modus_ponens,[status(thm)],[957, 956])).
% 0.48/0.69 tff(959,plain,
% 0.48/0.69 ($false),
% 0.48/0.69 inference(unit_resolution,[status(thm)],[958, 14, 2, 3, 952])).
% 0.48/0.69 tff(960,plain,((~r(s(s(s(s(z)))), s(z))) | (~r(z, s(z))) | (~b(s(s(s(elem!1))), z)) | (~(s(s(s(s(elem!1)))) = s(s(elem!1)))) | (~b(s(z), z))), inference(lemma,lemma(discharge,[]))).
% 0.48/0.69 tff(961,plain,
% 0.48/0.69 (~r(z, s(z))),
% 0.48/0.69 inference(unit_resolution,[status(thm)],[960, 950, 157, 255, 237])).
% 0.48/0.69 tff(962,plain,
% 0.48/0.69 (b(z, s(z))),
% 0.48/0.69 inference(unit_resolution,[status(thm)],[599, 961])).
% 0.48/0.69 tff(963,plain,
% 0.48/0.69 (((~![X0: $i, X2: $i, X1: $i] : ((~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(z))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(z))), z)))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(z))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(z))), z)))),
% 0.48/0.69 inference(rewrite,[status(thm)],[])).
% 0.48/0.69 tff(964,plain,
% 0.48/0.69 ((~![X0: $i, X2: $i, X1: $i] : ((~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(z))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(z))), z)))),
% 0.48/0.69 inference(quant_inst,[status(thm)],[])).
% 0.48/0.69 tff(965,plain,
% 0.48/0.69 ((~![X0: $i, X2: $i, X1: $i] : ((~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(z))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(z))), z))),
% 0.48/0.69 inference(modus_ponens,[status(thm)],[964, 963])).
% 0.48/0.69 tff(966,plain,
% 0.48/0.69 (~b(s(s(s(z))), z)),
% 0.48/0.69 inference(unit_resolution,[status(thm)],[965, 117, 962, 848])).
% 0.48/0.69 tff(967,plain,
% 0.48/0.69 (r(s(s(s(z))), z)),
% 0.48/0.69 inference(unit_resolution,[status(thm)],[823, 966])).
% 0.48/0.69 tff(968,plain,
% 0.48/0.69 ($false),
% 0.48/0.69 inference(unit_resolution,[status(thm)],[827, 14, 182, 967, 942])).
% 0.48/0.69 tff(969,plain,((~b(s(s(s(z))), s(z))) | (~r(s(s(elem!1)), z)) | (~b(s(s(s(elem!1))), z)) | (~(s(s(s(s(elem!1)))) = s(s(elem!1)))) | (~b(s(z), z)) | (~b(s(s(elem!1)), s(z)))), inference(lemma,lemma(discharge,[]))).
% 0.48/0.69 tff(970,plain,
% 0.48/0.69 (~b(s(s(s(z))), s(z))),
% 0.48/0.69 inference(unit_resolution,[status(thm)],[969, 182, 932, 255, 237, 936])).
% 0.48/0.69 tff(971,plain,
% 0.48/0.69 (r(s(s(s(z))), s(z))),
% 0.48/0.69 inference(unit_resolution,[status(thm)],[347, 970])).
% 0.48/0.69 tff(972,plain,
% 0.48/0.69 (b(z, s(elem!1)) <=> b(z, s(s(s(elem!1))))),
% 0.48/0.69 inference(monotonicity,[status(thm)],[260])).
% 0.48/0.69 tff(973,plain,
% 0.48/0.69 (b(z, s(s(s(elem!1)))) <=> b(z, s(elem!1))),
% 0.48/0.69 inference(symmetry,[status(thm)],[972])).
% 0.48/0.69 tff(974,assumption,(r(z, s(s(s(elem!1))))), introduced(assumption)).
% 0.48/0.69 tff(975,plain,
% 0.48/0.69 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(elem!1)), z)) | (~r(z, s(s(s(elem!1))))) | (~r(s(s(elem!1)), s(s(s(elem!1))))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(elem!1)), z)) | (~r(z, s(s(s(elem!1))))) | (~r(s(s(elem!1)), s(s(s(elem!1))))))),
% 0.48/0.69 inference(rewrite,[status(thm)],[])).
% 0.48/0.69 tff(976,plain,
% 0.48/0.69 (((~r(z, s(s(s(elem!1))))) | (~r(s(s(elem!1)), s(s(s(elem!1))))) | (~r(s(s(elem!1)), z))) <=> ((~r(s(s(elem!1)), z)) | (~r(z, s(s(s(elem!1))))) | (~r(s(s(elem!1)), s(s(s(elem!1))))))),
% 0.48/0.69 inference(rewrite,[status(thm)],[])).
% 0.48/0.69 tff(977,plain,
% 0.48/0.69 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(s(elem!1))))) | (~r(s(s(elem!1)), s(s(s(elem!1))))) | (~r(s(s(elem!1)), z)))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(elem!1)), z)) | (~r(z, s(s(s(elem!1))))) | (~r(s(s(elem!1)), s(s(s(elem!1)))))))),
% 0.48/0.69 inference(monotonicity,[status(thm)],[976])).
% 0.48/0.69 tff(978,plain,
% 0.48/0.69 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(s(elem!1))))) | (~r(s(s(elem!1)), s(s(s(elem!1))))) | (~r(s(s(elem!1)), z)))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(elem!1)), z)) | (~r(z, s(s(s(elem!1))))) | (~r(s(s(elem!1)), s(s(s(elem!1))))))),
% 0.48/0.69 inference(transitivity,[status(thm)],[977, 975])).
% 0.48/0.69 tff(979,plain,
% 0.48/0.69 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(s(elem!1))))) | (~r(s(s(elem!1)), s(s(s(elem!1))))) | (~r(s(s(elem!1)), z)))),
% 0.48/0.69 inference(quant_inst,[status(thm)],[])).
% 0.48/0.69 tff(980,plain,
% 0.48/0.69 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(elem!1)), z)) | (~r(z, s(s(s(elem!1))))) | (~r(s(s(elem!1)), s(s(s(elem!1)))))),
% 0.48/0.69 inference(modus_ponens,[status(thm)],[979, 978])).
% 0.48/0.69 tff(981,plain,
% 0.48/0.69 ($false),
% 0.48/0.69 inference(unit_resolution,[status(thm)],[980, 14, 974, 182, 195])).
% 0.48/0.69 tff(982,plain,((~r(z, s(s(s(elem!1))))) | (~r(s(s(elem!1)), z)) | (~r(s(s(elem!1)), s(s(s(elem!1)))))), inference(lemma,lemma(discharge,[]))).
% 0.48/0.69 tff(983,plain,
% 0.48/0.69 (~r(z, s(s(s(elem!1))))),
% 0.48/0.69 inference(unit_resolution,[status(thm)],[982, 930, 182])).
% 0.48/0.69 tff(984,plain,
% 0.48/0.69 (b(z, s(s(s(elem!1))))),
% 0.48/0.69 inference(unit_resolution,[status(thm)],[692, 983])).
% 0.48/0.69 tff(985,plain,
% 0.48/0.69 (b(z, s(elem!1))),
% 0.48/0.69 inference(modus_ponens,[status(thm)],[984, 973])).
% 0.48/0.69 tff(986,plain,
% 0.48/0.69 (r(s(z), s(elem!1))),
% 0.48/0.69 inference(unit_resolution,[status(thm)],[642, 934, 255])).
% 0.48/0.69 tff(987,plain,
% 0.48/0.69 (~r(s(s(s(z))), s(elem!1))),
% 0.48/0.69 inference(unit_resolution,[status(thm)],[635, 971, 986])).
% 0.48/0.69 tff(988,plain,
% 0.48/0.69 (b(s(s(s(z))), s(elem!1))),
% 0.48/0.69 inference(unit_resolution,[status(thm)],[627, 46, 624, 987])).
% 0.48/0.69 tff(989,plain,
% 0.48/0.69 (((~![X0: $i, X2: $i, X1: $i] : ((~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(s(z))))) | (~b(z, s(elem!1))) | (~b(s(s(s(z))), s(elem!1))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(s(s(z))))) | (~b(z, s(elem!1))) | (~b(s(s(s(z))), s(elem!1))))),
% 0.48/0.69 inference(rewrite,[status(thm)],[])).
% 0.48/0.69 tff(990,plain,
% 0.48/0.69 (((~b(s(s(s(z))), s(elem!1))) | (~b(z, s(elem!1))) | (~b(z, s(s(s(z)))))) <=> ((~b(z, s(s(s(z))))) | (~b(z, s(elem!1))) | (~b(s(s(s(z))), s(elem!1))))),
% 0.48/0.69 inference(rewrite,[status(thm)],[])).
% 0.48/0.69 tff(991,plain,
% 0.48/0.69 (((~![X0: $i, X2: $i, X1: $i] : ((~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), s(elem!1))) | (~b(z, s(elem!1))) | (~b(z, s(s(s(z))))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(s(z))))) | (~b(z, s(elem!1))) | (~b(s(s(s(z))), s(elem!1)))))),
% 0.48/0.69 inference(monotonicity,[status(thm)],[990])).
% 0.48/0.69 tff(992,plain,
% 0.48/0.69 (((~![X0: $i, X2: $i, X1: $i] : ((~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), s(elem!1))) | (~b(z, s(elem!1))) | (~b(z, s(s(s(z))))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(s(s(z))))) | (~b(z, s(elem!1))) | (~b(s(s(s(z))), s(elem!1))))),
% 0.48/0.69 inference(transitivity,[status(thm)],[991, 989])).
% 0.48/0.69 tff(993,plain,
% 0.48/0.69 ((~![X0: $i, X2: $i, X1: $i] : ((~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), s(elem!1))) | (~b(z, s(elem!1))) | (~b(z, s(s(s(z))))))),
% 0.48/0.69 inference(quant_inst,[status(thm)],[])).
% 0.48/0.69 tff(994,plain,
% 0.48/0.69 ((~![X0: $i, X2: $i, X1: $i] : ((~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(s(s(z))))) | (~b(z, s(elem!1))) | (~b(s(s(s(z))), s(elem!1)))),
% 0.48/0.69 inference(modus_ponens,[status(thm)],[993, 992])).
% 0.48/0.69 tff(995,plain,
% 0.48/0.69 (~b(z, s(s(s(z))))),
% 0.48/0.69 inference(unit_resolution,[status(thm)],[994, 117, 988, 985])).
% 0.48/0.69 tff(996,plain,
% 0.48/0.69 (r(z, s(s(s(z))))),
% 0.48/0.69 inference(unit_resolution,[status(thm)],[711, 995])).
% 0.48/0.69 tff(997,plain,
% 0.48/0.69 (b(s(elem!1), z)),
% 0.48/0.69 inference(modus_ponens,[status(thm)],[932, 379])).
% 0.48/0.69 tff(998,plain,
% 0.48/0.69 (((~![X0: $i, X2: $i, X1: $i] : ((~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), z)) | (~b(s(elem!1), z)) | (~b(s(elem!1), s(z))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), z)) | (~b(s(elem!1), z)) | (~b(s(elem!1), s(z))))),
% 0.48/0.69 inference(rewrite,[status(thm)],[])).
% 0.48/0.69 tff(999,plain,
% 0.48/0.69 ((~![X0: $i, X2: $i, X1: $i] : ((~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), z)) | (~b(s(elem!1), z)) | (~b(s(elem!1), s(z))))),
% 0.48/0.69 inference(quant_inst,[status(thm)],[])).
% 0.48/0.69 tff(1000,plain,
% 0.48/0.69 ((~![X0: $i, X2: $i, X1: $i] : ((~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), z)) | (~b(s(elem!1), z)) | (~b(s(elem!1), s(z)))),
% 0.48/0.69 inference(modus_ponens,[status(thm)],[999, 998])).
% 0.48/0.69 tff(1001,plain,
% 0.48/0.69 ((~b(s(elem!1), z)) | (~b(s(elem!1), s(z)))),
% 0.48/0.69 inference(unit_resolution,[status(thm)],[1000, 117, 237])).
% 0.48/0.69 tff(1002,plain,
% 0.48/0.69 (~b(s(elem!1), s(z))),
% 0.48/0.69 inference(unit_resolution,[status(thm)],[1001, 997])).
% 0.48/0.69 tff(1003,plain,
% 0.48/0.69 (~b(s(s(s(elem!1))), s(z))),
% 0.48/0.69 inference(modus_ponens,[status(thm)],[1002, 430])).
% 0.48/0.69 tff(1004,plain,
% 0.48/0.69 (r(s(s(s(elem!1))), s(z))),
% 0.48/0.69 inference(unit_resolution,[status(thm)],[467, 1003])).
% 0.48/0.69 tff(1005,plain,
% 0.48/0.69 (r(s(elem!1), s(z))),
% 0.48/0.69 inference(modus_ponens,[status(thm)],[1004, 428])).
% 0.48/0.69 tff(1006,plain,
% 0.48/0.69 (~r(s(elem!1), s(s(s(z))))),
% 0.48/0.69 inference(unit_resolution,[status(thm)],[488, 14, 971, 1005])).
% 0.48/0.69 tff(1007,plain,
% 0.48/0.69 ((s(elem!1) = s(s(s(z)))) | b(s(elem!1), s(s(s(z))))),
% 0.48/0.69 inference(unit_resolution,[status(thm)],[493, 46, 1006])).
% 0.48/0.69 tff(1008,plain,
% 0.48/0.69 (b(s(elem!1), s(s(s(z))))),
% 0.48/0.69 inference(unit_resolution,[status(thm)],[1007, 485])).
% 0.48/0.69 tff(1009,plain,
% 0.48/0.69 (~r(s(s(s(s(z)))), s(z))),
% 0.48/0.69 inference(unit_resolution,[status(thm)],[538, 1008, 477, 1005, 971])).
% 0.48/0.69 tff(1010,plain,
% 0.48/0.69 (b(s(s(s(s(z)))), s(z))),
% 0.48/0.69 inference(unit_resolution,[status(thm)],[554, 1009])).
% 0.48/0.69 tff(1011,plain,
% 0.48/0.69 (~b(z, s(z))),
% 0.48/0.69 inference(unit_resolution,[status(thm)],[589, 1010, 320, 182, 267, 936])).
% 0.48/0.69 tff(1012,plain,
% 0.48/0.69 (r(z, s(z))),
% 0.48/0.69 inference(unit_resolution,[status(thm)],[599, 1011])).
% 0.48/0.69 tff(1013,plain,
% 0.48/0.69 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(z))) | (~r(z, s(s(s(z))))) | (~r(s(s(s(z))), s(z))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, s(z))) | (~r(z, s(s(s(z))))) | (~r(s(s(s(z))), s(z))))),
% 0.48/0.69 inference(rewrite,[status(thm)],[])).
% 0.48/0.69 tff(1014,plain,
% 0.48/0.69 (((~r(s(s(s(z))), s(z))) | (~r(z, s(z))) | (~r(z, s(s(s(z)))))) <=> ((~r(z, s(z))) | (~r(z, s(s(s(z))))) | (~r(s(s(s(z))), s(z))))),
% 0.48/0.69 inference(rewrite,[status(thm)],[])).
% 0.48/0.69 tff(1015,plain,
% 0.48/0.69 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(z))), s(z))) | (~r(z, s(z))) | (~r(z, s(s(s(z))))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(z))) | (~r(z, s(s(s(z))))) | (~r(s(s(s(z))), s(z)))))),
% 0.48/0.69 inference(monotonicity,[status(thm)],[1014])).
% 0.48/0.69 tff(1016,plain,
% 0.48/0.69 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(z))), s(z))) | (~r(z, s(z))) | (~r(z, s(s(s(z))))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, s(z))) | (~r(z, s(s(s(z))))) | (~r(s(s(s(z))), s(z))))),
% 0.55/0.70 inference(transitivity,[status(thm)],[1015, 1013])).
% 0.55/0.70 tff(1017,plain,
% 0.55/0.70 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(z))), s(z))) | (~r(z, s(z))) | (~r(z, s(s(s(z))))))),
% 0.55/0.70 inference(quant_inst,[status(thm)],[])).
% 0.55/0.70 tff(1018,plain,
% 0.55/0.70 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, s(z))) | (~r(z, s(s(s(z))))) | (~r(s(s(s(z))), s(z)))),
% 0.55/0.70 inference(modus_ponens,[status(thm)],[1017, 1016])).
% 0.55/0.70 tff(1019,plain,
% 0.55/0.70 ($false),
% 0.55/0.70 inference(unit_resolution,[status(thm)],[1018, 14, 1012, 996, 971])).
% 0.55/0.70 tff(1020,plain,((~r(s(s(elem!1)), z)) | (~(s(s(s(s(elem!1)))) = s(s(elem!1)))) | (~b(s(z), z)) | (s(s(elem!1)) = s(s(s(elem!1))))), inference(lemma,lemma(discharge,[]))).
% 0.55/0.70 tff(1021,plain,
% 0.55/0.70 (~r(s(s(elem!1)), z)),
% 0.55/0.70 inference(unit_resolution,[status(thm)],[1020, 145, 237, 255])).
% 0.55/0.70 tff(1022,plain,
% 0.55/0.70 (((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((s(s(elem!1)) = z) | b(s(s(elem!1)), z) | r(s(s(elem!1)), z))) <=> ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (s(s(elem!1)) = z) | b(s(s(elem!1)), z) | r(s(s(elem!1)), z))),
% 0.55/0.70 inference(rewrite,[status(thm)],[])).
% 0.55/0.70 tff(1023,plain,
% 0.55/0.70 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((s(s(elem!1)) = z) | b(s(s(elem!1)), z) | r(s(s(elem!1)), z))),
% 0.55/0.70 inference(quant_inst,[status(thm)],[])).
% 0.55/0.70 tff(1024,plain,
% 0.55/0.70 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (s(s(elem!1)) = z) | b(s(s(elem!1)), z) | r(s(s(elem!1)), z)),
% 0.55/0.70 inference(modus_ponens,[status(thm)],[1023, 1022])).
% 0.55/0.70 tff(1025,plain,
% 0.55/0.70 (b(s(s(elem!1)), z) | r(s(s(elem!1)), z)),
% 0.55/0.70 inference(unit_resolution,[status(thm)],[1024, 46, 228])).
% 0.55/0.70 tff(1026,plain,
% 0.55/0.70 (b(s(s(elem!1)), z)),
% 0.55/0.70 inference(unit_resolution,[status(thm)],[1025, 1021])).
% 0.55/0.70 tff(1027,plain,
% 0.55/0.70 (((~![X0: $i, X2: $i, X1: $i] : ((~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))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~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))))),
% 0.55/0.70 inference(rewrite,[status(thm)],[])).
% 0.55/0.70 tff(1028,plain,
% 0.55/0.70 ((~![X0: $i, X2: $i, X1: $i] : ((~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))))),
% 0.55/0.70 inference(quant_inst,[status(thm)],[])).
% 0.55/0.70 tff(1029,plain,
% 0.55/0.70 ((~![X0: $i, X2: $i, X1: $i] : ((~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)))),
% 0.55/0.70 inference(modus_ponens,[status(thm)],[1028, 1027])).
% 0.55/0.70 tff(1030,plain,
% 0.55/0.70 (~b(s(s(elem!1)), s(z))),
% 0.55/0.70 inference(unit_resolution,[status(thm)],[1029, 117, 1026, 237])).
% 0.55/0.70 tff(1031,plain,
% 0.55/0.70 (r(s(s(elem!1)), s(z))),
% 0.55/0.70 inference(unit_resolution,[status(thm)],[178, 1030])).
% 0.55/0.70 tff(1032,plain,
% 0.55/0.70 (~r(s(s(s(z))), s(s(elem!1)))),
% 0.55/0.70 inference(unit_resolution,[status(thm)],[750, 14, 1031, 283])).
% 0.55/0.70 tff(1033,plain,
% 0.55/0.70 (~r(s(s(s(z))), elem!1)),
% 0.55/0.70 inference(modus_ponens,[status(thm)],[1032, 282])).
% 0.55/0.70 tff(1034,plain,
% 0.55/0.70 (b(s(s(s(z))), elem!1)),
% 0.55/0.70 inference(unit_resolution,[status(thm)],[756, 1033, 280])).
% 0.55/0.70 tff(1035,plain,
% 0.55/0.70 (b(s(s(s(z))), s(s(elem!1)))),
% 0.55/0.70 inference(modus_ponens,[status(thm)],[1034, 269])).
% 0.55/0.70 tff(1036,assumption,(b(s(s(elem!1)), z)), introduced(assumption)).
% 0.55/0.70 tff(1037,plain,
% 0.55/0.70 (~b(s(s(elem!1)), s(z))),
% 0.55/0.70 inference(unit_resolution,[status(thm)],[1029, 117, 1036, 237])).
% 0.55/0.70 tff(1038,plain,
% 0.55/0.70 (r(s(s(elem!1)), s(z))),
% 0.55/0.70 inference(unit_resolution,[status(thm)],[178, 1037])).
% 0.55/0.70 tff(1039,plain,
% 0.55/0.70 (((~![X0: $i, X2: $i, X1: $i] : ((~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), z)) | (~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), z)))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(elem!1)), z)) | (~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), z)))),
% 0.55/0.70 inference(rewrite,[status(thm)],[])).
% 0.55/0.70 tff(1040,plain,
% 0.55/0.70 (((~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)), z)) | (~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), z)))),
% 0.55/0.70 inference(rewrite,[status(thm)],[])).
% 0.55/0.70 tff(1041,plain,
% 0.55/0.70 (((~![X0: $i, X2: $i, X1: $i] : ((~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~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, X2: $i, X1: $i] : ((~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), z)) | (~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), z))))),
% 0.55/0.70 inference(monotonicity,[status(thm)],[1040])).
% 0.55/0.70 tff(1042,plain,
% 0.55/0.70 (((~![X0: $i, X2: $i, X1: $i] : ((~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~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, X2: $i, X1: $i] : ((~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(elem!1)), z)) | (~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), z)))),
% 0.55/0.70 inference(transitivity,[status(thm)],[1041, 1039])).
% 0.55/0.70 tff(1043,plain,
% 0.55/0.70 ((~![X0: $i, X2: $i, X1: $i] : ((~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), z)) | (~b(s(s(elem!1)), z)) | (~b(s(s(elem!1)), s(s(s(elem!1))))))),
% 0.55/0.70 inference(quant_inst,[status(thm)],[])).
% 0.55/0.70 tff(1044,plain,
% 0.55/0.70 ((~![X0: $i, X2: $i, X1: $i] : ((~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(elem!1)), z)) | (~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), z))),
% 0.55/0.70 inference(modus_ponens,[status(thm)],[1043, 1042])).
% 0.55/0.70 tff(1045,plain,
% 0.55/0.70 ($false),
% 0.55/0.70 inference(unit_resolution,[status(thm)],[1044, 117, 157, 1036, 324])).
% 0.55/0.70 tff(1046,plain,((~b(s(s(s(elem!1))), z)) | (~b(s(s(elem!1)), z)) | (~b(s(s(elem!1)), s(s(s(elem!1)))))), inference(lemma,lemma(discharge,[]))).
% 0.55/0.70 tff(1047,plain,
% 0.55/0.70 (~b(s(s(elem!1)), s(s(s(elem!1))))),
% 0.55/0.70 inference(unit_resolution,[status(thm)],[1046, 157, 1036])).
% 0.55/0.70 tff(1048,plain,
% 0.55/0.70 (r(s(s(elem!1)), s(s(s(elem!1))))),
% 0.55/0.70 inference(unit_resolution,[status(thm)],[253, 1047, 145])).
% 0.55/0.70 tff(1049,plain,
% 0.55/0.70 ($false),
% 0.55/0.70 inference(unit_resolution,[status(thm)],[221, 913, 1048, 1038])).
% 0.55/0.70 tff(1050,plain,((~b(s(s(s(elem!1))), z)) | (s(s(elem!1)) = s(s(s(elem!1)))) | (~b(s(z), z)) | (~b(s(s(elem!1)), z))), inference(lemma,lemma(discharge,[]))).
% 0.55/0.70 tff(1051,plain,
% 0.55/0.70 (~b(s(s(s(elem!1))), z)),
% 0.55/0.70 inference(unit_resolution,[status(thm)],[1050, 145, 237, 1026])).
% 0.55/0.70 tff(1052,plain,
% 0.55/0.70 (r(s(s(s(elem!1))), z)),
% 0.55/0.70 inference(unit_resolution,[status(thm)],[211, 1051])).
% 0.55/0.70 tff(1053,plain,
% 0.55/0.70 (r(s(elem!1), z)),
% 0.55/0.70 inference(unit_resolution,[status(thm)],[880, 1052, 255])).
% 0.55/0.70 tff(1054,plain,
% 0.55/0.70 (((~![X0: $i, X2: $i, X1: $i] : ((~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), z)) | (~b(s(s(elem!1)), z)) | (~b(s(z), s(s(elem!1)))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), z)) | (~b(s(s(elem!1)), z)) | (~b(s(z), s(s(elem!1)))))),
% 0.55/0.70 inference(rewrite,[status(thm)],[])).
% 0.55/0.70 tff(1055,plain,
% 0.55/0.70 (((~b(s(s(elem!1)), z)) | (~b(s(z), z)) | (~b(s(z), s(s(elem!1))))) <=> ((~b(s(z), z)) | (~b(s(s(elem!1)), z)) | (~b(s(z), s(s(elem!1)))))),
% 0.55/0.70 inference(rewrite,[status(thm)],[])).
% 0.55/0.70 tff(1056,plain,
% 0.55/0.70 (((~![X0: $i, X2: $i, X1: $i] : ((~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), z)) | (~b(s(z), z)) | (~b(s(z), s(s(elem!1)))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), z)) | (~b(s(s(elem!1)), z)) | (~b(s(z), s(s(elem!1))))))),
% 0.55/0.70 inference(monotonicity,[status(thm)],[1055])).
% 0.55/0.70 tff(1057,plain,
% 0.55/0.70 (((~![X0: $i, X2: $i, X1: $i] : ((~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), z)) | (~b(s(z), z)) | (~b(s(z), s(s(elem!1)))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), z)) | (~b(s(s(elem!1)), z)) | (~b(s(z), s(s(elem!1)))))),
% 0.55/0.70 inference(transitivity,[status(thm)],[1056, 1054])).
% 0.55/0.70 tff(1058,plain,
% 0.55/0.70 ((~![X0: $i, X2: $i, X1: $i] : ((~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), z)) | (~b(s(z), z)) | (~b(s(z), s(s(elem!1)))))),
% 0.55/0.70 inference(quant_inst,[status(thm)],[])).
% 0.55/0.70 tff(1059,plain,
% 0.55/0.70 ((~![X0: $i, X2: $i, X1: $i] : ((~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), z)) | (~b(s(s(elem!1)), z)) | (~b(s(z), s(s(elem!1))))),
% 0.55/0.70 inference(modus_ponens,[status(thm)],[1058, 1057])).
% 0.55/0.70 tff(1060,plain,
% 0.55/0.70 (~b(s(z), s(s(elem!1)))),
% 0.55/0.70 inference(unit_resolution,[status(thm)],[1059, 117, 1026, 237])).
% 0.55/0.70 tff(1061,plain,
% 0.55/0.70 (r(s(z), s(s(elem!1)))),
% 0.55/0.70 inference(unit_resolution,[status(thm)],[416, 1060])).
% 0.55/0.70 tff(1062,plain,
% 0.55/0.70 (b(s(s(s(z))), s(s(elem!1))) <=> b(s(s(s(z))), elem!1)),
% 0.55/0.70 inference(monotonicity,[status(thm)],[556])).
% 0.55/0.70 tff(1063,plain,
% 0.55/0.70 ((~b(s(s(s(z))), s(s(elem!1)))) <=> (~b(s(s(s(z))), elem!1))),
% 0.55/0.70 inference(monotonicity,[status(thm)],[1062])).
% 0.55/0.70 tff(1064,plain,
% 0.55/0.70 (b(s(s(s(s(z)))), elem!1) <=> b(s(s(s(s(z)))), s(s(elem!1)))),
% 0.55/0.70 inference(symmetry,[status(thm)],[560])).
% 0.55/0.70 tff(1065,plain,
% 0.55/0.70 ((~r(s(s(s(s(z)))), s(s(elem!1)))) <=> (~r(s(s(s(s(z)))), elem!1))),
% 0.55/0.70 inference(monotonicity,[status(thm)],[557])).
% 0.55/0.70 tff(1066,plain,
% 0.55/0.70 (~r(s(s(s(s(z)))), s(s(elem!1)))),
% 0.55/0.70 inference(unit_resolution,[status(thm)],[803, 14, 181, 3])).
% 0.55/0.70 tff(1067,plain,
% 0.55/0.70 (~r(s(s(s(s(z)))), elem!1)),
% 0.55/0.70 inference(modus_ponens,[status(thm)],[1066, 1065])).
% 0.55/0.70 tff(1068,plain,
% 0.55/0.70 (b(s(s(s(s(z)))), elem!1)),
% 0.55/0.70 inference(unit_resolution,[status(thm)],[571, 1067, 559])).
% 0.55/0.70 tff(1069,plain,
% 0.55/0.70 (b(s(s(s(s(z)))), s(s(elem!1)))),
% 0.55/0.70 inference(modus_ponens,[status(thm)],[1068, 1064])).
% 0.55/0.70 tff(1070,plain,
% 0.55/0.70 ($false),
% 0.55/0.70 inference(unit_resolution,[status(thm)],[926, 117, 530, 837, 1069])).
% 0.55/0.70 tff(1071,plain,((~r(s(s(s(s(z)))), s(z))) | (~b(s(s(s(z))), s(s(elem!1)))) | (~(s(s(elem!1)) = elem!1)) | (s(s(s(s(z)))) = elem!1) | (~r(s(s(s(z))), s(z))) | (~r(s(s(elem!1)), s(z)))), inference(lemma,lemma(discharge,[]))).
% 0.55/0.70 tff(1072,plain,
% 0.55/0.70 (~b(s(s(s(z))), s(s(elem!1)))),
% 0.55/0.70 inference(unit_resolution,[status(thm)],[1071, 283, 556, 559, 3, 181])).
% 0.55/0.70 tff(1073,plain,
% 0.55/0.70 (~b(s(s(s(z))), elem!1)),
% 0.55/0.70 inference(modus_ponens,[status(thm)],[1072, 1063])).
% 0.55/0.70 tff(1074,assumption,(~(s(s(s(z))) = elem!1)), introduced(assumption)).
% 0.55/0.70 tff(1075,plain,
% 0.55/0.70 (r(s(s(s(z))), s(s(elem!1))) <=> r(s(s(s(z))), elem!1)),
% 0.55/0.70 inference(monotonicity,[status(thm)],[556])).
% 0.55/0.70 tff(1076,plain,
% 0.55/0.70 ((~r(s(s(s(z))), s(s(elem!1)))) <=> (~r(s(s(s(z))), elem!1))),
% 0.55/0.70 inference(monotonicity,[status(thm)],[1075])).
% 0.55/0.70 tff(1077,plain,
% 0.55/0.70 (~r(s(s(s(z))), s(s(elem!1)))),
% 0.55/0.70 inference(unit_resolution,[status(thm)],[750, 14, 181, 283])).
% 0.55/0.70 tff(1078,plain,
% 0.55/0.70 (~r(s(s(s(z))), elem!1)),
% 0.55/0.70 inference(modus_ponens,[status(thm)],[1077, 1076])).
% 0.55/0.70 tff(1079,plain,
% 0.55/0.70 (b(s(s(s(z))), elem!1)),
% 0.55/0.70 inference(unit_resolution,[status(thm)],[756, 1078, 1074])).
% 0.55/0.70 tff(1080,plain,
% 0.55/0.70 ($false),
% 0.55/0.70 inference(unit_resolution,[status(thm)],[1079, 1073])).
% 0.55/0.70 tff(1081,plain,((~r(s(s(s(z))), s(z))) | (~(s(s(elem!1)) = elem!1)) | (s(s(s(z))) = elem!1) | (~r(s(s(elem!1)), s(z))) | (s(s(s(s(z)))) = elem!1) | (~r(s(s(s(s(z)))), s(z)))), inference(lemma,lemma(discharge,[]))).
% 0.55/0.70 tff(1082,plain,
% 0.55/0.70 (~r(s(s(s(z))), s(z))),
% 0.55/0.70 inference(unit_resolution,[status(thm)],[1081, 3, 280, 181, 320, 267])).
% 0.55/0.70 tff(1083,plain,
% 0.55/0.70 (b(s(s(s(z))), s(z))),
% 0.55/0.70 inference(unit_resolution,[status(thm)],[347, 1082])).
% 0.55/0.70 tff(1084,plain,
% 0.55/0.70 ((~(s(s(s(s(s(s(elem!1)))))) = s(s(s(s(z)))))) <=> (~(elem!1 = s(s(s(s(z))))))),
% 0.55/0.70 inference(monotonicity,[status(thm)],[300])).
% 0.55/0.70 tff(1085,plain,
% 0.55/0.70 (~(elem!1 = s(s(s(s(z)))))),
% 0.55/0.70 inference(modus_ponens,[status(thm)],[319, 1084])).
% 0.55/0.70 tff(1086,plain,
% 0.55/0.70 (r(s(s(elem!1)), s(s(s(s(z))))) <=> r(elem!1, s(s(s(s(z)))))),
% 0.55/0.70 inference(monotonicity,[status(thm)],[267])).
% 0.55/0.70 tff(1087,plain,
% 0.55/0.70 ((~r(s(s(elem!1)), s(s(s(s(z)))))) <=> (~r(elem!1, s(s(s(s(z))))))),
% 0.55/0.70 inference(monotonicity,[status(thm)],[1086])).
% 0.55/0.70 tff(1088,plain,
% 0.55/0.70 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(elem!1)), s(z))) | (~r(s(s(s(s(z)))), s(z))) | (~r(s(s(elem!1)), s(s(s(s(z)))))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(elem!1)), s(z))) | (~r(s(s(s(s(z)))), s(z))) | (~r(s(s(elem!1)), s(s(s(s(z)))))))),
% 0.55/0.70 inference(rewrite,[status(thm)],[])).
% 0.55/0.70 tff(1089,plain,
% 0.55/0.70 (((~r(s(s(s(s(z)))), s(z))) | (~r(s(s(elem!1)), s(z))) | (~r(s(s(elem!1)), s(s(s(s(z))))))) <=> ((~r(s(s(elem!1)), s(z))) | (~r(s(s(s(s(z)))), s(z))) | (~r(s(s(elem!1)), s(s(s(s(z)))))))),
% 0.55/0.70 inference(rewrite,[status(thm)],[])).
% 0.55/0.70 tff(1090,plain,
% 0.55/0.70 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(z)))), s(z))) | (~r(s(s(elem!1)), s(z))) | (~r(s(s(elem!1)), s(s(s(s(z)))))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(elem!1)), s(z))) | (~r(s(s(s(s(z)))), s(z))) | (~r(s(s(elem!1)), s(s(s(s(z))))))))),
% 0.55/0.70 inference(monotonicity,[status(thm)],[1089])).
% 0.55/0.70 tff(1091,plain,
% 0.55/0.70 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(z)))), s(z))) | (~r(s(s(elem!1)), s(z))) | (~r(s(s(elem!1)), s(s(s(s(z)))))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(elem!1)), s(z))) | (~r(s(s(s(s(z)))), s(z))) | (~r(s(s(elem!1)), s(s(s(s(z)))))))),
% 0.55/0.70 inference(transitivity,[status(thm)],[1090, 1088])).
% 0.55/0.70 tff(1092,plain,
% 0.55/0.70 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(z)))), s(z))) | (~r(s(s(elem!1)), s(z))) | (~r(s(s(elem!1)), s(s(s(s(z)))))))),
% 0.55/0.70 inference(quant_inst,[status(thm)],[])).
% 0.55/0.70 tff(1093,plain,
% 0.55/0.70 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(elem!1)), s(z))) | (~r(s(s(s(s(z)))), s(z))) | (~r(s(s(elem!1)), s(s(s(s(z))))))),
% 0.55/0.70 inference(modus_ponens,[status(thm)],[1092, 1091])).
% 0.55/0.70 tff(1094,plain,
% 0.55/0.70 (~r(s(s(elem!1)), s(s(s(s(z)))))),
% 0.55/0.70 inference(unit_resolution,[status(thm)],[1093, 14, 181, 3])).
% 0.55/0.70 tff(1095,plain,
% 0.55/0.70 (~r(elem!1, s(s(s(s(z)))))),
% 0.55/0.70 inference(modus_ponens,[status(thm)],[1094, 1087])).
% 0.55/0.70 tff(1096,plain,
% 0.55/0.70 (((~![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))))))),
% 0.55/0.70 inference(rewrite,[status(thm)],[])).
% 0.55/0.70 tff(1097,plain,
% 0.55/0.70 ((~![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))))))),
% 0.55/0.70 inference(quant_inst,[status(thm)],[])).
% 0.55/0.70 tff(1098,plain,
% 0.55/0.70 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (elem!1 = s(s(s(s(z))))) | b(elem!1, s(s(s(s(z))))) | r(elem!1, s(s(s(s(z)))))),
% 0.55/0.70 inference(modus_ponens,[status(thm)],[1097, 1096])).
% 0.55/0.70 tff(1099,plain,
% 0.55/0.70 ((elem!1 = s(s(s(s(z))))) | b(elem!1, s(s(s(s(z))))) | r(elem!1, s(s(s(s(z)))))),
% 0.55/0.70 inference(unit_resolution,[status(thm)],[1098, 46])).
% 0.55/0.70 tff(1100,plain,
% 0.55/0.70 (b(elem!1, s(s(s(s(z)))))),
% 0.55/0.70 inference(unit_resolution,[status(thm)],[1099, 1095, 1085])).
% 0.55/0.70 tff(1101,plain,
% 0.55/0.70 (b(s(s(elem!1)), s(s(s(s(z))))) <=> b(elem!1, s(s(s(s(z)))))),
% 0.55/0.70 inference(monotonicity,[status(thm)],[556])).
% 0.55/0.70 tff(1102,plain,
% 0.55/0.70 (b(elem!1, s(s(s(s(z))))) <=> b(s(s(elem!1)), s(s(s(s(z)))))),
% 0.55/0.70 inference(symmetry,[status(thm)],[1101])).
% 0.55/0.70 tff(1103,assumption,(b(elem!1, s(s(s(s(z)))))), introduced(assumption)).
% 0.55/0.70 tff(1104,plain,
% 0.55/0.70 (b(s(s(elem!1)), s(s(s(s(z)))))),
% 0.55/0.70 inference(modus_ponens,[status(thm)],[1103, 1102])).
% 0.55/0.70 tff(1105,assumption,(~b(s(s(elem!1)), s(s(s(s(z)))))), introduced(assumption)).
% 0.55/0.70 tff(1106,plain,
% 0.55/0.70 ($false),
% 0.55/0.70 inference(unit_resolution,[status(thm)],[1105, 1104])).
% 0.55/0.70 tff(1107,plain,(b(s(s(elem!1)), s(s(s(s(z))))) | (~b(elem!1, s(s(s(s(z)))))) | (~(s(s(elem!1)) = elem!1))), inference(lemma,lemma(discharge,[]))).
% 0.55/0.70 tff(1108,plain,
% 0.55/0.70 (b(s(s(elem!1)), s(s(s(s(z)))))),
% 0.55/0.70 inference(unit_resolution,[status(thm)],[1107, 1100, 267])).
% 0.55/0.70 tff(1109,assumption,(b(s(s(elem!1)), s(s(s(s(z)))))), introduced(assumption)).
% 0.55/0.70 tff(1110,assumption,(b(z, s(s(s(s(z)))))), introduced(assumption)).
% 0.55/0.70 tff(1111,plain,
% 0.55/0.70 (((~![X0: $i, X2: $i, X1: $i] : ((~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), z)) | (~b(z, s(s(s(s(z)))))) | (~b(s(s(elem!1)), s(s(s(s(z)))))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(elem!1)), z)) | (~b(z, s(s(s(s(z)))))) | (~b(s(s(elem!1)), s(s(s(s(z)))))))),
% 0.55/0.70 inference(rewrite,[status(thm)],[])).
% 0.55/0.70 tff(1112,plain,
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% 0.55/0.70 inference(rewrite,[status(thm)],[])).
% 0.55/0.70 tff(1113,plain,
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% 0.55/0.70 inference(monotonicity,[status(thm)],[1112])).
% 0.55/0.70 tff(1114,plain,
% 0.55/0.70 (((~![X0: $i, X2: $i, X1: $i] : ((~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(s(s(z)))))) | (~b(s(s(elem!1)), s(s(s(s(z)))))) | (~b(s(s(elem!1)), z)))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(elem!1)), z)) | (~b(z, s(s(s(s(z)))))) | (~b(s(s(elem!1)), s(s(s(s(z)))))))),
% 0.55/0.70 inference(transitivity,[status(thm)],[1113, 1111])).
% 0.55/0.70 tff(1115,plain,
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% 0.55/0.70 inference(quant_inst,[status(thm)],[])).
% 0.55/0.70 tff(1116,plain,
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% 0.55/0.70 inference(modus_ponens,[status(thm)],[1115, 1114])).
% 0.55/0.70 tff(1117,plain,
% 0.55/0.70 ($false),
% 0.55/0.70 inference(unit_resolution,[status(thm)],[1116, 117, 1036, 1110, 1109])).
% 0.55/0.70 tff(1118,plain,((~b(z, s(s(s(s(z)))))) | (~b(s(s(elem!1)), z)) | (~b(s(s(elem!1)), s(s(s(s(z))))))), inference(lemma,lemma(discharge,[]))).
% 0.55/0.70 tff(1119,plain,
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% 0.55/0.70 inference(unit_resolution,[status(thm)],[1118, 1108, 1036])).
% 0.55/0.70 tff(1120,plain,
% 0.55/0.70 (r(z, s(s(s(s(z)))))),
% 0.55/0.70 inference(unit_resolution,[status(thm)],[51, 1119])).
% 0.55/0.70 tff(1121,plain,
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% 0.55/0.70 inference(unit_resolution,[status(thm)],[22, 1120, 3])).
% 0.55/0.70 tff(1122,plain,
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% 0.55/0.70 inference(unit_resolution,[status(thm)],[599, 1121])).
% 0.55/0.70 tff(1123,plain,
% 0.55/0.70 (~b(s(s(s(z))), z)),
% 0.55/0.70 inference(unit_resolution,[status(thm)],[965, 117, 1122, 1083])).
% 0.55/0.70 tff(1124,plain,
% 0.55/0.70 (r(s(s(s(z))), z)),
% 0.55/0.70 inference(unit_resolution,[status(thm)],[823, 1123])).
% 0.55/0.70 tff(1125,plain,
% 0.55/0.70 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(z))), z)) | (~r(s(elem!1), z)) | (~r(s(elem!1), s(s(s(z))))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(z))), z)) | (~r(s(elem!1), z)) | (~r(s(elem!1), s(s(s(z))))))),
% 0.55/0.70 inference(rewrite,[status(thm)],[])).
% 0.55/0.70 tff(1126,plain,
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% 0.55/0.70 inference(quant_inst,[status(thm)],[])).
% 0.55/0.70 tff(1127,plain,
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% 0.55/0.70 inference(modus_ponens,[status(thm)],[1126, 1125])).
% 0.55/0.70 tff(1128,plain,
% 0.55/0.70 (~r(s(elem!1), s(s(s(z))))),
% 0.55/0.70 inference(unit_resolution,[status(thm)],[1127, 14, 1124, 439])).
% 0.55/0.70 tff(1129,plain,
% 0.55/0.70 ((s(elem!1) = s(s(s(z)))) | b(s(elem!1), s(s(s(z))))),
% 0.55/0.70 inference(unit_resolution,[status(thm)],[493, 46, 1128])).
% 0.55/0.70 tff(1130,plain,
% 0.55/0.70 (b(s(elem!1), s(s(s(z))))),
% 0.55/0.70 inference(unit_resolution,[status(thm)],[1129, 485])).
% 0.55/0.70 tff(1131,plain,
% 0.55/0.70 (~r(s(s(s(z))), s(elem!1))),
% 0.55/0.70 inference(unit_resolution,[status(thm)],[875, 1124, 439])).
% 0.55/0.70 tff(1132,plain,
% 0.55/0.70 (b(s(s(s(z))), s(elem!1))),
% 0.55/0.70 inference(unit_resolution,[status(thm)],[627, 46, 624, 1131])).
% 0.55/0.70 tff(1133,plain,
% 0.55/0.70 (b(s(z), s(elem!1))),
% 0.55/0.70 inference(modus_ponens,[status(thm)],[238, 727])).
% 0.55/0.70 tff(1134,plain,
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% 0.55/0.71 inference(rewrite,[status(thm)],[])).
% 0.55/0.71 tff(1135,plain,
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% 0.55/0.71 inference(quant_inst,[status(thm)],[])).
% 0.55/0.71 tff(1136,plain,
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% 0.55/0.71 inference(modus_ponens,[status(thm)],[1135, 1134])).
% 0.55/0.71 tff(1137,plain,
% 0.55/0.71 (~b(s(z), s(elem!1))),
% 0.55/0.71 inference(unit_resolution,[status(thm)],[1136, 117, 848, 387])).
% 0.55/0.71 tff(1138,plain,
% 0.55/0.71 ($false),
% 0.55/0.71 inference(unit_resolution,[status(thm)],[1137, 1133])).
% 0.55/0.71 tff(1139,plain,((~b(s(z), s(s(s(elem!1))))) | (~(s(s(s(s(elem!1)))) = s(s(elem!1)))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(z))), s(elem!1)))), inference(lemma,lemma(discharge,[]))).
% 0.55/0.71 tff(1140,plain,
% 0.55/0.71 (~b(s(z), s(s(s(elem!1))))),
% 0.55/0.71 inference(unit_resolution,[status(thm)],[1139, 1083, 255, 1132])).
% 0.55/0.71 tff(1141,plain,
% 0.55/0.71 (r(s(z), s(s(s(elem!1))))),
% 0.55/0.71 inference(unit_resolution,[status(thm)],[235, 1140])).
% 0.55/0.71 tff(1142,plain,
% 0.55/0.71 (~r(s(s(elem!1)), s(s(s(elem!1))))),
% 0.55/0.71 inference(unit_resolution,[status(thm)],[221, 1141, 181])).
% 0.55/0.71 tff(1143,plain,
% 0.55/0.71 (b(s(s(elem!1)), s(s(s(elem!1))))),
% 0.55/0.71 inference(unit_resolution,[status(thm)],[253, 1142, 145])).
% 0.55/0.71 tff(1144,plain,
% 0.55/0.71 (b(s(s(elem!1)), s(elem!1))),
% 0.55/0.71 inference(unit_resolution,[status(thm)],[834, 1143, 255])).
% 0.55/0.71 tff(1145,plain,
% 0.55/0.71 (~b(s(s(s(z))), s(s(elem!1)))),
% 0.55/0.71 inference(unit_resolution,[status(thm)],[842, 1144, 1132])).
% 0.55/0.71 tff(1146,plain,
% 0.55/0.71 (~b(s(s(s(z))), elem!1)),
% 0.55/0.71 inference(modus_ponens,[status(thm)],[1145, 938])).
% 0.55/0.71 tff(1147,plain,
% 0.55/0.71 (r(s(s(s(z))), elem!1)),
% 0.55/0.71 inference(unit_resolution,[status(thm)],[756, 1146, 280])).
% 0.55/0.71 tff(1148,plain,
% 0.55/0.71 (r(s(s(s(z))), s(s(elem!1)))),
% 0.55/0.71 inference(modus_ponens,[status(thm)],[1147, 937])).
% 0.55/0.71 tff(1149,assumption,(r(s(z), s(s(elem!1)))), introduced(assumption)).
% 0.55/0.71 tff(1150,plain,
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% 0.55/0.71 inference(rewrite,[status(thm)],[])).
% 0.55/0.71 tff(1151,plain,
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% 0.55/0.71 inference(rewrite,[status(thm)],[])).
% 0.55/0.71 tff(1152,plain,
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% 0.55/0.71 inference(monotonicity,[status(thm)],[1151])).
% 0.55/0.71 tff(1153,plain,
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% 0.55/0.71 inference(transitivity,[status(thm)],[1152, 1150])).
% 0.55/0.71 tff(1154,plain,
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% 0.55/0.71 inference(quant_inst,[status(thm)],[])).
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% 0.55/0.71 inference(modus_ponens,[status(thm)],[1154, 1153])).
% 0.55/0.71 tff(1156,plain,
% 0.55/0.71 (~r(s(z), s(s(s(z))))),
% 0.55/0.71 inference(unit_resolution,[status(thm)],[1155, 14, 1149, 1148])).
% 0.55/0.71 tff(1157,plain,
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% 0.55/0.71 inference(rewrite,[status(thm)],[])).
% 0.55/0.71 tff(1159,plain,
% 0.55/0.71 (((~b(s(z), s(s(s(z))))) | (~b(s(elem!1), s(s(s(z))))) | (~b(s(elem!1), s(z)))) <=> ((~b(s(z), s(s(s(z))))) | (~b(s(elem!1), s(z))) | (~b(s(elem!1), s(s(s(z))))))),
% 0.55/0.71 inference(rewrite,[status(thm)],[])).
% 0.55/0.71 tff(1160,plain,
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% 0.55/0.71 inference(monotonicity,[status(thm)],[1159])).
% 0.55/0.71 tff(1161,plain,
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% 0.55/0.71 inference(transitivity,[status(thm)],[1160, 1158])).
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% 0.55/0.71 inference(quant_inst,[status(thm)],[])).
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% 0.55/0.71 inference(modus_ponens,[status(thm)],[1162, 1161])).
% 0.55/0.71 tff(1164,plain,
% 0.55/0.71 (~b(s(elem!1), s(z))),
% 0.55/0.71 inference(unit_resolution,[status(thm)],[1163, 117, 1157, 1130])).
% 0.55/0.71 tff(1165,plain,
% 0.55/0.71 (~b(s(s(s(elem!1))), s(z))),
% 0.55/0.71 inference(modus_ponens,[status(thm)],[1164, 430])).
% 0.55/0.71 tff(1166,plain,
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% 0.55/0.71 inference(unit_resolution,[status(thm)],[467, 1165])).
% 0.55/0.71 tff(1167,plain,
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% 0.55/0.71 tff(1168,plain,
% 0.55/0.71 (~r(s(s(s(s(z)))), s(elem!1))),
% 0.55/0.71 inference(unit_resolution,[status(thm)],[499, 14, 3, 1167])).
% 0.55/0.71 tff(1169,plain,
% 0.55/0.71 (b(s(s(s(s(z)))), s(elem!1))),
% 0.55/0.71 inference(unit_resolution,[status(thm)],[504, 46, 477, 1168])).
% 0.55/0.71 tff(1170,plain,
% 0.55/0.71 (~r(s(s(s(s(z)))), elem!1)),
% 0.55/0.71 inference(modus_ponens,[status(thm)],[1066, 322])).
% 0.55/0.71 tff(1171,plain,
% 0.55/0.71 (b(s(s(s(s(z)))), elem!1)),
% 0.55/0.71 inference(unit_resolution,[status(thm)],[571, 1170, 320])).
% 0.55/0.71 tff(1172,plain,
% 0.55/0.71 (b(s(s(s(s(z)))), s(s(elem!1)))),
% 0.55/0.71 inference(modus_ponens,[status(thm)],[1171, 292])).
% 0.55/0.71 tff(1173,plain,
% 0.55/0.71 (((~![X0: $i, X2: $i, X1: $i] : ((~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), s(elem!1))) | (~b(s(s(s(s(z)))), s(elem!1))) | (~b(s(s(s(s(z)))), s(s(elem!1)))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(elem!1)), s(elem!1))) | (~b(s(s(s(s(z)))), s(elem!1))) | (~b(s(s(s(s(z)))), s(s(elem!1)))))),
% 0.55/0.71 inference(rewrite,[status(thm)],[])).
% 0.55/0.71 tff(1174,plain,
% 0.55/0.71 ((~![X0: $i, X2: $i, X1: $i] : ((~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), s(elem!1))) | (~b(s(s(s(s(z)))), s(elem!1))) | (~b(s(s(s(s(z)))), s(s(elem!1)))))),
% 0.55/0.71 inference(quant_inst,[status(thm)],[])).
% 0.55/0.71 tff(1175,plain,
% 0.55/0.71 ((~![X0: $i, X2: $i, X1: $i] : ((~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(elem!1)), s(elem!1))) | (~b(s(s(s(s(z)))), s(elem!1))) | (~b(s(s(s(s(z)))), s(s(elem!1))))),
% 0.55/0.71 inference(modus_ponens,[status(thm)],[1174, 1173])).
% 0.55/0.71 tff(1176,plain,
% 0.55/0.71 ($false),
% 0.55/0.71 inference(unit_resolution,[status(thm)],[1175, 117, 1144, 1172, 1169])).
% 0.55/0.71 tff(1177,plain,((~r(s(s(s(s(z)))), s(z))) | (~(s(s(s(s(elem!1)))) = s(s(elem!1)))) | (~r(s(z), s(s(elem!1)))) | (s(s(elem!1)) = s(s(s(elem!1)))) | (~r(s(s(elem!1)), s(z))) | (~r(s(elem!1), z)) | (~b(s(s(elem!1)), z))), inference(lemma,lemma(discharge,[]))).
% 0.55/0.71 tff(1178,plain,
% 0.55/0.71 (~r(s(s(s(s(z)))), s(z))),
% 0.55/0.71 inference(unit_resolution,[status(thm)],[1177, 1061, 255, 145, 1031, 1053, 1026])).
% 0.55/0.71 tff(1179,plain,
% 0.55/0.71 (b(s(s(s(s(z)))), s(z))),
% 0.55/0.71 inference(unit_resolution,[status(thm)],[554, 1178])).
% 0.55/0.71 tff(1180,plain,
% 0.55/0.71 (~r(s(s(elem!1)), s(s(s(z))))),
% 0.55/0.71 inference(unit_resolution,[status(thm)],[667, 14, 1031, 283])).
% 0.55/0.71 tff(1181,plain,
% 0.55/0.71 (~r(elem!1, s(s(s(z))))),
% 0.55/0.71 inference(modus_ponens,[status(thm)],[1180, 337])).
% 0.55/0.71 tff(1182,plain,
% 0.55/0.71 (b(elem!1, s(s(s(z))))),
% 0.55/0.71 inference(unit_resolution,[status(thm)],[400, 1181, 335])).
% 0.55/0.71 tff(1183,plain,
% 0.55/0.71 (r(s(s(s(elem!1))), s(s(elem!1))) <=> r(s(elem!1), s(s(elem!1)))),
% 0.55/0.71 inference(symmetry,[status(thm)],[436])).
% 0.55/0.71 tff(1184,plain,
% 0.55/0.71 (r(s(s(s(elem!1))), elem!1) <=> r(s(s(s(elem!1))), s(s(elem!1)))),
% 0.55/0.71 inference(monotonicity,[status(thm)],[349])).
% 0.55/0.71 tff(1185,plain,
% 0.55/0.71 (b(elem!1, z) <=> b(s(s(elem!1)), z)),
% 0.55/0.71 inference(monotonicity,[status(thm)],[349])).
% 0.55/0.71 tff(1186,plain,
% 0.55/0.71 (b(s(s(elem!1)), z) <=> b(elem!1, z)),
% 0.55/0.71 inference(symmetry,[status(thm)],[1185])).
% 0.55/0.71 tff(1187,plain,
% 0.55/0.71 (b(elem!1, z)),
% 0.55/0.71 inference(modus_ponens,[status(thm)],[1026, 1186])).
% 0.55/0.71 tff(1188,assumption,(~b(s(s(s(elem!1))), z)), introduced(assumption)).
% 0.55/0.71 tff(1189,assumption,(elem!1 = s(s(s(elem!1)))), introduced(assumption)).
% 0.55/0.71 tff(1190,plain,
% 0.55/0.71 (b(elem!1, z) <=> b(s(s(s(elem!1))), z)),
% 0.55/0.71 inference(monotonicity,[status(thm)],[1189])).
% 0.55/0.71 tff(1191,plain,
% 0.55/0.71 (b(s(s(s(elem!1))), z) <=> b(elem!1, z)),
% 0.55/0.71 inference(symmetry,[status(thm)],[1190])).
% 0.55/0.71 tff(1192,plain,
% 0.55/0.71 ((~b(s(s(s(elem!1))), z)) <=> (~b(elem!1, z))),
% 0.55/0.71 inference(monotonicity,[status(thm)],[1191])).
% 0.55/0.71 tff(1193,plain,
% 0.55/0.71 (~b(elem!1, z)),
% 0.55/0.71 inference(modus_ponens,[status(thm)],[1188, 1192])).
% 0.55/0.71 tff(1194,assumption,(b(elem!1, z)), introduced(assumption)).
% 0.55/0.71 tff(1195,plain,
% 0.55/0.71 ($false),
% 0.55/0.71 inference(unit_resolution,[status(thm)],[1194, 1193])).
% 0.55/0.71 tff(1196,plain,((~(elem!1 = s(s(s(elem!1))))) | (~b(elem!1, z)) | b(s(s(s(elem!1))), z)), inference(lemma,lemma(discharge,[]))).
% 0.55/0.71 tff(1197,plain,
% 0.55/0.71 (~(elem!1 = s(s(s(elem!1))))),
% 0.55/0.71 inference(unit_resolution,[status(thm)],[1196, 1188, 1187])).
% 0.55/0.71 tff(1198,plain,
% 0.55/0.71 ((s(s(s(elem!1))) = elem!1) <=> (elem!1 = s(s(s(elem!1))))),
% 0.55/0.71 inference(commutativity,[status(thm)],[])).
% 0.55/0.71 tff(1199,assumption,(s(s(s(elem!1))) = elem!1), introduced(assumption)).
% 0.55/0.71 tff(1200,plain,
% 0.55/0.71 (elem!1 = s(s(s(elem!1)))),
% 0.55/0.71 inference(modus_ponens,[status(thm)],[1199, 1198])).
% 0.55/0.71 tff(1201,assumption,(~(elem!1 = s(s(s(elem!1))))), introduced(assumption)).
% 0.55/0.71 tff(1202,plain,
% 0.55/0.71 ($false),
% 0.55/0.71 inference(unit_resolution,[status(thm)],[1201, 1200])).
% 0.55/0.71 tff(1203,plain,((~(s(s(s(elem!1))) = elem!1)) | (elem!1 = s(s(s(elem!1))))), inference(lemma,lemma(discharge,[]))).
% 0.55/0.71 tff(1204,plain,
% 0.55/0.71 (~(s(s(s(elem!1))) = elem!1)),
% 0.55/0.71 inference(unit_resolution,[status(thm)],[1203, 1197])).
% 0.55/0.71 tff(1205,plain,
% 0.55/0.71 (b(s(s(s(elem!1))), elem!1) <=> b(s(s(s(elem!1))), s(s(elem!1)))),
% 0.55/0.71 inference(monotonicity,[status(thm)],[349])).
% 0.55/0.71 tff(1206,plain,
% 0.55/0.71 (b(s(s(s(elem!1))), s(s(elem!1))) <=> b(s(s(s(elem!1))), elem!1)),
% 0.55/0.71 inference(symmetry,[status(thm)],[1205])).
% 0.55/0.71 tff(1207,plain,
% 0.55/0.71 (b(s(elem!1), s(s(elem!1))) <=> b(s(s(s(elem!1))), elem!1)),
% 0.55/0.71 inference(transitivity,[status(thm)],[431, 1206])).
% 0.55/0.71 tff(1208,plain,
% 0.55/0.71 ((~b(s(elem!1), s(s(elem!1)))) <=> (~b(s(s(s(elem!1))), elem!1))),
% 0.55/0.71 inference(monotonicity,[status(thm)],[1207])).
% 0.55/0.71 tff(1209,assumption,(b(elem!1, s(s(s(z))))), introduced(assumption)).
% 0.55/0.71 tff(1210,plain,
% 0.55/0.71 (b(s(s(elem!1)), s(s(s(z))))),
% 0.55/0.71 inference(modus_ponens,[status(thm)],[1209, 330])).
% 0.55/0.71 tff(1211,plain,
% 0.55/0.71 (r(s(s(s(elem!1))), z)),
% 0.55/0.71 inference(unit_resolution,[status(thm)],[211, 1188])).
% 0.55/0.71 tff(1212,plain,
% 0.55/0.71 (r(s(elem!1), z)),
% 0.55/0.71 inference(unit_resolution,[status(thm)],[880, 1211, 255])).
% 0.55/0.71 tff(1213,plain,
% 0.55/0.71 (((~![X0: $i, X2: $i, X1: $i] : ((~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), z)) | (~b(s(s(s(z))), z)) | (~b(s(s(s(z))), s(s(elem!1)))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(elem!1)), z)) | (~b(s(s(s(z))), z)) | (~b(s(s(s(z))), s(s(elem!1)))))),
% 0.55/0.71 inference(rewrite,[status(thm)],[])).
% 0.55/0.71 tff(1214,plain,
% 0.55/0.71 ((~![X0: $i, X2: $i, X1: $i] : ((~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), z)) | (~b(s(s(s(z))), z)) | (~b(s(s(s(z))), s(s(elem!1)))))),
% 0.55/0.71 inference(quant_inst,[status(thm)],[])).
% 0.55/0.71 tff(1215,plain,
% 0.55/0.71 ((~![X0: $i, X2: $i, X1: $i] : ((~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(elem!1)), z)) | (~b(s(s(s(z))), z)) | (~b(s(s(s(z))), s(s(elem!1))))),
% 0.55/0.71 inference(modus_ponens,[status(thm)],[1214, 1213])).
% 0.55/0.71 tff(1216,plain,
% 0.55/0.71 ($false),
% 0.55/0.71 inference(unit_resolution,[status(thm)],[1215, 117, 1036, 338, 837])).
% 0.55/0.71 tff(1217,plain,((~b(s(s(s(z))), z)) | (~b(s(s(elem!1)), z)) | (~b(s(s(s(z))), s(s(elem!1))))), inference(lemma,lemma(discharge,[]))).
% 0.55/0.71 tff(1218,plain,
% 0.55/0.71 (~b(s(s(s(z))), z)),
% 0.55/0.71 inference(unit_resolution,[status(thm)],[1217, 837, 1026])).
% 0.55/0.71 tff(1219,plain,
% 0.55/0.71 (r(s(s(s(z))), z)),
% 0.55/0.71 inference(unit_resolution,[status(thm)],[823, 1218])).
% 0.55/0.71 tff(1220,plain,
% 0.55/0.71 (~r(s(elem!1), s(s(s(z))))),
% 0.55/0.71 inference(unit_resolution,[status(thm)],[1127, 14, 1219, 1212])).
% 0.55/0.71 tff(1221,plain,
% 0.55/0.71 ((s(elem!1) = s(s(s(z)))) | b(s(elem!1), s(s(s(z))))),
% 0.55/0.71 inference(unit_resolution,[status(thm)],[493, 46, 1220])).
% 0.55/0.71 tff(1222,plain,
% 0.55/0.71 (b(s(elem!1), s(s(s(z))))),
% 0.55/0.71 inference(unit_resolution,[status(thm)],[1221, 485])).
% 0.55/0.71 tff(1223,plain,
% 0.55/0.71 (((~![X0: $i, X2: $i, X1: $i] : ((~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), s(s(elem!1)))) | (~b(s(s(elem!1)), s(s(s(z))))) | (~b(s(elem!1), s(s(s(z))))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(elem!1), s(s(elem!1)))) | (~b(s(s(elem!1)), s(s(s(z))))) | (~b(s(elem!1), s(s(s(z))))))),
% 0.55/0.71 inference(rewrite,[status(thm)],[])).
% 0.55/0.71 tff(1224,plain,
% 0.55/0.71 (((~b(s(s(elem!1)), s(s(s(z))))) | (~b(s(elem!1), s(s(s(z))))) | (~b(s(elem!1), s(s(elem!1))))) <=> ((~b(s(elem!1), s(s(elem!1)))) | (~b(s(s(elem!1)), s(s(s(z))))) | (~b(s(elem!1), s(s(s(z))))))),
% 0.55/0.71 inference(rewrite,[status(thm)],[])).
% 0.55/0.71 tff(1225,plain,
% 0.55/0.71 (((~![X0: $i, X2: $i, X1: $i] : ((~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), s(s(s(z))))) | (~b(s(elem!1), s(s(s(z))))) | (~b(s(elem!1), s(s(elem!1)))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), s(s(elem!1)))) | (~b(s(s(elem!1)), s(s(s(z))))) | (~b(s(elem!1), s(s(s(z)))))))),
% 0.55/0.71 inference(monotonicity,[status(thm)],[1224])).
% 0.55/0.71 tff(1226,plain,
% 0.55/0.71 (((~![X0: $i, X2: $i, X1: $i] : ((~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), s(s(s(z))))) | (~b(s(elem!1), s(s(s(z))))) | (~b(s(elem!1), s(s(elem!1)))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(elem!1), s(s(elem!1)))) | (~b(s(s(elem!1)), s(s(s(z))))) | (~b(s(elem!1), s(s(s(z))))))),
% 0.55/0.71 inference(transitivity,[status(thm)],[1225, 1223])).
% 0.55/0.71 tff(1227,plain,
% 0.55/0.71 ((~![X0: $i, X2: $i, X1: $i] : ((~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), s(s(s(z))))) | (~b(s(elem!1), s(s(s(z))))) | (~b(s(elem!1), s(s(elem!1)))))),
% 0.55/0.71 inference(quant_inst,[status(thm)],[])).
% 0.55/0.71 tff(1228,plain,
% 0.55/0.71 ((~![X0: $i, X2: $i, X1: $i] : ((~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(elem!1), s(s(elem!1)))) | (~b(s(s(elem!1)), s(s(s(z))))) | (~b(s(elem!1), s(s(s(z)))))),
% 0.55/0.71 inference(modus_ponens,[status(thm)],[1227, 1226])).
% 0.55/0.71 tff(1229,plain,
% 0.55/0.71 ((~b(s(elem!1), s(s(elem!1)))) | (~b(s(s(elem!1)), s(s(s(z)))))),
% 0.55/0.71 inference(unit_resolution,[status(thm)],[1228, 117, 1222])).
% 0.55/0.71 tff(1230,plain,
% 0.55/0.71 (~b(s(elem!1), s(s(elem!1)))),
% 0.55/0.71 inference(unit_resolution,[status(thm)],[1229, 1210])).
% 0.55/0.71 tff(1231,plain,
% 0.55/0.71 (~b(s(s(s(elem!1))), elem!1)),
% 0.55/0.71 inference(modus_ponens,[status(thm)],[1230, 1208])).
% 0.55/0.71 tff(1232,plain,
% 0.55/0.71 (((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((s(s(s(elem!1))) = elem!1) | b(s(s(s(elem!1))), elem!1) | r(s(s(s(elem!1))), elem!1))) <=> ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (s(s(s(elem!1))) = elem!1) | b(s(s(s(elem!1))), elem!1) | r(s(s(s(elem!1))), elem!1))),
% 0.55/0.71 inference(rewrite,[status(thm)],[])).
% 0.55/0.71 tff(1233,plain,
% 0.55/0.71 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((s(s(s(elem!1))) = elem!1) | b(s(s(s(elem!1))), elem!1) | r(s(s(s(elem!1))), elem!1))),
% 0.55/0.71 inference(quant_inst,[status(thm)],[])).
% 0.55/0.71 tff(1234,plain,
% 0.55/0.71 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (s(s(s(elem!1))) = elem!1) | b(s(s(s(elem!1))), elem!1) | r(s(s(s(elem!1))), elem!1)),
% 0.55/0.71 inference(modus_ponens,[status(thm)],[1233, 1232])).
% 0.55/0.71 tff(1235,plain,
% 0.55/0.71 ((s(s(s(elem!1))) = elem!1) | b(s(s(s(elem!1))), elem!1) | r(s(s(s(elem!1))), elem!1)),
% 0.55/0.71 inference(unit_resolution,[status(thm)],[1234, 46])).
% 0.55/0.71 tff(1236,plain,
% 0.55/0.71 (r(s(s(s(elem!1))), elem!1)),
% 0.55/0.71 inference(unit_resolution,[status(thm)],[1235, 1231, 1204])).
% 0.55/0.71 tff(1237,plain,
% 0.55/0.71 (r(s(s(s(elem!1))), s(s(elem!1)))),
% 0.55/0.71 inference(modus_ponens,[status(thm)],[1236, 1184])).
% 0.55/0.71 tff(1238,plain,
% 0.55/0.71 (r(s(elem!1), s(s(elem!1)))),
% 0.55/0.71 inference(modus_ponens,[status(thm)],[1237, 1183])).
% 0.55/0.71 tff(1239,plain,
% 0.55/0.71 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(s(elem!1)))) | (~r(s(elem!1), s(z))) | (~r(s(elem!1), s(s(elem!1)))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(z), s(s(elem!1)))) | (~r(s(elem!1), s(z))) | (~r(s(elem!1), s(s(elem!1)))))),
% 0.55/0.71 inference(rewrite,[status(thm)],[])).
% 0.55/0.71 tff(1240,plain,
% 0.55/0.71 (((~r(s(z), s(s(elem!1)))) | (~r(s(elem!1), s(s(elem!1)))) | (~r(s(elem!1), s(z)))) <=> ((~r(s(z), s(s(elem!1)))) | (~r(s(elem!1), s(z))) | (~r(s(elem!1), s(s(elem!1)))))),
% 0.55/0.71 inference(rewrite,[status(thm)],[])).
% 0.55/0.71 tff(1241,plain,
% 0.55/0.71 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(s(elem!1)))) | (~r(s(elem!1), s(s(elem!1)))) | (~r(s(elem!1), s(z))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(s(elem!1)))) | (~r(s(elem!1), s(z))) | (~r(s(elem!1), s(s(elem!1))))))),
% 0.55/0.71 inference(monotonicity,[status(thm)],[1240])).
% 0.55/0.71 tff(1242,plain,
% 0.55/0.71 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(s(elem!1)))) | (~r(s(elem!1), s(s(elem!1)))) | (~r(s(elem!1), s(z))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(z), s(s(elem!1)))) | (~r(s(elem!1), s(z))) | (~r(s(elem!1), s(s(elem!1)))))),
% 0.55/0.71 inference(transitivity,[status(thm)],[1241, 1239])).
% 0.55/0.71 tff(1243,plain,
% 0.55/0.71 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(s(elem!1)))) | (~r(s(elem!1), s(s(elem!1)))) | (~r(s(elem!1), s(z))))),
% 0.55/0.71 inference(quant_inst,[status(thm)],[])).
% 0.55/0.71 tff(1244,plain,
% 0.55/0.71 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(z), s(s(elem!1)))) | (~r(s(elem!1), s(z))) | (~r(s(elem!1), s(s(elem!1))))),
% 0.55/0.71 inference(modus_ponens,[status(thm)],[1243, 1242])).
% 0.55/0.71 tff(1245,plain,
% 0.55/0.71 ((~r(s(elem!1), s(z))) | (~r(s(elem!1), s(s(elem!1))))),
% 0.55/0.71 inference(unit_resolution,[status(thm)],[1244, 14, 1061])).
% 0.55/0.71 tff(1246,plain,
% 0.55/0.71 (~r(s(elem!1), s(z))),
% 0.55/0.71 inference(unit_resolution,[status(thm)],[1245, 1238])).
% 0.55/0.71 tff(1247,plain,
% 0.55/0.71 (~r(s(s(s(elem!1))), s(z))),
% 0.55/0.71 inference(modus_ponens,[status(thm)],[1246, 747])).
% 0.55/0.71 tff(1248,plain,
% 0.55/0.71 (b(s(s(s(elem!1))), s(z))),
% 0.55/0.71 inference(unit_resolution,[status(thm)],[467, 1247])).
% 0.55/0.71 tff(1249,plain,
% 0.55/0.71 (b(s(elem!1), s(z))),
% 0.55/0.71 inference(modus_ponens,[status(thm)],[1248, 746])).
% 0.55/0.71 tff(1250,plain,
% 0.55/0.71 (~r(s(s(s(z))), s(elem!1))),
% 0.55/0.71 inference(unit_resolution,[status(thm)],[875, 1212, 1219])).
% 0.55/0.71 tff(1251,plain,
% 0.55/0.71 (b(s(s(s(z))), s(elem!1))),
% 0.55/0.71 inference(unit_resolution,[status(thm)],[627, 46, 624, 1250])).
% 0.55/0.71 tff(1252,plain,
% 0.55/0.71 (~b(s(s(elem!1)), s(elem!1))),
% 0.55/0.71 inference(unit_resolution,[status(thm)],[842, 1251, 837])).
% 0.55/0.71 tff(1253,plain,
% 0.55/0.71 (~b(s(s(elem!1)), s(s(s(elem!1))))),
% 0.55/0.72 inference(unit_resolution,[status(thm)],[834, 1252, 255])).
% 0.55/0.72 tff(1254,plain,
% 0.55/0.72 (r(s(s(elem!1)), s(s(s(elem!1))))),
% 0.55/0.72 inference(unit_resolution,[status(thm)],[253, 1253, 145])).
% 0.55/0.72 tff(1255,plain,
% 0.55/0.72 (~r(s(z), s(s(s(elem!1))))),
% 0.55/0.72 inference(unit_resolution,[status(thm)],[221, 1254, 1031])).
% 0.55/0.72 tff(1256,plain,
% 0.55/0.72 (b(s(z), s(s(s(elem!1))))),
% 0.55/0.72 inference(unit_resolution,[status(thm)],[235, 1255])).
% 0.55/0.72 tff(1257,plain,
% 0.55/0.72 (b(s(z), s(elem!1))),
% 0.55/0.72 inference(modus_ponens,[status(thm)],[1256, 727])).
% 0.55/0.72 tff(1258,plain,
% 0.55/0.72 (((~![X0: $i, X2: $i, X1: $i] : ((~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(s(z))))) | (~b(s(z), s(elem!1))) | (~b(s(s(s(z))), s(elem!1))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), s(s(s(z))))) | (~b(s(z), s(elem!1))) | (~b(s(s(s(z))), s(elem!1))))),
% 0.55/0.72 inference(rewrite,[status(thm)],[])).
% 0.55/0.72 tff(1259,plain,
% 0.55/0.72 (((~b(s(s(s(z))), s(elem!1))) | (~b(s(z), s(elem!1))) | (~b(s(z), s(s(s(z)))))) <=> ((~b(s(z), s(s(s(z))))) | (~b(s(z), s(elem!1))) | (~b(s(s(s(z))), s(elem!1))))),
% 0.55/0.72 inference(rewrite,[status(thm)],[])).
% 0.55/0.72 tff(1260,plain,
% 0.55/0.72 (((~![X0: $i, X2: $i, X1: $i] : ((~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), s(elem!1))) | (~b(s(z), s(elem!1))) | (~b(s(z), s(s(s(z))))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(s(z))))) | (~b(s(z), s(elem!1))) | (~b(s(s(s(z))), s(elem!1)))))),
% 0.55/0.72 inference(monotonicity,[status(thm)],[1259])).
% 0.55/0.72 tff(1261,plain,
% 0.55/0.72 (((~![X0: $i, X2: $i, X1: $i] : ((~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), s(elem!1))) | (~b(s(z), s(elem!1))) | (~b(s(z), s(s(s(z))))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), s(s(s(z))))) | (~b(s(z), s(elem!1))) | (~b(s(s(s(z))), s(elem!1))))),
% 0.55/0.72 inference(transitivity,[status(thm)],[1260, 1258])).
% 0.55/0.72 tff(1262,plain,
% 0.55/0.72 ((~![X0: $i, X2: $i, X1: $i] : ((~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), s(elem!1))) | (~b(s(z), s(elem!1))) | (~b(s(z), s(s(s(z))))))),
% 0.55/0.72 inference(quant_inst,[status(thm)],[])).
% 0.55/0.72 tff(1263,plain,
% 0.55/0.72 ((~![X0: $i, X2: $i, X1: $i] : ((~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), s(s(s(z))))) | (~b(s(z), s(elem!1))) | (~b(s(s(s(z))), s(elem!1)))),
% 0.55/0.72 inference(modus_ponens,[status(thm)],[1262, 1261])).
% 0.55/0.72 tff(1264,plain,
% 0.55/0.72 ((~b(s(z), s(s(s(z))))) | (~b(s(z), s(elem!1)))),
% 0.55/0.72 inference(unit_resolution,[status(thm)],[1263, 117, 1251])).
% 0.55/0.72 tff(1265,plain,
% 0.55/0.72 (~b(s(z), s(s(s(z))))),
% 0.55/0.72 inference(unit_resolution,[status(thm)],[1264, 1257])).
% 0.55/0.72 tff(1266,plain,
% 0.55/0.72 (r(s(z), s(s(s(z))))),
% 0.55/0.72 inference(unit_resolution,[status(thm)],[376, 1265])).
% 0.55/0.72 tff(1267,plain,
% 0.55/0.72 (~b(z, s(s(s(elem!1))))),
% 0.55/0.72 inference(unit_resolution,[status(thm)],[682, 1256, 237])).
% 0.55/0.72 tff(1268,plain,
% 0.55/0.72 (r(z, s(s(s(elem!1))))),
% 0.55/0.72 inference(unit_resolution,[status(thm)],[692, 1267])).
% 0.55/0.72 tff(1269,plain,
% 0.55/0.72 (r(z, s(elem!1))),
% 0.55/0.72 inference(modus_ponens,[status(thm)],[1268, 673])).
% 0.55/0.72 tff(1270,plain,
% 0.55/0.72 (r(s(s(elem!1)), s(elem!1)) <=> r(s(s(elem!1)), s(s(s(elem!1))))),
% 0.55/0.72 inference(monotonicity,[status(thm)],[260])).
% 0.55/0.72 tff(1271,plain,
% 0.55/0.72 (r(s(s(elem!1)), s(s(s(elem!1)))) <=> r(s(s(elem!1)), s(elem!1))),
% 0.55/0.72 inference(symmetry,[status(thm)],[1270])).
% 0.55/0.72 tff(1272,plain,
% 0.55/0.72 (r(s(s(elem!1)), s(elem!1))),
% 0.55/0.72 inference(modus_ponens,[status(thm)],[1254, 1271])).
% 0.55/0.72 tff(1273,plain,
% 0.55/0.72 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(elem!1)))) | (~r(s(s(elem!1)), s(elem!1))) | (~r(z, s(elem!1))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, s(s(elem!1)))) | (~r(s(s(elem!1)), s(elem!1))) | (~r(z, s(elem!1))))),
% 0.55/0.72 inference(rewrite,[status(thm)],[])).
% 0.55/0.72 tff(1274,plain,
% 0.55/0.72 (((~r(s(s(elem!1)), s(elem!1))) | (~r(z, s(elem!1))) | (~r(z, s(s(elem!1))))) <=> ((~r(z, s(s(elem!1)))) | (~r(s(s(elem!1)), s(elem!1))) | (~r(z, s(elem!1))))),
% 0.55/0.72 inference(rewrite,[status(thm)],[])).
% 0.55/0.72 tff(1275,plain,
% 0.55/0.72 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(elem!1)), s(elem!1))) | (~r(z, s(elem!1))) | (~r(z, s(s(elem!1)))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(elem!1)))) | (~r(s(s(elem!1)), s(elem!1))) | (~r(z, s(elem!1)))))),
% 0.55/0.72 inference(monotonicity,[status(thm)],[1274])).
% 0.55/0.72 tff(1276,plain,
% 0.55/0.72 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(elem!1)), s(elem!1))) | (~r(z, s(elem!1))) | (~r(z, s(s(elem!1)))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, s(s(elem!1)))) | (~r(s(s(elem!1)), s(elem!1))) | (~r(z, s(elem!1))))),
% 0.55/0.72 inference(transitivity,[status(thm)],[1275, 1273])).
% 0.55/0.72 tff(1277,plain,
% 0.55/0.72 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(elem!1)), s(elem!1))) | (~r(z, s(elem!1))) | (~r(z, s(s(elem!1)))))),
% 0.55/0.72 inference(quant_inst,[status(thm)],[])).
% 0.55/0.72 tff(1278,plain,
% 0.55/0.72 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, s(s(elem!1)))) | (~r(s(s(elem!1)), s(elem!1))) | (~r(z, s(elem!1)))),
% 0.55/0.72 inference(modus_ponens,[status(thm)],[1277, 1276])).
% 0.55/0.72 tff(1279,plain,
% 0.55/0.72 ((~r(z, s(s(elem!1)))) | (~r(s(s(elem!1)), s(elem!1))) | (~r(z, s(elem!1)))),
% 0.55/0.72 inference(unit_resolution,[status(thm)],[1278, 14])).
% 0.55/0.72 tff(1280,plain,
% 0.55/0.72 (~r(z, s(s(elem!1)))),
% 0.55/0.72 inference(unit_resolution,[status(thm)],[1279, 1272, 1269])).
% 0.55/0.72 tff(1281,plain,
% 0.55/0.72 ((z = s(s(elem!1))) | b(z, s(s(elem!1)))),
% 0.55/0.72 inference(unit_resolution,[status(thm)],[723, 46, 1280])).
% 0.55/0.72 tff(1282,plain,
% 0.55/0.72 (b(z, s(s(elem!1)))),
% 0.55/0.72 inference(unit_resolution,[status(thm)],[1281, 328])).
% 0.55/0.72 tff(1283,plain,
% 0.55/0.72 (((~![X0: $i, X2: $i, X1: $i] : ((~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(elem!1)))) | (~b(z, s(s(s(z))))) | (~b(s(s(s(z))), s(s(elem!1)))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(s(elem!1)))) | (~b(z, s(s(s(z))))) | (~b(s(s(s(z))), s(s(elem!1)))))),
% 0.55/0.72 inference(rewrite,[status(thm)],[])).
% 0.55/0.72 tff(1284,plain,
% 0.55/0.72 (((~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(s(z))), s(s(elem!1)))))),
% 0.55/0.72 inference(rewrite,[status(thm)],[])).
% 0.55/0.72 tff(1285,plain,
% 0.55/0.72 (((~![X0: $i, X2: $i, X1: $i] : ((~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(z, s(s(s(z))))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(elem!1)))) | (~b(z, s(s(s(z))))) | (~b(s(s(s(z))), s(s(elem!1))))))),
% 0.55/0.72 inference(monotonicity,[status(thm)],[1284])).
% 0.55/0.72 tff(1286,plain,
% 0.55/0.72 (((~![X0: $i, X2: $i, X1: $i] : ((~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(z, s(s(s(z))))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(s(elem!1)))) | (~b(z, s(s(s(z))))) | (~b(s(s(s(z))), s(s(elem!1)))))),
% 0.55/0.72 inference(transitivity,[status(thm)],[1285, 1283])).
% 0.55/0.72 tff(1287,plain,
% 0.55/0.72 ((~![X0: $i, X2: $i, X1: $i] : ((~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(z, s(s(s(z))))))),
% 0.55/0.72 inference(quant_inst,[status(thm)],[])).
% 0.55/0.72 tff(1288,plain,
% 0.55/0.72 ((~![X0: $i, X2: $i, X1: $i] : ((~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(s(elem!1)))) | (~b(z, s(s(s(z))))) | (~b(s(s(s(z))), s(s(elem!1))))),
% 0.55/0.72 inference(modus_ponens,[status(thm)],[1287, 1286])).
% 0.55/0.72 tff(1289,plain,
% 0.55/0.72 (~b(z, s(s(s(z))))),
% 0.55/0.72 inference(unit_resolution,[status(thm)],[1288, 117, 1282, 837])).
% 0.55/0.72 tff(1290,plain,
% 0.55/0.72 (r(z, s(s(s(z))))),
% 0.55/0.72 inference(unit_resolution,[status(thm)],[711, 1289])).
% 0.55/0.72 tff(1291,plain,
% 0.55/0.72 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(z))) | (~r(z, s(s(s(z))))) | (~r(s(z), s(s(s(z))))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, s(z))) | (~r(z, s(s(s(z))))) | (~r(s(z), s(s(s(z))))))),
% 0.55/0.72 inference(rewrite,[status(thm)],[])).
% 0.55/0.72 tff(1292,plain,
% 0.55/0.72 (((~r(s(z), s(s(s(z))))) | (~r(z, s(s(s(z))))) | (~r(z, s(z)))) <=> ((~r(z, s(z))) | (~r(z, s(s(s(z))))) | (~r(s(z), s(s(s(z))))))),
% 0.55/0.72 inference(rewrite,[status(thm)],[])).
% 0.55/0.72 tff(1293,plain,
% 0.55/0.72 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(s(s(z))))) | (~r(z, s(s(s(z))))) | (~r(z, s(z))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(z))) | (~r(z, s(s(s(z))))) | (~r(s(z), s(s(s(z)))))))),
% 0.55/0.72 inference(monotonicity,[status(thm)],[1292])).
% 0.55/0.72 tff(1294,plain,
% 0.55/0.72 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(s(s(z))))) | (~r(z, s(s(s(z))))) | (~r(z, s(z))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, s(z))) | (~r(z, s(s(s(z))))) | (~r(s(z), s(s(s(z))))))),
% 0.55/0.72 inference(transitivity,[status(thm)],[1293, 1291])).
% 0.55/0.72 tff(1295,plain,
% 0.55/0.72 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(s(s(z))))) | (~r(z, s(s(s(z))))) | (~r(z, s(z))))),
% 0.55/0.72 inference(quant_inst,[status(thm)],[])).
% 0.55/0.72 tff(1296,plain,
% 0.55/0.72 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, s(z))) | (~r(z, s(s(s(z))))) | (~r(s(z), s(s(s(z)))))),
% 0.55/0.72 inference(modus_ponens,[status(thm)],[1295, 1294])).
% 0.55/0.72 tff(1297,plain,
% 0.55/0.72 (~r(z, s(z))),
% 0.55/0.72 inference(unit_resolution,[status(thm)],[1296, 14, 1290, 1266])).
% 0.55/0.72 tff(1298,plain,
% 0.55/0.72 (b(z, s(z))),
% 0.55/0.72 inference(unit_resolution,[status(thm)],[599, 1297])).
% 0.55/0.72 tff(1299,plain,
% 0.55/0.72 (~b(s(elem!1), s(z))),
% 0.55/0.72 inference(unit_resolution,[status(thm)],[798, 1298, 477, 562, 1212])).
% 0.55/0.72 tff(1300,plain,
% 0.55/0.72 ($false),
% 0.55/0.72 inference(unit_resolution,[status(thm)],[1299, 1249])).
% 0.55/0.72 tff(1301,plain,(b(s(s(s(elem!1))), z) | (~(s(s(s(s(elem!1)))) = s(s(elem!1)))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(z))), s(s(elem!1)))) | (~b(elem!1, s(s(s(z))))) | (~b(s(z), z)) | (s(s(elem!1)) = s(s(s(elem!1))))), inference(lemma,lemma(discharge,[]))).
% 0.55/0.72 tff(1302,plain,
% 0.55/0.72 (~b(s(s(s(z))), s(s(elem!1)))),
% 0.55/0.72 inference(unit_resolution,[status(thm)],[1301, 1182, 255, 1051, 1179, 237, 145])).
% 0.55/0.72 tff(1303,plain,
% 0.55/0.72 ($false),
% 0.55/0.72 inference(unit_resolution,[status(thm)],[1302, 1035])).
% 0.55/0.72 tff(1304,plain,((~r(s(s(s(z))), s(z))) | (~(s(s(s(s(elem!1)))) = s(s(elem!1)))) | (~b(s(z), z)) | (s(s(elem!1)) = s(s(s(elem!1))))), inference(lemma,lemma(discharge,[]))).
% 0.55/0.72 tff(1305,plain,
% 0.55/0.72 (~r(s(s(s(z))), s(z))),
% 0.55/0.72 inference(unit_resolution,[status(thm)],[1304, 145, 237, 255])).
% 0.55/0.72 tff(1306,plain,
% 0.55/0.72 (b(s(s(s(z))), s(z))),
% 0.55/0.72 inference(unit_resolution,[status(thm)],[347, 1305])).
% 0.55/0.72 tff(1307,plain,
% 0.55/0.72 (b(s(s(s(s(elem!1)))), z) <=> b(s(s(elem!1)), z)),
% 0.55/0.72 inference(monotonicity,[status(thm)],[255])).
% 0.55/0.72 tff(1308,plain,
% 0.55/0.72 (b(s(s(elem!1)), z) <=> b(s(s(s(s(elem!1)))), z)),
% 0.55/0.72 inference(symmetry,[status(thm)],[1307])).
% 0.55/0.72 tff(1309,plain,
% 0.55/0.72 (b(s(s(s(s(elem!1)))), z)),
% 0.55/0.72 inference(modus_ponens,[status(thm)],[1026, 1308])).
% 0.55/0.72 tff(1310,assumption,(b(s(s(s(s(elem!1)))), z)), introduced(assumption)).
% 0.55/0.72 tff(1311,assumption,(b(s(s(s(s(elem!1)))), s(z))), introduced(assumption)).
% 0.55/0.72 tff(1312,plain,
% 0.55/0.72 (((~![X0: $i, X2: $i, X1: $i] : ((~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), z)) | (~b(s(s(s(s(elem!1)))), z)) | (~b(s(s(s(s(elem!1)))), s(z))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), z)) | (~b(s(s(s(s(elem!1)))), z)) | (~b(s(s(s(s(elem!1)))), s(z))))),
% 0.55/0.72 inference(rewrite,[status(thm)],[])).
% 0.55/0.72 tff(1313,plain,
% 0.55/0.72 ((~![X0: $i, X2: $i, X1: $i] : ((~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), z)) | (~b(s(s(s(s(elem!1)))), z)) | (~b(s(s(s(s(elem!1)))), s(z))))),
% 0.55/0.72 inference(quant_inst,[status(thm)],[])).
% 0.55/0.72 tff(1314,plain,
% 0.55/0.72 ((~![X0: $i, X2: $i, X1: $i] : ((~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), z)) | (~b(s(s(s(s(elem!1)))), z)) | (~b(s(s(s(s(elem!1)))), s(z)))),
% 0.55/0.72 inference(modus_ponens,[status(thm)],[1313, 1312])).
% 0.55/0.72 tff(1315,plain,
% 0.55/0.72 ($false),
% 0.55/0.72 inference(unit_resolution,[status(thm)],[1314, 117, 237, 1311, 1310])).
% 0.55/0.72 tff(1316,plain,((~b(s(s(s(s(elem!1)))), z)) | (~b(s(z), z)) | (~b(s(s(s(s(elem!1)))), s(z)))), inference(lemma,lemma(discharge,[]))).
% 0.55/0.72 tff(1317,plain,
% 0.55/0.72 (~b(s(s(s(s(elem!1)))), s(z))),
% 0.55/0.72 inference(unit_resolution,[status(thm)],[1316, 1309, 237])).
% 0.55/0.72 tff(1318,assumption,(s(s(s(s(elem!1)))) = s(z)), introduced(assumption)).
% 0.55/0.72 tff(1319,plain,
% 0.55/0.72 (inj_0(s(s(s(s(elem!1))))) = inj_0(s(z))),
% 0.55/0.72 inference(monotonicity,[status(thm)],[1318])).
% 0.55/0.72 tff(1320,plain,
% 0.55/0.72 (s(s(s(elem!1))) = z),
% 0.55/0.72 inference(transitivity,[status(thm)],[295, 1319, 90])).
% 0.55/0.72 tff(1321,plain,
% 0.55/0.72 ($false),
% 0.55/0.72 inference(unit_resolution,[status(thm)],[207, 1320])).
% 0.55/0.72 tff(1322,plain,(~(s(s(s(s(elem!1)))) = s(z))), inference(lemma,lemma(discharge,[]))).
% 0.55/0.72 tff(1323,plain,
% 0.55/0.72 (((~![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)))),
% 0.55/0.72 inference(rewrite,[status(thm)],[])).
% 0.55/0.72 tff(1324,plain,
% 0.55/0.72 ((~![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)))),
% 0.55/0.72 inference(quant_inst,[status(thm)],[])).
% 0.55/0.72 tff(1325,plain,
% 0.55/0.72 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (s(s(s(s(elem!1)))) = s(z)) | b(s(s(s(s(elem!1)))), s(z)) | r(s(s(s(s(elem!1)))), s(z))),
% 0.55/0.72 inference(modus_ponens,[status(thm)],[1324, 1323])).
% 0.55/0.72 tff(1326,plain,
% 0.55/0.72 ((s(s(s(s(elem!1)))) = s(z)) | b(s(s(s(s(elem!1)))), s(z)) | r(s(s(s(s(elem!1)))), s(z))),
% 0.55/0.72 inference(unit_resolution,[status(thm)],[1325, 46])).
% 0.55/0.72 tff(1327,plain,
% 0.55/0.72 (b(s(s(s(s(elem!1)))), s(z)) | r(s(s(s(s(elem!1)))), s(z))),
% 0.55/0.72 inference(unit_resolution,[status(thm)],[1326, 1322])).
% 0.55/0.72 tff(1328,plain,
% 0.55/0.72 (r(s(s(s(s(elem!1)))), s(z))),
% 0.55/0.72 inference(unit_resolution,[status(thm)],[1327, 1317])).
% 0.55/0.72 tff(1329,plain,
% 0.55/0.72 (~r(s(s(s(z))), z)),
% 0.55/0.72 inference(unit_resolution,[status(thm)],[897, 574, 562, 848])).
% 0.55/0.72 tff(1330,plain,
% 0.55/0.72 (b(s(s(s(z))), z)),
% 0.55/0.72 inference(unit_resolution,[status(thm)],[823, 1329])).
% 0.55/0.72 tff(1331,plain,
% 0.55/0.72 ($false),
% 0.55/0.72 inference(unit_resolution,[status(thm)],[965, 117, 574, 1330, 848])).
% 0.55/0.72 tff(1332,plain,((~b(z, s(z))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(s(z)))), s(z)))), inference(lemma,lemma(discharge,[]))).
% 0.55/0.72 tff(1333,plain,
% 0.55/0.72 (~b(z, s(z))),
% 0.55/0.72 inference(unit_resolution,[status(thm)],[1332, 1306, 1179])).
% 0.55/0.72 tff(1334,plain,
% 0.55/0.72 (r(z, s(z))),
% 0.55/0.72 inference(unit_resolution,[status(thm)],[599, 1333])).
% 0.55/0.72 tff(1335,plain,
% 0.55/0.72 (r(s(z), s(elem!1))),
% 0.55/0.72 inference(unit_resolution,[status(thm)],[642, 213, 255])).
% 0.55/0.72 tff(1336,assumption,(r(s(s(s(s(elem!1)))), s(z))), introduced(assumption)).
% 0.55/0.72 tff(1337,assumption,(r(s(s(s(s(elem!1)))), s(s(s(elem!1))))), introduced(assumption)).
% 0.55/0.72 tff(1338,plain,
% 0.55/0.72 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(s(s(elem!1))))) | (~r(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~r(s(s(s(s(elem!1)))), s(z))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(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))))),
% 0.55/0.72 inference(rewrite,[status(thm)],[])).
% 0.55/0.72 tff(1339,plain,
% 0.55/0.72 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(s(s(elem!1))))) | (~r(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~r(s(s(s(s(elem!1)))), s(z))))),
% 0.55/0.72 inference(quant_inst,[status(thm)],[])).
% 0.55/0.72 tff(1340,plain,
% 0.55/0.72 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(z), s(s(s(elem!1))))) | (~r(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~r(s(s(s(s(elem!1)))), s(z)))),
% 0.55/0.72 inference(modus_ponens,[status(thm)],[1339, 1338])).
% 0.55/0.72 tff(1341,plain,
% 0.55/0.72 ($false),
% 0.55/0.72 inference(unit_resolution,[status(thm)],[1340, 14, 213, 1336, 1337])).
% 0.55/0.72 tff(1342,plain,((~r(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~r(s(z), s(s(s(elem!1))))) | (~r(s(s(s(s(elem!1)))), s(z)))), inference(lemma,lemma(discharge,[]))).
% 0.55/0.72 tff(1343,plain,
% 0.55/0.72 (~r(s(s(s(s(elem!1)))), s(s(s(elem!1))))),
% 0.55/0.72 inference(unit_resolution,[status(thm)],[1342, 213, 1336])).
% 0.55/0.72 tff(1344,plain,
% 0.55/0.72 (((~![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)))))),
% 0.55/0.72 inference(rewrite,[status(thm)],[])).
% 0.55/0.72 tff(1345,plain,
% 0.55/0.72 ((~![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)))))),
% 0.55/0.72 inference(quant_inst,[status(thm)],[])).
% 0.55/0.72 tff(1346,plain,
% 0.55/0.72 ((~![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))))),
% 0.55/0.72 inference(modus_ponens,[status(thm)],[1345, 1344])).
% 0.55/0.72 tff(1347,plain,
% 0.55/0.72 ((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))))),
% 0.55/0.72 inference(unit_resolution,[status(thm)],[1346, 46])).
% 0.55/0.72 tff(1348,plain,
% 0.55/0.72 (b(s(s(s(s(elem!1)))), s(s(s(elem!1))))),
% 0.55/0.72 inference(unit_resolution,[status(thm)],[1347, 1343, 287])).
% 0.55/0.72 tff(1349,assumption,(b(s(s(s(s(elem!1)))), s(s(s(elem!1))))), introduced(assumption)).
% 0.55/0.72 tff(1350,plain,
% 0.55/0.72 (b(z, s(s(s(s(elem!1))))) <=> b(z, s(s(elem!1)))),
% 0.55/0.72 inference(monotonicity,[status(thm)],[255])).
% 0.55/0.72 tff(1351,plain,
% 0.55/0.72 (b(z, s(s(elem!1))) <=> b(z, s(s(s(s(elem!1)))))),
% 0.55/0.72 inference(symmetry,[status(thm)],[1350])).
% 0.55/0.72 tff(1352,plain,
% 0.55/0.72 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(z))) | (~r(s(s(elem!1)), s(z))) | (~r(z, s(s(elem!1)))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, s(z))) | (~r(s(s(elem!1)), s(z))) | (~r(z, s(s(elem!1)))))),
% 0.55/0.72 inference(rewrite,[status(thm)],[])).
% 0.55/0.72 tff(1353,plain,
% 0.55/0.72 (((~r(s(s(elem!1)), s(z))) | (~r(z, s(z))) | (~r(z, s(s(elem!1))))) <=> ((~r(z, s(z))) | (~r(s(s(elem!1)), s(z))) | (~r(z, s(s(elem!1)))))),
% 0.55/0.72 inference(rewrite,[status(thm)],[])).
% 0.55/0.72 tff(1354,plain,
% 0.55/0.72 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(elem!1)), s(z))) | (~r(z, s(z))) | (~r(z, s(s(elem!1)))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(z))) | (~r(s(s(elem!1)), s(z))) | (~r(z, s(s(elem!1))))))),
% 0.55/0.72 inference(monotonicity,[status(thm)],[1353])).
% 0.55/0.72 tff(1355,plain,
% 0.55/0.72 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(elem!1)), s(z))) | (~r(z, s(z))) | (~r(z, s(s(elem!1)))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, s(z))) | (~r(s(s(elem!1)), s(z))) | (~r(z, s(s(elem!1)))))),
% 0.55/0.72 inference(transitivity,[status(thm)],[1354, 1352])).
% 0.55/0.72 tff(1356,plain,
% 0.55/0.72 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(elem!1)), s(z))) | (~r(z, s(z))) | (~r(z, s(s(elem!1)))))),
% 0.55/0.72 inference(quant_inst,[status(thm)],[])).
% 0.55/0.72 tff(1357,plain,
% 0.55/0.72 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, s(z))) | (~r(s(s(elem!1)), s(z))) | (~r(z, s(s(elem!1))))),
% 0.55/0.72 inference(modus_ponens,[status(thm)],[1356, 1355])).
% 0.55/0.72 tff(1358,plain,
% 0.55/0.72 (~r(z, s(s(elem!1)))),
% 0.55/0.72 inference(unit_resolution,[status(thm)],[1357, 14, 181, 2])).
% 0.55/0.72 tff(1359,plain,
% 0.55/0.72 ((z = s(s(elem!1))) | b(z, s(s(elem!1)))),
% 0.55/0.72 inference(unit_resolution,[status(thm)],[723, 46, 1358])).
% 0.55/0.72 tff(1360,plain,
% 0.55/0.72 (b(z, s(s(elem!1)))),
% 0.55/0.72 inference(unit_resolution,[status(thm)],[1359, 328])).
% 0.55/0.72 tff(1361,plain,
% 0.55/0.72 (b(z, s(s(s(s(elem!1)))))),
% 0.55/0.72 inference(modus_ponens,[status(thm)],[1360, 1351])).
% 0.55/0.72 tff(1362,assumption,(b(z, s(s(s(s(elem!1)))))), introduced(assumption)).
% 0.55/0.72 tff(1363,plain,
% 0.55/0.72 (((~![X0: $i, X2: $i, X1: $i] : ((~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(s(elem!1))))) | (~b(z, s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), s(s(s(elem!1))))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(s(s(elem!1))))) | (~b(z, s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), s(s(s(elem!1))))))),
% 0.55/0.73 inference(rewrite,[status(thm)],[])).
% 0.55/0.73 tff(1364,plain,
% 0.55/0.73 (((~b(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~b(z, s(s(s(elem!1))))) | (~b(z, s(s(s(s(elem!1))))))) <=> ((~b(z, s(s(s(elem!1))))) | (~b(z, s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), s(s(s(elem!1))))))),
% 0.55/0.73 inference(rewrite,[status(thm)],[])).
% 0.55/0.73 tff(1365,plain,
% 0.55/0.73 (((~![X0: $i, X2: $i, X1: $i] : ((~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~b(z, s(s(s(elem!1))))) | (~b(z, s(s(s(s(elem!1)))))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(s(elem!1))))) | (~b(z, s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), s(s(s(elem!1)))))))),
% 0.55/0.73 inference(monotonicity,[status(thm)],[1364])).
% 0.55/0.73 tff(1366,plain,
% 0.55/0.73 (((~![X0: $i, X2: $i, X1: $i] : ((~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~b(z, s(s(s(elem!1))))) | (~b(z, s(s(s(s(elem!1)))))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(s(s(elem!1))))) | (~b(z, s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), s(s(s(elem!1))))))),
% 0.55/0.73 inference(transitivity,[status(thm)],[1365, 1363])).
% 0.55/0.73 tff(1367,plain,
% 0.55/0.73 ((~![X0: $i, X2: $i, X1: $i] : ((~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~b(z, s(s(s(elem!1))))) | (~b(z, s(s(s(s(elem!1)))))))),
% 0.55/0.73 inference(quant_inst,[status(thm)],[])).
% 0.55/0.73 tff(1368,plain,
% 0.55/0.73 ((~![X0: $i, X2: $i, X1: $i] : ((~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(s(s(elem!1))))) | (~b(z, s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), s(s(s(elem!1)))))),
% 0.55/0.73 inference(modus_ponens,[status(thm)],[1367, 1366])).
% 0.55/0.73 tff(1369,plain,
% 0.55/0.73 ($false),
% 0.55/0.73 inference(unit_resolution,[status(thm)],[1368, 117, 674, 1349, 1362])).
% 0.55/0.73 tff(1370,plain,((~b(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~b(z, s(s(s(elem!1))))) | (~b(z, s(s(s(s(elem!1))))))), inference(lemma,lemma(discharge,[]))).
% 0.55/0.73 tff(1371,plain,
% 0.55/0.73 (~b(z, s(s(s(elem!1))))),
% 0.55/0.73 inference(unit_resolution,[status(thm)],[1370, 1361, 1349])).
% 0.55/0.73 tff(1372,plain,
% 0.55/0.73 (r(z, s(s(s(elem!1))))),
% 0.55/0.73 inference(unit_resolution,[status(thm)],[692, 1371])).
% 0.55/0.73 tff(1373,plain,
% 0.55/0.73 (r(z, s(elem!1))),
% 0.55/0.73 inference(modus_ponens,[status(thm)],[1372, 673])).
% 0.55/0.73 tff(1374,plain,
% 0.55/0.73 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(elem!1))) | (~r(z, s(z))) | (~r(z, s(elem!1))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(z), s(elem!1))) | (~r(z, s(z))) | (~r(z, s(elem!1))))),
% 0.55/0.73 inference(rewrite,[status(thm)],[])).
% 0.55/0.73 tff(1375,plain,
% 0.55/0.73 (((~r(s(z), s(elem!1))) | (~r(z, s(elem!1))) | (~r(z, s(z)))) <=> ((~r(s(z), s(elem!1))) | (~r(z, s(z))) | (~r(z, s(elem!1))))),
% 0.55/0.73 inference(rewrite,[status(thm)],[])).
% 0.55/0.73 tff(1376,plain,
% 0.55/0.73 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(elem!1))) | (~r(z, s(elem!1))) | (~r(z, s(z))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(elem!1))) | (~r(z, s(z))) | (~r(z, s(elem!1)))))),
% 0.55/0.73 inference(monotonicity,[status(thm)],[1375])).
% 0.55/0.73 tff(1377,plain,
% 0.55/0.73 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(elem!1))) | (~r(z, s(elem!1))) | (~r(z, s(z))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(z), s(elem!1))) | (~r(z, s(z))) | (~r(z, s(elem!1))))),
% 0.55/0.73 inference(transitivity,[status(thm)],[1376, 1374])).
% 0.55/0.73 tff(1378,plain,
% 0.55/0.73 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(elem!1))) | (~r(z, s(elem!1))) | (~r(z, s(z))))),
% 0.55/0.73 inference(quant_inst,[status(thm)],[])).
% 0.55/0.73 tff(1379,plain,
% 0.55/0.73 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(z), s(elem!1))) | (~r(z, s(z))) | (~r(z, s(elem!1)))),
% 0.55/0.73 inference(modus_ponens,[status(thm)],[1378, 1377])).
% 0.55/0.73 tff(1380,plain,
% 0.55/0.73 (~r(z, s(elem!1))),
% 0.55/0.73 inference(unit_resolution,[status(thm)],[1379, 14, 2, 630])).
% 0.55/0.73 tff(1381,plain,
% 0.55/0.73 ($false),
% 0.55/0.73 inference(unit_resolution,[status(thm)],[1380, 1373])).
% 0.55/0.73 tff(1382,plain,((~r(z, s(z))) | (~(s(s(s(s(elem!1)))) = s(s(elem!1)))) | (~r(s(z), s(elem!1))) | (~b(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~r(s(s(elem!1)), s(z)))), inference(lemma,lemma(discharge,[]))).
% 0.55/0.73 tff(1383,plain,
% 0.55/0.73 ($false),
% 0.55/0.73 inference(unit_resolution,[status(thm)],[1382, 1348, 1335, 255, 2, 181])).
% 0.55/0.73 tff(1384,plain,((~r(s(z), s(s(s(elem!1))))) | (~(s(s(s(s(elem!1)))) = s(s(elem!1)))) | (~r(z, s(z))) | (~r(s(s(elem!1)), s(z))) | (s(s(s(s(elem!1)))) = s(s(s(elem!1)))) | (~r(s(s(s(s(elem!1)))), s(z)))), inference(lemma,lemma(discharge,[]))).
% 0.55/0.73 tff(1385,plain,
% 0.55/0.73 (~r(s(z), s(s(s(elem!1))))),
% 0.55/0.73 inference(unit_resolution,[status(thm)],[1384, 1334, 255, 1031, 156, 1328])).
% 0.55/0.73 tff(1386,plain,
% 0.55/0.73 (b(s(z), s(s(s(elem!1))))),
% 0.55/0.73 inference(unit_resolution,[status(thm)],[235, 1385])).
% 0.55/0.73 tff(1387,plain,
% 0.55/0.73 (~b(s(s(s(z))), s(elem!1))),
% 0.55/0.73 inference(unit_resolution,[status(thm)],[1139, 1386, 255, 1306])).
% 0.55/0.73 tff(1388,plain,
% 0.55/0.73 ($false),
% 0.55/0.73 inference(unit_resolution,[status(thm)],[341, 117, 237, 338, 848])).
% 0.55/0.73 tff(1389,plain,((~b(s(s(s(z))), z)) | (~b(s(z), z)) | (~b(s(s(s(z))), s(z)))), inference(lemma,lemma(discharge,[]))).
% 0.55/0.73 tff(1390,plain,
% 0.55/0.73 (~b(s(s(s(z))), z)),
% 0.55/0.73 inference(unit_resolution,[status(thm)],[1389, 1306, 237])).
% 0.55/0.73 tff(1391,plain,
% 0.55/0.73 (r(s(s(s(z))), z)),
% 0.55/0.73 inference(unit_resolution,[status(thm)],[823, 1390])).
% 0.55/0.73 tff(1392,plain,
% 0.55/0.73 (~r(s(s(s(z))), s(elem!1))),
% 0.55/0.73 inference(unit_resolution,[status(thm)],[875, 1391, 1053])).
% 0.55/0.73 tff(1393,plain,
% 0.55/0.73 ($false),
% 0.55/0.73 inference(unit_resolution,[status(thm)],[627, 46, 624, 1392, 1387])).
% 0.55/0.73 tff(1394,plain,((s(s(elem!1)) = s(s(s(elem!1)))) | (~b(s(z), z)) | (~(s(s(s(s(elem!1)))) = s(s(elem!1))))), inference(lemma,lemma(discharge,[]))).
% 0.55/0.73 tff(1395,plain,
% 0.55/0.73 (~(s(s(s(s(elem!1)))) = s(s(elem!1)))),
% 0.55/0.73 inference(unit_resolution,[status(thm)],[1394, 194, 145])).
% 0.55/0.73 tff(1396,assumption,(r(s(s(s(s(elem!1)))), z)), introduced(assumption)).
% 0.55/0.73 tff(1397,assumption,(r(s(s(s(s(elem!1)))), s(s(elem!1)))), introduced(assumption)).
% 0.55/0.73 tff(1398,plain,
% 0.55/0.73 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(elem!1)), z)) | (~r(s(s(s(s(elem!1)))), z)) | (~r(s(s(s(s(elem!1)))), s(s(elem!1)))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(elem!1)), z)) | (~r(s(s(s(s(elem!1)))), z)) | (~r(s(s(s(s(elem!1)))), s(s(elem!1)))))),
% 0.55/0.73 inference(rewrite,[status(thm)],[])).
% 0.55/0.73 tff(1399,plain,
% 0.55/0.73 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(elem!1)), z)) | (~r(s(s(s(s(elem!1)))), z)) | (~r(s(s(s(s(elem!1)))), s(s(elem!1)))))),
% 0.55/0.73 inference(quant_inst,[status(thm)],[])).
% 0.55/0.73 tff(1400,plain,
% 0.55/0.73 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(elem!1)), z)) | (~r(s(s(s(s(elem!1)))), z)) | (~r(s(s(s(s(elem!1)))), s(s(elem!1))))),
% 0.55/0.73 inference(modus_ponens,[status(thm)],[1399, 1398])).
% 0.55/0.73 tff(1401,plain,
% 0.55/0.73 ($false),
% 0.55/0.73 inference(unit_resolution,[status(thm)],[1400, 14, 182, 1397, 1396])).
% 0.55/0.73 tff(1402,plain,((~r(s(s(s(s(elem!1)))), z)) | (~r(s(s(elem!1)), z)) | (~r(s(s(s(s(elem!1)))), s(s(elem!1))))), inference(lemma,lemma(discharge,[]))).
% 0.55/0.73 tff(1403,plain,
% 0.55/0.73 (~r(s(s(s(s(elem!1)))), s(s(elem!1)))),
% 0.55/0.73 inference(unit_resolution,[status(thm)],[1402, 1396, 182])).
% 0.55/0.73 tff(1404,plain,
% 0.55/0.73 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(z))), z)) | (~r(s(s(s(s(elem!1)))), z)) | (~r(s(s(s(z))), s(s(s(s(elem!1)))))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(z))), z)) | (~r(s(s(s(s(elem!1)))), z)) | (~r(s(s(s(z))), s(s(s(s(elem!1)))))))),
% 0.55/0.73 inference(rewrite,[status(thm)],[])).
% 0.55/0.73 tff(1405,plain,
% 0.55/0.73 (((~r(s(s(s(s(elem!1)))), z)) | (~r(s(s(s(z))), z)) | (~r(s(s(s(z))), s(s(s(s(elem!1))))))) <=> ((~r(s(s(s(z))), z)) | (~r(s(s(s(s(elem!1)))), z)) | (~r(s(s(s(z))), s(s(s(s(elem!1)))))))),
% 0.55/0.73 inference(rewrite,[status(thm)],[])).
% 0.55/0.73 tff(1406,plain,
% 0.55/0.73 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(elem!1)))), z)) | (~r(s(s(s(z))), z)) | (~r(s(s(s(z))), s(s(s(s(elem!1)))))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(z))), z)) | (~r(s(s(s(s(elem!1)))), z)) | (~r(s(s(s(z))), s(s(s(s(elem!1))))))))),
% 0.55/0.73 inference(monotonicity,[status(thm)],[1405])).
% 0.55/0.73 tff(1407,plain,
% 0.55/0.73 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(elem!1)))), z)) | (~r(s(s(s(z))), z)) | (~r(s(s(s(z))), s(s(s(s(elem!1)))))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(z))), z)) | (~r(s(s(s(s(elem!1)))), z)) | (~r(s(s(s(z))), s(s(s(s(elem!1)))))))),
% 0.55/0.73 inference(transitivity,[status(thm)],[1406, 1404])).
% 0.55/0.73 tff(1408,plain,
% 0.55/0.73 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(elem!1)))), z)) | (~r(s(s(s(z))), z)) | (~r(s(s(s(z))), s(s(s(s(elem!1)))))))),
% 0.55/0.73 inference(quant_inst,[status(thm)],[])).
% 0.55/0.73 tff(1409,plain,
% 0.55/0.73 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(z))), z)) | (~r(s(s(s(s(elem!1)))), z)) | (~r(s(s(s(z))), s(s(s(s(elem!1))))))),
% 0.55/0.73 inference(modus_ponens,[status(thm)],[1408, 1407])).
% 0.55/0.73 tff(1410,plain,
% 0.55/0.73 (~r(s(s(s(z))), s(s(s(s(elem!1)))))),
% 0.55/0.73 inference(unit_resolution,[status(thm)],[1409, 14, 180, 1396])).
% 0.55/0.73 tff(1411,plain,
% 0.55/0.73 (((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((s(s(s(z))) = s(s(s(s(elem!1))))) | b(s(s(s(z))), s(s(s(s(elem!1))))) | r(s(s(s(z))), s(s(s(s(elem!1))))))) <=> ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (s(s(s(z))) = s(s(s(s(elem!1))))) | b(s(s(s(z))), s(s(s(s(elem!1))))) | r(s(s(s(z))), s(s(s(s(elem!1))))))),
% 0.55/0.73 inference(rewrite,[status(thm)],[])).
% 0.55/0.73 tff(1412,plain,
% 0.55/0.73 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((s(s(s(z))) = s(s(s(s(elem!1))))) | b(s(s(s(z))), s(s(s(s(elem!1))))) | r(s(s(s(z))), s(s(s(s(elem!1))))))),
% 0.55/0.73 inference(quant_inst,[status(thm)],[])).
% 0.55/0.73 tff(1413,plain,
% 0.55/0.73 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (s(s(s(z))) = s(s(s(s(elem!1))))) | b(s(s(s(z))), s(s(s(s(elem!1))))) | r(s(s(s(z))), s(s(s(s(elem!1)))))),
% 0.55/0.73 inference(modus_ponens,[status(thm)],[1412, 1411])).
% 0.55/0.73 tff(1414,plain,
% 0.55/0.73 (b(s(s(s(z))), s(s(s(s(elem!1)))))),
% 0.55/0.73 inference(unit_resolution,[status(thm)],[1413, 46, 279, 1410])).
% 0.55/0.73 tff(1415,plain,
% 0.55/0.73 (~(s(s(s(s(elem!1)))) = s(s(elem!1)))),
% 0.55/0.73 inference(unit_resolution,[status(thm)],[1394, 237, 145])).
% 0.55/0.73 tff(1416,assumption,(b(s(s(s(s(elem!1)))), s(s(elem!1)))), introduced(assumption)).
% 0.55/0.73 tff(1417,assumption,(~(s(s(s(z))) = s(s(elem!1)))), introduced(assumption)).
% 0.55/0.73 tff(1418,plain,
% 0.55/0.73 (~r(s(s(s(z))), s(s(elem!1)))),
% 0.55/0.73 inference(unit_resolution,[status(thm)],[827, 14, 182, 180])).
% 0.55/0.73 tff(1419,plain,
% 0.55/0.73 (((~![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))))),
% 0.55/0.73 inference(rewrite,[status(thm)],[])).
% 0.55/0.73 tff(1420,plain,
% 0.55/0.73 ((~![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))))),
% 0.55/0.73 inference(quant_inst,[status(thm)],[])).
% 0.55/0.73 tff(1421,plain,
% 0.55/0.73 ((~![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)))),
% 0.55/0.73 inference(modus_ponens,[status(thm)],[1420, 1419])).
% 0.55/0.73 tff(1422,plain,
% 0.55/0.73 (b(s(s(s(z))), s(s(elem!1)))),
% 0.55/0.73 inference(unit_resolution,[status(thm)],[1421, 46, 1418, 1417])).
% 0.55/0.73 tff(1423,plain,
% 0.55/0.73 (((~![X0: $i, X2: $i, X1: $i] : ((~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(elem!1)))), s(s(elem!1)))) | (~b(s(s(s(z))), s(s(s(s(elem!1)))))) | (~b(s(s(s(z))), s(s(elem!1)))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(elem!1)))), s(s(elem!1)))) | (~b(s(s(s(z))), s(s(s(s(elem!1)))))) | (~b(s(s(s(z))), s(s(elem!1)))))),
% 0.55/0.73 inference(rewrite,[status(thm)],[])).
% 0.55/0.73 tff(1424,plain,
% 0.55/0.73 (((~b(s(s(s(s(elem!1)))), s(s(elem!1)))) | (~b(s(s(s(z))), s(s(elem!1)))) | (~b(s(s(s(z))), s(s(s(s(elem!1))))))) <=> ((~b(s(s(s(s(elem!1)))), s(s(elem!1)))) | (~b(s(s(s(z))), s(s(s(s(elem!1)))))) | (~b(s(s(s(z))), s(s(elem!1)))))),
% 0.55/0.73 inference(rewrite,[status(thm)],[])).
% 0.55/0.73 tff(1425,plain,
% 0.55/0.73 (((~![X0: $i, X2: $i, X1: $i] : ((~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(elem!1)))), s(s(elem!1)))) | (~b(s(s(s(z))), s(s(elem!1)))) | (~b(s(s(s(z))), s(s(s(s(elem!1)))))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(elem!1)))), s(s(elem!1)))) | (~b(s(s(s(z))), s(s(s(s(elem!1)))))) | (~b(s(s(s(z))), s(s(elem!1))))))),
% 0.55/0.73 inference(monotonicity,[status(thm)],[1424])).
% 0.55/0.73 tff(1426,plain,
% 0.55/0.73 (((~![X0: $i, X2: $i, X1: $i] : ((~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(elem!1)))), s(s(elem!1)))) | (~b(s(s(s(z))), s(s(elem!1)))) | (~b(s(s(s(z))), s(s(s(s(elem!1)))))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(elem!1)))), s(s(elem!1)))) | (~b(s(s(s(z))), s(s(s(s(elem!1)))))) | (~b(s(s(s(z))), s(s(elem!1)))))),
% 0.55/0.73 inference(transitivity,[status(thm)],[1425, 1423])).
% 0.55/0.73 tff(1427,plain,
% 0.55/0.73 ((~![X0: $i, X2: $i, X1: $i] : ((~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(elem!1)))), s(s(elem!1)))) | (~b(s(s(s(z))), s(s(elem!1)))) | (~b(s(s(s(z))), s(s(s(s(elem!1)))))))),
% 0.55/0.73 inference(quant_inst,[status(thm)],[])).
% 0.55/0.73 tff(1428,plain,
% 0.55/0.73 ((~![X0: $i, X2: $i, X1: $i] : ((~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(elem!1)))), s(s(elem!1)))) | (~b(s(s(s(z))), s(s(s(s(elem!1)))))) | (~b(s(s(s(z))), s(s(elem!1))))),
% 0.55/0.73 inference(modus_ponens,[status(thm)],[1427, 1426])).
% 0.55/0.73 tff(1429,plain,
% 0.55/0.73 ($false),
% 0.55/0.73 inference(unit_resolution,[status(thm)],[1428, 117, 1416, 1422, 1414])).
% 0.55/0.73 tff(1430,plain,((~r(s(s(s(z))), z)) | (~b(s(s(s(s(elem!1)))), s(s(elem!1)))) | (s(s(s(z))) = s(s(elem!1))) | (~r(s(s(s(s(elem!1)))), z)) | (~r(s(s(elem!1)), z))), inference(lemma,lemma(discharge,[]))).
% 0.55/0.73 tff(1431,plain,
% 0.55/0.73 (s(s(s(z))) = s(s(elem!1))),
% 0.55/0.73 inference(unit_resolution,[status(thm)],[1430, 182, 180, 1396, 1416])).
% 0.55/0.73 tff(1432,assumption,(s(s(s(s(s(s(elem!1)))))) = elem!1), introduced(assumption)).
% 0.55/0.73 tff(1433,plain,
% 0.55/0.73 (elem!1 = s(s(s(s(s(s(elem!1))))))),
% 0.55/0.73 inference(symmetry,[status(thm)],[1432])).
% 0.55/0.73 tff(1434,assumption,(s(s(s(z))) = s(s(elem!1))), introduced(assumption)).
% 0.55/0.73 tff(1435,plain,
% 0.55/0.73 (inj_0(s(s(s(z)))) = inj_0(s(s(elem!1)))),
% 0.55/0.73 inference(monotonicity,[status(thm)],[1434])).
% 0.55/0.73 tff(1436,plain,
% 0.55/0.73 (s(s(z)) = s(elem!1)),
% 0.55/0.73 inference(transitivity,[status(thm)],[95, 1435, 166])).
% 0.55/0.73 tff(1437,plain,
% 0.55/0.73 (inj_0(s(s(z))) = inj_0(s(elem!1))),
% 0.55/0.73 inference(monotonicity,[status(thm)],[1436])).
% 0.55/0.73 tff(1438,plain,
% 0.55/0.73 (s(z) = s(s(s(s(s(s(elem!1))))))),
% 0.55/0.73 inference(transitivity,[status(thm)],[131, 1437, 257, 1433])).
% 0.55/0.73 tff(1439,plain,
% 0.55/0.73 (inj_0(s(z)) = inj_0(s(s(s(s(s(s(elem!1)))))))),
% 0.55/0.73 inference(monotonicity,[status(thm)],[1438])).
% 0.55/0.73 tff(1440,plain,
% 0.55/0.73 (inj_0(s(s(s(s(s(s(elem!1))))))) = inj_0(s(z))),
% 0.55/0.73 inference(symmetry,[status(thm)],[1439])).
% 0.55/0.73 tff(1441,plain,
% 0.55/0.73 (s(s(s(s(s(elem!1))))) = inj_0(s(s(s(s(s(s(elem!1)))))))),
% 0.55/0.73 inference(symmetry,[status(thm)],[304])).
% 0.55/0.73 tff(1442,plain,
% 0.55/0.73 (s(s(s(s(s(elem!1))))) = z),
% 0.55/0.73 inference(transitivity,[status(thm)],[1441, 1440, 90])).
% 0.55/0.73 tff(1443,plain,
% 0.55/0.73 ((~![X: $i] : (~(s(X) = z))) | (~(s(s(s(s(s(elem!1))))) = z))),
% 0.55/0.73 inference(quant_inst,[status(thm)],[])).
% 0.55/0.73 tff(1444,plain,
% 0.55/0.73 (~(s(s(s(s(s(elem!1))))) = z)),
% 0.55/0.73 inference(unit_resolution,[status(thm)],[1443, 33])).
% 0.55/0.73 tff(1445,plain,
% 0.55/0.73 ($false),
% 0.55/0.73 inference(unit_resolution,[status(thm)],[1444, 1442])).
% 0.55/0.73 tff(1446,plain,((~(s(s(s(s(s(s(elem!1)))))) = elem!1)) | (~(s(s(s(z))) = s(s(elem!1))))), inference(lemma,lemma(discharge,[]))).
% 0.55/0.73 tff(1447,plain,
% 0.55/0.73 (~(s(s(s(s(s(s(elem!1)))))) = elem!1)),
% 0.55/0.73 inference(unit_resolution,[status(thm)],[1446, 1431])).
% 0.55/0.73 tff(1448,plain,
% 0.55/0.73 (inj_0(s(s(s(z)))) = inj_0(s(s(elem!1)))),
% 0.55/0.73 inference(monotonicity,[status(thm)],[1431])).
% 0.55/0.73 tff(1449,plain,
% 0.55/0.73 (s(s(z)) = s(elem!1)),
% 0.55/0.73 inference(transitivity,[status(thm)],[95, 1448, 166])).
% 0.55/0.73 tff(1450,plain,
% 0.55/0.73 (inj_0(s(s(z))) = inj_0(s(elem!1))),
% 0.55/0.73 inference(monotonicity,[status(thm)],[1449])).
% 0.55/0.73 tff(1451,plain,
% 0.55/0.73 (s(z) = elem!1),
% 0.55/0.73 inference(transitivity,[status(thm)],[131, 1450, 257])).
% 0.55/0.73 tff(1452,plain,
% 0.55/0.73 (r(s(s(elem!1)), s(z)) <=> r(s(s(elem!1)), elem!1)),
% 0.55/0.73 inference(monotonicity,[status(thm)],[1451])).
% 0.55/0.73 tff(1453,plain,
% 0.55/0.73 (((~![X0: $i, X2: $i, X1: $i] : ((~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(s(s(elem!1)))), s(z))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~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(s(s(elem!1)))), s(z))))),
% 0.55/0.73 inference(rewrite,[status(thm)],[])).
% 0.55/0.73 tff(1454,plain,
% 0.55/0.73 ((~![X0: $i, X2: $i, X1: $i] : ((~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(s(s(elem!1)))), s(z))))),
% 0.55/0.73 inference(quant_inst,[status(thm)],[])).
% 0.55/0.73 tff(1455,plain,
% 0.55/0.73 ((~![X0: $i, X2: $i, X1: $i] : ((~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), s(s(elem!1)))) | (~b(s(s(s(s(elem!1)))), s(s(elem!1)))) | (~b(s(s(s(s(elem!1)))), s(z)))),
% 0.55/0.73 inference(modus_ponens,[status(thm)],[1454, 1453])).
% 0.55/0.73 tff(1456,plain,
% 0.55/0.73 ($false),
% 0.55/0.73 inference(unit_resolution,[status(thm)],[1455, 117, 452, 1416, 1311])).
% 0.55/0.73 tff(1457,plain,((~b(s(z), s(s(elem!1)))) | (~b(s(s(s(s(elem!1)))), s(s(elem!1)))) | (~b(s(s(s(s(elem!1)))), s(z)))), inference(lemma,lemma(discharge,[]))).
% 0.55/0.73 tff(1458,plain,
% 0.55/0.73 (~b(s(z), s(s(elem!1)))),
% 0.55/0.73 inference(unit_resolution,[status(thm)],[1457, 1416, 1311])).
% 0.55/0.73 tff(1459,plain,
% 0.55/0.73 (r(s(z), s(s(elem!1)))),
% 0.55/0.73 inference(unit_resolution,[status(thm)],[416, 1458])).
% 0.55/0.73 tff(1460,plain,
% 0.55/0.73 (((~![X0: $i, X2: $i, X1: $i] : ((~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)))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~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)))),
% 0.55/0.73 inference(rewrite,[status(thm)],[])).
% 0.55/0.73 tff(1461,plain,
% 0.55/0.73 (((~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)))),
% 0.55/0.73 inference(rewrite,[status(thm)],[])).
% 0.55/0.73 tff(1462,plain,
% 0.55/0.73 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(elem!1)), z)) | (~r(s(z), z)) | (~r(s(z), s(s(elem!1)))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(s(elem!1)))) | (~r(s(s(elem!1)), z)) | (~r(s(z), z))))),
% 0.55/0.73 inference(monotonicity,[status(thm)],[1461])).
% 0.55/0.73 tff(1463,plain,
% 0.55/0.73 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(elem!1)), z)) | (~r(s(z), z)) | (~r(s(z), s(s(elem!1)))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(z), s(s(elem!1)))) | (~r(s(s(elem!1)), z)) | (~r(s(z), z)))),
% 0.55/0.73 inference(transitivity,[status(thm)],[1462, 1460])).
% 0.55/0.73 tff(1464,plain,
% 0.55/0.73 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(elem!1)), z)) | (~r(s(z), z)) | (~r(s(z), s(s(elem!1)))))),
% 0.55/0.73 inference(quant_inst,[status(thm)],[])).
% 0.55/0.73 tff(1465,plain,
% 0.55/0.73 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(z), s(s(elem!1)))) | (~r(s(s(elem!1)), z)) | (~r(s(z), z))),
% 0.55/0.73 inference(modus_ponens,[status(thm)],[1464, 1463])).
% 0.55/0.73 tff(1466,plain,
% 0.55/0.73 ($false),
% 0.55/0.73 inference(unit_resolution,[status(thm)],[1465, 14, 1149, 182, 183])).
% 0.55/0.73 tff(1467,plain,((~r(s(z), z)) | (~r(s(z), s(s(elem!1)))) | (~r(s(s(elem!1)), z))), inference(lemma,lemma(discharge,[]))).
% 0.55/0.73 tff(1468,plain,
% 0.55/0.73 (~r(s(z), z)),
% 0.55/0.73 inference(unit_resolution,[status(thm)],[1467, 182, 1149])).
% 0.55/0.73 tff(1469,plain,
% 0.55/0.74 (b(s(z), z)),
% 0.55/0.74 inference(unit_resolution,[status(thm)],[193, 1468])).
% 0.55/0.74 tff(1470,plain,
% 0.55/0.74 (~b(s(z), s(s(s(elem!1))))),
% 0.55/0.74 inference(unit_resolution,[status(thm)],[246, 212, 1469])).
% 0.55/0.74 tff(1471,plain,
% 0.55/0.74 (r(s(z), s(s(s(elem!1))))),
% 0.55/0.74 inference(unit_resolution,[status(thm)],[235, 1470])).
% 0.55/0.74 tff(1472,plain,
% 0.55/0.74 (((~![X0: $i, X2: $i, X1: $i] : ((~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))))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~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))))))),
% 0.55/0.74 inference(rewrite,[status(thm)],[])).
% 0.55/0.74 tff(1473,plain,
% 0.55/0.74 (((~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))))))),
% 0.55/0.74 inference(rewrite,[status(thm)],[])).
% 0.55/0.74 tff(1474,plain,
% 0.55/0.74 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(elem!1)), s(s(s(elem!1))))) | (~r(s(z), s(s(s(elem!1))))) | (~r(s(z), s(s(elem!1)))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(s(elem!1)))) | (~r(s(z), s(s(s(elem!1))))) | (~r(s(s(elem!1)), s(s(s(elem!1)))))))),
% 0.55/0.74 inference(monotonicity,[status(thm)],[1473])).
% 0.55/0.74 tff(1475,plain,
% 0.55/0.74 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(elem!1)), s(s(s(elem!1))))) | (~r(s(z), s(s(s(elem!1))))) | (~r(s(z), s(s(elem!1)))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(z), s(s(elem!1)))) | (~r(s(z), s(s(s(elem!1))))) | (~r(s(s(elem!1)), s(s(s(elem!1))))))),
% 0.55/0.74 inference(transitivity,[status(thm)],[1474, 1472])).
% 0.55/0.74 tff(1476,plain,
% 0.55/0.74 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(elem!1)), s(s(s(elem!1))))) | (~r(s(z), s(s(s(elem!1))))) | (~r(s(z), s(s(elem!1)))))),
% 0.55/0.74 inference(quant_inst,[status(thm)],[])).
% 0.55/0.74 tff(1477,plain,
% 0.55/0.74 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(z), s(s(elem!1)))) | (~r(s(z), s(s(s(elem!1))))) | (~r(s(s(elem!1)), s(s(s(elem!1)))))),
% 0.55/0.74 inference(modus_ponens,[status(thm)],[1476, 1475])).
% 0.55/0.74 tff(1478,plain,
% 0.55/0.74 ($false),
% 0.55/0.74 inference(unit_resolution,[status(thm)],[1477, 14, 1149, 195, 1471])).
% 0.55/0.74 tff(1479,plain,((~r(s(s(elem!1)), s(s(s(elem!1))))) | (~r(s(z), s(s(elem!1)))) | (~r(s(s(elem!1)), z))), inference(lemma,lemma(discharge,[]))).
% 0.55/0.74 tff(1480,plain,
% 0.55/0.74 (~r(s(s(elem!1)), s(s(s(elem!1))))),
% 0.55/0.74 inference(unit_resolution,[status(thm)],[1479, 182, 1459])).
% 0.55/0.74 tff(1481,plain,
% 0.55/0.74 (b(s(s(elem!1)), s(s(s(elem!1))))),
% 0.55/0.74 inference(unit_resolution,[status(thm)],[253, 1480, 145])).
% 0.55/0.74 tff(1482,plain,
% 0.55/0.74 (~r(s(s(elem!1)), s(s(s(elem!1))))),
% 0.55/0.74 inference(unit_resolution,[status(thm)],[982, 974, 182])).
% 0.55/0.74 tff(1483,plain,
% 0.55/0.74 (b(s(s(elem!1)), s(s(s(elem!1))))),
% 0.55/0.74 inference(unit_resolution,[status(thm)],[253, 1482, 145])).
% 0.55/0.74 tff(1484,plain,
% 0.55/0.74 (((~![X0: $i, X2: $i, X1: $i] : ((~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(s(elem!1)))), s(s(elem!1)))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~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(s(elem!1)))), s(s(elem!1)))))),
% 0.55/0.74 inference(rewrite,[status(thm)],[])).
% 0.55/0.74 tff(1485,plain,
% 0.55/0.74 ((~![X0: $i, X2: $i, X1: $i] : ((~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(s(elem!1)))), s(s(elem!1)))))),
% 0.55/0.74 inference(quant_inst,[status(thm)],[])).
% 0.55/0.74 tff(1486,plain,
% 0.55/0.74 ((~![X0: $i, X2: $i, X1: $i] : ((~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~b(s(s(s(s(elem!1)))), s(s(elem!1))))),
% 0.55/0.74 inference(modus_ponens,[status(thm)],[1485, 1484])).
% 0.55/0.74 tff(1487,plain,
% 0.55/0.74 ($false),
% 0.55/0.74 inference(unit_resolution,[status(thm)],[1486, 117, 324, 1416, 1349])).
% 0.55/0.74 tff(1488,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))))), inference(lemma,lemma(discharge,[]))).
% 0.55/0.74 tff(1489,plain,
% 0.55/0.74 (~b(s(s(s(s(elem!1)))), s(s(s(elem!1))))),
% 0.55/0.74 inference(unit_resolution,[status(thm)],[1488, 1483, 1416])).
% 0.55/0.74 tff(1490,plain,
% 0.55/0.74 (r(s(s(s(s(elem!1)))), s(s(s(elem!1))))),
% 0.55/0.74 inference(unit_resolution,[status(thm)],[1347, 1489, 156])).
% 0.55/0.74 tff(1491,plain,
% 0.55/0.74 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(s(elem!1))))) | (~r(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~r(s(s(s(s(elem!1)))), z)))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, s(s(s(elem!1))))) | (~r(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~r(s(s(s(s(elem!1)))), z)))),
% 0.55/0.74 inference(rewrite,[status(thm)],[])).
% 0.55/0.74 tff(1492,plain,
% 0.55/0.74 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(s(elem!1))))) | (~r(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~r(s(s(s(s(elem!1)))), z)))),
% 0.55/0.74 inference(quant_inst,[status(thm)],[])).
% 0.55/0.74 tff(1493,plain,
% 0.55/0.74 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, s(s(s(elem!1))))) | (~r(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~r(s(s(s(s(elem!1)))), z))),
% 0.55/0.74 inference(modus_ponens,[status(thm)],[1492, 1491])).
% 0.55/0.74 tff(1494,plain,
% 0.55/0.74 ($false),
% 0.55/0.74 inference(unit_resolution,[status(thm)],[1493, 14, 974, 1490, 1396])).
% 0.55/0.74 tff(1495,plain,((~r(z, s(s(s(elem!1))))) | (~r(s(s(s(s(elem!1)))), z)) | (~b(s(s(s(s(elem!1)))), s(s(elem!1)))) | (s(s(elem!1)) = s(s(s(elem!1)))) | (~r(s(s(elem!1)), z))), inference(lemma,lemma(discharge,[]))).
% 0.55/0.74 tff(1496,plain,
% 0.55/0.74 (~r(z, s(s(s(elem!1))))),
% 0.55/0.74 inference(unit_resolution,[status(thm)],[1495, 182, 1396, 145, 1416])).
% 0.55/0.74 tff(1497,plain,
% 0.55/0.74 (b(z, s(s(s(elem!1))))),
% 0.55/0.74 inference(unit_resolution,[status(thm)],[692, 1496])).
% 0.55/0.74 tff(1498,plain,
% 0.55/0.74 (~b(s(z), s(s(s(elem!1))))),
% 0.55/0.74 inference(unit_resolution,[status(thm)],[682, 1497, 237])).
% 0.55/0.74 tff(1499,plain,
% 0.55/0.74 (r(s(z), s(s(s(elem!1))))),
% 0.55/0.74 inference(unit_resolution,[status(thm)],[235, 1498])).
% 0.55/0.74 tff(1500,plain,
% 0.55/0.74 (~b(s(s(s(s(elem!1)))), s(s(s(elem!1))))),
% 0.55/0.74 inference(unit_resolution,[status(thm)],[1488, 1416, 324])).
% 0.55/0.74 tff(1501,plain,
% 0.55/0.74 (r(s(s(s(s(elem!1)))), s(s(s(elem!1))))),
% 0.55/0.74 inference(unit_resolution,[status(thm)],[1347, 1500, 287])).
% 0.55/0.74 tff(1502,plain,
% 0.55/0.74 (~r(s(s(s(s(elem!1)))), s(z))),
% 0.55/0.74 inference(unit_resolution,[status(thm)],[1342, 1501, 213])).
% 0.55/0.74 tff(1503,plain,
% 0.55/0.74 (b(s(s(s(s(elem!1)))), s(z))),
% 0.55/0.74 inference(unit_resolution,[status(thm)],[1327, 1502])).
% 0.55/0.74 tff(1504,plain,
% 0.55/0.74 (((~![X0: $i, X2: $i, X1: $i] : ((~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(s(s(elem!1)))), s(s(elem!1)))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(elem!1)), s(z))) | (~b(s(s(s(s(elem!1)))), s(z))) | (~b(s(s(s(s(elem!1)))), s(s(elem!1)))))),
% 0.55/0.74 inference(rewrite,[status(thm)],[])).
% 0.55/0.74 tff(1505,plain,
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% 0.55/0.74 inference(quant_inst,[status(thm)],[])).
% 0.55/0.74 tff(1506,plain,
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% 0.55/0.74 inference(modus_ponens,[status(thm)],[1505, 1504])).
% 0.55/0.74 tff(1507,plain,
% 0.55/0.74 ($false),
% 0.55/0.74 inference(unit_resolution,[status(thm)],[1506, 117, 470, 1416, 1503])).
% 0.55/0.74 tff(1508,plain,((~b(s(s(s(s(elem!1)))), s(s(elem!1)))) | (~b(s(s(elem!1)), s(z))) | (~r(s(z), s(s(s(elem!1))))) | (s(s(s(s(elem!1)))) = s(s(s(elem!1)))) | (~b(s(s(elem!1)), s(s(s(elem!1)))))), inference(lemma,lemma(discharge,[]))).
% 0.55/0.74 tff(1509,plain,
% 0.55/0.74 (~b(s(s(elem!1)), s(z))),
% 0.55/0.74 inference(unit_resolution,[status(thm)],[1508, 1499, 1416, 156, 1481])).
% 0.55/0.74 tff(1510,plain,
% 0.55/0.74 (r(s(s(elem!1)), s(z))),
% 0.55/0.74 inference(unit_resolution,[status(thm)],[178, 1509])).
% 0.55/0.74 tff(1511,plain,
% 0.55/0.74 (r(s(s(elem!1)), elem!1)),
% 0.55/0.74 inference(modus_ponens,[status(thm)],[1510, 1452])).
% 0.55/0.74 tff(1512,plain,
% 0.55/0.74 ((elem!1 = s(s(s(elem!1)))) <=> (s(s(s(elem!1))) = elem!1)),
% 0.55/0.74 inference(symmetry,[status(thm)],[1198])).
% 0.55/0.74 tff(1513,plain,
% 0.55/0.74 ((s(z) = s(s(s(elem!1)))) <=> (elem!1 = s(s(s(elem!1))))),
% 0.55/0.74 inference(monotonicity,[status(thm)],[1451])).
% 0.55/0.74 tff(1514,plain,
% 0.55/0.74 ((s(z) = s(s(s(elem!1)))) <=> (s(s(s(elem!1))) = elem!1)),
% 0.55/0.74 inference(transitivity,[status(thm)],[1513, 1512])).
% 0.55/0.74 tff(1515,plain,
% 0.55/0.74 ((~(s(z) = s(s(s(elem!1))))) <=> (~(s(s(s(elem!1))) = elem!1))),
% 0.55/0.74 inference(monotonicity,[status(thm)],[1514])).
% 0.55/0.74 tff(1516,plain,
% 0.55/0.74 (~(s(s(s(elem!1))) = elem!1)),
% 0.55/0.74 inference(modus_ponens,[status(thm)],[230, 1515])).
% 0.55/0.74 tff(1517,plain,
% 0.55/0.74 (b(s(z), z) <=> b(elem!1, z)),
% 0.55/0.74 inference(monotonicity,[status(thm)],[1451])).
% 0.55/0.74 tff(1518,plain,
% 0.55/0.74 (b(elem!1, z)),
% 0.55/0.74 inference(modus_ponens,[status(thm)],[237, 1517])).
% 0.55/0.74 tff(1519,plain,
% 0.55/0.74 (~b(s(s(s(s(elem!1)))), s(s(s(elem!1))))),
% 0.55/0.74 inference(unit_resolution,[status(thm)],[1488, 1481, 1416])).
% 0.55/0.74 tff(1520,plain,
% 0.55/0.74 (r(s(s(s(s(elem!1)))), s(s(s(elem!1))))),
% 0.55/0.74 inference(unit_resolution,[status(thm)],[1347, 1519, 156])).
% 0.55/0.74 tff(1521,plain,
% 0.55/0.74 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), z)) | (~r(s(s(s(s(elem!1)))), z)) | (~r(s(s(s(s(elem!1)))), s(s(s(elem!1))))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(elem!1))), z)) | (~r(s(s(s(s(elem!1)))), z)) | (~r(s(s(s(s(elem!1)))), s(s(s(elem!1))))))),
% 0.55/0.74 inference(rewrite,[status(thm)],[])).
% 0.55/0.74 tff(1522,plain,
% 0.55/0.74 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), z)) | (~r(s(s(s(s(elem!1)))), z)) | (~r(s(s(s(s(elem!1)))), s(s(s(elem!1))))))),
% 0.55/0.74 inference(quant_inst,[status(thm)],[])).
% 0.55/0.74 tff(1523,plain,
% 0.55/0.74 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(elem!1))), z)) | (~r(s(s(s(s(elem!1)))), z)) | (~r(s(s(s(s(elem!1)))), s(s(s(elem!1)))))),
% 0.55/0.74 inference(modus_ponens,[status(thm)],[1522, 1521])).
% 0.55/0.74 tff(1524,plain,
% 0.55/0.74 ($false),
% 0.55/0.74 inference(unit_resolution,[status(thm)],[1523, 14, 196, 1337, 1396])).
% 0.55/0.74 tff(1525,plain,((~r(s(s(s(elem!1))), z)) | (~r(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~r(s(s(s(s(elem!1)))), z))), inference(lemma,lemma(discharge,[]))).
% 0.55/0.74 tff(1526,plain,
% 0.55/0.74 (~r(s(s(s(elem!1))), z)),
% 0.55/0.74 inference(unit_resolution,[status(thm)],[1525, 1520, 1396])).
% 0.55/0.74 tff(1527,plain,
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% 0.55/0.74 inference(unit_resolution,[status(thm)],[211, 1526])).
% 0.55/0.74 tff(1528,plain,
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% 0.55/0.74 inference(rewrite,[status(thm)],[])).
% 0.55/0.74 tff(1529,plain,
% 0.55/0.74 (((~b(elem!1, z)) | (~b(s(s(s(elem!1))), z)) | (~b(s(s(s(elem!1))), elem!1))) <=> ((~b(s(s(s(elem!1))), elem!1)) | (~b(elem!1, z)) | (~b(s(s(s(elem!1))), z)))),
% 0.55/0.74 inference(rewrite,[status(thm)],[])).
% 0.55/0.74 tff(1530,plain,
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% 0.55/0.74 inference(monotonicity,[status(thm)],[1529])).
% 0.55/0.74 tff(1531,plain,
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% 0.55/0.74 inference(transitivity,[status(thm)],[1530, 1528])).
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% 0.55/0.74 inference(quant_inst,[status(thm)],[])).
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% 0.55/0.74 inference(modus_ponens,[status(thm)],[1532, 1531])).
% 0.55/0.74 tff(1534,plain,
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% 0.55/0.74 inference(unit_resolution,[status(thm)],[1533, 117, 1527, 1518])).
% 0.55/0.74 tff(1535,plain,
% 0.55/0.74 (r(s(s(s(elem!1))), elem!1)),
% 0.55/0.74 inference(unit_resolution,[status(thm)],[1235, 1534, 1516])).
% 0.55/0.74 tff(1536,plain,
% 0.55/0.74 ((s(s(s(elem!1))) = s(s(elem!1))) <=> (s(s(elem!1)) = s(s(s(elem!1))))),
% 0.55/0.74 inference(commutativity,[status(thm)],[])).
% 0.55/0.74 tff(1537,plain,
% 0.55/0.74 ((s(s(elem!1)) = s(s(s(elem!1)))) <=> (s(s(s(elem!1))) = s(s(elem!1)))),
% 0.55/0.74 inference(symmetry,[status(thm)],[1536])).
% 0.55/0.74 tff(1538,plain,
% 0.55/0.74 ((~(s(s(elem!1)) = s(s(s(elem!1))))) <=> (~(s(s(s(elem!1))) = s(s(elem!1))))),
% 0.55/0.74 inference(monotonicity,[status(thm)],[1537])).
% 0.55/0.74 tff(1539,plain,
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% 0.55/0.74 inference(modus_ponens,[status(thm)],[145, 1538])).
% 0.55/0.74 tff(1540,plain,
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% 0.55/0.74 inference(rewrite,[status(thm)],[])).
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% 0.55/0.74 inference(quant_inst,[status(thm)],[])).
% 0.55/0.74 tff(1542,plain,
% 0.55/0.74 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(elem!1)), elem!1)) | (~r(s(s(s(elem!1))), elem!1)) | (~r(s(s(s(elem!1))), s(s(elem!1))))),
% 0.55/0.74 inference(modus_ponens,[status(thm)],[1541, 1540])).
% 0.55/0.74 tff(1543,plain,
% 0.55/0.74 (~r(s(s(s(elem!1))), s(s(elem!1)))),
% 0.55/0.74 inference(unit_resolution,[status(thm)],[1542, 14, 1511, 1535])).
% 0.55/0.74 tff(1544,plain,
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% 0.55/0.74 inference(rewrite,[status(thm)],[])).
% 0.55/0.74 tff(1545,plain,
% 0.55/0.74 ((~![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))))),
% 0.55/0.74 inference(quant_inst,[status(thm)],[])).
% 0.55/0.74 tff(1546,plain,
% 0.55/0.74 ((~![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)))),
% 0.55/0.74 inference(modus_ponens,[status(thm)],[1545, 1544])).
% 0.55/0.74 tff(1547,plain,
% 0.55/0.74 ((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)))),
% 0.55/0.74 inference(unit_resolution,[status(thm)],[1546, 46])).
% 0.55/0.74 tff(1548,plain,
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% 0.55/0.74 inference(unit_resolution,[status(thm)],[1547, 1543, 1539])).
% 0.55/0.74 tff(1549,plain,
% 0.55/0.74 (s(s(s(s(z)))) = s(s(s(elem!1)))),
% 0.55/0.74 inference(monotonicity,[status(thm)],[1434])).
% 0.55/0.74 tff(1550,plain,
% 0.55/0.74 (s(s(s(elem!1))) = s(s(s(s(z))))),
% 0.55/0.74 inference(symmetry,[status(thm)],[1549])).
% 0.55/0.74 tff(1551,plain,
% 0.55/0.74 ((s(s(s(s(s(s(elem!1)))))) = s(s(s(elem!1)))) <=> (s(s(s(s(s(s(elem!1)))))) = s(s(s(s(z)))))),
% 0.55/0.74 inference(monotonicity,[status(thm)],[1550])).
% 0.55/0.74 tff(1552,plain,
% 0.55/0.74 ((s(s(s(s(s(s(elem!1)))))) = s(s(s(s(z))))) <=> (s(s(s(s(s(s(elem!1)))))) = s(s(s(elem!1))))),
% 0.55/0.74 inference(symmetry,[status(thm)],[1551])).
% 0.55/0.74 tff(1553,plain,
% 0.55/0.74 ((~(s(s(s(s(s(s(elem!1)))))) = s(s(s(s(z)))))) <=> (~(s(s(s(s(s(s(elem!1)))))) = s(s(s(elem!1)))))),
% 0.55/0.74 inference(monotonicity,[status(thm)],[1552])).
% 0.55/0.74 tff(1554,plain,
% 0.55/0.74 (~(s(s(s(s(s(s(elem!1)))))) = s(s(s(elem!1))))),
% 0.55/0.74 inference(modus_ponens,[status(thm)],[319, 1553])).
% 0.55/0.74 tff(1555,assumption,(r(s(s(s(s(s(s(elem!1)))))), elem!1)), introduced(assumption)).
% 0.55/0.74 tff(1556,assumption,(r(s(s(s(elem!1))), elem!1)), introduced(assumption)).
% 0.55/0.74 tff(1557,plain,
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% 0.55/0.74 inference(rewrite,[status(thm)],[])).
% 0.55/0.74 tff(1558,plain,
% 0.55/0.74 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), elem!1)) | (~r(s(s(s(s(s(s(elem!1)))))), elem!1)) | (~r(s(s(s(s(s(s(elem!1)))))), s(s(s(elem!1))))))),
% 0.55/0.74 inference(quant_inst,[status(thm)],[])).
% 0.55/0.74 tff(1559,plain,
% 0.55/0.74 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(elem!1))), elem!1)) | (~r(s(s(s(s(s(s(elem!1)))))), elem!1)) | (~r(s(s(s(s(s(s(elem!1)))))), s(s(s(elem!1)))))),
% 0.55/0.74 inference(modus_ponens,[status(thm)],[1558, 1557])).
% 0.55/0.74 tff(1560,plain,
% 0.55/0.74 (~r(s(s(s(s(s(s(elem!1)))))), s(s(s(elem!1))))),
% 0.55/0.74 inference(unit_resolution,[status(thm)],[1559, 14, 1556, 1555])).
% 0.55/0.74 tff(1561,plain,
% 0.55/0.74 (((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((s(s(s(s(s(s(elem!1)))))) = s(s(s(elem!1)))) | b(s(s(s(s(s(s(elem!1)))))), s(s(s(elem!1)))) | r(s(s(s(s(s(s(elem!1)))))), s(s(s(elem!1)))))) <=> ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (s(s(s(s(s(s(elem!1)))))) = s(s(s(elem!1)))) | b(s(s(s(s(s(s(elem!1)))))), s(s(s(elem!1)))) | r(s(s(s(s(s(s(elem!1)))))), s(s(s(elem!1)))))),
% 0.55/0.74 inference(rewrite,[status(thm)],[])).
% 0.55/0.74 tff(1562,plain,
% 0.55/0.74 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((s(s(s(s(s(s(elem!1)))))) = s(s(s(elem!1)))) | b(s(s(s(s(s(s(elem!1)))))), s(s(s(elem!1)))) | r(s(s(s(s(s(s(elem!1)))))), s(s(s(elem!1)))))),
% 0.55/0.74 inference(quant_inst,[status(thm)],[])).
% 0.55/0.74 tff(1563,plain,
% 0.55/0.74 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (s(s(s(s(s(s(elem!1)))))) = s(s(s(elem!1)))) | b(s(s(s(s(s(s(elem!1)))))), s(s(s(elem!1)))) | r(s(s(s(s(s(s(elem!1)))))), s(s(s(elem!1))))),
% 0.55/0.74 inference(modus_ponens,[status(thm)],[1562, 1561])).
% 0.55/0.74 tff(1564,plain,
% 0.55/0.74 ((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))))),
% 0.55/0.74 inference(unit_resolution,[status(thm)],[1563, 46, 1560])).
% 0.55/0.74 tff(1565,plain,
% 0.55/0.74 (b(s(s(s(s(s(s(elem!1)))))), s(s(s(elem!1))))),
% 0.55/0.74 inference(unit_resolution,[status(thm)],[1564, 1554])).
% 0.55/0.74 tff(1566,plain,
% 0.55/0.74 (s(s(elem!1)) = s(s(s(z)))),
% 0.55/0.74 inference(symmetry,[status(thm)],[1434])).
% 0.55/0.74 tff(1567,plain,
% 0.55/0.74 ((s(s(s(s(s(s(elem!1)))))) = s(s(elem!1))) <=> (s(s(s(s(s(s(elem!1)))))) = s(s(s(z))))),
% 0.55/0.74 inference(monotonicity,[status(thm)],[1566])).
% 0.55/0.74 tff(1568,plain,
% 0.55/0.74 ((s(s(s(s(s(s(elem!1)))))) = s(s(s(z)))) <=> (s(s(s(s(s(s(elem!1)))))) = s(s(elem!1)))),
% 0.55/0.74 inference(symmetry,[status(thm)],[1567])).
% 0.55/0.74 tff(1569,plain,
% 0.55/0.74 ((~(s(s(s(s(s(s(elem!1)))))) = s(s(s(z))))) <=> (~(s(s(s(s(s(s(elem!1)))))) = s(s(elem!1))))),
% 0.55/0.74 inference(monotonicity,[status(thm)],[1568])).
% 0.55/0.74 tff(1570,assumption,(s(s(s(s(s(s(elem!1)))))) = s(s(s(z)))), introduced(assumption)).
% 0.55/0.74 tff(1571,plain,
% 0.55/0.74 (inj_0(s(s(s(s(s(s(elem!1))))))) = inj_0(s(s(s(z))))),
% 0.55/0.74 inference(monotonicity,[status(thm)],[1570])).
% 0.55/0.74 tff(1572,plain,
% 0.55/0.74 (s(s(s(s(s(elem!1))))) = s(s(z))),
% 0.55/0.74 inference(transitivity,[status(thm)],[1441, 1571, 94])).
% 0.55/0.74 tff(1573,plain,
% 0.55/0.74 (inj_0(s(s(s(s(s(elem!1)))))) = inj_0(s(s(z)))),
% 0.55/0.74 inference(monotonicity,[status(thm)],[1572])).
% 0.55/0.74 tff(1574,plain,
% 0.55/0.74 (s(s(s(s(elem!1)))) = inj_0(s(s(s(s(s(elem!1))))))),
% 0.55/0.74 inference(symmetry,[status(thm)],[310])).
% 0.55/0.74 tff(1575,plain,
% 0.55/0.74 (s(s(s(s(elem!1)))) = s(z)),
% 0.55/0.74 inference(transitivity,[status(thm)],[1574, 1573, 82])).
% 0.55/0.74 tff(1576,plain,
% 0.55/0.74 ($false),
% 0.55/0.74 inference(unit_resolution,[status(thm)],[1322, 1575])).
% 0.55/0.75 tff(1577,plain,(~(s(s(s(s(s(s(elem!1)))))) = s(s(s(z))))), inference(lemma,lemma(discharge,[]))).
% 0.55/0.75 tff(1578,plain,
% 0.55/0.75 (~(s(s(s(s(s(s(elem!1)))))) = s(s(elem!1)))),
% 0.55/0.75 inference(modus_ponens,[status(thm)],[1577, 1569])).
% 0.55/0.75 tff(1579,assumption,(r(s(s(elem!1)), elem!1)), introduced(assumption)).
% 0.55/0.75 tff(1580,plain,
% 0.55/0.75 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(elem!1)), elem!1)) | (~r(s(s(s(s(s(s(elem!1)))))), elem!1)) | (~r(s(s(s(s(s(s(elem!1)))))), s(s(elem!1)))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(elem!1)), elem!1)) | (~r(s(s(s(s(s(s(elem!1)))))), elem!1)) | (~r(s(s(s(s(s(s(elem!1)))))), s(s(elem!1)))))),
% 0.55/0.75 inference(rewrite,[status(thm)],[])).
% 0.55/0.75 tff(1581,plain,
% 0.55/0.75 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(elem!1)), elem!1)) | (~r(s(s(s(s(s(s(elem!1)))))), elem!1)) | (~r(s(s(s(s(s(s(elem!1)))))), s(s(elem!1)))))),
% 0.55/0.75 inference(quant_inst,[status(thm)],[])).
% 0.55/0.75 tff(1582,plain,
% 0.55/0.75 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(elem!1)), elem!1)) | (~r(s(s(s(s(s(s(elem!1)))))), elem!1)) | (~r(s(s(s(s(s(s(elem!1)))))), s(s(elem!1))))),
% 0.55/0.75 inference(modus_ponens,[status(thm)],[1581, 1580])).
% 0.55/0.75 tff(1583,plain,
% 0.55/0.75 (~r(s(s(s(s(s(s(elem!1)))))), s(s(elem!1)))),
% 0.55/0.75 inference(unit_resolution,[status(thm)],[1582, 14, 1579, 1555])).
% 0.55/0.75 tff(1584,plain,
% 0.55/0.75 (((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((s(s(s(s(s(s(elem!1)))))) = s(s(elem!1))) | b(s(s(s(s(s(s(elem!1)))))), s(s(elem!1))) | r(s(s(s(s(s(s(elem!1)))))), s(s(elem!1))))) <=> ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (s(s(s(s(s(s(elem!1)))))) = s(s(elem!1))) | b(s(s(s(s(s(s(elem!1)))))), s(s(elem!1))) | r(s(s(s(s(s(s(elem!1)))))), s(s(elem!1))))),
% 0.55/0.75 inference(rewrite,[status(thm)],[])).
% 0.55/0.75 tff(1585,plain,
% 0.55/0.75 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((s(s(s(s(s(s(elem!1)))))) = s(s(elem!1))) | b(s(s(s(s(s(s(elem!1)))))), s(s(elem!1))) | r(s(s(s(s(s(s(elem!1)))))), s(s(elem!1))))),
% 0.55/0.75 inference(quant_inst,[status(thm)],[])).
% 0.55/0.75 tff(1586,plain,
% 0.55/0.75 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (s(s(s(s(s(s(elem!1)))))) = s(s(elem!1))) | b(s(s(s(s(s(s(elem!1)))))), s(s(elem!1))) | r(s(s(s(s(s(s(elem!1)))))), s(s(elem!1)))),
% 0.55/0.75 inference(modus_ponens,[status(thm)],[1585, 1584])).
% 0.55/0.75 tff(1587,plain,
% 0.55/0.75 ((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)))),
% 0.55/0.75 inference(unit_resolution,[status(thm)],[1586, 46, 1583])).
% 0.55/0.75 tff(1588,plain,
% 0.55/0.75 (b(s(s(s(s(s(s(elem!1)))))), s(s(elem!1)))),
% 0.55/0.75 inference(unit_resolution,[status(thm)],[1587, 1578])).
% 0.55/0.75 tff(1589,assumption,(b(s(s(s(elem!1))), s(s(elem!1)))), introduced(assumption)).
% 0.55/0.75 tff(1590,plain,
% 0.55/0.75 (((~![X0: $i, X2: $i, X1: $i] : ((~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(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)))))), s(s(s(elem!1))))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(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)))))), s(s(s(elem!1))))))),
% 0.55/0.75 inference(rewrite,[status(thm)],[])).
% 0.55/0.75 tff(1591,plain,
% 0.55/0.75 ((~![X0: $i, X2: $i, X1: $i] : ((~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(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)))))), s(s(s(elem!1))))))),
% 0.55/0.75 inference(quant_inst,[status(thm)],[])).
% 0.55/0.75 tff(1592,plain,
% 0.55/0.75 ((~![X0: $i, X2: $i, X1: $i] : ((~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(s(s(s(s(s(elem!1)))))), s(s(elem!1)))) | (~b(s(s(s(s(s(s(elem!1)))))), s(s(s(elem!1)))))),
% 0.55/0.75 inference(modus_ponens,[status(thm)],[1591, 1590])).
% 0.55/0.75 tff(1593,plain,
% 0.55/0.75 ($false),
% 0.55/0.75 inference(unit_resolution,[status(thm)],[1592, 117, 1589, 1588, 1565])).
% 0.55/0.75 tff(1594,plain,((~r(s(s(s(s(s(s(elem!1)))))), elem!1)) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~(s(s(s(z))) = s(s(elem!1)))) | (~r(s(s(s(elem!1))), elem!1)) | (~r(s(s(elem!1)), elem!1))), inference(lemma,lemma(discharge,[]))).
% 0.55/0.75 tff(1595,plain,
% 0.55/0.75 (~r(s(s(s(s(s(s(elem!1)))))), elem!1)),
% 0.55/0.75 inference(unit_resolution,[status(thm)],[1594, 1548, 1431, 1535, 1511])).
% 0.55/0.75 tff(1596,plain,
% 0.55/0.75 (((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((s(s(s(s(s(s(elem!1)))))) = elem!1) | b(s(s(s(s(s(s(elem!1)))))), elem!1) | r(s(s(s(s(s(s(elem!1)))))), elem!1))) <=> ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (s(s(s(s(s(s(elem!1)))))) = elem!1) | b(s(s(s(s(s(s(elem!1)))))), elem!1) | r(s(s(s(s(s(s(elem!1)))))), elem!1))),
% 0.55/0.75 inference(rewrite,[status(thm)],[])).
% 0.55/0.75 tff(1597,plain,
% 0.55/0.75 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((s(s(s(s(s(s(elem!1)))))) = elem!1) | b(s(s(s(s(s(s(elem!1)))))), elem!1) | r(s(s(s(s(s(s(elem!1)))))), elem!1))),
% 0.55/0.75 inference(quant_inst,[status(thm)],[])).
% 0.55/0.75 tff(1598,plain,
% 0.55/0.75 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (s(s(s(s(s(s(elem!1)))))) = elem!1) | b(s(s(s(s(s(s(elem!1)))))), elem!1) | r(s(s(s(s(s(s(elem!1)))))), elem!1)),
% 0.55/0.75 inference(modus_ponens,[status(thm)],[1597, 1596])).
% 0.55/0.75 tff(1599,plain,
% 0.55/0.75 ((s(s(s(s(s(s(elem!1)))))) = elem!1) | b(s(s(s(s(s(s(elem!1)))))), elem!1) | r(s(s(s(s(s(s(elem!1)))))), elem!1)),
% 0.55/0.75 inference(unit_resolution,[status(thm)],[1598, 46])).
% 0.55/0.75 tff(1600,plain,
% 0.55/0.75 (b(s(s(s(s(s(s(elem!1)))))), elem!1)),
% 0.55/0.75 inference(unit_resolution,[status(thm)],[1599, 1595, 1447])).
% 0.55/0.75 tff(1601,plain,
% 0.55/0.75 (b(s(s(s(s(elem!1)))), s(z)) <=> b(s(s(s(s(elem!1)))), elem!1)),
% 0.55/0.75 inference(monotonicity,[status(thm)],[1451])).
% 0.55/0.75 tff(1602,plain,
% 0.55/0.75 (b(s(s(s(s(elem!1)))), elem!1)),
% 0.55/0.75 inference(modus_ponens,[status(thm)],[1311, 1601])).
% 0.55/0.75 tff(1603,plain,
% 0.55/0.75 (((~![X0: $i, X2: $i, X1: $i] : ((~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~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(s(s(elem!1)))))), s(s(s(s(elem!1)))))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~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(s(s(elem!1)))))), s(s(s(s(elem!1)))))))),
% 0.55/0.75 inference(rewrite,[status(thm)],[])).
% 0.55/0.75 tff(1604,plain,
% 0.55/0.75 ((~![X0: $i, X2: $i, X1: $i] : ((~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~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(s(s(elem!1)))))), s(s(s(s(elem!1)))))))),
% 0.55/0.75 inference(quant_inst,[status(thm)],[])).
% 0.55/0.75 tff(1605,plain,
% 0.55/0.75 ((~![X0: $i, X2: $i, X1: $i] : ((~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(elem!1)))), elem!1)) | (~b(s(s(s(s(s(s(elem!1)))))), elem!1)) | (~b(s(s(s(s(s(s(elem!1)))))), s(s(s(s(elem!1))))))),
% 0.55/0.75 inference(modus_ponens,[status(thm)],[1604, 1603])).
% 0.55/0.75 tff(1606,plain,
% 0.55/0.75 (~b(s(s(s(s(s(s(elem!1)))))), s(s(s(s(elem!1)))))),
% 0.55/0.75 inference(unit_resolution,[status(thm)],[1605, 117, 1602, 1600])).
% 0.55/0.75 tff(1607,assumption,(s(s(s(s(s(s(elem!1)))))) = s(s(s(s(elem!1))))), introduced(assumption)).
% 0.55/0.75 tff(1608,plain,
% 0.55/0.75 (inj_0(s(s(s(s(s(s(elem!1))))))) = inj_0(s(s(s(s(elem!1)))))),
% 0.55/0.75 inference(monotonicity,[status(thm)],[1607])).
% 0.55/0.75 tff(1609,plain,
% 0.55/0.75 (inj_0(s(s(s(s(elem!1))))) = inj_0(s(s(s(s(s(s(elem!1)))))))),
% 0.55/0.75 inference(symmetry,[status(thm)],[1608])).
% 0.55/0.75 tff(1610,plain,
% 0.55/0.75 (s(s(s(elem!1))) = s(s(s(s(s(elem!1)))))),
% 0.55/0.75 inference(transitivity,[status(thm)],[295, 1609, 304])).
% 0.55/0.75 tff(1611,plain,
% 0.55/0.75 (inj_0(s(s(s(elem!1)))) = inj_0(s(s(s(s(s(elem!1))))))),
% 0.55/0.75 inference(monotonicity,[status(thm)],[1610])).
% 0.55/0.75 tff(1612,plain,
% 0.55/0.75 (inj_0(s(s(s(s(s(elem!1)))))) = inj_0(s(s(s(elem!1))))),
% 0.55/0.75 inference(symmetry,[status(thm)],[1611])).
% 0.55/0.75 tff(1613,plain,
% 0.55/0.75 (s(s(s(s(elem!1)))) = s(s(elem!1))),
% 0.55/0.75 inference(transitivity,[status(thm)],[1574, 1612, 151])).
% 0.55/0.75 tff(1614,plain,
% 0.55/0.75 ($false),
% 0.55/0.75 inference(unit_resolution,[status(thm)],[146, 1613])).
% 0.55/0.75 tff(1615,plain,((~(s(s(s(s(s(s(elem!1)))))) = s(s(s(s(elem!1)))))) | (s(s(s(s(elem!1)))) = s(s(elem!1)))), inference(lemma,lemma(discharge,[]))).
% 0.55/0.75 tff(1616,plain,
% 0.55/0.75 (~(s(s(s(s(s(s(elem!1)))))) = s(s(s(s(elem!1)))))),
% 0.55/0.75 inference(unit_resolution,[status(thm)],[1615, 1415])).
% 0.55/0.75 tff(1617,plain,
% 0.55/0.75 (((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((s(s(s(s(s(s(elem!1)))))) = s(s(s(s(elem!1))))) | b(s(s(s(s(s(s(elem!1)))))), s(s(s(s(elem!1))))) | r(s(s(s(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(s(s(s(elem!1)))))) = s(s(s(s(elem!1))))) | b(s(s(s(s(s(s(elem!1)))))), s(s(s(s(elem!1))))) | r(s(s(s(s(s(s(elem!1)))))), s(s(s(s(elem!1))))))),
% 0.55/0.75 inference(rewrite,[status(thm)],[])).
% 0.55/0.75 tff(1618,plain,
% 0.55/0.75 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((s(s(s(s(s(s(elem!1)))))) = s(s(s(s(elem!1))))) | b(s(s(s(s(s(s(elem!1)))))), s(s(s(s(elem!1))))) | r(s(s(s(s(s(s(elem!1)))))), s(s(s(s(elem!1))))))),
% 0.55/0.75 inference(quant_inst,[status(thm)],[])).
% 0.55/0.75 tff(1619,plain,
% 0.55/0.75 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (s(s(s(s(s(s(elem!1)))))) = s(s(s(s(elem!1))))) | b(s(s(s(s(s(s(elem!1)))))), s(s(s(s(elem!1))))) | r(s(s(s(s(s(s(elem!1)))))), s(s(s(s(elem!1)))))),
% 0.55/0.75 inference(modus_ponens,[status(thm)],[1618, 1617])).
% 0.55/0.75 tff(1620,plain,
% 0.55/0.75 (r(s(s(s(s(s(s(elem!1)))))), s(s(s(s(elem!1)))))),
% 0.55/0.75 inference(unit_resolution,[status(thm)],[1619, 46, 1616, 1606])).
% 0.55/0.75 tff(1621,plain,
% 0.55/0.75 ((z = s(s(s(s(elem!1))))) <=> (s(s(s(s(elem!1)))) = z)),
% 0.55/0.75 inference(commutativity,[status(thm)],[])).
% 0.55/0.75 tff(1622,plain,
% 0.55/0.75 ((s(s(s(s(elem!1)))) = z) <=> (z = s(s(s(s(elem!1)))))),
% 0.55/0.75 inference(symmetry,[status(thm)],[1621])).
% 0.55/0.75 tff(1623,plain,
% 0.55/0.75 ((~(s(s(s(s(elem!1)))) = z)) <=> (~(z = s(s(s(s(elem!1))))))),
% 0.55/0.75 inference(monotonicity,[status(thm)],[1622])).
% 0.55/0.75 tff(1624,plain,
% 0.55/0.75 ((~![X: $i] : (~(s(X) = z))) | (~(s(s(s(s(elem!1)))) = z))),
% 0.55/0.75 inference(quant_inst,[status(thm)],[])).
% 0.55/0.75 tff(1625,plain,
% 0.55/0.75 (~(s(s(s(s(elem!1)))) = z)),
% 0.55/0.75 inference(unit_resolution,[status(thm)],[1624, 33])).
% 0.55/0.75 tff(1626,plain,
% 0.55/0.75 (~(z = s(s(s(s(elem!1)))))),
% 0.55/0.75 inference(modus_ponens,[status(thm)],[1625, 1623])).
% 0.55/0.75 tff(1627,plain,
% 0.55/0.75 (~r(z, s(z))),
% 0.55/0.75 inference(unit_resolution,[status(thm)],[868, 1510, 182])).
% 0.55/0.75 tff(1628,plain,
% 0.55/0.75 (b(z, s(z))),
% 0.55/0.75 inference(unit_resolution,[status(thm)],[599, 1627])).
% 0.55/0.75 tff(1629,plain,
% 0.55/0.75 (~b(s(s(s(s(elem!1)))), s(s(s(elem!1))))),
% 0.55/0.75 inference(unit_resolution,[status(thm)],[1370, 1362, 674])).
% 0.55/0.75 tff(1630,plain,
% 0.55/0.75 (r(s(s(s(s(elem!1)))), s(s(s(elem!1))))),
% 0.55/0.75 inference(unit_resolution,[status(thm)],[1347, 1629, 287])).
% 0.55/0.75 tff(1631,plain,
% 0.55/0.75 (~r(s(s(s(s(elem!1)))), s(z))),
% 0.55/0.75 inference(unit_resolution,[status(thm)],[1342, 1630, 213])).
% 0.55/0.75 tff(1632,plain,
% 0.55/0.75 (b(s(s(s(s(elem!1)))), s(z))),
% 0.55/0.75 inference(unit_resolution,[status(thm)],[1327, 1631])).
% 0.55/0.75 tff(1633,plain,
% 0.55/0.75 (((~![X0: $i, X2: $i, X1: $i] : ((~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(z))) | (~b(z, s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), s(z))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(z))) | (~b(z, s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), s(z))))),
% 0.55/0.75 inference(rewrite,[status(thm)],[])).
% 0.55/0.75 tff(1634,plain,
% 0.55/0.75 (((~b(s(s(s(s(elem!1)))), s(z))) | (~b(z, s(z))) | (~b(z, s(s(s(s(elem!1))))))) <=> ((~b(z, s(z))) | (~b(z, s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), s(z))))),
% 0.55/0.75 inference(rewrite,[status(thm)],[])).
% 0.55/0.75 tff(1635,plain,
% 0.55/0.75 (((~![X0: $i, X2: $i, X1: $i] : ((~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(elem!1)))), s(z))) | (~b(z, s(z))) | (~b(z, s(s(s(s(elem!1)))))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(z))) | (~b(z, s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), s(z)))))),
% 0.55/0.75 inference(monotonicity,[status(thm)],[1634])).
% 0.55/0.75 tff(1636,plain,
% 0.55/0.75 (((~![X0: $i, X2: $i, X1: $i] : ((~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(elem!1)))), s(z))) | (~b(z, s(z))) | (~b(z, s(s(s(s(elem!1)))))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(z))) | (~b(z, s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), s(z))))),
% 0.55/0.75 inference(transitivity,[status(thm)],[1635, 1633])).
% 0.55/0.75 tff(1637,plain,
% 0.55/0.75 ((~![X0: $i, X2: $i, X1: $i] : ((~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(elem!1)))), s(z))) | (~b(z, s(z))) | (~b(z, s(s(s(s(elem!1)))))))),
% 0.55/0.75 inference(quant_inst,[status(thm)],[])).
% 0.55/0.75 tff(1638,plain,
% 0.55/0.75 ((~![X0: $i, X2: $i, X1: $i] : ((~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(z))) | (~b(z, s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), s(z)))),
% 0.55/0.75 inference(modus_ponens,[status(thm)],[1637, 1636])).
% 0.55/0.75 tff(1639,plain,
% 0.55/0.75 ($false),
% 0.55/0.75 inference(unit_resolution,[status(thm)],[1638, 117, 1632, 1362, 574])).
% 0.55/0.75 tff(1640,plain,((~b(z, s(s(s(s(elem!1)))))) | (~b(z, s(z))) | (~r(s(z), s(s(s(elem!1))))) | (s(s(s(s(elem!1)))) = s(s(s(elem!1)))) | (~b(z, s(s(s(elem!1)))))), inference(lemma,lemma(discharge,[]))).
% 0.55/0.75 tff(1641,plain,
% 0.55/0.75 (~b(z, s(s(s(s(elem!1)))))),
% 0.55/0.75 inference(unit_resolution,[status(thm)],[1640, 1628, 156, 1497, 1499])).
% 0.55/0.75 tff(1642,plain,
% 0.55/0.75 (((~![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))))))),
% 0.55/0.75 inference(rewrite,[status(thm)],[])).
% 0.55/0.75 tff(1643,plain,
% 0.55/0.75 ((~![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))))))),
% 0.55/0.75 inference(quant_inst,[status(thm)],[])).
% 0.55/0.75 tff(1644,plain,
% 0.55/0.75 ((~![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)))))),
% 0.55/0.75 inference(modus_ponens,[status(thm)],[1643, 1642])).
% 0.55/0.75 tff(1645,plain,
% 0.55/0.75 ((z = s(s(s(s(elem!1))))) | r(z, s(s(s(s(elem!1)))))),
% 0.55/0.75 inference(unit_resolution,[status(thm)],[1644, 46, 1641])).
% 0.55/0.75 tff(1646,plain,
% 0.55/0.75 (r(z, s(s(s(s(elem!1)))))),
% 0.55/0.75 inference(unit_resolution,[status(thm)],[1645, 1626])).
% 0.55/0.75 tff(1647,plain,
% 0.55/0.75 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(s(s(elem!1)))))) | (~r(s(s(s(s(s(s(elem!1)))))), s(s(s(s(elem!1)))))) | (~r(s(s(s(s(s(s(elem!1)))))), z)))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, s(s(s(s(elem!1)))))) | (~r(s(s(s(s(s(s(elem!1)))))), s(s(s(s(elem!1)))))) | (~r(s(s(s(s(s(s(elem!1)))))), z)))),
% 0.55/0.75 inference(rewrite,[status(thm)],[])).
% 0.55/0.75 tff(1648,plain,
% 0.55/0.75 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(s(s(elem!1)))))) | (~r(s(s(s(s(s(s(elem!1)))))), s(s(s(s(elem!1)))))) | (~r(s(s(s(s(s(s(elem!1)))))), z)))),
% 0.55/0.75 inference(quant_inst,[status(thm)],[])).
% 0.55/0.75 tff(1649,plain,
% 0.55/0.75 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, s(s(s(s(elem!1)))))) | (~r(s(s(s(s(s(s(elem!1)))))), s(s(s(s(elem!1)))))) | (~r(s(s(s(s(s(s(elem!1)))))), z))),
% 0.55/0.75 inference(modus_ponens,[status(thm)],[1648, 1647])).
% 0.55/0.75 tff(1650,plain,
% 0.55/0.75 (~r(s(s(s(s(s(s(elem!1)))))), z)),
% 0.55/0.75 inference(unit_resolution,[status(thm)],[1649, 14, 1646, 1620])).
% 0.55/0.75 tff(1651,plain,
% 0.55/0.75 (inj_0(s(elem!1)) = inj_0(s(s(z)))),
% 0.55/0.75 inference(symmetry,[status(thm)],[1450])).
% 0.55/0.75 tff(1652,plain,
% 0.55/0.75 (elem!1 = inj_0(s(elem!1))),
% 0.55/0.75 inference(symmetry,[status(thm)],[257])).
% 0.55/0.75 tff(1653,plain,
% 0.55/0.75 (elem!1 = s(z)),
% 0.55/0.75 inference(transitivity,[status(thm)],[1652, 1651, 82])).
% 0.55/0.75 tff(1654,plain,
% 0.55/0.75 (b(z, elem!1) <=> b(z, s(z))),
% 0.55/0.75 inference(monotonicity,[status(thm)],[1653])).
% 0.55/0.75 tff(1655,plain,
% 0.55/0.75 (b(z, s(z)) <=> b(z, elem!1)),
% 0.55/0.75 inference(symmetry,[status(thm)],[1654])).
% 0.55/0.75 tff(1656,plain,
% 0.55/0.75 (b(z, elem!1)),
% 0.55/0.75 inference(modus_ponens,[status(thm)],[1628, 1655])).
% 0.55/0.75 tff(1657,plain,
% 0.55/0.75 (((~![X0: $i, X2: $i, X1: $i] : ((~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, elem!1)) | (~b(s(s(s(s(s(s(elem!1)))))), elem!1)) | (~b(s(s(s(s(s(s(elem!1)))))), z)))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, elem!1)) | (~b(s(s(s(s(s(s(elem!1)))))), elem!1)) | (~b(s(s(s(s(s(s(elem!1)))))), z)))),
% 0.55/0.75 inference(rewrite,[status(thm)],[])).
% 0.55/0.75 tff(1658,plain,
% 0.55/0.75 ((~![X0: $i, X2: $i, X1: $i] : ((~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, elem!1)) | (~b(s(s(s(s(s(s(elem!1)))))), elem!1)) | (~b(s(s(s(s(s(s(elem!1)))))), z)))),
% 0.55/0.75 inference(quant_inst,[status(thm)],[])).
% 0.55/0.75 tff(1659,plain,
% 0.55/0.75 ((~![X0: $i, X2: $i, X1: $i] : ((~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, elem!1)) | (~b(s(s(s(s(s(s(elem!1)))))), elem!1)) | (~b(s(s(s(s(s(s(elem!1)))))), z))),
% 0.55/0.75 inference(modus_ponens,[status(thm)],[1658, 1657])).
% 0.55/0.75 tff(1660,plain,
% 0.55/0.75 ((~b(z, elem!1)) | (~b(s(s(s(s(s(s(elem!1)))))), z))),
% 0.55/0.75 inference(unit_resolution,[status(thm)],[1659, 117, 1600])).
% 0.55/0.75 tff(1661,plain,
% 0.55/0.75 (~b(s(s(s(s(s(s(elem!1)))))), z)),
% 0.55/0.75 inference(unit_resolution,[status(thm)],[1660, 1656])).
% 0.55/0.75 tff(1662,plain,
% 0.55/0.75 ((~![X: $i] : (~(s(X) = z))) | (~(s(s(s(s(s(s(elem!1)))))) = z))),
% 0.55/0.75 inference(quant_inst,[status(thm)],[])).
% 0.55/0.75 tff(1663,plain,
% 0.55/0.75 (~(s(s(s(s(s(s(elem!1)))))) = z)),
% 0.55/0.75 inference(unit_resolution,[status(thm)],[1662, 33])).
% 0.55/0.75 tff(1664,plain,
% 0.55/0.75 (((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((s(s(s(s(s(s(elem!1)))))) = z) | b(s(s(s(s(s(s(elem!1)))))), z) | r(s(s(s(s(s(s(elem!1)))))), z))) <=> ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (s(s(s(s(s(s(elem!1)))))) = z) | b(s(s(s(s(s(s(elem!1)))))), z) | r(s(s(s(s(s(s(elem!1)))))), z))),
% 0.55/0.75 inference(rewrite,[status(thm)],[])).
% 0.55/0.75 tff(1665,plain,
% 0.55/0.75 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((s(s(s(s(s(s(elem!1)))))) = z) | b(s(s(s(s(s(s(elem!1)))))), z) | r(s(s(s(s(s(s(elem!1)))))), z))),
% 0.55/0.75 inference(quant_inst,[status(thm)],[])).
% 0.55/0.75 tff(1666,plain,
% 0.55/0.75 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (s(s(s(s(s(s(elem!1)))))) = z) | b(s(s(s(s(s(s(elem!1)))))), z) | r(s(s(s(s(s(s(elem!1)))))), z)),
% 0.55/0.75 inference(modus_ponens,[status(thm)],[1665, 1664])).
% 0.55/0.75 tff(1667,plain,
% 0.55/0.75 ($false),
% 0.55/0.75 inference(unit_resolution,[status(thm)],[1666, 46, 1663, 1661, 1650])).
% 0.55/0.75 tff(1668,plain,((~r(s(s(elem!1)), z)) | (~r(s(s(s(s(elem!1)))), z)) | (s(s(elem!1)) = s(s(s(elem!1)))) | (~b(s(s(s(s(elem!1)))), s(z))) | (~b(s(z), z)) | (~b(s(s(s(s(elem!1)))), s(s(elem!1)))) | (~r(s(s(s(z))), z))), inference(lemma,lemma(discharge,[]))).
% 0.55/0.75 tff(1669,plain,
% 0.55/0.75 (~r(s(s(elem!1)), z)),
% 0.55/0.75 inference(unit_resolution,[status(thm)],[1668, 1416, 145, 1311, 237, 1396, 180])).
% 0.55/0.75 tff(1670,plain,
% 0.55/0.75 (b(s(s(elem!1)), z)),
% 0.55/0.75 inference(unit_resolution,[status(thm)],[1025, 1669])).
% 0.55/0.75 tff(1671,plain,
% 0.55/0.75 (~b(s(s(s(elem!1))), z)),
% 0.55/0.75 inference(unit_resolution,[status(thm)],[1050, 1670, 237, 145])).
% 0.55/0.75 tff(1672,plain,
% 0.55/0.75 (r(s(s(s(elem!1))), z)),
% 0.55/0.75 inference(unit_resolution,[status(thm)],[211, 1671])).
% 0.55/0.75 tff(1673,plain,
% 0.55/0.75 (~r(s(s(s(s(elem!1)))), s(s(s(elem!1))))),
% 0.55/0.75 inference(unit_resolution,[status(thm)],[1525, 1672, 1396])).
% 0.55/0.75 tff(1674,plain,
% 0.55/0.75 (b(s(s(s(s(elem!1)))), s(s(s(elem!1))))),
% 0.55/0.75 inference(unit_resolution,[status(thm)],[1347, 1673, 156])).
% 0.55/0.75 tff(1675,plain,
% 0.55/0.75 (((~![X0: $i, X2: $i, X1: $i] : ((~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(s(elem!1))))) | (~b(s(s(s(s(elem!1)))), s(z))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~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(s(elem!1))))) | (~b(s(s(s(s(elem!1)))), s(z))))),
% 0.55/0.75 inference(rewrite,[status(thm)],[])).
% 0.55/0.75 tff(1676,plain,
% 0.55/0.75 ((~![X0: $i, X2: $i, X1: $i] : ((~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(s(elem!1))))) | (~b(s(s(s(s(elem!1)))), s(z))))),
% 0.55/0.75 inference(quant_inst,[status(thm)],[])).
% 0.55/0.75 tff(1677,plain,
% 0.55/0.75 ((~![X0: $i, X2: $i, X1: $i] : ((~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), s(s(s(elem!1))))) | (~b(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~b(s(s(s(s(elem!1)))), s(z)))),
% 0.55/0.75 inference(modus_ponens,[status(thm)],[1676, 1675])).
% 0.55/0.75 tff(1678,plain,
% 0.55/0.75 ($false),
% 0.55/0.75 inference(unit_resolution,[status(thm)],[1677, 117, 238, 1311, 1349])).
% 0.55/0.75 tff(1679,plain,((~b(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~b(s(z), s(s(s(elem!1))))) | (~b(s(s(s(s(elem!1)))), s(z)))), inference(lemma,lemma(discharge,[]))).
% 0.55/0.75 tff(1680,plain,
% 0.55/0.75 (~b(s(z), s(s(s(elem!1))))),
% 0.55/0.75 inference(unit_resolution,[status(thm)],[1679, 1674, 1311])).
% 0.55/0.75 tff(1681,plain,
% 0.55/0.75 (r(s(z), s(s(s(elem!1))))),
% 0.55/0.76 inference(unit_resolution,[status(thm)],[235, 1680])).
% 0.55/0.76 tff(1682,plain,
% 0.55/0.76 (~b(s(s(elem!1)), s(s(s(elem!1))))),
% 0.55/0.76 inference(unit_resolution,[status(thm)],[1488, 1674, 1416])).
% 0.55/0.76 tff(1683,plain,
% 0.55/0.76 (r(s(s(elem!1)), s(s(s(elem!1))))),
% 0.55/0.76 inference(unit_resolution,[status(thm)],[253, 1682, 145])).
% 0.55/0.76 tff(1684,plain,
% 0.55/0.76 ($false),
% 0.55/0.76 inference(unit_resolution,[status(thm)],[1477, 14, 1459, 1683, 1681])).
% 0.55/0.76 tff(1685,plain,((~b(s(s(s(s(elem!1)))), s(s(elem!1)))) | (s(s(elem!1)) = s(s(s(elem!1)))) | (~b(s(s(s(s(elem!1)))), s(z))) | (~r(s(s(s(s(elem!1)))), z)) | (~b(s(z), z)) | (~r(s(s(s(z))), z))), inference(lemma,lemma(discharge,[]))).
% 0.55/0.76 tff(1686,plain,
% 0.55/0.76 (~b(s(s(s(s(elem!1)))), s(s(elem!1)))),
% 0.55/0.76 inference(unit_resolution,[status(thm)],[1685, 237, 1311, 1396, 145, 180])).
% 0.55/0.76 tff(1687,plain,
% 0.55/0.76 (((~![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))))),
% 0.55/0.76 inference(rewrite,[status(thm)],[])).
% 0.55/0.76 tff(1688,plain,
% 0.55/0.76 ((~![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))))),
% 0.55/0.76 inference(quant_inst,[status(thm)],[])).
% 0.55/0.76 tff(1689,plain,
% 0.55/0.76 ((~![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)))),
% 0.55/0.76 inference(modus_ponens,[status(thm)],[1688, 1687])).
% 0.55/0.76 tff(1690,plain,
% 0.55/0.76 ((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)))),
% 0.55/0.76 inference(unit_resolution,[status(thm)],[1689, 46])).
% 0.55/0.76 tff(1691,plain,
% 0.55/0.76 (r(s(s(s(s(elem!1)))), s(s(elem!1)))),
% 0.55/0.76 inference(unit_resolution,[status(thm)],[1690, 1686, 1415])).
% 0.55/0.76 tff(1692,plain,
% 0.55/0.76 (~r(s(s(elem!1)), z)),
% 0.55/0.76 inference(unit_resolution,[status(thm)],[1402, 1691, 1396])).
% 0.55/0.76 tff(1693,plain,
% 0.55/0.76 (b(s(s(elem!1)), z)),
% 0.55/0.76 inference(unit_resolution,[status(thm)],[1025, 1692])).
% 0.55/0.76 tff(1694,plain,
% 0.55/0.76 (~b(s(s(s(elem!1))), z)),
% 0.55/0.76 inference(unit_resolution,[status(thm)],[1050, 1693, 237, 145])).
% 0.55/0.76 tff(1695,plain,
% 0.55/0.76 (r(s(s(s(elem!1))), z)),
% 0.55/0.76 inference(unit_resolution,[status(thm)],[211, 1694])).
% 0.55/0.76 tff(1696,plain,
% 0.55/0.76 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), z)) | (~r(s(s(s(s(elem!1)))), z)) | (~r(s(s(s(elem!1))), s(s(s(s(elem!1)))))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(elem!1))), z)) | (~r(s(s(s(s(elem!1)))), z)) | (~r(s(s(s(elem!1))), s(s(s(s(elem!1)))))))),
% 0.55/0.76 inference(rewrite,[status(thm)],[])).
% 0.55/0.76 tff(1697,plain,
% 0.55/0.76 (((~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(s(elem!1)))), z)) | (~r(s(s(s(elem!1))), s(s(s(s(elem!1)))))))),
% 0.55/0.76 inference(rewrite,[status(thm)],[])).
% 0.55/0.76 tff(1698,plain,
% 0.55/0.76 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(elem!1)))), z)) | (~r(s(s(s(elem!1))), z)) | (~r(s(s(s(elem!1))), s(s(s(s(elem!1)))))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), z)) | (~r(s(s(s(s(elem!1)))), z)) | (~r(s(s(s(elem!1))), s(s(s(s(elem!1))))))))),
% 0.55/0.76 inference(monotonicity,[status(thm)],[1697])).
% 0.55/0.76 tff(1699,plain,
% 0.55/0.76 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(elem!1)))), z)) | (~r(s(s(s(elem!1))), z)) | (~r(s(s(s(elem!1))), s(s(s(s(elem!1)))))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(elem!1))), z)) | (~r(s(s(s(s(elem!1)))), z)) | (~r(s(s(s(elem!1))), s(s(s(s(elem!1)))))))),
% 0.55/0.76 inference(transitivity,[status(thm)],[1698, 1696])).
% 0.55/0.76 tff(1700,plain,
% 0.55/0.76 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(elem!1)))), z)) | (~r(s(s(s(elem!1))), z)) | (~r(s(s(s(elem!1))), s(s(s(s(elem!1)))))))),
% 0.55/0.76 inference(quant_inst,[status(thm)],[])).
% 0.55/0.76 tff(1701,plain,
% 0.55/0.76 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(elem!1))), z)) | (~r(s(s(s(s(elem!1)))), z)) | (~r(s(s(s(elem!1))), s(s(s(s(elem!1))))))),
% 0.55/0.76 inference(modus_ponens,[status(thm)],[1700, 1699])).
% 0.55/0.76 tff(1702,plain,
% 0.55/0.76 (~r(s(s(s(elem!1))), s(s(s(s(elem!1)))))),
% 0.55/0.76 inference(unit_resolution,[status(thm)],[1701, 14, 1695, 1396])).
% 0.55/0.76 tff(1703,plain,
% 0.55/0.76 (b(s(s(s(elem!1))), s(s(s(s(elem!1)))))),
% 0.55/0.76 inference(unit_resolution,[status(thm)],[448, 1702, 290])).
% 0.55/0.76 tff(1704,plain,
% 0.55/0.76 (((~![X0: $i, X2: $i, X1: $i] : ((~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), s(s(s(s(elem!1)))))) | (~b(s(s(s(elem!1))), s(s(s(s(elem!1)))))) | (~b(s(s(s(z))), s(s(s(elem!1))))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(z))), s(s(s(s(elem!1)))))) | (~b(s(s(s(elem!1))), s(s(s(s(elem!1)))))) | (~b(s(s(s(z))), s(s(s(elem!1))))))),
% 0.55/0.76 inference(rewrite,[status(thm)],[])).
% 0.55/0.76 tff(1705,plain,
% 0.55/0.76 (((~b(s(s(s(elem!1))), s(s(s(s(elem!1)))))) | (~b(s(s(s(z))), s(s(s(s(elem!1)))))) | (~b(s(s(s(z))), s(s(s(elem!1)))))) <=> ((~b(s(s(s(z))), s(s(s(s(elem!1)))))) | (~b(s(s(s(elem!1))), s(s(s(s(elem!1)))))) | (~b(s(s(s(z))), s(s(s(elem!1))))))),
% 0.55/0.76 inference(rewrite,[status(thm)],[])).
% 0.55/0.76 tff(1706,plain,
% 0.55/0.76 (((~![X0: $i, X2: $i, X1: $i] : ((~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), s(s(s(s(elem!1)))))) | (~b(s(s(s(z))), s(s(s(s(elem!1)))))) | (~b(s(s(s(z))), s(s(s(elem!1))))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), s(s(s(s(elem!1)))))) | (~b(s(s(s(elem!1))), s(s(s(s(elem!1)))))) | (~b(s(s(s(z))), s(s(s(elem!1)))))))),
% 0.55/0.76 inference(monotonicity,[status(thm)],[1705])).
% 0.55/0.76 tff(1707,plain,
% 0.55/0.76 (((~![X0: $i, X2: $i, X1: $i] : ((~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), s(s(s(s(elem!1)))))) | (~b(s(s(s(z))), s(s(s(s(elem!1)))))) | (~b(s(s(s(z))), s(s(s(elem!1))))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(z))), s(s(s(s(elem!1)))))) | (~b(s(s(s(elem!1))), s(s(s(s(elem!1)))))) | (~b(s(s(s(z))), s(s(s(elem!1))))))),
% 0.55/0.76 inference(transitivity,[status(thm)],[1706, 1704])).
% 0.55/0.76 tff(1708,plain,
% 0.55/0.76 ((~![X0: $i, X2: $i, X1: $i] : ((~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), s(s(s(s(elem!1)))))) | (~b(s(s(s(z))), s(s(s(s(elem!1)))))) | (~b(s(s(s(z))), s(s(s(elem!1))))))),
% 0.55/0.76 inference(quant_inst,[status(thm)],[])).
% 0.55/0.76 tff(1709,plain,
% 0.55/0.76 ((~![X0: $i, X2: $i, X1: $i] : ((~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(z))), s(s(s(s(elem!1)))))) | (~b(s(s(s(elem!1))), s(s(s(s(elem!1)))))) | (~b(s(s(s(z))), s(s(s(elem!1)))))),
% 0.55/0.76 inference(modus_ponens,[status(thm)],[1708, 1707])).
% 0.55/0.76 tff(1710,plain,
% 0.55/0.76 (~b(s(s(s(z))), s(s(s(elem!1))))),
% 0.55/0.76 inference(unit_resolution,[status(thm)],[1709, 117, 1703, 1414])).
% 0.55/0.76 tff(1711,plain,
% 0.55/0.76 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), z)) | (~r(s(s(s(z))), z)) | (~r(s(s(s(z))), s(s(s(elem!1))))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(elem!1))), z)) | (~r(s(s(s(z))), z)) | (~r(s(s(s(z))), s(s(s(elem!1))))))),
% 0.55/0.76 inference(rewrite,[status(thm)],[])).
% 0.55/0.76 tff(1712,plain,
% 0.55/0.76 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), z)) | (~r(s(s(s(z))), z)) | (~r(s(s(s(z))), s(s(s(elem!1))))))),
% 0.55/0.76 inference(quant_inst,[status(thm)],[])).
% 0.55/0.76 tff(1713,plain,
% 0.55/0.76 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(elem!1))), z)) | (~r(s(s(s(z))), z)) | (~r(s(s(s(z))), s(s(s(elem!1)))))),
% 0.55/0.76 inference(modus_ponens,[status(thm)],[1712, 1711])).
% 0.55/0.76 tff(1714,plain,
% 0.55/0.76 (~r(s(s(s(z))), s(s(s(elem!1))))),
% 0.55/0.76 inference(unit_resolution,[status(thm)],[1713, 14, 1695, 180])).
% 0.55/0.76 tff(1715,plain,
% 0.55/0.76 (((~![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)))))),
% 0.55/0.76 inference(rewrite,[status(thm)],[])).
% 0.55/0.76 tff(1716,plain,
% 0.55/0.76 ((~![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)))))),
% 0.55/0.76 inference(quant_inst,[status(thm)],[])).
% 0.55/0.76 tff(1717,plain,
% 0.55/0.76 ((~![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))))),
% 0.55/0.76 inference(modus_ponens,[status(thm)],[1716, 1715])).
% 0.55/0.76 tff(1718,plain,
% 0.55/0.76 ((s(s(s(z))) = s(s(s(elem!1)))) | b(s(s(s(z))), s(s(s(elem!1))))),
% 0.55/0.76 inference(unit_resolution,[status(thm)],[1717, 46, 1714])).
% 0.55/0.76 tff(1719,plain,
% 0.55/0.76 (s(s(s(z))) = s(s(s(elem!1)))),
% 0.55/0.76 inference(unit_resolution,[status(thm)],[1718, 1710])).
% 0.55/0.76 tff(1720,plain,
% 0.55/0.76 (s(s(s(elem!1))) = s(s(s(z)))),
% 0.55/0.76 inference(symmetry,[status(thm)],[1719])).
% 0.55/0.76 tff(1721,plain,
% 0.55/0.76 ((s(s(s(s(s(s(elem!1)))))) = s(s(s(elem!1)))) <=> (s(s(s(s(s(s(elem!1)))))) = s(s(s(z))))),
% 0.55/0.76 inference(monotonicity,[status(thm)],[1720])).
% 0.55/0.76 tff(1722,plain,
% 0.55/0.76 ((s(s(s(s(s(s(elem!1)))))) = s(s(s(z)))) <=> (s(s(s(s(s(s(elem!1)))))) = s(s(s(elem!1))))),
% 0.55/0.76 inference(symmetry,[status(thm)],[1721])).
% 0.55/0.76 tff(1723,plain,
% 0.55/0.76 ((~(s(s(s(s(s(s(elem!1)))))) = s(s(s(z))))) <=> (~(s(s(s(s(s(s(elem!1)))))) = s(s(s(elem!1)))))),
% 0.55/0.76 inference(monotonicity,[status(thm)],[1722])).
% 0.55/0.76 tff(1724,plain,
% 0.55/0.76 (~(s(s(s(s(s(s(elem!1)))))) = s(s(s(elem!1))))),
% 0.55/0.76 inference(modus_ponens,[status(thm)],[1577, 1723])).
% 0.55/0.76 tff(1725,plain,
% 0.55/0.76 (inj_0(s(s(s(z)))) = inj_0(s(s(s(elem!1))))),
% 0.55/0.76 inference(monotonicity,[status(thm)],[1719])).
% 0.55/0.76 tff(1726,plain,
% 0.55/0.76 (s(s(z)) = s(s(elem!1))),
% 0.55/0.76 inference(transitivity,[status(thm)],[95, 1725, 151])).
% 0.55/0.76 tff(1727,plain,
% 0.55/0.76 (inj_0(s(s(z))) = inj_0(s(s(elem!1)))),
% 0.55/0.76 inference(monotonicity,[status(thm)],[1726])).
% 0.55/0.76 tff(1728,plain,
% 0.55/0.76 (s(z) = s(elem!1)),
% 0.55/0.76 inference(transitivity,[status(thm)],[131, 1727, 166])).
% 0.55/0.76 tff(1729,plain,
% 0.55/0.76 (inj_0(s(z)) = inj_0(s(elem!1))),
% 0.55/0.76 inference(monotonicity,[status(thm)],[1728])).
% 0.55/0.76 tff(1730,plain,
% 0.55/0.76 (z = inj_0(s(z))),
% 0.55/0.76 inference(symmetry,[status(thm)],[90])).
% 0.55/0.76 tff(1731,plain,
% 0.55/0.76 (z = elem!1),
% 0.55/0.76 inference(transitivity,[status(thm)],[1730, 1729, 257])).
% 0.55/0.76 tff(1732,plain,
% 0.55/0.76 ((s(s(s(s(s(s(elem!1)))))) = z) <=> (s(s(s(s(s(s(elem!1)))))) = elem!1)),
% 0.55/0.76 inference(monotonicity,[status(thm)],[1731])).
% 0.55/0.76 tff(1733,plain,
% 0.55/0.76 ((~(s(s(s(s(s(s(elem!1)))))) = z)) <=> (~(s(s(s(s(s(s(elem!1)))))) = elem!1))),
% 0.55/0.76 inference(monotonicity,[status(thm)],[1732])).
% 0.55/0.76 tff(1734,plain,
% 0.55/0.76 (~(s(s(s(s(s(s(elem!1)))))) = elem!1)),
% 0.55/0.76 inference(modus_ponens,[status(thm)],[1663, 1733])).
% 0.55/0.76 tff(1735,plain,
% 0.55/0.76 (b(s(s(elem!1)), z) <=> b(s(s(elem!1)), elem!1)),
% 0.55/0.76 inference(monotonicity,[status(thm)],[1731])).
% 0.55/0.76 tff(1736,plain,
% 0.55/0.76 (b(s(s(elem!1)), elem!1)),
% 0.55/0.76 inference(modus_ponens,[status(thm)],[1693, 1735])).
% 0.55/0.76 tff(1737,plain,
% 0.55/0.76 (b(s(z), z) <=> b(s(z), elem!1)),
% 0.55/0.76 inference(monotonicity,[status(thm)],[1731])).
% 0.55/0.76 tff(1738,plain,
% 0.55/0.76 (b(s(z), elem!1)),
% 0.55/0.76 inference(modus_ponens,[status(thm)],[237, 1737])).
% 0.55/0.76 tff(1739,plain,
% 0.55/0.76 (~b(s(z), s(s(elem!1)))),
% 0.55/0.76 inference(unit_resolution,[status(thm)],[1059, 117, 1693, 237])).
% 0.55/0.76 tff(1740,plain,
% 0.55/0.76 (r(s(z), s(s(elem!1)))),
% 0.55/0.76 inference(unit_resolution,[status(thm)],[416, 1739])).
% 0.55/0.76 tff(1741,assumption,(s(s(s(z))) = s(s(s(elem!1)))), introduced(assumption)).
% 0.55/0.76 tff(1742,plain,
% 0.55/0.76 (inj_0(s(s(s(z)))) = inj_0(s(s(s(elem!1))))),
% 0.55/0.76 inference(monotonicity,[status(thm)],[1741])).
% 0.55/0.76 tff(1743,plain,
% 0.55/0.76 (s(s(z)) = s(s(elem!1))),
% 0.55/0.76 inference(transitivity,[status(thm)],[95, 1742, 151])).
% 0.55/0.76 tff(1744,plain,
% 0.55/0.76 (inj_0(s(s(z))) = inj_0(s(s(elem!1)))),
% 0.55/0.76 inference(monotonicity,[status(thm)],[1743])).
% 0.55/0.76 tff(1745,plain,
% 0.55/0.76 (inj_0(s(s(elem!1))) = inj_0(s(s(z)))),
% 0.55/0.76 inference(symmetry,[status(thm)],[1744])).
% 0.55/0.76 tff(1746,plain,
% 0.55/0.76 (s(elem!1) = s(z)),
% 0.55/0.76 inference(transitivity,[status(thm)],[167, 1745, 82])).
% 0.55/0.76 tff(1747,plain,
% 0.55/0.76 (r(s(elem!1), s(s(elem!1))) <=> r(s(z), s(s(elem!1)))),
% 0.55/0.76 inference(monotonicity,[status(thm)],[1746])).
% 0.55/0.76 tff(1748,plain,
% 0.55/0.76 (r(s(z), s(s(elem!1))) <=> r(s(elem!1), s(s(elem!1)))),
% 0.55/0.76 inference(symmetry,[status(thm)],[1747])).
% 0.55/0.76 tff(1749,plain,
% 0.55/0.76 (r(s(elem!1), s(s(elem!1)))),
% 0.55/0.76 inference(modus_ponens,[status(thm)],[1149, 1748])).
% 0.55/0.76 tff(1750,assumption,(~r(s(elem!1), s(s(elem!1)))), introduced(assumption)).
% 0.55/0.76 tff(1751,plain,
% 0.55/0.76 ($false),
% 0.55/0.76 inference(unit_resolution,[status(thm)],[1750, 1749])).
% 0.55/0.76 tff(1752,plain,(r(s(elem!1), s(s(elem!1))) | (~r(s(z), s(s(elem!1)))) | (~(s(s(s(z))) = s(s(s(elem!1)))))), inference(lemma,lemma(discharge,[]))).
% 0.55/0.76 tff(1753,plain,
% 0.55/0.76 (r(s(elem!1), s(s(elem!1)))),
% 0.55/0.76 inference(unit_resolution,[status(thm)],[1752, 1740, 1719])).
% 0.55/0.76 tff(1754,plain,
% 0.55/0.76 (s(s(s(s(z)))) = s(s(s(s(elem!1))))),
% 0.55/0.76 inference(monotonicity,[status(thm)],[1741])).
% 0.55/0.76 tff(1755,plain,
% 0.55/0.76 (s(s(s(s(s(z))))) = s(s(s(s(s(elem!1)))))),
% 0.55/0.76 inference(monotonicity,[status(thm)],[1754])).
% 0.55/0.76 tff(1756,plain,
% 0.55/0.76 (s(s(s(s(s(s(z)))))) = s(s(s(s(s(s(elem!1))))))),
% 0.55/0.76 inference(monotonicity,[status(thm)],[1755])).
% 0.55/0.76 tff(1757,plain,
% 0.55/0.76 (s(s(s(s(s(s(elem!1)))))) = s(s(s(s(s(s(z))))))),
% 0.55/0.76 inference(symmetry,[status(thm)],[1756])).
% 0.55/0.76 tff(1758,plain,
% 0.55/0.76 ((s(s(s(s(s(s(elem!1)))))) = s(elem!1)) <=> (s(s(s(s(s(s(z)))))) = s(z))),
% 0.55/0.76 inference(monotonicity,[status(thm)],[1757, 1746])).
% 0.55/0.76 tff(1759,plain,
% 0.55/0.76 ((s(s(s(s(s(s(z)))))) = s(z)) <=> (s(s(s(s(s(s(elem!1)))))) = s(elem!1))),
% 0.55/0.76 inference(symmetry,[status(thm)],[1758])).
% 0.55/0.76 tff(1760,plain,
% 0.55/0.76 ((~(s(s(s(s(s(s(z)))))) = s(z))) <=> (~(s(s(s(s(s(s(elem!1)))))) = s(elem!1)))),
% 0.55/0.76 inference(monotonicity,[status(thm)],[1759])).
% 0.55/0.76 tff(1761,assumption,(s(s(s(s(s(s(z)))))) = s(z)), introduced(assumption)).
% 0.55/0.76 tff(1762,plain,
% 0.55/0.76 (inj_0(s(s(s(s(s(s(z))))))) = inj_0(s(z))),
% 0.55/0.76 inference(monotonicity,[status(thm)],[1761])).
% 0.55/0.76 tff(1763,plain,
% 0.55/0.76 ((~![Xk!0: $i] : (inj_0(s(Xk!0)) = Xk!0)) | (inj_0(s(s(s(s(s(s(z))))))) = s(s(s(s(s(z))))))),
% 0.55/0.76 inference(quant_inst,[status(thm)],[])).
% 0.55/0.76 tff(1764,plain,
% 0.55/0.76 (inj_0(s(s(s(s(s(s(z))))))) = s(s(s(s(s(z)))))),
% 0.55/0.76 inference(unit_resolution,[status(thm)],[1763, 80])).
% 0.55/0.76 tff(1765,plain,
% 0.55/0.76 (s(s(s(s(s(z))))) = inj_0(s(s(s(s(s(s(z)))))))),
% 0.55/0.76 inference(symmetry,[status(thm)],[1764])).
% 0.55/0.76 tff(1766,plain,
% 0.55/0.76 (s(s(s(s(s(z))))) = z),
% 0.55/0.76 inference(transitivity,[status(thm)],[1765, 1762, 90])).
% 0.55/0.76 tff(1767,plain,
% 0.55/0.76 ((~![X: $i] : (~(s(X) = z))) | (~(s(s(s(s(s(z))))) = z))),
% 0.55/0.76 inference(quant_inst,[status(thm)],[])).
% 0.55/0.76 tff(1768,plain,
% 0.55/0.76 (~(s(s(s(s(s(z))))) = z)),
% 0.55/0.76 inference(unit_resolution,[status(thm)],[1767, 33])).
% 0.55/0.76 tff(1769,plain,
% 0.55/0.76 ($false),
% 0.55/0.76 inference(unit_resolution,[status(thm)],[1768, 1766])).
% 0.55/0.76 tff(1770,plain,(~(s(s(s(s(s(s(z)))))) = s(z))), inference(lemma,lemma(discharge,[]))).
% 0.55/0.76 tff(1771,plain,
% 0.55/0.76 (~(s(s(s(s(s(s(elem!1)))))) = s(elem!1))),
% 0.55/0.76 inference(modus_ponens,[status(thm)],[1770, 1760])).
% 0.55/0.76 tff(1772,plain,
% 0.55/0.76 (inj_0(s(s(s(elem!1)))) = inj_0(s(s(s(z))))),
% 0.55/0.76 inference(symmetry,[status(thm)],[1742])).
% 0.55/0.76 tff(1773,plain,
% 0.55/0.76 (s(s(elem!1)) = s(s(z))),
% 0.55/0.76 inference(transitivity,[status(thm)],[152, 1772, 94])).
% 0.55/0.76 tff(1774,plain,
% 0.55/0.76 ((s(s(s(s(s(s(elem!1)))))) = s(s(elem!1))) <=> (s(s(s(s(s(s(z)))))) = s(s(z)))),
% 0.55/0.76 inference(monotonicity,[status(thm)],[1757, 1773])).
% 0.55/0.76 tff(1775,plain,
% 0.55/0.76 ((s(s(s(s(s(s(z)))))) = s(s(z))) <=> (s(s(s(s(s(s(elem!1)))))) = s(s(elem!1)))),
% 0.55/0.76 inference(symmetry,[status(thm)],[1774])).
% 0.55/0.76 tff(1776,plain,
% 0.55/0.76 ((~(s(s(s(s(s(s(z)))))) = s(s(z)))) <=> (~(s(s(s(s(s(s(elem!1)))))) = s(s(elem!1))))),
% 0.55/0.76 inference(monotonicity,[status(thm)],[1775])).
% 0.55/0.76 tff(1777,assumption,(s(s(s(s(s(s(z)))))) = s(s(z))), introduced(assumption)).
% 0.55/0.76 tff(1778,plain,
% 0.55/0.76 (inj_0(s(s(s(s(s(s(z))))))) = inj_0(s(s(z)))),
% 0.55/0.76 inference(monotonicity,[status(thm)],[1777])).
% 0.55/0.76 tff(1779,plain,
% 0.55/0.76 (s(s(s(s(s(z))))) = s(z)),
% 0.55/0.76 inference(transitivity,[status(thm)],[1765, 1778, 82])).
% 0.55/0.76 tff(1780,plain,
% 0.55/0.76 (inj_0(s(s(s(s(s(z)))))) = inj_0(s(z))),
% 0.55/0.76 inference(monotonicity,[status(thm)],[1779])).
% 0.55/0.76 tff(1781,plain,
% 0.55/0.76 ((~![Xk!0: $i] : (inj_0(s(Xk!0)) = Xk!0)) | (inj_0(s(s(s(s(s(z)))))) = s(s(s(s(z)))))),
% 0.55/0.76 inference(quant_inst,[status(thm)],[])).
% 0.55/0.76 tff(1782,plain,
% 0.55/0.76 (inj_0(s(s(s(s(s(z)))))) = s(s(s(s(z))))),
% 0.55/0.76 inference(unit_resolution,[status(thm)],[1781, 80])).
% 0.55/0.76 tff(1783,plain,
% 0.55/0.76 (s(s(s(s(z)))) = inj_0(s(s(s(s(s(z))))))),
% 0.55/0.76 inference(symmetry,[status(thm)],[1782])).
% 0.55/0.76 tff(1784,plain,
% 0.55/0.76 (s(s(s(s(z)))) = z),
% 0.55/0.76 inference(transitivity,[status(thm)],[1783, 1780, 90])).
% 0.55/0.76 tff(1785,plain,
% 0.55/0.76 ($false),
% 0.55/0.76 inference(unit_resolution,[status(thm)],[35, 1784])).
% 0.55/0.76 tff(1786,plain,(~(s(s(s(s(s(s(z)))))) = s(s(z)))), inference(lemma,lemma(discharge,[]))).
% 0.55/0.76 tff(1787,plain,
% 0.55/0.76 (~(s(s(s(s(s(s(elem!1)))))) = s(s(elem!1)))),
% 0.55/0.76 inference(modus_ponens,[status(thm)],[1786, 1776])).
% 0.55/0.76 tff(1788,assumption,(b(s(s(s(s(s(s(elem!1)))))), elem!1)), introduced(assumption)).
% 0.55/0.76 tff(1789,assumption,(b(s(s(elem!1)), elem!1)), introduced(assumption)).
% 0.55/0.76 tff(1790,plain,
% 0.55/0.76 (((~![X0: $i, X2: $i, X1: $i] : ((~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(s(s(s(s(s(s(elem!1)))))), s(s(elem!1)))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~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(s(s(s(s(s(s(elem!1)))))), s(s(elem!1)))))),
% 0.55/0.76 inference(rewrite,[status(thm)],[])).
% 0.55/0.76 tff(1791,plain,
% 0.55/0.76 ((~![X0: $i, X2: $i, X1: $i] : ((~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(s(s(s(s(s(s(elem!1)))))), s(s(elem!1)))))),
% 0.55/0.76 inference(quant_inst,[status(thm)],[])).
% 0.55/0.76 tff(1792,plain,
% 0.55/0.76 ((~![X0: $i, X2: $i, X1: $i] : ((~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(s(s(s(s(s(s(elem!1)))))), s(s(elem!1))))),
% 0.55/0.76 inference(modus_ponens,[status(thm)],[1791, 1790])).
% 0.55/0.76 tff(1793,plain,
% 0.55/0.76 (~b(s(s(s(s(s(s(elem!1)))))), s(s(elem!1)))),
% 0.55/0.76 inference(unit_resolution,[status(thm)],[1792, 117, 1789, 1788])).
% 0.55/0.76 tff(1794,plain,
% 0.55/0.76 ((s(s(s(s(s(s(elem!1)))))) = s(s(elem!1))) | r(s(s(s(s(s(s(elem!1)))))), s(s(elem!1)))),
% 0.55/0.76 inference(unit_resolution,[status(thm)],[1586, 46, 1793])).
% 0.55/0.76 tff(1795,plain,
% 0.55/0.76 (r(s(s(s(s(s(s(elem!1)))))), s(s(elem!1)))),
% 0.55/0.76 inference(unit_resolution,[status(thm)],[1794, 1787])).
% 0.55/0.76 tff(1796,assumption,(r(s(elem!1), s(s(elem!1)))), introduced(assumption)).
% 0.55/0.76 tff(1797,plain,
% 0.55/0.76 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(elem!1), s(s(elem!1)))) | (~r(s(s(s(s(s(s(elem!1)))))), s(s(elem!1)))) | (~r(s(s(s(s(s(s(elem!1)))))), s(elem!1))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(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(elem!1))))),
% 0.55/0.76 inference(rewrite,[status(thm)],[])).
% 0.55/0.76 tff(1798,plain,
% 0.55/0.76 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(elem!1), s(s(elem!1)))) | (~r(s(s(s(s(s(s(elem!1)))))), s(s(elem!1)))) | (~r(s(s(s(s(s(s(elem!1)))))), s(elem!1))))),
% 0.55/0.76 inference(quant_inst,[status(thm)],[])).
% 0.55/0.76 tff(1799,plain,
% 0.55/0.76 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(elem!1), s(s(elem!1)))) | (~r(s(s(s(s(s(s(elem!1)))))), s(s(elem!1)))) | (~r(s(s(s(s(s(s(elem!1)))))), s(elem!1)))),
% 0.55/0.76 inference(modus_ponens,[status(thm)],[1798, 1797])).
% 0.55/0.76 tff(1800,plain,
% 0.55/0.76 (~r(s(s(s(s(s(s(elem!1)))))), s(elem!1))),
% 0.55/0.76 inference(unit_resolution,[status(thm)],[1799, 14, 1796, 1795])).
% 0.55/0.76 tff(1801,plain,
% 0.55/0.76 (b(s(elem!1), elem!1) <=> b(s(z), elem!1)),
% 0.55/0.76 inference(monotonicity,[status(thm)],[1746])).
% 0.55/0.76 tff(1802,plain,
% 0.55/0.76 (b(s(z), elem!1) <=> b(s(elem!1), elem!1)),
% 0.55/0.76 inference(symmetry,[status(thm)],[1801])).
% 0.55/0.76 tff(1803,assumption,(b(s(z), elem!1)), introduced(assumption)).
% 0.55/0.76 tff(1804,plain,
% 0.55/0.76 (b(s(elem!1), elem!1)),
% 0.55/0.76 inference(modus_ponens,[status(thm)],[1803, 1802])).
% 0.55/0.76 tff(1805,plain,
% 0.55/0.76 (((~![X0: $i, X2: $i, X1: $i] : ((~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(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(elem!1))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(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(elem!1))))),
% 0.55/0.76 inference(rewrite,[status(thm)],[])).
% 0.55/0.76 tff(1806,plain,
% 0.55/0.76 ((~![X0: $i, X2: $i, X1: $i] : ((~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(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(elem!1))))),
% 0.55/0.76 inference(quant_inst,[status(thm)],[])).
% 0.55/0.76 tff(1807,plain,
% 0.55/0.76 ((~![X0: $i, X2: $i, X1: $i] : ((~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(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(elem!1)))),
% 0.55/0.76 inference(modus_ponens,[status(thm)],[1806, 1805])).
% 0.55/0.76 tff(1808,plain,
% 0.55/0.76 ((~b(s(elem!1), elem!1)) | (~b(s(s(s(s(s(s(elem!1)))))), s(elem!1)))),
% 0.55/0.76 inference(unit_resolution,[status(thm)],[1807, 117, 1788])).
% 0.55/0.76 tff(1809,plain,
% 0.55/0.76 (~b(s(s(s(s(s(s(elem!1)))))), s(elem!1))),
% 0.55/0.76 inference(unit_resolution,[status(thm)],[1808, 1804])).
% 0.55/0.76 tff(1810,plain,
% 0.55/0.76 (((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((s(s(s(s(s(s(elem!1)))))) = s(elem!1)) | b(s(s(s(s(s(s(elem!1)))))), s(elem!1)) | r(s(s(s(s(s(s(elem!1)))))), s(elem!1)))) <=> ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (s(s(s(s(s(s(elem!1)))))) = s(elem!1)) | b(s(s(s(s(s(s(elem!1)))))), s(elem!1)) | r(s(s(s(s(s(s(elem!1)))))), s(elem!1)))),
% 0.55/0.76 inference(rewrite,[status(thm)],[])).
% 0.55/0.76 tff(1811,plain,
% 0.55/0.76 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((s(s(s(s(s(s(elem!1)))))) = s(elem!1)) | b(s(s(s(s(s(s(elem!1)))))), s(elem!1)) | r(s(s(s(s(s(s(elem!1)))))), s(elem!1)))),
% 0.55/0.76 inference(quant_inst,[status(thm)],[])).
% 0.55/0.76 tff(1812,plain,
% 0.55/0.76 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (s(s(s(s(s(s(elem!1)))))) = s(elem!1)) | b(s(s(s(s(s(s(elem!1)))))), s(elem!1)) | r(s(s(s(s(s(s(elem!1)))))), s(elem!1))),
% 0.55/0.76 inference(modus_ponens,[status(thm)],[1811, 1810])).
% 0.55/0.76 tff(1813,plain,
% 0.55/0.76 ((s(s(s(s(s(s(elem!1)))))) = s(elem!1)) | r(s(s(s(s(s(s(elem!1)))))), s(elem!1))),
% 0.55/0.76 inference(unit_resolution,[status(thm)],[1812, 46, 1809])).
% 0.55/0.76 tff(1814,plain,
% 0.55/0.76 ($false),
% 0.55/0.76 inference(unit_resolution,[status(thm)],[1813, 1800, 1771])).
% 0.55/0.76 tff(1815,plain,((~b(s(s(s(s(s(s(elem!1)))))), elem!1)) | (~r(s(elem!1), s(s(elem!1)))) | (~(s(s(s(z))) = s(s(s(elem!1))))) | (~b(s(z), elem!1)) | (~b(s(s(elem!1)), elem!1))), inference(lemma,lemma(discharge,[]))).
% 0.55/0.76 tff(1816,plain,
% 0.55/0.76 (~b(s(s(s(s(s(s(elem!1)))))), elem!1)),
% 0.55/0.76 inference(unit_resolution,[status(thm)],[1815, 1753, 1719, 1738, 1736])).
% 0.55/0.76 tff(1817,plain,
% 0.55/0.76 (r(s(s(s(s(s(s(elem!1)))))), elem!1)),
% 0.55/0.76 inference(unit_resolution,[status(thm)],[1599, 1816, 1734])).
% 0.55/0.76 tff(1818,plain,
% 0.55/0.76 (r(s(s(s(s(elem!1)))), z) <=> r(s(s(s(s(elem!1)))), elem!1)),
% 0.55/0.76 inference(monotonicity,[status(thm)],[1731])).
% 0.55/0.76 tff(1819,plain,
% 0.55/0.76 (r(s(s(s(s(elem!1)))), elem!1)),
% 0.55/0.76 inference(modus_ponens,[status(thm)],[1396, 1818])).
% 0.55/0.76 tff(1820,plain,
% 0.55/0.76 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(elem!1)))), elem!1)) | (~r(s(s(s(s(s(s(elem!1)))))), elem!1)) | (~r(s(s(s(s(s(s(elem!1)))))), s(s(s(s(elem!1)))))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(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(s(elem!1)))))))),
% 0.55/0.76 inference(rewrite,[status(thm)],[])).
% 0.55/0.76 tff(1821,plain,
% 0.55/0.76 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(elem!1)))), elem!1)) | (~r(s(s(s(s(s(s(elem!1)))))), elem!1)) | (~r(s(s(s(s(s(s(elem!1)))))), s(s(s(s(elem!1)))))))),
% 0.55/0.76 inference(quant_inst,[status(thm)],[])).
% 0.55/0.76 tff(1822,plain,
% 0.55/0.76 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(s(elem!1)))), elem!1)) | (~r(s(s(s(s(s(s(elem!1)))))), elem!1)) | (~r(s(s(s(s(s(s(elem!1)))))), s(s(s(s(elem!1))))))),
% 0.55/0.76 inference(modus_ponens,[status(thm)],[1821, 1820])).
% 0.55/0.76 tff(1823,plain,
% 0.55/0.77 (~r(s(s(s(s(s(s(elem!1)))))), s(s(s(s(elem!1)))))),
% 0.55/0.77 inference(unit_resolution,[status(thm)],[1822, 14, 1819, 1817])).
% 0.55/0.77 tff(1824,plain,
% 0.55/0.77 (b(s(s(s(s(s(s(elem!1)))))), s(s(s(s(elem!1)))))),
% 0.55/0.77 inference(unit_resolution,[status(thm)],[1619, 46, 1616, 1823])).
% 0.55/0.77 tff(1825,plain,
% 0.55/0.77 (((~![X0: $i, X2: $i, X1: $i] : ((~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), s(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(s(s(s(elem!1)))))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(elem!1))), s(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(s(s(s(elem!1)))))))),
% 0.55/0.77 inference(rewrite,[status(thm)],[])).
% 0.55/0.77 tff(1826,plain,
% 0.55/0.77 (((~b(s(s(s(elem!1))), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(s(s(elem!1)))))), s(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(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(s(s(s(elem!1)))))))),
% 0.55/0.77 inference(rewrite,[status(thm)],[])).
% 0.55/0.77 tff(1827,plain,
% 0.55/0.77 (((~![X0: $i, X2: $i, X1: $i] : ((~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(s(s(elem!1)))))), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(s(s(elem!1)))))), s(s(s(elem!1))))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), s(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(s(s(s(elem!1))))))))),
% 0.55/0.77 inference(monotonicity,[status(thm)],[1826])).
% 0.55/0.77 tff(1828,plain,
% 0.55/0.77 (((~![X0: $i, X2: $i, X1: $i] : ((~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(s(s(elem!1)))))), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(s(s(elem!1)))))), s(s(s(elem!1))))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(elem!1))), s(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(s(s(s(elem!1)))))))),
% 0.55/0.77 inference(transitivity,[status(thm)],[1827, 1825])).
% 0.55/0.77 tff(1829,plain,
% 0.55/0.77 ((~![X0: $i, X2: $i, X1: $i] : ((~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(s(s(elem!1)))))), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(s(s(elem!1)))))), s(s(s(elem!1))))))),
% 0.55/0.77 inference(quant_inst,[status(thm)],[])).
% 0.55/0.77 tff(1830,plain,
% 0.55/0.77 ((~![X0: $i, X2: $i, X1: $i] : ((~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(elem!1))), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(s(s(elem!1)))))), s(s(s(elem!1))))) | (~b(s(s(s(s(s(s(elem!1)))))), s(s(s(s(elem!1))))))),
% 0.55/0.77 inference(modus_ponens,[status(thm)],[1829, 1828])).
% 0.55/0.77 tff(1831,plain,
% 0.55/0.77 (~b(s(s(s(s(s(s(elem!1)))))), s(s(s(elem!1))))),
% 0.55/0.77 inference(unit_resolution,[status(thm)],[1830, 117, 1703, 1824])).
% 0.55/0.77 tff(1832,plain,
% 0.55/0.77 (r(s(s(s(elem!1))), z) <=> r(s(s(s(elem!1))), elem!1)),
% 0.55/0.77 inference(monotonicity,[status(thm)],[1731])).
% 0.55/0.77 tff(1833,plain,
% 0.55/0.77 (r(s(s(s(elem!1))), elem!1)),
% 0.55/0.77 inference(modus_ponens,[status(thm)],[1695, 1832])).
% 0.55/0.77 tff(1834,plain,
% 0.55/0.77 (~r(s(s(s(s(s(s(elem!1)))))), s(s(s(elem!1))))),
% 0.55/0.77 inference(unit_resolution,[status(thm)],[1559, 14, 1833, 1817])).
% 0.55/0.77 tff(1835,plain,
% 0.55/0.77 ((s(s(s(s(s(s(elem!1)))))) = s(s(s(elem!1)))) | b(s(s(s(s(s(s(elem!1)))))), s(s(s(elem!1))))),
% 0.55/0.77 inference(unit_resolution,[status(thm)],[1563, 46, 1834])).
% 0.55/0.77 tff(1836,plain,
% 0.55/0.77 ($false),
% 0.55/0.77 inference(unit_resolution,[status(thm)],[1835, 1831, 1724])).
% 0.55/0.77 tff(1837,plain,((~b(s(z), z)) | (~r(s(s(s(s(elem!1)))), z)) | (~r(s(s(s(z))), z)) | (s(s(elem!1)) = s(s(s(elem!1)))) | (~b(s(s(s(s(elem!1)))), s(z)))), inference(lemma,lemma(discharge,[]))).
% 0.55/0.77 tff(1838,plain,
% 0.55/0.77 (~b(s(s(s(s(elem!1)))), s(z))),
% 0.55/0.77 inference(unit_resolution,[status(thm)],[1837, 237, 145, 180, 1396])).
% 0.55/0.77 tff(1839,plain,
% 0.55/0.77 (r(s(s(s(s(elem!1)))), s(z))),
% 0.55/0.77 inference(unit_resolution,[status(thm)],[1327, 1838])).
% 0.55/0.77 tff(1840,plain,
% 0.55/0.77 (~r(s(s(s(s(elem!1)))), s(s(s(elem!1))))),
% 0.55/0.77 inference(unit_resolution,[status(thm)],[1342, 1839, 213])).
% 0.55/0.77 tff(1841,assumption,(~r(s(s(s(s(elem!1)))), s(s(elem!1)))), introduced(assumption)).
% 0.55/0.77 tff(1842,plain,
% 0.55/0.77 (b(s(s(s(s(elem!1)))), s(s(elem!1)))),
% 0.55/0.77 inference(unit_resolution,[status(thm)],[1690, 1415, 1841])).
% 0.55/0.77 tff(1843,plain,
% 0.55/0.77 (~b(s(s(s(s(elem!1)))), s(s(s(elem!1))))),
% 0.55/0.77 inference(unit_resolution,[status(thm)],[1488, 1842, 324])).
% 0.55/0.77 tff(1844,plain,
% 0.55/0.77 ($false),
% 0.55/0.77 inference(unit_resolution,[status(thm)],[1347, 1843, 1840, 156])).
% 0.55/0.77 tff(1845,plain,((~b(s(z), z)) | (~b(s(s(elem!1)), s(s(s(elem!1))))) | (~r(s(z), s(s(s(elem!1))))) | r(s(s(s(s(elem!1)))), s(s(elem!1))) | (s(s(elem!1)) = s(s(s(elem!1)))) | (~r(s(s(s(z))), z)) | (~r(s(s(s(s(elem!1)))), z))), inference(lemma,lemma(discharge,[]))).
% 0.55/0.77 tff(1846,plain,
% 0.55/0.77 ($false),
% 0.55/0.77 inference(unit_resolution,[status(thm)],[1845, 1403, 1396, 237, 324, 145, 180, 213])).
% 0.55/0.77 tff(1847,plain,((~r(s(s(s(s(elem!1)))), z)) | (~b(s(z), z)) | (~b(s(s(elem!1)), s(s(s(elem!1))))) | (s(s(elem!1)) = s(s(s(elem!1)))) | (~r(s(s(s(z))), z)) | (~r(s(z), s(s(s(elem!1))))) | (~r(s(s(elem!1)), z))), inference(lemma,lemma(discharge,[]))).
% 0.55/0.77 tff(1848,plain,
% 0.55/0.77 (~r(s(s(s(s(elem!1)))), z)),
% 0.55/0.77 inference(unit_resolution,[status(thm)],[1847, 213, 254, 145, 180, 194, 182])).
% 0.55/0.77 tff(1849,assumption,(~b(s(s(s(s(elem!1)))), z)), introduced(assumption)).
% 0.55/0.77 tff(1850,assumption,(~r(s(s(s(s(elem!1)))), z)), introduced(assumption)).
% 0.55/0.77 tff(1851,plain,
% 0.55/0.77 (((~![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))),
% 0.55/0.77 inference(rewrite,[status(thm)],[])).
% 0.55/0.77 tff(1852,plain,
% 0.55/0.77 ((~![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))),
% 0.55/0.77 inference(quant_inst,[status(thm)],[])).
% 0.55/0.77 tff(1853,plain,
% 0.55/0.77 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (s(s(s(s(elem!1)))) = z) | b(s(s(s(s(elem!1)))), z) | r(s(s(s(s(elem!1)))), z)),
% 0.55/0.77 inference(modus_ponens,[status(thm)],[1852, 1851])).
% 0.55/0.77 tff(1854,plain,
% 0.55/0.77 ($false),
% 0.55/0.77 inference(unit_resolution,[status(thm)],[1853, 46, 1625, 1850, 1849])).
% 0.55/0.77 tff(1855,plain,(r(s(s(s(s(elem!1)))), z) | b(s(s(s(s(elem!1)))), z)), inference(lemma,lemma(discharge,[]))).
% 0.55/0.77 tff(1856,plain,
% 0.55/0.77 (b(s(s(s(s(elem!1)))), z)),
% 0.55/0.77 inference(unit_resolution,[status(thm)],[1855, 1848])).
% 0.55/0.77 tff(1857,plain,
% 0.55/0.77 (~b(s(s(s(s(elem!1)))), s(z))),
% 0.55/0.77 inference(unit_resolution,[status(thm)],[1316, 1856, 194])).
% 0.55/0.77 tff(1858,plain,
% 0.55/0.77 (r(s(s(s(s(elem!1)))), s(z))),
% 0.55/0.77 inference(unit_resolution,[status(thm)],[1327, 1857])).
% 0.55/0.77 tff(1859,plain,
% 0.55/0.77 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(elem!1)), s(z))) | (~r(s(s(s(s(elem!1)))), s(z))) | (~r(s(s(s(s(elem!1)))), s(s(elem!1)))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(elem!1)), s(z))) | (~r(s(s(s(s(elem!1)))), s(z))) | (~r(s(s(s(s(elem!1)))), s(s(elem!1)))))),
% 0.55/0.77 inference(rewrite,[status(thm)],[])).
% 0.55/0.77 tff(1860,plain,
% 0.55/0.77 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(elem!1)), s(z))) | (~r(s(s(s(s(elem!1)))), s(z))) | (~r(s(s(s(s(elem!1)))), s(s(elem!1)))))),
% 0.55/0.77 inference(quant_inst,[status(thm)],[])).
% 0.55/0.77 tff(1861,plain,
% 0.55/0.77 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(elem!1)), s(z))) | (~r(s(s(s(s(elem!1)))), s(z))) | (~r(s(s(s(s(elem!1)))), s(s(elem!1))))),
% 0.55/0.77 inference(modus_ponens,[status(thm)],[1860, 1859])).
% 0.55/0.77 tff(1862,plain,
% 0.55/0.77 ($false),
% 0.55/0.77 inference(unit_resolution,[status(thm)],[1861, 14, 181, 1397, 1336])).
% 0.55/0.77 tff(1863,plain,((~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(z)))), inference(lemma,lemma(discharge,[]))).
% 0.55/0.77 tff(1864,plain,
% 0.55/0.77 (~r(s(s(s(s(elem!1)))), s(s(elem!1)))),
% 0.55/0.77 inference(unit_resolution,[status(thm)],[1863, 1858, 181])).
% 0.55/0.77 tff(1865,plain,
% 0.55/0.77 (b(s(s(s(s(elem!1)))), s(s(elem!1)))),
% 0.55/0.77 inference(unit_resolution,[status(thm)],[1690, 1864, 1395])).
% 0.55/0.77 tff(1866,plain,
% 0.55/0.77 (~r(s(s(s(s(elem!1)))), s(s(s(elem!1))))),
% 0.55/0.77 inference(unit_resolution,[status(thm)],[1342, 1858, 213])).
% 0.55/0.77 tff(1867,plain,
% 0.55/0.77 (b(s(s(s(s(elem!1)))), s(s(s(elem!1))))),
% 0.55/0.77 inference(unit_resolution,[status(thm)],[1347, 1866, 156])).
% 0.55/0.77 tff(1868,plain,
% 0.55/0.77 ($false),
% 0.55/0.77 inference(unit_resolution,[status(thm)],[1488, 1867, 1865, 254])).
% 0.55/0.77 tff(1869,plain,((~r(s(z), s(s(s(elem!1))))) | (~r(s(s(elem!1)), s(z))) | (s(s(elem!1)) = s(s(s(elem!1)))) | (~r(s(s(s(z))), z)) | (~r(s(s(elem!1)), z))), inference(lemma,lemma(discharge,[]))).
% 0.55/0.77 tff(1870,plain,
% 0.55/0.77 (~r(s(z), s(s(s(elem!1))))),
% 0.55/0.77 inference(unit_resolution,[status(thm)],[1869, 182, 145, 180, 181])).
% 0.55/0.77 tff(1871,plain,
% 0.55/0.77 (b(s(z), s(s(s(elem!1))))),
% 0.55/0.77 inference(unit_resolution,[status(thm)],[235, 1870])).
% 0.55/0.77 tff(1872,plain,
% 0.55/0.77 (~b(z, s(s(s(elem!1))))),
% 0.55/0.77 inference(unit_resolution,[status(thm)],[682, 1871, 194])).
% 0.55/0.77 tff(1873,plain,
% 0.55/0.77 (r(z, s(s(s(elem!1))))),
% 0.55/0.77 inference(unit_resolution,[status(thm)],[692, 1872])).
% 0.55/0.77 tff(1874,plain,
% 0.55/0.77 (((~![X0: $i, X2: $i, X1: $i] : ((~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~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))))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~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))))))),
% 0.55/0.77 inference(rewrite,[status(thm)],[])).
% 0.55/0.77 tff(1875,plain,
% 0.55/0.77 (((~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(z), s(s(elem!1)))) | (~b(s(z), s(s(s(elem!1))))) | (~b(s(s(elem!1)), s(s(s(elem!1))))))),
% 0.55/0.77 inference(rewrite,[status(thm)],[])).
% 0.55/0.77 tff(1876,plain,
% 0.55/0.77 (((~![X0: $i, X2: $i, X1: $i] : ((~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)))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~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)))))))),
% 0.55/0.77 inference(monotonicity,[status(thm)],[1875])).
% 0.55/0.77 tff(1877,plain,
% 0.55/0.77 (((~![X0: $i, X2: $i, X1: $i] : ((~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)))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~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))))))),
% 0.55/0.77 inference(transitivity,[status(thm)],[1876, 1874])).
% 0.55/0.77 tff(1878,plain,
% 0.55/0.77 ((~![X0: $i, X2: $i, X1: $i] : ((~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)))))),
% 0.55/0.77 inference(quant_inst,[status(thm)],[])).
% 0.55/0.77 tff(1879,plain,
% 0.55/0.77 ((~![X0: $i, X2: $i, X1: $i] : ((~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~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)))))),
% 0.55/0.77 inference(modus_ponens,[status(thm)],[1878, 1877])).
% 0.55/0.77 tff(1880,plain,
% 0.55/0.77 (~b(s(z), s(s(elem!1)))),
% 0.55/0.77 inference(unit_resolution,[status(thm)],[1879, 117, 254, 1871])).
% 0.55/0.77 tff(1881,plain,
% 0.55/0.77 (r(s(z), s(s(elem!1)))),
% 0.55/0.77 inference(unit_resolution,[status(thm)],[416, 1880])).
% 0.55/0.77 tff(1882,plain,
% 0.55/0.77 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~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, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~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))))),
% 0.55/0.77 inference(rewrite,[status(thm)],[])).
% 0.55/0.77 tff(1883,plain,
% 0.55/0.77 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~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))))),
% 0.55/0.77 inference(quant_inst,[status(thm)],[])).
% 0.55/0.77 tff(1884,plain,
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% 0.55/0.77 tff(1909,plain,
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% 0.55/0.78 inference(monotonicity,[status(thm)],[1953])).
% 0.55/0.78 tff(1955,plain,
% 0.55/0.78 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(elem!1), s(s(s(s(elem!1)))))) | (~r(s(s(s(s(s(s(elem!1)))))), s(s(s(s(elem!1)))))) | (~r(s(s(s(s(s(s(elem!1)))))), s(elem!1))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(s(s(s(elem!1)))))), s(s(s(s(elem!1)))))) | (~r(s(elem!1), s(s(s(s(elem!1)))))) | (~r(s(s(s(s(s(s(elem!1)))))), s(elem!1))))),
% 0.55/0.78 inference(transitivity,[status(thm)],[1954, 1952])).
% 0.55/0.78 tff(1956,plain,
% 0.55/0.78 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(elem!1), s(s(s(s(elem!1)))))) | (~r(s(s(s(s(s(s(elem!1)))))), s(s(s(s(elem!1)))))) | (~r(s(s(s(s(s(s(elem!1)))))), s(elem!1))))),
% 0.55/0.78 inference(quant_inst,[status(thm)],[])).
% 0.55/0.78 tff(1957,plain,
% 0.55/0.78 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(s(s(s(elem!1)))))), s(s(s(s(elem!1)))))) | (~r(s(elem!1), s(s(s(s(elem!1)))))) | (~r(s(s(s(s(s(s(elem!1)))))), s(elem!1)))),
% 0.55/0.78 inference(modus_ponens,[status(thm)],[1956, 1955])).
% 0.55/0.78 tff(1958,plain,
% 0.55/0.78 ((~r(s(elem!1), s(s(s(s(elem!1)))))) | (~r(s(s(s(s(s(s(elem!1)))))), s(elem!1)))),
% 0.55/0.78 inference(unit_resolution,[status(thm)],[1957, 14, 1951])).
% 0.55/0.78 tff(1959,plain,
% 0.55/0.78 (~r(s(s(s(s(s(s(elem!1)))))), s(elem!1))),
% 0.55/0.78 inference(unit_resolution,[status(thm)],[1958, 1940])).
% 0.55/0.78 tff(1960,plain,
% 0.55/0.78 (b(s(z), z) <=> b(s(z), elem!1)),
% 0.55/0.78 inference(monotonicity,[status(thm)],[1943])).
% 0.55/0.78 tff(1961,plain,
% 0.55/0.78 (b(s(z), elem!1)),
% 0.55/0.78 inference(modus_ponens,[status(thm)],[237, 1960])).
% 0.55/0.78 tff(1962,plain,
% 0.55/0.78 (b(s(elem!1), elem!1)),
% 0.55/0.78 inference(modus_ponens,[status(thm)],[1961, 1802])).
% 0.55/0.78 tff(1963,plain,
% 0.55/0.78 ((~b(s(elem!1), elem!1)) | (~b(s(s(s(s(s(s(elem!1)))))), s(elem!1)))),
% 0.55/0.78 inference(unit_resolution,[status(thm)],[1807, 117, 1947])).
% 0.55/0.78 tff(1964,plain,
% 0.55/0.78 (~b(s(s(s(s(s(s(elem!1)))))), s(elem!1))),
% 0.55/0.78 inference(unit_resolution,[status(thm)],[1963, 1962])).
% 0.55/0.78 tff(1965,plain,
% 0.55/0.78 ((s(s(s(s(s(s(elem!1)))))) = s(elem!1)) | r(s(s(s(s(s(s(elem!1)))))), s(elem!1))),
% 0.55/0.78 inference(unit_resolution,[status(thm)],[1812, 46, 1964])).
% 0.55/0.78 tff(1966,plain,
% 0.55/0.78 ($false),
% 0.55/0.78 inference(unit_resolution,[status(thm)],[1965, 1959, 1771])).
% 0.55/0.78 tff(1967,plain,((~(s(s(s(z))) = s(s(s(elem!1))))) | (s(s(s(s(s(s(elem!1)))))) = s(s(s(s(elem!1))))) | r(s(s(s(s(s(s(elem!1)))))), elem!1) | (~b(s(s(s(s(elem!1)))), z)) | (~b(s(z), z))), inference(lemma,lemma(discharge,[]))).
% 0.55/0.78 tff(1968,plain,
% 0.55/0.78 (~(s(s(s(z))) = s(s(s(elem!1))))),
% 0.55/0.78 inference(unit_resolution,[status(thm)],[1967, 1920, 1919, 1310, 237])).
% 0.55/0.78 tff(1969,assumption,(~r(s(s(s(z))), s(s(s(elem!1))))), introduced(assumption)).
% 0.55/0.78 tff(1970,plain,
% 0.55/0.78 ((s(s(s(z))) = s(s(s(elem!1)))) | b(s(s(s(z))), s(s(s(elem!1))))),
% 0.55/0.78 inference(unit_resolution,[status(thm)],[1717, 46, 1969])).
% 0.55/0.78 tff(1971,plain,
% 0.55/0.78 (b(s(s(s(z))), s(s(s(elem!1))))),
% 0.55/0.78 inference(unit_resolution,[status(thm)],[1970, 1968])).
% 0.55/0.78 tff(1972,plain,
% 0.55/0.78 (((~![X0: $i, X2: $i, X1: $i] : ((~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(z))), s(s(elem!1)))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~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(z))), s(s(elem!1)))))),
% 0.55/0.78 inference(rewrite,[status(thm)],[])).
% 0.55/0.78 tff(1973,plain,
% 0.55/0.78 ((~![X0: $i, X2: $i, X1: $i] : ((~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(z))), s(s(elem!1)))))),
% 0.55/0.78 inference(quant_inst,[status(thm)],[])).
% 0.55/0.78 tff(1974,plain,
% 0.55/0.78 ((~![X0: $i, X2: $i, X1: $i] : ((~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(z))), s(s(elem!1))))),
% 0.55/0.78 inference(modus_ponens,[status(thm)],[1973, 1972])).
% 0.55/0.78 tff(1975,plain,
% 0.55/0.78 (~b(s(s(s(z))), s(s(elem!1)))),
% 0.55/0.78 inference(unit_resolution,[status(thm)],[1974, 117, 324, 1971])).
% 0.55/0.78 tff(1976,assumption,(~r(s(s(s(z))), s(s(elem!1)))), introduced(assumption)).
% 0.55/0.78 tff(1977,plain,
% 0.55/0.78 ((s(s(s(z))) = s(s(elem!1))) | b(s(s(s(z))), s(s(elem!1)))),
% 0.55/0.78 inference(unit_resolution,[status(thm)],[1421, 46, 1976])).
% 0.55/0.78 tff(1978,plain,
% 0.55/0.78 (s(s(s(z))) = s(s(elem!1))),
% 0.55/0.78 inference(unit_resolution,[status(thm)],[1977, 1975])).
% 0.55/0.78 tff(1979,plain,
% 0.55/0.78 (inj_0(s(s(s(z)))) = inj_0(s(s(elem!1)))),
% 0.55/0.78 inference(monotonicity,[status(thm)],[1978])).
% 0.55/0.78 tff(1980,plain,
% 0.55/0.78 (s(s(z)) = s(elem!1)),
% 0.55/0.78 inference(transitivity,[status(thm)],[95, 1979, 166])).
% 0.55/0.78 tff(1981,plain,
% 0.55/0.78 (inj_0(s(s(z))) = inj_0(s(elem!1))),
% 0.55/0.78 inference(monotonicity,[status(thm)],[1980])).
% 0.55/0.78 tff(1982,plain,
% 0.55/0.78 (s(z) = elem!1),
% 0.55/0.78 inference(transitivity,[status(thm)],[131, 1981, 257])).
% 0.55/0.78 tff(1983,plain,
% 0.55/0.78 (b(s(s(s(elem!1))), s(z)) <=> b(s(s(s(elem!1))), elem!1)),
% 0.55/0.78 inference(monotonicity,[status(thm)],[1982])).
% 0.55/0.78 tff(1984,plain,
% 0.55/0.78 (b(s(s(s(elem!1))), elem!1) <=> b(s(s(s(elem!1))), s(z))),
% 0.55/0.78 inference(symmetry,[status(thm)],[1983])).
% 0.55/0.78 tff(1985,plain,
% 0.55/0.78 ((~b(s(s(s(elem!1))), elem!1)) <=> (~b(s(s(s(elem!1))), s(z)))),
% 0.55/0.78 inference(monotonicity,[status(thm)],[1984])).
% 0.55/0.78 tff(1986,plain,
% 0.55/0.78 (~(s(s(s(s(s(s(elem!1)))))) = elem!1)),
% 0.55/0.78 inference(unit_resolution,[status(thm)],[1446, 1978])).
% 0.55/0.78 tff(1987,plain,
% 0.55/0.78 (b(s(s(s(s(s(s(elem!1)))))), elem!1)),
% 0.55/0.78 inference(unit_resolution,[status(thm)],[1599, 1986, 1920])).
% 0.55/0.78 tff(1988,plain,
% 0.55/0.78 (inj_0(s(elem!1)) = inj_0(s(s(z)))),
% 0.55/0.78 inference(symmetry,[status(thm)],[1437])).
% 0.55/0.78 tff(1989,plain,
% 0.55/0.78 (elem!1 = s(z)),
% 0.55/0.78 inference(transitivity,[status(thm)],[1652, 1988, 82])).
% 0.55/0.78 tff(1990,plain,
% 0.55/0.78 (b(z, elem!1) <=> b(z, s(z))),
% 0.55/0.78 inference(monotonicity,[status(thm)],[1989])).
% 0.55/0.78 tff(1991,plain,
% 0.55/0.78 (b(z, s(z)) <=> b(z, elem!1)),
% 0.55/0.78 inference(symmetry,[status(thm)],[1990])).
% 0.55/0.78 tff(1992,plain,
% 0.55/0.78 (b(z, elem!1)),
% 0.55/0.78 inference(modus_ponens,[status(thm)],[574, 1991])).
% 0.55/0.78 tff(1993,plain,
% 0.55/0.78 ((~b(z, elem!1)) | (~b(s(s(s(s(s(s(elem!1)))))), z))),
% 0.55/0.78 inference(unit_resolution,[status(thm)],[1659, 117, 1788])).
% 0.55/0.78 tff(1994,plain,
% 0.55/0.78 (~b(s(s(s(s(s(s(elem!1)))))), z)),
% 0.55/0.78 inference(unit_resolution,[status(thm)],[1993, 1992])).
% 0.55/0.78 tff(1995,plain,
% 0.55/0.78 (r(s(s(s(s(s(s(elem!1)))))), z)),
% 0.55/0.78 inference(unit_resolution,[status(thm)],[1666, 46, 1663, 1994])).
% 0.55/0.78 tff(1996,assumption,(b(s(s(s(elem!1))), elem!1)), introduced(assumption)).
% 0.55/0.78 tff(1997,plain,
% 0.55/0.78 (((~![X0: $i, X2: $i, X1: $i] : ((~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(s(s(s(s(s(s(elem!1)))))), s(s(s(elem!1))))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~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(s(s(s(s(s(s(elem!1)))))), s(s(s(elem!1))))))),
% 0.55/0.78 inference(rewrite,[status(thm)],[])).
% 0.55/0.78 tff(1998,plain,
% 0.55/0.78 ((~![X0: $i, X2: $i, X1: $i] : ((~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(s(s(s(s(s(s(elem!1)))))), s(s(s(elem!1))))))),
% 0.55/0.78 inference(quant_inst,[status(thm)],[])).
% 0.55/0.78 tff(1999,plain,
% 0.55/0.78 ((~![X0: $i, X2: $i, X1: $i] : ((~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(s(s(s(s(s(s(elem!1)))))), s(s(s(elem!1)))))),
% 0.55/0.78 inference(modus_ponens,[status(thm)],[1998, 1997])).
% 0.55/0.78 tff(2000,plain,
% 0.55/0.78 (~b(s(s(s(s(s(s(elem!1)))))), s(s(s(elem!1))))),
% 0.55/0.78 inference(unit_resolution,[status(thm)],[1999, 117, 1996, 1788])).
% 0.55/0.78 tff(2001,plain,
% 0.55/0.78 ((s(s(s(s(s(s(elem!1)))))) = s(s(s(elem!1)))) | r(s(s(s(s(s(s(elem!1)))))), s(s(s(elem!1))))),
% 0.55/0.78 inference(unit_resolution,[status(thm)],[1563, 46, 2000])).
% 0.55/0.78 tff(2002,plain,
% 0.55/0.78 (r(s(s(s(s(s(s(elem!1)))))), s(s(s(elem!1))))),
% 0.55/0.78 inference(unit_resolution,[status(thm)],[2001, 1554])).
% 0.55/0.78 tff(2003,plain,
% 0.55/0.78 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), z)) | (~r(s(s(s(s(s(s(elem!1)))))), z)) | (~r(s(s(s(s(s(s(elem!1)))))), s(s(s(elem!1))))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(elem!1))), z)) | (~r(s(s(s(s(s(s(elem!1)))))), z)) | (~r(s(s(s(s(s(s(elem!1)))))), s(s(s(elem!1))))))),
% 0.55/0.78 inference(rewrite,[status(thm)],[])).
% 0.55/0.78 tff(2004,plain,
% 0.55/0.78 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), z)) | (~r(s(s(s(s(s(s(elem!1)))))), z)) | (~r(s(s(s(s(s(s(elem!1)))))), s(s(s(elem!1))))))),
% 0.55/0.78 inference(quant_inst,[status(thm)],[])).
% 0.55/0.78 tff(2005,plain,
% 0.55/0.78 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(elem!1))), z)) | (~r(s(s(s(s(s(s(elem!1)))))), z)) | (~r(s(s(s(s(s(s(elem!1)))))), s(s(s(elem!1)))))),
% 0.55/0.78 inference(modus_ponens,[status(thm)],[2004, 2003])).
% 0.55/0.78 tff(2006,plain,
% 0.55/0.78 ($false),
% 0.55/0.78 inference(unit_resolution,[status(thm)],[2005, 14, 196, 2002, 1995])).
% 0.55/0.78 tff(2007,plain,((~b(s(s(s(s(s(s(elem!1)))))), elem!1)) | (~r(s(s(s(elem!1))), z)) | (~(s(s(s(z))) = s(s(elem!1)))) | (~b(z, s(z))) | (~b(s(s(s(elem!1))), elem!1))), inference(lemma,lemma(discharge,[]))).
% 0.55/0.78 tff(2008,plain,
% 0.55/0.78 (~b(s(s(s(elem!1))), elem!1)),
% 0.55/0.78 inference(unit_resolution,[status(thm)],[2007, 1987, 574, 1978, 196])).
% 0.55/0.78 tff(2009,plain,
% 0.55/0.78 (~b(s(s(s(elem!1))), s(z))),
% 0.55/0.78 inference(modus_ponens,[status(thm)],[2008, 1985])).
% 0.55/0.78 tff(2010,assumption,(b(s(s(s(elem!1))), s(z))), introduced(assumption)).
% 0.55/0.78 tff(2011,plain,
% 0.55/0.78 ($false),
% 0.55/0.78 inference(unit_resolution,[status(thm)],[2010, 2009])).
% 0.55/0.78 tff(2012,plain,(r(s(s(s(s(s(s(elem!1)))))), elem!1) | (~b(s(s(s(elem!1))), s(z))) | (~b(z, s(z))) | (~r(s(s(s(elem!1))), z)) | r(s(s(s(z))), s(s(elem!1))) | (~b(s(s(elem!1)), s(s(s(elem!1))))) | r(s(s(s(z))), s(s(s(elem!1)))) | (s(s(s(s(s(s(elem!1)))))) = s(s(s(s(elem!1))))) | (~b(s(s(s(s(elem!1)))), z)) | (~b(s(z), z))), inference(lemma,lemma(discharge,[]))).
% 0.55/0.78 tff(2013,plain,
% 0.55/0.78 (r(s(s(s(s(s(s(elem!1)))))), elem!1)),
% 0.55/0.78 inference(unit_resolution,[status(thm)],[2012, 1918, 1902, 1899, 1418, 254, 1900, 1897, 1894, 194])).
% 0.55/0.78 tff(2014,plain,
% 0.55/0.78 ((s(s(s(z))) = s(s(s(s(s(s(elem!1))))))) <=> (s(s(s(s(s(s(elem!1)))))) = s(s(s(z))))),
% 0.55/0.78 inference(commutativity,[status(thm)],[])).
% 0.55/0.78 tff(2015,plain,
% 0.55/0.78 ((s(s(elem!1)) = s(s(s(s(s(s(elem!1))))))) <=> (s(s(s(z))) = s(s(s(s(s(s(elem!1)))))))),
% 0.55/0.78 inference(monotonicity,[status(thm)],[1566])).
% 0.55/0.78 tff(2016,plain,
% 0.55/0.78 ((s(s(elem!1)) = s(s(s(s(s(s(elem!1))))))) <=> (s(s(s(s(s(s(elem!1)))))) = s(s(s(z))))),
% 0.55/0.78 inference(transitivity,[status(thm)],[2015, 2014])).
% 0.55/0.78 tff(2017,plain,
% 0.55/0.78 ((s(s(s(s(s(s(elem!1)))))) = s(s(s(z)))) <=> (s(s(elem!1)) = s(s(s(s(s(s(elem!1)))))))),
% 0.55/0.78 inference(symmetry,[status(thm)],[2016])).
% 0.55/0.78 tff(2018,plain,
% 0.55/0.78 ((~(s(s(s(s(s(s(elem!1)))))) = s(s(s(z))))) <=> (~(s(s(elem!1)) = s(s(s(s(s(s(elem!1))))))))),
% 0.55/0.78 inference(monotonicity,[status(thm)],[2017])).
% 0.55/0.78 tff(2019,plain,
% 0.55/0.78 (~(s(s(elem!1)) = s(s(s(s(s(s(elem!1)))))))),
% 0.55/0.78 inference(modus_ponens,[status(thm)],[1577, 2018])).
% 0.55/0.78 tff(2020,plain,
% 0.55/0.78 (s(z) = elem!1),
% 0.55/0.78 inference(transitivity,[status(thm)],[131, 1437, 257])).
% 0.55/0.78 tff(2021,plain,
% 0.55/0.78 (r(s(s(s(s(elem!1)))), s(z)) <=> r(s(s(s(s(elem!1)))), elem!1)),
% 0.55/0.78 inference(monotonicity,[status(thm)],[2020])).
% 0.55/0.78 tff(2022,plain,
% 0.55/0.78 (r(s(s(s(s(elem!1)))), elem!1)),
% 0.55/0.78 inference(modus_ponens,[status(thm)],[1336, 2021])).
% 0.55/0.78 tff(2023,plain,
% 0.55/0.78 (~r(s(s(s(s(s(s(elem!1)))))), s(s(s(s(elem!1)))))),
% 0.55/0.78 inference(unit_resolution,[status(thm)],[1822, 14, 2022, 1555])).
% 0.55/0.78 tff(2024,plain,
% 0.55/0.78 (~(s(s(s(s(s(s(elem!1)))))) = s(s(s(s(elem!1)))))),
% 0.55/0.78 inference(unit_resolution,[status(thm)],[1615, 146])).
% 0.55/0.78 tff(2025,plain,
% 0.55/0.78 (b(s(s(s(s(s(s(elem!1)))))), s(s(s(s(elem!1)))))),
% 0.55/0.78 inference(unit_resolution,[status(thm)],[1619, 46, 2024, 2023])).
% 0.55/0.78 tff(2026,plain,
% 0.55/0.78 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(elem!1)), s(z))) | (~r(s(s(elem!1)), s(s(s(s(elem!1)))))) | (~r(s(s(s(s(elem!1)))), s(z))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(elem!1)), s(z))) | (~r(s(s(elem!1)), s(s(s(s(elem!1)))))) | (~r(s(s(s(s(elem!1)))), s(z))))),
% 0.55/0.78 inference(rewrite,[status(thm)],[])).
% 0.55/0.78 tff(2027,plain,
% 0.55/0.78 (((~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(s(elem!1)), s(z))) | (~r(s(s(elem!1)), s(s(s(s(elem!1)))))) | (~r(s(s(s(s(elem!1)))), s(z))))),
% 0.55/0.78 inference(rewrite,[status(thm)],[])).
% 0.55/0.78 tff(2028,plain,
% 0.55/0.78 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(elem!1)))), s(z))) | (~r(s(s(elem!1)), s(z))) | (~r(s(s(elem!1)), s(s(s(s(elem!1)))))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(elem!1)), s(z))) | (~r(s(s(elem!1)), s(s(s(s(elem!1)))))) | (~r(s(s(s(s(elem!1)))), s(z)))))),
% 0.55/0.78 inference(monotonicity,[status(thm)],[2027])).
% 0.55/0.78 tff(2029,plain,
% 0.55/0.78 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(elem!1)))), s(z))) | (~r(s(s(elem!1)), s(z))) | (~r(s(s(elem!1)), s(s(s(s(elem!1)))))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(elem!1)), s(z))) | (~r(s(s(elem!1)), s(s(s(s(elem!1)))))) | (~r(s(s(s(s(elem!1)))), s(z))))),
% 0.55/0.78 inference(transitivity,[status(thm)],[2028, 2026])).
% 0.55/0.78 tff(2030,plain,
% 0.55/0.78 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(elem!1)))), s(z))) | (~r(s(s(elem!1)), s(z))) | (~r(s(s(elem!1)), s(s(s(s(elem!1)))))))),
% 0.55/0.78 inference(quant_inst,[status(thm)],[])).
% 0.55/0.78 tff(2031,plain,
% 0.55/0.78 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(elem!1)), s(z))) | (~r(s(s(elem!1)), s(s(s(s(elem!1)))))) | (~r(s(s(s(s(elem!1)))), s(z)))),
% 0.55/0.78 inference(modus_ponens,[status(thm)],[2030, 2029])).
% 0.55/0.78 tff(2032,plain,
% 0.55/0.78 (~r(s(s(elem!1)), s(s(s(s(elem!1)))))),
% 0.55/0.78 inference(unit_resolution,[status(thm)],[2031, 14, 181, 1336])).
% 0.55/0.78 tff(2033,plain,
% 0.55/0.78 ((s(s(elem!1)) = s(s(s(s(elem!1))))) <=> (s(s(s(s(elem!1)))) = s(s(elem!1)))),
% 0.55/0.78 inference(commutativity,[status(thm)],[])).
% 0.55/0.78 tff(2034,plain,
% 0.55/0.78 ((s(s(s(s(elem!1)))) = s(s(elem!1))) <=> (s(s(elem!1)) = s(s(s(s(elem!1)))))),
% 0.55/0.78 inference(symmetry,[status(thm)],[2033])).
% 0.55/0.78 tff(2035,plain,
% 0.55/0.78 ((~(s(s(s(s(elem!1)))) = s(s(elem!1)))) <=> (~(s(s(elem!1)) = s(s(s(s(elem!1))))))),
% 0.55/0.78 inference(monotonicity,[status(thm)],[2034])).
% 0.55/0.78 tff(2036,plain,
% 0.55/0.78 (~(s(s(elem!1)) = s(s(s(s(elem!1)))))),
% 0.55/0.78 inference(modus_ponens,[status(thm)],[146, 2035])).
% 0.55/0.78 tff(2037,plain,
% 0.55/0.78 (((~![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))))))),
% 0.55/0.78 inference(rewrite,[status(thm)],[])).
% 0.55/0.78 tff(2038,plain,
% 0.55/0.78 ((~![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))))))),
% 0.55/0.78 inference(quant_inst,[status(thm)],[])).
% 0.55/0.78 tff(2039,plain,
% 0.55/0.78 ((~![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)))))),
% 0.55/0.78 inference(modus_ponens,[status(thm)],[2038, 2037])).
% 0.55/0.78 tff(2040,plain,
% 0.55/0.78 ((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)))))),
% 0.55/0.78 inference(unit_resolution,[status(thm)],[2039, 46])).
% 0.55/0.78 tff(2041,plain,
% 0.55/0.78 (b(s(s(elem!1)), s(s(s(s(elem!1)))))),
% 0.55/0.78 inference(unit_resolution,[status(thm)],[2040, 2036, 2032])).
% 0.55/0.78 tff(2042,plain,
% 0.55/0.78 (((~![X0: $i, X2: $i, X1: $i] : ((~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(s(s(elem!1)))))), s(s(s(s(elem!1)))))) | (~b(s(s(elem!1)), s(s(s(s(s(s(elem!1)))))))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(elem!1)), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(s(s(elem!1)))))), s(s(s(s(elem!1)))))) | (~b(s(s(elem!1)), s(s(s(s(s(s(elem!1)))))))))),
% 0.55/0.78 inference(rewrite,[status(thm)],[])).
% 0.55/0.78 tff(2043,plain,
% 0.55/0.78 (((~b(s(s(s(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(s(s(s(elem!1))))))))) <=> ((~b(s(s(elem!1)), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(s(s(elem!1)))))), s(s(s(s(elem!1)))))) | (~b(s(s(elem!1)), s(s(s(s(s(s(elem!1)))))))))),
% 0.55/0.78 inference(rewrite,[status(thm)],[])).
% 0.55/0.78 tff(2044,plain,
% 0.55/0.78 (((~![X0: $i, X2: $i, X1: $i] : ((~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(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(s(s(s(elem!1)))))))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(s(s(elem!1)))))), s(s(s(s(elem!1)))))) | (~b(s(s(elem!1)), s(s(s(s(s(s(elem!1))))))))))),
% 0.55/0.79 inference(monotonicity,[status(thm)],[2043])).
% 0.55/0.79 tff(2045,plain,
% 0.55/0.79 (((~![X0: $i, X2: $i, X1: $i] : ((~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(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(s(s(s(elem!1)))))))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(elem!1)), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(s(s(elem!1)))))), s(s(s(s(elem!1)))))) | (~b(s(s(elem!1)), s(s(s(s(s(s(elem!1)))))))))),
% 0.55/0.79 inference(transitivity,[status(thm)],[2044, 2042])).
% 0.55/0.79 tff(2046,plain,
% 0.55/0.79 ((~![X0: $i, X2: $i, X1: $i] : ((~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(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(s(s(s(elem!1)))))))))),
% 0.55/0.79 inference(quant_inst,[status(thm)],[])).
% 0.55/0.79 tff(2047,plain,
% 0.55/0.79 ((~![X0: $i, X2: $i, X1: $i] : ((~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(elem!1)), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(s(s(elem!1)))))), s(s(s(s(elem!1)))))) | (~b(s(s(elem!1)), s(s(s(s(s(s(elem!1))))))))),
% 0.55/0.79 inference(modus_ponens,[status(thm)],[2046, 2045])).
% 0.55/0.79 tff(2048,plain,
% 0.55/0.79 (~b(s(s(elem!1)), s(s(s(s(s(s(elem!1)))))))),
% 0.55/0.79 inference(unit_resolution,[status(thm)],[2047, 117, 2041, 2025])).
% 0.55/0.79 tff(2049,plain,
% 0.55/0.79 (r(s(s(elem!1)), s(z)) <=> r(s(s(elem!1)), elem!1)),
% 0.55/0.79 inference(monotonicity,[status(thm)],[2020])).
% 0.55/0.79 tff(2050,plain,
% 0.55/0.79 (r(s(s(elem!1)), elem!1)),
% 0.55/0.79 inference(modus_ponens,[status(thm)],[181, 2049])).
% 0.55/0.79 tff(2051,plain,
% 0.55/0.79 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(elem!1)), elem!1)) | (~r(s(s(s(s(s(s(elem!1)))))), elem!1)) | (~r(s(s(elem!1)), s(s(s(s(s(s(elem!1)))))))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(elem!1)), elem!1)) | (~r(s(s(s(s(s(s(elem!1)))))), elem!1)) | (~r(s(s(elem!1)), s(s(s(s(s(s(elem!1)))))))))),
% 0.55/0.79 inference(rewrite,[status(thm)],[])).
% 0.55/0.79 tff(2052,plain,
% 0.55/0.79 (((~r(s(s(s(s(s(s(elem!1)))))), elem!1)) | (~r(s(s(elem!1)), elem!1)) | (~r(s(s(elem!1)), s(s(s(s(s(s(elem!1))))))))) <=> ((~r(s(s(elem!1)), elem!1)) | (~r(s(s(s(s(s(s(elem!1)))))), elem!1)) | (~r(s(s(elem!1)), s(s(s(s(s(s(elem!1)))))))))),
% 0.55/0.79 inference(rewrite,[status(thm)],[])).
% 0.55/0.79 tff(2053,plain,
% 0.55/0.79 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(s(s(elem!1)))))), elem!1)) | (~r(s(s(elem!1)), elem!1)) | (~r(s(s(elem!1)), s(s(s(s(s(s(elem!1)))))))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(elem!1)), elem!1)) | (~r(s(s(s(s(s(s(elem!1)))))), elem!1)) | (~r(s(s(elem!1)), s(s(s(s(s(s(elem!1))))))))))),
% 0.55/0.79 inference(monotonicity,[status(thm)],[2052])).
% 0.55/0.79 tff(2054,plain,
% 0.55/0.79 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(s(s(elem!1)))))), elem!1)) | (~r(s(s(elem!1)), elem!1)) | (~r(s(s(elem!1)), s(s(s(s(s(s(elem!1)))))))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(elem!1)), elem!1)) | (~r(s(s(s(s(s(s(elem!1)))))), elem!1)) | (~r(s(s(elem!1)), s(s(s(s(s(s(elem!1)))))))))),
% 0.55/0.79 inference(transitivity,[status(thm)],[2053, 2051])).
% 0.55/0.79 tff(2055,plain,
% 0.55/0.79 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(s(s(elem!1)))))), elem!1)) | (~r(s(s(elem!1)), elem!1)) | (~r(s(s(elem!1)), s(s(s(s(s(s(elem!1)))))))))),
% 0.55/0.79 inference(quant_inst,[status(thm)],[])).
% 0.55/0.79 tff(2056,plain,
% 0.55/0.79 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(elem!1)), elem!1)) | (~r(s(s(s(s(s(s(elem!1)))))), elem!1)) | (~r(s(s(elem!1)), s(s(s(s(s(s(elem!1))))))))),
% 0.55/0.79 inference(modus_ponens,[status(thm)],[2055, 2054])).
% 0.55/0.79 tff(2057,plain,
% 0.55/0.79 (~r(s(s(elem!1)), s(s(s(s(s(s(elem!1)))))))),
% 0.55/0.79 inference(unit_resolution,[status(thm)],[2056, 14, 2050, 1555])).
% 0.55/0.79 tff(2058,plain,
% 0.55/0.79 (((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((s(s(elem!1)) = s(s(s(s(s(s(elem!1))))))) | b(s(s(elem!1)), s(s(s(s(s(s(elem!1))))))) | r(s(s(elem!1)), s(s(s(s(s(s(elem!1))))))))) <=> ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (s(s(elem!1)) = s(s(s(s(s(s(elem!1))))))) | b(s(s(elem!1)), s(s(s(s(s(s(elem!1))))))) | r(s(s(elem!1)), s(s(s(s(s(s(elem!1))))))))),
% 0.55/0.79 inference(rewrite,[status(thm)],[])).
% 0.55/0.79 tff(2059,plain,
% 0.55/0.79 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((s(s(elem!1)) = s(s(s(s(s(s(elem!1))))))) | b(s(s(elem!1)), s(s(s(s(s(s(elem!1))))))) | r(s(s(elem!1)), s(s(s(s(s(s(elem!1))))))))),
% 0.55/0.79 inference(quant_inst,[status(thm)],[])).
% 0.55/0.79 tff(2060,plain,
% 0.55/0.79 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (s(s(elem!1)) = s(s(s(s(s(s(elem!1))))))) | b(s(s(elem!1)), s(s(s(s(s(s(elem!1))))))) | r(s(s(elem!1)), s(s(s(s(s(s(elem!1)))))))),
% 0.55/0.79 inference(modus_ponens,[status(thm)],[2059, 2058])).
% 0.55/0.79 tff(2061,plain,
% 0.55/0.79 ((s(s(elem!1)) = s(s(s(s(s(s(elem!1))))))) | b(s(s(elem!1)), s(s(s(s(s(s(elem!1)))))))),
% 0.55/0.79 inference(unit_resolution,[status(thm)],[2060, 46, 2057])).
% 0.55/0.79 tff(2062,plain,
% 0.55/0.79 ($false),
% 0.55/0.79 inference(unit_resolution,[status(thm)],[2061, 2048, 2019])).
% 0.55/0.79 tff(2063,plain,((~(s(s(s(z))) = s(s(elem!1)))) | (s(s(s(s(elem!1)))) = s(s(elem!1))) | (~r(s(s(s(s(s(s(elem!1)))))), elem!1)) | (~r(s(s(s(s(elem!1)))), s(z))) | (~r(s(s(elem!1)), s(z)))), inference(lemma,lemma(discharge,[]))).
% 0.55/0.79 tff(2064,plain,
% 0.55/0.79 (~(s(s(s(z))) = s(s(elem!1)))),
% 0.55/0.79 inference(unit_resolution,[status(thm)],[2063, 1395, 2013, 1896, 181])).
% 0.55/0.79 tff(2065,plain,
% 0.55/0.79 ((s(s(s(z))) = s(s(elem!1))) | b(s(s(s(z))), s(s(elem!1)))),
% 0.55/0.79 inference(unit_resolution,[status(thm)],[1421, 46, 1418])).
% 0.55/0.79 tff(2066,plain,
% 0.55/0.79 (b(s(s(s(z))), s(s(elem!1)))),
% 0.55/0.79 inference(unit_resolution,[status(thm)],[2065, 2064])).
% 0.55/0.79 tff(2067,plain,
% 0.55/0.79 (~b(s(s(s(z))), s(s(s(s(elem!1)))))),
% 0.55/0.79 inference(unit_resolution,[status(thm)],[1428, 117, 1892, 2066])).
% 0.55/0.79 tff(2068,plain,
% 0.55/0.79 (r(s(s(s(z))), s(s(s(s(elem!1)))))),
% 0.55/0.79 inference(unit_resolution,[status(thm)],[1413, 46, 279, 2067])).
% 0.55/0.79 tff(2069,plain,
% 0.55/0.79 (~b(s(z), s(s(s(s(elem!1)))))),
% 0.55/0.79 inference(unit_resolution,[status(thm)],[1928, 117, 194, 1894])).
% 0.55/0.79 tff(2070,plain,
% 0.55/0.79 (r(s(z), s(s(s(s(elem!1)))))),
% 0.55/0.79 inference(unit_resolution,[status(thm)],[1938, 2069])).
% 0.55/0.79 tff(2071,plain,
% 0.55/0.79 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(s(s(s(elem!1)))))) | (~r(s(s(s(z))), s(s(s(s(elem!1)))))) | (~r(s(s(s(z))), s(z))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(z), s(s(s(s(elem!1)))))) | (~r(s(s(s(z))), s(s(s(s(elem!1)))))) | (~r(s(s(s(z))), s(z))))),
% 0.55/0.79 inference(rewrite,[status(thm)],[])).
% 0.55/0.79 tff(2072,plain,
% 0.55/0.79 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(s(s(s(elem!1)))))) | (~r(s(s(s(z))), s(s(s(s(elem!1)))))) | (~r(s(s(s(z))), s(z))))),
% 0.55/0.79 inference(quant_inst,[status(thm)],[])).
% 0.55/0.79 tff(2073,plain,
% 0.55/0.79 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(z), s(s(s(s(elem!1)))))) | (~r(s(s(s(z))), s(s(s(s(elem!1)))))) | (~r(s(s(s(z))), s(z)))),
% 0.55/0.79 inference(modus_ponens,[status(thm)],[2072, 2071])).
% 0.55/0.79 tff(2074,plain,
% 0.55/0.79 (~r(s(s(s(z))), s(z))),
% 0.55/0.79 inference(unit_resolution,[status(thm)],[2073, 14, 2070, 2068])).
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% 0.55/0.79 (b(s(s(s(z))), s(z))),
% 0.55/0.79 inference(unit_resolution,[status(thm)],[347, 2074])).
% 0.55/0.79 tff(2076,plain,
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% 0.55/0.79 inference(quant_inst,[status(thm)],[])).
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% 0.55/0.79 inference(modus_ponens,[status(thm)],[2077, 2076])).
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% 0.55/0.79 inference(unit_resolution,[status(thm)],[2078, 117, 1918, 2075])).
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% 0.55/0.79 inference(unit_resolution,[status(thm)],[1717, 46, 1900])).
% 0.55/0.79 tff(2081,plain,
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% 0.55/0.79 inference(unit_resolution,[status(thm)],[2080, 2079])).
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% 0.55/0.79 inference(monotonicity,[status(thm)],[2081])).
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% 0.55/0.79 inference(modus_ponens,[status(thm)],[2066, 2082])).
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% 0.55/0.79 inference(monotonicity,[status(thm)],[2081])).
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% 0.55/0.79 inference(monotonicity,[status(thm)],[2085])).
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% 0.55/0.79 inference(monotonicity,[status(thm)],[2089])).
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% 0.55/0.79 tff(2092,plain,
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% 0.55/0.79 inference(monotonicity,[status(thm)],[2089])).
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% 0.55/0.79 inference(symmetry,[status(thm)],[1741])).
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% 0.55/0.79 inference(monotonicity,[status(thm)],[2094])).
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% 0.55/0.79 inference(symmetry,[status(thm)],[2095])).
% 0.55/0.79 tff(2097,plain,
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% 0.55/0.79 inference(monotonicity,[status(thm)],[2096])).
% 0.55/0.79 tff(2098,plain,
% 0.55/0.79 (~(s(s(s(s(s(s(elem!1)))))) = s(s(s(elem!1))))),
% 0.55/0.79 inference(modus_ponens,[status(thm)],[1577, 2097])).
% 0.55/0.79 tff(2099,plain,
% 0.55/0.79 (b(s(s(s(s(s(s(elem!1)))))), s(s(s(elem!1))))),
% 0.55/0.79 inference(unit_resolution,[status(thm)],[1564, 2098])).
% 0.55/0.79 tff(2100,plain,
% 0.55/0.79 (b(s(s(s(s(s(s(elem!1)))))), s(s(elem!1)))),
% 0.55/0.79 inference(unit_resolution,[status(thm)],[1587, 1787])).
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% 0.55/0.79 inference(unit_resolution,[status(thm)],[1592, 117, 1589, 2100, 2099])).
% 0.55/0.79 tff(2102,plain,((~r(s(s(s(s(s(s(elem!1)))))), elem!1)) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~(s(s(s(z))) = s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), elem!1)) | (~r(s(s(elem!1)), elem!1))), inference(lemma,lemma(discharge,[]))).
% 0.55/0.79 tff(2103,plain,
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% 0.55/0.79 tff(2104,plain,((~r(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(z))), z))), inference(lemma,lemma(discharge,[]))).
% 0.55/0.79 tff(2105,plain,
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% 0.55/0.79 inference(unit_resolution,[status(thm)],[1314, 117, 237, 1310])).
% 0.55/0.79 tff(2108,plain,
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% 0.55/0.79 inference(unit_resolution,[status(thm)],[1327, 2107])).
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% 0.55/0.79 inference(rewrite,[status(thm)],[])).
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% 0.55/0.79 inference(quant_inst,[status(thm)],[])).
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% 0.55/0.79 tff(2118,plain,
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% 0.55/0.79 tff(2123,plain,
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% 0.55/0.79 inference(unit_resolution,[status(thm)],[2122, 2119, 180])).
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% 0.55/0.79 inference(monotonicity,[status(thm)],[2134])).
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% 0.55/0.79 tff(2162,plain,
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% 0.55/0.79 inference(unit_resolution,[status(thm)],[2161, 2157, 2136])).
% 0.55/0.79 tff(2163,plain,((~b(s(z), z)) | (~b(s(s(elem!1)), z)) | (~r(s(s(s(z))), z)) | (s(s(elem!1)) = s(s(s(elem!1))))), inference(lemma,lemma(discharge,[]))).
% 0.55/0.79 tff(2164,plain,
% 0.55/0.79 (~b(s(z), z)),
% 0.55/0.79 inference(unit_resolution,[status(thm)],[2163, 2106, 180, 145])).
% 0.55/0.79 tff(2165,plain,
% 0.55/0.79 (r(s(z), z)),
% 0.55/0.79 inference(unit_resolution,[status(thm)],[193, 2164])).
% 0.55/0.79 tff(2166,plain,
% 0.55/0.79 ((s(s(s(z))) = s(s(s(elem!1)))) <=> (s(s(s(elem!1))) = s(s(s(z))))),
% 0.55/0.79 inference(commutativity,[status(thm)],[])).
% 0.55/0.79 tff(2167,assumption,(~r(s(s(elem!1)), z)), introduced(assumption)).
% 0.55/0.79 tff(2168,plain,
% 0.55/0.79 (b(s(s(elem!1)), z)),
% 0.55/0.79 inference(unit_resolution,[status(thm)],[1025, 2167])).
% 0.55/0.79 tff(2169,plain,
% 0.55/0.79 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), z)) | (~r(s(s(s(z))), z)) | (~r(s(s(s(z))), s(z))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(z), z)) | (~r(s(s(s(z))), z)) | (~r(s(s(s(z))), s(z))))),
% 0.55/0.79 inference(rewrite,[status(thm)],[])).
% 0.55/0.79 tff(2170,plain,
% 0.55/0.79 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), z)) | (~r(s(s(s(z))), z)) | (~r(s(s(s(z))), s(z))))),
% 0.55/0.79 inference(quant_inst,[status(thm)],[])).
% 0.55/0.79 tff(2171,plain,
% 0.55/0.79 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(z), z)) | (~r(s(s(s(z))), z)) | (~r(s(s(s(z))), s(z)))),
% 0.55/0.79 inference(modus_ponens,[status(thm)],[2170, 2169])).
% 0.55/0.79 tff(2172,plain,
% 0.55/0.79 ($false),
% 0.55/0.79 inference(unit_resolution,[status(thm)],[2171, 14, 183, 180, 283])).
% 0.55/0.79 tff(2173,plain,((~r(s(s(s(z))), z)) | (~r(s(z), z)) | (~r(s(s(s(z))), s(z)))), inference(lemma,lemma(discharge,[]))).
% 0.55/0.79 tff(2174,plain,
% 0.55/0.79 (~r(s(s(s(z))), s(z))),
% 0.55/0.79 inference(unit_resolution,[status(thm)],[2173, 183, 180])).
% 0.55/0.79 tff(2175,plain,
% 0.55/0.79 (b(s(s(s(z))), s(z))),
% 0.55/0.79 inference(unit_resolution,[status(thm)],[347, 2174])).
% 0.55/0.79 tff(2176,plain,
% 0.55/0.79 (b(s(s(s(z))), s(s(s(s(elem!1)))))),
% 0.55/0.79 inference(unit_resolution,[status(thm)],[2122, 1396, 180])).
% 0.55/0.79 tff(2177,assumption,(b(s(s(s(z))), s(s(s(s(elem!1)))))), introduced(assumption)).
% 0.55/0.79 tff(2178,plain,
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% 0.55/0.79 inference(rewrite,[status(thm)],[])).
% 0.55/0.79 tff(2179,plain,
% 0.55/0.79 (((~b(s(s(s(s(elem!1)))), s(z))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(z))), s(s(s(s(elem!1))))))) <=> ((~b(s(s(s(z))), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), s(z))) | (~b(s(s(s(z))), s(z))))),
% 0.55/0.79 inference(rewrite,[status(thm)],[])).
% 0.55/0.79 tff(2180,plain,
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% 0.55/0.79 inference(monotonicity,[status(thm)],[2179])).
% 0.55/0.79 tff(2181,plain,
% 0.55/0.79 (((~![X0: $i, X2: $i, X1: $i] : ((~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(elem!1)))), s(z))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(z))), s(s(s(s(elem!1)))))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(z))), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), s(z))) | (~b(s(s(s(z))), s(z))))),
% 0.55/0.79 inference(transitivity,[status(thm)],[2180, 2178])).
% 0.55/0.79 tff(2182,plain,
% 0.55/0.79 ((~![X0: $i, X2: $i, X1: $i] : ((~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(elem!1)))), s(z))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(z))), s(s(s(s(elem!1)))))))),
% 0.55/0.79 inference(quant_inst,[status(thm)],[])).
% 0.55/0.79 tff(2183,plain,
% 0.55/0.79 ((~![X0: $i, X2: $i, X1: $i] : ((~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(z))), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), s(z))) | (~b(s(s(s(z))), s(z)))),
% 0.55/0.79 inference(modus_ponens,[status(thm)],[2182, 2181])).
% 0.55/0.79 tff(2184,plain,
% 0.55/0.79 ($false),
% 0.55/0.79 inference(unit_resolution,[status(thm)],[2183, 117, 1311, 848, 2177])).
% 0.55/0.79 tff(2185,plain,((~b(s(s(s(z))), s(z))) | (~b(s(s(s(s(elem!1)))), s(z))) | (~b(s(s(s(z))), s(s(s(s(elem!1))))))), inference(lemma,lemma(discharge,[]))).
% 0.55/0.79 tff(2186,plain,
% 0.55/0.79 (~b(s(s(s(s(elem!1)))), s(z))),
% 0.55/0.79 inference(unit_resolution,[status(thm)],[2185, 2176, 2175])).
% 0.55/0.79 tff(2187,plain,
% 0.55/0.79 (r(s(s(s(s(elem!1)))), s(z))),
% 0.55/0.79 inference(unit_resolution,[status(thm)],[1327, 2186])).
% 0.55/0.79 tff(2188,plain,
% 0.55/0.79 (~r(s(s(s(s(elem!1)))), s(s(elem!1)))),
% 0.55/0.79 inference(unit_resolution,[status(thm)],[1863, 1336, 181])).
% 0.55/0.79 tff(2189,plain,
% 0.55/0.79 (b(s(s(s(s(elem!1)))), s(s(elem!1)))),
% 0.55/0.79 inference(unit_resolution,[status(thm)],[1690, 2188, 146])).
% 0.55/0.79 tff(2190,plain,
% 0.55/0.79 ($false),
% 0.55/0.79 inference(unit_resolution,[status(thm)],[2111, 117, 1036, 1416, 1310])).
% 0.55/0.79 tff(2191,plain,((~b(s(s(s(s(elem!1)))), z)) | (~b(s(s(elem!1)), z)) | (~b(s(s(s(s(elem!1)))), s(s(elem!1))))), inference(lemma,lemma(discharge,[]))).
% 0.55/0.79 tff(2192,plain,
% 0.55/0.80 (~b(s(s(s(s(elem!1)))), z)),
% 0.55/0.80 inference(unit_resolution,[status(thm)],[2191, 2189, 1036])).
% 0.55/0.80 tff(2193,plain,
% 0.55/0.80 (r(s(s(s(s(elem!1)))), z)),
% 0.55/0.80 inference(unit_resolution,[status(thm)],[1853, 46, 1625, 2192])).
% 0.55/0.80 tff(2194,plain,
% 0.55/0.80 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), z)) | (~r(s(s(s(s(elem!1)))), z)) | (~r(s(s(s(s(elem!1)))), s(z))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(z), z)) | (~r(s(s(s(s(elem!1)))), z)) | (~r(s(s(s(s(elem!1)))), s(z))))),
% 0.55/0.80 inference(rewrite,[status(thm)],[])).
% 0.55/0.80 tff(2195,plain,
% 0.55/0.80 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), z)) | (~r(s(s(s(s(elem!1)))), z)) | (~r(s(s(s(s(elem!1)))), s(z))))),
% 0.55/0.80 inference(quant_inst,[status(thm)],[])).
% 0.55/0.80 tff(2196,plain,
% 0.55/0.80 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(z), z)) | (~r(s(s(s(s(elem!1)))), z)) | (~r(s(s(s(s(elem!1)))), s(z)))),
% 0.55/0.80 inference(modus_ponens,[status(thm)],[2195, 2194])).
% 0.55/0.80 tff(2197,plain,
% 0.55/0.80 ($false),
% 0.55/0.80 inference(unit_resolution,[status(thm)],[2196, 14, 183, 1336, 2193])).
% 0.55/0.80 tff(2198,plain,((~r(s(s(s(s(elem!1)))), s(z))) | (~r(s(z), z)) | (~b(s(s(elem!1)), z)) | (s(s(s(s(elem!1)))) = s(s(elem!1))) | (~r(s(s(elem!1)), s(z)))), inference(lemma,lemma(discharge,[]))).
% 0.55/0.80 tff(2199,plain,
% 0.55/0.80 (s(s(s(s(elem!1)))) = s(s(elem!1))),
% 0.55/0.80 inference(unit_resolution,[status(thm)],[2198, 2187, 2168, 181, 183])).
% 0.55/0.80 tff(2200,plain,
% 0.55/0.80 (r(s(s(s(s(elem!1)))), z) <=> r(s(s(elem!1)), z)),
% 0.55/0.80 inference(monotonicity,[status(thm)],[2199])).
% 0.55/0.80 tff(2201,plain,
% 0.55/0.80 (r(s(s(elem!1)), z) <=> r(s(s(s(s(elem!1)))), z)),
% 0.55/0.80 inference(symmetry,[status(thm)],[2200])).
% 0.55/0.80 tff(2202,plain,
% 0.55/0.80 ((~r(s(s(elem!1)), z)) <=> (~r(s(s(s(s(elem!1)))), z))),
% 0.55/0.80 inference(monotonicity,[status(thm)],[2201])).
% 0.55/0.80 tff(2203,plain,
% 0.55/0.80 (~r(s(s(s(s(elem!1)))), z)),
% 0.55/0.80 inference(modus_ponens,[status(thm)],[2167, 2202])).
% 0.55/0.80 tff(2204,plain,
% 0.55/0.80 ($false),
% 0.55/0.80 inference(unit_resolution,[status(thm)],[1396, 2203])).
% 0.55/0.80 tff(2205,plain,((~r(s(s(s(s(elem!1)))), z)) | r(s(s(elem!1)), z) | (~r(s(s(elem!1)), s(z))) | (~r(s(z), z)) | (~r(s(s(s(z))), z))), inference(lemma,lemma(discharge,[]))).
% 0.55/0.80 tff(2206,plain,
% 0.55/0.80 (~r(s(s(s(s(elem!1)))), z)),
% 0.55/0.80 inference(unit_resolution,[status(thm)],[2205, 2165, 179, 2105, 180])).
% 0.55/0.80 tff(2207,plain,
% 0.55/0.80 (b(s(s(s(s(elem!1)))), z)),
% 0.55/0.80 inference(unit_resolution,[status(thm)],[1855, 2206])).
% 0.55/0.80 tff(2208,plain,
% 0.55/0.80 (~b(s(s(s(s(elem!1)))), s(s(elem!1)))),
% 0.55/0.80 inference(unit_resolution,[status(thm)],[2191, 2207, 2106])).
% 0.55/0.80 tff(2209,plain,
% 0.55/0.80 (~r(s(s(s(s(elem!1)))), s(z))),
% 0.55/0.80 inference(unit_resolution,[status(thm)],[2198, 146, 2106, 179, 2165])).
% 0.55/0.80 tff(2210,plain,
% 0.55/0.80 (b(s(s(s(s(elem!1)))), s(z))),
% 0.55/0.80 inference(unit_resolution,[status(thm)],[1327, 2209])).
% 0.55/0.80 tff(2211,assumption,(~b(s(s(s(s(elem!1)))), s(s(elem!1)))), introduced(assumption)).
% 0.55/0.80 tff(2212,plain,
% 0.55/0.80 (~r(s(z), s(s(s(elem!1))))),
% 0.55/0.80 inference(unit_resolution,[status(thm)],[221, 195, 179])).
% 0.55/0.80 tff(2213,plain,
% 0.55/0.80 (b(s(z), s(s(s(elem!1))))),
% 0.55/0.80 inference(unit_resolution,[status(thm)],[235, 2212])).
% 0.55/0.80 tff(2214,plain,
% 0.55/0.80 (~b(s(s(s(s(elem!1)))), s(s(s(elem!1))))),
% 0.55/0.80 inference(unit_resolution,[status(thm)],[1679, 1311, 2213])).
% 0.55/0.80 tff(2215,plain,
% 0.55/0.80 (r(s(s(s(s(elem!1)))), s(s(s(elem!1))))),
% 0.55/0.80 inference(unit_resolution,[status(thm)],[1347, 2214, 287])).
% 0.55/0.80 tff(2216,plain,
% 0.55/0.80 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(elem!1)), s(s(s(elem!1))))) | (~r(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~r(s(s(s(s(elem!1)))), s(s(elem!1)))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(elem!1)), 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)))))),
% 0.55/0.80 inference(rewrite,[status(thm)],[])).
% 0.55/0.80 tff(2217,plain,
% 0.55/0.80 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(elem!1)), s(s(s(elem!1))))) | (~r(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~r(s(s(s(s(elem!1)))), s(s(elem!1)))))),
% 0.55/0.80 inference(quant_inst,[status(thm)],[])).
% 0.65/0.80 tff(2218,plain,
% 0.65/0.80 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(elem!1)), s(s(s(elem!1))))) | (~r(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~r(s(s(s(s(elem!1)))), s(s(elem!1))))),
% 0.65/0.80 inference(modus_ponens,[status(thm)],[2217, 2216])).
% 0.65/0.80 tff(2219,plain,
% 0.65/0.80 ($false),
% 0.65/0.80 inference(unit_resolution,[status(thm)],[2218, 14, 195, 1397, 1337])).
% 0.65/0.80 tff(2220,plain,((~r(s(s(elem!1)), 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(s(elem!1)))))), inference(lemma,lemma(discharge,[]))).
% 0.65/0.80 tff(2221,plain,
% 0.65/0.80 (~r(s(s(s(s(elem!1)))), s(s(elem!1)))),
% 0.65/0.80 inference(unit_resolution,[status(thm)],[2220, 2215, 195])).
% 0.65/0.80 tff(2222,plain,
% 0.65/0.80 (s(s(s(s(elem!1)))) = s(s(elem!1))),
% 0.65/0.80 inference(unit_resolution,[status(thm)],[1690, 2221, 2211])).
% 0.65/0.80 tff(2223,plain,
% 0.65/0.80 (b(s(s(s(s(elem!1)))), s(z)) <=> b(s(s(elem!1)), s(z))),
% 0.65/0.80 inference(monotonicity,[status(thm)],[2222])).
% 0.65/0.80 tff(2224,plain,
% 0.65/0.80 (b(s(s(elem!1)), s(z)) <=> b(s(s(s(s(elem!1)))), s(z))),
% 0.65/0.80 inference(symmetry,[status(thm)],[2223])).
% 0.65/0.80 tff(2225,plain,
% 0.65/0.80 ((~b(s(s(elem!1)), s(z))) <=> (~b(s(s(s(s(elem!1)))), s(z)))),
% 0.65/0.80 inference(monotonicity,[status(thm)],[2224])).
% 0.65/0.80 tff(2226,plain,
% 0.65/0.80 (~b(s(s(s(s(elem!1)))), s(z))),
% 0.65/0.80 inference(modus_ponens,[status(thm)],[158, 2225])).
% 0.65/0.80 tff(2227,plain,
% 0.65/0.80 ($false),
% 0.65/0.80 inference(unit_resolution,[status(thm)],[1311, 2226])).
% 0.65/0.80 tff(2228,plain,((~b(s(s(s(s(elem!1)))), s(z))) | b(s(s(elem!1)), s(z)) | b(s(s(s(s(elem!1)))), s(s(elem!1))) | (~r(s(s(elem!1)), s(s(s(elem!1))))) | (s(s(s(s(elem!1)))) = s(s(s(elem!1))))), inference(lemma,lemma(discharge,[]))).
% 0.65/0.80 tff(2229,plain,
% 0.65/0.80 (~r(s(s(elem!1)), s(s(s(elem!1))))),
% 0.65/0.80 inference(unit_resolution,[status(thm)],[2228, 2210, 158, 2208, 156])).
% 0.65/0.80 tff(2230,plain,
% 0.65/0.80 (b(s(s(elem!1)), s(s(s(elem!1))))),
% 0.65/0.80 inference(unit_resolution,[status(thm)],[253, 2229, 145])).
% 0.65/0.80 tff(2231,plain,
% 0.65/0.80 (r(s(s(s(s(elem!1)))), s(s(elem!1)))),
% 0.65/0.80 inference(unit_resolution,[status(thm)],[1690, 146, 2208])).
% 0.65/0.80 tff(2232,assumption,(s(s(s(elem!1))) = s(s(s(z)))), introduced(assumption)).
% 0.65/0.80 tff(2233,plain,
% 0.65/0.80 (s(s(s(s(elem!1)))) = s(s(s(s(z))))),
% 0.65/0.80 inference(monotonicity,[status(thm)],[2232])).
% 0.65/0.80 tff(2234,plain,
% 0.65/0.80 (s(s(s(s(s(elem!1))))) = s(s(s(s(s(z)))))),
% 0.65/0.80 inference(monotonicity,[status(thm)],[2233])).
% 0.65/0.80 tff(2235,plain,
% 0.65/0.80 (s(s(s(s(s(s(elem!1)))))) = s(s(s(s(s(s(z))))))),
% 0.65/0.80 inference(monotonicity,[status(thm)],[2234])).
% 0.65/0.80 tff(2236,plain,
% 0.65/0.80 (s(s(s(s(s(s(z)))))) = s(s(s(s(s(s(elem!1))))))),
% 0.65/0.80 inference(symmetry,[status(thm)],[2235])).
% 0.65/0.80 tff(2237,plain,
% 0.65/0.80 ((s(s(s(s(s(s(z)))))) = s(s(s(s(z))))) <=> (s(s(s(s(s(s(elem!1)))))) = s(s(s(s(z)))))),
% 0.65/0.80 inference(monotonicity,[status(thm)],[2236])).
% 0.65/0.80 tff(2238,plain,
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% 0.65/0.80 inference(monotonicity,[status(thm)],[2238])).
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% 0.65/0.80 inference(monotonicity,[status(thm)],[2236])).
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% 0.65/0.80 inference(unit_resolution,[status(thm)],[347, 2276])).
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% 0.65/0.80 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((s(s(s(s(s(s(z)))))) = s(s(z))) | b(s(s(s(s(s(s(z)))))), s(s(z))) | r(s(s(s(s(s(s(z)))))), s(s(z))))),
% 0.65/0.80 inference(quant_inst,[status(thm)],[])).
% 0.65/0.80 tff(2304,plain,
% 0.65/0.80 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (s(s(s(s(s(s(z)))))) = s(s(z))) | b(s(s(s(s(s(s(z)))))), s(s(z))) | r(s(s(s(s(s(s(z)))))), s(s(z)))),
% 0.65/0.80 inference(modus_ponens,[status(thm)],[2303, 2302])).
% 0.65/0.80 tff(2305,plain,
% 0.65/0.80 (r(s(s(s(s(s(s(z)))))), s(s(z)))),
% 0.65/0.80 inference(unit_resolution,[status(thm)],[2304, 46, 1786, 2301])).
% 0.65/0.80 tff(2306,plain,
% 0.65/0.80 (s(s(s(s(z)))) = s(s(s(s(elem!1))))),
% 0.65/0.80 inference(symmetry,[status(thm)],[2233])).
% 0.65/0.80 tff(2307,plain,
% 0.65/0.80 (r(s(s(s(s(z)))), s(s(z))) <=> r(s(s(s(s(elem!1)))), s(s(elem!1)))),
% 0.65/0.80 inference(monotonicity,[status(thm)],[2306, 2243])).
% 0.65/0.80 tff(2308,plain,
% 0.65/0.80 (r(s(s(s(s(elem!1)))), s(s(elem!1))) <=> r(s(s(s(s(z)))), s(s(z)))),
% 0.65/0.80 inference(symmetry,[status(thm)],[2307])).
% 0.65/0.80 tff(2309,plain,
% 0.65/0.80 (r(s(s(s(s(z)))), s(s(z)))),
% 0.65/0.80 inference(modus_ponens,[status(thm)],[1397, 2308])).
% 0.65/0.80 tff(2310,plain,
% 0.65/0.80 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(z)))), s(s(z)))) | (~r(s(s(s(s(s(s(z)))))), s(s(z)))) | (~r(s(s(s(s(s(s(z)))))), s(s(s(s(z)))))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(s(z)))), s(s(z)))) | (~r(s(s(s(s(s(s(z)))))), s(s(z)))) | (~r(s(s(s(s(s(s(z)))))), s(s(s(s(z)))))))),
% 0.65/0.80 inference(rewrite,[status(thm)],[])).
% 0.65/0.80 tff(2311,plain,
% 0.65/0.80 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(z)))), s(s(z)))) | (~r(s(s(s(s(s(s(z)))))), s(s(z)))) | (~r(s(s(s(s(s(s(z)))))), s(s(s(s(z)))))))),
% 0.65/0.80 inference(quant_inst,[status(thm)],[])).
% 0.65/0.80 tff(2312,plain,
% 0.65/0.80 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(s(z)))), s(s(z)))) | (~r(s(s(s(s(s(s(z)))))), s(s(z)))) | (~r(s(s(s(s(s(s(z)))))), s(s(s(s(z))))))),
% 0.65/0.80 inference(modus_ponens,[status(thm)],[2311, 2310])).
% 0.65/0.80 tff(2313,plain,
% 0.65/0.80 (~r(s(s(s(s(s(s(z)))))), s(s(s(s(z)))))),
% 0.65/0.80 inference(unit_resolution,[status(thm)],[2312, 14, 2309, 2305])).
% 0.65/0.80 tff(2314,plain,
% 0.65/0.80 (b(s(s(s(s(elem!1)))), z) <=> b(s(s(s(s(z)))), z)),
% 0.65/0.80 inference(monotonicity,[status(thm)],[2233])).
% 0.65/0.81 tff(2315,plain,
% 0.65/0.81 (b(s(s(s(s(z)))), z)),
% 0.65/0.81 inference(modus_ponens,[status(thm)],[1310, 2314])).
% 0.65/0.81 tff(2316,plain,
% 0.65/0.81 (((~![X0: $i, X2: $i, X1: $i] : ((~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(z)))), z)) | (~b(s(s(s(s(s(s(z)))))), z)) | (~b(s(s(s(s(s(s(z)))))), s(s(s(s(z)))))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(s(s(s(z)))))), z)) | (~b(s(s(s(s(s(s(z)))))), s(s(s(s(z)))))))),
% 0.65/0.81 inference(rewrite,[status(thm)],[])).
% 0.65/0.81 tff(2317,plain,
% 0.65/0.81 ((~![X0: $i, X2: $i, X1: $i] : ((~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(z)))), z)) | (~b(s(s(s(s(s(s(z)))))), z)) | (~b(s(s(s(s(s(s(z)))))), s(s(s(s(z)))))))),
% 0.65/0.81 inference(quant_inst,[status(thm)],[])).
% 0.65/0.81 tff(2318,plain,
% 0.65/0.81 ((~![X0: $i, X2: $i, X1: $i] : ((~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(s(s(s(z)))))), z)) | (~b(s(s(s(s(s(s(z)))))), s(s(s(s(z))))))),
% 0.65/0.81 inference(modus_ponens,[status(thm)],[2317, 2316])).
% 0.65/0.81 tff(2319,plain,
% 0.65/0.81 ((~b(s(s(s(s(s(s(z)))))), z)) | (~b(s(s(s(s(s(s(z)))))), s(s(s(s(z))))))),
% 0.65/0.81 inference(unit_resolution,[status(thm)],[2318, 117, 2315])).
% 0.65/0.81 tff(2320,plain,
% 0.65/0.81 (~b(s(s(s(s(s(s(z)))))), s(s(s(s(z)))))),
% 0.65/0.81 inference(unit_resolution,[status(thm)],[2319, 2296])).
% 0.65/0.81 tff(2321,plain,
% 0.65/0.81 (((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((s(s(s(s(s(s(z)))))) = s(s(s(s(z))))) | b(s(s(s(s(s(s(z)))))), s(s(s(s(z))))) | r(s(s(s(s(s(s(z)))))), s(s(s(s(z))))))) <=> ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (s(s(s(s(s(s(z)))))) = s(s(s(s(z))))) | b(s(s(s(s(s(s(z)))))), s(s(s(s(z))))) | r(s(s(s(s(s(s(z)))))), s(s(s(s(z))))))),
% 0.65/0.81 inference(rewrite,[status(thm)],[])).
% 0.65/0.81 tff(2322,plain,
% 0.65/0.81 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((s(s(s(s(s(s(z)))))) = s(s(s(s(z))))) | b(s(s(s(s(s(s(z)))))), s(s(s(s(z))))) | r(s(s(s(s(s(s(z)))))), s(s(s(s(z))))))),
% 0.65/0.81 inference(quant_inst,[status(thm)],[])).
% 0.65/0.81 tff(2323,plain,
% 0.65/0.81 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (s(s(s(s(s(s(z)))))) = s(s(s(s(z))))) | b(s(s(s(s(s(s(z)))))), s(s(s(s(z))))) | r(s(s(s(s(s(s(z)))))), s(s(s(s(z)))))),
% 0.65/0.81 inference(modus_ponens,[status(thm)],[2322, 2321])).
% 0.65/0.81 tff(2324,plain,
% 0.65/0.81 ((s(s(s(s(s(s(z)))))) = s(s(s(s(z))))) | r(s(s(s(s(s(s(z)))))), s(s(s(s(z)))))),
% 0.65/0.81 inference(unit_resolution,[status(thm)],[2323, 46, 2320])).
% 0.65/0.81 tff(2325,plain,
% 0.65/0.81 ($false),
% 0.65/0.81 inference(unit_resolution,[status(thm)],[2324, 2313, 2240])).
% 0.65/0.81 tff(2326,plain,((~(s(s(s(elem!1))) = s(s(s(z))))) | (~b(s(s(elem!1)), z)) | (~r(s(s(s(z))), z)) | (~r(s(z), z)) | (~r(s(s(s(s(elem!1)))), s(s(elem!1)))) | (~b(s(s(s(s(elem!1)))), z))), inference(lemma,lemma(discharge,[]))).
% 0.65/0.81 tff(2327,plain,
% 0.65/0.81 (~(s(s(s(elem!1))) = s(s(s(z))))),
% 0.65/0.81 inference(unit_resolution,[status(thm)],[2326, 2231, 180, 2165, 2106, 2207])).
% 0.65/0.81 tff(2328,assumption,(~(s(s(s(elem!1))) = s(s(s(z))))), introduced(assumption)).
% 0.65/0.81 tff(2329,assumption,(r(s(s(s(elem!1))), s(s(s(z))))), introduced(assumption)).
% 0.65/0.81 tff(2330,plain,
% 0.65/0.81 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), z)) | (~r(s(s(s(z))), z)) | (~r(s(s(s(elem!1))), s(s(s(z))))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(elem!1))), z)) | (~r(s(s(s(z))), z)) | (~r(s(s(s(elem!1))), s(s(s(z))))))),
% 0.65/0.81 inference(rewrite,[status(thm)],[])).
% 0.65/0.81 tff(2331,plain,
% 0.65/0.81 (((~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(z))), z)) | (~r(s(s(s(elem!1))), s(s(s(z))))))),
% 0.65/0.81 inference(rewrite,[status(thm)],[])).
% 0.65/0.81 tff(2332,plain,
% 0.65/0.81 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(z))), z)) | (~r(s(s(s(elem!1))), z)) | (~r(s(s(s(elem!1))), s(s(s(z))))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), z)) | (~r(s(s(s(z))), z)) | (~r(s(s(s(elem!1))), s(s(s(z)))))))),
% 0.65/0.81 inference(monotonicity,[status(thm)],[2331])).
% 0.65/0.81 tff(2333,plain,
% 0.65/0.81 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(z))), z)) | (~r(s(s(s(elem!1))), z)) | (~r(s(s(s(elem!1))), s(s(s(z))))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(elem!1))), z)) | (~r(s(s(s(z))), z)) | (~r(s(s(s(elem!1))), s(s(s(z))))))),
% 0.65/0.81 inference(transitivity,[status(thm)],[2332, 2330])).
% 0.65/0.81 tff(2334,plain,
% 0.65/0.81 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(z))), z)) | (~r(s(s(s(elem!1))), z)) | (~r(s(s(s(elem!1))), s(s(s(z))))))),
% 0.65/0.81 inference(quant_inst,[status(thm)],[])).
% 0.65/0.81 tff(2335,plain,
% 0.65/0.81 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(elem!1))), z)) | (~r(s(s(s(z))), z)) | (~r(s(s(s(elem!1))), s(s(s(z)))))),
% 0.65/0.81 inference(modus_ponens,[status(thm)],[2334, 2333])).
% 0.65/0.81 tff(2336,plain,
% 0.65/0.81 ($false),
% 0.65/0.81 inference(unit_resolution,[status(thm)],[2335, 14, 196, 180, 2329])).
% 0.65/0.81 tff(2337,plain,((~r(s(s(s(z))), z)) | (~r(s(s(s(elem!1))), z)) | (~r(s(s(s(elem!1))), s(s(s(z)))))), inference(lemma,lemma(discharge,[]))).
% 0.65/0.81 tff(2338,plain,
% 0.65/0.81 (~r(s(s(s(elem!1))), s(s(s(z))))),
% 0.65/0.81 inference(unit_resolution,[status(thm)],[2337, 196, 180])).
% 0.65/0.81 tff(2339,plain,
% 0.65/0.81 (((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((s(s(s(elem!1))) = s(s(s(z)))) | b(s(s(s(elem!1))), s(s(s(z)))) | r(s(s(s(elem!1))), s(s(s(z)))))) <=> ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (s(s(s(elem!1))) = s(s(s(z)))) | b(s(s(s(elem!1))), s(s(s(z)))) | r(s(s(s(elem!1))), s(s(s(z)))))),
% 0.65/0.81 inference(rewrite,[status(thm)],[])).
% 0.65/0.81 tff(2340,plain,
% 0.65/0.81 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((s(s(s(elem!1))) = s(s(s(z)))) | b(s(s(s(elem!1))), s(s(s(z)))) | r(s(s(s(elem!1))), s(s(s(z)))))),
% 0.65/0.81 inference(quant_inst,[status(thm)],[])).
% 0.65/0.81 tff(2341,plain,
% 0.65/0.81 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (s(s(s(elem!1))) = s(s(s(z)))) | b(s(s(s(elem!1))), s(s(s(z)))) | r(s(s(s(elem!1))), s(s(s(z))))),
% 0.65/0.81 inference(modus_ponens,[status(thm)],[2340, 2339])).
% 0.65/0.81 tff(2342,plain,
% 0.65/0.81 (b(s(s(s(elem!1))), s(s(s(z))))),
% 0.65/0.81 inference(unit_resolution,[status(thm)],[2341, 46, 2338, 2328])).
% 0.65/0.81 tff(2343,plain,
% 0.65/0.81 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), z)) | (~r(s(s(s(elem!1))), z)) | (~r(s(s(s(elem!1))), s(z))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(z), z)) | (~r(s(s(s(elem!1))), z)) | (~r(s(s(s(elem!1))), s(z))))),
% 0.65/0.81 inference(rewrite,[status(thm)],[])).
% 0.65/0.81 tff(2344,plain,
% 0.65/0.81 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), z)) | (~r(s(s(s(elem!1))), z)) | (~r(s(s(s(elem!1))), s(z))))),
% 0.65/0.81 inference(quant_inst,[status(thm)],[])).
% 0.65/0.81 tff(2345,plain,
% 0.65/0.81 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(z), z)) | (~r(s(s(s(elem!1))), z)) | (~r(s(s(s(elem!1))), s(z)))),
% 0.65/0.81 inference(modus_ponens,[status(thm)],[2344, 2343])).
% 0.65/0.81 tff(2346,plain,
% 0.65/0.81 (~r(s(s(s(elem!1))), s(z))),
% 0.65/0.81 inference(unit_resolution,[status(thm)],[2345, 14, 196, 183])).
% 0.65/0.81 tff(2347,plain,
% 0.65/0.81 (b(s(s(s(elem!1))), s(z))),
% 0.65/0.81 inference(unit_resolution,[status(thm)],[467, 2346])).
% 0.65/0.81 tff(2348,plain,
% 0.65/0.81 (((~![X0: $i, X2: $i, X1: $i] : ((~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), s(z))) | (~b(s(s(s(elem!1))), s(s(s(z))))) | (~b(s(s(s(z))), s(z))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(s(s(elem!1))), s(s(s(z))))) | (~b(s(s(s(z))), s(z))))),
% 0.65/0.81 inference(rewrite,[status(thm)],[])).
% 0.65/0.81 tff(2349,plain,
% 0.65/0.81 (((~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(elem!1))), s(s(s(z))))) | (~b(s(s(s(z))), s(z))))),
% 0.65/0.81 inference(rewrite,[status(thm)],[])).
% 0.65/0.81 tff(2350,plain,
% 0.65/0.81 (((~![X0: $i, X2: $i, X1: $i] : ((~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(s(elem!1))), s(s(s(z))))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), s(z))) | (~b(s(s(s(elem!1))), s(s(s(z))))) | (~b(s(s(s(z))), s(z)))))),
% 0.65/0.81 inference(monotonicity,[status(thm)],[2349])).
% 0.65/0.81 tff(2351,plain,
% 0.65/0.81 (((~![X0: $i, X2: $i, X1: $i] : ((~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(s(elem!1))), s(s(s(z))))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(s(s(elem!1))), s(s(s(z))))) | (~b(s(s(s(z))), s(z))))),
% 0.65/0.81 inference(transitivity,[status(thm)],[2350, 2348])).
% 0.65/0.81 tff(2352,plain,
% 0.65/0.81 ((~![X0: $i, X2: $i, X1: $i] : ((~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(s(elem!1))), s(s(s(z))))))),
% 0.65/0.81 inference(quant_inst,[status(thm)],[])).
% 0.65/0.81 tff(2353,plain,
% 0.65/0.81 ((~![X0: $i, X2: $i, X1: $i] : ((~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(s(s(elem!1))), s(s(s(z))))) | (~b(s(s(s(z))), s(z)))),
% 0.65/0.81 inference(modus_ponens,[status(thm)],[2352, 2351])).
% 0.65/0.81 tff(2354,plain,
% 0.65/0.81 ($false),
% 0.65/0.81 inference(unit_resolution,[status(thm)],[2353, 117, 2347, 2277, 2342])).
% 0.65/0.81 tff(2355,plain,((~r(s(s(s(elem!1))), z)) | (s(s(s(elem!1))) = s(s(s(z)))) | (~r(s(z), z)) | (~r(s(s(s(z))), z))), inference(lemma,lemma(discharge,[]))).
% 0.65/0.81 tff(2356,plain,
% 0.65/0.81 (~r(s(s(s(elem!1))), z)),
% 0.65/0.81 inference(unit_resolution,[status(thm)],[2355, 2327, 180, 2165])).
% 0.65/0.81 tff(2357,plain,
% 0.65/0.81 (b(s(s(s(elem!1))), z)),
% 0.65/0.81 inference(unit_resolution,[status(thm)],[211, 2356])).
% 0.65/0.81 tff(2358,plain,
% 0.65/0.81 ($false),
% 0.65/0.81 inference(unit_resolution,[status(thm)],[1046, 2357, 2230, 2106])).
% 0.65/0.81 tff(2359,plain,((s(s(s(s(elem!1)))) = s(s(elem!1))) | (s(s(elem!1)) = s(s(s(elem!1)))) | (~r(s(s(s(z))), z)) | b(s(s(elem!1)), s(z))), inference(lemma,lemma(discharge,[]))).
% 0.65/0.81 tff(2360,plain,
% 0.65/0.81 (s(s(s(s(elem!1)))) = s(s(elem!1))),
% 0.65/0.81 inference(unit_resolution,[status(thm)],[2359, 180, 145, 158])).
% 0.65/0.81 tff(2361,plain,
% 0.65/0.81 (inj_0(s(s(s(s(elem!1))))) = inj_0(s(s(elem!1)))),
% 0.65/0.81 inference(monotonicity,[status(thm)],[2360])).
% 0.65/0.81 tff(2362,plain,
% 0.65/0.81 (inj_0(s(s(elem!1))) = inj_0(s(s(s(s(elem!1)))))),
% 0.65/0.81 inference(symmetry,[status(thm)],[2361])).
% 0.65/0.81 tff(2363,plain,
% 0.65/0.81 (s(elem!1) = s(s(s(elem!1)))),
% 0.65/0.81 inference(transitivity,[status(thm)],[167, 2362, 144])).
% 0.65/0.81 tff(2364,plain,
% 0.65/0.81 ((s(s(s(z))) = s(elem!1)) <=> (s(s(s(z))) = s(s(s(elem!1))))),
% 0.65/0.81 inference(monotonicity,[status(thm)],[2363])).
% 0.65/0.81 tff(2365,plain,
% 0.65/0.81 ((s(s(s(z))) = s(elem!1)) <=> (s(s(s(elem!1))) = s(s(s(z))))),
% 0.65/0.81 inference(transitivity,[status(thm)],[2364, 2166])).
% 0.65/0.81 tff(2366,plain,
% 0.65/0.81 ((~(s(s(s(z))) = s(elem!1))) <=> (~(s(s(s(elem!1))) = s(s(s(z)))))),
% 0.65/0.81 inference(monotonicity,[status(thm)],[2365])).
% 0.65/0.81 tff(2367,plain,
% 0.65/0.81 (~(s(s(s(z))) = s(elem!1))),
% 0.65/0.81 inference(unit_resolution,[status(thm)],[623, 2360])).
% 0.65/0.81 tff(2368,plain,
% 0.65/0.81 (~(s(s(s(elem!1))) = s(s(s(z))))),
% 0.65/0.81 inference(modus_ponens,[status(thm)],[2367, 2366])).
% 0.65/0.81 tff(2369,plain,
% 0.65/0.81 (~r(s(s(s(elem!1))), z)),
% 0.65/0.81 inference(unit_resolution,[status(thm)],[2355, 2368, 180, 2165])).
% 0.65/0.81 tff(2370,plain,
% 0.65/0.81 (b(s(s(s(elem!1))), z)),
% 0.65/0.81 inference(unit_resolution,[status(thm)],[211, 2369])).
% 0.65/0.81 tff(2371,plain,
% 0.65/0.81 (~b(s(s(elem!1)), s(s(s(elem!1))))),
% 0.65/0.81 inference(unit_resolution,[status(thm)],[1046, 2370, 2106])).
% 0.65/0.81 tff(2372,plain,
% 0.65/0.81 (r(s(s(elem!1)), s(s(s(elem!1))))),
% 0.65/0.81 inference(unit_resolution,[status(thm)],[253, 2371, 145])).
% 0.65/0.81 tff(2373,plain,
% 0.65/0.81 (~r(s(s(s(s(elem!1)))), z)),
% 0.65/0.81 inference(unit_resolution,[status(thm)],[2205, 183, 179, 2167, 180])).
% 0.65/0.81 tff(2374,plain,
% 0.65/0.81 (b(s(s(s(s(elem!1)))), z)),
% 0.65/0.81 inference(unit_resolution,[status(thm)],[1855, 2373])).
% 0.65/0.81 tff(2375,plain,
% 0.65/0.81 (~b(s(s(s(s(elem!1)))), s(s(elem!1)))),
% 0.65/0.81 inference(unit_resolution,[status(thm)],[2191, 2374, 2168])).
% 0.65/0.81 tff(2376,plain,
% 0.65/0.81 (~b(s(s(s(s(elem!1)))), s(z))),
% 0.65/0.81 inference(unit_resolution,[status(thm)],[2228, 2375, 158, 195, 287])).
% 0.65/0.81 tff(2377,plain,
% 0.65/0.81 (r(s(s(s(s(elem!1)))), s(z))),
% 0.65/0.81 inference(unit_resolution,[status(thm)],[1327, 2376])).
% 0.65/0.81 tff(2378,plain,
% 0.65/0.81 (s(s(s(s(elem!1)))) = s(s(elem!1))),
% 0.65/0.81 inference(unit_resolution,[status(thm)],[2198, 2377, 2168, 179, 183])).
% 0.65/0.81 tff(2379,plain,
% 0.65/0.81 (inj_0(s(s(s(s(elem!1))))) = inj_0(s(s(elem!1)))),
% 0.65/0.81 inference(monotonicity,[status(thm)],[2378])).
% 0.65/0.81 tff(2380,plain,
% 0.65/0.81 (inj_0(s(s(elem!1))) = inj_0(s(s(s(s(elem!1)))))),
% 0.65/0.81 inference(symmetry,[status(thm)],[2379])).
% 0.65/0.81 tff(2381,plain,
% 0.65/0.81 (s(elem!1) = s(s(s(elem!1)))),
% 0.65/0.81 inference(transitivity,[status(thm)],[167, 2380, 144])).
% 0.65/0.81 tff(2382,plain,
% 0.65/0.81 (b(s(elem!1), z) <=> b(s(s(s(elem!1))), z)),
% 0.65/0.81 inference(monotonicity,[status(thm)],[2381])).
% 0.65/0.81 tff(2383,plain,
% 0.65/0.81 (b(s(s(s(elem!1))), z) <=> b(s(elem!1), z)),
% 0.65/0.81 inference(symmetry,[status(thm)],[2382])).
% 0.65/0.81 tff(2384,plain,
% 0.65/0.81 ((s(s(s(z))) = s(elem!1)) <=> (s(s(s(z))) = s(s(s(elem!1))))),
% 0.65/0.81 inference(monotonicity,[status(thm)],[2381])).
% 0.65/0.81 tff(2385,plain,
% 0.65/0.81 ((s(s(s(z))) = s(elem!1)) <=> (s(s(s(elem!1))) = s(s(s(z))))),
% 0.65/0.81 inference(transitivity,[status(thm)],[2384, 2166])).
% 0.65/0.81 tff(2386,plain,
% 0.65/0.81 ((~(s(s(s(z))) = s(elem!1))) <=> (~(s(s(s(elem!1))) = s(s(s(z)))))),
% 0.65/0.81 inference(monotonicity,[status(thm)],[2385])).
% 0.65/0.81 tff(2387,plain,
% 0.65/0.81 (~(s(s(s(z))) = s(elem!1))),
% 0.65/0.81 inference(unit_resolution,[status(thm)],[623, 2378])).
% 0.65/0.81 tff(2388,plain,
% 0.65/0.81 (~(s(s(s(elem!1))) = s(s(s(z))))),
% 0.65/0.81 inference(modus_ponens,[status(thm)],[2387, 2386])).
% 0.65/0.81 tff(2389,plain,
% 0.65/0.81 (~r(s(s(s(elem!1))), z)),
% 0.65/0.81 inference(unit_resolution,[status(thm)],[2355, 2388, 180, 183])).
% 0.65/0.81 tff(2390,plain,
% 0.65/0.81 (b(s(s(s(elem!1))), z)),
% 0.65/0.81 inference(unit_resolution,[status(thm)],[211, 2389])).
% 0.65/0.81 tff(2391,plain,
% 0.65/0.81 (b(s(elem!1), z)),
% 0.65/0.81 inference(modus_ponens,[status(thm)],[2390, 2383])).
% 0.65/0.81 tff(2392,plain,
% 0.65/0.81 (s(s(s(elem!1))) = s(elem!1)),
% 0.65/0.81 inference(transitivity,[status(thm)],[295, 2379, 166])).
% 0.65/0.81 tff(2393,plain,
% 0.65/0.81 (b(s(s(s(elem!1))), s(z)) <=> b(s(elem!1), s(z))),
% 0.65/0.81 inference(monotonicity,[status(thm)],[2392])).
% 0.65/0.81 tff(2394,assumption,(~b(s(s(elem!1)), s(s(s(elem!1))))), introduced(assumption)).
% 0.65/0.81 tff(2395,plain,
% 0.65/0.81 (s(s(elem!1)) = elem!1),
% 0.65/0.81 inference(unit_resolution,[status(thm)],[266, 2378])).
% 0.65/0.81 tff(2396,plain,
% 0.65/0.81 ((elem!1 = s(s(elem!1))) <=> (s(s(elem!1)) = elem!1)),
% 0.65/0.81 inference(commutativity,[status(thm)],[])).
% 0.65/0.81 tff(2397,plain,
% 0.65/0.81 ((s(s(elem!1)) = elem!1) <=> (elem!1 = s(s(elem!1)))),
% 0.65/0.81 inference(symmetry,[status(thm)],[2396])).
% 0.65/0.81 tff(2398,plain,
% 0.65/0.81 (elem!1 = s(s(elem!1))),
% 0.65/0.81 inference(modus_ponens,[status(thm)],[556, 2397])).
% 0.65/0.81 tff(2399,assumption,(~(elem!1 = s(s(elem!1)))), introduced(assumption)).
% 0.65/0.81 tff(2400,plain,
% 0.65/0.81 ($false),
% 0.65/0.81 inference(unit_resolution,[status(thm)],[2399, 2398])).
% 0.65/0.81 tff(2401,plain,((~(s(s(elem!1)) = elem!1)) | (elem!1 = s(s(elem!1)))), inference(lemma,lemma(discharge,[]))).
% 0.65/0.81 tff(2402,plain,
% 0.65/0.81 (elem!1 = s(s(elem!1))),
% 0.65/0.81 inference(unit_resolution,[status(thm)],[2401, 2395])).
% 0.65/0.81 tff(2403,assumption,(elem!1 = s(s(elem!1))), introduced(assumption)).
% 0.65/0.81 tff(2404,plain,
% 0.65/0.81 (s(elem!1) = s(s(s(elem!1)))),
% 0.65/0.81 inference(monotonicity,[status(thm)],[2403])).
% 0.65/0.81 tff(2405,plain,
% 0.65/0.81 (s(s(s(elem!1))) = s(elem!1)),
% 0.65/0.81 inference(symmetry,[status(thm)],[2404])).
% 0.65/0.81 tff(2406,plain,
% 0.65/0.81 (s(s(s(s(elem!1)))) = s(s(elem!1))),
% 0.65/0.81 inference(monotonicity,[status(thm)],[2405])).
% 0.65/0.81 tff(2407,plain,
% 0.65/0.81 (b(s(s(s(s(elem!1)))), s(s(s(elem!1)))) <=> b(s(s(elem!1)), s(s(s(elem!1))))),
% 0.65/0.81 inference(monotonicity,[status(thm)],[2406])).
% 0.65/0.81 tff(2408,plain,
% 0.65/0.81 (b(s(s(elem!1)), s(s(s(elem!1)))) <=> b(s(s(s(s(elem!1)))), s(s(s(elem!1))))),
% 0.65/0.81 inference(symmetry,[status(thm)],[2407])).
% 0.65/0.81 tff(2409,plain,
% 0.65/0.81 ((~b(s(s(elem!1)), s(s(s(elem!1))))) <=> (~b(s(s(s(s(elem!1)))), s(s(s(elem!1)))))),
% 0.65/0.81 inference(monotonicity,[status(thm)],[2408])).
% 0.65/0.81 tff(2410,plain,
% 0.65/0.81 (~b(s(s(s(s(elem!1)))), s(s(s(elem!1))))),
% 0.65/0.81 inference(modus_ponens,[status(thm)],[2394, 2409])).
% 0.65/0.81 tff(2411,plain,
% 0.65/0.81 ($false),
% 0.65/0.81 inference(unit_resolution,[status(thm)],[1349, 2410])).
% 0.65/0.81 tff(2412,plain,((~(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))))), inference(lemma,lemma(discharge,[]))).
% 0.65/0.81 tff(2413,plain,
% 0.65/0.81 (~b(s(s(s(s(elem!1)))), s(s(s(elem!1))))),
% 0.65/0.81 inference(unit_resolution,[status(thm)],[2412, 2402, 2394])).
% 0.65/0.81 tff(2414,plain,
% 0.65/0.81 (r(s(s(s(s(elem!1)))), s(s(s(elem!1))))),
% 0.65/0.81 inference(unit_resolution,[status(thm)],[1347, 2413, 287])).
% 0.65/0.81 tff(2415,plain,
% 0.65/0.81 (~r(s(s(s(elem!1))), s(z))),
% 0.65/0.81 inference(unit_resolution,[status(thm)],[1916, 2414, 2377])).
% 0.65/0.81 tff(2416,plain,
% 0.65/0.81 (b(s(s(s(elem!1))), s(z))),
% 0.65/0.81 inference(unit_resolution,[status(thm)],[467, 2415])).
% 0.65/0.81 tff(2417,plain,
% 0.65/0.81 (b(s(elem!1), s(z))),
% 0.65/0.81 inference(modus_ponens,[status(thm)],[2416, 2393])).
% 0.65/0.81 tff(2418,plain,
% 0.65/0.81 ((s(s(elem!1)) = s(s(s(s(z))))) <=> (s(s(s(s(z)))) = s(s(elem!1)))),
% 0.65/0.81 inference(commutativity,[status(thm)],[])).
% 0.65/0.81 tff(2419,plain,
% 0.65/0.81 (elem!1 = s(s(elem!1))),
% 0.65/0.81 inference(symmetry,[status(thm)],[2395])).
% 0.65/0.81 tff(2420,plain,
% 0.65/0.81 ((elem!1 = s(s(s(s(z))))) <=> (s(s(elem!1)) = s(s(s(s(z)))))),
% 0.65/0.81 inference(monotonicity,[status(thm)],[2419])).
% 0.65/0.81 tff(2421,plain,
% 0.65/0.81 ((elem!1 = s(s(s(s(z))))) <=> (s(s(s(s(z)))) = s(s(elem!1)))),
% 0.65/0.81 inference(transitivity,[status(thm)],[2420, 2418])).
% 0.65/0.81 tff(2422,plain,
% 0.65/0.81 ((s(s(s(s(z)))) = s(s(elem!1))) <=> (elem!1 = s(s(s(s(z)))))),
% 0.65/0.81 inference(symmetry,[status(thm)],[2421])).
% 0.65/0.81 tff(2423,plain,
% 0.65/0.81 (s(s(s(s(s(elem!1))))) = s(s(s(elem!1)))),
% 0.65/0.81 inference(monotonicity,[status(thm)],[2378])).
% 0.65/0.81 tff(2424,plain,
% 0.65/0.81 (s(s(s(s(s(elem!1))))) = s(elem!1)),
% 0.65/0.81 inference(transitivity,[status(thm)],[2423, 295, 2379, 166])).
% 0.65/0.81 tff(2425,plain,
% 0.65/0.81 (s(s(s(s(s(s(elem!1)))))) = s(s(elem!1))),
% 0.65/0.81 inference(monotonicity,[status(thm)],[2424])).
% 0.65/0.81 tff(2426,plain,
% 0.65/0.81 ((s(s(s(s(s(s(elem!1)))))) = s(s(s(s(z))))) <=> (s(s(elem!1)) = s(s(s(s(z)))))),
% 0.65/0.81 inference(monotonicity,[status(thm)],[2425])).
% 0.65/0.81 tff(2427,plain,
% 0.65/0.81 ((s(s(s(s(s(s(elem!1)))))) = s(s(s(s(z))))) <=> (s(s(s(s(z)))) = s(s(elem!1)))),
% 0.65/0.81 inference(transitivity,[status(thm)],[2426, 2418])).
% 0.65/0.81 tff(2428,plain,
% 0.65/0.81 ((s(s(s(s(s(s(elem!1)))))) = s(s(s(s(z))))) <=> (elem!1 = s(s(s(s(z)))))),
% 0.65/0.81 inference(transitivity,[status(thm)],[2427, 2422])).
% 0.65/0.81 tff(2429,plain,
% 0.65/0.81 ((~(s(s(s(s(s(s(elem!1)))))) = s(s(s(s(z)))))) <=> (~(elem!1 = s(s(s(s(z))))))),
% 0.65/0.81 inference(monotonicity,[status(thm)],[2428])).
% 0.65/0.81 tff(2430,plain,
% 0.65/0.81 (~(elem!1 = s(s(s(s(z)))))),
% 0.65/0.81 inference(modus_ponens,[status(thm)],[319, 2429])).
% 0.65/0.81 tff(2431,plain,
% 0.65/0.81 (~(s(s(s(s(z)))) = s(elem!1))),
% 0.65/0.81 inference(unit_resolution,[status(thm)],[476, 2378])).
% 0.65/0.81 tff(2432,plain,
% 0.65/0.81 ((s(elem!1) = s(s(s(z)))) <=> (s(s(s(z))) = s(elem!1))),
% 0.65/0.81 inference(commutativity,[status(thm)],[])).
% 0.65/0.81 tff(2433,plain,
% 0.65/0.81 ((s(s(s(z))) = s(elem!1)) <=> (s(elem!1) = s(s(s(z))))),
% 0.65/0.81 inference(symmetry,[status(thm)],[2432])).
% 0.65/0.81 tff(2434,plain,
% 0.65/0.81 ((~(s(s(s(z))) = s(elem!1))) <=> (~(s(elem!1) = s(s(s(z)))))),
% 0.65/0.81 inference(monotonicity,[status(thm)],[2433])).
% 0.65/0.81 tff(2435,plain,
% 0.65/0.81 (~(s(elem!1) = s(s(s(z))))),
% 0.65/0.81 inference(modus_ponens,[status(thm)],[2387, 2434])).
% 0.65/0.81 tff(2436,plain,
% 0.65/0.81 (((~![X0: $i, X2: $i, X1: $i] : ((~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), s(z))) | (~b(s(elem!1), s(z))) | (~b(s(elem!1), s(s(s(z))))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(z))), s(z))) | (~b(s(elem!1), s(z))) | (~b(s(elem!1), s(s(s(z))))))),
% 0.65/0.81 inference(rewrite,[status(thm)],[])).
% 0.65/0.81 tff(2437,plain,
% 0.65/0.81 ((~![X0: $i, X2: $i, X1: $i] : ((~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), s(z))) | (~b(s(elem!1), s(z))) | (~b(s(elem!1), s(s(s(z))))))),
% 0.65/0.81 inference(quant_inst,[status(thm)],[])).
% 0.65/0.81 tff(2438,plain,
% 0.65/0.81 ((~![X0: $i, X2: $i, X1: $i] : ((~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(z))), s(z))) | (~b(s(elem!1), s(z))) | (~b(s(elem!1), s(s(s(z)))))),
% 0.65/0.81 inference(modus_ponens,[status(thm)],[2437, 2436])).
% 0.65/0.81 tff(2439,plain,
% 0.65/0.81 (~b(s(elem!1), s(s(s(z))))),
% 0.65/0.81 inference(unit_resolution,[status(thm)],[2438, 117, 2175, 2417])).
% 0.65/0.81 tff(2440,plain,
% 0.65/0.81 ((s(elem!1) = s(s(s(z)))) | r(s(elem!1), s(s(s(z))))),
% 0.65/0.81 inference(unit_resolution,[status(thm)],[493, 46, 2439])).
% 0.65/0.81 tff(2441,plain,
% 0.65/0.81 (r(s(elem!1), s(s(s(z))))),
% 0.65/0.81 inference(unit_resolution,[status(thm)],[2440, 2435])).
% 0.65/0.81 tff(2442,assumption,(r(s(elem!1), s(s(s(z))))), introduced(assumption)).
% 0.65/0.81 tff(2443,plain,
% 0.65/0.81 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(z)))), s(s(s(z))))) | (~r(s(elem!1), s(s(s(z))))) | (~r(s(s(s(s(z)))), s(elem!1))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(s(z)))), s(s(s(z))))) | (~r(s(elem!1), s(s(s(z))))) | (~r(s(s(s(s(z)))), s(elem!1))))),
% 0.65/0.81 inference(rewrite,[status(thm)],[])).
% 0.65/0.81 tff(2444,plain,
% 0.65/0.81 (((~r(s(elem!1), s(s(s(z))))) | (~r(s(s(s(s(z)))), s(s(s(z))))) | (~r(s(s(s(s(z)))), s(elem!1)))) <=> ((~r(s(s(s(s(z)))), s(s(s(z))))) | (~r(s(elem!1), s(s(s(z))))) | (~r(s(s(s(s(z)))), s(elem!1))))),
% 0.65/0.81 inference(rewrite,[status(thm)],[])).
% 0.65/0.81 tff(2445,plain,
% 0.65/0.81 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(elem!1), s(s(s(z))))) | (~r(s(s(s(s(z)))), s(s(s(z))))) | (~r(s(s(s(s(z)))), s(elem!1))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(z)))), s(s(s(z))))) | (~r(s(elem!1), s(s(s(z))))) | (~r(s(s(s(s(z)))), s(elem!1)))))),
% 0.65/0.81 inference(monotonicity,[status(thm)],[2444])).
% 0.65/0.81 tff(2446,plain,
% 0.65/0.81 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(elem!1), s(s(s(z))))) | (~r(s(s(s(s(z)))), s(s(s(z))))) | (~r(s(s(s(s(z)))), s(elem!1))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(s(z)))), s(s(s(z))))) | (~r(s(elem!1), s(s(s(z))))) | (~r(s(s(s(s(z)))), s(elem!1))))),
% 0.65/0.81 inference(transitivity,[status(thm)],[2445, 2443])).
% 0.65/0.81 tff(2447,plain,
% 0.65/0.81 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(elem!1), s(s(s(z))))) | (~r(s(s(s(s(z)))), s(s(s(z))))) | (~r(s(s(s(s(z)))), s(elem!1))))),
% 0.65/0.81 inference(quant_inst,[status(thm)],[])).
% 0.65/0.81 tff(2448,plain,
% 0.65/0.81 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(s(z)))), s(s(s(z))))) | (~r(s(elem!1), s(s(s(z))))) | (~r(s(s(s(s(z)))), s(elem!1)))),
% 0.65/0.81 inference(modus_ponens,[status(thm)],[2447, 2446])).
% 0.65/0.81 tff(2449,plain,
% 0.65/0.81 ($false),
% 0.65/0.81 inference(unit_resolution,[status(thm)],[2448, 14, 892, 2442, 793])).
% 0.65/0.81 tff(2450,plain,((~b(s(s(s(s(z)))), s(z))) | (~r(s(elem!1), s(s(s(z))))) | (s(s(s(s(z)))) = s(elem!1)) | (~b(s(elem!1), s(z))) | (~b(s(s(s(z))), s(z)))), inference(lemma,lemma(discharge,[]))).
% 0.65/0.81 tff(2451,plain,
% 0.65/0.81 (~b(s(s(s(s(z)))), s(z))),
% 0.65/0.81 inference(unit_resolution,[status(thm)],[2450, 2441, 2431, 2417, 2175])).
% 0.65/0.81 tff(2452,plain,
% 0.65/0.81 (r(s(s(s(s(z)))), s(z))),
% 0.65/0.81 inference(unit_resolution,[status(thm)],[554, 2451])).
% 0.65/0.81 tff(2453,plain,
% 0.65/0.81 (r(s(s(elem!1)), s(s(s(s(z))))) <=> r(elem!1, s(s(s(s(z)))))),
% 0.65/0.81 inference(monotonicity,[status(thm)],[556])).
% 0.65/0.81 tff(2454,plain,
% 0.65/0.81 (r(elem!1, s(s(s(s(z))))) <=> r(s(s(elem!1)), s(s(s(s(z)))))),
% 0.65/0.81 inference(symmetry,[status(thm)],[2453])).
% 0.65/0.81 tff(2455,assumption,(~(elem!1 = s(s(s(s(z)))))), introduced(assumption)).
% 0.65/0.81 tff(2456,plain,
% 0.65/0.81 (~b(s(s(elem!1)), s(s(s(s(z)))))),
% 0.65/0.81 inference(unit_resolution,[status(thm)],[1118, 52, 1036])).
% 0.65/0.81 tff(2457,plain,
% 0.65/0.81 (~b(elem!1, s(s(s(s(z)))))),
% 0.65/0.81 inference(unit_resolution,[status(thm)],[1107, 2456, 556])).
% 0.65/0.81 tff(2458,plain,
% 0.65/0.81 (r(elem!1, s(s(s(s(z)))))),
% 0.65/0.81 inference(unit_resolution,[status(thm)],[1099, 2457, 2455])).
% 0.65/0.81 tff(2459,plain,
% 0.65/0.81 (r(s(s(elem!1)), s(s(s(s(z)))))),
% 0.65/0.81 inference(modus_ponens,[status(thm)],[2458, 2454])).
% 0.65/0.81 tff(2460,plain,
% 0.65/0.81 ($false),
% 0.65/0.81 inference(unit_resolution,[status(thm)],[1094, 2459])).
% 0.65/0.81 tff(2461,plain,((~r(s(s(s(s(z)))), s(z))) | (~(s(s(elem!1)) = elem!1)) | (~r(s(s(elem!1)), s(z))) | (elem!1 = s(s(s(s(z))))) | (~b(s(s(elem!1)), z)) | (~r(z, s(z)))), inference(lemma,lemma(discharge,[]))).
% 0.65/0.81 tff(2462,plain,
% 0.65/0.81 (~r(z, s(z))),
% 0.65/0.81 inference(unit_resolution,[status(thm)],[2461, 2452, 179, 2430, 2168, 2395])).
% 0.65/0.81 tff(2463,plain,
% 0.65/0.81 (b(z, s(z))),
% 0.65/0.81 inference(unit_resolution,[status(thm)],[599, 2462])).
% 0.65/0.81 tff(2464,plain,
% 0.65/0.81 (((~![X0: $i, X2: $i, X1: $i] : ((~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(z))) | (~b(s(elem!1), z)) | (~b(s(elem!1), s(z))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(z))) | (~b(s(elem!1), z)) | (~b(s(elem!1), s(z))))),
% 0.65/0.81 inference(rewrite,[status(thm)],[])).
% 0.65/0.82 tff(2465,plain,
% 0.65/0.82 (((~b(z, s(z))) | (~b(s(elem!1), s(z))) | (~b(s(elem!1), z))) <=> ((~b(z, s(z))) | (~b(s(elem!1), z)) | (~b(s(elem!1), s(z))))),
% 0.65/0.82 inference(rewrite,[status(thm)],[])).
% 0.65/0.82 tff(2466,plain,
% 0.65/0.82 (((~![X0: $i, X2: $i, X1: $i] : ((~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(z))) | (~b(s(elem!1), s(z))) | (~b(s(elem!1), z)))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(z))) | (~b(s(elem!1), z)) | (~b(s(elem!1), s(z)))))),
% 0.65/0.82 inference(monotonicity,[status(thm)],[2465])).
% 0.65/0.82 tff(2467,plain,
% 0.65/0.82 (((~![X0: $i, X2: $i, X1: $i] : ((~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(z))) | (~b(s(elem!1), s(z))) | (~b(s(elem!1), z)))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(z))) | (~b(s(elem!1), z)) | (~b(s(elem!1), s(z))))),
% 0.65/0.82 inference(transitivity,[status(thm)],[2466, 2464])).
% 0.65/0.82 tff(2468,plain,
% 0.65/0.82 ((~![X0: $i, X2: $i, X1: $i] : ((~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(z))) | (~b(s(elem!1), s(z))) | (~b(s(elem!1), z)))),
% 0.65/0.82 inference(quant_inst,[status(thm)],[])).
% 0.65/0.82 tff(2469,plain,
% 0.65/0.82 ((~![X0: $i, X2: $i, X1: $i] : ((~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(z))) | (~b(s(elem!1), z)) | (~b(s(elem!1), s(z)))),
% 0.65/0.82 inference(modus_ponens,[status(thm)],[2468, 2467])).
% 0.65/0.82 tff(2470,plain,
% 0.65/0.82 ($false),
% 0.65/0.82 inference(unit_resolution,[status(thm)],[2469, 117, 2463, 2417, 2391])).
% 0.65/0.82 tff(2471,plain,((~r(s(z), z)) | (~r(s(s(s(z))), z)) | (s(s(s(s(elem!1)))) = s(s(s(elem!1)))) | b(s(s(elem!1)), s(s(s(elem!1)))) | b(s(s(elem!1)), s(z)) | (~r(s(s(elem!1)), s(s(s(elem!1))))) | r(s(s(elem!1)), z)), inference(lemma,lemma(discharge,[]))).
% 0.65/0.82 tff(2472,plain,
% 0.65/0.82 ($false),
% 0.65/0.82 inference(unit_resolution,[status(thm)],[2471, 2372, 2371, 156, 180, 158, 2165, 2105])).
% 0.65/0.82 tff(2473,plain,((~r(s(s(s(z))), z)) | b(s(s(elem!1)), s(z)) | (s(s(elem!1)) = s(s(s(elem!1))))), inference(lemma,lemma(discharge,[]))).
% 0.65/0.82 tff(2474,plain,
% 0.65/0.82 (~r(s(s(s(z))), z)),
% 0.65/0.82 inference(unit_resolution,[status(thm)],[2473, 158, 145])).
% 0.65/0.82 tff(2475,plain,
% 0.65/0.82 (b(s(s(s(z))), z)),
% 0.65/0.82 inference(unit_resolution,[status(thm)],[823, 2474])).
% 0.65/0.82 tff(2476,plain,
% 0.65/0.82 (((~![X0: $i, X2: $i, X1: $i] : ((~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(elem!1)))), z)) | (~b(s(s(s(z))), s(s(s(s(elem!1)))))) | (~b(s(s(s(z))), z)))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(elem!1)))), z)) | (~b(s(s(s(z))), s(s(s(s(elem!1)))))) | (~b(s(s(s(z))), z)))),
% 0.65/0.82 inference(rewrite,[status(thm)],[])).
% 0.65/0.82 tff(2477,plain,
% 0.65/0.82 (((~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(s(s(s(elem!1)))), z)) | (~b(s(s(s(z))), s(s(s(s(elem!1)))))) | (~b(s(s(s(z))), z)))),
% 0.65/0.82 inference(rewrite,[status(thm)],[])).
% 0.65/0.82 tff(2478,plain,
% 0.65/0.82 (((~![X0: $i, X2: $i, X1: $i] : ((~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~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, X2: $i, X1: $i] : ((~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(elem!1)))), z)) | (~b(s(s(s(z))), s(s(s(s(elem!1)))))) | (~b(s(s(s(z))), z))))),
% 0.65/0.82 inference(monotonicity,[status(thm)],[2477])).
% 0.65/0.82 tff(2479,plain,
% 0.65/0.82 (((~![X0: $i, X2: $i, X1: $i] : ((~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~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, X2: $i, X1: $i] : ((~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(elem!1)))), z)) | (~b(s(s(s(z))), s(s(s(s(elem!1)))))) | (~b(s(s(s(z))), z)))),
% 0.65/0.82 inference(transitivity,[status(thm)],[2478, 2476])).
% 0.65/0.82 tff(2480,plain,
% 0.65/0.82 ((~![X0: $i, X2: $i, X1: $i] : ((~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~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)))))))),
% 0.65/0.82 inference(quant_inst,[status(thm)],[])).
% 0.65/0.82 tff(2481,plain,
% 0.65/0.82 ((~![X0: $i, X2: $i, X1: $i] : ((~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(elem!1)))), z)) | (~b(s(s(s(z))), s(s(s(s(elem!1)))))) | (~b(s(s(s(z))), z))),
% 0.65/0.82 inference(modus_ponens,[status(thm)],[2480, 2479])).
% 0.65/0.82 tff(2482,plain,
% 0.65/0.82 (~b(s(s(s(z))), s(s(s(s(elem!1)))))),
% 0.65/0.82 inference(unit_resolution,[status(thm)],[2481, 117, 338, 1310])).
% 0.65/0.82 tff(2483,plain,
% 0.65/0.82 (r(s(s(s(z))), s(s(s(s(elem!1)))))),
% 0.65/0.82 inference(unit_resolution,[status(thm)],[1413, 46, 279, 2482])).
% 0.65/0.82 tff(2484,plain,
% 0.65/0.82 (~b(s(s(s(s(elem!1)))), s(z))),
% 0.65/0.82 inference(unit_resolution,[status(thm)],[1316, 237, 1310])).
% 0.65/0.82 tff(2485,plain,
% 0.65/0.82 (~b(s(s(s(z))), s(z))),
% 0.65/0.82 inference(unit_resolution,[status(thm)],[1389, 338, 237])).
% 0.65/0.82 tff(2486,plain,
% 0.65/0.82 (r(s(s(s(z))), s(z))),
% 0.65/0.82 inference(unit_resolution,[status(thm)],[347, 2485])).
% 0.65/0.82 tff(2487,plain,
% 0.65/0.82 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(elem!1)))), s(z))) | (~r(s(s(s(z))), s(s(s(s(elem!1)))))) | (~r(s(s(s(z))), s(z))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(s(elem!1)))), s(z))) | (~r(s(s(s(z))), s(s(s(s(elem!1)))))) | (~r(s(s(s(z))), s(z))))),
% 0.65/0.82 inference(rewrite,[status(thm)],[])).
% 0.65/0.82 tff(2488,plain,
% 0.65/0.82 (((~r(s(s(s(s(elem!1)))), s(z))) | (~r(s(s(s(z))), s(z))) | (~r(s(s(s(z))), s(s(s(s(elem!1))))))) <=> ((~r(s(s(s(s(elem!1)))), s(z))) | (~r(s(s(s(z))), s(s(s(s(elem!1)))))) | (~r(s(s(s(z))), s(z))))),
% 0.65/0.82 inference(rewrite,[status(thm)],[])).
% 0.65/0.82 tff(2489,plain,
% 0.65/0.82 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(elem!1)))), s(z))) | (~r(s(s(s(z))), s(z))) | (~r(s(s(s(z))), s(s(s(s(elem!1)))))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(elem!1)))), s(z))) | (~r(s(s(s(z))), s(s(s(s(elem!1)))))) | (~r(s(s(s(z))), s(z)))))),
% 0.65/0.82 inference(monotonicity,[status(thm)],[2488])).
% 0.65/0.82 tff(2490,plain,
% 0.65/0.82 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(elem!1)))), s(z))) | (~r(s(s(s(z))), s(z))) | (~r(s(s(s(z))), s(s(s(s(elem!1)))))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(s(elem!1)))), s(z))) | (~r(s(s(s(z))), s(s(s(s(elem!1)))))) | (~r(s(s(s(z))), s(z))))),
% 0.65/0.82 inference(transitivity,[status(thm)],[2489, 2487])).
% 0.65/0.82 tff(2491,plain,
% 0.65/0.82 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(elem!1)))), s(z))) | (~r(s(s(s(z))), s(z))) | (~r(s(s(s(z))), s(s(s(s(elem!1)))))))),
% 0.65/0.82 inference(quant_inst,[status(thm)],[])).
% 0.65/0.82 tff(2492,plain,
% 0.65/0.82 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(s(elem!1)))), s(z))) | (~r(s(s(s(z))), s(s(s(s(elem!1)))))) | (~r(s(s(s(z))), s(z)))),
% 0.65/0.82 inference(modus_ponens,[status(thm)],[2491, 2490])).
% 0.65/0.82 tff(2493,plain,
% 0.65/0.82 (~r(s(s(s(z))), s(s(s(s(elem!1)))))),
% 0.65/0.82 inference(unit_resolution,[status(thm)],[2492, 14, 1336, 2486])).
% 0.65/0.82 tff(2494,plain,
% 0.65/0.82 ($false),
% 0.65/0.82 inference(unit_resolution,[status(thm)],[1413, 46, 279, 2482, 2493])).
% 0.65/0.82 tff(2495,plain,((~b(s(s(s(z))), z)) | (~r(s(s(s(s(elem!1)))), s(z))) | (~b(s(s(s(s(elem!1)))), z)) | (~b(s(z), z))), inference(lemma,lemma(discharge,[]))).
% 0.65/0.82 tff(2496,plain,
% 0.65/0.82 (~r(s(s(s(s(elem!1)))), s(z))),
% 0.65/0.82 inference(unit_resolution,[status(thm)],[2495, 237, 338, 1310])).
% 0.65/0.82 tff(2497,plain,
% 0.65/0.82 ($false),
% 0.65/0.82 inference(unit_resolution,[status(thm)],[1327, 2496, 2484])).
% 0.65/0.82 tff(2498,plain,((~b(s(z), z)) | (~b(s(s(s(z))), z)) | (~b(s(s(s(s(elem!1)))), z))), inference(lemma,lemma(discharge,[]))).
% 0.65/0.82 tff(2499,plain,
% 0.65/0.82 (~b(s(z), z)),
% 0.65/0.82 inference(unit_resolution,[status(thm)],[2498, 1310, 338])).
% 0.65/0.82 tff(2500,plain,
% 0.65/0.82 (r(s(z), z)),
% 0.65/0.82 inference(unit_resolution,[status(thm)],[193, 2499])).
% 0.65/0.82 tff(2501,plain,
% 0.65/0.82 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), z)) | (~r(s(z), s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), z)))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(z), z)) | (~r(s(z), s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), z)))),
% 0.65/0.82 inference(rewrite,[status(thm)],[])).
% 0.65/0.82 tff(2502,plain,
% 0.65/0.82 (((~r(s(s(s(elem!1))), z)) | (~r(s(z), z)) | (~r(s(z), s(s(s(elem!1)))))) <=> ((~r(s(z), z)) | (~r(s(z), s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), z)))),
% 0.65/0.82 inference(rewrite,[status(thm)],[])).
% 0.65/0.82 tff(2503,plain,
% 0.65/0.82 (((~![X0: $i, X2: $i, X1: $i] : ((~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))))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), z)) | (~r(s(z), s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), z))))),
% 0.65/0.82 inference(monotonicity,[status(thm)],[2502])).
% 0.65/0.82 tff(2504,plain,
% 0.65/0.82 (((~![X0: $i, X2: $i, X1: $i] : ((~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))))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(z), z)) | (~r(s(z), s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), z)))),
% 0.65/0.82 inference(transitivity,[status(thm)],[2503, 2501])).
% 0.65/0.82 tff(2505,plain,
% 0.65/0.82 ((~![X0: $i, X2: $i, X1: $i] : ((~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))))))),
% 0.65/0.82 inference(quant_inst,[status(thm)],[])).
% 0.65/0.82 tff(2506,plain,
% 0.65/0.82 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(z), z)) | (~r(s(z), s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), z))),
% 0.65/0.82 inference(modus_ponens,[status(thm)],[2505, 2504])).
% 0.65/0.82 tff(2507,plain,
% 0.65/0.82 ($false),
% 0.65/0.82 inference(unit_resolution,[status(thm)],[2506, 14, 196, 213, 183])).
% 0.65/0.82 tff(2508,plain,((~r(s(s(s(elem!1))), z)) | (~r(s(z), s(s(s(elem!1))))) | (~r(s(z), z))), inference(lemma,lemma(discharge,[]))).
% 0.65/0.82 tff(2509,plain,
% 0.65/0.82 (~r(s(z), s(s(s(elem!1))))),
% 0.65/0.82 inference(unit_resolution,[status(thm)],[2508, 196, 2500])).
% 0.65/0.82 tff(2510,plain,
% 0.65/0.82 (b(s(z), s(s(s(elem!1))))),
% 0.65/0.82 inference(unit_resolution,[status(thm)],[235, 2509])).
% 0.65/0.82 tff(2511,plain,
% 0.65/0.82 (~r(s(s(s(elem!1))), s(z))),
% 0.65/0.82 inference(unit_resolution,[status(thm)],[2345, 14, 196, 2500])).
% 0.65/0.82 tff(2512,plain,
% 0.65/0.82 (b(s(s(s(elem!1))), s(z))),
% 0.65/0.82 inference(unit_resolution,[status(thm)],[467, 2511])).
% 0.65/0.82 tff(2513,plain,
% 0.65/0.82 (~r(s(s(elem!1)), z)),
% 0.65/0.82 inference(unit_resolution,[status(thm)],[204, 195, 196])).
% 0.65/0.82 tff(2514,plain,
% 0.65/0.82 (b(s(s(elem!1)), z)),
% 0.65/0.82 inference(unit_resolution,[status(thm)],[1025, 2513])).
% 0.65/0.82 tff(2515,plain,
% 0.65/0.82 (~b(s(s(s(s(elem!1)))), s(s(elem!1)))),
% 0.65/0.82 inference(unit_resolution,[status(thm)],[2191, 1036, 1310])).
% 0.65/0.82 tff(2516,plain,
% 0.65/0.82 (r(s(s(s(s(elem!1)))), s(s(elem!1)))),
% 0.65/0.82 inference(unit_resolution,[status(thm)],[1690, 146, 2515])).
% 0.65/0.82 tff(2517,plain,
% 0.65/0.82 (~b(s(s(s(z))), s(s(elem!1)))),
% 0.65/0.82 inference(unit_resolution,[status(thm)],[1217, 338, 1036])).
% 0.65/0.82 tff(2518,plain,
% 0.65/0.82 (r(s(s(s(z))), s(s(elem!1)))),
% 0.65/0.82 inference(unit_resolution,[status(thm)],[1421, 46, 2517, 1417])).
% 0.65/0.82 tff(2519,plain,
% 0.65/0.82 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(elem!1)))), s(s(elem!1)))) | (~r(s(s(s(z))), s(s(s(s(elem!1)))))) | (~r(s(s(s(z))), s(s(elem!1)))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(s(elem!1)))), s(s(elem!1)))) | (~r(s(s(s(z))), s(s(s(s(elem!1)))))) | (~r(s(s(s(z))), s(s(elem!1)))))),
% 0.65/0.82 inference(rewrite,[status(thm)],[])).
% 0.65/0.82 tff(2520,plain,
% 0.65/0.82 (((~r(s(s(s(s(elem!1)))), s(s(elem!1)))) | (~r(s(s(s(z))), s(s(elem!1)))) | (~r(s(s(s(z))), s(s(s(s(elem!1))))))) <=> ((~r(s(s(s(s(elem!1)))), s(s(elem!1)))) | (~r(s(s(s(z))), s(s(s(s(elem!1)))))) | (~r(s(s(s(z))), s(s(elem!1)))))),
% 0.65/0.82 inference(rewrite,[status(thm)],[])).
% 0.65/0.82 tff(2521,plain,
% 0.65/0.82 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(elem!1)))), s(s(elem!1)))) | (~r(s(s(s(z))), s(s(elem!1)))) | (~r(s(s(s(z))), s(s(s(s(elem!1)))))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(elem!1)))), s(s(elem!1)))) | (~r(s(s(s(z))), s(s(s(s(elem!1)))))) | (~r(s(s(s(z))), s(s(elem!1))))))),
% 0.65/0.82 inference(monotonicity,[status(thm)],[2520])).
% 0.65/0.82 tff(2522,plain,
% 0.65/0.82 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(elem!1)))), s(s(elem!1)))) | (~r(s(s(s(z))), s(s(elem!1)))) | (~r(s(s(s(z))), s(s(s(s(elem!1)))))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(s(elem!1)))), s(s(elem!1)))) | (~r(s(s(s(z))), s(s(s(s(elem!1)))))) | (~r(s(s(s(z))), s(s(elem!1)))))),
% 0.65/0.82 inference(transitivity,[status(thm)],[2521, 2519])).
% 0.65/0.82 tff(2523,plain,
% 0.65/0.82 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(elem!1)))), s(s(elem!1)))) | (~r(s(s(s(z))), s(s(elem!1)))) | (~r(s(s(s(z))), s(s(s(s(elem!1)))))))),
% 0.65/0.82 inference(quant_inst,[status(thm)],[])).
% 0.65/0.82 tff(2524,plain,
% 0.65/0.82 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(s(elem!1)))), s(s(elem!1)))) | (~r(s(s(s(z))), s(s(s(s(elem!1)))))) | (~r(s(s(s(z))), s(s(elem!1))))),
% 0.65/0.82 inference(modus_ponens,[status(thm)],[2523, 2522])).
% 0.65/0.82 tff(2525,plain,
% 0.65/0.82 ($false),
% 0.65/0.82 inference(unit_resolution,[status(thm)],[2524, 14, 1397, 2518, 2483])).
% 0.65/0.82 tff(2526,plain,((~b(s(s(s(z))), z)) | (~r(s(s(s(s(elem!1)))), s(s(elem!1)))) | (s(s(s(z))) = s(s(elem!1))) | (~b(s(s(s(s(elem!1)))), z)) | (~b(s(s(elem!1)), z))), inference(lemma,lemma(discharge,[]))).
% 0.65/0.82 tff(2527,plain,
% 0.65/0.82 (s(s(s(z))) = s(s(elem!1))),
% 0.65/0.82 inference(unit_resolution,[status(thm)],[2526, 2516, 338, 1310, 1036])).
% 0.65/0.82 tff(2528,plain,
% 0.65/0.82 (inj_0(s(s(s(z)))) = inj_0(s(s(elem!1)))),
% 0.65/0.82 inference(monotonicity,[status(thm)],[2527])).
% 0.65/0.82 tff(2529,plain,
% 0.65/0.82 (s(s(z)) = s(elem!1)),
% 0.65/0.82 inference(transitivity,[status(thm)],[95, 2528, 166])).
% 0.65/0.82 tff(2530,plain,
% 0.65/0.82 (inj_0(s(s(z))) = inj_0(s(elem!1))),
% 0.65/0.82 inference(monotonicity,[status(thm)],[2529])).
% 0.65/0.82 tff(2531,plain,
% 0.65/0.82 (inj_0(s(elem!1)) = inj_0(s(s(z)))),
% 0.65/0.82 inference(symmetry,[status(thm)],[2530])).
% 0.65/0.82 tff(2532,plain,
% 0.65/0.82 (elem!1 = s(z)),
% 0.65/0.82 inference(transitivity,[status(thm)],[1652, 2531, 82])).
% 0.65/0.82 tff(2533,plain,
% 0.65/0.82 (r(z, elem!1) <=> r(z, s(z))),
% 0.65/0.82 inference(monotonicity,[status(thm)],[2532])).
% 0.65/0.82 tff(2534,plain,
% 0.65/0.82 (r(z, s(z)) <=> r(z, elem!1)),
% 0.65/0.82 inference(symmetry,[status(thm)],[2533])).
% 0.65/0.82 tff(2535,plain,
% 0.65/0.82 (~r(s(s(elem!1)), s(z))),
% 0.65/0.82 inference(unit_resolution,[status(thm)],[2198, 146, 1336, 1036, 2500])).
% 0.65/0.82 tff(2536,plain,
% 0.65/0.82 (b(s(s(elem!1)), s(z))),
% 0.65/0.82 inference(unit_resolution,[status(thm)],[178, 2535])).
% 0.65/0.82 tff(2537,plain,
% 0.65/0.82 (((~![X0: $i, X2: $i, X1: $i] : ((~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), z)) | (~b(s(s(elem!1)), s(z))) | (~b(z, s(z))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(elem!1)), z)) | (~b(s(s(elem!1)), s(z))) | (~b(z, s(z))))),
% 0.65/0.82 inference(rewrite,[status(thm)],[])).
% 0.65/0.82 tff(2538,plain,
% 0.65/0.82 (((~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(s(elem!1)), s(z))) | (~b(z, s(z))))),
% 0.65/0.82 inference(rewrite,[status(thm)],[])).
% 0.65/0.82 tff(2539,plain,
% 0.65/0.82 (((~![X0: $i, X2: $i, X1: $i] : ((~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(z))) | (~b(s(s(elem!1)), s(z))) | (~b(s(s(elem!1)), z)))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), z)) | (~b(s(s(elem!1)), s(z))) | (~b(z, s(z)))))),
% 0.65/0.82 inference(monotonicity,[status(thm)],[2538])).
% 0.65/0.82 tff(2540,plain,
% 0.65/0.82 (((~![X0: $i, X2: $i, X1: $i] : ((~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(z))) | (~b(s(s(elem!1)), s(z))) | (~b(s(s(elem!1)), z)))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(elem!1)), z)) | (~b(s(s(elem!1)), s(z))) | (~b(z, s(z))))),
% 0.65/0.82 inference(transitivity,[status(thm)],[2539, 2537])).
% 0.65/0.82 tff(2541,plain,
% 0.65/0.82 ((~![X0: $i, X2: $i, X1: $i] : ((~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(z))) | (~b(s(s(elem!1)), s(z))) | (~b(s(s(elem!1)), z)))),
% 0.65/0.82 inference(quant_inst,[status(thm)],[])).
% 0.65/0.82 tff(2542,plain,
% 0.65/0.82 ((~![X0: $i, X2: $i, X1: $i] : ((~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(elem!1)), z)) | (~b(s(s(elem!1)), s(z))) | (~b(z, s(z)))),
% 0.65/0.82 inference(modus_ponens,[status(thm)],[2541, 2540])).
% 0.65/0.82 tff(2543,plain,
% 0.65/0.82 ($false),
% 0.65/0.82 inference(unit_resolution,[status(thm)],[2542, 117, 470, 1036, 574])).
% 0.65/0.82 tff(2544,plain,((~b(z, s(z))) | (~b(s(s(elem!1)), s(z))) | (~b(s(s(elem!1)), z))), inference(lemma,lemma(discharge,[]))).
% 0.65/0.83 tff(2545,plain,
% 0.65/0.83 (~b(s(s(elem!1)), z)),
% 0.65/0.83 inference(unit_resolution,[status(thm)],[2544, 574, 470])).
% 0.65/0.83 tff(2546,plain,
% 0.65/0.83 (r(s(s(elem!1)), z)),
% 0.65/0.83 inference(unit_resolution,[status(thm)],[1025, 2545])).
% 0.65/0.83 tff(2547,plain,
% 0.65/0.83 (((~![X0: $i, X2: $i, X1: $i] : ((~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), s(z))) | (~b(s(z), s(s(s(elem!1))))) | (~b(s(s(elem!1)), s(s(s(elem!1))))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(elem!1)), s(z))) | (~b(s(z), s(s(s(elem!1))))) | (~b(s(s(elem!1)), s(s(s(elem!1))))))),
% 0.65/0.83 inference(rewrite,[status(thm)],[])).
% 0.65/0.83 tff(2548,plain,
% 0.65/0.83 (((~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(z))) | (~b(s(z), s(s(s(elem!1))))) | (~b(s(s(elem!1)), s(s(s(elem!1))))))),
% 0.65/0.83 inference(rewrite,[status(thm)],[])).
% 0.65/0.83 tff(2549,plain,
% 0.65/0.83 (((~![X0: $i, X2: $i, X1: $i] : ((~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(elem!1)), s(z))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), s(z))) | (~b(s(z), s(s(s(elem!1))))) | (~b(s(s(elem!1)), s(s(s(elem!1)))))))),
% 0.65/0.83 inference(monotonicity,[status(thm)],[2548])).
% 0.65/0.83 tff(2550,plain,
% 0.65/0.83 (((~![X0: $i, X2: $i, X1: $i] : ((~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(elem!1)), s(z))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(elem!1)), s(z))) | (~b(s(z), s(s(s(elem!1))))) | (~b(s(s(elem!1)), s(s(s(elem!1))))))),
% 0.65/0.83 inference(transitivity,[status(thm)],[2549, 2547])).
% 0.65/0.83 tff(2551,plain,
% 0.65/0.83 ((~![X0: $i, X2: $i, X1: $i] : ((~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(elem!1)), s(z))))),
% 0.65/0.83 inference(quant_inst,[status(thm)],[])).
% 0.65/0.83 tff(2552,plain,
% 0.65/0.83 ((~![X0: $i, X2: $i, X1: $i] : ((~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(elem!1)), s(z))) | (~b(s(z), s(s(s(elem!1))))) | (~b(s(s(elem!1)), s(s(s(elem!1)))))),
% 0.65/0.83 inference(modus_ponens,[status(thm)],[2551, 2550])).
% 0.65/0.83 tff(2553,plain,
% 0.65/0.83 ($false),
% 0.65/0.83 inference(unit_resolution,[status(thm)],[2552, 117, 470, 324, 238])).
% 0.65/0.83 tff(2554,plain,((~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(s(s(elem!1)), s(z))) | (~b(s(z), s(s(s(elem!1)))))), inference(lemma,lemma(discharge,[]))).
% 0.65/0.83 tff(2555,plain,
% 0.65/0.83 (~b(s(s(elem!1)), s(s(s(elem!1))))),
% 0.65/0.83 inference(unit_resolution,[status(thm)],[2554, 238, 470])).
% 0.65/0.83 tff(2556,plain,
% 0.65/0.83 (r(s(s(elem!1)), s(s(s(elem!1))))),
% 0.65/0.83 inference(unit_resolution,[status(thm)],[253, 2555, 145])).
% 0.65/0.83 tff(2557,plain,
% 0.65/0.83 (~r(z, s(s(s(elem!1))))),
% 0.65/0.83 inference(unit_resolution,[status(thm)],[982, 2556, 2546])).
% 0.65/0.83 tff(2558,plain,
% 0.65/0.83 (b(z, s(s(s(elem!1))))),
% 0.65/0.83 inference(unit_resolution,[status(thm)],[692, 2557])).
% 0.65/0.83 tff(2559,plain,
% 0.65/0.83 (((~![X0: $i, X2: $i, X1: $i] : ((~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(s(elem!1))))) | (~b(z, s(z))) | (~b(s(z), s(s(s(elem!1))))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(s(s(elem!1))))) | (~b(z, s(z))) | (~b(s(z), s(s(s(elem!1))))))),
% 0.65/0.83 inference(rewrite,[status(thm)],[])).
% 0.65/0.83 tff(2560,plain,
% 0.65/0.83 (((~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(z, s(z))) | (~b(s(z), s(s(s(elem!1))))))),
% 0.65/0.83 inference(rewrite,[status(thm)],[])).
% 0.65/0.83 tff(2561,plain,
% 0.65/0.83 (((~![X0: $i, X2: $i, X1: $i] : ((~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(z, s(z))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(s(elem!1))))) | (~b(z, s(z))) | (~b(s(z), s(s(s(elem!1)))))))),
% 0.65/0.83 inference(monotonicity,[status(thm)],[2560])).
% 0.65/0.83 tff(2562,plain,
% 0.65/0.83 (((~![X0: $i, X2: $i, X1: $i] : ((~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(z, s(z))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(s(s(elem!1))))) | (~b(z, s(z))) | (~b(s(z), s(s(s(elem!1))))))),
% 0.65/0.83 inference(transitivity,[status(thm)],[2561, 2559])).
% 0.65/0.83 tff(2563,plain,
% 0.65/0.83 ((~![X0: $i, X2: $i, X1: $i] : ((~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(z, s(z))))),
% 0.65/0.83 inference(quant_inst,[status(thm)],[])).
% 0.65/0.83 tff(2564,plain,
% 0.65/0.83 ((~![X0: $i, X2: $i, X1: $i] : ((~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(s(s(elem!1))))) | (~b(z, s(z))) | (~b(s(z), s(s(s(elem!1)))))),
% 0.65/0.83 inference(modus_ponens,[status(thm)],[2563, 2562])).
% 0.65/0.83 tff(2565,plain,
% 0.65/0.83 ($false),
% 0.65/0.83 inference(unit_resolution,[status(thm)],[2564, 117, 2558, 238, 574])).
% 0.65/0.83 tff(2566,plain,((~b(s(z), s(s(s(elem!1))))) | (~b(z, s(z))) | (s(s(elem!1)) = s(s(s(elem!1)))) | (~b(s(s(elem!1)), s(z)))), inference(lemma,lemma(discharge,[]))).
% 0.65/0.83 tff(2567,plain,
% 0.65/0.83 (~b(z, s(z))),
% 0.65/0.83 inference(unit_resolution,[status(thm)],[2566, 2536, 145, 238])).
% 0.65/0.83 tff(2568,plain,
% 0.65/0.83 (r(z, s(z))),
% 0.65/0.83 inference(unit_resolution,[status(thm)],[599, 2567])).
% 0.65/0.83 tff(2569,plain,
% 0.65/0.83 (r(z, elem!1)),
% 0.65/0.83 inference(modus_ponens,[status(thm)],[2568, 2534])).
% 0.65/0.83 tff(2570,plain,
% 0.65/0.83 (~(s(s(s(s(s(s(elem!1)))))) = elem!1)),
% 0.65/0.83 inference(unit_resolution,[status(thm)],[1446, 2527])).
% 0.65/0.83 tff(2571,plain,
% 0.65/0.83 (s(z) = elem!1),
% 0.65/0.83 inference(transitivity,[status(thm)],[131, 2530, 257])).
% 0.65/0.83 tff(2572,plain,
% 0.65/0.83 (b(s(s(elem!1)), s(z)) <=> b(s(s(elem!1)), elem!1)),
% 0.65/0.83 inference(monotonicity,[status(thm)],[2571])).
% 0.65/0.83 tff(2573,plain,
% 0.65/0.83 (b(s(s(elem!1)), elem!1)),
% 0.65/0.83 inference(modus_ponens,[status(thm)],[2536, 2572])).
% 0.65/0.83 tff(2574,plain,
% 0.65/0.83 (b(s(s(s(elem!1))), s(z)) <=> b(s(s(s(elem!1))), elem!1)),
% 0.65/0.83 inference(monotonicity,[status(thm)],[2571])).
% 0.65/0.83 tff(2575,plain,
% 0.65/0.83 (b(s(s(s(elem!1))), elem!1)),
% 0.65/0.83 inference(modus_ponens,[status(thm)],[2010, 2574])).
% 0.65/0.83 tff(2576,plain,
% 0.65/0.83 (((~![X0: $i, X2: $i, X1: $i] : ((~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(s(s(elem!1))), s(s(elem!1)))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~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(s(s(elem!1))), s(s(elem!1)))))),
% 0.65/0.83 inference(rewrite,[status(thm)],[])).
% 0.65/0.83 tff(2577,plain,
% 0.65/0.83 ((~![X0: $i, X2: $i, X1: $i] : ((~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(s(s(elem!1))), s(s(elem!1)))))),
% 0.65/0.83 inference(quant_inst,[status(thm)],[])).
% 0.65/0.83 tff(2578,plain,
% 0.65/0.83 ((~![X0: $i, X2: $i, X1: $i] : ((~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(s(s(elem!1))), s(s(elem!1))))),
% 0.65/0.83 inference(modus_ponens,[status(thm)],[2577, 2576])).
% 0.65/0.83 tff(2579,plain,
% 0.65/0.83 (~b(s(s(s(elem!1))), s(s(elem!1)))),
% 0.65/0.83 inference(unit_resolution,[status(thm)],[2578, 117, 2573, 2575])).
% 0.65/0.83 tff(2580,plain,
% 0.65/0.83 (r(s(s(s(elem!1))), s(s(elem!1)))),
% 0.65/0.83 inference(unit_resolution,[status(thm)],[1547, 1539, 2579])).
% 0.65/0.83 tff(2581,plain,
% 0.65/0.83 (r(s(s(s(s(s(s(elem!1)))))), s(s(elem!1)))),
% 0.65/0.83 inference(unit_resolution,[status(thm)],[1794, 1578])).
% 0.65/0.83 tff(2582,assumption,(r(s(s(s(elem!1))), s(s(elem!1)))), introduced(assumption)).
% 0.65/0.83 tff(2583,plain,
% 0.65/0.83 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), s(s(elem!1)))) | (~r(s(s(s(s(s(s(elem!1)))))), s(s(elem!1)))) | (~r(s(s(s(s(s(s(elem!1)))))), s(s(s(elem!1))))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(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))))))),
% 0.65/0.83 inference(rewrite,[status(thm)],[])).
% 0.65/0.83 tff(2584,plain,
% 0.65/0.83 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), s(s(elem!1)))) | (~r(s(s(s(s(s(s(elem!1)))))), s(s(elem!1)))) | (~r(s(s(s(s(s(s(elem!1)))))), s(s(s(elem!1))))))),
% 0.65/0.83 inference(quant_inst,[status(thm)],[])).
% 0.65/0.83 tff(2585,plain,
% 0.65/0.83 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(elem!1))), s(s(elem!1)))) | (~r(s(s(s(s(s(s(elem!1)))))), s(s(elem!1)))) | (~r(s(s(s(s(s(s(elem!1)))))), s(s(s(elem!1)))))),
% 0.65/0.83 inference(modus_ponens,[status(thm)],[2584, 2583])).
% 0.65/0.83 tff(2586,plain,
% 0.65/0.83 ($false),
% 0.65/0.83 inference(unit_resolution,[status(thm)],[2585, 14, 2582, 2581, 2002])).
% 0.65/0.83 tff(2587,plain,((~b(s(s(s(s(s(s(elem!1)))))), elem!1)) | (~r(s(s(s(elem!1))), s(s(elem!1)))) | (~(s(s(s(z))) = s(s(elem!1)))) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(s(elem!1)), elem!1))), inference(lemma,lemma(discharge,[]))).
% 0.65/0.83 tff(2588,plain,
% 0.65/0.83 (~b(s(s(s(s(s(s(elem!1)))))), elem!1)),
% 0.65/0.83 inference(unit_resolution,[status(thm)],[2587, 2580, 2527, 2575, 2573])).
% 0.65/0.83 tff(2589,plain,
% 0.65/0.83 (r(s(s(s(s(s(s(elem!1)))))), elem!1)),
% 0.65/0.83 inference(unit_resolution,[status(thm)],[1599, 2588, 2570])).
% 0.65/0.83 tff(2590,plain,
% 0.65/0.83 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, elem!1)) | (~r(s(s(s(s(s(s(elem!1)))))), elem!1)) | (~r(s(s(s(s(s(s(elem!1)))))), z)))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, elem!1)) | (~r(s(s(s(s(s(s(elem!1)))))), elem!1)) | (~r(s(s(s(s(s(s(elem!1)))))), z)))),
% 0.65/0.83 inference(rewrite,[status(thm)],[])).
% 0.65/0.83 tff(2591,plain,
% 0.65/0.83 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, elem!1)) | (~r(s(s(s(s(s(s(elem!1)))))), elem!1)) | (~r(s(s(s(s(s(s(elem!1)))))), z)))),
% 0.65/0.83 inference(quant_inst,[status(thm)],[])).
% 0.65/0.83 tff(2592,plain,
% 0.65/0.83 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, elem!1)) | (~r(s(s(s(s(s(s(elem!1)))))), elem!1)) | (~r(s(s(s(s(s(s(elem!1)))))), z))),
% 0.65/0.83 inference(modus_ponens,[status(thm)],[2591, 2590])).
% 0.65/0.83 tff(2593,plain,
% 0.65/0.83 (~r(s(s(s(s(s(s(elem!1)))))), z)),
% 0.65/0.83 inference(unit_resolution,[status(thm)],[2592, 14, 2589, 2569])).
% 0.65/0.83 tff(2594,plain,
% 0.65/0.83 (b(s(s(s(s(s(s(elem!1)))))), z)),
% 0.65/0.83 inference(unit_resolution,[status(thm)],[1666, 46, 1663, 2593])).
% 0.65/0.83 tff(2595,plain,
% 0.65/0.83 (r(s(s(s(s(elem!1)))), s(z)) <=> r(s(s(s(s(elem!1)))), elem!1)),
% 0.65/0.83 inference(monotonicity,[status(thm)],[2571])).
% 0.65/0.83 tff(2596,plain,
% 0.65/0.83 (r(s(s(s(s(elem!1)))), elem!1)),
% 0.65/0.83 inference(modus_ponens,[status(thm)],[1336, 2595])).
% 0.65/0.83 tff(2597,plain,
% 0.65/0.83 (~r(s(s(s(s(s(s(elem!1)))))), s(s(s(s(elem!1)))))),
% 0.65/0.83 inference(unit_resolution,[status(thm)],[1822, 14, 2596, 2589])).
% 0.65/0.83 tff(2598,plain,
% 0.65/0.83 (b(s(s(s(s(s(s(elem!1)))))), s(s(s(s(elem!1)))))),
% 0.65/0.83 inference(unit_resolution,[status(thm)],[1619, 46, 2024, 2597])).
% 0.65/0.83 tff(2599,plain,
% 0.65/0.83 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, elem!1)) | (~r(z, s(s(s(s(elem!1)))))) | (~r(s(s(s(s(elem!1)))), elem!1)))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, elem!1)) | (~r(z, s(s(s(s(elem!1)))))) | (~r(s(s(s(s(elem!1)))), elem!1)))),
% 0.65/0.83 inference(rewrite,[status(thm)],[])).
% 0.65/0.83 tff(2600,plain,
% 0.65/0.83 (((~r(s(s(s(s(elem!1)))), elem!1)) | (~r(z, elem!1)) | (~r(z, s(s(s(s(elem!1))))))) <=> ((~r(z, elem!1)) | (~r(z, s(s(s(s(elem!1)))))) | (~r(s(s(s(s(elem!1)))), elem!1)))),
% 0.65/0.83 inference(rewrite,[status(thm)],[])).
% 0.65/0.83 tff(2601,plain,
% 0.65/0.83 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(elem!1)))), elem!1)) | (~r(z, elem!1)) | (~r(z, s(s(s(s(elem!1)))))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, elem!1)) | (~r(z, s(s(s(s(elem!1)))))) | (~r(s(s(s(s(elem!1)))), elem!1))))),
% 0.65/0.83 inference(monotonicity,[status(thm)],[2600])).
% 0.65/0.83 tff(2602,plain,
% 0.65/0.83 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(elem!1)))), elem!1)) | (~r(z, elem!1)) | (~r(z, s(s(s(s(elem!1)))))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, elem!1)) | (~r(z, s(s(s(s(elem!1)))))) | (~r(s(s(s(s(elem!1)))), elem!1)))),
% 0.65/0.83 inference(transitivity,[status(thm)],[2601, 2599])).
% 0.65/0.83 tff(2603,plain,
% 0.65/0.83 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(elem!1)))), elem!1)) | (~r(z, elem!1)) | (~r(z, s(s(s(s(elem!1)))))))),
% 0.65/0.83 inference(quant_inst,[status(thm)],[])).
% 0.65/0.83 tff(2604,plain,
% 0.65/0.83 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, elem!1)) | (~r(z, s(s(s(s(elem!1)))))) | (~r(s(s(s(s(elem!1)))), elem!1))),
% 0.65/0.83 inference(modus_ponens,[status(thm)],[2603, 2602])).
% 0.65/0.83 tff(2605,plain,
% 0.65/0.83 ((~r(z, elem!1)) | (~r(z, s(s(s(s(elem!1))))))),
% 0.65/0.83 inference(unit_resolution,[status(thm)],[2604, 14, 2596])).
% 0.65/0.83 tff(2606,plain,
% 0.65/0.83 (~r(z, s(s(s(s(elem!1)))))),
% 0.65/0.83 inference(unit_resolution,[status(thm)],[2605, 2569])).
% 0.65/0.83 tff(2607,plain,
% 0.65/0.83 ((z = s(s(s(s(elem!1))))) | b(z, s(s(s(s(elem!1)))))),
% 0.65/0.83 inference(unit_resolution,[status(thm)],[1644, 46, 2606])).
% 0.65/0.83 tff(2608,plain,
% 0.65/0.83 (b(z, s(s(s(s(elem!1)))))),
% 0.65/0.83 inference(unit_resolution,[status(thm)],[2607, 1626])).
% 0.65/0.83 tff(2609,plain,
% 0.65/0.83 (((~![X0: $i, X2: $i, X1: $i] : ((~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(s(s(elem!1)))))) | (~b(s(s(s(s(s(s(elem!1)))))), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(s(s(elem!1)))))), z)))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(s(s(s(elem!1)))))) | (~b(s(s(s(s(s(s(elem!1)))))), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(s(s(elem!1)))))), z)))),
% 0.65/0.83 inference(rewrite,[status(thm)],[])).
% 0.65/0.83 tff(2610,plain,
% 0.65/0.83 ((~![X0: $i, X2: $i, X1: $i] : ((~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(s(s(elem!1)))))) | (~b(s(s(s(s(s(s(elem!1)))))), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(s(s(elem!1)))))), z)))),
% 0.65/0.83 inference(quant_inst,[status(thm)],[])).
% 0.65/0.83 tff(2611,plain,
% 0.65/0.83 ((~![X0: $i, X2: $i, X1: $i] : ((~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(s(s(s(elem!1)))))) | (~b(s(s(s(s(s(s(elem!1)))))), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(s(s(elem!1)))))), z))),
% 0.65/0.83 inference(modus_ponens,[status(thm)],[2610, 2609])).
% 0.65/0.83 tff(2612,plain,
% 0.65/0.83 ($false),
% 0.65/0.83 inference(unit_resolution,[status(thm)],[2611, 117, 2608, 2598, 2594])).
% 0.65/0.83 tff(2613,plain,((s(s(s(s(elem!1)))) = s(s(elem!1))) | (s(s(elem!1)) = s(s(s(elem!1)))) | (~b(s(s(s(elem!1))), s(z))) | (~r(s(s(s(s(elem!1)))), s(z))) | (~b(s(z), s(s(s(elem!1))))) | (~b(s(s(s(z))), z)) | (~b(s(s(s(s(elem!1)))), z)) | (~b(s(s(elem!1)), z))), inference(lemma,lemma(discharge,[]))).
% 0.65/0.83 tff(2614,plain,
% 0.65/0.83 (s(s(s(s(elem!1)))) = s(s(elem!1))),
% 0.65/0.83 inference(unit_resolution,[status(thm)],[2613, 2514, 2512, 1336, 2510, 338, 1310, 145])).
% 0.65/0.83 tff(2615,plain,
% 0.65/0.83 (inj_0(s(s(s(s(elem!1))))) = inj_0(s(s(elem!1)))),
% 0.65/0.83 inference(monotonicity,[status(thm)],[2614])).
% 0.65/0.83 tff(2616,plain,
% 0.65/0.83 (inj_0(s(s(elem!1))) = inj_0(s(s(s(s(elem!1)))))),
% 0.65/0.83 inference(symmetry,[status(thm)],[2615])).
% 0.65/0.83 tff(2617,plain,
% 0.65/0.83 (s(elem!1) = s(s(s(elem!1)))),
% 0.65/0.83 inference(transitivity,[status(thm)],[167, 2616, 144])).
% 0.65/0.83 tff(2618,plain,
% 0.65/0.83 (r(s(s(elem!1)), s(elem!1)) <=> r(s(s(elem!1)), s(s(s(elem!1))))),
% 0.65/0.83 inference(monotonicity,[status(thm)],[2617])).
% 0.65/0.83 tff(2619,plain,
% 0.65/0.83 (r(s(s(elem!1)), s(s(s(elem!1)))) <=> r(s(s(elem!1)), s(elem!1))),
% 0.65/0.83 inference(symmetry,[status(thm)],[2618])).
% 0.65/0.83 tff(2620,plain,
% 0.65/0.83 (r(s(s(elem!1)), s(elem!1))),
% 0.65/0.83 inference(modus_ponens,[status(thm)],[195, 2619])).
% 0.65/0.83 tff(2621,plain,
% 0.65/0.83 (r(s(s(s(z))), s(s(s(s(elem!1))))) <=> r(s(s(s(z))), s(s(elem!1)))),
% 0.65/0.83 inference(monotonicity,[status(thm)],[2614])).
% 0.65/0.83 tff(2622,plain,
% 0.65/0.83 (r(s(s(s(z))), s(s(elem!1)))),
% 0.65/0.83 inference(modus_ponens,[status(thm)],[2483, 2621])).
% 0.65/0.83 tff(2623,plain,
% 0.65/0.83 (r(s(s(s(s(elem!1)))), s(z)) <=> r(s(s(elem!1)), s(z))),
% 0.65/0.83 inference(monotonicity,[status(thm)],[2614])).
% 0.65/0.83 tff(2624,plain,
% 0.65/0.83 (r(s(s(elem!1)), s(z))),
% 0.65/0.83 inference(modus_ponens,[status(thm)],[1336, 2623])).
% 0.65/0.83 tff(2625,plain,
% 0.65/0.83 ($false),
% 0.65/0.83 inference(unit_resolution,[status(thm)],[750, 14, 181, 283, 943])).
% 0.65/0.83 tff(2626,plain,((~r(s(s(s(z))), s(z))) | (~r(s(s(elem!1)), s(z))) | (~r(s(s(s(z))), s(s(elem!1))))), inference(lemma,lemma(discharge,[]))).
% 0.65/0.83 tff(2627,plain,
% 0.65/0.83 (~r(s(s(s(z))), s(z))),
% 0.65/0.83 inference(unit_resolution,[status(thm)],[2626, 2624, 2622])).
% 0.65/0.83 tff(2628,plain,
% 0.65/0.83 (b(s(s(s(z))), s(z))),
% 0.65/0.83 inference(unit_resolution,[status(thm)],[347, 2627])).
% 0.65/0.83 tff(2629,plain,
% 0.65/0.83 (~b(s(s(s(z))), s(elem!1))),
% 0.65/0.83 inference(unit_resolution,[status(thm)],[1139, 2628, 2510, 2614])).
% 0.65/0.83 tff(2630,plain,
% 0.65/0.83 (~(s(s(s(z))) = s(elem!1))),
% 0.65/0.83 inference(unit_resolution,[status(thm)],[623, 2614])).
% 0.65/0.83 tff(2631,plain,
% 0.65/0.83 (r(s(s(s(z))), s(elem!1))),
% 0.65/0.83 inference(unit_resolution,[status(thm)],[627, 46, 2630, 2629])).
% 0.65/0.83 tff(2632,plain,
% 0.65/0.83 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(elem!1)), s(elem!1))) | (~r(s(s(s(z))), s(elem!1))) | (~r(s(s(s(z))), s(s(elem!1)))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(elem!1)), s(elem!1))) | (~r(s(s(s(z))), s(elem!1))) | (~r(s(s(s(z))), s(s(elem!1)))))),
% 0.65/0.83 inference(rewrite,[status(thm)],[])).
% 0.65/0.83 tff(2633,plain,
% 0.65/0.83 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(elem!1)), s(elem!1))) | (~r(s(s(s(z))), s(elem!1))) | (~r(s(s(s(z))), s(s(elem!1)))))),
% 0.65/0.83 inference(quant_inst,[status(thm)],[])).
% 0.65/0.83 tff(2634,plain,
% 0.65/0.83 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(elem!1)), s(elem!1))) | (~r(s(s(s(z))), s(elem!1))) | (~r(s(s(s(z))), s(s(elem!1))))),
% 0.65/0.83 inference(modus_ponens,[status(thm)],[2633, 2632])).
% 0.65/0.83 tff(2635,plain,
% 0.65/0.83 (~r(s(s(elem!1)), s(elem!1))),
% 0.65/0.83 inference(unit_resolution,[status(thm)],[2634, 14, 2631, 2622])).
% 0.65/0.83 tff(2636,plain,
% 0.65/0.83 ($false),
% 0.65/0.83 inference(unit_resolution,[status(thm)],[2635, 2620])).
% 0.65/0.83 tff(2637,plain,((~r(s(s(elem!1)), s(s(s(elem!1))))) | (~r(s(s(s(s(elem!1)))), s(z))) | (~b(s(s(s(z))), z)) | (~b(s(s(s(s(elem!1)))), z)) | (s(s(elem!1)) = s(s(s(elem!1)))) | (~r(s(s(s(elem!1))), z))), inference(lemma,lemma(discharge,[]))).
% 0.65/0.83 tff(2638,plain,
% 0.65/0.83 (~r(s(s(elem!1)), s(s(s(elem!1))))),
% 0.65/0.83 inference(unit_resolution,[status(thm)],[2637, 1336, 338, 1310, 145, 196])).
% 0.65/0.83 tff(2639,plain,
% 0.65/0.83 (b(s(s(elem!1)), s(s(s(elem!1))))),
% 0.65/0.83 inference(unit_resolution,[status(thm)],[253, 2638, 145])).
% 0.65/0.83 tff(2640,plain,
% 0.65/0.83 (~b(s(z), s(s(elem!1)))),
% 0.65/0.83 inference(unit_resolution,[status(thm)],[1879, 117, 2639, 2510])).
% 0.65/0.83 tff(2641,plain,
% 0.65/0.83 (r(s(z), s(s(elem!1)))),
% 0.65/0.83 inference(unit_resolution,[status(thm)],[416, 2640])).
% 0.65/0.83 tff(2642,plain,
% 0.65/0.83 (~r(s(s(elem!1)), z)),
% 0.65/0.83 inference(unit_resolution,[status(thm)],[1467, 2641, 2500])).
% 0.65/0.83 tff(2643,plain,
% 0.65/0.83 (b(s(s(elem!1)), z)),
% 0.65/0.83 inference(unit_resolution,[status(thm)],[1025, 2642])).
% 0.65/0.83 tff(2644,plain,
% 0.65/0.83 (s(s(s(s(elem!1)))) = s(s(elem!1))),
% 0.65/0.83 inference(unit_resolution,[status(thm)],[2613, 2643, 2512, 1336, 2510, 338, 1310, 145])).
% 0.65/0.83 tff(2645,plain,
% 0.65/0.83 (inj_0(s(s(s(s(elem!1))))) = inj_0(s(s(elem!1)))),
% 0.65/0.83 inference(monotonicity,[status(thm)],[2644])).
% 0.65/0.83 tff(2646,plain,
% 0.65/0.83 (s(s(s(elem!1))) = s(elem!1)),
% 0.65/0.83 inference(transitivity,[status(thm)],[295, 2645, 166])).
% 0.65/0.83 tff(2647,plain,
% 0.65/0.83 (b(s(s(s(elem!1))), s(z)) <=> b(s(elem!1), s(z))),
% 0.65/0.83 inference(monotonicity,[status(thm)],[2646])).
% 0.65/0.83 tff(2648,plain,
% 0.65/0.83 (b(s(elem!1), s(z))),
% 0.65/0.83 inference(modus_ponens,[status(thm)],[2512, 2647])).
% 0.65/0.83 tff(2649,plain,
% 0.65/0.83 (~b(s(s(elem!1)), s(z))),
% 0.65/0.83 inference(unit_resolution,[status(thm)],[2554, 2639, 2510])).
% 0.65/0.83 tff(2650,plain,
% 0.65/0.83 (r(s(s(elem!1)), s(z))),
% 0.65/0.83 inference(unit_resolution,[status(thm)],[178, 2649])).
% 0.65/0.83 tff(2651,plain,
% 0.65/0.83 (r(s(elem!1), z)),
% 0.65/0.83 inference(unit_resolution,[status(thm)],[880, 2644, 196])).
% 0.65/0.83 tff(2652,plain,
% 0.65/0.83 (~r(s(s(s(s(z)))), s(z))),
% 0.65/0.83 inference(unit_resolution,[status(thm)],[1177, 2651, 2641, 145, 2644, 2643, 2650])).
% 0.65/0.83 tff(2653,plain,
% 0.65/0.83 (b(s(s(s(s(z)))), s(z))),
% 0.65/0.83 inference(unit_resolution,[status(thm)],[554, 2652])).
% 0.65/0.83 tff(2654,plain,
% 0.65/0.83 (~b(s(s(s(s(z)))), s(elem!1))),
% 0.65/0.83 inference(unit_resolution,[status(thm)],[791, 117, 2653, 2648])).
% 0.65/0.83 tff(2655,plain,
% 0.65/0.83 (~(s(s(s(s(z)))) = s(elem!1))),
% 0.65/0.83 inference(unit_resolution,[status(thm)],[476, 2644])).
% 0.65/0.83 tff(2656,plain,
% 0.65/0.83 (r(s(s(s(s(z)))), s(elem!1))),
% 0.65/0.83 inference(unit_resolution,[status(thm)],[504, 46, 2655, 2654])).
% 0.65/0.83 tff(2657,plain,
% 0.65/0.83 (r(s(s(s(z))), s(s(s(s(elem!1))))) <=> r(s(s(s(z))), s(s(elem!1)))),
% 0.65/0.83 inference(monotonicity,[status(thm)],[2644])).
% 0.65/0.83 tff(2658,plain,
% 0.65/0.83 (r(s(s(s(z))), s(s(elem!1)))),
% 0.65/0.83 inference(modus_ponens,[status(thm)],[2483, 2657])).
% 0.65/0.83 tff(2659,plain,
% 0.65/0.83 (((~![X0: $i, X2: $i, X1: $i] : ((~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(z))), s(s(elem!1)))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~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(z))), s(s(elem!1)))))),
% 0.65/0.83 inference(rewrite,[status(thm)],[])).
% 0.65/0.83 tff(2660,plain,
% 0.65/0.83 (((~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(s(z))), s(z))) | (~r(s(s(s(z))), s(s(elem!1)))))),
% 0.65/0.83 inference(rewrite,[status(thm)],[])).
% 0.65/0.83 tff(2661,plain,
% 0.65/0.83 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~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, X2: $i, X1: $i] : ((~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(z))), s(s(elem!1))))))),
% 0.65/0.83 inference(monotonicity,[status(thm)],[2660])).
% 0.65/0.83 tff(2662,plain,
% 0.65/0.83 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~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, X2: $i, X1: $i] : ((~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(z))), s(s(elem!1)))))),
% 0.65/0.83 inference(transitivity,[status(thm)],[2661, 2659])).
% 0.65/0.83 tff(2663,plain,
% 0.65/0.83 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(s(elem!1)))) | (~r(s(s(s(z))), s(s(elem!1)))) | (~r(s(s(s(z))), s(z))))),
% 0.65/0.83 inference(quant_inst,[status(thm)],[])).
% 0.65/0.83 tff(2664,plain,
% 0.65/0.83 ((~![X0: $i, X2: $i, X1: $i] : ((~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(z))), s(s(elem!1))))),
% 0.65/0.83 inference(modus_ponens,[status(thm)],[2663, 2662])).
% 0.65/0.83 tff(2665,plain,
% 0.65/0.83 (~r(s(s(s(z))), s(z))),
% 0.65/0.83 inference(unit_resolution,[status(thm)],[2664, 14, 2641, 2658])).
% 0.65/0.83 tff(2666,plain,
% 0.65/0.83 (b(s(s(s(z))), s(z))),
% 0.65/0.83 inference(unit_resolution,[status(thm)],[347, 2665])).
% 0.65/0.83 tff(2667,plain,
% 0.65/0.83 (~b(s(s(s(z))), s(elem!1))),
% 0.65/0.83 inference(unit_resolution,[status(thm)],[1139, 2666, 2510, 2644])).
% 0.65/0.83 tff(2668,plain,
% 0.65/0.83 (~(s(s(s(z))) = s(elem!1))),
% 0.65/0.83 inference(unit_resolution,[status(thm)],[623, 2644])).
% 0.65/0.83 tff(2669,plain,
% 0.65/0.83 (r(s(s(s(z))), s(elem!1))),
% 0.65/0.83 inference(unit_resolution,[status(thm)],[627, 46, 2668, 2667])).
% 0.65/0.83 tff(2670,plain,
% 0.65/0.83 (((~![X0: $i, X2: $i, X1: $i] : ((~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), s(z))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(z))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(z))))),
% 0.65/0.83 inference(rewrite,[status(thm)],[])).
% 0.65/0.83 tff(2671,plain,
% 0.65/0.83 (((~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(z))), s(s(s(s(z))))))) <=> ((~b(s(s(s(z))), s(z))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(z))))),
% 0.65/0.83 inference(rewrite,[status(thm)],[])).
% 0.65/0.83 tff(2672,plain,
% 0.65/0.83 (((~![X0: $i, X2: $i, X1: $i] : ((~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(s(s(z))), s(s(s(s(z)))))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), s(z))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(z)))))),
% 0.65/0.83 inference(monotonicity,[status(thm)],[2671])).
% 0.65/0.83 tff(2673,plain,
% 0.65/0.83 (((~![X0: $i, X2: $i, X1: $i] : ((~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(s(s(z))), s(s(s(s(z)))))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(z))))),
% 0.65/0.83 inference(transitivity,[status(thm)],[2672, 2670])).
% 0.65/0.84 tff(2674,plain,
% 0.65/0.84 ((~![X0: $i, X2: $i, X1: $i] : ((~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(s(s(z))), s(s(s(s(z)))))))),
% 0.65/0.84 inference(quant_inst,[status(thm)],[])).
% 0.65/0.84 tff(2675,plain,
% 0.65/0.84 ((~![X0: $i, X2: $i, X1: $i] : ((~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(z)))),
% 0.65/0.84 inference(modus_ponens,[status(thm)],[2674, 2673])).
% 0.65/0.84 tff(2676,plain,
% 0.65/0.84 (~b(s(s(s(z))), s(s(s(s(z)))))),
% 0.65/0.84 inference(unit_resolution,[status(thm)],[2675, 117, 2653, 2666])).
% 0.65/0.84 tff(2677,plain,
% 0.65/0.84 ((s(s(s(z))) = s(s(s(s(z))))) <=> (s(s(s(s(z)))) = s(s(s(z))))),
% 0.65/0.84 inference(commutativity,[status(thm)],[])).
% 0.65/0.84 tff(2678,plain,
% 0.65/0.84 ((s(s(s(s(z)))) = s(s(s(z)))) <=> (s(s(s(z))) = s(s(s(s(z)))))),
% 0.65/0.84 inference(symmetry,[status(thm)],[2677])).
% 0.65/0.84 tff(2679,plain,
% 0.65/0.84 ((~(s(s(s(s(z)))) = s(s(s(z))))) <=> (~(s(s(s(z))) = s(s(s(s(z))))))),
% 0.65/0.84 inference(monotonicity,[status(thm)],[2678])).
% 0.65/0.84 tff(2680,plain,
% 0.65/0.84 (~(s(s(s(z))) = s(s(s(s(z)))))),
% 0.65/0.84 inference(modus_ponens,[status(thm)],[524, 2679])).
% 0.65/0.84 tff(2681,plain,
% 0.65/0.84 (((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((s(s(s(z))) = s(s(s(s(z))))) | b(s(s(s(z))), s(s(s(s(z))))) | r(s(s(s(z))), s(s(s(s(z))))))) <=> ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (s(s(s(z))) = s(s(s(s(z))))) | b(s(s(s(z))), s(s(s(s(z))))) | r(s(s(s(z))), s(s(s(s(z))))))),
% 0.65/0.84 inference(rewrite,[status(thm)],[])).
% 0.65/0.84 tff(2682,plain,
% 0.65/0.84 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((s(s(s(z))) = s(s(s(s(z))))) | b(s(s(s(z))), s(s(s(s(z))))) | r(s(s(s(z))), s(s(s(s(z))))))),
% 0.65/0.84 inference(quant_inst,[status(thm)],[])).
% 0.65/0.84 tff(2683,plain,
% 0.65/0.84 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (s(s(s(z))) = s(s(s(s(z))))) | b(s(s(s(z))), s(s(s(s(z))))) | r(s(s(s(z))), s(s(s(s(z)))))),
% 0.65/0.84 inference(modus_ponens,[status(thm)],[2682, 2681])).
% 0.65/0.84 tff(2684,plain,
% 0.65/0.84 ((s(s(s(z))) = s(s(s(s(z))))) | b(s(s(s(z))), s(s(s(s(z))))) | r(s(s(s(z))), s(s(s(s(z)))))),
% 0.65/0.84 inference(unit_resolution,[status(thm)],[2683, 46])).
% 0.65/0.84 tff(2685,plain,
% 0.65/0.84 (b(s(s(s(z))), s(s(s(s(z))))) | r(s(s(s(z))), s(s(s(s(z)))))),
% 0.65/0.84 inference(unit_resolution,[status(thm)],[2684, 2680])).
% 0.65/0.84 tff(2686,plain,
% 0.65/0.84 (r(s(s(s(z))), s(s(s(s(z)))))),
% 0.65/0.84 inference(unit_resolution,[status(thm)],[2685, 2676])).
% 0.65/0.84 tff(2687,plain,
% 0.65/0.84 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(z))), s(s(s(s(z)))))) | (~r(s(s(s(z))), s(elem!1))) | (~r(s(s(s(s(z)))), s(elem!1))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(z))), s(s(s(s(z)))))) | (~r(s(s(s(z))), s(elem!1))) | (~r(s(s(s(s(z)))), s(elem!1))))),
% 0.65/0.84 inference(rewrite,[status(thm)],[])).
% 0.65/0.84 tff(2688,plain,
% 0.65/0.84 (((~r(s(s(s(s(z)))), s(elem!1))) | (~r(s(s(s(z))), s(elem!1))) | (~r(s(s(s(z))), s(s(s(s(z))))))) <=> ((~r(s(s(s(z))), s(s(s(s(z)))))) | (~r(s(s(s(z))), s(elem!1))) | (~r(s(s(s(s(z)))), s(elem!1))))),
% 0.65/0.84 inference(rewrite,[status(thm)],[])).
% 0.65/0.84 tff(2689,plain,
% 0.65/0.84 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(z)))), s(elem!1))) | (~r(s(s(s(z))), s(elem!1))) | (~r(s(s(s(z))), s(s(s(s(z)))))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(z))), s(s(s(s(z)))))) | (~r(s(s(s(z))), s(elem!1))) | (~r(s(s(s(s(z)))), s(elem!1)))))),
% 0.65/0.84 inference(monotonicity,[status(thm)],[2688])).
% 0.65/0.84 tff(2690,plain,
% 0.65/0.84 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(z)))), s(elem!1))) | (~r(s(s(s(z))), s(elem!1))) | (~r(s(s(s(z))), s(s(s(s(z)))))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(z))), s(s(s(s(z)))))) | (~r(s(s(s(z))), s(elem!1))) | (~r(s(s(s(s(z)))), s(elem!1))))),
% 0.65/0.84 inference(transitivity,[status(thm)],[2689, 2687])).
% 0.65/0.84 tff(2691,plain,
% 0.65/0.84 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(z)))), s(elem!1))) | (~r(s(s(s(z))), s(elem!1))) | (~r(s(s(s(z))), s(s(s(s(z)))))))),
% 0.65/0.84 inference(quant_inst,[status(thm)],[])).
% 0.65/0.84 tff(2692,plain,
% 0.65/0.84 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(z))), s(s(s(s(z)))))) | (~r(s(s(s(z))), s(elem!1))) | (~r(s(s(s(s(z)))), s(elem!1)))),
% 0.65/0.84 inference(modus_ponens,[status(thm)],[2691, 2690])).
% 0.65/0.84 tff(2693,plain,
% 0.65/0.84 ($false),
% 0.65/0.84 inference(unit_resolution,[status(thm)],[2692, 14, 2686, 2669, 2656])).
% 0.65/0.84 tff(2694,plain,((~r(s(s(s(s(elem!1)))), s(z))) | (s(s(elem!1)) = s(s(s(elem!1)))) | (~r(s(s(s(elem!1))), z)) | (~b(s(s(s(z))), z)) | (~b(s(s(s(s(elem!1)))), z))), inference(lemma,lemma(discharge,[]))).
% 0.65/0.84 tff(2695,plain,
% 0.65/0.84 (~r(s(s(s(s(elem!1)))), s(z))),
% 0.65/0.84 inference(unit_resolution,[status(thm)],[2694, 1211, 145, 338, 1310])).
% 0.65/0.84 tff(2696,plain,
% 0.65/0.84 (b(s(s(s(s(elem!1)))), s(z))),
% 0.65/0.84 inference(unit_resolution,[status(thm)],[1327, 2695])).
% 0.65/0.84 tff(2697,plain,
% 0.65/0.84 (~b(s(s(s(z))), s(s(s(s(elem!1)))))),
% 0.65/0.84 inference(unit_resolution,[status(thm)],[2183, 117, 1311, 848])).
% 0.65/0.84 tff(2698,plain,
% 0.65/0.84 (r(s(s(s(z))), s(s(s(s(elem!1)))))),
% 0.65/0.84 inference(unit_resolution,[status(thm)],[1413, 46, 279, 2697])).
% 0.65/0.84 tff(2699,plain,
% 0.65/0.84 (~r(s(s(s(elem!1))), s(z))),
% 0.65/0.84 inference(unit_resolution,[status(thm)],[2345, 14, 1211, 183])).
% 0.65/0.84 tff(2700,plain,
% 0.65/0.84 (b(s(s(s(elem!1))), s(z))),
% 0.65/0.84 inference(unit_resolution,[status(thm)],[467, 2699])).
% 0.65/0.84 tff(2701,plain,
% 0.65/0.84 (((~![X0: $i, X2: $i, X1: $i] : ((~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), s(z))) | (~b(s(s(s(elem!1))), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), s(z))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(s(s(elem!1))), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), s(z))))),
% 0.65/0.84 inference(rewrite,[status(thm)],[])).
% 0.65/0.84 tff(2702,plain,
% 0.65/0.84 (((~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(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))))),
% 0.65/0.84 inference(rewrite,[status(thm)],[])).
% 0.65/0.84 tff(2703,plain,
% 0.65/0.84 (((~![X0: $i, X2: $i, X1: $i] : ((~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(s(elem!1))), s(s(s(s(elem!1)))))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), s(z))) | (~b(s(s(s(elem!1))), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), s(z)))))),
% 0.65/0.84 inference(monotonicity,[status(thm)],[2702])).
% 0.65/0.84 tff(2704,plain,
% 0.65/0.84 (((~![X0: $i, X2: $i, X1: $i] : ((~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(s(elem!1))), s(s(s(s(elem!1)))))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(s(s(elem!1))), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), s(z))))),
% 0.65/0.84 inference(transitivity,[status(thm)],[2703, 2701])).
% 0.65/0.84 tff(2705,plain,
% 0.65/0.84 ((~![X0: $i, X2: $i, X1: $i] : ((~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(s(elem!1))), s(s(s(s(elem!1)))))))),
% 0.65/0.84 inference(quant_inst,[status(thm)],[])).
% 0.65/0.84 tff(2706,plain,
% 0.65/0.84 ((~![X0: $i, X2: $i, X1: $i] : ((~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(s(s(elem!1))), s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), s(z)))),
% 0.65/0.84 inference(modus_ponens,[status(thm)],[2705, 2704])).
% 0.65/0.84 tff(2707,plain,
% 0.65/0.84 (~b(s(s(s(elem!1))), s(s(s(s(elem!1)))))),
% 0.65/0.84 inference(unit_resolution,[status(thm)],[2706, 117, 1311, 2700])).
% 0.65/0.84 tff(2708,plain,
% 0.65/0.84 (r(s(s(s(elem!1))), s(s(s(s(elem!1)))))),
% 0.65/0.84 inference(unit_resolution,[status(thm)],[448, 2707, 323])).
% 0.65/0.84 tff(2709,plain,
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% 0.65/0.84 inference(rewrite,[status(thm)],[])).
% 0.65/0.84 tff(2710,plain,
% 0.65/0.84 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(z))), s(s(s(s(elem!1)))))) | (~r(s(s(s(elem!1))), s(s(s(s(elem!1)))))) | (~r(s(s(s(elem!1))), s(s(s(z))))))),
% 0.65/0.84 inference(quant_inst,[status(thm)],[])).
% 0.65/0.84 tff(2711,plain,
% 0.65/0.84 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(z))), s(s(s(s(elem!1)))))) | (~r(s(s(s(elem!1))), s(s(s(s(elem!1)))))) | (~r(s(s(s(elem!1))), s(s(s(z)))))),
% 0.65/0.84 inference(modus_ponens,[status(thm)],[2710, 2709])).
% 0.65/0.84 tff(2712,plain,
% 0.65/0.84 (~r(s(s(s(elem!1))), s(s(s(z))))),
% 0.65/0.84 inference(unit_resolution,[status(thm)],[2711, 14, 2708, 2698])).
% 0.65/0.84 tff(2713,plain,
% 0.65/0.84 (~b(s(s(s(elem!1))), s(s(s(z))))),
% 0.65/0.84 inference(unit_resolution,[status(thm)],[2353, 117, 2700, 848])).
% 0.65/0.84 tff(2714,plain,
% 0.65/0.84 ((s(s(s(elem!1))) = s(s(s(z)))) | r(s(s(s(elem!1))), s(s(s(z))))),
% 0.65/0.84 inference(unit_resolution,[status(thm)],[2341, 46, 2713])).
% 0.65/0.84 tff(2715,plain,
% 0.65/0.84 (s(s(s(elem!1))) = s(s(s(z)))),
% 0.65/0.84 inference(unit_resolution,[status(thm)],[2714, 2712])).
% 0.65/0.84 tff(2716,plain,
% 0.65/0.84 (b(s(s(s(elem!1))), z) <=> b(s(s(s(z))), z)),
% 0.65/0.84 inference(monotonicity,[status(thm)],[2715])).
% 0.65/0.84 tff(2717,plain,
% 0.65/0.84 (b(s(s(s(z))), z) <=> b(s(s(s(elem!1))), z)),
% 0.65/0.84 inference(symmetry,[status(thm)],[2716])).
% 0.65/0.84 tff(2718,plain,
% 0.65/0.84 (b(s(s(s(elem!1))), z)),
% 0.65/0.84 inference(modus_ponens,[status(thm)],[338, 2717])).
% 0.65/0.84 tff(2719,plain,
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% 0.65/0.84 inference(unit_resolution,[status(thm)],[1188, 2718])).
% 0.65/0.84 tff(2720,plain,(b(s(s(s(elem!1))), z) | (~b(s(s(s(z))), z)) | (s(s(s(elem!1))) = s(s(s(s(elem!1))))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(s(elem!1)))), s(z))) | (~r(s(z), z))), inference(lemma,lemma(discharge,[]))).
% 0.65/0.84 tff(2721,plain,
% 0.65/0.84 (~b(s(s(s(z))), s(z))),
% 0.65/0.84 inference(unit_resolution,[status(thm)],[2720, 2696, 338, 290, 1188, 2500])).
% 0.65/0.84 tff(2722,plain,
% 0.65/0.84 (r(s(s(s(z))), s(z))),
% 0.65/0.84 inference(unit_resolution,[status(thm)],[347, 2721])).
% 0.65/0.84 tff(2723,plain,
% 0.65/0.84 (~r(s(z), s(s(s(elem!1))))),
% 0.65/0.84 inference(unit_resolution,[status(thm)],[2508, 1211, 2500])).
% 0.65/0.84 tff(2724,plain,
% 0.65/0.84 (b(s(z), s(s(s(elem!1))))),
% 0.65/0.84 inference(unit_resolution,[status(thm)],[235, 2723])).
% 0.65/0.84 tff(2725,plain,
% 0.65/0.84 (~b(s(s(s(s(elem!1)))), s(s(s(elem!1))))),
% 0.65/0.84 inference(unit_resolution,[status(thm)],[1679, 2696, 2724])).
% 0.65/0.84 tff(2726,plain,
% 0.65/0.84 (r(s(s(s(s(elem!1)))), s(s(s(elem!1))))),
% 0.65/0.84 inference(unit_resolution,[status(thm)],[1347, 2725, 156])).
% 0.65/0.84 tff(2727,plain,
% 0.65/0.84 (~r(s(z), s(s(s(elem!1))))),
% 0.65/0.84 inference(unit_resolution,[status(thm)],[2508, 196, 183])).
% 0.65/0.84 tff(2728,plain,
% 0.65/0.84 (b(s(z), s(s(s(elem!1))))),
% 0.65/0.84 inference(unit_resolution,[status(thm)],[235, 2727])).
% 0.65/0.84 tff(2729,plain,
% 0.65/0.84 (~r(s(s(elem!1)), s(s(s(elem!1))))),
% 0.65/0.84 inference(unit_resolution,[status(thm)],[204, 182, 196])).
% 0.65/0.84 tff(2730,plain,
% 0.65/0.84 (b(s(s(elem!1)), s(s(s(elem!1))))),
% 0.65/0.84 inference(unit_resolution,[status(thm)],[253, 2729, 145])).
% 0.65/0.84 tff(2731,plain,
% 0.65/0.84 (~b(s(s(elem!1)), s(z))),
% 0.65/0.84 inference(unit_resolution,[status(thm)],[2554, 2730, 2728])).
% 0.65/0.84 tff(2732,plain,
% 0.65/0.84 (r(s(s(elem!1)), s(z))),
% 0.65/0.84 inference(unit_resolution,[status(thm)],[178, 2731])).
% 0.65/0.84 tff(2733,plain,
% 0.65/0.84 ($false),
% 0.65/0.84 inference(unit_resolution,[status(thm)],[186, 14, 2732, 182, 183])).
% 0.65/0.84 tff(2734,plain,((~r(s(s(elem!1)), z)) | (~r(s(z), z)) | (s(s(elem!1)) = s(s(s(elem!1)))) | (~r(s(s(s(elem!1))), z))), inference(lemma,lemma(discharge,[]))).
% 0.65/0.84 tff(2735,plain,
% 0.65/0.84 (~r(s(s(elem!1)), z)),
% 0.65/0.84 inference(unit_resolution,[status(thm)],[2734, 1211, 145, 2500])).
% 0.65/0.84 tff(2736,plain,
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% 0.65/0.84 inference(unit_resolution,[status(thm)],[1025, 2735])).
% 0.65/0.84 tff(2737,plain,
% 0.65/0.84 (~b(s(s(s(s(elem!1)))), s(s(elem!1)))),
% 0.65/0.84 inference(unit_resolution,[status(thm)],[2191, 2736, 1310])).
% 0.65/0.84 tff(2738,plain,
% 0.65/0.84 (~r(s(s(s(elem!1))), s(z))),
% 0.65/0.84 inference(unit_resolution,[status(thm)],[2345, 14, 1211, 2500])).
% 0.65/0.84 tff(2739,plain,
% 0.65/0.84 (b(s(s(s(elem!1))), s(z))),
% 0.65/0.84 inference(unit_resolution,[status(thm)],[467, 2738])).
% 0.65/0.84 tff(2740,plain,
% 0.65/0.84 (~b(s(s(elem!1)), s(s(s(elem!1))))),
% 0.65/0.84 inference(unit_resolution,[status(thm)],[2554, 470, 238])).
% 0.65/0.84 tff(2741,plain,
% 0.65/0.84 (r(s(s(elem!1)), s(s(s(elem!1))))),
% 0.65/0.84 inference(unit_resolution,[status(thm)],[253, 2740, 145])).
% 0.65/0.84 tff(2742,plain,
% 0.65/0.84 (~r(s(s(s(s(elem!1)))), s(s(elem!1)))),
% 0.65/0.84 inference(unit_resolution,[status(thm)],[2220, 2741, 1337])).
% 0.65/0.84 tff(2743,plain,
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% 0.65/0.84 inference(unit_resolution,[status(thm)],[1690, 2742, 2211])).
% 0.65/0.84 tff(2744,plain,
% 0.65/0.84 (inj_0(s(s(s(s(elem!1))))) = inj_0(s(s(elem!1)))),
% 0.65/0.84 inference(monotonicity,[status(thm)],[2743])).
% 0.65/0.84 tff(2745,plain,
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% 0.65/0.84 tff(2746,plain,
% 0.65/0.84 (b(s(s(s(elem!1))), s(z)) <=> b(s(elem!1), s(z))),
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% 0.65/0.84 tff(2747,plain,
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% 0.65/0.84 inference(modus_ponens,[status(thm)],[2010, 2746])).
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% 0.65/0.84 tff(2749,plain,
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% 0.65/0.84 tff(2750,plain,
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% 0.65/0.84 ((elem!1 = s(s(s(s(z))))) <=> (s(s(elem!1)) = s(s(s(s(z)))))),
% 0.65/0.84 inference(monotonicity,[status(thm)],[2750])).
% 0.65/0.84 tff(2752,plain,
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% 0.65/0.84 inference(transitivity,[status(thm)],[2751, 2418])).
% 0.65/0.84 tff(2753,plain,
% 0.65/0.84 ((s(s(s(s(z)))) = s(s(elem!1))) <=> (elem!1 = s(s(s(s(z)))))),
% 0.65/0.84 inference(symmetry,[status(thm)],[2752])).
% 0.65/0.84 tff(2754,plain,
% 0.65/0.84 (s(s(s(s(s(elem!1))))) = s(s(s(elem!1)))),
% 0.65/0.84 inference(monotonicity,[status(thm)],[2743])).
% 0.65/0.84 tff(2755,plain,
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% 0.65/0.84 inference(transitivity,[status(thm)],[2754, 295, 2744, 166])).
% 0.65/0.84 tff(2756,plain,
% 0.65/0.84 (s(s(s(s(s(s(elem!1)))))) = s(s(elem!1))),
% 0.65/0.84 inference(monotonicity,[status(thm)],[2755])).
% 0.65/0.84 tff(2757,plain,
% 0.65/0.84 ((s(s(s(s(s(s(elem!1)))))) = s(s(s(s(z))))) <=> (s(s(elem!1)) = s(s(s(s(z)))))),
% 0.65/0.84 inference(monotonicity,[status(thm)],[2756])).
% 0.65/0.84 tff(2758,plain,
% 0.65/0.84 ((s(s(s(s(s(s(elem!1)))))) = s(s(s(s(z))))) <=> (s(s(s(s(z)))) = s(s(elem!1)))),
% 0.65/0.84 inference(transitivity,[status(thm)],[2757, 2418])).
% 0.65/0.84 tff(2759,plain,
% 0.65/0.84 ((s(s(s(s(s(s(elem!1)))))) = s(s(s(s(z))))) <=> (s(s(s(s(z)))) = elem!1)),
% 0.65/0.84 inference(transitivity,[status(thm)],[2758, 2753, 294])).
% 0.65/0.84 tff(2760,plain,
% 0.65/0.84 ((~(s(s(s(s(s(s(elem!1)))))) = s(s(s(s(z)))))) <=> (~(s(s(s(s(z)))) = elem!1))),
% 0.65/0.84 inference(monotonicity,[status(thm)],[2759])).
% 0.65/0.84 tff(2761,plain,
% 0.65/0.84 (~(s(s(s(s(z)))) = elem!1)),
% 0.65/0.84 inference(modus_ponens,[status(thm)],[319, 2760])).
% 0.65/0.84 tff(2762,plain,
% 0.65/0.84 (inj_0(s(s(elem!1))) = inj_0(s(s(s(s(elem!1)))))),
% 0.65/0.84 inference(symmetry,[status(thm)],[2744])).
% 0.65/0.84 tff(2763,plain,
% 0.65/0.84 (s(elem!1) = s(s(s(elem!1)))),
% 0.65/0.84 inference(transitivity,[status(thm)],[167, 2762, 144])).
% 0.65/0.84 tff(2764,plain,
% 0.65/0.84 (r(s(s(elem!1)), s(elem!1)) <=> r(s(s(elem!1)), s(s(s(elem!1))))),
% 0.65/0.84 inference(monotonicity,[status(thm)],[2763])).
% 0.65/0.84 tff(2765,plain,
% 0.65/0.84 (r(s(s(elem!1)), s(s(s(elem!1)))) <=> r(s(s(elem!1)), s(elem!1))),
% 0.65/0.84 inference(symmetry,[status(thm)],[2764])).
% 0.65/0.84 tff(2766,plain,
% 0.65/0.84 (r(s(s(elem!1)), s(elem!1))),
% 0.65/0.84 inference(modus_ponens,[status(thm)],[2741, 2765])).
% 0.65/0.84 tff(2767,assumption,(r(s(s(elem!1)), s(elem!1))), introduced(assumption)).
% 0.65/0.84 tff(2768,plain,
% 0.65/0.84 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(elem!1)), s(elem!1))) | (~r(s(s(s(s(z)))), s(elem!1))) | (~r(s(s(s(s(z)))), s(s(elem!1)))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(elem!1)), s(elem!1))) | (~r(s(s(s(s(z)))), s(elem!1))) | (~r(s(s(s(s(z)))), s(s(elem!1)))))),
% 0.65/0.84 inference(rewrite,[status(thm)],[])).
% 0.65/0.84 tff(2769,plain,
% 0.65/0.84 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(elem!1)), s(elem!1))) | (~r(s(s(s(s(z)))), s(elem!1))) | (~r(s(s(s(s(z)))), s(s(elem!1)))))),
% 0.65/0.84 inference(quant_inst,[status(thm)],[])).
% 0.65/0.84 tff(2770,plain,
% 0.65/0.84 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(elem!1)), s(elem!1))) | (~r(s(s(s(s(z)))), s(elem!1))) | (~r(s(s(s(s(z)))), s(s(elem!1))))),
% 0.65/0.84 inference(modus_ponens,[status(thm)],[2769, 2768])).
% 0.65/0.84 tff(2771,plain,
% 0.65/0.84 (~r(s(s(s(s(z)))), s(s(elem!1)))),
% 0.65/0.84 inference(unit_resolution,[status(thm)],[2770, 14, 2767, 793])).
% 0.65/0.84 tff(2772,plain,
% 0.65/0.84 ($false),
% 0.65/0.84 inference(unit_resolution,[status(thm)],[2771, 573])).
% 0.65/0.84 tff(2773,plain,((~b(s(s(s(s(z)))), s(z))) | (~(s(s(elem!1)) = elem!1)) | (~r(s(s(elem!1)), s(elem!1))) | (s(s(s(s(z)))) = elem!1) | (s(s(s(s(z)))) = s(elem!1)) | (~b(s(elem!1), s(z))) | (~b(s(s(elem!1)), s(z)))), inference(lemma,lemma(discharge,[]))).
% 0.65/0.84 tff(2774,plain,
% 0.65/0.84 (~b(s(s(s(s(z)))), s(z))),
% 0.65/0.84 inference(unit_resolution,[status(thm)],[2773, 2749, 2766, 2761, 2748, 2747, 470])).
% 0.65/0.84 tff(2775,plain,
% 0.65/0.84 (r(s(s(s(s(z)))), s(z))),
% 0.65/0.84 inference(unit_resolution,[status(thm)],[554, 2774])).
% 0.65/0.84 tff(2776,plain,
% 0.65/0.84 (~b(z, s(z))),
% 0.65/0.84 inference(unit_resolution,[status(thm)],[2566, 470, 145, 238])).
% 0.65/0.84 tff(2777,plain,
% 0.65/0.84 (r(z, s(z))),
% 0.65/0.84 inference(unit_resolution,[status(thm)],[599, 2776])).
% 0.65/0.84 tff(2778,plain,
% 0.65/0.84 (~r(z, s(s(s(s(z)))))),
% 0.65/0.84 inference(unit_resolution,[status(thm)],[22, 2775, 2777])).
% 0.65/0.84 tff(2779,plain,
% 0.65/0.84 (b(z, s(s(s(s(z)))))),
% 0.65/0.84 inference(unit_resolution,[status(thm)],[51, 2778])).
% 0.65/0.84 tff(2780,assumption,(b(s(s(s(z))), s(s(s(s(z)))))), introduced(assumption)).
% 0.65/0.84 tff(2781,plain,
% 0.65/0.84 (((~![X0: $i, X2: $i, X1: $i] : ((~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(z, s(s(s(s(z)))))) | (~b(s(s(s(z))), z)))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(z, s(s(s(s(z)))))) | (~b(s(s(s(z))), z)))),
% 0.65/0.84 inference(rewrite,[status(thm)],[])).
% 0.65/0.84 tff(2782,plain,
% 0.65/0.84 (((~b(z, s(s(s(s(z)))))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(z))), z))) <=> ((~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(z, s(s(s(s(z)))))) | (~b(s(s(s(z))), z)))),
% 0.65/0.84 inference(rewrite,[status(thm)],[])).
% 0.65/0.84 tff(2783,plain,
% 0.65/0.84 (((~![X0: $i, X2: $i, X1: $i] : ((~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(s(s(z)))))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(z))), z)))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(z, s(s(s(s(z)))))) | (~b(s(s(s(z))), z))))),
% 0.65/0.84 inference(monotonicity,[status(thm)],[2782])).
% 0.65/0.84 tff(2784,plain,
% 0.65/0.84 (((~![X0: $i, X2: $i, X1: $i] : ((~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(s(s(z)))))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(z))), z)))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(z, s(s(s(s(z)))))) | (~b(s(s(s(z))), z)))),
% 0.65/0.84 inference(transitivity,[status(thm)],[2783, 2781])).
% 0.65/0.84 tff(2785,plain,
% 0.65/0.84 ((~![X0: $i, X2: $i, X1: $i] : ((~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(s(s(z)))))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(z))), z)))),
% 0.65/0.84 inference(quant_inst,[status(thm)],[])).
% 0.65/0.84 tff(2786,plain,
% 0.65/0.84 ((~![X0: $i, X2: $i, X1: $i] : ((~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(z, s(s(s(s(z)))))) | (~b(s(s(s(z))), z))),
% 0.65/0.84 inference(modus_ponens,[status(thm)],[2785, 2784])).
% 0.65/0.84 tff(2787,plain,
% 0.65/0.84 ($false),
% 0.65/0.84 inference(unit_resolution,[status(thm)],[2786, 117, 1110, 2780, 338])).
% 0.65/0.84 tff(2788,plain,((~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(z, s(s(s(s(z)))))) | (~b(s(s(s(z))), z))), inference(lemma,lemma(discharge,[]))).
% 0.65/0.84 tff(2789,plain,
% 0.65/0.84 (~b(s(s(s(z))), s(s(s(s(z)))))),
% 0.65/0.84 inference(unit_resolution,[status(thm)],[2788, 2779, 338])).
% 0.65/0.84 tff(2790,plain,
% 0.65/0.84 (r(s(s(s(z))), s(s(s(s(z)))))),
% 0.65/0.84 inference(unit_resolution,[status(thm)],[2685, 2789])).
% 0.65/0.84 tff(2791,plain,
% 0.65/0.84 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(z))), s(z))) | (~r(s(s(s(z))), s(s(s(s(z)))))) | (~r(s(s(s(s(z)))), s(z))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(z))), s(z))) | (~r(s(s(s(z))), s(s(s(s(z)))))) | (~r(s(s(s(s(z)))), s(z))))),
% 0.65/0.84 inference(rewrite,[status(thm)],[])).
% 0.65/0.85 tff(2792,plain,
% 0.65/0.85 (((~r(s(s(s(s(z)))), s(z))) | (~r(s(s(s(z))), s(z))) | (~r(s(s(s(z))), s(s(s(s(z))))))) <=> ((~r(s(s(s(z))), s(z))) | (~r(s(s(s(z))), s(s(s(s(z)))))) | (~r(s(s(s(s(z)))), s(z))))),
% 0.65/0.85 inference(rewrite,[status(thm)],[])).
% 0.65/0.85 tff(2793,plain,
% 0.65/0.85 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(z)))), s(z))) | (~r(s(s(s(z))), s(z))) | (~r(s(s(s(z))), s(s(s(s(z)))))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(z))), s(z))) | (~r(s(s(s(z))), s(s(s(s(z)))))) | (~r(s(s(s(s(z)))), s(z)))))),
% 0.65/0.85 inference(monotonicity,[status(thm)],[2792])).
% 0.65/0.85 tff(2794,plain,
% 0.65/0.85 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(z)))), s(z))) | (~r(s(s(s(z))), s(z))) | (~r(s(s(s(z))), s(s(s(s(z)))))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(z))), s(z))) | (~r(s(s(s(z))), s(s(s(s(z)))))) | (~r(s(s(s(s(z)))), s(z))))),
% 0.65/0.85 inference(transitivity,[status(thm)],[2793, 2791])).
% 0.65/0.85 tff(2795,plain,
% 0.65/0.85 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(z)))), s(z))) | (~r(s(s(s(z))), s(z))) | (~r(s(s(s(z))), s(s(s(s(z)))))))),
% 0.65/0.85 inference(quant_inst,[status(thm)],[])).
% 0.65/0.85 tff(2796,plain,
% 0.65/0.85 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(z))), s(z))) | (~r(s(s(s(z))), s(s(s(s(z)))))) | (~r(s(s(s(s(z)))), s(z)))),
% 0.65/0.85 inference(modus_ponens,[status(thm)],[2795, 2794])).
% 0.65/0.85 tff(2797,plain,
% 0.65/0.85 ($false),
% 0.65/0.85 inference(unit_resolution,[status(thm)],[2796, 14, 2790, 2775, 283])).
% 0.65/0.85 tff(2798,plain,((~b(s(s(elem!1)), s(z))) | (~r(s(s(s(z))), s(z))) | (~b(s(s(s(z))), z)) | (~b(s(s(s(elem!1))), s(z))) | b(s(s(s(s(elem!1)))), s(s(elem!1))) | (~r(s(s(s(s(elem!1)))), s(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,[]))).
% 0.65/0.85 tff(2799,plain,
% 0.65/0.85 (~b(s(s(elem!1)), s(z))),
% 0.65/0.85 inference(unit_resolution,[status(thm)],[2798, 2722, 338, 2739, 2737, 2726, 145, 2724])).
% 0.65/0.85 tff(2800,plain,
% 0.65/0.85 (r(s(s(elem!1)), s(z))),
% 0.65/0.85 inference(unit_resolution,[status(thm)],[178, 2799])).
% 0.65/0.85 tff(2801,plain,
% 0.65/0.85 (~r(s(s(s(z))), s(s(elem!1)))),
% 0.65/0.85 inference(unit_resolution,[status(thm)],[2626, 2800, 2722])).
% 0.65/0.85 tff(2802,plain,
% 0.65/0.85 (~b(s(s(s(z))), s(s(elem!1)))),
% 0.65/0.85 inference(unit_resolution,[status(thm)],[1217, 2736, 338])).
% 0.65/0.85 tff(2803,plain,
% 0.65/0.85 ((s(s(s(z))) = s(s(elem!1))) | r(s(s(s(z))), s(s(elem!1)))),
% 0.65/0.85 inference(unit_resolution,[status(thm)],[1421, 46, 2802])).
% 0.65/0.85 tff(2804,plain,
% 0.65/0.85 (s(s(s(z))) = s(s(elem!1))),
% 0.65/0.85 inference(unit_resolution,[status(thm)],[2803, 2801])).
% 0.65/0.85 tff(2805,plain,
% 0.65/0.85 (s(s(s(s(z)))) = s(s(s(elem!1)))),
% 0.65/0.85 inference(monotonicity,[status(thm)],[2804])).
% 0.65/0.85 tff(2806,plain,
% 0.65/0.85 (s(s(s(elem!1))) = s(s(s(s(z))))),
% 0.65/0.85 inference(symmetry,[status(thm)],[2805])).
% 0.65/0.85 tff(2807,plain,
% 0.65/0.85 ((s(s(s(s(s(s(elem!1)))))) = s(s(s(elem!1)))) <=> (s(s(s(s(s(s(elem!1)))))) = s(s(s(s(z)))))),
% 0.65/0.85 inference(monotonicity,[status(thm)],[2806])).
% 0.65/0.85 tff(2808,plain,
% 0.65/0.85 ((s(s(s(s(s(s(elem!1)))))) = s(s(s(s(z))))) <=> (s(s(s(s(s(s(elem!1)))))) = s(s(s(elem!1))))),
% 0.65/0.85 inference(symmetry,[status(thm)],[2807])).
% 0.65/0.85 tff(2809,plain,
% 0.65/0.85 ((~(s(s(s(s(s(s(elem!1)))))) = s(s(s(s(z)))))) <=> (~(s(s(s(s(s(s(elem!1)))))) = s(s(s(elem!1)))))),
% 0.65/0.85 inference(monotonicity,[status(thm)],[2808])).
% 0.65/0.85 tff(2810,plain,
% 0.65/0.85 (~(s(s(s(s(s(s(elem!1)))))) = s(s(s(elem!1))))),
% 0.65/0.85 inference(modus_ponens,[status(thm)],[319, 2809])).
% 0.65/0.85 tff(2811,plain,
% 0.65/0.85 (~(s(s(s(s(s(s(elem!1)))))) = elem!1)),
% 0.65/0.85 inference(unit_resolution,[status(thm)],[1446, 2804])).
% 0.65/0.85 tff(2812,plain,
% 0.65/0.85 (inj_0(s(s(s(z)))) = inj_0(s(s(elem!1)))),
% 0.65/0.85 inference(monotonicity,[status(thm)],[2804])).
% 0.65/0.85 tff(2813,plain,
% 0.65/0.85 (s(s(z)) = s(elem!1)),
% 0.65/0.85 inference(transitivity,[status(thm)],[95, 2812, 166])).
% 0.65/0.85 tff(2814,plain,
% 0.65/0.85 (inj_0(s(s(z))) = inj_0(s(elem!1))),
% 0.65/0.85 inference(monotonicity,[status(thm)],[2813])).
% 0.65/0.85 tff(2815,plain,
% 0.65/0.85 (s(z) = elem!1),
% 0.65/0.85 inference(transitivity,[status(thm)],[131, 2814, 257])).
% 0.65/0.85 tff(2816,plain,
% 0.65/0.85 (r(s(s(elem!1)), s(z)) <=> r(s(s(elem!1)), elem!1)),
% 0.65/0.85 inference(monotonicity,[status(thm)],[2815])).
% 0.65/0.85 tff(2817,plain,
% 0.65/0.85 (r(s(s(elem!1)), elem!1)),
% 0.65/0.85 inference(modus_ponens,[status(thm)],[2800, 2816])).
% 0.65/0.85 tff(2818,plain,
% 0.65/0.85 (inj_0(s(elem!1)) = inj_0(s(s(z)))),
% 0.65/0.85 inference(symmetry,[status(thm)],[2814])).
% 0.65/0.85 tff(2819,plain,
% 0.65/0.85 (elem!1 = s(z)),
% 0.65/0.85 inference(transitivity,[status(thm)],[1652, 2818, 82])).
% 0.65/0.85 tff(2820,plain,
% 0.65/0.85 (r(z, elem!1) <=> r(z, s(z))),
% 0.65/0.85 inference(monotonicity,[status(thm)],[2819])).
% 0.65/0.85 tff(2821,plain,
% 0.65/0.85 (r(z, s(z)) <=> r(z, elem!1)),
% 0.65/0.85 inference(symmetry,[status(thm)],[2820])).
% 0.65/0.85 tff(2822,plain,
% 0.65/0.85 (b(z, elem!1) <=> b(z, s(z))),
% 0.65/0.85 inference(monotonicity,[status(thm)],[2819])).
% 0.65/0.85 tff(2823,plain,
% 0.65/0.85 ((~b(z, elem!1)) <=> (~b(z, s(z)))),
% 0.65/0.85 inference(monotonicity,[status(thm)],[2822])).
% 0.65/0.85 tff(2824,plain,
% 0.65/0.85 (r(z, s(s(s(s(z))))) <=> r(z, s(s(s(elem!1))))),
% 0.65/0.85 inference(monotonicity,[status(thm)],[2805])).
% 0.65/0.85 tff(2825,plain,
% 0.65/0.85 (r(s(s(s(z))), s(s(s(s(z))))) <=> r(s(s(elem!1)), s(s(s(elem!1))))),
% 0.65/0.85 inference(monotonicity,[status(thm)],[2804, 2805])).
% 0.65/0.85 tff(2826,plain,
% 0.65/0.85 (r(s(s(elem!1)), s(s(s(elem!1)))) <=> r(s(s(s(z))), s(s(s(s(z)))))),
% 0.65/0.85 inference(symmetry,[status(thm)],[2825])).
% 0.65/0.85 tff(2827,plain,
% 0.65/0.85 ((~r(s(s(elem!1)), s(s(s(elem!1))))) <=> (~r(s(s(s(z))), s(s(s(s(z))))))),
% 0.65/0.85 inference(monotonicity,[status(thm)],[2826])).
% 0.65/0.85 tff(2828,plain,
% 0.65/0.85 (r(s(s(s(z))), s(s(s(elem!1)))) <=> r(s(s(elem!1)), s(s(s(elem!1))))),
% 0.65/0.85 inference(monotonicity,[status(thm)],[2804])).
% 0.65/0.85 tff(2829,plain,
% 0.65/0.85 ((~r(s(s(s(z))), s(s(s(elem!1))))) <=> (~r(s(s(elem!1)), s(s(s(elem!1)))))),
% 0.65/0.85 inference(monotonicity,[status(thm)],[2828])).
% 0.65/0.85 tff(2830,plain,
% 0.65/0.85 (~b(s(s(s(elem!1))), s(s(s(s(elem!1)))))),
% 0.65/0.85 inference(unit_resolution,[status(thm)],[2706, 117, 2696, 2739])).
% 0.65/0.85 tff(2831,plain,
% 0.65/0.85 (r(s(s(s(elem!1))), s(s(s(s(elem!1)))))),
% 0.65/0.85 inference(unit_resolution,[status(thm)],[448, 2830, 290])).
% 0.65/0.85 tff(2832,plain,
% 0.65/0.85 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(z))), s(s(s(elem!1))))) | (~r(s(s(s(z))), s(s(s(s(elem!1)))))) | (~r(s(s(s(elem!1))), s(s(s(s(elem!1)))))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(z))), s(s(s(elem!1))))) | (~r(s(s(s(z))), s(s(s(s(elem!1)))))) | (~r(s(s(s(elem!1))), s(s(s(s(elem!1)))))))),
% 0.65/0.85 inference(rewrite,[status(thm)],[])).
% 0.65/0.85 tff(2833,plain,
% 0.65/0.85 (((~r(s(s(s(elem!1))), s(s(s(s(elem!1)))))) | (~r(s(s(s(z))), s(s(s(s(elem!1)))))) | (~r(s(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(s(s(elem!1)))))) | (~r(s(s(s(elem!1))), s(s(s(s(elem!1)))))))),
% 0.65/0.85 inference(rewrite,[status(thm)],[])).
% 0.65/0.85 tff(2834,plain,
% 0.65/0.85 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), s(s(s(s(elem!1)))))) | (~r(s(s(s(z))), s(s(s(s(elem!1)))))) | (~r(s(s(s(z))), s(s(s(elem!1))))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(z))), s(s(s(elem!1))))) | (~r(s(s(s(z))), s(s(s(s(elem!1)))))) | (~r(s(s(s(elem!1))), s(s(s(s(elem!1))))))))),
% 0.65/0.85 inference(monotonicity,[status(thm)],[2833])).
% 0.65/0.85 tff(2835,plain,
% 0.65/0.85 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), s(s(s(s(elem!1)))))) | (~r(s(s(s(z))), s(s(s(s(elem!1)))))) | (~r(s(s(s(z))), s(s(s(elem!1))))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(z))), s(s(s(elem!1))))) | (~r(s(s(s(z))), s(s(s(s(elem!1)))))) | (~r(s(s(s(elem!1))), s(s(s(s(elem!1)))))))),
% 0.65/0.85 inference(transitivity,[status(thm)],[2834, 2832])).
% 0.65/0.85 tff(2836,plain,
% 0.65/0.85 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), s(s(s(s(elem!1)))))) | (~r(s(s(s(z))), s(s(s(s(elem!1)))))) | (~r(s(s(s(z))), s(s(s(elem!1))))))),
% 0.65/0.85 inference(quant_inst,[status(thm)],[])).
% 0.65/0.85 tff(2837,plain,
% 0.65/0.85 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(z))), s(s(s(elem!1))))) | (~r(s(s(s(z))), s(s(s(s(elem!1)))))) | (~r(s(s(s(elem!1))), s(s(s(s(elem!1))))))),
% 0.65/0.85 inference(modus_ponens,[status(thm)],[2836, 2835])).
% 0.65/0.85 tff(2838,plain,
% 0.65/0.85 (~r(s(s(s(z))), s(s(s(elem!1))))),
% 0.65/0.85 inference(unit_resolution,[status(thm)],[2837, 14, 2831, 2483])).
% 0.65/0.85 tff(2839,plain,
% 0.65/0.85 (~r(s(s(elem!1)), s(s(s(elem!1))))),
% 0.65/0.85 inference(modus_ponens,[status(thm)],[2838, 2829])).
% 0.65/0.85 tff(2840,plain,
% 0.65/0.85 (~r(s(s(s(z))), s(s(s(s(z)))))),
% 0.65/0.85 inference(modus_ponens,[status(thm)],[2839, 2827])).
% 0.65/0.85 tff(2841,plain,
% 0.65/0.85 (b(s(s(s(z))), s(s(s(s(z)))))),
% 0.65/0.85 inference(unit_resolution,[status(thm)],[2685, 2840])).
% 0.65/0.85 tff(2842,plain,
% 0.65/0.85 (~b(z, s(s(s(s(z)))))),
% 0.65/0.85 inference(unit_resolution,[status(thm)],[2788, 2841, 338])).
% 0.65/0.85 tff(2843,plain,
% 0.65/0.85 (r(z, s(s(s(s(z)))))),
% 0.65/0.85 inference(unit_resolution,[status(thm)],[51, 2842])).
% 0.65/0.85 tff(2844,plain,
% 0.65/0.85 (r(z, s(s(s(elem!1))))),
% 0.65/0.85 inference(modus_ponens,[status(thm)],[2843, 2824])).
% 0.65/0.85 tff(2845,plain,
% 0.65/0.85 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(s(elem!1))))) | (~r(z, s(s(s(s(elem!1)))))) | (~r(s(s(s(s(elem!1)))), s(s(s(elem!1))))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, s(s(s(elem!1))))) | (~r(z, s(s(s(s(elem!1)))))) | (~r(s(s(s(s(elem!1)))), s(s(s(elem!1))))))),
% 0.65/0.85 inference(rewrite,[status(thm)],[])).
% 0.65/0.85 tff(2846,plain,
% 0.65/0.85 (((~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(z, s(s(s(s(elem!1)))))) | (~r(s(s(s(s(elem!1)))), s(s(s(elem!1))))))),
% 0.65/0.85 inference(rewrite,[status(thm)],[])).
% 0.65/0.85 tff(2847,plain,
% 0.65/0.85 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~r(z, s(s(s(elem!1))))) | (~r(z, s(s(s(s(elem!1)))))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(s(elem!1))))) | (~r(z, s(s(s(s(elem!1)))))) | (~r(s(s(s(s(elem!1)))), s(s(s(elem!1)))))))),
% 0.65/0.85 inference(monotonicity,[status(thm)],[2846])).
% 0.65/0.85 tff(2848,plain,
% 0.65/0.85 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~r(z, s(s(s(elem!1))))) | (~r(z, s(s(s(s(elem!1)))))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, s(s(s(elem!1))))) | (~r(z, s(s(s(s(elem!1)))))) | (~r(s(s(s(s(elem!1)))), s(s(s(elem!1))))))),
% 0.65/0.85 inference(transitivity,[status(thm)],[2847, 2845])).
% 0.65/0.85 tff(2849,plain,
% 0.65/0.85 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~r(z, s(s(s(elem!1))))) | (~r(z, s(s(s(s(elem!1)))))))),
% 0.65/0.85 inference(quant_inst,[status(thm)],[])).
% 0.65/0.85 tff(2850,plain,
% 0.65/0.85 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, s(s(s(elem!1))))) | (~r(z, s(s(s(s(elem!1)))))) | (~r(s(s(s(s(elem!1)))), s(s(s(elem!1)))))),
% 0.65/0.85 inference(modus_ponens,[status(thm)],[2849, 2848])).
% 0.65/0.85 tff(2851,plain,
% 0.65/0.85 (~r(z, s(s(s(s(elem!1)))))),
% 0.65/0.85 inference(unit_resolution,[status(thm)],[2850, 14, 2844, 2726])).
% 0.65/0.85 tff(2852,plain,
% 0.65/0.85 ((z = s(s(s(s(elem!1))))) | b(z, s(s(s(s(elem!1)))))),
% 0.65/0.85 inference(unit_resolution,[status(thm)],[1644, 46, 2851])).
% 0.65/0.85 tff(2853,plain,
% 0.65/0.85 (b(z, s(s(s(s(elem!1)))))),
% 0.65/0.85 inference(unit_resolution,[status(thm)],[2852, 1626])).
% 0.65/0.85 tff(2854,plain,
% 0.65/0.85 ((s(s(s(s(elem!1)))) = elem!1) <=> (elem!1 = s(s(s(s(elem!1)))))),
% 0.65/0.85 inference(commutativity,[status(thm)],[])).
% 0.65/0.85 tff(2855,plain,
% 0.65/0.85 ((s(s(s(s(elem!1)))) = s(z)) <=> (s(s(s(s(elem!1)))) = elem!1)),
% 0.65/0.85 inference(monotonicity,[status(thm)],[2815])).
% 0.65/0.85 tff(2856,plain,
% 0.65/0.85 ((s(s(s(s(elem!1)))) = s(z)) <=> (elem!1 = s(s(s(s(elem!1)))))),
% 0.65/0.85 inference(transitivity,[status(thm)],[2855, 2854])).
% 0.65/0.85 tff(2857,plain,
% 0.65/0.85 ((~(s(s(s(s(elem!1)))) = s(z))) <=> (~(elem!1 = s(s(s(s(elem!1))))))),
% 0.65/0.85 inference(monotonicity,[status(thm)],[2856])).
% 0.65/0.85 tff(2858,plain,
% 0.65/0.85 (~(elem!1 = s(s(s(s(elem!1)))))),
% 0.65/0.85 inference(modus_ponens,[status(thm)],[1322, 2857])).
% 0.65/0.85 tff(2859,plain,
% 0.65/0.85 (r(s(s(s(s(elem!1)))), s(s(s(z)))) <=> r(s(s(s(s(elem!1)))), s(s(elem!1)))),
% 0.65/0.85 inference(monotonicity,[status(thm)],[2804])).
% 0.65/0.85 tff(2860,plain,
% 0.65/0.85 ((s(s(s(s(elem!1)))) = s(s(s(z)))) <=> (s(s(s(z))) = s(s(s(s(elem!1)))))),
% 0.65/0.85 inference(commutativity,[status(thm)],[])).
% 0.65/0.85 tff(2861,plain,
% 0.65/0.85 ((s(s(s(z))) = s(s(s(s(elem!1))))) <=> (s(s(s(s(elem!1)))) = s(s(s(z))))),
% 0.65/0.85 inference(symmetry,[status(thm)],[2860])).
% 0.65/0.85 tff(2862,plain,
% 0.65/0.85 ((~(s(s(s(z))) = s(s(s(s(elem!1)))))) <=> (~(s(s(s(s(elem!1)))) = s(s(s(z)))))),
% 0.65/0.85 inference(monotonicity,[status(thm)],[2861])).
% 0.65/0.85 tff(2863,plain,
% 0.65/0.85 (~(s(s(s(s(elem!1)))) = s(s(s(z))))),
% 0.65/0.85 inference(modus_ponens,[status(thm)],[279, 2862])).
% 0.65/0.85 tff(2864,plain,
% 0.65/0.85 (((~![X0: $i, X2: $i, X1: $i] : ((~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), z)) | (~b(s(s(s(s(elem!1)))), z)) | (~b(s(s(s(s(elem!1)))), s(s(s(z))))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(z))), z)) | (~b(s(s(s(s(elem!1)))), z)) | (~b(s(s(s(s(elem!1)))), s(s(s(z))))))),
% 0.65/0.85 inference(rewrite,[status(thm)],[])).
% 0.65/0.85 tff(2865,plain,
% 0.65/0.85 ((~![X0: $i, X2: $i, X1: $i] : ((~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), z)) | (~b(s(s(s(s(elem!1)))), z)) | (~b(s(s(s(s(elem!1)))), s(s(s(z))))))),
% 0.65/0.85 inference(quant_inst,[status(thm)],[])).
% 0.65/0.85 tff(2866,plain,
% 0.65/0.85 ((~![X0: $i, X2: $i, X1: $i] : ((~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(z))), z)) | (~b(s(s(s(s(elem!1)))), z)) | (~b(s(s(s(s(elem!1)))), s(s(s(z)))))),
% 0.65/0.85 inference(modus_ponens,[status(thm)],[2865, 2864])).
% 0.65/0.85 tff(2867,plain,
% 0.65/0.85 (~b(s(s(s(s(elem!1)))), s(s(s(z))))),
% 0.65/0.85 inference(unit_resolution,[status(thm)],[2866, 117, 338, 1310])).
% 0.65/0.85 tff(2868,plain,
% 0.65/0.85 (((~![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)))))),
% 0.65/0.85 inference(rewrite,[status(thm)],[])).
% 0.65/0.85 tff(2869,plain,
% 0.65/0.85 ((~![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)))))),
% 0.65/0.85 inference(quant_inst,[status(thm)],[])).
% 0.65/0.85 tff(2870,plain,
% 0.65/0.85 ((~![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))))),
% 0.65/0.85 inference(modus_ponens,[status(thm)],[2869, 2868])).
% 0.65/0.85 tff(2871,plain,
% 0.65/0.85 ((s(s(s(s(elem!1)))) = s(s(s(z)))) | r(s(s(s(s(elem!1)))), s(s(s(z))))),
% 0.65/0.85 inference(unit_resolution,[status(thm)],[2870, 46, 2867])).
% 0.65/0.85 tff(2872,plain,
% 0.65/0.85 (r(s(s(s(s(elem!1)))), s(s(s(z))))),
% 0.65/0.85 inference(unit_resolution,[status(thm)],[2871, 2863])).
% 0.65/0.85 tff(2873,plain,
% 0.65/0.85 (r(s(s(s(s(elem!1)))), s(s(elem!1)))),
% 0.65/0.85 inference(modus_ponens,[status(thm)],[2872, 2859])).
% 0.65/0.85 tff(2874,plain,
% 0.65/0.85 ((s(z) = s(s(elem!1))) <=> (elem!1 = s(s(elem!1)))),
% 0.65/0.85 inference(monotonicity,[status(thm)],[2815])).
% 0.65/0.85 tff(2875,plain,
% 0.65/0.85 ((s(z) = s(s(elem!1))) <=> (s(s(elem!1)) = elem!1)),
% 0.65/0.85 inference(transitivity,[status(thm)],[2874, 2396])).
% 0.65/0.85 tff(2876,plain,
% 0.65/0.85 ((s(z) = s(s(elem!1))) <=> (elem!1 = s(s(elem!1)))),
% 0.65/0.85 inference(transitivity,[status(thm)],[2875, 2397])).
% 0.65/0.85 tff(2877,plain,
% 0.65/0.85 ((~(s(z) = s(s(elem!1)))) <=> (~(elem!1 = s(s(elem!1))))),
% 0.65/0.85 inference(monotonicity,[status(thm)],[2876])).
% 0.65/0.85 tff(2878,plain,
% 0.65/0.85 (~(elem!1 = s(s(elem!1)))),
% 0.65/0.85 inference(modus_ponens,[status(thm)],[172, 2877])).
% 0.65/0.85 tff(2879,plain,
% 0.65/0.85 (b(s(s(elem!1)), s(s(s(elem!1))))),
% 0.65/0.85 inference(unit_resolution,[status(thm)],[253, 2839, 145])).
% 0.65/0.85 tff(2880,plain,
% 0.65/0.85 (b(s(z), s(s(s(elem!1)))) <=> b(elem!1, s(s(s(elem!1))))),
% 0.65/0.85 inference(monotonicity,[status(thm)],[2815])).
% 0.65/0.85 tff(2881,plain,
% 0.65/0.85 (b(elem!1, s(s(s(elem!1))))),
% 0.65/0.85 inference(modus_ponens,[status(thm)],[2724, 2880])).
% 0.65/0.85 tff(2882,assumption,(b(elem!1, s(s(elem!1)))), introduced(assumption)).
% 0.65/0.85 tff(2883,plain,
% 0.65/0.85 (((~![X0: $i, X2: $i, X1: $i] : ((~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(s(elem!1)))) | (~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(elem!1, s(s(s(elem!1))))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(s(elem!1)))) | (~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(elem!1, s(s(s(elem!1))))))),
% 0.65/0.85 inference(rewrite,[status(thm)],[])).
% 0.65/0.85 tff(2884,plain,
% 0.65/0.85 (((~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(elem!1, s(s(s(elem!1))))) | (~b(elem!1, s(s(elem!1))))) <=> ((~b(elem!1, s(s(elem!1)))) | (~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(elem!1, s(s(s(elem!1))))))),
% 0.65/0.85 inference(rewrite,[status(thm)],[])).
% 0.65/0.85 tff(2885,plain,
% 0.65/0.85 (((~![X0: $i, X2: $i, X1: $i] : ((~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(elem!1, s(s(elem!1)))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(s(elem!1)))) | (~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(elem!1, s(s(s(elem!1)))))))),
% 0.65/0.85 inference(monotonicity,[status(thm)],[2884])).
% 0.65/0.85 tff(2886,plain,
% 0.65/0.85 (((~![X0: $i, X2: $i, X1: $i] : ((~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(elem!1, s(s(elem!1)))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(s(elem!1)))) | (~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(elem!1, s(s(s(elem!1))))))),
% 0.65/0.85 inference(transitivity,[status(thm)],[2885, 2883])).
% 0.65/0.85 tff(2887,plain,
% 0.65/0.85 ((~![X0: $i, X2: $i, X1: $i] : ((~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(elem!1, s(s(elem!1)))))),
% 0.65/0.85 inference(quant_inst,[status(thm)],[])).
% 0.65/0.85 tff(2888,plain,
% 0.65/0.85 ((~![X0: $i, X2: $i, X1: $i] : ((~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(s(elem!1)))) | (~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(elem!1, s(s(s(elem!1)))))),
% 0.65/0.85 inference(modus_ponens,[status(thm)],[2887, 2886])).
% 0.65/0.85 tff(2889,plain,
% 0.65/0.85 ($false),
% 0.65/0.85 inference(unit_resolution,[status(thm)],[2888, 117, 2882, 324, 645])).
% 0.65/0.85 tff(2890,plain,((~b(elem!1, s(s(s(elem!1))))) | (~b(elem!1, s(s(elem!1)))) | (~b(s(s(elem!1)), s(s(s(elem!1)))))), inference(lemma,lemma(discharge,[]))).
% 0.65/0.85 tff(2891,plain,
% 0.65/0.85 (~b(elem!1, s(s(elem!1)))),
% 0.65/0.85 inference(unit_resolution,[status(thm)],[2890, 2881, 2879])).
% 0.65/0.85 tff(2892,plain,
% 0.65/0.85 (((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((elem!1 = s(s(elem!1))) | b(elem!1, s(s(elem!1))) | r(elem!1, s(s(elem!1))))) <=> ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (elem!1 = s(s(elem!1))) | b(elem!1, s(s(elem!1))) | r(elem!1, s(s(elem!1))))),
% 0.65/0.85 inference(rewrite,[status(thm)],[])).
% 0.65/0.85 tff(2893,plain,
% 0.65/0.85 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((elem!1 = s(s(elem!1))) | b(elem!1, s(s(elem!1))) | r(elem!1, s(s(elem!1))))),
% 0.65/0.85 inference(quant_inst,[status(thm)],[])).
% 0.65/0.85 tff(2894,plain,
% 0.65/0.85 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (elem!1 = s(s(elem!1))) | b(elem!1, s(s(elem!1))) | r(elem!1, s(s(elem!1)))),
% 0.65/0.85 inference(modus_ponens,[status(thm)],[2893, 2892])).
% 0.65/0.85 tff(2895,plain,
% 0.65/0.85 ((elem!1 = s(s(elem!1))) | b(elem!1, s(s(elem!1))) | r(elem!1, s(s(elem!1)))),
% 0.65/0.85 inference(unit_resolution,[status(thm)],[2894, 46])).
% 0.65/0.85 tff(2896,plain,
% 0.65/0.85 (r(elem!1, s(s(elem!1)))),
% 0.65/0.85 inference(unit_resolution,[status(thm)],[2895, 2891, 2878])).
% 0.65/0.85 tff(2897,plain,
% 0.65/0.85 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(s(elem!1)))) | (~r(s(s(s(s(elem!1)))), s(s(elem!1)))) | (~r(elem!1, s(s(s(s(elem!1)))))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(elem!1, s(s(elem!1)))) | (~r(s(s(s(s(elem!1)))), s(s(elem!1)))) | (~r(elem!1, s(s(s(s(elem!1)))))))),
% 0.65/0.85 inference(rewrite,[status(thm)],[])).
% 0.65/0.85 tff(2898,plain,
% 0.65/0.85 (((~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(elem!1)))) | (~r(s(s(s(s(elem!1)))), s(s(elem!1)))) | (~r(elem!1, s(s(s(s(elem!1)))))))),
% 0.65/0.85 inference(rewrite,[status(thm)],[])).
% 0.65/0.85 tff(2899,plain,
% 0.65/0.85 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(elem!1)))), s(s(elem!1)))) | (~r(elem!1, s(s(elem!1)))) | (~r(elem!1, s(s(s(s(elem!1)))))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(s(elem!1)))) | (~r(s(s(s(s(elem!1)))), s(s(elem!1)))) | (~r(elem!1, s(s(s(s(elem!1))))))))),
% 0.65/0.85 inference(monotonicity,[status(thm)],[2898])).
% 0.65/0.85 tff(2900,plain,
% 0.65/0.85 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(elem!1)))), s(s(elem!1)))) | (~r(elem!1, s(s(elem!1)))) | (~r(elem!1, s(s(s(s(elem!1)))))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(elem!1, s(s(elem!1)))) | (~r(s(s(s(s(elem!1)))), s(s(elem!1)))) | (~r(elem!1, s(s(s(s(elem!1)))))))),
% 0.65/0.85 inference(transitivity,[status(thm)],[2899, 2897])).
% 0.65/0.85 tff(2901,plain,
% 0.65/0.85 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(elem!1)))), s(s(elem!1)))) | (~r(elem!1, s(s(elem!1)))) | (~r(elem!1, s(s(s(s(elem!1)))))))),
% 0.65/0.85 inference(quant_inst,[status(thm)],[])).
% 0.65/0.85 tff(2902,plain,
% 0.65/0.85 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(elem!1, s(s(elem!1)))) | (~r(s(s(s(s(elem!1)))), s(s(elem!1)))) | (~r(elem!1, s(s(s(s(elem!1))))))),
% 0.65/0.85 inference(modus_ponens,[status(thm)],[2901, 2900])).
% 0.65/0.85 tff(2903,plain,
% 0.65/0.85 (~r(elem!1, s(s(s(s(elem!1)))))),
% 0.65/0.85 inference(unit_resolution,[status(thm)],[2902, 14, 2896, 2873])).
% 0.65/0.85 tff(2904,plain,
% 0.65/0.85 (((~![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))))))),
% 0.65/0.85 inference(rewrite,[status(thm)],[])).
% 0.65/0.85 tff(2905,plain,
% 0.65/0.85 ((~![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))))))),
% 0.65/0.85 inference(quant_inst,[status(thm)],[])).
% 0.65/0.85 tff(2906,plain,
% 0.65/0.85 ((~![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)))))),
% 0.65/0.85 inference(modus_ponens,[status(thm)],[2905, 2904])).
% 0.65/0.85 tff(2907,plain,
% 0.65/0.85 ((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)))))),
% 0.65/0.85 inference(unit_resolution,[status(thm)],[2906, 46])).
% 0.65/0.85 tff(2908,plain,
% 0.65/0.85 (b(elem!1, s(s(s(s(elem!1)))))),
% 0.65/0.85 inference(unit_resolution,[status(thm)],[2907, 2903, 2858])).
% 0.65/0.85 tff(2909,plain,
% 0.65/0.85 (((~![X0: $i, X2: $i, X1: $i] : ((~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(s(s(elem!1)))))) | (~b(elem!1, s(s(s(s(elem!1)))))) | (~b(z, elem!1)))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(s(s(s(elem!1)))))) | (~b(elem!1, s(s(s(s(elem!1)))))) | (~b(z, elem!1)))),
% 0.65/0.85 inference(rewrite,[status(thm)],[])).
% 0.65/0.85 tff(2910,plain,
% 0.65/0.85 (((~b(elem!1, s(s(s(s(elem!1)))))) | (~b(z, s(s(s(s(elem!1)))))) | (~b(z, elem!1))) <=> ((~b(z, s(s(s(s(elem!1)))))) | (~b(elem!1, s(s(s(s(elem!1)))))) | (~b(z, elem!1)))),
% 0.65/0.85 inference(rewrite,[status(thm)],[])).
% 0.65/0.85 tff(2911,plain,
% 0.65/0.85 (((~![X0: $i, X2: $i, X1: $i] : ((~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(s(s(s(elem!1)))))) | (~b(z, s(s(s(s(elem!1)))))) | (~b(z, elem!1)))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(s(s(elem!1)))))) | (~b(elem!1, s(s(s(s(elem!1)))))) | (~b(z, elem!1))))),
% 0.65/0.85 inference(monotonicity,[status(thm)],[2910])).
% 0.65/0.85 tff(2912,plain,
% 0.65/0.85 (((~![X0: $i, X2: $i, X1: $i] : ((~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(s(s(s(elem!1)))))) | (~b(z, s(s(s(s(elem!1)))))) | (~b(z, elem!1)))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(s(s(s(elem!1)))))) | (~b(elem!1, s(s(s(s(elem!1)))))) | (~b(z, elem!1)))),
% 0.65/0.85 inference(transitivity,[status(thm)],[2911, 2909])).
% 0.65/0.85 tff(2913,plain,
% 0.65/0.85 ((~![X0: $i, X2: $i, X1: $i] : ((~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(s(s(s(elem!1)))))) | (~b(z, s(s(s(s(elem!1)))))) | (~b(z, elem!1)))),
% 0.65/0.86 inference(quant_inst,[status(thm)],[])).
% 0.65/0.86 tff(2914,plain,
% 0.65/0.86 ((~![X0: $i, X2: $i, X1: $i] : ((~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(s(s(s(elem!1)))))) | (~b(elem!1, s(s(s(s(elem!1)))))) | (~b(z, elem!1))),
% 0.65/0.86 inference(modus_ponens,[status(thm)],[2913, 2912])).
% 0.65/0.86 tff(2915,plain,
% 0.65/0.86 (~b(z, elem!1)),
% 0.65/0.86 inference(unit_resolution,[status(thm)],[2914, 117, 2908, 2853])).
% 0.65/0.86 tff(2916,plain,
% 0.65/0.86 (~b(z, s(z))),
% 0.65/0.86 inference(modus_ponens,[status(thm)],[2915, 2823])).
% 0.65/0.86 tff(2917,plain,
% 0.65/0.86 (r(z, s(z))),
% 0.65/0.86 inference(unit_resolution,[status(thm)],[599, 2916])).
% 0.65/0.86 tff(2918,plain,
% 0.65/0.86 (r(z, elem!1)),
% 0.65/0.86 inference(modus_ponens,[status(thm)],[2917, 2821])).
% 0.65/0.86 tff(2919,assumption,(r(z, elem!1)), introduced(assumption)).
% 0.65/0.86 tff(2920,plain,
% 0.65/0.86 (~r(s(s(s(s(s(s(elem!1)))))), z)),
% 0.65/0.86 inference(unit_resolution,[status(thm)],[2592, 14, 1555, 2919])).
% 0.65/0.86 tff(2921,plain,
% 0.65/0.86 (b(s(s(s(s(s(s(elem!1)))))), z)),
% 0.65/0.86 inference(unit_resolution,[status(thm)],[1666, 46, 1663, 2920])).
% 0.65/0.86 tff(2922,plain,
% 0.65/0.86 (((~![X0: $i, X2: $i, X1: $i] : ((~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), z)) | (~b(s(s(s(s(s(s(elem!1)))))), z)) | (~b(s(s(s(s(s(s(elem!1)))))), s(s(elem!1)))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(elem!1)), z)) | (~b(s(s(s(s(s(s(elem!1)))))), z)) | (~b(s(s(s(s(s(s(elem!1)))))), s(s(elem!1)))))),
% 0.65/0.86 inference(rewrite,[status(thm)],[])).
% 0.65/0.86 tff(2923,plain,
% 0.65/0.86 ((~![X0: $i, X2: $i, X1: $i] : ((~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), z)) | (~b(s(s(s(s(s(s(elem!1)))))), z)) | (~b(s(s(s(s(s(s(elem!1)))))), s(s(elem!1)))))),
% 0.65/0.86 inference(quant_inst,[status(thm)],[])).
% 0.65/0.86 tff(2924,plain,
% 0.65/0.86 ((~![X0: $i, X2: $i, X1: $i] : ((~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(elem!1)), z)) | (~b(s(s(s(s(s(s(elem!1)))))), z)) | (~b(s(s(s(s(s(s(elem!1)))))), s(s(elem!1))))),
% 0.65/0.86 inference(modus_ponens,[status(thm)],[2923, 2922])).
% 0.65/0.86 tff(2925,plain,
% 0.65/0.86 (~b(s(s(s(s(s(s(elem!1)))))), s(s(elem!1)))),
% 0.65/0.86 inference(unit_resolution,[status(thm)],[2924, 117, 1036, 2921])).
% 0.65/0.86 tff(2926,plain,
% 0.65/0.86 ($false),
% 0.65/0.86 inference(unit_resolution,[status(thm)],[1587, 2925, 1578])).
% 0.65/0.86 tff(2927,plain,((~r(s(s(s(s(s(s(elem!1)))))), elem!1)) | (~b(s(s(elem!1)), z)) | (~(s(s(s(z))) = s(s(elem!1)))) | (~r(z, elem!1)) | (~r(s(s(elem!1)), elem!1))), inference(lemma,lemma(discharge,[]))).
% 0.65/0.86 tff(2928,plain,
% 0.65/0.86 (~r(s(s(s(s(s(s(elem!1)))))), elem!1)),
% 0.65/0.86 inference(unit_resolution,[status(thm)],[2927, 2736, 2804, 2918, 2817])).
% 0.65/0.86 tff(2929,plain,
% 0.65/0.86 (b(s(s(s(s(s(s(elem!1)))))), elem!1)),
% 0.65/0.86 inference(unit_resolution,[status(thm)],[1599, 2928, 2811])).
% 0.65/0.86 tff(2930,plain,
% 0.65/0.86 (b(s(s(s(s(elem!1)))), s(z)) <=> b(s(s(s(s(elem!1)))), elem!1)),
% 0.65/0.86 inference(monotonicity,[status(thm)],[2815])).
% 0.65/0.86 tff(2931,plain,
% 0.65/0.86 (b(s(s(s(s(elem!1)))), elem!1)),
% 0.65/0.86 inference(modus_ponens,[status(thm)],[2696, 2930])).
% 0.65/0.86 tff(2932,plain,
% 0.65/0.86 (~b(s(s(s(s(s(s(elem!1)))))), s(s(s(s(elem!1)))))),
% 0.65/0.86 inference(unit_resolution,[status(thm)],[1605, 117, 2931, 2929])).
% 0.65/0.86 tff(2933,plain,
% 0.65/0.86 ((s(s(s(z))) = s(s(s(s(elem!1))))) <=> (s(s(elem!1)) = s(s(s(s(elem!1)))))),
% 0.65/0.86 inference(monotonicity,[status(thm)],[2804])).
% 0.65/0.86 tff(2934,plain,
% 0.65/0.86 ((s(s(s(z))) = s(s(s(s(elem!1))))) <=> (s(s(s(s(elem!1)))) = s(s(elem!1)))),
% 0.65/0.86 inference(transitivity,[status(thm)],[2933, 2033])).
% 0.65/0.86 tff(2935,plain,
% 0.65/0.86 ((~(s(s(s(z))) = s(s(s(s(elem!1)))))) <=> (~(s(s(s(s(elem!1)))) = s(s(elem!1))))),
% 0.65/0.86 inference(monotonicity,[status(thm)],[2934])).
% 0.65/0.86 tff(2936,plain,
% 0.65/0.86 (~(s(s(s(s(elem!1)))) = s(s(elem!1)))),
% 0.65/0.86 inference(modus_ponens,[status(thm)],[279, 2935])).
% 0.65/0.86 tff(2937,plain,
% 0.65/0.86 (~(s(s(s(s(s(s(elem!1)))))) = s(s(s(s(elem!1)))))),
% 0.65/0.86 inference(unit_resolution,[status(thm)],[1615, 2936])).
% 0.65/0.86 tff(2938,plain,
% 0.65/0.86 (r(s(s(s(s(s(s(elem!1)))))), s(s(s(s(elem!1)))))),
% 0.65/0.86 inference(unit_resolution,[status(thm)],[1619, 46, 2937, 2932])).
% 0.65/0.86 tff(2939,plain,
% 0.65/0.86 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), s(s(s(s(elem!1)))))) | (~r(s(s(s(s(s(s(elem!1)))))), s(s(s(s(elem!1)))))) | (~r(s(s(s(s(s(s(elem!1)))))), s(s(s(elem!1))))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(elem!1))), s(s(s(s(elem!1)))))) | (~r(s(s(s(s(s(s(elem!1)))))), s(s(s(s(elem!1)))))) | (~r(s(s(s(s(s(s(elem!1)))))), s(s(s(elem!1))))))),
% 0.65/0.86 inference(rewrite,[status(thm)],[])).
% 0.65/0.86 tff(2940,plain,
% 0.65/0.86 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), s(s(s(s(elem!1)))))) | (~r(s(s(s(s(s(s(elem!1)))))), s(s(s(s(elem!1)))))) | (~r(s(s(s(s(s(s(elem!1)))))), s(s(s(elem!1))))))),
% 0.65/0.86 inference(quant_inst,[status(thm)],[])).
% 0.65/0.86 tff(2941,plain,
% 0.65/0.86 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(elem!1))), s(s(s(s(elem!1)))))) | (~r(s(s(s(s(s(s(elem!1)))))), s(s(s(s(elem!1)))))) | (~r(s(s(s(s(s(s(elem!1)))))), s(s(s(elem!1)))))),
% 0.65/0.86 inference(modus_ponens,[status(thm)],[2940, 2939])).
% 0.65/0.86 tff(2942,plain,
% 0.65/0.86 (~r(s(s(s(s(s(s(elem!1)))))), s(s(s(elem!1))))),
% 0.65/0.86 inference(unit_resolution,[status(thm)],[2941, 14, 2831, 2938])).
% 0.65/0.86 tff(2943,plain,
% 0.65/0.86 (b(s(s(s(elem!1))), s(z)) <=> b(s(s(s(elem!1))), elem!1)),
% 0.65/0.86 inference(monotonicity,[status(thm)],[2815])).
% 0.65/0.86 tff(2944,plain,
% 0.65/0.86 (b(s(s(s(elem!1))), elem!1)),
% 0.65/0.86 inference(modus_ponens,[status(thm)],[2739, 2943])).
% 0.65/0.86 tff(2945,plain,
% 0.65/0.86 (~b(s(s(s(s(s(s(elem!1)))))), s(s(s(elem!1))))),
% 0.65/0.86 inference(unit_resolution,[status(thm)],[1999, 117, 2944, 2929])).
% 0.65/0.86 tff(2946,plain,
% 0.65/0.86 ((s(s(s(s(s(s(elem!1)))))) = s(s(s(elem!1)))) | r(s(s(s(s(s(s(elem!1)))))), s(s(s(elem!1))))),
% 0.65/0.86 inference(unit_resolution,[status(thm)],[1563, 46, 2945])).
% 0.65/0.86 tff(2947,plain,
% 0.65/0.86 ($false),
% 0.65/0.86 inference(unit_resolution,[status(thm)],[2946, 2942, 2810])).
% 0.65/0.86 tff(2948,plain,(b(s(s(s(elem!1))), z) | (~b(s(s(s(z))), z)) | (s(s(elem!1)) = s(s(s(elem!1)))) | (~b(s(s(s(s(elem!1)))), z))), inference(lemma,lemma(discharge,[]))).
% 0.65/0.86 tff(2949,plain,
% 0.65/0.86 (b(s(s(s(elem!1))), z)),
% 0.65/0.86 inference(unit_resolution,[status(thm)],[2948, 145, 338, 1310])).
% 0.65/0.86 tff(2950,plain,
% 0.65/0.86 (((~![X0: $i, X2: $i, X1: $i] : ((~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), z)) | (~b(s(s(s(s(elem!1)))), z)) | (~b(s(s(s(elem!1))), s(s(s(s(elem!1)))))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(elem!1))), z)) | (~b(s(s(s(s(elem!1)))), z)) | (~b(s(s(s(elem!1))), s(s(s(s(elem!1)))))))),
% 0.65/0.86 inference(rewrite,[status(thm)],[])).
% 0.65/0.86 tff(2951,plain,
% 0.65/0.86 (((~b(s(s(s(s(elem!1)))), z)) | (~b(s(s(s(elem!1))), z)) | (~b(s(s(s(elem!1))), s(s(s(s(elem!1))))))) <=> ((~b(s(s(s(elem!1))), z)) | (~b(s(s(s(s(elem!1)))), z)) | (~b(s(s(s(elem!1))), s(s(s(s(elem!1)))))))),
% 0.65/0.86 inference(rewrite,[status(thm)],[])).
% 0.65/0.86 tff(2952,plain,
% 0.65/0.86 (((~![X0: $i, X2: $i, X1: $i] : ((~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(s(s(elem!1))), s(s(s(s(elem!1)))))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), z)) | (~b(s(s(s(s(elem!1)))), z)) | (~b(s(s(s(elem!1))), s(s(s(s(elem!1))))))))),
% 0.65/0.86 inference(monotonicity,[status(thm)],[2951])).
% 0.65/0.86 tff(2953,plain,
% 0.65/0.86 (((~![X0: $i, X2: $i, X1: $i] : ((~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(s(s(elem!1))), s(s(s(s(elem!1)))))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(elem!1))), z)) | (~b(s(s(s(s(elem!1)))), z)) | (~b(s(s(s(elem!1))), s(s(s(s(elem!1)))))))),
% 0.65/0.86 inference(transitivity,[status(thm)],[2952, 2950])).
% 0.65/0.86 tff(2954,plain,
% 0.65/0.86 ((~![X0: $i, X2: $i, X1: $i] : ((~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(s(s(elem!1))), s(s(s(s(elem!1)))))))),
% 0.65/0.86 inference(quant_inst,[status(thm)],[])).
% 0.65/0.86 tff(2955,plain,
% 0.65/0.86 ((~![X0: $i, X2: $i, X1: $i] : ((~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(elem!1))), z)) | (~b(s(s(s(s(elem!1)))), z)) | (~b(s(s(s(elem!1))), s(s(s(s(elem!1))))))),
% 0.65/0.86 inference(modus_ponens,[status(thm)],[2954, 2953])).
% 0.65/0.86 tff(2956,plain,
% 0.65/0.86 (~b(s(s(s(elem!1))), s(s(s(s(elem!1)))))),
% 0.65/0.86 inference(unit_resolution,[status(thm)],[2955, 117, 2949, 1310])).
% 0.65/0.86 tff(2957,plain,
% 0.65/0.86 (r(s(s(s(elem!1))), s(s(s(s(elem!1)))))),
% 0.65/0.86 inference(unit_resolution,[status(thm)],[448, 2956, 290])).
% 0.65/0.86 tff(2958,plain,
% 0.65/0.86 (~r(s(s(s(elem!1))), s(s(s(z))))),
% 0.65/0.86 inference(unit_resolution,[status(thm)],[2711, 14, 2957, 2483])).
% 0.65/0.86 tff(2959,assumption,(b(s(s(s(elem!1))), s(s(s(z))))), introduced(assumption)).
% 0.65/0.86 tff(2960,plain,
% 0.65/0.86 (((~![X0: $i, X2: $i, X1: $i] : ((~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), z)) | (~b(s(s(s(elem!1))), s(s(s(z))))) | (~b(s(s(s(z))), z)))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(elem!1))), z)) | (~b(s(s(s(elem!1))), s(s(s(z))))) | (~b(s(s(s(z))), z)))),
% 0.65/0.86 inference(rewrite,[status(thm)],[])).
% 0.65/0.86 tff(2961,plain,
% 0.65/0.86 (((~b(s(s(s(z))), z)) | (~b(s(s(s(elem!1))), z)) | (~b(s(s(s(elem!1))), s(s(s(z)))))) <=> ((~b(s(s(s(elem!1))), z)) | (~b(s(s(s(elem!1))), s(s(s(z))))) | (~b(s(s(s(z))), z)))),
% 0.65/0.86 inference(rewrite,[status(thm)],[])).
% 0.65/0.86 tff(2962,plain,
% 0.65/0.86 (((~![X0: $i, X2: $i, X1: $i] : ((~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~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, X2: $i, X1: $i] : ((~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), z)) | (~b(s(s(s(elem!1))), s(s(s(z))))) | (~b(s(s(s(z))), z))))),
% 0.65/0.86 inference(monotonicity,[status(thm)],[2961])).
% 0.65/0.86 tff(2963,plain,
% 0.65/0.86 (((~![X0: $i, X2: $i, X1: $i] : ((~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~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, X2: $i, X1: $i] : ((~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(elem!1))), z)) | (~b(s(s(s(elem!1))), s(s(s(z))))) | (~b(s(s(s(z))), z)))),
% 0.65/0.86 inference(transitivity,[status(thm)],[2962, 2960])).
% 0.65/0.86 tff(2964,plain,
% 0.65/0.86 ((~![X0: $i, X2: $i, X1: $i] : ((~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), z)) | (~b(s(s(s(elem!1))), z)) | (~b(s(s(s(elem!1))), s(s(s(z))))))),
% 0.65/0.86 inference(quant_inst,[status(thm)],[])).
% 0.65/0.86 tff(2965,plain,
% 0.65/0.86 ((~![X0: $i, X2: $i, X1: $i] : ((~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(elem!1))), z)) | (~b(s(s(s(elem!1))), s(s(s(z))))) | (~b(s(s(s(z))), z))),
% 0.65/0.86 inference(modus_ponens,[status(thm)],[2964, 2963])).
% 0.65/0.86 tff(2966,plain,
% 0.65/0.86 ($false),
% 0.65/0.86 inference(unit_resolution,[status(thm)],[2965, 117, 157, 338, 2959])).
% 0.65/0.86 tff(2967,plain,((~b(s(s(s(elem!1))), z)) | (~b(s(s(s(z))), z)) | (~b(s(s(s(elem!1))), s(s(s(z)))))), inference(lemma,lemma(discharge,[]))).
% 0.65/0.86 tff(2968,plain,
% 0.65/0.86 (~b(s(s(s(elem!1))), s(s(s(z))))),
% 0.65/0.86 inference(unit_resolution,[status(thm)],[2967, 2949, 338])).
% 0.65/0.86 tff(2969,plain,
% 0.65/0.86 ((s(s(s(elem!1))) = s(s(s(z)))) | r(s(s(s(elem!1))), s(s(s(z))))),
% 0.65/0.86 inference(unit_resolution,[status(thm)],[2341, 46, 2968])).
% 0.65/0.86 tff(2970,plain,
% 0.65/0.86 (s(s(s(elem!1))) = s(s(s(z)))),
% 0.65/0.86 inference(unit_resolution,[status(thm)],[2969, 2958])).
% 0.65/0.86 tff(2971,plain,
% 0.65/0.86 (inj_0(s(s(s(elem!1)))) = inj_0(s(s(s(z))))),
% 0.65/0.86 inference(monotonicity,[status(thm)],[2970])).
% 0.65/0.86 tff(2972,plain,
% 0.65/0.86 (s(s(elem!1)) = s(s(z))),
% 0.65/0.86 inference(transitivity,[status(thm)],[152, 2971, 94])).
% 0.65/0.86 tff(2973,plain,
% 0.65/0.86 (inj_0(s(s(elem!1))) = inj_0(s(s(z)))),
% 0.65/0.86 inference(monotonicity,[status(thm)],[2972])).
% 0.65/0.86 tff(2974,plain,
% 0.65/0.86 (s(elem!1) = s(z)),
% 0.65/0.86 inference(transitivity,[status(thm)],[167, 2973, 82])).
% 0.65/0.86 tff(2975,plain,
% 0.65/0.86 (inj_0(s(elem!1)) = inj_0(s(z))),
% 0.65/0.86 inference(monotonicity,[status(thm)],[2974])).
% 0.65/0.86 tff(2976,plain,
% 0.65/0.86 (elem!1 = z),
% 0.65/0.86 inference(transitivity,[status(thm)],[1652, 2975, 90])).
% 0.65/0.86 tff(2977,plain,
% 0.65/0.86 ((s(s(s(s(s(s(elem!1)))))) = elem!1) <=> (s(s(s(s(s(s(elem!1)))))) = z)),
% 0.65/0.86 inference(monotonicity,[status(thm)],[2976])).
% 0.65/0.86 tff(2978,plain,
% 0.65/0.86 ((s(s(s(s(s(s(elem!1)))))) = z) <=> (s(s(s(s(s(s(elem!1)))))) = elem!1)),
% 0.65/0.86 inference(symmetry,[status(thm)],[2977])).
% 0.65/0.86 tff(2979,plain,
% 0.65/0.86 ((~(s(s(s(s(s(s(elem!1)))))) = z)) <=> (~(s(s(s(s(s(s(elem!1)))))) = elem!1))),
% 0.65/0.86 inference(monotonicity,[status(thm)],[2978])).
% 0.65/0.86 tff(2980,plain,
% 0.65/0.86 (~(s(s(s(s(s(s(elem!1)))))) = elem!1)),
% 0.65/0.86 inference(modus_ponens,[status(thm)],[1663, 2979])).
% 0.65/0.86 tff(2981,plain,
% 0.65/0.86 (b(s(s(elem!1)), s(elem!1)) <=> b(s(s(z)), s(z))),
% 0.65/0.86 inference(monotonicity,[status(thm)],[2972, 2974])).
% 0.65/0.86 tff(2982,plain,
% 0.65/0.86 (b(s(s(z)), s(z)) <=> b(s(s(elem!1)), s(elem!1))),
% 0.65/0.86 inference(symmetry,[status(thm)],[2981])).
% 0.65/0.86 tff(2983,plain,
% 0.65/0.86 (b(s(s(elem!1)), s(z)) <=> b(s(s(z)), s(z))),
% 0.65/0.86 inference(monotonicity,[status(thm)],[2972])).
% 0.65/0.86 tff(2984,plain,
% 0.65/0.86 (((~![X0: $i, X2: $i, X1: $i] : ((~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), z)) | (~b(s(s(s(s(elem!1)))), z)) | (~b(s(s(s(s(elem!1)))), s(s(s(elem!1))))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(elem!1))), z)) | (~b(s(s(s(s(elem!1)))), z)) | (~b(s(s(s(s(elem!1)))), s(s(s(elem!1))))))),
% 0.65/0.86 inference(rewrite,[status(thm)],[])).
% 0.65/0.86 tff(2985,plain,
% 0.65/0.86 ((~![X0: $i, X2: $i, X1: $i] : ((~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), z)) | (~b(s(s(s(s(elem!1)))), z)) | (~b(s(s(s(s(elem!1)))), s(s(s(elem!1))))))),
% 0.65/0.86 inference(quant_inst,[status(thm)],[])).
% 0.65/0.86 tff(2986,plain,
% 0.65/0.86 ((~![X0: $i, X2: $i, X1: $i] : ((~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(elem!1))), z)) | (~b(s(s(s(s(elem!1)))), z)) | (~b(s(s(s(s(elem!1)))), s(s(s(elem!1)))))),
% 0.65/0.86 inference(modus_ponens,[status(thm)],[2985, 2984])).
% 0.65/0.86 tff(2987,plain,
% 0.65/0.86 ($false),
% 0.65/0.86 inference(unit_resolution,[status(thm)],[2986, 117, 157, 1349, 1310])).
% 0.65/0.86 tff(2988,plain,((~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))), inference(lemma,lemma(discharge,[]))).
% 0.65/0.86 tff(2989,plain,
% 0.65/0.86 (~b(s(s(s(s(elem!1)))), s(s(s(elem!1))))),
% 0.65/0.86 inference(unit_resolution,[status(thm)],[2988, 157, 1310])).
% 0.65/0.86 tff(2990,plain,
% 0.65/0.86 (r(s(s(s(s(elem!1)))), s(s(s(elem!1))))),
% 0.65/0.86 inference(unit_resolution,[status(thm)],[1347, 156, 2989])).
% 0.65/0.86 tff(2991,plain,
% 0.65/0.86 (~b(s(s(elem!1)), s(s(s(elem!1))))),
% 0.65/0.86 inference(unit_resolution,[status(thm)],[1046, 1036, 157])).
% 0.65/0.86 tff(2992,plain,
% 0.65/0.86 (r(s(s(elem!1)), s(s(s(elem!1))))),
% 0.65/0.86 inference(unit_resolution,[status(thm)],[253, 2991, 145])).
% 0.65/0.86 tff(2993,plain,
% 0.65/0.86 (~r(s(s(s(s(elem!1)))), s(s(elem!1)))),
% 0.65/0.86 inference(unit_resolution,[status(thm)],[2220, 2992, 2990])).
% 0.65/0.86 tff(2994,plain,
% 0.65/0.86 (s(s(s(s(elem!1)))) = s(s(elem!1))),
% 0.65/0.86 inference(unit_resolution,[status(thm)],[1690, 2993, 2515])).
% 0.65/0.86 tff(2995,plain,
% 0.65/0.86 (inj_0(s(s(s(s(elem!1))))) = inj_0(s(s(elem!1)))),
% 0.65/0.86 inference(monotonicity,[status(thm)],[2994])).
% 0.65/0.86 tff(2996,plain,
% 0.65/0.86 (inj_0(s(s(elem!1))) = inj_0(s(s(s(s(elem!1)))))),
% 0.65/0.86 inference(symmetry,[status(thm)],[2995])).
% 0.65/0.86 tff(2997,plain,
% 0.65/0.86 (s(elem!1) = s(s(s(elem!1)))),
% 0.65/0.86 inference(transitivity,[status(thm)],[167, 2996, 144])).
% 0.65/0.86 tff(2998,plain,
% 0.65/0.86 (r(s(s(elem!1)), s(elem!1)) <=> r(s(s(elem!1)), s(s(s(elem!1))))),
% 0.65/0.86 inference(monotonicity,[status(thm)],[2997])).
% 0.65/0.86 tff(2999,plain,
% 0.65/0.86 (r(s(s(elem!1)), s(s(s(elem!1)))) <=> r(s(s(elem!1)), s(elem!1))),
% 0.65/0.86 inference(symmetry,[status(thm)],[2998])).
% 0.65/0.86 tff(3000,plain,
% 0.65/0.86 (r(s(s(elem!1)), s(elem!1))),
% 0.65/0.86 inference(modus_ponens,[status(thm)],[2992, 2999])).
% 0.65/0.86 tff(3001,plain,
% 0.65/0.86 (s(s(elem!1)) = elem!1),
% 0.65/0.86 inference(unit_resolution,[status(thm)],[266, 2994])).
% 0.65/0.86 tff(3002,plain,
% 0.65/0.86 (elem!1 = s(s(elem!1))),
% 0.65/0.86 inference(symmetry,[status(thm)],[3001])).
% 0.65/0.86 tff(3003,plain,
% 0.65/0.86 (r(s(s(s(z))), elem!1) <=> r(s(s(s(z))), s(s(elem!1)))),
% 0.65/0.86 inference(monotonicity,[status(thm)],[3002])).
% 0.65/0.86 tff(3004,plain,
% 0.65/0.86 ((s(s(s(z))) = elem!1) <=> (s(s(s(z))) = s(s(elem!1)))),
% 0.65/0.86 inference(monotonicity,[status(thm)],[3002])).
% 0.65/0.86 tff(3005,plain,
% 0.65/0.86 ((s(s(s(z))) = s(s(elem!1))) <=> (s(s(s(z))) = elem!1)),
% 0.65/0.86 inference(symmetry,[status(thm)],[3004])).
% 0.65/0.86 tff(3006,plain,
% 0.65/0.86 ((~(s(s(s(z))) = s(s(elem!1)))) <=> (~(s(s(s(z))) = elem!1))),
% 0.65/0.86 inference(monotonicity,[status(thm)],[3005])).
% 0.65/0.86 tff(3007,plain,
% 0.65/0.86 ((s(s(s(z))) = s(s(s(s(elem!1))))) <=> (s(s(s(z))) = s(s(elem!1)))),
% 0.65/0.86 inference(monotonicity,[status(thm)],[2994])).
% 0.65/0.86 tff(3008,plain,
% 0.65/0.86 ((~(s(s(s(z))) = s(s(s(s(elem!1)))))) <=> (~(s(s(s(z))) = s(s(elem!1))))),
% 0.65/0.86 inference(monotonicity,[status(thm)],[3007])).
% 0.65/0.86 tff(3009,plain,
% 0.65/0.86 (~(s(s(s(z))) = s(s(elem!1)))),
% 0.65/0.86 inference(modus_ponens,[status(thm)],[279, 3008])).
% 0.65/0.86 tff(3010,plain,
% 0.65/0.86 (~(s(s(s(z))) = elem!1)),
% 0.65/0.86 inference(modus_ponens,[status(thm)],[3009, 3006])).
% 0.65/0.86 tff(3011,plain,
% 0.65/0.86 (b(s(s(s(z))), elem!1) <=> b(s(s(s(z))), s(s(elem!1)))),
% 0.65/0.86 inference(monotonicity,[status(thm)],[3002])).
% 0.65/0.86 tff(3012,plain,
% 0.65/0.86 (b(s(s(s(z))), s(s(elem!1))) <=> b(s(s(s(z))), elem!1)),
% 0.65/0.86 inference(symmetry,[status(thm)],[3011])).
% 0.65/0.86 tff(3013,plain,
% 0.65/0.86 ((~b(s(s(s(z))), s(s(elem!1)))) <=> (~b(s(s(s(z))), elem!1))),
% 0.65/0.86 inference(monotonicity,[status(thm)],[3012])).
% 0.65/0.86 tff(3014,plain,
% 0.65/0.86 (~b(s(s(s(z))), s(s(elem!1)))),
% 0.65/0.86 inference(unit_resolution,[status(thm)],[1217, 1036, 338])).
% 0.65/0.86 tff(3015,plain,
% 0.65/0.86 (~b(s(s(s(z))), elem!1)),
% 0.65/0.86 inference(modus_ponens,[status(thm)],[3014, 3013])).
% 0.65/0.86 tff(3016,plain,
% 0.65/0.86 (r(s(s(s(z))), elem!1)),
% 0.65/0.86 inference(unit_resolution,[status(thm)],[756, 3015, 3010])).
% 0.65/0.86 tff(3017,plain,
% 0.65/0.86 (r(s(s(s(z))), s(s(elem!1)))),
% 0.65/0.86 inference(modus_ponens,[status(thm)],[3016, 3003])).
% 0.65/0.86 tff(3018,plain,
% 0.65/0.86 (s(s(s(elem!1))) = s(elem!1)),
% 0.65/0.86 inference(transitivity,[status(thm)],[295, 2995, 166])).
% 0.65/0.86 tff(3019,plain,
% 0.65/0.86 (b(s(s(s(z))), s(s(s(elem!1)))) <=> b(s(s(s(z))), s(elem!1))),
% 0.65/0.86 inference(monotonicity,[status(thm)],[3018])).
% 0.65/0.86 tff(3020,plain,
% 0.65/0.86 ((~b(s(s(s(z))), s(s(s(elem!1))))) <=> (~b(s(s(s(z))), s(elem!1)))),
% 0.65/0.86 inference(monotonicity,[status(thm)],[3019])).
% 0.65/0.86 tff(3021,plain,
% 0.65/0.86 (((~![X0: $i, X2: $i, X1: $i] : ((~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~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, X2: $i, X1: $i] : ((~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(elem!1))), z)) | (~b(s(s(s(z))), z)) | (~b(s(s(s(z))), s(s(s(elem!1))))))),
% 0.65/0.86 inference(rewrite,[status(thm)],[])).
% 0.65/0.86 tff(3022,plain,
% 0.65/0.86 ((~![X0: $i, X2: $i, X1: $i] : ((~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), z)) | (~b(s(s(s(z))), z)) | (~b(s(s(s(z))), s(s(s(elem!1))))))),
% 0.65/0.86 inference(quant_inst,[status(thm)],[])).
% 0.65/0.86 tff(3023,plain,
% 0.65/0.86 ((~![X0: $i, X2: $i, X1: $i] : ((~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(elem!1))), z)) | (~b(s(s(s(z))), z)) | (~b(s(s(s(z))), s(s(s(elem!1)))))),
% 0.65/0.86 inference(modus_ponens,[status(thm)],[3022, 3021])).
% 0.65/0.86 tff(3024,plain,
% 0.65/0.86 (~b(s(s(s(z))), s(s(s(elem!1))))),
% 0.65/0.86 inference(unit_resolution,[status(thm)],[3023, 117, 157, 338])).
% 0.65/0.86 tff(3025,plain,
% 0.65/0.86 (~b(s(s(s(z))), s(elem!1))),
% 0.65/0.86 inference(modus_ponens,[status(thm)],[3024, 3020])).
% 0.65/0.86 tff(3026,plain,
% 0.65/0.86 (~(s(s(s(z))) = s(elem!1))),
% 0.65/0.86 inference(unit_resolution,[status(thm)],[623, 2994])).
% 0.65/0.86 tff(3027,plain,
% 0.65/0.86 (r(s(s(s(z))), s(elem!1))),
% 0.65/0.86 inference(unit_resolution,[status(thm)],[627, 46, 3026, 3025])).
% 0.65/0.86 tff(3028,plain,
% 0.65/0.86 (~r(s(s(elem!1)), s(elem!1))),
% 0.65/0.86 inference(unit_resolution,[status(thm)],[2634, 14, 3027, 3017])).
% 0.65/0.86 tff(3029,plain,
% 0.65/0.86 ($false),
% 0.65/0.86 inference(unit_resolution,[status(thm)],[3028, 3000])).
% 0.65/0.86 tff(3030,plain,((~b(s(s(elem!1)), z)) | (s(s(elem!1)) = s(s(s(elem!1)))) | (~b(s(s(s(z))), z)) | (~b(s(s(s(elem!1))), z)) | (~b(s(s(s(s(elem!1)))), z))), inference(lemma,lemma(discharge,[]))).
% 0.65/0.86 tff(3031,plain,
% 0.65/0.86 (~b(s(s(elem!1)), z)),
% 0.65/0.86 inference(unit_resolution,[status(thm)],[3030, 2949, 338, 145, 1310])).
% 0.65/0.86 tff(3032,plain,
% 0.65/0.86 (r(s(s(elem!1)), z)),
% 0.65/0.86 inference(unit_resolution,[status(thm)],[1025, 3031])).
% 0.65/0.86 tff(3033,plain,
% 0.65/0.86 (~r(s(s(elem!1)), s(z))),
% 0.65/0.86 inference(unit_resolution,[status(thm)],[186, 14, 3032, 2500])).
% 0.65/0.86 tff(3034,plain,
% 0.65/0.86 (b(s(s(elem!1)), s(z))),
% 0.65/0.86 inference(unit_resolution,[status(thm)],[178, 3033])).
% 0.65/0.86 tff(3035,plain,
% 0.65/0.86 (b(s(s(z)), s(z))),
% 0.65/0.86 inference(modus_ponens,[status(thm)],[3034, 2983])).
% 0.65/0.86 tff(3036,plain,
% 0.65/0.86 (b(s(s(elem!1)), s(elem!1))),
% 0.65/0.86 inference(modus_ponens,[status(thm)],[3035, 2982])).
% 0.65/0.86 tff(3037,plain,
% 0.65/0.86 (r(s(s(elem!1)), elem!1) <=> r(s(s(z)), elem!1)),
% 0.65/0.86 inference(monotonicity,[status(thm)],[2972])).
% 0.65/0.86 tff(3038,plain,
% 0.65/0.86 (r(s(s(z)), elem!1) <=> r(s(s(elem!1)), elem!1)),
% 0.65/0.86 inference(symmetry,[status(thm)],[3037])).
% 0.65/0.86 tff(3039,plain,
% 0.65/0.86 (inj_0(s(z)) = inj_0(s(elem!1))),
% 0.65/0.86 inference(symmetry,[status(thm)],[2975])).
% 0.65/0.86 tff(3040,plain,
% 0.65/0.86 (z = elem!1),
% 0.65/0.86 inference(transitivity,[status(thm)],[1730, 3039, 257])).
% 0.65/0.86 tff(3041,plain,
% 0.65/0.86 (r(s(s(elem!1)), z) <=> r(s(s(z)), elem!1)),
% 0.65/0.86 inference(monotonicity,[status(thm)],[2972, 3040])).
% 0.65/0.86 tff(3042,plain,
% 0.65/0.86 (r(s(s(elem!1)), z) <=> r(s(s(elem!1)), elem!1)),
% 0.65/0.86 inference(transitivity,[status(thm)],[3041, 3038])).
% 0.65/0.86 tff(3043,plain,
% 0.65/0.86 (r(s(s(elem!1)), elem!1)),
% 0.65/0.86 inference(modus_ponens,[status(thm)],[3032, 3042])).
% 0.65/0.86 tff(3044,plain,
% 0.65/0.86 (~r(s(s(s(z))), s(s(s(elem!1))))),
% 0.65/0.86 inference(unit_resolution,[status(thm)],[2837, 14, 2957, 2483])).
% 0.65/0.86 tff(3045,plain,
% 0.65/0.86 (~b(s(s(s(z))), s(s(s(elem!1))))),
% 0.65/0.86 inference(unit_resolution,[status(thm)],[3023, 117, 2949, 338])).
% 0.65/0.86 tff(3046,plain,
% 0.65/0.86 ((s(s(s(z))) = s(s(s(elem!1)))) | r(s(s(s(z))), s(s(s(elem!1))))),
% 0.65/0.86 inference(unit_resolution,[status(thm)],[1717, 46, 3045])).
% 0.65/0.86 tff(3047,plain,
% 0.65/0.86 (s(s(s(z))) = s(s(s(elem!1)))),
% 0.65/0.86 inference(unit_resolution,[status(thm)],[3046, 3044])).
% 0.65/0.86 tff(3048,plain,
% 0.65/0.86 (r(s(elem!1), elem!1) <=> r(s(z), elem!1)),
% 0.65/0.86 inference(monotonicity,[status(thm)],[2974])).
% 0.65/0.86 tff(3049,plain,
% 0.65/0.86 (r(s(z), elem!1) <=> r(s(elem!1), elem!1)),
% 0.65/0.86 inference(symmetry,[status(thm)],[3048])).
% 0.65/0.86 tff(3050,plain,
% 0.65/0.86 (r(s(z), elem!1) <=> r(s(z), z)),
% 0.65/0.86 inference(monotonicity,[status(thm)],[2976])).
% 0.65/0.86 tff(3051,plain,
% 0.65/0.86 (r(s(z), z) <=> r(s(z), elem!1)),
% 0.65/0.86 inference(symmetry,[status(thm)],[3050])).
% 0.65/0.86 tff(3052,plain,
% 0.65/0.86 (r(s(z), z) <=> r(s(elem!1), elem!1)),
% 0.65/0.86 inference(transitivity,[status(thm)],[3051, 3049])).
% 0.65/0.86 tff(3053,plain,
% 0.65/0.86 (r(s(elem!1), elem!1)),
% 0.65/0.86 inference(modus_ponens,[status(thm)],[2500, 3052])).
% 0.65/0.86 tff(3054,assumption,(r(s(elem!1), elem!1)), introduced(assumption)).
% 0.65/0.86 tff(3055,plain,
% 0.65/0.86 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(elem!1), elem!1)) | (~r(s(s(s(s(s(s(elem!1)))))), elem!1)) | (~r(s(s(s(s(s(s(elem!1)))))), s(elem!1))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(elem!1), elem!1)) | (~r(s(s(s(s(s(s(elem!1)))))), elem!1)) | (~r(s(s(s(s(s(s(elem!1)))))), s(elem!1))))),
% 0.65/0.86 inference(rewrite,[status(thm)],[])).
% 0.65/0.86 tff(3056,plain,
% 0.65/0.86 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(elem!1), elem!1)) | (~r(s(s(s(s(s(s(elem!1)))))), elem!1)) | (~r(s(s(s(s(s(s(elem!1)))))), s(elem!1))))),
% 0.65/0.86 inference(quant_inst,[status(thm)],[])).
% 0.65/0.86 tff(3057,plain,
% 0.65/0.86 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(elem!1), elem!1)) | (~r(s(s(s(s(s(s(elem!1)))))), elem!1)) | (~r(s(s(s(s(s(s(elem!1)))))), s(elem!1)))),
% 0.65/0.86 inference(modus_ponens,[status(thm)],[3056, 3055])).
% 0.65/0.86 tff(3058,plain,
% 0.65/0.86 (~r(s(s(s(s(s(s(elem!1)))))), s(elem!1))),
% 0.65/0.86 inference(unit_resolution,[status(thm)],[3057, 14, 1555, 3054])).
% 0.65/0.86 tff(3059,plain,
% 0.65/0.86 ((s(s(s(s(s(s(elem!1)))))) = s(elem!1)) | b(s(s(s(s(s(s(elem!1)))))), s(elem!1))),
% 0.65/0.86 inference(unit_resolution,[status(thm)],[1812, 46, 3058])).
% 0.65/0.86 tff(3060,plain,
% 0.65/0.86 (b(s(s(s(s(s(s(elem!1)))))), s(elem!1))),
% 0.65/0.86 inference(unit_resolution,[status(thm)],[3059, 1771])).
% 0.65/0.86 tff(3061,plain,
% 0.65/0.86 (((~![X0: $i, X2: $i, X1: $i] : ((~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), s(elem!1))) | (~b(s(s(s(s(s(s(elem!1)))))), s(elem!1))) | (~b(s(s(s(s(s(s(elem!1)))))), s(s(elem!1)))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(elem!1)), s(elem!1))) | (~b(s(s(s(s(s(s(elem!1)))))), s(elem!1))) | (~b(s(s(s(s(s(s(elem!1)))))), s(s(elem!1)))))),
% 0.65/0.86 inference(rewrite,[status(thm)],[])).
% 0.65/0.86 tff(3062,plain,
% 0.65/0.86 ((~![X0: $i, X2: $i, X1: $i] : ((~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), s(elem!1))) | (~b(s(s(s(s(s(s(elem!1)))))), s(elem!1))) | (~b(s(s(s(s(s(s(elem!1)))))), s(s(elem!1)))))),
% 0.65/0.86 inference(quant_inst,[status(thm)],[])).
% 0.65/0.86 tff(3063,plain,
% 0.65/0.86 ((~![X0: $i, X2: $i, X1: $i] : ((~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(elem!1)), s(elem!1))) | (~b(s(s(s(s(s(s(elem!1)))))), s(elem!1))) | (~b(s(s(s(s(s(s(elem!1)))))), s(s(elem!1))))),
% 0.65/0.86 inference(modus_ponens,[status(thm)],[3062, 3061])).
% 0.65/0.86 tff(3064,plain,
% 0.65/0.86 ($false),
% 0.65/0.86 inference(unit_resolution,[status(thm)],[3063, 117, 836, 3060, 2100])).
% 0.65/0.86 tff(3065,plain,((~r(s(s(s(s(s(s(elem!1)))))), elem!1)) | (~b(s(s(elem!1)), s(elem!1))) | (~(s(s(s(z))) = s(s(s(elem!1))))) | (~r(s(s(elem!1)), elem!1)) | (~r(s(elem!1), elem!1))), inference(lemma,lemma(discharge,[]))).
% 0.65/0.86 tff(3066,plain,
% 0.65/0.86 (~r(s(s(s(s(s(s(elem!1)))))), elem!1)),
% 0.65/0.86 inference(unit_resolution,[status(thm)],[3065, 3053, 3047, 3043, 3036])).
% 0.65/0.86 tff(3067,plain,
% 0.65/0.86 (b(s(s(s(elem!1))), elem!1) <=> b(s(s(s(z))), elem!1)),
% 0.65/0.86 inference(monotonicity,[status(thm)],[2970])).
% 0.65/0.86 tff(3068,plain,
% 0.65/0.86 (b(s(s(s(z))), elem!1) <=> b(s(s(s(elem!1))), elem!1)),
% 0.65/0.86 inference(symmetry,[status(thm)],[3067])).
% 0.65/0.86 tff(3069,plain,
% 0.65/0.86 (b(s(s(s(z))), elem!1) <=> b(s(s(s(z))), z)),
% 0.65/0.86 inference(monotonicity,[status(thm)],[2255])).
% 0.65/0.86 tff(3070,plain,
% 0.65/0.86 (b(s(s(s(z))), z) <=> b(s(s(s(z))), elem!1)),
% 0.65/0.86 inference(symmetry,[status(thm)],[3069])).
% 0.65/0.87 tff(3071,plain,
% 0.65/0.87 (b(s(s(s(z))), elem!1)),
% 0.65/0.87 inference(modus_ponens,[status(thm)],[338, 3070])).
% 0.65/0.87 tff(3072,assumption,(~b(s(s(s(z))), elem!1)), introduced(assumption)).
% 0.65/0.87 tff(3073,plain,
% 0.65/0.87 ($false),
% 0.65/0.87 inference(unit_resolution,[status(thm)],[3072, 3071])).
% 0.65/0.87 tff(3074,plain,((~(s(s(s(elem!1))) = s(s(s(z))))) | b(s(s(s(z))), elem!1) | (~b(s(s(s(z))), z))), inference(lemma,lemma(discharge,[]))).
% 0.65/0.87 tff(3075,plain,
% 0.65/0.87 (b(s(s(s(z))), elem!1)),
% 0.65/0.87 inference(unit_resolution,[status(thm)],[3074, 2970, 338])).
% 0.65/0.87 tff(3076,plain,
% 0.65/0.87 (b(s(s(s(elem!1))), elem!1)),
% 0.65/0.87 inference(modus_ponens,[status(thm)],[3075, 3068])).
% 0.65/0.87 tff(3077,plain,
% 0.65/0.87 (s(s(s(s(elem!1)))) = s(s(s(s(z))))),
% 0.65/0.87 inference(monotonicity,[status(thm)],[2970])).
% 0.65/0.87 tff(3078,plain,
% 0.65/0.87 (b(s(s(s(s(elem!1)))), elem!1) <=> b(s(s(s(s(z)))), elem!1)),
% 0.65/0.87 inference(monotonicity,[status(thm)],[3077])).
% 0.65/0.87 tff(3079,plain,
% 0.65/0.87 (b(s(s(s(s(z)))), elem!1) <=> b(s(s(s(s(elem!1)))), elem!1)),
% 0.65/0.87 inference(symmetry,[status(thm)],[3078])).
% 0.65/0.87 tff(3080,plain,
% 0.65/0.87 (b(s(s(s(s(z)))), elem!1) <=> b(s(s(s(s(z)))), z)),
% 0.65/0.87 inference(monotonicity,[status(thm)],[2976])).
% 0.65/0.87 tff(3081,plain,
% 0.65/0.87 (b(s(s(s(s(z)))), z) <=> b(s(s(s(s(z)))), elem!1)),
% 0.65/0.87 inference(symmetry,[status(thm)],[3080])).
% 0.65/0.87 tff(3082,plain,
% 0.65/0.87 (b(s(s(s(s(z)))), z) <=> b(s(s(s(s(elem!1)))), elem!1)),
% 0.65/0.87 inference(transitivity,[status(thm)],[3081, 3079])).
% 0.65/0.87 tff(3083,plain,
% 0.65/0.87 (b(s(s(s(s(elem!1)))), z) <=> b(s(s(s(s(z)))), z)),
% 0.65/0.87 inference(monotonicity,[status(thm)],[3077])).
% 0.65/0.87 tff(3084,plain,
% 0.65/0.87 (b(s(s(s(s(z)))), z)),
% 0.65/0.87 inference(modus_ponens,[status(thm)],[1310, 3083])).
% 0.65/0.87 tff(3085,plain,
% 0.65/0.87 (b(s(s(s(s(elem!1)))), elem!1)),
% 0.65/0.87 inference(modus_ponens,[status(thm)],[3084, 3082])).
% 0.65/0.87 tff(3086,assumption,(b(s(s(s(s(elem!1)))), elem!1)), introduced(assumption)).
% 0.65/0.87 tff(3087,plain,
% 0.65/0.87 (~b(s(s(s(s(s(s(elem!1)))))), s(s(s(s(elem!1)))))),
% 0.65/0.87 inference(unit_resolution,[status(thm)],[1605, 117, 3086, 1788])).
% 0.65/0.87 tff(3088,plain,
% 0.65/0.87 ((s(s(s(s(s(s(elem!1)))))) = s(s(s(s(z))))) <=> (s(s(s(s(s(s(elem!1)))))) = s(s(s(s(elem!1)))))),
% 0.65/0.87 inference(monotonicity,[status(thm)],[1754])).
% 0.65/0.87 tff(3089,plain,
% 0.65/0.87 ((~(s(s(s(s(s(s(elem!1)))))) = s(s(s(s(z)))))) <=> (~(s(s(s(s(s(s(elem!1)))))) = s(s(s(s(elem!1))))))),
% 0.65/0.87 inference(monotonicity,[status(thm)],[3088])).
% 0.65/0.87 tff(3090,plain,
% 0.65/0.87 (~(s(s(s(s(s(s(elem!1)))))) = s(s(s(s(elem!1)))))),
% 0.65/0.87 inference(modus_ponens,[status(thm)],[319, 3089])).
% 0.65/0.87 tff(3091,plain,
% 0.65/0.87 (r(s(s(s(s(s(s(elem!1)))))), s(s(s(s(elem!1)))))),
% 0.65/0.87 inference(unit_resolution,[status(thm)],[1619, 46, 3090, 3087])).
% 0.65/0.87 tff(3092,assumption,(r(s(s(s(elem!1))), s(s(s(s(elem!1)))))), introduced(assumption)).
% 0.65/0.87 tff(3093,plain,
% 0.65/0.87 (~r(s(s(s(s(s(s(elem!1)))))), s(s(s(elem!1))))),
% 0.65/0.87 inference(unit_resolution,[status(thm)],[2941, 14, 3092, 3091])).
% 0.65/0.87 tff(3094,plain,
% 0.65/0.87 ($false),
% 0.65/0.87 inference(unit_resolution,[status(thm)],[2001, 3093, 2098])).
% 0.65/0.87 tff(3095,plain,((~b(s(s(s(s(s(s(elem!1)))))), elem!1)) | (~r(s(s(s(elem!1))), s(s(s(s(elem!1)))))) | (~(s(s(s(z))) = s(s(s(elem!1))))) | (~b(s(s(s(s(elem!1)))), elem!1)) | (~b(s(s(s(elem!1))), elem!1))), inference(lemma,lemma(discharge,[]))).
% 0.65/0.87 tff(3096,plain,
% 0.65/0.87 (~b(s(s(s(s(s(s(elem!1)))))), elem!1)),
% 0.65/0.87 inference(unit_resolution,[status(thm)],[3095, 3085, 2957, 3047, 3076])).
% 0.65/0.87 tff(3097,plain,
% 0.65/0.87 ($false),
% 0.65/0.87 inference(unit_resolution,[status(thm)],[1599, 3096, 3066, 2980])).
% 0.65/0.87 tff(3098,plain,((s(s(elem!1)) = s(s(s(elem!1)))) | (~b(s(s(s(s(elem!1)))), z)) | (~b(s(s(s(z))), z))), inference(lemma,lemma(discharge,[]))).
% 0.65/0.87 tff(3099,plain,
% 0.65/0.87 (~b(s(s(s(s(elem!1)))), z)),
% 0.65/0.87 inference(unit_resolution,[status(thm)],[3098, 338, 145])).
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% 0.65/0.87 inference(rewrite,[status(thm)],[])).
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% 0.65/0.87 inference(quant_inst,[status(thm)],[])).
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% 0.65/0.87 inference(modus_ponens,[status(thm)],[3191, 3190])).
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% 0.65/0.87 inference(unit_resolution,[status(thm)],[3192, 14, 3189, 3176])).
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% 0.65/0.87 tff(3232,plain,
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% 0.65/0.87 inference(rewrite,[status(thm)],[])).
% 0.65/0.87 tff(3242,plain,
% 0.65/0.87 (((~r(s(s(s(z))), s(s(elem!1)))) | (~r(s(s(s(elem!1))), s(s(elem!1)))) | (~r(s(s(s(elem!1))), s(s(s(z)))))) <=> ((~r(s(s(s(elem!1))), s(s(elem!1)))) | (~r(s(s(s(elem!1))), s(s(s(z))))) | (~r(s(s(s(z))), s(s(elem!1)))))),
% 0.65/0.87 inference(rewrite,[status(thm)],[])).
% 0.65/0.87 tff(3243,plain,
% 0.65/0.87 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(z))), s(s(elem!1)))) | (~r(s(s(s(elem!1))), s(s(elem!1)))) | (~r(s(s(s(elem!1))), s(s(s(z))))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), s(s(elem!1)))) | (~r(s(s(s(elem!1))), s(s(s(z))))) | (~r(s(s(s(z))), s(s(elem!1))))))),
% 0.65/0.88 inference(monotonicity,[status(thm)],[3242])).
% 0.65/0.88 tff(3244,plain,
% 0.65/0.88 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(z))), s(s(elem!1)))) | (~r(s(s(s(elem!1))), s(s(elem!1)))) | (~r(s(s(s(elem!1))), s(s(s(z))))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(elem!1))), s(s(elem!1)))) | (~r(s(s(s(elem!1))), s(s(s(z))))) | (~r(s(s(s(z))), s(s(elem!1)))))),
% 0.65/0.88 inference(transitivity,[status(thm)],[3243, 3241])).
% 0.65/0.88 tff(3245,plain,
% 0.65/0.88 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(z))), s(s(elem!1)))) | (~r(s(s(s(elem!1))), s(s(elem!1)))) | (~r(s(s(s(elem!1))), s(s(s(z))))))),
% 0.65/0.88 inference(quant_inst,[status(thm)],[])).
% 0.65/0.88 tff(3246,plain,
% 0.65/0.88 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(elem!1))), s(s(elem!1)))) | (~r(s(s(s(elem!1))), s(s(s(z))))) | (~r(s(s(s(z))), s(s(elem!1))))),
% 0.65/0.88 inference(modus_ponens,[status(thm)],[3245, 3244])).
% 0.65/0.88 tff(3247,plain,
% 0.65/0.88 ($false),
% 0.65/0.88 inference(unit_resolution,[status(thm)],[3246, 14, 2582, 2329, 943])).
% 0.65/0.88 tff(3248,plain,((~r(s(s(s(z))), s(s(elem!1)))) | (~r(s(s(s(elem!1))), s(s(elem!1)))) | (~r(s(s(s(elem!1))), s(s(s(z)))))), inference(lemma,lemma(discharge,[]))).
% 0.65/0.88 tff(3249,plain,
% 0.65/0.88 (~r(s(s(s(elem!1))), s(s(s(z))))),
% 0.65/0.88 inference(unit_resolution,[status(thm)],[3248, 3240, 2582])).
% 0.65/0.88 tff(3250,assumption,(~b(s(s(s(elem!1))), s(s(s(z))))), introduced(assumption)).
% 0.65/0.88 tff(3251,plain,
% 0.65/0.88 ((s(s(s(elem!1))) = s(s(s(z)))) | r(s(s(s(elem!1))), s(s(s(z))))),
% 0.65/0.88 inference(unit_resolution,[status(thm)],[2341, 46, 3250])).
% 0.65/0.88 tff(3252,plain,
% 0.65/0.88 (s(s(s(elem!1))) = s(s(s(z)))),
% 0.65/0.88 inference(unit_resolution,[status(thm)],[3251, 3249])).
% 0.65/0.88 tff(3253,plain,
% 0.65/0.88 (inj_0(s(s(s(elem!1)))) = inj_0(s(s(s(z))))),
% 0.65/0.88 inference(monotonicity,[status(thm)],[3252])).
% 0.65/0.88 tff(3254,plain,
% 0.65/0.88 (inj_0(s(s(s(z)))) = inj_0(s(s(s(elem!1))))),
% 0.65/0.88 inference(symmetry,[status(thm)],[3253])).
% 0.65/0.88 tff(3255,plain,
% 0.65/0.88 (s(s(z)) = s(s(elem!1))),
% 0.65/0.88 inference(transitivity,[status(thm)],[95, 3254, 151])).
% 0.65/0.88 tff(3256,plain,
% 0.65/0.88 (b(s(s(z)), z) <=> b(s(s(elem!1)), z)),
% 0.65/0.88 inference(monotonicity,[status(thm)],[3255])).
% 0.65/0.88 tff(3257,plain,
% 0.65/0.88 (b(s(s(elem!1)), z) <=> b(s(s(z)), z)),
% 0.65/0.88 inference(symmetry,[status(thm)],[3256])).
% 0.65/0.88 tff(3258,plain,
% 0.65/0.88 (b(s(s(z)), z)),
% 0.65/0.88 inference(modus_ponens,[status(thm)],[1036, 3257])).
% 0.65/0.88 tff(3259,plain,
% 0.65/0.88 (s(s(elem!1)) = s(s(z))),
% 0.65/0.88 inference(transitivity,[status(thm)],[152, 3253, 94])).
% 0.65/0.88 tff(3260,plain,
% 0.65/0.88 (inj_0(s(s(elem!1))) = inj_0(s(s(z)))),
% 0.65/0.88 inference(monotonicity,[status(thm)],[3259])).
% 0.65/0.88 tff(3261,plain,
% 0.65/0.88 (s(elem!1) = s(z)),
% 0.65/0.88 inference(transitivity,[status(thm)],[167, 3260, 82])).
% 0.65/0.88 tff(3262,plain,
% 0.65/0.88 (inj_0(s(elem!1)) = inj_0(s(z))),
% 0.65/0.88 inference(monotonicity,[status(thm)],[3261])).
% 0.65/0.88 tff(3263,plain,
% 0.65/0.88 (elem!1 = z),
% 0.65/0.88 inference(transitivity,[status(thm)],[1652, 3262, 90])).
% 0.65/0.88 tff(3264,plain,
% 0.65/0.88 (s(s(s(s(elem!1)))) = s(s(s(s(z))))),
% 0.65/0.88 inference(monotonicity,[status(thm)],[3252])).
% 0.65/0.88 tff(3265,plain,
% 0.65/0.88 (s(s(s(s(s(elem!1))))) = s(s(s(s(s(z)))))),
% 0.65/0.88 inference(monotonicity,[status(thm)],[3264])).
% 0.65/0.88 tff(3266,plain,
% 0.65/0.88 (s(s(s(s(s(s(elem!1)))))) = s(s(s(s(s(s(z))))))),
% 0.65/0.88 inference(monotonicity,[status(thm)],[3265])).
% 0.65/0.88 tff(3267,plain,
% 0.65/0.88 (b(s(s(s(s(s(s(elem!1)))))), elem!1) <=> b(s(s(s(s(s(s(z)))))), z)),
% 0.65/0.88 inference(monotonicity,[status(thm)],[3266, 3263])).
% 0.65/0.88 tff(3268,plain,
% 0.65/0.88 ((s(s(s(s(s(s(elem!1)))))) = elem!1) <=> (s(s(s(s(s(s(elem!1)))))) = z)),
% 0.65/0.88 inference(monotonicity,[status(thm)],[3263])).
% 0.65/0.88 tff(3269,plain,
% 0.65/0.88 ((s(s(s(s(s(s(elem!1)))))) = z) <=> (s(s(s(s(s(s(elem!1)))))) = elem!1)),
% 0.65/0.88 inference(symmetry,[status(thm)],[3268])).
% 0.65/0.88 tff(3270,plain,
% 0.65/0.88 ((~(s(s(s(s(s(s(elem!1)))))) = z)) <=> (~(s(s(s(s(s(s(elem!1)))))) = elem!1))),
% 0.65/0.88 inference(monotonicity,[status(thm)],[3269])).
% 0.65/0.88 tff(3271,plain,
% 0.65/0.88 (~(s(s(s(s(s(s(elem!1)))))) = elem!1)),
% 0.65/0.88 inference(modus_ponens,[status(thm)],[1663, 3270])).
% 0.65/0.88 tff(3272,plain,
% 0.65/0.88 (b(s(s(s(s(s(s(elem!1)))))), elem!1)),
% 0.65/0.88 inference(unit_resolution,[status(thm)],[1599, 3271, 1920])).
% 0.65/0.88 tff(3273,plain,
% 0.65/0.88 (b(s(s(s(s(s(s(z)))))), z)),
% 0.65/0.88 inference(modus_ponens,[status(thm)],[3272, 3267])).
% 0.65/0.88 tff(3274,plain,
% 0.65/0.88 ((~b(s(s(z)), z)) | (~b(s(s(s(s(s(s(z)))))), s(s(z))))),
% 0.65/0.88 inference(unit_resolution,[status(thm)],[2299, 117, 3273])).
% 0.65/0.88 tff(3275,plain,
% 0.65/0.88 (~b(s(s(s(s(s(s(z)))))), s(s(z)))),
% 0.65/0.88 inference(unit_resolution,[status(thm)],[3274, 3258])).
% 0.65/0.88 tff(3276,plain,
% 0.65/0.88 (r(s(s(s(s(s(s(z)))))), s(s(z)))),
% 0.65/0.88 inference(unit_resolution,[status(thm)],[2304, 46, 1786, 3275])).
% 0.65/0.88 tff(3277,plain,
% 0.65/0.88 (s(s(s(s(s(s(z)))))) = s(s(s(s(s(s(elem!1))))))),
% 0.65/0.88 inference(symmetry,[status(thm)],[3266])).
% 0.65/0.88 tff(3278,plain,
% 0.65/0.88 ((s(s(s(s(s(s(z)))))) = s(s(s(z)))) <=> (s(s(s(s(s(s(elem!1)))))) = s(s(s(z))))),
% 0.65/0.88 inference(monotonicity,[status(thm)],[3277])).
% 0.65/0.88 tff(3279,plain,
% 0.65/0.88 ((s(s(s(s(s(s(elem!1)))))) = s(s(s(z)))) <=> (s(s(s(s(s(s(z)))))) = s(s(s(z))))),
% 0.65/0.88 inference(symmetry,[status(thm)],[3278])).
% 0.65/0.88 tff(3280,plain,
% 0.65/0.88 ((~(s(s(s(s(s(s(elem!1)))))) = s(s(s(z))))) <=> (~(s(s(s(s(s(s(z)))))) = s(s(s(z)))))),
% 0.65/0.88 inference(monotonicity,[status(thm)],[3279])).
% 0.65/0.88 tff(3281,plain,
% 0.65/0.88 (~(s(s(s(s(s(s(z)))))) = s(s(s(z))))),
% 0.65/0.88 inference(modus_ponens,[status(thm)],[1577, 3280])).
% 0.65/0.88 tff(3282,plain,
% 0.65/0.88 (~b(s(s(s(s(s(s(z)))))), s(s(s(z))))),
% 0.65/0.88 inference(unit_resolution,[status(thm)],[3167, 117, 338, 3273])).
% 0.65/0.88 tff(3283,plain,
% 0.65/0.88 ((s(s(s(s(s(s(z)))))) = s(s(s(z)))) | r(s(s(s(s(s(s(z)))))), s(s(s(z))))),
% 0.65/0.88 inference(unit_resolution,[status(thm)],[2289, 46, 3282])).
% 0.65/0.88 tff(3284,plain,
% 0.65/0.88 (r(s(s(s(s(s(s(z)))))), s(s(s(z))))),
% 0.65/0.88 inference(unit_resolution,[status(thm)],[3283, 3281])).
% 0.65/0.88 tff(3285,plain,
% 0.65/0.88 (r(s(s(s(z))), s(s(z))) <=> r(s(s(s(z))), s(s(elem!1)))),
% 0.65/0.88 inference(monotonicity,[status(thm)],[3255])).
% 0.65/0.88 tff(3286,plain,
% 0.65/0.88 (r(s(s(s(z))), s(s(elem!1))) <=> r(s(s(s(z))), s(s(z)))),
% 0.65/0.88 inference(symmetry,[status(thm)],[3285])).
% 0.65/0.88 tff(3287,plain,
% 0.65/0.88 (r(s(s(s(z))), s(s(z)))),
% 0.65/0.88 inference(modus_ponens,[status(thm)],[3240, 3286])).
% 0.65/0.88 tff(3288,plain,
% 0.65/0.88 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(z))), s(s(z)))) | (~r(s(s(s(s(s(s(z)))))), s(s(z)))) | (~r(s(s(s(s(s(s(z)))))), s(s(s(z))))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(z))), s(s(z)))) | (~r(s(s(s(s(s(s(z)))))), s(s(z)))) | (~r(s(s(s(s(s(s(z)))))), s(s(s(z))))))),
% 0.65/0.88 inference(rewrite,[status(thm)],[])).
% 0.65/0.88 tff(3289,plain,
% 0.65/0.88 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(z))), s(s(z)))) | (~r(s(s(s(s(s(s(z)))))), s(s(z)))) | (~r(s(s(s(s(s(s(z)))))), s(s(s(z))))))),
% 0.65/0.88 inference(quant_inst,[status(thm)],[])).
% 0.65/0.88 tff(3290,plain,
% 0.65/0.88 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(z))), s(s(z)))) | (~r(s(s(s(s(s(s(z)))))), s(s(z)))) | (~r(s(s(s(s(s(s(z)))))), s(s(s(z)))))),
% 0.65/0.88 inference(modus_ponens,[status(thm)],[3289, 3288])).
% 0.65/0.88 tff(3291,plain,
% 0.65/0.88 ($false),
% 0.65/0.88 inference(unit_resolution,[status(thm)],[3290, 14, 3287, 3284, 3276])).
% 0.65/0.88 tff(3292,plain,(r(s(s(s(s(s(s(elem!1)))))), elem!1) | (~b(s(s(elem!1)), z)) | (~b(s(s(s(z))), z)) | b(s(s(s(elem!1))), s(s(s(z)))) | (~r(s(s(s(elem!1))), s(s(elem!1)))) | (s(s(s(s(s(s(elem!1)))))) = s(s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(s(s(s(elem!1)))), s(z))) | (~r(s(s(s(elem!1))), s(s(s(s(elem!1))))))), inference(lemma,lemma(discharge,[]))).
% 0.65/0.88 tff(3293,plain,
% 0.65/0.88 (r(s(s(s(s(s(s(elem!1)))))), elem!1)),
% 0.65/0.88 inference(unit_resolution,[status(thm)],[3292, 3224, 338, 1036, 3212, 1919, 3220, 1311, 3223])).
% 0.65/0.88 tff(3294,plain,
% 0.65/0.88 (r(z, s(z)) <=> r(z, elem!1)),
% 0.65/0.88 inference(monotonicity,[status(thm)],[2020])).
% 0.65/0.88 tff(3295,plain,
% 0.65/0.88 (((~![X0: $i, X2: $i, X1: $i] : ((~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, elem!1)) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(s(s(elem!1))), z)))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, elem!1)) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(s(s(elem!1))), z)))),
% 0.65/0.88 inference(rewrite,[status(thm)],[])).
% 0.65/0.88 tff(3296,plain,
% 0.65/0.88 ((~![X0: $i, X2: $i, X1: $i] : ((~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, elem!1)) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(s(s(elem!1))), z)))),
% 0.65/0.88 inference(quant_inst,[status(thm)],[])).
% 0.65/0.88 tff(3297,plain,
% 0.65/0.88 ((~![X0: $i, X2: $i, X1: $i] : ((~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, elem!1)) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(s(s(elem!1))), z))),
% 0.65/0.88 inference(modus_ponens,[status(thm)],[3296, 3295])).
% 0.65/0.88 tff(3298,plain,
% 0.65/0.88 (~b(z, elem!1)),
% 0.65/0.88 inference(unit_resolution,[status(thm)],[3297, 117, 157, 1996])).
% 0.65/0.88 tff(3299,plain,
% 0.65/0.88 ($false),
% 0.65/0.88 inference(unit_resolution,[status(thm)],[3298, 1992])).
% 0.65/0.88 tff(3300,plain,((~b(z, s(z))) | (~(s(s(s(z))) = s(s(elem!1)))) | (~b(s(s(s(elem!1))), z)) | (~b(s(s(s(elem!1))), elem!1))), inference(lemma,lemma(discharge,[]))).
% 0.65/0.88 tff(3301,plain,
% 0.65/0.88 (~b(z, s(z))),
% 0.65/0.88 inference(unit_resolution,[status(thm)],[3300, 1434, 157, 3233])).
% 0.65/0.88 tff(3302,plain,
% 0.65/0.88 (r(z, s(z))),
% 0.65/0.88 inference(unit_resolution,[status(thm)],[599, 3301])).
% 0.65/0.88 tff(3303,plain,
% 0.65/0.88 (r(z, elem!1)),
% 0.65/0.88 inference(modus_ponens,[status(thm)],[3302, 3294])).
% 0.65/0.88 tff(3304,plain,
% 0.65/0.88 (~r(z, elem!1)),
% 0.65/0.88 inference(unit_resolution,[status(thm)],[2927, 2050, 1555, 1434, 1036])).
% 0.65/0.88 tff(3305,plain,
% 0.65/0.88 ($false),
% 0.65/0.88 inference(unit_resolution,[status(thm)],[3304, 3303])).
% 0.65/0.88 tff(3306,plain,((~(s(s(s(z))) = s(s(elem!1)))) | (~b(s(s(s(elem!1))), z)) | (~r(s(s(s(s(s(s(elem!1)))))), elem!1)) | (~b(s(s(elem!1)), z)) | (~b(s(s(s(elem!1))), s(z))) | (~r(s(s(elem!1)), s(z)))), inference(lemma,lemma(discharge,[]))).
% 0.65/0.88 tff(3307,plain,
% 0.65/0.88 (~(s(s(s(z))) = s(s(elem!1)))),
% 0.65/0.88 inference(unit_resolution,[status(thm)],[3306, 3207, 3293, 1036, 3220, 179])).
% 0.65/0.88 tff(3308,plain,
% 0.65/0.88 (r(s(s(s(z))), s(s(elem!1)))),
% 0.65/0.88 inference(unit_resolution,[status(thm)],[3239, 3307])).
% 0.65/0.88 tff(3309,plain,
% 0.65/0.88 (~r(s(s(s(elem!1))), s(s(s(z))))),
% 0.65/0.88 inference(unit_resolution,[status(thm)],[3248, 3308, 3212])).
% 0.65/0.88 tff(3310,plain,
% 0.65/0.88 ((s(s(s(elem!1))) = s(s(s(z)))) | r(s(s(s(elem!1))), s(s(s(z))))),
% 0.65/0.88 inference(unit_resolution,[status(thm)],[2341, 46, 3224])).
% 0.65/0.88 tff(3311,plain,
% 0.65/0.88 (s(s(s(elem!1))) = s(s(s(z)))),
% 0.65/0.88 inference(unit_resolution,[status(thm)],[3310, 3309])).
% 0.65/0.88 tff(3312,plain,
% 0.65/0.88 (inj_0(s(s(s(elem!1)))) = inj_0(s(s(s(z))))),
% 0.65/0.88 inference(monotonicity,[status(thm)],[3311])).
% 0.65/0.88 tff(3313,plain,
% 0.65/0.88 (s(s(elem!1)) = s(s(z))),
% 0.65/0.88 inference(transitivity,[status(thm)],[152, 3312, 94])).
% 0.65/0.88 tff(3314,plain,
% 0.65/0.88 (inj_0(s(s(elem!1))) = inj_0(s(s(z)))),
% 0.65/0.88 inference(monotonicity,[status(thm)],[3313])).
% 0.65/0.88 tff(3315,plain,
% 0.65/0.88 (s(elem!1) = s(z)),
% 0.65/0.88 inference(transitivity,[status(thm)],[167, 3314, 82])).
% 0.65/0.88 tff(3316,plain,
% 0.65/0.88 (inj_0(s(elem!1)) = inj_0(s(z))),
% 0.65/0.88 inference(monotonicity,[status(thm)],[3315])).
% 0.65/0.88 tff(3317,plain,
% 0.65/0.88 (elem!1 = z),
% 0.65/0.88 inference(transitivity,[status(thm)],[1652, 3316, 90])).
% 0.65/0.88 tff(3318,plain,
% 0.65/0.88 (s(s(s(s(elem!1)))) = s(s(s(s(z))))),
% 0.65/0.88 inference(monotonicity,[status(thm)],[3311])).
% 0.65/0.88 tff(3319,plain,
% 0.65/0.88 (s(s(s(s(s(elem!1))))) = s(s(s(s(s(z)))))),
% 0.65/0.88 inference(monotonicity,[status(thm)],[3318])).
% 0.65/0.88 tff(3320,plain,
% 0.65/0.88 (s(s(s(s(s(s(elem!1)))))) = s(s(s(s(s(s(z))))))),
% 0.65/0.88 inference(monotonicity,[status(thm)],[3319])).
% 0.65/0.88 tff(3321,plain,
% 0.65/0.88 (r(s(s(s(s(s(s(elem!1)))))), elem!1) <=> r(s(s(s(s(s(s(z)))))), z)),
% 0.65/0.88 inference(monotonicity,[status(thm)],[3320, 3317])).
% 0.65/0.88 tff(3322,plain,
% 0.65/0.88 (r(s(s(s(s(s(s(z)))))), z)),
% 0.65/0.88 inference(modus_ponens,[status(thm)],[3293, 3321])).
% 0.65/0.88 tff(3323,plain,
% 0.65/0.88 (~r(s(s(s(s(s(s(z)))))), s(z))),
% 0.65/0.88 inference(unit_resolution,[status(thm)],[2269, 14, 183, 3322])).
% 0.65/0.88 tff(3324,plain,
% 0.65/0.88 (b(s(s(s(s(s(s(z)))))), s(z))),
% 0.65/0.88 inference(unit_resolution,[status(thm)],[2274, 46, 1770, 3323])).
% 0.65/0.88 tff(3325,plain,
% 0.65/0.88 (b(s(s(s(s(elem!1)))), s(z)) <=> b(s(s(s(s(z)))), s(z))),
% 0.65/0.88 inference(monotonicity,[status(thm)],[3318])).
% 0.65/0.88 tff(3326,plain,
% 0.65/0.88 (b(s(s(s(s(z)))), s(z))),
% 0.65/0.88 inference(modus_ponens,[status(thm)],[1311, 3325])).
% 0.65/0.88 tff(3327,plain,
% 0.65/0.88 (((~![X0: $i, X2: $i, X1: $i] : ((~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(s(s(s(z)))))), s(z))) | (~b(s(s(s(s(z)))), s(s(s(s(s(s(z)))))))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(s(s(s(z)))))), s(z))) | (~b(s(s(s(s(z)))), s(s(s(s(s(s(z)))))))))),
% 0.65/0.88 inference(rewrite,[status(thm)],[])).
% 0.65/0.88 tff(3328,plain,
% 0.65/0.88 (((~b(s(s(s(s(s(s(z)))))), s(z))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(s(z)))), s(s(s(s(s(s(z))))))))) <=> ((~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(s(s(s(z)))))), s(z))) | (~b(s(s(s(s(z)))), s(s(s(s(s(s(z)))))))))),
% 0.65/0.88 inference(rewrite,[status(thm)],[])).
% 0.65/0.88 tff(3329,plain,
% 0.65/0.88 (((~![X0: $i, X2: $i, X1: $i] : ((~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(s(z)))))), s(z))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(s(z)))), s(s(s(s(s(s(z)))))))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(s(s(s(z)))))), s(z))) | (~b(s(s(s(s(z)))), s(s(s(s(s(s(z))))))))))),
% 0.65/0.88 inference(monotonicity,[status(thm)],[3328])).
% 0.65/0.88 tff(3330,plain,
% 0.65/0.88 (((~![X0: $i, X2: $i, X1: $i] : ((~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(s(z)))))), s(z))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(s(z)))), s(s(s(s(s(s(z)))))))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(s(s(s(z)))))), s(z))) | (~b(s(s(s(s(z)))), s(s(s(s(s(s(z)))))))))),
% 0.65/0.88 inference(transitivity,[status(thm)],[3329, 3327])).
% 0.65/0.88 tff(3331,plain,
% 0.65/0.88 ((~![X0: $i, X2: $i, X1: $i] : ((~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(s(z)))))), s(z))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(s(z)))), s(s(s(s(s(s(z)))))))))),
% 0.65/0.88 inference(quant_inst,[status(thm)],[])).
% 0.65/0.88 tff(3332,plain,
% 0.65/0.88 ((~![X0: $i, X2: $i, X1: $i] : ((~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(s(s(s(z)))))), s(z))) | (~b(s(s(s(s(z)))), s(s(s(s(s(s(z))))))))),
% 0.65/0.88 inference(modus_ponens,[status(thm)],[3331, 3330])).
% 0.65/0.88 tff(3333,plain,
% 0.65/0.88 (~b(s(s(s(s(z)))), s(s(s(s(s(s(z)))))))),
% 0.65/0.88 inference(unit_resolution,[status(thm)],[3332, 117, 3326, 3324])).
% 0.65/0.88 tff(3334,plain,
% 0.65/0.88 (r(s(s(s(s(elem!1)))), z) <=> r(s(s(s(s(z)))), z)),
% 0.65/0.88 inference(monotonicity,[status(thm)],[3318])).
% 0.65/0.88 tff(3335,plain,
% 0.65/0.88 (r(s(s(s(s(z)))), z)),
% 0.65/0.88 inference(modus_ponens,[status(thm)],[1396, 3334])).
% 0.65/0.88 tff(3336,plain,
% 0.65/0.88 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(z)))), z)) | (~r(s(s(s(s(s(s(z)))))), z)) | (~r(s(s(s(s(z)))), s(s(s(s(s(s(z)))))))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(s(z)))), z)) | (~r(s(s(s(s(s(s(z)))))), z)) | (~r(s(s(s(s(z)))), s(s(s(s(s(s(z)))))))))),
% 0.65/0.88 inference(rewrite,[status(thm)],[])).
% 0.65/0.88 tff(3337,plain,
% 0.65/0.88 (((~r(s(s(s(s(s(s(z)))))), z)) | (~r(s(s(s(s(z)))), z)) | (~r(s(s(s(s(z)))), s(s(s(s(s(s(z))))))))) <=> ((~r(s(s(s(s(z)))), z)) | (~r(s(s(s(s(s(s(z)))))), z)) | (~r(s(s(s(s(z)))), s(s(s(s(s(s(z)))))))))),
% 0.65/0.88 inference(rewrite,[status(thm)],[])).
% 0.65/0.88 tff(3338,plain,
% 0.65/0.88 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(s(s(z)))))), z)) | (~r(s(s(s(s(z)))), z)) | (~r(s(s(s(s(z)))), s(s(s(s(s(s(z)))))))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(z)))), z)) | (~r(s(s(s(s(s(s(z)))))), z)) | (~r(s(s(s(s(z)))), s(s(s(s(s(s(z))))))))))),
% 0.65/0.88 inference(monotonicity,[status(thm)],[3337])).
% 0.65/0.88 tff(3339,plain,
% 0.65/0.88 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(s(s(z)))))), z)) | (~r(s(s(s(s(z)))), z)) | (~r(s(s(s(s(z)))), s(s(s(s(s(s(z)))))))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(s(z)))), z)) | (~r(s(s(s(s(s(s(z)))))), z)) | (~r(s(s(s(s(z)))), s(s(s(s(s(s(z)))))))))),
% 0.65/0.88 inference(transitivity,[status(thm)],[3338, 3336])).
% 0.65/0.88 tff(3340,plain,
% 0.65/0.88 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(s(s(z)))))), z)) | (~r(s(s(s(s(z)))), z)) | (~r(s(s(s(s(z)))), s(s(s(s(s(s(z)))))))))),
% 0.65/0.88 inference(quant_inst,[status(thm)],[])).
% 0.65/0.88 tff(3341,plain,
% 0.65/0.88 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(s(z)))), z)) | (~r(s(s(s(s(s(s(z)))))), z)) | (~r(s(s(s(s(z)))), s(s(s(s(s(s(z))))))))),
% 0.65/0.88 inference(modus_ponens,[status(thm)],[3340, 3339])).
% 0.65/0.88 tff(3342,plain,
% 0.65/0.88 (~r(s(s(s(s(z)))), s(s(s(s(s(s(z)))))))),
% 0.65/0.88 inference(unit_resolution,[status(thm)],[3341, 14, 3335, 3322])).
% 0.65/0.88 tff(3343,plain,
% 0.65/0.88 (((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((s(s(s(s(z)))) = s(s(s(s(s(s(z))))))) | b(s(s(s(s(z)))), s(s(s(s(s(s(z))))))) | r(s(s(s(s(z)))), s(s(s(s(s(s(z))))))))) <=> ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (s(s(s(s(z)))) = s(s(s(s(s(s(z))))))) | b(s(s(s(s(z)))), s(s(s(s(s(s(z))))))) | r(s(s(s(s(z)))), s(s(s(s(s(s(z))))))))),
% 0.65/0.88 inference(rewrite,[status(thm)],[])).
% 0.65/0.88 tff(3344,plain,
% 0.65/0.88 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((s(s(s(s(z)))) = s(s(s(s(s(s(z))))))) | b(s(s(s(s(z)))), s(s(s(s(s(s(z))))))) | r(s(s(s(s(z)))), s(s(s(s(s(s(z))))))))),
% 0.65/0.88 inference(quant_inst,[status(thm)],[])).
% 0.65/0.88 tff(3345,plain,
% 0.65/0.88 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (s(s(s(s(z)))) = s(s(s(s(s(s(z))))))) | b(s(s(s(s(z)))), s(s(s(s(s(s(z))))))) | r(s(s(s(s(z)))), s(s(s(s(s(s(z)))))))),
% 0.65/0.88 inference(modus_ponens,[status(thm)],[3344, 3343])).
% 0.65/0.88 tff(3346,plain,
% 0.65/0.88 (s(s(s(s(z)))) = s(s(s(s(s(s(z))))))),
% 0.65/0.88 inference(unit_resolution,[status(thm)],[3345, 46, 3342, 3333])).
% 0.65/0.88 tff(3347,plain,
% 0.65/0.88 (s(s(s(s(s(s(z)))))) = s(s(s(s(z))))),
% 0.65/0.88 inference(symmetry,[status(thm)],[3346])).
% 0.65/0.88 tff(3348,plain,
% 0.65/0.88 (s(s(s(s(s(s(elem!1)))))) = s(s(s(s(z))))),
% 0.65/0.88 inference(transitivity,[status(thm)],[3320, 3347])).
% 0.65/0.88 tff(3349,plain,
% 0.65/0.88 ($false),
% 0.65/0.88 inference(unit_resolution,[status(thm)],[319, 3348])).
% 0.65/0.88 tff(3350,plain,((~r(s(s(elem!1)), s(s(s(elem!1))))) | (~r(s(z), z)) | (~r(s(s(s(s(elem!1)))), z)) | (~b(s(s(s(s(elem!1)))), s(z))) | (~b(s(s(elem!1)), z)) | (~b(s(s(s(z))), z)) | (s(s(s(s(s(s(elem!1)))))) = s(s(s(s(elem!1))))) | (s(s(s(elem!1))) = s(s(elem!1))) | (s(s(s(s(elem!1)))) = s(s(s(elem!1)))) | b(s(s(elem!1)), s(z))), inference(lemma,lemma(discharge,[]))).
% 0.65/0.88 tff(3351,plain,
% 0.65/0.88 (~r(s(s(elem!1)), s(s(s(elem!1))))),
% 0.65/0.88 inference(unit_resolution,[status(thm)],[3350, 183, 3202, 3200, 3198, 2475, 2024, 1539, 156, 158])).
% 0.65/0.88 tff(3352,plain,
% 0.65/0.88 (b(s(s(elem!1)), s(s(s(elem!1))))),
% 0.65/0.88 inference(unit_resolution,[status(thm)],[253, 3351, 145])).
% 0.65/0.88 tff(3353,plain,
% 0.65/0.88 (~b(s(s(s(elem!1))), z)),
% 0.65/0.88 inference(unit_resolution,[status(thm)],[1046, 3352, 3198])).
% 0.65/0.88 tff(3354,plain,
% 0.65/0.88 (r(s(s(s(elem!1))), z)),
% 0.65/0.88 inference(unit_resolution,[status(thm)],[211, 3353])).
% 0.65/0.88 tff(3355,plain,
% 0.65/0.88 (~r(s(z), s(s(s(elem!1))))),
% 0.65/0.88 inference(unit_resolution,[status(thm)],[2508, 3354, 183])).
% 0.65/0.88 tff(3356,plain,
% 0.65/0.88 (b(s(z), s(s(s(elem!1))))),
% 0.65/0.88 inference(unit_resolution,[status(thm)],[235, 3355])).
% 0.65/0.88 tff(3357,plain,
% 0.65/0.88 (~r(s(s(s(s(elem!1)))), s(s(s(elem!1))))),
% 0.65/0.88 inference(unit_resolution,[status(thm)],[1525, 3354, 3202])).
% 0.65/0.88 tff(3358,plain,
% 0.65/0.88 (b(s(s(s(s(elem!1)))), s(s(s(elem!1))))),
% 0.65/0.88 inference(unit_resolution,[status(thm)],[1347, 3357, 156])).
% 0.65/0.88 tff(3359,plain,
% 0.65/0.88 ($false),
% 0.65/0.88 inference(unit_resolution,[status(thm)],[1679, 3358, 3356, 3200])).
% 0.65/0.88 tff(3360,plain,((~r(s(z), z)) | (s(s(elem!1)) = s(s(s(elem!1)))) | b(s(s(elem!1)), s(z)) | (s(s(s(s(elem!1)))) = s(s(elem!1)))), inference(lemma,lemma(discharge,[]))).
% 0.65/0.88 tff(3361,plain,
% 0.65/0.88 (~r(s(z), z)),
% 0.65/0.88 inference(unit_resolution,[status(thm)],[3360, 146, 158, 145])).
% 0.65/0.88 tff(3362,plain,
% 0.65/0.88 (b(s(z), z)),
% 0.65/0.88 inference(unit_resolution,[status(thm)],[193, 3361])).
% 0.65/0.88 tff(3363,plain,
% 0.65/0.88 (~b(s(s(s(z))), s(z))),
% 0.65/0.88 inference(unit_resolution,[status(thm)],[1389, 3362, 2475])).
% 0.65/0.88 tff(3364,plain,
% 0.65/0.88 (r(s(s(s(z))), s(z))),
% 0.65/0.88 inference(unit_resolution,[status(thm)],[347, 3363])).
% 0.65/0.88 tff(3365,plain,
% 0.65/0.88 (~r(s(s(s(z))), s(s(elem!1)))),
% 0.65/0.88 inference(unit_resolution,[status(thm)],[2626, 3364, 179])).
% 0.65/0.88 tff(3366,plain,
% 0.65/0.88 (~b(s(s(s(z))), s(s(elem!1)))),
% 0.65/0.88 inference(unit_resolution,[status(thm)],[1217, 3198, 2475])).
% 0.65/0.88 tff(3367,plain,
% 0.65/0.88 ((s(s(s(z))) = s(s(elem!1))) | r(s(s(s(z))), s(s(elem!1)))),
% 0.65/0.88 inference(unit_resolution,[status(thm)],[1421, 46, 3366])).
% 0.65/0.88 tff(3368,plain,
% 0.65/0.88 (s(s(s(z))) = s(s(elem!1))),
% 0.65/0.88 inference(unit_resolution,[status(thm)],[3367, 3365])).
% 0.65/0.88 tff(3369,plain,
% 0.65/0.88 (r(s(s(s(elem!1))), s(s(s(z)))) <=> r(s(s(s(elem!1))), s(s(elem!1)))),
% 0.65/0.88 inference(monotonicity,[status(thm)],[3368])).
% 0.65/0.88 tff(3370,plain,
% 0.65/0.88 (r(s(s(s(elem!1))), s(s(elem!1))) <=> r(s(s(s(elem!1))), s(s(s(z))))),
% 0.65/0.88 inference(symmetry,[status(thm)],[3369])).
% 0.65/0.88 tff(3371,plain,
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% 0.65/0.88 inference(monotonicity,[status(thm)],[3368])).
% 0.65/0.88 tff(3372,plain,
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% 0.65/0.88 inference(transitivity,[status(thm)],[95, 3371, 166])).
% 0.65/0.88 tff(3373,plain,
% 0.65/0.88 (inj_0(s(s(z))) = inj_0(s(elem!1))),
% 0.65/0.88 inference(monotonicity,[status(thm)],[3372])).
% 0.65/0.88 tff(3374,plain,
% 0.65/0.88 (s(z) = elem!1),
% 0.65/0.88 inference(transitivity,[status(thm)],[131, 3373, 257])).
% 0.65/0.88 tff(3375,plain,
% 0.65/0.88 (r(s(s(elem!1)), s(z)) <=> r(s(s(elem!1)), elem!1)),
% 0.65/0.88 inference(monotonicity,[status(thm)],[3374])).
% 0.65/0.88 tff(3376,plain,
% 0.65/0.88 (r(s(s(elem!1)), elem!1)),
% 0.65/0.88 inference(modus_ponens,[status(thm)],[179, 3375])).
% 0.65/0.88 tff(3377,plain,
% 0.65/0.88 (~(s(s(s(s(s(s(elem!1)))))) = elem!1)),
% 0.65/0.88 inference(unit_resolution,[status(thm)],[1446, 3368])).
% 0.65/0.88 tff(3378,plain,
% 0.65/0.88 (~r(s(s(s(z))), s(s(elem!1)))),
% 0.65/0.88 inference(unit_resolution,[status(thm)],[2626, 3160, 181])).
% 0.65/0.88 tff(3379,plain,
% 0.65/0.88 (~r(s(s(elem!1)), z)),
% 0.65/0.88 inference(unit_resolution,[status(thm)],[3196, 146, 145, 338, 181])).
% 0.65/0.88 tff(3380,plain,
% 0.65/0.88 (b(s(s(elem!1)), z)),
% 0.65/0.88 inference(unit_resolution,[status(thm)],[1025, 3379])).
% 0.65/0.88 tff(3381,plain,
% 0.65/0.88 (~b(s(s(s(z))), s(s(elem!1)))),
% 0.65/0.88 inference(unit_resolution,[status(thm)],[1217, 3380, 338])).
% 0.65/0.88 tff(3382,plain,
% 0.65/0.88 ((s(s(s(z))) = s(s(elem!1))) | r(s(s(s(z))), s(s(elem!1)))),
% 0.65/0.88 inference(unit_resolution,[status(thm)],[1421, 46, 3381])).
% 0.65/0.88 tff(3383,plain,
% 0.65/0.88 (s(s(s(z))) = s(s(elem!1))),
% 0.65/0.88 inference(unit_resolution,[status(thm)],[3382, 3378])).
% 0.65/0.88 tff(3384,plain,
% 0.65/0.88 (inj_0(s(s(s(z)))) = inj_0(s(s(elem!1)))),
% 0.65/0.88 inference(monotonicity,[status(thm)],[3383])).
% 0.65/0.88 tff(3385,plain,
% 0.65/0.88 (s(s(z)) = s(elem!1)),
% 0.65/0.88 inference(transitivity,[status(thm)],[95, 3384, 166])).
% 0.65/0.88 tff(3386,plain,
% 0.65/0.88 (inj_0(s(s(z))) = inj_0(s(elem!1))),
% 0.65/0.88 inference(monotonicity,[status(thm)],[3385])).
% 0.65/0.88 tff(3387,plain,
% 0.65/0.88 (inj_0(s(elem!1)) = inj_0(s(s(z)))),
% 0.65/0.88 inference(symmetry,[status(thm)],[3386])).
% 0.65/0.88 tff(3388,plain,
% 0.65/0.88 (elem!1 = s(z)),
% 0.65/0.88 inference(transitivity,[status(thm)],[1652, 3387, 82])).
% 0.65/0.88 tff(3389,plain,
% 0.65/0.88 (b(z, elem!1) <=> b(z, s(z))),
% 0.65/0.88 inference(monotonicity,[status(thm)],[3388])).
% 0.65/0.88 tff(3390,plain,
% 0.65/0.88 (b(z, s(z)) <=> b(z, elem!1)),
% 0.65/0.88 inference(symmetry,[status(thm)],[3389])).
% 0.65/0.88 tff(3391,plain,
% 0.65/0.88 (s(z) = elem!1),
% 0.65/0.88 inference(transitivity,[status(thm)],[131, 3386, 257])).
% 0.65/0.88 tff(3392,plain,
% 0.65/0.88 (r(z, s(z)) <=> r(z, elem!1)),
% 0.65/0.88 inference(monotonicity,[status(thm)],[3391])).
% 0.65/0.88 tff(3393,plain,
% 0.65/0.88 (r(z, elem!1) <=> r(z, s(z))),
% 0.65/0.88 inference(symmetry,[status(thm)],[3392])).
% 0.65/0.88 tff(3394,plain,
% 0.65/0.88 ((~r(z, elem!1)) <=> (~r(z, s(z)))),
% 0.65/0.88 inference(monotonicity,[status(thm)],[3393])).
% 0.65/0.88 tff(3395,plain,
% 0.65/0.88 (r(s(z), s(s(s(elem!1)))) <=> r(elem!1, s(s(s(elem!1))))),
% 0.65/0.88 inference(monotonicity,[status(thm)],[3391])).
% 0.65/0.88 tff(3396,plain,
% 0.65/0.88 (~b(s(s(s(elem!1))), z)),
% 0.65/0.88 inference(unit_resolution,[status(thm)],[1050, 237, 3380, 145])).
% 0.65/0.88 tff(3397,plain,
% 0.65/0.88 (r(s(s(s(elem!1))), z)),
% 0.65/0.88 inference(unit_resolution,[status(thm)],[211, 3396])).
% 0.65/0.88 tff(3398,plain,
% 0.65/0.88 (~r(s(s(s(s(elem!1)))), s(s(s(elem!1))))),
% 0.65/0.88 inference(unit_resolution,[status(thm)],[1525, 3397, 3100])).
% 0.65/0.88 tff(3399,plain,
% 0.65/0.88 (b(s(s(s(s(elem!1)))), s(s(s(elem!1))))),
% 0.65/0.88 inference(unit_resolution,[status(thm)],[1347, 3398, 156])).
% 0.65/0.88 tff(3400,plain,
% 0.65/0.88 ((s(z) = s(s(elem!1))) <=> (elem!1 = s(s(elem!1)))),
% 0.65/0.88 inference(monotonicity,[status(thm)],[3391])).
% 0.65/0.88 tff(3401,plain,
% 0.65/0.88 ((s(z) = s(s(elem!1))) <=> (s(s(elem!1)) = elem!1)),
% 0.65/0.88 inference(transitivity,[status(thm)],[3400, 2396])).
% 0.65/0.88 tff(3402,plain,
% 0.65/0.88 ((s(z) = s(s(elem!1))) <=> (elem!1 = s(s(elem!1)))),
% 0.65/0.88 inference(transitivity,[status(thm)],[3401, 2397])).
% 0.65/0.88 tff(3403,plain,
% 0.65/0.88 ((~(s(z) = s(s(elem!1)))) <=> (~(elem!1 = s(s(elem!1))))),
% 0.65/0.88 inference(monotonicity,[status(thm)],[3402])).
% 0.65/0.89 tff(3404,plain,
% 0.65/0.89 (~(elem!1 = s(s(elem!1)))),
% 0.65/0.89 inference(modus_ponens,[status(thm)],[172, 3403])).
% 0.65/0.89 tff(3405,plain,
% 0.65/0.89 (b(s(z), z) <=> b(elem!1, z)),
% 0.65/0.89 inference(monotonicity,[status(thm)],[3391])).
% 0.65/0.89 tff(3406,plain,
% 0.65/0.89 (b(elem!1, z)),
% 0.65/0.89 inference(modus_ponens,[status(thm)],[237, 3405])).
% 0.65/0.89 tff(3407,plain,
% 0.65/0.89 (((~![X0: $i, X2: $i, X1: $i] : ((~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), z)) | (~b(elem!1, s(s(elem!1)))) | (~b(elem!1, z)))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(elem!1)), z)) | (~b(elem!1, s(s(elem!1)))) | (~b(elem!1, z)))),
% 0.65/0.89 inference(rewrite,[status(thm)],[])).
% 0.65/0.89 tff(3408,plain,
% 0.65/0.89 (((~b(s(s(elem!1)), z)) | (~b(elem!1, z)) | (~b(elem!1, s(s(elem!1))))) <=> ((~b(s(s(elem!1)), z)) | (~b(elem!1, s(s(elem!1)))) | (~b(elem!1, z)))),
% 0.65/0.89 inference(rewrite,[status(thm)],[])).
% 0.65/0.89 tff(3409,plain,
% 0.65/0.89 (((~![X0: $i, X2: $i, X1: $i] : ((~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), z)) | (~b(elem!1, z)) | (~b(elem!1, s(s(elem!1)))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), z)) | (~b(elem!1, s(s(elem!1)))) | (~b(elem!1, z))))),
% 0.65/0.89 inference(monotonicity,[status(thm)],[3408])).
% 0.65/0.89 tff(3410,plain,
% 0.65/0.89 (((~![X0: $i, X2: $i, X1: $i] : ((~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), z)) | (~b(elem!1, z)) | (~b(elem!1, s(s(elem!1)))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(elem!1)), z)) | (~b(elem!1, s(s(elem!1)))) | (~b(elem!1, z)))),
% 0.65/0.89 inference(transitivity,[status(thm)],[3409, 3407])).
% 0.65/0.89 tff(3411,plain,
% 0.65/0.89 ((~![X0: $i, X2: $i, X1: $i] : ((~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), z)) | (~b(elem!1, z)) | (~b(elem!1, s(s(elem!1)))))),
% 0.65/0.89 inference(quant_inst,[status(thm)],[])).
% 0.65/0.89 tff(3412,plain,
% 0.65/0.89 ((~![X0: $i, X2: $i, X1: $i] : ((~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(elem!1)), z)) | (~b(elem!1, s(s(elem!1)))) | (~b(elem!1, z))),
% 0.65/0.89 inference(modus_ponens,[status(thm)],[3411, 3410])).
% 0.65/0.89 tff(3413,plain,
% 0.65/0.89 (~b(elem!1, s(s(elem!1)))),
% 0.65/0.89 inference(unit_resolution,[status(thm)],[3412, 117, 3380, 3406])).
% 0.65/0.89 tff(3414,plain,
% 0.65/0.89 (r(elem!1, s(s(elem!1)))),
% 0.65/0.89 inference(unit_resolution,[status(thm)],[2895, 3413, 3404])).
% 0.65/0.89 tff(3415,plain,
% 0.65/0.89 (r(z, elem!1) <=> r(z, s(z))),
% 0.65/0.89 inference(symmetry,[status(thm)],[3294])).
% 0.65/0.89 tff(3416,plain,
% 0.65/0.89 ((~r(z, elem!1)) <=> (~r(z, s(z)))),
% 0.65/0.89 inference(monotonicity,[status(thm)],[3415])).
% 0.65/0.89 tff(3417,plain,
% 0.65/0.89 (b(z, s(s(s(z)))) <=> b(z, s(s(elem!1)))),
% 0.65/0.89 inference(monotonicity,[status(thm)],[1434])).
% 0.65/0.89 tff(3418,plain,
% 0.65/0.89 (r(z, s(s(elem!1))) <=> r(z, s(s(s(z))))),
% 0.65/0.89 inference(monotonicity,[status(thm)],[1566])).
% 0.65/0.89 tff(3419,plain,
% 0.65/0.89 ((~r(z, s(s(elem!1)))) <=> (~r(z, s(s(s(z)))))),
% 0.65/0.89 inference(monotonicity,[status(thm)],[3418])).
% 0.65/0.89 tff(3420,plain,
% 0.65/0.89 (~r(s(s(s(s(elem!1)))), s(s(s(elem!1))))),
% 0.65/0.89 inference(unit_resolution,[status(thm)],[1525, 196, 1396])).
% 0.65/0.89 tff(3421,plain,
% 0.65/0.89 (b(s(s(s(s(elem!1)))), s(s(s(elem!1))))),
% 0.65/0.89 inference(unit_resolution,[status(thm)],[1347, 3420, 156])).
% 0.65/0.89 tff(3422,plain,
% 0.65/0.89 (~b(s(s(elem!1)), s(s(s(elem!1))))),
% 0.65/0.89 inference(unit_resolution,[status(thm)],[1488, 2189, 3421])).
% 0.65/0.89 tff(3423,plain,
% 0.65/0.89 (r(s(s(elem!1)), s(s(s(elem!1))))),
% 0.65/0.89 inference(unit_resolution,[status(thm)],[253, 3422, 145])).
% 0.65/0.89 tff(3424,plain,
% 0.65/0.89 (~r(s(z), s(s(s(elem!1))))),
% 0.65/0.89 inference(unit_resolution,[status(thm)],[221, 3423, 181])).
% 0.65/0.89 tff(3425,plain,
% 0.65/0.89 (b(s(z), s(s(s(elem!1))))),
% 0.65/0.89 inference(unit_resolution,[status(thm)],[235, 3424])).
% 0.65/0.89 tff(3426,plain,
% 0.65/0.89 (~b(z, s(s(s(elem!1))))),
% 0.65/0.89 inference(unit_resolution,[status(thm)],[682, 3425, 237])).
% 0.65/0.89 tff(3427,plain,
% 0.65/0.89 (r(z, s(s(s(elem!1))))),
% 0.65/0.89 inference(unit_resolution,[status(thm)],[692, 3426])).
% 0.65/0.89 tff(3428,plain,
% 0.65/0.89 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(elem!1)))) | (~r(z, s(s(s(elem!1))))) | (~r(s(s(elem!1)), s(s(s(elem!1))))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, s(s(elem!1)))) | (~r(z, s(s(s(elem!1))))) | (~r(s(s(elem!1)), s(s(s(elem!1))))))),
% 0.65/0.89 inference(rewrite,[status(thm)],[])).
% 0.65/0.89 tff(3429,plain,
% 0.65/0.89 (((~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(elem!1)))) | (~r(z, s(s(s(elem!1))))) | (~r(s(s(elem!1)), s(s(s(elem!1))))))),
% 0.65/0.89 inference(rewrite,[status(thm)],[])).
% 0.65/0.89 tff(3430,plain,
% 0.65/0.89 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(elem!1)), s(s(s(elem!1))))) | (~r(z, s(s(s(elem!1))))) | (~r(z, s(s(elem!1)))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(elem!1)))) | (~r(z, s(s(s(elem!1))))) | (~r(s(s(elem!1)), s(s(s(elem!1)))))))),
% 0.65/0.89 inference(monotonicity,[status(thm)],[3429])).
% 0.65/0.89 tff(3431,plain,
% 0.65/0.89 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(elem!1)), s(s(s(elem!1))))) | (~r(z, s(s(s(elem!1))))) | (~r(z, s(s(elem!1)))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, s(s(elem!1)))) | (~r(z, s(s(s(elem!1))))) | (~r(s(s(elem!1)), s(s(s(elem!1))))))),
% 0.65/0.89 inference(transitivity,[status(thm)],[3430, 3428])).
% 0.65/0.89 tff(3432,plain,
% 0.65/0.89 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(elem!1)), s(s(s(elem!1))))) | (~r(z, s(s(s(elem!1))))) | (~r(z, s(s(elem!1)))))),
% 0.65/0.89 inference(quant_inst,[status(thm)],[])).
% 0.65/0.89 tff(3433,plain,
% 0.65/0.89 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, s(s(elem!1)))) | (~r(z, s(s(s(elem!1))))) | (~r(s(s(elem!1)), s(s(s(elem!1)))))),
% 0.65/0.89 inference(modus_ponens,[status(thm)],[3432, 3431])).
% 0.65/0.89 tff(3434,plain,
% 0.65/0.89 (~r(z, s(s(elem!1)))),
% 0.65/0.89 inference(unit_resolution,[status(thm)],[3433, 14, 3427, 3423])).
% 0.65/0.89 tff(3435,plain,
% 0.65/0.89 (~r(z, s(s(s(z))))),
% 0.65/0.89 inference(modus_ponens,[status(thm)],[3434, 3419])).
% 0.65/0.89 tff(3436,plain,
% 0.65/0.89 (b(z, s(s(s(z))))),
% 0.65/0.89 inference(unit_resolution,[status(thm)],[711, 3435])).
% 0.65/0.89 tff(3437,plain,
% 0.65/0.89 (b(z, s(s(elem!1)))),
% 0.65/0.89 inference(modus_ponens,[status(thm)],[3436, 3417])).
% 0.65/0.89 tff(3438,plain,
% 0.65/0.89 (((~![X0: $i, X2: $i, X1: $i] : ((~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(elem!1)))) | (~b(z, s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), s(s(elem!1)))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(s(elem!1)))) | (~b(z, s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), s(s(elem!1)))))),
% 0.65/0.89 inference(rewrite,[status(thm)],[])).
% 0.65/0.89 tff(3439,plain,
% 0.65/0.89 (((~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(z, s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), s(s(elem!1)))))),
% 0.65/0.89 inference(rewrite,[status(thm)],[])).
% 0.65/0.89 tff(3440,plain,
% 0.65/0.89 (((~![X0: $i, X2: $i, X1: $i] : ((~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~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, X2: $i, X1: $i] : ((~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(elem!1)))) | (~b(z, s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), s(s(elem!1))))))),
% 0.65/0.89 inference(monotonicity,[status(thm)],[3439])).
% 0.65/0.89 tff(3441,plain,
% 0.65/0.89 (((~![X0: $i, X2: $i, X1: $i] : ((~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~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, X2: $i, X1: $i] : ((~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(s(elem!1)))) | (~b(z, s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), s(s(elem!1)))))),
% 0.65/0.89 inference(transitivity,[status(thm)],[3440, 3438])).
% 0.65/0.89 tff(3442,plain,
% 0.65/0.89 ((~![X0: $i, X2: $i, X1: $i] : ((~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~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)))))))),
% 0.65/0.89 inference(quant_inst,[status(thm)],[])).
% 0.65/0.89 tff(3443,plain,
% 0.65/0.89 ((~![X0: $i, X2: $i, X1: $i] : ((~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(s(elem!1)))) | (~b(z, s(s(s(s(elem!1)))))) | (~b(s(s(s(s(elem!1)))), s(s(elem!1))))),
% 0.65/0.89 inference(modus_ponens,[status(thm)],[3442, 3441])).
% 0.65/0.89 tff(3444,plain,
% 0.65/0.89 (~b(z, s(s(s(s(elem!1)))))),
% 0.65/0.89 inference(unit_resolution,[status(thm)],[3443, 117, 2189, 3437])).
% 0.65/0.89 tff(3445,plain,
% 0.65/0.89 ((z = s(s(s(s(elem!1))))) | r(z, s(s(s(s(elem!1)))))),
% 0.65/0.89 inference(unit_resolution,[status(thm)],[1644, 46, 3444])).
% 0.65/0.89 tff(3446,plain,
% 0.65/0.89 (r(z, s(s(s(s(elem!1)))))),
% 0.65/0.89 inference(unit_resolution,[status(thm)],[3445, 1626])).
% 0.65/0.89 tff(3447,plain,
% 0.65/0.89 ((s(s(s(s(elem!1)))) = s(z)) <=> (s(s(s(s(elem!1)))) = elem!1)),
% 0.65/0.89 inference(monotonicity,[status(thm)],[2020])).
% 0.65/0.89 tff(3448,plain,
% 0.65/0.89 ((s(s(s(s(elem!1)))) = s(z)) <=> (elem!1 = s(s(s(s(elem!1)))))),
% 0.65/0.89 inference(transitivity,[status(thm)],[3447, 2854])).
% 0.65/0.89 tff(3449,plain,
% 0.65/0.89 ((~(s(s(s(s(elem!1)))) = s(z))) <=> (~(elem!1 = s(s(s(s(elem!1))))))),
% 0.65/0.89 inference(monotonicity,[status(thm)],[3448])).
% 0.65/0.89 tff(3450,plain,
% 0.65/0.89 (~(elem!1 = s(s(s(s(elem!1)))))),
% 0.65/0.89 inference(modus_ponens,[status(thm)],[1322, 3449])).
% 0.65/0.89 tff(3451,plain,
% 0.65/0.89 ((s(z) = s(s(s(elem!1)))) <=> (elem!1 = s(s(s(elem!1))))),
% 0.65/0.89 inference(monotonicity,[status(thm)],[2020])).
% 0.65/0.89 tff(3452,plain,
% 0.65/0.89 ((~(s(z) = s(s(s(elem!1))))) <=> (~(elem!1 = s(s(s(elem!1)))))),
% 0.65/0.89 inference(monotonicity,[status(thm)],[3451])).
% 0.65/0.89 tff(3453,plain,
% 0.65/0.89 (~(elem!1 = s(s(s(elem!1))))),
% 0.65/0.89 inference(modus_ponens,[status(thm)],[230, 3452])).
% 0.65/0.89 tff(3454,assumption,(r(elem!1, s(s(elem!1)))), introduced(assumption)).
% 0.65/0.89 tff(3455,assumption,(r(elem!1, s(s(s(elem!1))))), introduced(assumption)).
% 0.65/0.89 tff(3456,plain,
% 0.65/0.89 (((~![X0: $i, X2: $i, X1: $i] : ((~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))))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~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))))))),
% 0.65/0.89 inference(rewrite,[status(thm)],[])).
% 0.65/0.89 tff(3457,plain,
% 0.65/0.89 (((~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))))))),
% 0.65/0.89 inference(rewrite,[status(thm)],[])).
% 0.65/0.89 tff(3458,plain,
% 0.65/0.89 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(elem!1)), s(s(s(elem!1))))) | (~r(elem!1, s(s(s(elem!1))))) | (~r(elem!1, s(s(elem!1)))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(s(elem!1)))) | (~r(elem!1, s(s(s(elem!1))))) | (~r(s(s(elem!1)), s(s(s(elem!1)))))))),
% 0.65/0.89 inference(monotonicity,[status(thm)],[3457])).
% 0.65/0.89 tff(3459,plain,
% 0.65/0.89 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(elem!1)), s(s(s(elem!1))))) | (~r(elem!1, s(s(s(elem!1))))) | (~r(elem!1, s(s(elem!1)))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(elem!1, s(s(elem!1)))) | (~r(elem!1, s(s(s(elem!1))))) | (~r(s(s(elem!1)), s(s(s(elem!1))))))),
% 0.65/0.89 inference(transitivity,[status(thm)],[3458, 3456])).
% 0.65/0.89 tff(3460,plain,
% 0.65/0.89 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(elem!1)), s(s(s(elem!1))))) | (~r(elem!1, s(s(s(elem!1))))) | (~r(elem!1, s(s(elem!1)))))),
% 0.65/0.89 inference(quant_inst,[status(thm)],[])).
% 0.65/0.89 tff(3461,plain,
% 0.65/0.89 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(elem!1, s(s(elem!1)))) | (~r(elem!1, s(s(s(elem!1))))) | (~r(s(s(elem!1)), s(s(s(elem!1)))))),
% 0.65/0.89 inference(modus_ponens,[status(thm)],[3460, 3459])).
% 0.65/0.89 tff(3462,plain,
% 0.65/0.89 ($false),
% 0.65/0.89 inference(unit_resolution,[status(thm)],[3461, 14, 3454, 195, 3455])).
% 0.65/0.89 tff(3463,plain,((~r(elem!1, s(s(s(elem!1))))) | (~r(elem!1, s(s(elem!1)))) | (~r(s(s(elem!1)), s(s(s(elem!1)))))), inference(lemma,lemma(discharge,[]))).
% 0.65/0.89 tff(3464,plain,
% 0.65/0.89 (~r(elem!1, s(s(s(elem!1))))),
% 0.65/0.89 inference(unit_resolution,[status(thm)],[3463, 3423, 3454])).
% 0.65/0.89 tff(3465,plain,
% 0.65/0.89 (((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((elem!1 = s(s(s(elem!1)))) | b(elem!1, s(s(s(elem!1)))) | r(elem!1, s(s(s(elem!1)))))) <=> ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (elem!1 = s(s(s(elem!1)))) | b(elem!1, s(s(s(elem!1)))) | r(elem!1, s(s(s(elem!1)))))),
% 0.65/0.89 inference(rewrite,[status(thm)],[])).
% 0.65/0.89 tff(3466,plain,
% 0.65/0.89 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((elem!1 = s(s(s(elem!1)))) | b(elem!1, s(s(s(elem!1)))) | r(elem!1, s(s(s(elem!1)))))),
% 0.65/0.89 inference(quant_inst,[status(thm)],[])).
% 0.65/0.89 tff(3467,plain,
% 0.65/0.89 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (elem!1 = s(s(s(elem!1)))) | b(elem!1, s(s(s(elem!1)))) | r(elem!1, s(s(s(elem!1))))),
% 0.65/0.89 inference(modus_ponens,[status(thm)],[3466, 3465])).
% 0.65/0.89 tff(3468,plain,
% 0.65/0.89 ((elem!1 = s(s(s(elem!1)))) | b(elem!1, s(s(s(elem!1)))) | r(elem!1, s(s(s(elem!1))))),
% 0.65/0.89 inference(unit_resolution,[status(thm)],[3467, 46])).
% 0.65/0.89 tff(3469,plain,
% 0.65/0.89 (b(elem!1, s(s(s(elem!1))))),
% 0.65/0.89 inference(unit_resolution,[status(thm)],[3468, 3464, 3453])).
% 0.65/0.89 tff(3470,plain,
% 0.65/0.89 (((~![X0: $i, X2: $i, X1: $i] : ((~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(s(s(elem!1))))) | (~b(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~b(elem!1, s(s(s(s(elem!1)))))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(s(s(elem!1))))) | (~b(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~b(elem!1, s(s(s(s(elem!1)))))))),
% 0.65/0.89 inference(rewrite,[status(thm)],[])).
% 0.65/0.89 tff(3471,plain,
% 0.65/0.89 (((~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(s(elem!1)))), s(s(s(elem!1))))) | (~b(elem!1, s(s(s(s(elem!1)))))))),
% 0.65/0.89 inference(rewrite,[status(thm)],[])).
% 0.65/0.89 tff(3472,plain,
% 0.65/0.89 (((~![X0: $i, X2: $i, X1: $i] : ((~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~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, X2: $i, X1: $i] : ((~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(s(s(elem!1))))) | (~b(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~b(elem!1, s(s(s(s(elem!1))))))))),
% 0.65/0.89 inference(monotonicity,[status(thm)],[3471])).
% 0.65/0.89 tff(3473,plain,
% 0.65/0.89 (((~![X0: $i, X2: $i, X1: $i] : ((~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~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, X2: $i, X1: $i] : ((~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(s(s(elem!1))))) | (~b(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~b(elem!1, s(s(s(s(elem!1)))))))),
% 0.65/0.89 inference(transitivity,[status(thm)],[3472, 3470])).
% 0.65/0.89 tff(3474,plain,
% 0.65/0.89 ((~![X0: $i, X2: $i, X1: $i] : ((~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~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)))))))),
% 0.65/0.89 inference(quant_inst,[status(thm)],[])).
% 0.65/0.89 tff(3475,plain,
% 0.65/0.89 ((~![X0: $i, X2: $i, X1: $i] : ((~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(s(s(elem!1))))) | (~b(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~b(elem!1, s(s(s(s(elem!1))))))),
% 0.65/0.89 inference(modus_ponens,[status(thm)],[3474, 3473])).
% 0.65/0.89 tff(3476,plain,
% 0.65/0.89 (~b(elem!1, s(s(s(s(elem!1)))))),
% 0.65/0.89 inference(unit_resolution,[status(thm)],[3475, 117, 3469, 3421])).
% 0.65/0.89 tff(3477,plain,
% 0.65/0.89 (r(elem!1, s(s(s(s(elem!1)))))),
% 0.65/0.89 inference(unit_resolution,[status(thm)],[2907, 3476, 3450])).
% 0.65/0.89 tff(3478,plain,
% 0.65/0.89 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, elem!1)) | (~r(z, s(s(s(s(elem!1)))))) | (~r(elem!1, s(s(s(s(elem!1)))))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, elem!1)) | (~r(z, s(s(s(s(elem!1)))))) | (~r(elem!1, s(s(s(s(elem!1)))))))),
% 0.65/0.89 inference(rewrite,[status(thm)],[])).
% 0.65/0.89 tff(3479,plain,
% 0.65/0.89 (((~r(elem!1, s(s(s(s(elem!1)))))) | (~r(z, s(s(s(s(elem!1)))))) | (~r(z, elem!1))) <=> ((~r(z, elem!1)) | (~r(z, s(s(s(s(elem!1)))))) | (~r(elem!1, s(s(s(s(elem!1)))))))),
% 0.65/0.89 inference(rewrite,[status(thm)],[])).
% 0.65/0.89 tff(3480,plain,
% 0.65/0.89 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(s(s(s(elem!1)))))) | (~r(z, s(s(s(s(elem!1)))))) | (~r(z, elem!1)))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, elem!1)) | (~r(z, s(s(s(s(elem!1)))))) | (~r(elem!1, s(s(s(s(elem!1))))))))),
% 0.65/0.89 inference(monotonicity,[status(thm)],[3479])).
% 0.65/0.89 tff(3481,plain,
% 0.65/0.89 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(s(s(s(elem!1)))))) | (~r(z, s(s(s(s(elem!1)))))) | (~r(z, elem!1)))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, elem!1)) | (~r(z, s(s(s(s(elem!1)))))) | (~r(elem!1, s(s(s(s(elem!1)))))))),
% 0.65/0.89 inference(transitivity,[status(thm)],[3480, 3478])).
% 0.65/0.89 tff(3482,plain,
% 0.65/0.89 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(s(s(s(elem!1)))))) | (~r(z, s(s(s(s(elem!1)))))) | (~r(z, elem!1)))),
% 0.65/0.89 inference(quant_inst,[status(thm)],[])).
% 0.65/0.89 tff(3483,plain,
% 0.65/0.89 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, elem!1)) | (~r(z, s(s(s(s(elem!1)))))) | (~r(elem!1, s(s(s(s(elem!1))))))),
% 0.65/0.89 inference(modus_ponens,[status(thm)],[3482, 3481])).
% 0.65/0.89 tff(3484,plain,
% 0.65/0.89 (~r(z, elem!1)),
% 0.65/0.89 inference(unit_resolution,[status(thm)],[3483, 14, 3477, 3446])).
% 0.65/0.89 tff(3485,plain,
% 0.65/0.89 (~r(z, s(z))),
% 0.65/0.89 inference(modus_ponens,[status(thm)],[3484, 3416])).
% 0.65/0.89 tff(3486,plain,
% 0.65/0.89 (b(z, s(z))),
% 0.65/0.89 inference(unit_resolution,[status(thm)],[599, 3485])).
% 0.65/0.89 tff(3487,plain,
% 0.65/0.89 ((s(z) = s(s(s(elem!1)))) <=> (s(s(s(elem!1))) = elem!1)),
% 0.65/0.89 inference(transitivity,[status(thm)],[3451, 1512])).
% 0.65/0.89 tff(3488,plain,
% 0.65/0.89 ((~(s(z) = s(s(s(elem!1))))) <=> (~(s(s(s(elem!1))) = elem!1))),
% 0.65/0.89 inference(monotonicity,[status(thm)],[3487])).
% 0.65/0.89 tff(3489,plain,
% 0.65/0.89 (~(s(s(s(elem!1))) = elem!1)),
% 0.65/0.89 inference(modus_ponens,[status(thm)],[230, 3488])).
% 0.65/0.89 tff(3490,plain,
% 0.65/0.89 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(elem!1)), elem!1)) | (~r(s(s(elem!1)), s(s(s(s(elem!1)))))) | (~r(s(s(s(s(elem!1)))), elem!1)))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(elem!1)), elem!1)) | (~r(s(s(elem!1)), s(s(s(s(elem!1)))))) | (~r(s(s(s(s(elem!1)))), elem!1)))),
% 0.65/0.89 inference(rewrite,[status(thm)],[])).
% 0.65/0.89 tff(3491,plain,
% 0.65/0.89 (((~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(s(s(elem!1)), s(s(s(s(elem!1)))))) | (~r(s(s(s(s(elem!1)))), elem!1)))),
% 0.65/0.89 inference(rewrite,[status(thm)],[])).
% 0.65/0.89 tff(3492,plain,
% 0.65/0.89 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(elem!1)))), elem!1)) | (~r(s(s(elem!1)), elem!1)) | (~r(s(s(elem!1)), s(s(s(s(elem!1)))))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(elem!1)), elem!1)) | (~r(s(s(elem!1)), s(s(s(s(elem!1)))))) | (~r(s(s(s(s(elem!1)))), elem!1))))),
% 0.65/0.89 inference(monotonicity,[status(thm)],[3491])).
% 0.65/0.89 tff(3493,plain,
% 0.65/0.89 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(elem!1)))), elem!1)) | (~r(s(s(elem!1)), elem!1)) | (~r(s(s(elem!1)), s(s(s(s(elem!1)))))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(elem!1)), elem!1)) | (~r(s(s(elem!1)), s(s(s(s(elem!1)))))) | (~r(s(s(s(s(elem!1)))), elem!1)))),
% 0.65/0.89 inference(transitivity,[status(thm)],[3492, 3490])).
% 0.65/0.89 tff(3494,plain,
% 0.65/0.89 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(elem!1)))), elem!1)) | (~r(s(s(elem!1)), elem!1)) | (~r(s(s(elem!1)), s(s(s(s(elem!1)))))))),
% 0.65/0.89 inference(quant_inst,[status(thm)],[])).
% 0.65/0.89 tff(3495,plain,
% 0.65/0.89 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(elem!1)), elem!1)) | (~r(s(s(elem!1)), s(s(s(s(elem!1)))))) | (~r(s(s(s(s(elem!1)))), elem!1))),
% 0.65/0.89 inference(modus_ponens,[status(thm)],[3494, 3493])).
% 0.65/0.89 tff(3496,plain,
% 0.65/0.89 (~r(s(s(elem!1)), s(s(s(s(elem!1)))))),
% 0.65/0.89 inference(unit_resolution,[status(thm)],[3495, 14, 2050, 2022])).
% 0.65/0.89 tff(3497,plain,
% 0.65/0.89 (b(s(s(elem!1)), s(s(s(s(elem!1)))))),
% 0.65/0.89 inference(unit_resolution,[status(thm)],[2040, 3496, 2036])).
% 0.65/0.89 tff(3498,plain,
% 0.65/0.89 (~r(s(s(s(elem!1))), s(s(s(s(elem!1)))))),
% 0.65/0.89 inference(unit_resolution,[status(thm)],[1701, 14, 196, 1396])).
% 0.65/0.89 tff(3499,plain,
% 0.65/0.89 (b(s(s(s(elem!1))), s(s(s(s(elem!1)))))),
% 0.65/0.89 inference(unit_resolution,[status(thm)],[448, 3498, 290])).
% 0.65/0.89 tff(3500,plain,
% 0.65/0.89 (((~![X0: $i, X2: $i, X1: $i] : ((~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(s(s(elem!1)))))) | (~b(s(s(elem!1)), s(s(s(s(elem!1)))))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~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(s(s(elem!1)))))) | (~b(s(s(elem!1)), s(s(s(s(elem!1)))))))),
% 0.65/0.89 inference(rewrite,[status(thm)],[])).
% 0.65/0.89 tff(3501,plain,
% 0.65/0.89 (((~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))), s(s(s(s(elem!1)))))) | (~b(s(s(elem!1)), s(s(s(s(elem!1)))))))),
% 0.65/0.89 inference(rewrite,[status(thm)],[])).
% 0.65/0.89 tff(3502,plain,
% 0.65/0.89 (((~![X0: $i, X2: $i, X1: $i] : ((~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(elem!1))), s(s(elem!1)))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~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(s(s(elem!1)))))) | (~b(s(s(elem!1)), s(s(s(s(elem!1))))))))),
% 0.65/0.89 inference(monotonicity,[status(thm)],[3501])).
% 0.65/0.89 tff(3503,plain,
% 0.65/0.89 (((~![X0: $i, X2: $i, X1: $i] : ((~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(elem!1))), s(s(elem!1)))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~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(s(s(elem!1)))))) | (~b(s(s(elem!1)), s(s(s(s(elem!1)))))))),
% 0.65/0.89 inference(transitivity,[status(thm)],[3502, 3500])).
% 0.65/0.89 tff(3504,plain,
% 0.65/0.89 ((~![X0: $i, X2: $i, X1: $i] : ((~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(elem!1))), s(s(elem!1)))))),
% 0.65/0.89 inference(quant_inst,[status(thm)],[])).
% 0.65/0.89 tff(3505,plain,
% 0.65/0.89 ((~![X0: $i, X2: $i, X1: $i] : ((~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(s(s(elem!1)))))) | (~b(s(s(elem!1)), s(s(s(s(elem!1))))))),
% 0.65/0.89 inference(modus_ponens,[status(thm)],[3504, 3503])).
% 0.65/0.89 tff(3506,plain,
% 0.65/0.89 (~b(s(s(s(elem!1))), s(s(elem!1)))),
% 0.65/0.89 inference(unit_resolution,[status(thm)],[3505, 117, 3499, 3497])).
% 0.65/0.89 tff(3507,plain,
% 0.65/0.89 (r(s(s(s(elem!1))), s(s(elem!1)))),
% 0.65/0.89 inference(unit_resolution,[status(thm)],[1547, 3506, 1539])).
% 0.65/0.89 tff(3508,plain,
% 0.65/0.89 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(s(elem!1)))) | (~r(s(s(s(elem!1))), s(s(elem!1)))) | (~r(s(s(s(elem!1))), elem!1)))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(elem!1, s(s(elem!1)))) | (~r(s(s(s(elem!1))), s(s(elem!1)))) | (~r(s(s(s(elem!1))), elem!1)))),
% 0.65/0.89 inference(rewrite,[status(thm)],[])).
% 0.65/0.89 tff(3509,plain,
% 0.65/0.89 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(s(elem!1)))) | (~r(s(s(s(elem!1))), s(s(elem!1)))) | (~r(s(s(s(elem!1))), elem!1)))),
% 0.65/0.89 inference(quant_inst,[status(thm)],[])).
% 0.65/0.89 tff(3510,plain,
% 0.65/0.89 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(elem!1, s(s(elem!1)))) | (~r(s(s(s(elem!1))), s(s(elem!1)))) | (~r(s(s(s(elem!1))), elem!1))),
% 0.65/0.89 inference(modus_ponens,[status(thm)],[3509, 3508])).
% 0.65/0.89 tff(3511,plain,
% 0.65/0.89 (~r(s(s(s(elem!1))), elem!1)),
% 0.65/0.89 inference(unit_resolution,[status(thm)],[3510, 14, 3454, 3507])).
% 0.65/0.89 tff(3512,plain,
% 0.65/0.89 (b(s(s(s(elem!1))), elem!1)),
% 0.65/0.89 inference(unit_resolution,[status(thm)],[1235, 3511, 3489])).
% 0.65/0.89 tff(3513,plain,
% 0.65/0.89 ($false),
% 0.65/0.89 inference(unit_resolution,[status(thm)],[2007, 3512, 3486, 196, 1434, 1788])).
% 0.65/0.89 tff(3514,plain,((~r(s(s(s(s(elem!1)))), s(z))) | (~r(s(s(s(elem!1))), z)) | (~(s(s(s(z))) = s(s(elem!1)))) | (~b(s(s(s(s(s(s(elem!1)))))), elem!1)) | (~r(elem!1, s(s(elem!1)))) | (~r(s(s(s(s(elem!1)))), z)) | (~b(s(z), z)) | (~r(s(s(elem!1)), s(z))) | (s(s(elem!1)) = s(s(s(elem!1)))) | (s(s(s(s(elem!1)))) = s(s(elem!1)))), inference(lemma,lemma(discharge,[]))).
% 0.65/0.89 tff(3515,plain,
% 0.65/0.89 (~r(s(s(s(s(elem!1)))), s(z))),
% 0.65/0.89 inference(unit_resolution,[status(thm)],[3514, 1788, 3383, 3397, 3414, 3100, 237, 181, 145, 146])).
% 0.65/0.89 tff(3516,plain,
% 0.65/0.89 (b(s(s(s(s(elem!1)))), s(z))),
% 0.65/0.89 inference(unit_resolution,[status(thm)],[1327, 3515])).
% 0.65/0.89 tff(3517,plain,
% 0.65/0.89 (~b(s(z), s(s(s(elem!1))))),
% 0.65/0.89 inference(unit_resolution,[status(thm)],[1679, 3516, 3399])).
% 0.65/0.89 tff(3518,plain,
% 0.65/0.89 (r(s(z), s(s(s(elem!1))))),
% 0.65/0.89 inference(unit_resolution,[status(thm)],[235, 3517])).
% 0.65/0.89 tff(3519,plain,
% 0.65/0.89 (r(elem!1, s(s(s(elem!1))))),
% 0.65/0.89 inference(modus_ponens,[status(thm)],[3518, 3395])).
% 0.65/0.89 tff(3520,plain,
% 0.65/0.89 (s(s(s(s(z)))) = s(s(s(elem!1)))),
% 0.65/0.89 inference(monotonicity,[status(thm)],[3383])).
% 0.65/0.89 tff(3521,plain,
% 0.65/0.89 (r(z, s(s(s(s(z))))) <=> r(z, s(s(s(elem!1))))),
% 0.65/0.89 inference(monotonicity,[status(thm)],[3520])).
% 0.65/0.89 tff(3522,plain,
% 0.65/0.89 (b(s(s(s(z))), s(s(s(s(z))))) <=> b(s(s(elem!1)), s(s(s(s(z)))))),
% 0.65/0.89 inference(monotonicity,[status(thm)],[3383])).
% 0.65/0.89 tff(3523,plain,
% 0.65/0.89 (b(s(s(elem!1)), s(s(s(s(z))))) <=> b(s(s(s(z))), s(s(s(s(z)))))),
% 0.65/0.89 inference(symmetry,[status(thm)],[3522])).
% 0.65/0.89 tff(3524,plain,
% 0.65/0.89 (s(s(s(elem!1))) = s(s(s(s(z))))),
% 0.65/0.89 inference(symmetry,[status(thm)],[3520])).
% 0.65/0.89 tff(3525,plain,
% 0.65/0.89 (b(s(s(elem!1)), s(s(s(elem!1)))) <=> b(s(s(elem!1)), s(s(s(s(z)))))),
% 0.65/0.89 inference(monotonicity,[status(thm)],[3524])).
% 0.65/0.89 tff(3526,plain,
% 0.65/0.89 (b(s(s(elem!1)), s(s(s(elem!1)))) <=> b(s(s(s(z))), s(s(s(s(z)))))),
% 0.65/0.89 inference(transitivity,[status(thm)],[3525, 3523])).
% 0.65/0.89 tff(3527,plain,
% 0.65/0.89 (~r(s(s(elem!1)), s(s(s(elem!1))))),
% 0.65/0.89 inference(unit_resolution,[status(thm)],[221, 3518, 181])).
% 0.65/0.89 tff(3528,plain,
% 0.65/0.89 (b(s(s(elem!1)), s(s(s(elem!1))))),
% 0.65/0.90 inference(unit_resolution,[status(thm)],[253, 3527, 145])).
% 0.65/0.90 tff(3529,plain,
% 0.65/0.90 (b(s(s(s(z))), s(s(s(s(z)))))),
% 0.65/0.90 inference(modus_ponens,[status(thm)],[3528, 3526])).
% 0.65/0.90 tff(3530,plain,
% 0.65/0.90 (~b(z, s(s(s(s(z)))))),
% 0.65/0.90 inference(unit_resolution,[status(thm)],[2788, 3529, 338])).
% 0.65/0.90 tff(3531,plain,
% 0.65/0.90 (r(z, s(s(s(s(z)))))),
% 0.65/0.90 inference(unit_resolution,[status(thm)],[51, 3530])).
% 0.65/0.90 tff(3532,plain,
% 0.65/0.90 (r(z, s(s(s(elem!1))))),
% 0.65/0.90 inference(modus_ponens,[status(thm)],[3531, 3521])).
% 0.65/0.90 tff(3533,plain,
% 0.65/0.90 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(s(s(elem!1))))) | (~r(z, s(s(s(elem!1))))) | (~r(z, elem!1)))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(elem!1, s(s(s(elem!1))))) | (~r(z, s(s(s(elem!1))))) | (~r(z, elem!1)))),
% 0.65/0.90 inference(rewrite,[status(thm)],[])).
% 0.65/0.90 tff(3534,plain,
% 0.65/0.90 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(s(s(elem!1))))) | (~r(z, s(s(s(elem!1))))) | (~r(z, elem!1)))),
% 0.65/0.90 inference(quant_inst,[status(thm)],[])).
% 0.65/0.90 tff(3535,plain,
% 0.65/0.90 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(elem!1, s(s(s(elem!1))))) | (~r(z, s(s(s(elem!1))))) | (~r(z, elem!1))),
% 0.65/0.90 inference(modus_ponens,[status(thm)],[3534, 3533])).
% 0.65/0.90 tff(3536,plain,
% 0.65/0.90 (~r(z, elem!1)),
% 0.65/0.90 inference(unit_resolution,[status(thm)],[3535, 14, 3532, 3519])).
% 0.65/0.90 tff(3537,plain,
% 0.65/0.90 (~r(z, s(z))),
% 0.65/0.90 inference(modus_ponens,[status(thm)],[3536, 3394])).
% 0.65/0.90 tff(3538,plain,
% 0.65/0.90 (b(z, s(z))),
% 0.65/0.90 inference(unit_resolution,[status(thm)],[599, 3537])).
% 0.65/0.90 tff(3539,plain,
% 0.65/0.90 (b(z, elem!1)),
% 0.65/0.90 inference(modus_ponens,[status(thm)],[3538, 3390])).
% 0.65/0.90 tff(3540,plain,
% 0.65/0.90 (~b(s(s(s(s(s(s(elem!1)))))), z)),
% 0.65/0.90 inference(unit_resolution,[status(thm)],[1659, 117, 1788, 3539])).
% 0.65/0.90 tff(3541,plain,
% 0.65/0.90 (r(s(s(s(s(s(s(elem!1)))))), z)),
% 0.65/0.90 inference(unit_resolution,[status(thm)],[1666, 46, 1663, 3540])).
% 0.65/0.90 tff(3542,plain,
% 0.65/0.90 (b(s(s(s(s(elem!1)))), s(z)) <=> b(s(s(s(s(elem!1)))), elem!1)),
% 0.75/0.90 inference(monotonicity,[status(thm)],[3391])).
% 0.75/0.90 tff(3543,plain,
% 0.75/0.90 (b(s(s(s(s(elem!1)))), elem!1)),
% 0.75/0.90 inference(modus_ponens,[status(thm)],[3516, 3542])).
% 0.75/0.90 tff(3544,plain,
% 0.75/0.90 (~b(s(s(s(s(s(s(elem!1)))))), s(s(s(s(elem!1)))))),
% 0.75/0.90 inference(unit_resolution,[status(thm)],[1605, 117, 3543, 1788])).
% 0.75/0.90 tff(3545,plain,
% 0.75/0.90 (r(s(s(s(s(s(s(elem!1)))))), s(s(s(s(elem!1)))))),
% 0.75/0.90 inference(unit_resolution,[status(thm)],[1619, 46, 2024, 3544])).
% 0.75/0.90 tff(3546,plain,
% 0.75/0.90 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(elem!1)))), z)) | (~r(s(s(s(s(s(s(elem!1)))))), z)) | (~r(s(s(s(s(s(s(elem!1)))))), s(s(s(s(elem!1)))))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(s(elem!1)))), z)) | (~r(s(s(s(s(s(s(elem!1)))))), z)) | (~r(s(s(s(s(s(s(elem!1)))))), s(s(s(s(elem!1)))))))),
% 0.75/0.90 inference(rewrite,[status(thm)],[])).
% 0.75/0.90 tff(3547,plain,
% 0.75/0.90 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(elem!1)))), z)) | (~r(s(s(s(s(s(s(elem!1)))))), z)) | (~r(s(s(s(s(s(s(elem!1)))))), s(s(s(s(elem!1)))))))),
% 0.75/0.90 inference(quant_inst,[status(thm)],[])).
% 0.75/0.90 tff(3548,plain,
% 0.75/0.90 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(s(elem!1)))), z)) | (~r(s(s(s(s(s(s(elem!1)))))), z)) | (~r(s(s(s(s(s(s(elem!1)))))), s(s(s(s(elem!1))))))),
% 0.75/0.90 inference(modus_ponens,[status(thm)],[3547, 3546])).
% 0.75/0.90 tff(3549,plain,
% 0.75/0.90 ($false),
% 0.75/0.90 inference(unit_resolution,[status(thm)],[3548, 14, 3100, 3545, 3541])).
% 0.75/0.90 tff(3550,plain,((~b(s(s(s(s(s(s(elem!1)))))), elem!1)) | (~b(s(s(s(z))), z)) | (s(s(elem!1)) = s(s(s(elem!1)))) | (~r(s(s(elem!1)), s(z))) | (~b(s(z), z)) | (s(s(s(s(elem!1)))) = s(s(elem!1)))), inference(lemma,lemma(discharge,[]))).
% 0.75/0.90 tff(3551,plain,
% 0.75/0.90 (~b(s(s(s(s(s(s(elem!1)))))), elem!1)),
% 0.75/0.90 inference(unit_resolution,[status(thm)],[3550, 3362, 145, 179, 2475, 146])).
% 0.75/0.90 tff(3552,plain,
% 0.75/0.90 (r(s(s(s(s(s(s(elem!1)))))), elem!1)),
% 0.75/0.90 inference(unit_resolution,[status(thm)],[1599, 3551, 3377])).
% 0.75/0.90 tff(3553,plain,
% 0.75/0.90 ((s(z) = s(s(s(elem!1)))) <=> (elem!1 = s(s(s(elem!1))))),
% 0.75/0.90 inference(monotonicity,[status(thm)],[3374])).
% 0.75/0.90 tff(3554,plain,
% 0.75/0.90 ((s(z) = s(s(s(elem!1)))) <=> (s(s(s(elem!1))) = elem!1)),
% 0.75/0.90 inference(transitivity,[status(thm)],[3553, 1512])).
% 0.75/0.90 tff(3555,plain,
% 0.75/0.90 ((~(s(z) = s(s(s(elem!1))))) <=> (~(s(s(s(elem!1))) = elem!1))),
% 0.75/0.90 inference(monotonicity,[status(thm)],[3554])).
% 0.75/0.90 tff(3556,plain,
% 0.75/0.90 (~(s(s(s(elem!1))) = elem!1)),
% 0.75/0.90 inference(modus_ponens,[status(thm)],[230, 3555])).
% 0.75/0.90 tff(3557,plain,
% 0.75/0.90 (~b(s(s(s(elem!1))), z)),
% 0.75/0.90 inference(unit_resolution,[status(thm)],[1050, 3362, 3198, 145])).
% 0.75/0.90 tff(3558,plain,
% 0.75/0.90 (r(s(s(s(elem!1))), z)),
% 0.75/0.90 inference(unit_resolution,[status(thm)],[211, 3557])).
% 0.75/0.90 tff(3559,plain,
% 0.75/0.90 (~r(s(s(s(elem!1))), s(s(s(s(elem!1)))))),
% 0.75/0.90 inference(unit_resolution,[status(thm)],[1701, 14, 3558, 3202])).
% 0.75/0.90 tff(3560,plain,
% 0.75/0.90 (b(s(s(s(elem!1))), s(s(s(s(elem!1)))))),
% 0.75/0.90 inference(unit_resolution,[status(thm)],[448, 3559, 290])).
% 0.75/0.90 tff(3561,plain,
% 0.75/0.90 ((s(s(s(s(elem!1)))) = s(z)) <=> (s(s(s(s(elem!1)))) = elem!1)),
% 0.75/0.90 inference(monotonicity,[status(thm)],[3374])).
% 0.75/0.90 tff(3562,plain,
% 0.75/0.90 ((s(s(s(s(elem!1)))) = s(z)) <=> (elem!1 = s(s(s(s(elem!1)))))),
% 0.75/0.90 inference(transitivity,[status(thm)],[3561, 2854])).
% 0.75/0.90 tff(3563,plain,
% 0.75/0.90 ((~(s(s(s(s(elem!1)))) = s(z))) <=> (~(elem!1 = s(s(s(s(elem!1))))))),
% 0.75/0.90 inference(monotonicity,[status(thm)],[3562])).
% 0.75/0.90 tff(3564,plain,
% 0.75/0.90 (~(elem!1 = s(s(s(s(elem!1)))))),
% 0.75/0.90 inference(modus_ponens,[status(thm)],[1322, 3563])).
% 0.75/0.90 tff(3565,plain,
% 0.75/0.90 (~r(s(s(s(s(elem!1)))), s(s(s(elem!1))))),
% 0.75/0.90 inference(unit_resolution,[status(thm)],[1525, 3558, 3202])).
% 0.75/0.90 tff(3566,plain,
% 0.75/0.90 (b(s(s(s(s(elem!1)))), s(s(s(elem!1))))),
% 0.75/0.90 inference(unit_resolution,[status(thm)],[1347, 3565, 156])).
% 0.75/0.90 tff(3567,plain,
% 0.75/0.90 (~r(s(s(s(s(elem!1)))), s(z))),
% 0.75/0.90 inference(unit_resolution,[status(thm)],[2063, 3552, 146, 3368, 179])).
% 0.75/0.90 tff(3568,plain,
% 0.75/0.90 (b(s(s(s(s(elem!1)))), s(z))),
% 0.75/0.90 inference(unit_resolution,[status(thm)],[1327, 3567])).
% 0.75/0.90 tff(3569,plain,
% 0.75/0.90 (~b(s(z), s(s(s(elem!1))))),
% 0.75/0.90 inference(unit_resolution,[status(thm)],[1679, 3568, 3566])).
% 0.75/0.90 tff(3570,plain,
% 0.75/0.90 (r(s(z), s(s(s(elem!1))))),
% 0.75/0.90 inference(unit_resolution,[status(thm)],[235, 3569])).
% 0.75/0.90 tff(3571,plain,
% 0.75/0.90 (~r(s(s(elem!1)), s(s(s(elem!1))))),
% 0.75/0.90 inference(unit_resolution,[status(thm)],[221, 3570, 179])).
% 0.75/0.90 tff(3572,plain,
% 0.75/0.90 (b(s(s(elem!1)), s(s(s(elem!1))))),
% 0.75/0.90 inference(unit_resolution,[status(thm)],[253, 3571, 145])).
% 0.75/0.90 tff(3573,plain,
% 0.75/0.90 (~b(s(s(s(s(elem!1)))), s(s(elem!1)))),
% 0.75/0.90 inference(unit_resolution,[status(thm)],[1488, 3572, 3566])).
% 0.75/0.90 tff(3574,plain,
% 0.75/0.90 (r(s(s(s(s(elem!1)))), s(s(elem!1)))),
% 0.75/0.90 inference(unit_resolution,[status(thm)],[1690, 3573, 146])).
% 0.75/0.90 tff(3575,plain,
% 0.75/0.90 ((s(z) = s(s(elem!1))) <=> (elem!1 = s(s(elem!1)))),
% 0.75/0.90 inference(monotonicity,[status(thm)],[3374])).
% 0.75/0.90 tff(3576,plain,
% 0.75/0.90 ((s(z) = s(s(elem!1))) <=> (s(s(elem!1)) = elem!1)),
% 0.75/0.90 inference(transitivity,[status(thm)],[3575, 2396])).
% 0.75/0.90 tff(3577,plain,
% 0.75/0.90 ((s(z) = s(s(elem!1))) <=> (elem!1 = s(s(elem!1)))),
% 0.75/0.90 inference(transitivity,[status(thm)],[3576, 2397])).
% 0.75/0.90 tff(3578,plain,
% 0.75/0.90 ((~(s(z) = s(s(elem!1)))) <=> (~(elem!1 = s(s(elem!1))))),
% 0.75/0.90 inference(monotonicity,[status(thm)],[3577])).
% 0.75/0.90 tff(3579,plain,
% 0.75/0.90 (~(elem!1 = s(s(elem!1)))),
% 0.75/0.90 inference(modus_ponens,[status(thm)],[172, 3578])).
% 0.75/0.90 tff(3580,plain,
% 0.75/0.90 (b(s(z), z) <=> b(elem!1, z)),
% 0.75/0.90 inference(monotonicity,[status(thm)],[3374])).
% 0.75/0.90 tff(3581,plain,
% 0.75/0.90 (b(elem!1, z)),
% 0.75/0.90 inference(modus_ponens,[status(thm)],[3362, 3580])).
% 0.75/0.90 tff(3582,plain,
% 0.75/0.90 (~b(elem!1, s(s(elem!1)))),
% 0.75/0.90 inference(unit_resolution,[status(thm)],[3412, 117, 3198, 3581])).
% 0.75/0.90 tff(3583,plain,
% 0.75/0.90 (r(elem!1, s(s(elem!1)))),
% 0.75/0.90 inference(unit_resolution,[status(thm)],[2895, 3582, 3579])).
% 0.75/0.90 tff(3584,plain,
% 0.75/0.90 (~r(elem!1, s(s(s(s(elem!1)))))),
% 0.75/0.90 inference(unit_resolution,[status(thm)],[2902, 14, 3583, 3574])).
% 0.75/0.90 tff(3585,plain,
% 0.75/0.90 (b(elem!1, s(s(s(s(elem!1)))))),
% 0.75/0.90 inference(unit_resolution,[status(thm)],[2907, 3584, 3564])).
% 0.75/0.90 tff(3586,plain,
% 0.75/0.90 (((~![X0: $i, X2: $i, X1: $i] : ((~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~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, X2: $i, X1: $i] : ((~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~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)))))))),
% 0.75/0.90 inference(rewrite,[status(thm)],[])).
% 0.75/0.90 tff(3587,plain,
% 0.75/0.90 (((~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(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)))))))),
% 0.75/0.90 inference(rewrite,[status(thm)],[])).
% 0.75/0.90 tff(3588,plain,
% 0.75/0.90 (((~![X0: $i, X2: $i, X1: $i] : ((~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~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, X2: $i, X1: $i] : ((~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~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))))))))),
% 0.75/0.90 inference(monotonicity,[status(thm)],[3587])).
% 0.75/0.90 tff(3589,plain,
% 0.75/0.90 (((~![X0: $i, X2: $i, X1: $i] : ((~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~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, X2: $i, X1: $i] : ((~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~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)))))))),
% 0.75/0.90 inference(transitivity,[status(thm)],[3588, 3586])).
% 0.75/0.90 tff(3590,plain,
% 0.75/0.90 ((~![X0: $i, X2: $i, X1: $i] : ((~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~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)))),
% 0.75/0.90 inference(quant_inst,[status(thm)],[])).
% 0.75/0.90 tff(3591,plain,
% 0.75/0.90 ((~![X0: $i, X2: $i, X1: $i] : ((~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~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))))))),
% 0.75/0.90 inference(modus_ponens,[status(thm)],[3590, 3589])).
% 0.75/0.90 tff(3592,plain,
% 0.75/0.90 (~b(s(s(s(elem!1))), elem!1)),
% 0.75/0.90 inference(unit_resolution,[status(thm)],[3591, 117, 3585, 3560])).
% 0.75/0.90 tff(3593,plain,
% 0.75/0.90 (r(s(s(s(elem!1))), elem!1)),
% 0.75/0.90 inference(unit_resolution,[status(thm)],[1235, 3592, 3556])).
% 0.75/0.90 tff(3594,plain,
% 0.75/0.90 (~b(s(s(s(elem!1))), s(s(elem!1)))),
% 0.75/0.90 inference(unit_resolution,[status(thm)],[1594, 3593, 3552, 3368, 3376])).
% 0.75/0.90 tff(3595,plain,
% 0.75/0.90 (r(s(s(s(elem!1))), s(s(elem!1)))),
% 0.75/0.90 inference(unit_resolution,[status(thm)],[1547, 3594, 1539])).
% 0.75/0.90 tff(3596,plain,
% 0.75/0.90 (r(s(s(s(elem!1))), s(s(s(z))))),
% 0.75/0.90 inference(modus_ponens,[status(thm)],[3595, 3370])).
% 0.75/0.90 tff(3597,plain,
% 0.75/0.90 (r(s(z), s(s(s(z)))) <=> r(s(z), s(s(elem!1)))),
% 0.75/0.90 inference(monotonicity,[status(thm)],[3368])).
% 0.75/0.90 tff(3598,plain,
% 0.75/0.90 (r(s(z), s(s(elem!1))) <=> r(s(z), s(s(s(z))))),
% 0.75/0.90 inference(symmetry,[status(thm)],[3597])).
% 0.75/0.90 tff(3599,plain,
% 0.75/0.90 (r(s(z), s(s(elem!1))) <=> r(elem!1, s(s(elem!1)))),
% 0.75/0.90 inference(monotonicity,[status(thm)],[3374])).
% 0.75/0.90 tff(3600,plain,
% 0.75/0.90 (r(elem!1, s(s(elem!1))) <=> r(s(z), s(s(elem!1)))),
% 0.75/0.90 inference(symmetry,[status(thm)],[3599])).
% 0.75/0.90 tff(3601,plain,
% 0.75/0.90 (r(elem!1, s(s(elem!1))) <=> r(s(z), s(s(s(z))))),
% 0.75/0.90 inference(transitivity,[status(thm)],[3600, 3598])).
% 0.75/0.90 tff(3602,plain,
% 0.75/0.90 (r(s(z), s(s(s(z))))),
% 0.75/0.90 inference(modus_ponens,[status(thm)],[3583, 3601])).
% 0.75/0.90 tff(3603,plain,
% 0.75/0.90 (~r(s(s(s(elem!1))), s(s(s(z))))),
% 0.75/0.90 inference(unit_resolution,[status(thm)],[3121, 3570, 3602])).
% 0.75/0.90 tff(3604,plain,
% 0.75/0.90 ($false),
% 0.75/0.90 inference(unit_resolution,[status(thm)],[3603, 3596])).
% 0.75/0.90 tff(3605,plain,((s(s(s(s(elem!1)))) = s(s(elem!1))) | (s(s(elem!1)) = s(s(s(elem!1)))) | b(s(s(elem!1)), s(z))), inference(lemma,lemma(discharge,[]))).
% 0.75/0.90 tff(3606,plain,
% 0.75/0.90 (s(s(s(s(elem!1)))) = s(s(elem!1))),
% 0.75/0.90 inference(unit_resolution,[status(thm)],[3605, 158, 145])).
% 0.75/0.90 tff(3607,plain,
% 0.75/0.90 (r(s(s(s(s(elem!1)))), z) <=> r(s(s(elem!1)), z)),
% 0.75/0.90 inference(monotonicity,[status(thm)],[3606])).
% 0.75/0.90 tff(3608,plain,
% 0.75/0.90 (r(s(s(elem!1)), z) <=> r(s(s(s(s(elem!1)))), z)),
% 0.75/0.90 inference(symmetry,[status(thm)],[3607])).
% 0.75/0.90 tff(3609,plain,
% 0.75/0.90 ((~r(s(s(elem!1)), z)) <=> (~r(s(s(s(s(elem!1)))), z))),
% 0.75/0.90 inference(monotonicity,[status(thm)],[3608])).
% 0.75/0.90 tff(3610,plain,
% 0.75/0.90 (~b(s(z), z)),
% 0.75/0.90 inference(unit_resolution,[status(thm)],[1394, 3606, 145])).
% 0.75/0.90 tff(3611,plain,
% 0.75/0.90 (r(s(z), z)),
% 0.75/0.90 inference(unit_resolution,[status(thm)],[193, 3610])).
% 0.75/0.90 tff(3612,plain,
% 0.75/0.90 (~r(s(s(elem!1)), z)),
% 0.75/0.90 inference(unit_resolution,[status(thm)],[188, 3611, 179])).
% 0.75/0.90 tff(3613,plain,
% 0.75/0.90 (~r(s(s(s(s(elem!1)))), z)),
% 0.75/0.90 inference(modus_ponens,[status(thm)],[3612, 3609])).
% 0.75/0.90 tff(3614,plain,
% 0.75/0.90 ($false),
% 0.75/0.90 inference(unit_resolution,[status(thm)],[3202, 3613])).
% 0.75/0.90 tff(3615,plain,(b(s(s(elem!1)), s(z)) | (s(s(elem!1)) = s(s(s(elem!1))))), inference(lemma,lemma(discharge,[]))).
% 0.75/0.90 tff(3616,plain,
% 0.75/0.90 (b(s(s(elem!1)), s(z))),
% 0.75/0.90 inference(unit_resolution,[status(thm)],[3615, 145])).
% 0.75/0.90 tff(3617,plain,
% 0.75/0.90 (~b(s(s(s(z))), z)),
% 0.75/0.90 inference(unit_resolution,[status(thm)],[3098, 1310, 145])).
% 0.75/0.90 tff(3618,plain,
% 0.75/0.90 (r(s(s(s(z))), z)),
% 0.75/0.90 inference(unit_resolution,[status(thm)],[823, 3617])).
% 0.75/0.90 tff(3619,plain,
% 0.75/0.90 (~b(s(s(s(s(elem!1)))), s(s(s(elem!1))))),
% 0.75/0.90 inference(unit_resolution,[status(thm)],[2988, 1310, 157])).
% 0.75/0.90 tff(3620,plain,
% 0.75/0.90 (r(s(s(s(s(elem!1)))), s(s(s(elem!1))))),
% 0.75/0.90 inference(unit_resolution,[status(thm)],[1347, 3619, 156])).
% 0.75/0.90 tff(3621,plain,
% 0.75/0.90 (~b(s(s(elem!1)), z)),
% 0.75/0.90 inference(unit_resolution,[status(thm)],[1046, 324, 157])).
% 0.75/0.90 tff(3622,plain,
% 0.75/0.90 (r(s(s(elem!1)), z)),
% 0.75/0.90 inference(unit_resolution,[status(thm)],[1025, 3621])).
% 0.75/0.90 tff(3623,plain,
% 0.75/0.90 (~r(s(s(s(z))), s(s(elem!1)))),
% 0.75/0.90 inference(unit_resolution,[status(thm)],[827, 14, 3622, 180])).
% 0.75/0.90 tff(3624,plain,
% 0.75/0.90 (r(s(s(s(s(elem!1)))), s(s(s(elem!1))))),
% 0.75/0.90 inference(unit_resolution,[status(thm)],[1347, 3619, 287])).
% 0.75/0.90 tff(3625,plain,
% 0.75/0.90 (~b(s(z), s(s(s(elem!1))))),
% 0.75/0.90 inference(unit_resolution,[status(thm)],[2554, 324, 470])).
% 0.75/0.90 tff(3626,plain,
% 0.75/0.90 (r(s(z), s(s(s(elem!1))))),
% 0.75/0.90 inference(unit_resolution,[status(thm)],[235, 3625])).
% 0.75/0.90 tff(3627,plain,
% 0.75/0.90 (~r(s(s(s(s(elem!1)))), s(z))),
% 0.75/0.90 inference(unit_resolution,[status(thm)],[1342, 3626, 3624])).
% 0.75/0.90 tff(3628,plain,
% 0.75/0.90 (b(s(s(s(s(elem!1)))), s(z))),
% 0.75/0.90 inference(unit_resolution,[status(thm)],[1327, 3627])).
% 0.75/0.90 tff(3629,plain,
% 0.75/0.90 (~b(s(z), z)),
% 0.75/0.90 inference(unit_resolution,[status(thm)],[1316, 3628, 1310])).
% 0.75/0.90 tff(3630,plain,
% 0.75/0.90 (r(s(z), z)),
% 0.75/0.90 inference(unit_resolution,[status(thm)],[193, 3629])).
% 0.75/0.90 tff(3631,plain,
% 0.75/0.90 (~r(s(s(s(z))), s(z))),
% 0.75/0.90 inference(unit_resolution,[status(thm)],[2173, 3630, 180])).
% 0.75/0.90 tff(3632,plain,
% 0.75/0.90 (b(s(s(s(z))), s(z))),
% 0.75/0.90 inference(unit_resolution,[status(thm)],[347, 3631])).
% 0.75/0.90 tff(3633,plain,
% 0.75/0.90 (~b(s(s(s(z))), s(s(elem!1)))),
% 0.75/0.90 inference(unit_resolution,[status(thm)],[853, 3632, 470])).
% 0.75/0.90 tff(3634,plain,
% 0.75/0.90 (s(s(s(z))) = s(s(elem!1))),
% 0.75/0.90 inference(unit_resolution,[status(thm)],[1421, 46, 3633, 3623])).
% 0.75/0.90 tff(3635,plain,
% 0.75/0.90 (s(s(s(s(z)))) = s(s(s(elem!1)))),
% 0.75/0.90 inference(monotonicity,[status(thm)],[3634])).
% 0.75/0.90 tff(3636,plain,
% 0.75/0.90 (s(s(s(elem!1))) = s(s(s(s(z))))),
% 0.75/0.90 inference(symmetry,[status(thm)],[3635])).
% 0.75/0.90 tff(3637,plain,
% 0.75/0.90 ((s(s(s(s(s(s(elem!1)))))) = s(s(s(elem!1)))) <=> (s(s(s(s(s(s(elem!1)))))) = s(s(s(s(z)))))),
% 0.75/0.90 inference(monotonicity,[status(thm)],[3636])).
% 0.75/0.90 tff(3638,plain,
% 0.75/0.90 ((s(s(s(s(s(s(elem!1)))))) = s(s(s(s(z))))) <=> (s(s(s(s(s(s(elem!1)))))) = s(s(s(elem!1))))),
% 0.75/0.90 inference(symmetry,[status(thm)],[3637])).
% 0.75/0.90 tff(3639,plain,
% 0.75/0.90 ((~(s(s(s(s(s(s(elem!1)))))) = s(s(s(s(z)))))) <=> (~(s(s(s(s(s(s(elem!1)))))) = s(s(s(elem!1)))))),
% 0.75/0.90 inference(monotonicity,[status(thm)],[3638])).
% 0.75/0.90 tff(3640,plain,
% 0.75/0.90 (~(s(s(s(s(s(s(elem!1)))))) = s(s(s(elem!1))))),
% 0.75/0.90 inference(modus_ponens,[status(thm)],[319, 3639])).
% 0.75/0.90 tff(3641,plain,
% 0.75/0.90 (inj_0(s(s(s(z)))) = inj_0(s(s(elem!1)))),
% 0.75/0.90 inference(monotonicity,[status(thm)],[3634])).
% 0.75/0.90 tff(3642,plain,
% 0.75/0.90 (s(s(z)) = s(elem!1)),
% 0.75/0.90 inference(transitivity,[status(thm)],[95, 3641, 166])).
% 0.75/0.90 tff(3643,plain,
% 0.75/0.90 (inj_0(s(s(z))) = inj_0(s(elem!1))),
% 0.75/0.90 inference(monotonicity,[status(thm)],[3642])).
% 0.75/0.90 tff(3644,plain,
% 0.75/0.90 (s(z) = elem!1),
% 0.75/0.90 inference(transitivity,[status(thm)],[131, 3643, 257])).
% 0.75/0.90 tff(3645,plain,
% 0.75/0.90 (r(z, s(z)) <=> r(z, elem!1)),
% 0.75/0.90 inference(monotonicity,[status(thm)],[3644])).
% 0.75/0.90 tff(3646,plain,
% 0.75/0.90 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(z))) | (~r(z, s(s(s(elem!1))))) | (~r(s(z), s(s(s(elem!1))))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, s(z))) | (~r(z, s(s(s(elem!1))))) | (~r(s(z), s(s(s(elem!1))))))),
% 0.75/0.90 inference(rewrite,[status(thm)],[])).
% 0.75/0.90 tff(3647,plain,
% 0.75/0.90 (((~r(s(z), s(s(s(elem!1))))) | (~r(z, s(s(s(elem!1))))) | (~r(z, s(z)))) <=> ((~r(z, s(z))) | (~r(z, s(s(s(elem!1))))) | (~r(s(z), s(s(s(elem!1))))))),
% 0.75/0.90 inference(rewrite,[status(thm)],[])).
% 0.75/0.90 tff(3648,plain,
% 0.75/0.90 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(s(s(elem!1))))) | (~r(z, s(s(s(elem!1))))) | (~r(z, s(z))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(z))) | (~r(z, s(s(s(elem!1))))) | (~r(s(z), s(s(s(elem!1)))))))),
% 0.75/0.90 inference(monotonicity,[status(thm)],[3647])).
% 0.75/0.90 tff(3649,plain,
% 0.75/0.90 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(s(s(elem!1))))) | (~r(z, s(s(s(elem!1))))) | (~r(z, s(z))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, s(z))) | (~r(z, s(s(s(elem!1))))) | (~r(s(z), s(s(s(elem!1))))))),
% 0.75/0.90 inference(transitivity,[status(thm)],[3648, 3646])).
% 0.75/0.90 tff(3650,plain,
% 0.75/0.90 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(s(s(elem!1))))) | (~r(z, s(s(s(elem!1))))) | (~r(z, s(z))))),
% 0.75/0.90 inference(quant_inst,[status(thm)],[])).
% 0.75/0.90 tff(3651,plain,
% 0.75/0.90 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, s(z))) | (~r(z, s(s(s(elem!1))))) | (~r(s(z), s(s(s(elem!1)))))),
% 0.75/0.90 inference(modus_ponens,[status(thm)],[3650, 3649])).
% 0.75/0.90 tff(3652,plain,
% 0.75/0.90 (~r(z, s(z))),
% 0.75/0.90 inference(unit_resolution,[status(thm)],[3651, 14, 974, 213])).
% 0.75/0.90 tff(3653,plain,
% 0.75/0.90 (b(z, s(z))),
% 0.75/0.90 inference(unit_resolution,[status(thm)],[599, 3652])).
% 0.75/0.90 tff(3654,plain,
% 0.75/0.90 (~r(s(s(s(s(elem!1)))), s(z))),
% 0.75/0.90 inference(unit_resolution,[status(thm)],[1342, 1337, 213])).
% 0.75/0.90 tff(3655,plain,
% 0.75/0.90 (b(s(s(s(s(elem!1)))), s(z))),
% 0.75/0.90 inference(unit_resolution,[status(thm)],[1327, 3654])).
% 0.75/0.90 tff(3656,plain,
% 0.75/0.90 (((~![X0: $i, X2: $i, X1: $i] : ((~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(z))) | (~b(s(s(s(s(elem!1)))), z)) | (~b(s(s(s(s(elem!1)))), s(z))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(z))) | (~b(s(s(s(s(elem!1)))), z)) | (~b(s(s(s(s(elem!1)))), s(z))))),
% 0.75/0.90 inference(rewrite,[status(thm)],[])).
% 0.75/0.90 tff(3657,plain,
% 0.75/0.90 (((~b(z, s(z))) | (~b(s(s(s(s(elem!1)))), s(z))) | (~b(s(s(s(s(elem!1)))), z))) <=> ((~b(z, s(z))) | (~b(s(s(s(s(elem!1)))), z)) | (~b(s(s(s(s(elem!1)))), s(z))))),
% 0.75/0.90 inference(rewrite,[status(thm)],[])).
% 0.75/0.90 tff(3658,plain,
% 0.75/0.90 (((~![X0: $i, X2: $i, X1: $i] : ((~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(z))) | (~b(s(s(s(s(elem!1)))), s(z))) | (~b(s(s(s(s(elem!1)))), z)))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(z))) | (~b(s(s(s(s(elem!1)))), z)) | (~b(s(s(s(s(elem!1)))), s(z)))))),
% 0.75/0.90 inference(monotonicity,[status(thm)],[3657])).
% 0.75/0.90 tff(3659,plain,
% 0.75/0.90 (((~![X0: $i, X2: $i, X1: $i] : ((~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(z))) | (~b(s(s(s(s(elem!1)))), s(z))) | (~b(s(s(s(s(elem!1)))), z)))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(z))) | (~b(s(s(s(s(elem!1)))), z)) | (~b(s(s(s(s(elem!1)))), s(z))))),
% 0.75/0.90 inference(transitivity,[status(thm)],[3658, 3656])).
% 0.75/0.90 tff(3660,plain,
% 0.75/0.90 ((~![X0: $i, X2: $i, X1: $i] : ((~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(z))) | (~b(s(s(s(s(elem!1)))), s(z))) | (~b(s(s(s(s(elem!1)))), z)))),
% 0.75/0.90 inference(quant_inst,[status(thm)],[])).
% 0.75/0.90 tff(3661,plain,
% 0.75/0.90 ((~![X0: $i, X2: $i, X1: $i] : ((~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(z))) | (~b(s(s(s(s(elem!1)))), z)) | (~b(s(s(s(s(elem!1)))), s(z)))),
% 0.75/0.90 inference(modus_ponens,[status(thm)],[3660, 3659])).
% 0.75/0.90 tff(3662,plain,
% 0.75/0.90 (~b(s(s(s(s(elem!1)))), z)),
% 0.75/0.90 inference(unit_resolution,[status(thm)],[3661, 117, 3655, 3653])).
% 0.75/0.90 tff(3663,plain,
% 0.75/0.90 (~r(s(s(s(s(elem!1)))), z)),
% 0.75/0.90 inference(unit_resolution,[status(thm)],[1493, 14, 974, 1337])).
% 0.75/0.90 tff(3664,plain,
% 0.75/0.90 ($false),
% 0.75/0.90 inference(unit_resolution,[status(thm)],[1853, 46, 1625, 3663, 3662])).
% 0.75/0.90 tff(3665,plain,((~r(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~r(z, s(s(s(elem!1))))) | (~r(s(z), s(s(s(elem!1)))))), inference(lemma,lemma(discharge,[]))).
% 0.75/0.90 tff(3666,plain,
% 0.75/0.90 (~r(z, s(s(s(elem!1))))),
% 0.75/0.90 inference(unit_resolution,[status(thm)],[3665, 3626, 3624])).
% 0.75/0.90 tff(3667,plain,
% 0.75/0.90 (b(z, s(s(s(elem!1))))),
% 0.75/0.90 inference(unit_resolution,[status(thm)],[692, 3666])).
% 0.75/0.90 tff(3668,plain,
% 0.75/0.90 (((~![X0: $i, X2: $i, X1: $i] : ((~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(s(elem!1))))) | (~b(z, s(s(elem!1)))) | (~b(s(s(elem!1)), s(s(s(elem!1))))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(s(s(elem!1))))) | (~b(z, s(s(elem!1)))) | (~b(s(s(elem!1)), s(s(s(elem!1))))))),
% 0.75/0.90 inference(rewrite,[status(thm)],[])).
% 0.75/0.90 tff(3669,plain,
% 0.75/0.90 (((~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(s(s(elem!1))))) | (~b(z, s(s(elem!1)))) | (~b(s(s(elem!1)), s(s(s(elem!1))))))),
% 0.75/0.90 inference(rewrite,[status(thm)],[])).
% 0.75/0.90 tff(3670,plain,
% 0.75/0.90 (((~![X0: $i, X2: $i, X1: $i] : ((~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)))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(s(elem!1))))) | (~b(z, s(s(elem!1)))) | (~b(s(s(elem!1)), s(s(s(elem!1)))))))),
% 0.75/0.90 inference(monotonicity,[status(thm)],[3669])).
% 0.75/0.90 tff(3671,plain,
% 0.75/0.90 (((~![X0: $i, X2: $i, X1: $i] : ((~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)))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(s(s(elem!1))))) | (~b(z, s(s(elem!1)))) | (~b(s(s(elem!1)), s(s(s(elem!1))))))),
% 0.75/0.90 inference(transitivity,[status(thm)],[3670, 3668])).
% 0.75/0.90 tff(3672,plain,
% 0.75/0.90 ((~![X0: $i, X2: $i, X1: $i] : ((~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)))))),
% 0.75/0.90 inference(quant_inst,[status(thm)],[])).
% 0.75/0.90 tff(3673,plain,
% 0.75/0.90 ((~![X0: $i, X2: $i, X1: $i] : ((~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(s(s(elem!1))))) | (~b(z, s(s(elem!1)))) | (~b(s(s(elem!1)), s(s(s(elem!1)))))),
% 0.75/0.90 inference(modus_ponens,[status(thm)],[3672, 3671])).
% 0.75/0.90 tff(3674,plain,
% 0.75/0.90 (~b(z, s(s(elem!1)))),
% 0.75/0.90 inference(unit_resolution,[status(thm)],[3673, 117, 3667, 324])).
% 0.75/0.90 tff(3675,plain,
% 0.75/0.90 ((z = s(s(elem!1))) | r(z, s(s(elem!1)))),
% 0.75/0.90 inference(unit_resolution,[status(thm)],[723, 46, 3674])).
% 0.75/0.90 tff(3676,plain,
% 0.75/0.90 (r(z, s(s(elem!1)))),
% 0.75/0.90 inference(unit_resolution,[status(thm)],[3675, 328])).
% 0.75/0.90 tff(3677,plain,
% 0.75/0.90 (~b(s(s(s(s(elem!1)))), s(s(elem!1)))),
% 0.75/0.90 inference(unit_resolution,[status(thm)],[1508, 3626, 470, 287, 324])).
% 0.75/0.90 tff(3678,plain,
% 0.75/0.90 (r(s(s(s(s(elem!1)))), s(s(elem!1)))),
% 0.75/0.90 inference(unit_resolution,[status(thm)],[1690, 3677, 146])).
% 0.75/0.90 tff(3679,plain,
% 0.75/0.90 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(elem!1)))) | (~r(z, s(s(s(s(elem!1)))))) | (~r(s(s(s(s(elem!1)))), s(s(elem!1)))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, s(s(elem!1)))) | (~r(z, s(s(s(s(elem!1)))))) | (~r(s(s(s(s(elem!1)))), s(s(elem!1)))))),
% 0.75/0.90 inference(rewrite,[status(thm)],[])).
% 0.75/0.90 tff(3680,plain,
% 0.75/0.90 (((~r(s(s(s(s(elem!1)))), s(s(elem!1)))) | (~r(z, s(s(elem!1)))) | (~r(z, s(s(s(s(elem!1))))))) <=> ((~r(z, s(s(elem!1)))) | (~r(z, s(s(s(s(elem!1)))))) | (~r(s(s(s(s(elem!1)))), s(s(elem!1)))))),
% 0.75/0.90 inference(rewrite,[status(thm)],[])).
% 0.75/0.90 tff(3681,plain,
% 0.75/0.90 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(elem!1)))), s(s(elem!1)))) | (~r(z, s(s(elem!1)))) | (~r(z, s(s(s(s(elem!1)))))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(elem!1)))) | (~r(z, s(s(s(s(elem!1)))))) | (~r(s(s(s(s(elem!1)))), s(s(elem!1))))))),
% 0.75/0.90 inference(monotonicity,[status(thm)],[3680])).
% 0.75/0.90 tff(3682,plain,
% 0.75/0.90 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(elem!1)))), s(s(elem!1)))) | (~r(z, s(s(elem!1)))) | (~r(z, s(s(s(s(elem!1)))))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, s(s(elem!1)))) | (~r(z, s(s(s(s(elem!1)))))) | (~r(s(s(s(s(elem!1)))), s(s(elem!1)))))),
% 0.75/0.90 inference(transitivity,[status(thm)],[3681, 3679])).
% 0.75/0.90 tff(3683,plain,
% 0.75/0.90 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(elem!1)))), s(s(elem!1)))) | (~r(z, s(s(elem!1)))) | (~r(z, s(s(s(s(elem!1)))))))),
% 0.75/0.90 inference(quant_inst,[status(thm)],[])).
% 0.75/0.90 tff(3684,plain,
% 0.75/0.90 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, s(s(elem!1)))) | (~r(z, s(s(s(s(elem!1)))))) | (~r(s(s(s(s(elem!1)))), s(s(elem!1))))),
% 0.75/0.90 inference(modus_ponens,[status(thm)],[3683, 3682])).
% 0.75/0.90 tff(3685,plain,
% 0.75/0.90 (~r(z, s(s(s(s(elem!1)))))),
% 0.75/0.90 inference(unit_resolution,[status(thm)],[3684, 14, 3678, 3676])).
% 0.75/0.90 tff(3686,plain,
% 0.75/0.90 ((z = s(s(s(s(elem!1))))) | b(z, s(s(s(s(elem!1)))))),
% 0.75/0.90 inference(unit_resolution,[status(thm)],[1644, 46, 3685])).
% 0.75/0.90 tff(3687,plain,
% 0.75/0.90 (b(z, s(s(s(s(elem!1)))))),
% 0.75/0.90 inference(unit_resolution,[status(thm)],[3686, 1626])).
% 0.75/0.90 tff(3688,plain,
% 0.75/0.90 (~b(z, s(z))),
% 0.75/0.90 inference(unit_resolution,[status(thm)],[1640, 3687, 287, 3626, 3667])).
% 0.75/0.90 tff(3689,plain,
% 0.75/0.90 (r(z, s(z))),
% 0.75/0.90 inference(unit_resolution,[status(thm)],[599, 3688])).
% 0.75/0.90 tff(3690,plain,
% 0.75/0.90 (r(z, elem!1)),
% 0.75/0.90 inference(modus_ponens,[status(thm)],[3689, 3645])).
% 0.75/0.91 tff(3691,plain,
% 0.75/0.91 (~(s(s(s(s(s(s(elem!1)))))) = elem!1)),
% 0.75/0.91 inference(unit_resolution,[status(thm)],[1446, 3634])).
% 0.75/0.91 tff(3692,plain,
% 0.75/0.91 (b(s(s(elem!1)), s(z)) <=> b(s(s(elem!1)), elem!1)),
% 0.75/0.91 inference(monotonicity,[status(thm)],[3644])).
% 0.75/0.91 tff(3693,plain,
% 0.75/0.91 (b(s(s(elem!1)), elem!1)),
% 0.75/0.91 inference(modus_ponens,[status(thm)],[470, 3692])).
% 0.75/0.91 tff(3694,plain,
% 0.75/0.91 (b(s(s(s(s(elem!1)))), s(z)) <=> b(s(s(s(s(elem!1)))), elem!1)),
% 0.75/0.91 inference(monotonicity,[status(thm)],[3644])).
% 0.75/0.91 tff(3695,plain,
% 0.75/0.91 (b(s(s(s(s(elem!1)))), elem!1)),
% 0.75/0.91 inference(modus_ponens,[status(thm)],[3628, 3694])).
% 0.75/0.91 tff(3696,plain,
% 0.75/0.91 (r(s(s(s(z))), s(s(s(s(elem!1))))) <=> r(s(s(elem!1)), s(s(s(s(elem!1)))))),
% 0.75/0.91 inference(monotonicity,[status(thm)],[3634])).
% 0.75/0.91 tff(3697,plain,
% 0.75/0.91 (~b(s(s(s(z))), s(s(s(s(elem!1)))))),
% 0.75/0.91 inference(unit_resolution,[status(thm)],[2185, 3632, 3628])).
% 0.75/0.91 tff(3698,plain,
% 0.75/0.91 (r(s(s(s(z))), s(s(s(s(elem!1)))))),
% 0.75/0.91 inference(unit_resolution,[status(thm)],[1413, 46, 279, 3697])).
% 0.75/0.91 tff(3699,plain,
% 0.75/0.91 (r(s(s(elem!1)), s(s(s(s(elem!1)))))),
% 0.75/0.91 inference(modus_ponens,[status(thm)],[3698, 3696])).
% 0.75/0.91 tff(3700,plain,
% 0.75/0.91 (r(s(s(s(s(s(s(elem!1)))))), s(s(s(s(elem!1)))))),
% 0.75/0.91 inference(unit_resolution,[status(thm)],[1619, 46, 1919, 3087])).
% 0.75/0.91 tff(3701,assumption,(r(s(s(elem!1)), s(s(s(s(elem!1)))))), introduced(assumption)).
% 0.75/0.91 tff(3702,plain,
% 0.75/0.91 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(elem!1)), s(s(s(s(elem!1)))))) | (~r(s(s(s(s(s(s(elem!1)))))), s(s(s(s(elem!1)))))) | (~r(s(s(s(s(s(s(elem!1)))))), s(s(elem!1)))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(elem!1)), s(s(s(s(elem!1)))))) | (~r(s(s(s(s(s(s(elem!1)))))), s(s(s(s(elem!1)))))) | (~r(s(s(s(s(s(s(elem!1)))))), s(s(elem!1)))))),
% 0.75/0.91 inference(rewrite,[status(thm)],[])).
% 0.75/0.91 tff(3703,plain,
% 0.75/0.91 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(elem!1)), s(s(s(s(elem!1)))))) | (~r(s(s(s(s(s(s(elem!1)))))), s(s(s(s(elem!1)))))) | (~r(s(s(s(s(s(s(elem!1)))))), s(s(elem!1)))))),
% 0.75/0.91 inference(quant_inst,[status(thm)],[])).
% 0.75/0.91 tff(3704,plain,
% 0.75/0.91 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(elem!1)), s(s(s(s(elem!1)))))) | (~r(s(s(s(s(s(s(elem!1)))))), s(s(s(s(elem!1)))))) | (~r(s(s(s(s(s(s(elem!1)))))), s(s(elem!1))))),
% 0.75/0.91 inference(modus_ponens,[status(thm)],[3703, 3702])).
% 0.75/0.91 tff(3705,plain,
% 0.75/0.91 (~r(s(s(s(s(s(s(elem!1)))))), s(s(elem!1)))),
% 0.75/0.91 inference(unit_resolution,[status(thm)],[3704, 14, 3701, 3700])).
% 0.75/0.91 tff(3706,plain,
% 0.75/0.91 ($false),
% 0.75/0.91 inference(unit_resolution,[status(thm)],[1794, 3705, 1578])).
% 0.75/0.91 tff(3707,plain,((~b(s(s(s(s(s(s(elem!1)))))), elem!1)) | (~r(s(s(elem!1)), s(s(s(s(elem!1)))))) | (~(s(s(s(z))) = s(s(elem!1)))) | (s(s(s(s(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,[]))).
% 0.75/0.91 tff(3708,plain,
% 0.75/0.91 (~b(s(s(s(s(s(s(elem!1)))))), elem!1)),
% 0.75/0.91 inference(unit_resolution,[status(thm)],[3707, 3699, 3634, 2024, 3695, 3693])).
% 0.75/0.91 tff(3709,plain,
% 0.75/0.91 (r(s(s(s(s(s(s(elem!1)))))), elem!1)),
% 0.75/0.91 inference(unit_resolution,[status(thm)],[1599, 3708, 3691])).
% 0.75/0.91 tff(3710,plain,
% 0.75/0.91 (~r(s(s(s(s(s(s(elem!1)))))), z)),
% 0.75/0.91 inference(unit_resolution,[status(thm)],[2592, 14, 3709, 3690])).
% 0.75/0.91 tff(3711,plain,
% 0.75/0.91 (b(s(s(s(s(s(s(elem!1)))))), z)),
% 0.75/0.91 inference(unit_resolution,[status(thm)],[1666, 46, 1663, 3710])).
% 0.75/0.91 tff(3712,plain,
% 0.75/0.91 (((~![X0: $i, X2: $i, X1: $i] : ((~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), z)) | (~b(s(s(s(s(s(s(elem!1)))))), z)) | (~b(s(s(s(s(s(s(elem!1)))))), s(s(s(elem!1))))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(elem!1))), z)) | (~b(s(s(s(s(s(s(elem!1)))))), z)) | (~b(s(s(s(s(s(s(elem!1)))))), s(s(s(elem!1))))))),
% 0.75/0.91 inference(rewrite,[status(thm)],[])).
% 0.75/0.91 tff(3713,plain,
% 0.75/0.91 ((~![X0: $i, X2: $i, X1: $i] : ((~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), z)) | (~b(s(s(s(s(s(s(elem!1)))))), z)) | (~b(s(s(s(s(s(s(elem!1)))))), s(s(s(elem!1))))))),
% 0.75/0.91 inference(quant_inst,[status(thm)],[])).
% 0.75/0.91 tff(3714,plain,
% 0.75/0.91 ((~![X0: $i, X2: $i, X1: $i] : ((~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(elem!1))), z)) | (~b(s(s(s(s(s(s(elem!1)))))), z)) | (~b(s(s(s(s(s(s(elem!1)))))), s(s(s(elem!1)))))),
% 0.75/0.91 inference(modus_ponens,[status(thm)],[3713, 3712])).
% 0.75/0.91 tff(3715,plain,
% 0.75/0.91 (~b(s(s(s(s(s(s(elem!1)))))), s(s(s(elem!1))))),
% 0.75/0.91 inference(unit_resolution,[status(thm)],[3714, 117, 157, 3711])).
% 0.75/0.91 tff(3716,plain,
% 0.75/0.91 ((s(z) = s(s(s(elem!1)))) <=> (elem!1 = s(s(s(elem!1))))),
% 0.75/0.91 inference(monotonicity,[status(thm)],[3644])).
% 0.75/0.91 tff(3717,plain,
% 0.75/0.91 ((s(z) = s(s(s(elem!1)))) <=> (s(s(s(elem!1))) = elem!1)),
% 0.75/0.91 inference(transitivity,[status(thm)],[3716, 1512])).
% 0.75/0.91 tff(3718,plain,
% 0.75/0.91 ((~(s(z) = s(s(s(elem!1))))) <=> (~(s(s(s(elem!1))) = elem!1))),
% 0.75/0.91 inference(monotonicity,[status(thm)],[3717])).
% 0.75/0.91 tff(3719,plain,
% 0.75/0.91 (~(s(s(s(elem!1))) = elem!1)),
% 0.75/0.91 inference(modus_ponens,[status(thm)],[230, 3718])).
% 0.75/0.91 tff(3720,plain,
% 0.75/0.91 (~b(s(s(s(elem!1))), s(s(s(s(elem!1)))))),
% 0.75/0.91 inference(unit_resolution,[status(thm)],[2955, 117, 157, 1310])).
% 0.75/0.91 tff(3721,plain,
% 0.75/0.91 (r(s(s(s(elem!1))), s(s(s(s(elem!1)))))),
% 0.75/0.91 inference(unit_resolution,[status(thm)],[448, 3720, 3221])).
% 0.75/0.91 tff(3722,plain,
% 0.75/0.91 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), s(s(elem!1)))) | (~r(s(s(elem!1)), s(s(s(s(elem!1)))))) | (~r(s(s(s(elem!1))), s(s(s(s(elem!1)))))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(elem!1))), 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)))))))),
% 0.75/0.91 inference(rewrite,[status(thm)],[])).
% 0.75/0.91 tff(3723,plain,
% 0.75/0.91 (((~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(elem!1)), s(s(s(s(elem!1)))))) | (~r(s(s(s(elem!1))), s(s(s(s(elem!1)))))))),
% 0.75/0.91 inference(rewrite,[status(thm)],[])).
% 0.75/0.91 tff(3724,plain,
% 0.75/0.91 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(elem!1)), s(s(s(s(elem!1)))))) | (~r(s(s(s(elem!1))), s(s(s(s(elem!1)))))) | (~r(s(s(s(elem!1))), s(s(elem!1)))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), s(s(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))))))))),
% 0.75/0.91 inference(monotonicity,[status(thm)],[3723])).
% 0.75/0.91 tff(3725,plain,
% 0.75/0.91 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(elem!1)), s(s(s(s(elem!1)))))) | (~r(s(s(s(elem!1))), s(s(s(s(elem!1)))))) | (~r(s(s(s(elem!1))), s(s(elem!1)))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(elem!1))), s(s(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)))))))),
% 0.75/0.91 inference(transitivity,[status(thm)],[3724, 3722])).
% 0.75/0.91 tff(3726,plain,
% 0.75/0.91 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(elem!1)), s(s(s(s(elem!1)))))) | (~r(s(s(s(elem!1))), s(s(s(s(elem!1)))))) | (~r(s(s(s(elem!1))), s(s(elem!1)))))),
% 0.75/0.91 inference(quant_inst,[status(thm)],[])).
% 0.75/0.91 tff(3727,plain,
% 0.75/0.91 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(elem!1))), s(s(elem!1)))) | (~r(s(s(elem!1)), s(s(s(s(elem!1)))))) | (~r(s(s(s(elem!1))), s(s(s(s(elem!1))))))),
% 0.75/0.91 inference(modus_ponens,[status(thm)],[3726, 3725])).
% 0.75/0.91 tff(3728,plain,
% 0.75/0.91 (~r(s(s(s(elem!1))), s(s(elem!1)))),
% 0.75/0.91 inference(unit_resolution,[status(thm)],[3727, 14, 3721, 3699])).
% 0.75/0.91 tff(3729,plain,
% 0.75/0.91 (b(s(s(s(elem!1))), s(s(elem!1)))),
% 0.75/0.91 inference(unit_resolution,[status(thm)],[1547, 3728, 3203])).
% 0.75/0.91 tff(3730,plain,
% 0.75/0.91 (b(elem!1, s(s(s(z)))) <=> b(elem!1, s(s(elem!1)))),
% 0.75/0.91 inference(monotonicity,[status(thm)],[3634])).
% 0.75/0.91 tff(3731,plain,
% 0.75/0.91 (~r(s(z), s(s(elem!1)))),
% 0.75/0.91 inference(unit_resolution,[status(thm)],[1467, 3630, 3622])).
% 0.75/0.91 tff(3732,plain,
% 0.75/0.91 (b(s(z), s(s(elem!1)))),
% 0.75/0.91 inference(unit_resolution,[status(thm)],[416, 3731])).
% 0.75/0.91 tff(3733,plain,
% 0.75/0.91 (b(s(z), s(s(elem!1))) <=> b(elem!1, s(s(elem!1)))),
% 0.75/0.91 inference(monotonicity,[status(thm)],[2020])).
% 0.75/0.91 tff(3734,plain,
% 0.75/0.91 (b(elem!1, s(s(elem!1))) <=> b(s(z), s(s(elem!1)))),
% 0.75/0.91 inference(symmetry,[status(thm)],[3733])).
% 0.75/0.91 tff(3735,plain,
% 0.75/0.91 ((~b(elem!1, s(s(elem!1)))) <=> (~b(s(z), s(s(elem!1))))),
% 0.75/0.91 inference(monotonicity,[status(thm)],[3734])).
% 0.75/0.91 tff(3736,plain,
% 0.75/0.91 (b(elem!1, s(s(s(z)))) <=> b(elem!1, s(s(elem!1)))),
% 0.75/0.91 inference(monotonicity,[status(thm)],[1434])).
% 0.75/0.91 tff(3737,plain,
% 0.75/0.91 ((~b(elem!1, s(s(s(z))))) <=> (~b(elem!1, s(s(elem!1))))),
% 0.75/0.91 inference(monotonicity,[status(thm)],[3736])).
% 0.75/0.91 tff(3738,assumption,(~b(elem!1, s(s(s(z))))), introduced(assumption)).
% 0.75/0.91 tff(3739,plain,
% 0.75/0.91 (~b(elem!1, s(s(elem!1)))),
% 0.75/0.91 inference(modus_ponens,[status(thm)],[3738, 3737])).
% 0.75/0.91 tff(3740,plain,
% 0.75/0.91 (~b(s(z), s(s(elem!1)))),
% 0.75/0.91 inference(modus_ponens,[status(thm)],[3739, 3735])).
% 0.75/0.91 tff(3741,plain,
% 0.75/0.91 ($false),
% 0.75/0.91 inference(unit_resolution,[status(thm)],[452, 3740])).
% 0.75/0.91 tff(3742,plain,((~(s(s(s(z))) = s(s(elem!1)))) | (~b(s(z), s(s(elem!1)))) | b(elem!1, s(s(s(z))))), inference(lemma,lemma(discharge,[]))).
% 0.75/0.91 tff(3743,plain,
% 0.75/0.91 (b(elem!1, s(s(s(z))))),
% 0.75/0.91 inference(unit_resolution,[status(thm)],[3742, 3634, 3732])).
% 0.75/0.91 tff(3744,plain,
% 0.75/0.91 (b(elem!1, s(s(elem!1)))),
% 0.75/0.91 inference(modus_ponens,[status(thm)],[3743, 3730])).
% 0.75/0.91 tff(3745,plain,
% 0.75/0.91 (((~![X0: $i, X2: $i, X1: $i] : ((~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), elem!1)) | (~b(elem!1, s(s(elem!1)))) | (~b(s(s(s(elem!1))), s(s(elem!1)))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(elem!1))), elem!1)) | (~b(elem!1, s(s(elem!1)))) | (~b(s(s(s(elem!1))), s(s(elem!1)))))),
% 0.75/0.91 inference(rewrite,[status(thm)],[])).
% 0.75/0.91 tff(3746,plain,
% 0.75/0.91 (((~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))), elem!1)) | (~b(elem!1, s(s(elem!1)))) | (~b(s(s(s(elem!1))), s(s(elem!1)))))),
% 0.75/0.91 inference(rewrite,[status(thm)],[])).
% 0.75/0.91 tff(3747,plain,
% 0.75/0.91 (((~![X0: $i, X2: $i, X1: $i] : ((~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(s(elem!1))), elem!1)))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), elem!1)) | (~b(elem!1, s(s(elem!1)))) | (~b(s(s(s(elem!1))), s(s(elem!1))))))),
% 0.75/0.91 inference(monotonicity,[status(thm)],[3746])).
% 0.75/0.91 tff(3748,plain,
% 0.75/0.91 (((~![X0: $i, X2: $i, X1: $i] : ((~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(s(elem!1))), elem!1)))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(elem!1))), elem!1)) | (~b(elem!1, s(s(elem!1)))) | (~b(s(s(s(elem!1))), s(s(elem!1)))))),
% 0.75/0.91 inference(transitivity,[status(thm)],[3747, 3745])).
% 0.75/0.91 tff(3749,plain,
% 0.75/0.91 ((~![X0: $i, X2: $i, X1: $i] : ((~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(s(elem!1))), elem!1)))),
% 0.75/0.91 inference(quant_inst,[status(thm)],[])).
% 0.75/0.91 tff(3750,plain,
% 0.75/0.91 ((~![X0: $i, X2: $i, X1: $i] : ((~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(elem!1))), elem!1)) | (~b(elem!1, s(s(elem!1)))) | (~b(s(s(s(elem!1))), s(s(elem!1))))),
% 0.75/0.91 inference(modus_ponens,[status(thm)],[3749, 3748])).
% 0.75/0.91 tff(3751,plain,
% 0.75/0.91 (~b(s(s(s(elem!1))), elem!1)),
% 0.75/0.91 inference(unit_resolution,[status(thm)],[3750, 117, 3744, 3729])).
% 0.75/0.91 tff(3752,plain,
% 0.75/0.91 (r(s(s(s(elem!1))), elem!1)),
% 0.75/0.91 inference(unit_resolution,[status(thm)],[1235, 3751, 3719])).
% 0.75/0.91 tff(3753,plain,
% 0.75/0.91 (~r(s(s(s(s(s(s(elem!1)))))), s(s(s(elem!1))))),
% 0.75/0.91 inference(unit_resolution,[status(thm)],[1559, 14, 3752, 3709])).
% 0.75/0.91 tff(3754,plain,
% 0.75/0.91 ((s(s(s(s(s(s(elem!1)))))) = s(s(s(elem!1)))) | b(s(s(s(s(s(s(elem!1)))))), s(s(s(elem!1))))),
% 0.75/0.91 inference(unit_resolution,[status(thm)],[1563, 46, 3753])).
% 0.75/0.91 tff(3755,plain,
% 0.75/0.91 ($false),
% 0.75/0.91 inference(unit_resolution,[status(thm)],[3754, 3715, 3640])).
% 0.75/0.91 tff(3756,plain,((~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), z)) | (s(s(s(elem!1))) = s(s(elem!1))) | (s(s(s(s(elem!1)))) = s(s(s(elem!1)))) | (~b(s(s(s(s(elem!1)))), z)) | (~b(s(s(elem!1)), s(z))) | (~r(s(s(s(z))), z)) | (s(s(s(s(elem!1)))) = s(s(elem!1)))), inference(lemma,lemma(discharge,[]))).
% 0.75/0.91 tff(3757,plain,
% 0.75/0.91 (~b(s(s(elem!1)), s(s(s(elem!1))))),
% 0.75/0.91 inference(unit_resolution,[status(thm)],[3756, 1310, 1539, 156, 157, 3616, 3618, 146])).
% 0.75/0.91 tff(3758,plain,
% 0.75/0.91 (r(s(s(elem!1)), s(s(s(elem!1))))),
% 0.75/0.91 inference(unit_resolution,[status(thm)],[253, 3757, 145])).
% 0.75/0.91 tff(3759,plain,
% 0.75/0.91 (~r(s(s(s(s(elem!1)))), s(s(elem!1)))),
% 0.75/0.91 inference(unit_resolution,[status(thm)],[2220, 3758, 3620])).
% 0.75/0.91 tff(3760,plain,
% 0.75/0.91 (b(s(s(s(s(elem!1)))), s(s(elem!1)))),
% 0.75/0.91 inference(unit_resolution,[status(thm)],[1690, 3759, 146])).
% 0.75/0.91 tff(3761,plain,
% 0.75/0.91 (~b(s(s(elem!1)), z)),
% 0.75/0.91 inference(unit_resolution,[status(thm)],[2191, 3760, 1310])).
% 0.75/0.91 tff(3762,plain,
% 0.75/0.91 (r(s(s(elem!1)), z)),
% 0.75/0.91 inference(unit_resolution,[status(thm)],[1025, 3761])).
% 0.75/0.91 tff(3763,plain,
% 0.75/0.91 (~r(s(s(s(z))), s(s(elem!1)))),
% 0.75/0.91 inference(unit_resolution,[status(thm)],[827, 14, 3762, 3618])).
% 0.75/0.91 tff(3764,plain,
% 0.75/0.91 (~r(s(z), s(s(elem!1)))),
% 0.75/0.91 inference(unit_resolution,[status(thm)],[1479, 3762, 3758])).
% 0.75/0.91 tff(3765,plain,
% 0.75/0.91 (b(s(z), s(s(elem!1)))),
% 0.75/0.91 inference(unit_resolution,[status(thm)],[416, 3764])).
% 0.75/0.91 tff(3766,plain,
% 0.75/0.91 (~b(s(s(s(s(elem!1)))), s(z))),
% 0.75/0.91 inference(unit_resolution,[status(thm)],[1457, 3765, 3760])).
% 0.75/0.91 tff(3767,plain,
% 0.75/0.91 (r(s(s(s(s(elem!1)))), s(z))),
% 0.75/0.91 inference(unit_resolution,[status(thm)],[1327, 3766])).
% 0.75/0.91 tff(3768,plain,
% 0.75/0.91 (~r(s(z), s(s(s(elem!1))))),
% 0.75/0.91 inference(unit_resolution,[status(thm)],[1342, 3767, 3620])).
% 0.75/0.91 tff(3769,plain,
% 0.75/0.91 (b(s(z), s(s(s(elem!1))))),
% 0.75/0.91 inference(unit_resolution,[status(thm)],[235, 3768])).
% 0.75/0.91 tff(3770,plain,
% 0.75/0.91 (~b(z, s(z))),
% 0.75/0.91 inference(unit_resolution,[status(thm)],[2566, 3769, 145, 3616])).
% 0.75/0.91 tff(3771,plain,
% 0.75/0.91 (r(z, s(z))),
% 0.75/0.91 inference(unit_resolution,[status(thm)],[599, 3770])).
% 0.75/0.91 tff(3772,plain,
% 0.75/0.91 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(z))) | (~r(s(s(s(z))), z)) | (~r(s(s(s(z))), s(z))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, s(z))) | (~r(s(s(s(z))), z)) | (~r(s(s(s(z))), s(z))))),
% 0.75/0.91 inference(rewrite,[status(thm)],[])).
% 0.75/0.91 tff(3773,plain,
% 0.75/0.91 (((~r(z, s(z))) | (~r(s(s(s(z))), s(z))) | (~r(s(s(s(z))), z))) <=> ((~r(z, s(z))) | (~r(s(s(s(z))), z)) | (~r(s(s(s(z))), s(z))))),
% 0.75/0.91 inference(rewrite,[status(thm)],[])).
% 0.75/0.91 tff(3774,plain,
% 0.75/0.91 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(z))) | (~r(s(s(s(z))), s(z))) | (~r(s(s(s(z))), z)))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(z))) | (~r(s(s(s(z))), z)) | (~r(s(s(s(z))), s(z)))))),
% 0.75/0.91 inference(monotonicity,[status(thm)],[3773])).
% 0.75/0.91 tff(3775,plain,
% 0.75/0.91 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(z))) | (~r(s(s(s(z))), s(z))) | (~r(s(s(s(z))), z)))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, s(z))) | (~r(s(s(s(z))), z)) | (~r(s(s(s(z))), s(z))))),
% 0.75/0.91 inference(transitivity,[status(thm)],[3774, 3772])).
% 0.75/0.91 tff(3776,plain,
% 0.75/0.91 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(z))) | (~r(s(s(s(z))), s(z))) | (~r(s(s(s(z))), z)))),
% 0.75/0.91 inference(quant_inst,[status(thm)],[])).
% 0.75/0.91 tff(3777,plain,
% 0.75/0.91 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, s(z))) | (~r(s(s(s(z))), z)) | (~r(s(s(s(z))), s(z)))),
% 0.75/0.91 inference(modus_ponens,[status(thm)],[3776, 3775])).
% 0.75/0.91 tff(3778,plain,
% 0.75/0.91 ($false),
% 0.75/0.91 inference(unit_resolution,[status(thm)],[3777, 14, 2, 180, 283])).
% 0.75/0.91 tff(3779,plain,((~r(z, s(z))) | (~r(s(s(s(z))), z)) | (~r(s(s(s(z))), s(z)))), inference(lemma,lemma(discharge,[]))).
% 0.75/0.91 tff(3780,plain,
% 0.75/0.91 (~r(s(s(s(z))), s(z))),
% 0.75/0.91 inference(unit_resolution,[status(thm)],[3779, 3771, 3618])).
% 0.75/0.91 tff(3781,plain,
% 0.75/0.91 (b(s(s(s(z))), s(z))),
% 0.75/0.91 inference(unit_resolution,[status(thm)],[347, 3780])).
% 0.75/0.91 tff(3782,plain,
% 0.75/0.91 (~b(s(s(s(z))), s(s(elem!1)))),
% 0.75/0.91 inference(unit_resolution,[status(thm)],[853, 3781, 3616])).
% 0.75/0.91 tff(3783,plain,
% 0.75/0.91 (s(s(s(z))) = s(s(elem!1))),
% 0.75/0.91 inference(unit_resolution,[status(thm)],[1421, 46, 3782, 3763])).
% 0.75/0.91 tff(3784,plain,
% 0.75/0.91 (inj_0(s(s(s(z)))) = inj_0(s(s(elem!1)))),
% 0.75/0.91 inference(monotonicity,[status(thm)],[3783])).
% 0.75/0.91 tff(3785,plain,
% 0.75/0.91 (s(s(z)) = s(elem!1)),
% 0.75/0.91 inference(transitivity,[status(thm)],[95, 3784, 166])).
% 0.75/0.91 tff(3786,plain,
% 0.75/0.91 (inj_0(s(s(z))) = inj_0(s(elem!1))),
% 0.75/0.91 inference(monotonicity,[status(thm)],[3785])).
% 0.75/0.91 tff(3787,plain,
% 0.75/0.91 (s(z) = elem!1),
% 0.75/0.91 inference(transitivity,[status(thm)],[131, 3786, 257])).
% 0.75/0.91 tff(3788,plain,
% 0.75/0.91 (r(z, s(z)) <=> r(z, elem!1)),
% 0.75/0.91 inference(monotonicity,[status(thm)],[3787])).
% 0.75/0.91 tff(3789,plain,
% 0.75/0.91 (r(z, elem!1)),
% 0.75/0.91 inference(modus_ponens,[status(thm)],[3771, 3788])).
% 0.75/0.91 tff(3790,plain,
% 0.75/0.91 (~(s(s(s(s(s(s(elem!1)))))) = elem!1)),
% 0.75/0.91 inference(unit_resolution,[status(thm)],[1446, 3783])).
% 0.75/0.91 tff(3791,plain,
% 0.75/0.91 (b(s(s(elem!1)), s(z)) <=> b(s(s(elem!1)), elem!1)),
% 0.75/0.91 inference(monotonicity,[status(thm)],[3787])).
% 0.75/0.91 tff(3792,plain,
% 0.75/0.91 (b(s(s(elem!1)), elem!1)),
% 0.75/0.91 inference(modus_ponens,[status(thm)],[3616, 3791])).
% 0.75/0.91 tff(3793,plain,
% 0.75/0.91 (~r(s(s(s(elem!1))), s(z))),
% 0.75/0.91 inference(unit_resolution,[status(thm)],[1916, 3767, 3620])).
% 0.75/0.91 tff(3794,plain,
% 0.75/0.91 (b(s(s(s(elem!1))), s(z))),
% 0.75/0.91 inference(unit_resolution,[status(thm)],[467, 3793])).
% 0.75/0.91 tff(3795,plain,
% 0.75/0.91 (((~![X0: $i, X2: $i, X1: $i] : ((~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(elem!1))), s(s(elem!1)))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~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(elem!1))), s(s(elem!1)))))),
% 0.75/0.91 inference(rewrite,[status(thm)],[])).
% 0.75/0.91 tff(3796,plain,
% 0.75/0.91 ((~![X0: $i, X2: $i, X1: $i] : ((~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(elem!1))), s(s(elem!1)))))),
% 0.75/0.91 inference(quant_inst,[status(thm)],[])).
% 0.75/0.91 tff(3797,plain,
% 0.75/0.91 ((~![X0: $i, X2: $i, X1: $i] : ((~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(elem!1))), s(s(elem!1))))),
% 0.75/0.91 inference(modus_ponens,[status(thm)],[3796, 3795])).
% 0.75/0.91 tff(3798,plain,
% 0.75/0.91 (~b(s(s(s(elem!1))), s(s(elem!1)))),
% 0.75/0.91 inference(unit_resolution,[status(thm)],[3797, 117, 3616, 3794])).
% 0.75/0.91 tff(3799,plain,
% 0.75/0.91 (r(s(s(s(elem!1))), s(s(elem!1)))),
% 0.75/0.91 inference(unit_resolution,[status(thm)],[1547, 3798, 1539])).
% 0.75/0.91 tff(3800,plain,
% 0.75/0.91 (b(s(s(s(elem!1))), s(z)) <=> b(s(s(s(elem!1))), elem!1)),
% 0.75/0.91 inference(monotonicity,[status(thm)],[3787])).
% 0.75/0.91 tff(3801,plain,
% 0.75/0.91 (b(s(s(s(elem!1))), elem!1)),
% 0.75/0.91 inference(modus_ponens,[status(thm)],[3794, 3800])).
% 0.75/0.91 tff(3802,plain,
% 0.75/0.91 (~b(s(s(s(s(s(s(elem!1)))))), elem!1)),
% 0.75/0.91 inference(unit_resolution,[status(thm)],[2587, 3801, 3799, 3783, 3792])).
% 0.75/0.91 tff(3803,plain,
% 0.75/0.91 (r(s(s(s(s(s(s(elem!1)))))), elem!1)),
% 0.75/0.91 inference(unit_resolution,[status(thm)],[1599, 3802, 3790])).
% 0.75/0.91 tff(3804,plain,
% 0.75/0.91 (~r(s(s(s(s(s(s(elem!1)))))), z)),
% 0.75/0.91 inference(unit_resolution,[status(thm)],[2592, 14, 3803, 3789])).
% 0.75/0.91 tff(3805,plain,
% 0.75/0.91 (b(s(s(s(s(s(s(elem!1)))))), z)),
% 0.75/0.91 inference(unit_resolution,[status(thm)],[1666, 46, 1663, 3804])).
% 0.75/0.91 tff(3806,plain,
% 0.75/0.91 (r(s(s(s(s(elem!1)))), s(z)) <=> r(s(s(s(s(elem!1)))), elem!1)),
% 0.75/0.91 inference(monotonicity,[status(thm)],[3787])).
% 0.75/0.91 tff(3807,plain,
% 0.75/0.91 (r(s(s(s(s(elem!1)))), elem!1)),
% 0.75/0.91 inference(modus_ponens,[status(thm)],[3767, 3806])).
% 0.75/0.91 tff(3808,plain,
% 0.75/0.91 (~r(s(s(s(s(s(s(elem!1)))))), s(s(s(s(elem!1)))))),
% 0.75/0.91 inference(unit_resolution,[status(thm)],[1822, 14, 3807, 3803])).
% 0.75/0.91 tff(3809,plain,
% 0.75/0.91 (b(s(s(s(s(s(s(elem!1)))))), s(s(s(s(elem!1)))))),
% 0.75/0.91 inference(unit_resolution,[status(thm)],[1619, 46, 2024, 3808])).
% 0.75/0.91 tff(3810,plain,
% 0.75/0.91 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(z))) | (~r(z, s(s(s(s(elem!1)))))) | (~r(s(s(s(s(elem!1)))), s(z))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, s(z))) | (~r(z, s(s(s(s(elem!1)))))) | (~r(s(s(s(s(elem!1)))), s(z))))),
% 0.75/0.91 inference(rewrite,[status(thm)],[])).
% 0.75/0.91 tff(3811,plain,
% 0.75/0.91 (((~r(s(s(s(s(elem!1)))), s(z))) | (~r(z, s(z))) | (~r(z, s(s(s(s(elem!1))))))) <=> ((~r(z, s(z))) | (~r(z, s(s(s(s(elem!1)))))) | (~r(s(s(s(s(elem!1)))), s(z))))),
% 0.75/0.91 inference(rewrite,[status(thm)],[])).
% 0.75/0.91 tff(3812,plain,
% 0.75/0.91 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(elem!1)))), s(z))) | (~r(z, s(z))) | (~r(z, s(s(s(s(elem!1)))))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(z))) | (~r(z, s(s(s(s(elem!1)))))) | (~r(s(s(s(s(elem!1)))), s(z)))))),
% 0.75/0.91 inference(monotonicity,[status(thm)],[3811])).
% 0.75/0.91 tff(3813,plain,
% 0.75/0.91 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(elem!1)))), s(z))) | (~r(z, s(z))) | (~r(z, s(s(s(s(elem!1)))))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, s(z))) | (~r(z, s(s(s(s(elem!1)))))) | (~r(s(s(s(s(elem!1)))), s(z))))),
% 0.75/0.91 inference(transitivity,[status(thm)],[3812, 3810])).
% 0.75/0.91 tff(3814,plain,
% 0.75/0.91 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(elem!1)))), s(z))) | (~r(z, s(z))) | (~r(z, s(s(s(s(elem!1)))))))),
% 0.75/0.91 inference(quant_inst,[status(thm)],[])).
% 0.75/0.91 tff(3815,plain,
% 0.75/0.91 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, s(z))) | (~r(z, s(s(s(s(elem!1)))))) | (~r(s(s(s(s(elem!1)))), s(z)))),
% 0.75/0.91 inference(modus_ponens,[status(thm)],[3814, 3813])).
% 0.75/0.91 tff(3816,plain,
% 0.75/0.91 (~r(z, s(s(s(s(elem!1)))))),
% 0.75/0.91 inference(unit_resolution,[status(thm)],[3815, 14, 3767, 3771])).
% 0.75/0.91 tff(3817,plain,
% 0.75/0.91 ((z = s(s(s(s(elem!1))))) | b(z, s(s(s(s(elem!1)))))),
% 0.75/0.91 inference(unit_resolution,[status(thm)],[1644, 46, 3816])).
% 0.75/0.91 tff(3818,plain,
% 0.75/0.91 (b(z, s(s(s(s(elem!1)))))),
% 0.75/0.91 inference(unit_resolution,[status(thm)],[3817, 1626])).
% 0.75/0.91 tff(3819,plain,
% 0.75/0.91 ($false),
% 0.75/0.91 inference(unit_resolution,[status(thm)],[2611, 117, 3818, 3809, 3805])).
% 0.75/0.91 tff(3820,plain,((~b(s(s(s(s(elem!1)))), z)) | (s(s(elem!1)) = s(s(s(elem!1)))) | (s(s(s(s(elem!1)))) = s(s(elem!1))) | (~b(s(s(s(elem!1))), z))), inference(lemma,lemma(discharge,[]))).
% 0.75/0.91 tff(3821,plain,
% 0.75/0.91 (~b(s(s(s(s(elem!1)))), z)),
% 0.75/0.91 inference(unit_resolution,[status(thm)],[3820, 157, 146, 145])).
% 0.75/0.91 tff(3822,plain,
% 0.75/0.91 (r(s(s(s(s(elem!1)))), z)),
% 0.75/0.91 inference(unit_resolution,[status(thm)],[1855, 3821])).
% 0.75/0.91 tff(3823,plain,
% 0.75/0.91 (~b(s(s(s(elem!1))), s(s(elem!1)))),
% 0.75/0.91 inference(unit_resolution,[status(thm)],[3210, 117, 157, 1036])).
% 0.75/0.91 tff(3824,plain,
% 0.75/0.91 (r(s(s(s(elem!1))), s(s(elem!1)))),
% 0.75/0.91 inference(unit_resolution,[status(thm)],[1547, 3823, 1539])).
% 0.75/0.91 tff(3825,plain,
% 0.75/0.91 (~b(s(z), z)),
% 0.75/0.91 inference(unit_resolution,[status(thm)],[1050, 1036, 157, 145])).
% 0.75/0.91 tff(3826,plain,
% 0.75/0.91 (r(s(z), z)),
% 0.75/0.91 inference(unit_resolution,[status(thm)],[193, 3825])).
% 0.75/0.91 tff(3827,plain,
% 0.75/0.91 (~r(s(s(s(s(elem!1)))), s(z))),
% 0.75/0.91 inference(unit_resolution,[status(thm)],[2196, 14, 183, 1396])).
% 0.75/0.91 tff(3828,plain,
% 0.75/0.91 (b(s(s(s(s(elem!1)))), s(z))),
% 0.75/0.91 inference(unit_resolution,[status(thm)],[1327, 3827])).
% 0.75/0.91 tff(3829,plain,
% 0.75/0.91 (b(s(s(s(z))), s(s(s(s(elem!1)))))),
% 0.75/0.91 inference(unit_resolution,[status(thm)],[2122, 180, 1396])).
% 0.75/0.91 tff(3830,plain,
% 0.75/0.91 (~b(s(s(s(z))), s(z))),
% 0.75/0.91 inference(unit_resolution,[status(thm)],[2185, 3829, 3828])).
% 0.75/0.91 tff(3831,plain,
% 0.75/0.91 ($false),
% 0.75/0.91 inference(unit_resolution,[status(thm)],[347, 3830, 2276])).
% 0.75/0.91 tff(3832,plain,((~r(s(s(s(z))), z)) | (~r(s(z), z)) | (~r(s(s(s(s(elem!1)))), z))), inference(lemma,lemma(discharge,[]))).
% 0.75/0.91 tff(3833,plain,
% 0.75/0.91 (~r(s(s(s(z))), z)),
% 0.75/0.91 inference(unit_resolution,[status(thm)],[3832, 3826, 1396])).
% 0.75/0.91 tff(3834,plain,
% 0.75/0.91 (b(s(s(s(z))), z)),
% 0.75/0.91 inference(unit_resolution,[status(thm)],[823, 3833])).
% 0.75/0.91 tff(3835,plain,
% 0.75/0.91 (~b(s(s(s(z))), s(s(elem!1)))),
% 0.75/0.91 inference(unit_resolution,[status(thm)],[1217, 3834, 1036])).
% 0.75/0.91 tff(3836,plain,
% 0.75/0.91 (r(s(s(s(z))), s(s(elem!1)))),
% 0.75/0.91 inference(unit_resolution,[status(thm)],[1421, 46, 3835, 1417])).
% 0.75/0.91 tff(3837,plain,
% 0.75/0.91 (~r(s(s(s(elem!1))), s(s(s(z))))),
% 0.75/0.91 inference(unit_resolution,[status(thm)],[3248, 3836, 3824])).
% 0.75/0.91 tff(3838,plain,
% 0.75/0.91 (~b(s(s(s(elem!1))), s(s(s(z))))),
% 0.75/0.91 inference(unit_resolution,[status(thm)],[2967, 3834, 157])).
% 0.75/0.91 tff(3839,plain,
% 0.75/0.91 ((s(s(s(elem!1))) = s(s(s(z)))) | r(s(s(s(elem!1))), s(s(s(z))))),
% 0.75/0.91 inference(unit_resolution,[status(thm)],[2341, 46, 3838])).
% 0.75/0.91 tff(3840,plain,
% 0.75/0.91 (s(s(s(elem!1))) = s(s(s(z)))),
% 0.75/0.91 inference(unit_resolution,[status(thm)],[3839, 3837])).
% 0.75/0.91 tff(3841,plain,
% 0.75/0.91 (inj_0(s(s(s(elem!1)))) = inj_0(s(s(s(z))))),
% 0.75/0.91 inference(monotonicity,[status(thm)],[3840])).
% 0.75/0.91 tff(3842,plain,
% 0.75/0.91 (inj_0(s(s(s(z)))) = inj_0(s(s(s(elem!1))))),
% 0.75/0.91 inference(symmetry,[status(thm)],[3841])).
% 0.75/0.91 tff(3843,plain,
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% 0.75/0.91 tff(3844,plain,
% 0.75/0.91 (b(s(s(z)), z) <=> b(s(s(elem!1)), z)),
% 0.75/0.91 inference(monotonicity,[status(thm)],[3843])).
% 0.75/0.91 tff(3845,plain,
% 0.75/0.91 (b(s(s(elem!1)), z) <=> b(s(s(z)), z)),
% 0.75/0.91 inference(symmetry,[status(thm)],[3844])).
% 0.75/0.91 tff(3846,plain,
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% 0.75/0.91 inference(modus_ponens,[status(thm)],[1036, 3845])).
% 0.75/0.91 tff(3847,plain,
% 0.75/0.91 (s(s(s(s(elem!1)))) = s(s(s(s(z))))),
% 0.75/0.91 inference(monotonicity,[status(thm)],[3840])).
% 0.75/0.91 tff(3848,plain,
% 0.75/0.91 (r(s(s(s(s(elem!1)))), z) <=> r(s(s(s(s(z)))), z)),
% 0.75/0.91 inference(monotonicity,[status(thm)],[3847])).
% 0.75/0.91 tff(3849,plain,
% 0.75/0.91 (r(s(s(s(s(z)))), z)),
% 0.75/0.91 inference(modus_ponens,[status(thm)],[1396, 3848])).
% 0.75/0.91 tff(3850,plain,
% 0.75/0.91 (b(s(s(s(s(elem!1)))), s(z)) <=> b(s(s(s(s(z)))), s(z))),
% 0.75/0.91 inference(monotonicity,[status(thm)],[3847])).
% 0.75/0.91 tff(3851,plain,
% 0.75/0.91 (~r(s(s(s(s(elem!1)))), s(z))),
% 0.75/0.91 inference(unit_resolution,[status(thm)],[2196, 14, 3826, 1396])).
% 0.75/0.91 tff(3852,plain,
% 0.75/0.91 (b(s(s(s(s(elem!1)))), s(z))),
% 0.75/0.91 inference(unit_resolution,[status(thm)],[1327, 3851])).
% 0.75/0.91 tff(3853,plain,
% 0.75/0.91 (b(s(s(s(s(z)))), s(z))),
% 0.75/0.91 inference(modus_ponens,[status(thm)],[3852, 3850])).
% 0.75/0.91 tff(3854,plain,
% 0.75/0.91 (~r(s(s(s(s(s(s(z)))))), s(z))),
% 0.75/0.91 inference(unit_resolution,[status(thm)],[2269, 14, 183, 2266])).
% 0.75/0.91 tff(3855,plain,
% 0.75/0.91 (b(s(s(s(s(s(s(z)))))), s(z))),
% 0.75/0.91 inference(unit_resolution,[status(thm)],[2274, 46, 1770, 3854])).
% 0.75/0.91 tff(3856,plain,
% 0.75/0.91 (((~![X0: $i, X2: $i, X1: $i] : ((~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(s(s(s(z)))))), s(z))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(s(z)))))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(s(s(s(z)))))), s(z))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(s(z)))))))),
% 0.75/0.91 inference(rewrite,[status(thm)],[])).
% 0.75/0.91 tff(3857,plain,
% 0.75/0.91 ((~![X0: $i, X2: $i, X1: $i] : ((~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(s(s(s(z)))))), s(z))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(s(z)))))))),
% 0.75/0.91 inference(quant_inst,[status(thm)],[])).
% 0.75/0.91 tff(3858,plain,
% 0.75/0.91 ((~![X0: $i, X2: $i, X1: $i] : ((~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(s(s(s(z)))))), s(z))) | (~b(s(s(s(s(s(s(z)))))), s(s(s(s(z))))))),
% 0.75/0.91 inference(modus_ponens,[status(thm)],[3857, 3856])).
% 0.75/0.91 tff(3859,plain,
% 0.75/0.91 (~b(s(s(s(s(s(s(z)))))), s(s(s(s(z)))))),
% 0.75/0.91 inference(unit_resolution,[status(thm)],[3858, 117, 562, 3855])).
% 0.75/0.91 tff(3860,assumption,(r(s(s(s(s(z)))), z)), introduced(assumption)).
% 0.75/0.91 tff(3861,plain,
% 0.75/0.91 (~r(s(s(s(s(s(s(z)))))), s(s(s(s(z)))))),
% 0.75/0.91 inference(unit_resolution,[status(thm)],[3192, 14, 3860, 2266])).
% 0.75/0.91 tff(3862,plain,
% 0.75/0.91 ((s(s(s(s(s(s(z)))))) = s(s(s(s(z))))) | b(s(s(s(s(s(s(z)))))), s(s(s(s(z)))))),
% 0.75/0.91 inference(unit_resolution,[status(thm)],[2323, 46, 3861])).
% 0.75/0.91 tff(3863,plain,
% 0.75/0.91 ($false),
% 0.75/0.91 inference(unit_resolution,[status(thm)],[3862, 3859, 2240])).
% 0.75/0.91 tff(3864,plain,((~r(s(s(s(s(s(s(z)))))), z)) | (~b(s(s(s(s(z)))), s(z))) | (~(s(s(s(elem!1))) = s(s(s(z))))) | (~r(s(s(s(s(z)))), z)) | (~r(s(z), z))), inference(lemma,lemma(discharge,[]))).
% 0.75/0.91 tff(3865,plain,
% 0.75/0.91 (~r(s(s(s(s(s(s(z)))))), z)),
% 0.75/0.91 inference(unit_resolution,[status(thm)],[3864, 3853, 3840, 3849, 3826])).
% 0.75/0.92 tff(3866,plain,
% 0.75/0.92 ((~![X: $i] : (~(s(X) = z))) | (~(s(s(s(s(s(s(z)))))) = z))),
% 0.75/0.92 inference(quant_inst,[status(thm)],[])).
% 0.75/0.92 tff(3867,plain,
% 0.75/0.92 (~(s(s(s(s(s(s(z)))))) = z)),
% 0.75/0.92 inference(unit_resolution,[status(thm)],[3866, 33])).
% 0.75/0.92 tff(3868,plain,
% 0.75/0.92 (((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((s(s(s(s(s(s(z)))))) = z) | b(s(s(s(s(s(s(z)))))), z) | r(s(s(s(s(s(s(z)))))), z))) <=> ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (s(s(s(s(s(s(z)))))) = z) | b(s(s(s(s(s(s(z)))))), z) | r(s(s(s(s(s(s(z)))))), z))),
% 0.75/0.92 inference(rewrite,[status(thm)],[])).
% 0.75/0.92 tff(3869,plain,
% 0.75/0.92 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((s(s(s(s(s(s(z)))))) = z) | b(s(s(s(s(s(s(z)))))), z) | r(s(s(s(s(s(s(z)))))), z))),
% 0.75/0.92 inference(quant_inst,[status(thm)],[])).
% 0.75/0.92 tff(3870,plain,
% 0.75/0.92 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (s(s(s(s(s(s(z)))))) = z) | b(s(s(s(s(s(s(z)))))), z) | r(s(s(s(s(s(s(z)))))), z)),
% 0.75/0.92 inference(modus_ponens,[status(thm)],[3869, 3868])).
% 0.75/0.92 tff(3871,plain,
% 0.75/0.92 (b(s(s(s(s(s(s(z)))))), z)),
% 0.75/0.92 inference(unit_resolution,[status(thm)],[3870, 46, 3867, 3865])).
% 0.75/0.92 tff(3872,plain,
% 0.75/0.92 ((~b(s(s(z)), z)) | (~b(s(s(s(s(s(s(z)))))), s(s(z))))),
% 0.75/0.92 inference(unit_resolution,[status(thm)],[2299, 117, 3871])).
% 0.75/0.92 tff(3873,plain,
% 0.75/0.92 (~b(s(s(s(s(s(s(z)))))), s(s(z)))),
% 0.75/0.92 inference(unit_resolution,[status(thm)],[3872, 3846])).
% 0.75/0.92 tff(3874,plain,
% 0.75/0.92 (r(s(s(s(s(s(s(z)))))), s(s(z)))),
% 0.75/0.92 inference(unit_resolution,[status(thm)],[2304, 46, 1786, 3873])).
% 0.75/0.92 tff(3875,plain,
% 0.75/0.92 (s(s(s(s(s(elem!1))))) = s(s(s(s(s(z)))))),
% 0.75/0.92 inference(monotonicity,[status(thm)],[3847])).
% 0.75/0.92 tff(3876,plain,
% 0.75/0.92 (s(s(s(s(s(s(elem!1)))))) = s(s(s(s(s(s(z))))))),
% 0.75/0.92 inference(monotonicity,[status(thm)],[3875])).
% 0.75/0.92 tff(3877,plain,
% 0.75/0.92 (s(s(s(s(s(s(z)))))) = s(s(s(s(s(s(elem!1))))))),
% 0.75/0.92 inference(symmetry,[status(thm)],[3876])).
% 0.75/0.92 tff(3878,plain,
% 0.75/0.92 ((s(s(s(s(s(s(z)))))) = s(s(s(z)))) <=> (s(s(s(s(s(s(elem!1)))))) = s(s(s(z))))),
% 0.75/0.92 inference(monotonicity,[status(thm)],[3877])).
% 0.75/0.92 tff(3879,plain,
% 0.75/0.92 ((s(s(s(s(s(s(elem!1)))))) = s(s(s(z)))) <=> (s(s(s(s(s(s(z)))))) = s(s(s(z))))),
% 0.75/0.92 inference(symmetry,[status(thm)],[3878])).
% 0.75/0.92 tff(3880,plain,
% 0.75/0.92 ((~(s(s(s(s(s(s(elem!1)))))) = s(s(s(z))))) <=> (~(s(s(s(s(s(s(z)))))) = s(s(s(z)))))),
% 0.75/0.92 inference(monotonicity,[status(thm)],[3879])).
% 0.75/0.92 tff(3881,plain,
% 0.75/0.92 (~(s(s(s(s(s(s(z)))))) = s(s(s(z))))),
% 0.75/0.92 inference(modus_ponens,[status(thm)],[1577, 3880])).
% 0.75/0.92 tff(3882,plain,
% 0.75/0.92 (~b(s(s(s(s(s(s(z)))))), s(s(s(z))))),
% 0.75/0.92 inference(unit_resolution,[status(thm)],[3167, 117, 3834, 3871])).
% 0.75/0.92 tff(3883,plain,
% 0.75/0.92 ((s(s(s(s(s(s(z)))))) = s(s(s(z)))) | r(s(s(s(s(s(s(z)))))), s(s(s(z))))),
% 0.75/0.92 inference(unit_resolution,[status(thm)],[2289, 46, 3882])).
% 0.75/0.92 tff(3884,plain,
% 0.75/0.92 (r(s(s(s(s(s(s(z)))))), s(s(s(z))))),
% 0.75/0.92 inference(unit_resolution,[status(thm)],[3883, 3881])).
% 0.75/0.92 tff(3885,plain,
% 0.75/0.92 (r(s(s(s(z))), s(s(z))) <=> r(s(s(s(z))), s(s(elem!1)))),
% 0.75/0.92 inference(monotonicity,[status(thm)],[3843])).
% 0.75/0.92 tff(3886,plain,
% 0.75/0.92 (r(s(s(s(z))), s(s(elem!1))) <=> r(s(s(s(z))), s(s(z)))),
% 0.75/0.92 inference(symmetry,[status(thm)],[3885])).
% 0.75/0.92 tff(3887,plain,
% 0.75/0.92 (r(s(s(s(z))), s(s(z)))),
% 0.75/0.92 inference(modus_ponens,[status(thm)],[3836, 3886])).
% 0.75/0.92 tff(3888,plain,
% 0.75/0.92 ($false),
% 0.75/0.92 inference(unit_resolution,[status(thm)],[3290, 14, 3887, 3884, 3874])).
% 0.75/0.92 tff(3889,plain,((~b(s(s(elem!1)), z)) | (~r(s(s(s(s(elem!1)))), z)) | (s(s(s(z))) = s(s(elem!1))) | (~b(s(s(s(elem!1))), z)) | (s(s(elem!1)) = s(s(s(elem!1))))), inference(lemma,lemma(discharge,[]))).
% 0.75/0.92 tff(3890,plain,
% 0.75/0.92 (~b(s(s(elem!1)), z)),
% 0.75/0.92 inference(unit_resolution,[status(thm)],[3889, 1417, 3822, 157, 145])).
% 0.75/0.92 tff(3891,plain,
% 0.75/0.92 (r(s(s(elem!1)), z)),
% 0.75/0.92 inference(unit_resolution,[status(thm)],[1025, 3890])).
% 0.75/0.92 tff(3892,plain,
% 0.75/0.92 (~r(s(s(s(s(elem!1)))), s(s(elem!1)))),
% 0.75/0.92 inference(unit_resolution,[status(thm)],[1402, 182, 1396])).
% 0.75/0.92 tff(3893,plain,
% 0.75/0.92 (b(s(s(s(s(elem!1)))), s(s(elem!1)))),
% 0.75/0.92 inference(unit_resolution,[status(thm)],[1690, 3892, 146])).
% 0.75/0.92 tff(3894,plain,
% 0.75/0.92 (~r(s(z), s(s(elem!1)))),
% 0.75/0.92 inference(unit_resolution,[status(thm)],[1479, 182, 195])).
% 0.75/0.92 tff(3895,plain,
% 0.75/0.92 (b(s(z), s(s(elem!1)))),
% 0.75/0.92 inference(unit_resolution,[status(thm)],[416, 3894])).
% 0.75/0.92 tff(3896,plain,
% 0.75/0.92 (((~![X0: $i, X2: $i, X1: $i] : ((~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(z), s(s(s(s(elem!1)))))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~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(z), s(s(s(s(elem!1)))))))),
% 0.75/0.92 inference(rewrite,[status(thm)],[])).
% 0.75/0.92 tff(3897,plain,
% 0.75/0.92 (((~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(z), s(s(elem!1)))) | (~b(s(s(s(s(elem!1)))), s(s(elem!1)))) | (~b(s(z), s(s(s(s(elem!1)))))))),
% 0.75/0.92 inference(rewrite,[status(thm)],[])).
% 0.75/0.92 tff(3898,plain,
% 0.75/0.92 (((~![X0: $i, X2: $i, X1: $i] : ((~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(z), s(s(s(s(elem!1)))))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~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(z), s(s(s(s(elem!1))))))))),
% 0.75/0.92 inference(monotonicity,[status(thm)],[3897])).
% 0.75/0.92 tff(3899,plain,
% 0.75/0.92 (((~![X0: $i, X2: $i, X1: $i] : ((~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(z), s(s(s(s(elem!1)))))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~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(z), s(s(s(s(elem!1)))))))),
% 0.75/0.92 inference(transitivity,[status(thm)],[3898, 3896])).
% 0.75/0.92 tff(3900,plain,
% 0.75/0.92 ((~![X0: $i, X2: $i, X1: $i] : ((~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(z), s(s(s(s(elem!1)))))))),
% 0.75/0.92 inference(quant_inst,[status(thm)],[])).
% 0.75/0.92 tff(3901,plain,
% 0.75/0.92 ((~![X0: $i, X2: $i, X1: $i] : ((~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(z), s(s(s(s(elem!1))))))),
% 0.75/0.92 inference(modus_ponens,[status(thm)],[3900, 3899])).
% 0.75/0.92 tff(3902,plain,
% 0.75/0.92 (~b(s(z), s(s(s(s(elem!1)))))),
% 0.75/0.92 inference(unit_resolution,[status(thm)],[3901, 117, 3895, 3893])).
% 0.75/0.92 tff(3903,plain,
% 0.75/0.92 (r(s(z), s(s(s(s(elem!1)))))),
% 0.75/0.92 inference(unit_resolution,[status(thm)],[1938, 3902])).
% 0.75/0.92 tff(3904,assumption,(r(s(z), s(s(s(s(elem!1)))))), introduced(assumption)).
% 0.75/0.92 tff(3905,plain,
% 0.75/0.92 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), z)) | (~r(s(z), s(s(s(s(elem!1)))))) | (~r(s(s(s(s(elem!1)))), z)))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(z), z)) | (~r(s(z), s(s(s(s(elem!1)))))) | (~r(s(s(s(s(elem!1)))), z)))),
% 0.75/0.92 inference(rewrite,[status(thm)],[])).
% 0.75/0.92 tff(3906,plain,
% 0.75/0.92 (((~r(s(s(s(s(elem!1)))), z)) | (~r(s(z), z)) | (~r(s(z), s(s(s(s(elem!1))))))) <=> ((~r(s(z), z)) | (~r(s(z), s(s(s(s(elem!1)))))) | (~r(s(s(s(s(elem!1)))), z)))),
% 0.75/0.92 inference(rewrite,[status(thm)],[])).
% 0.75/0.92 tff(3907,plain,
% 0.75/0.92 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(elem!1)))), z)) | (~r(s(z), z)) | (~r(s(z), s(s(s(s(elem!1)))))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), z)) | (~r(s(z), s(s(s(s(elem!1)))))) | (~r(s(s(s(s(elem!1)))), z))))),
% 0.75/0.92 inference(monotonicity,[status(thm)],[3906])).
% 0.75/0.92 tff(3908,plain,
% 0.75/0.92 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(elem!1)))), z)) | (~r(s(z), z)) | (~r(s(z), s(s(s(s(elem!1)))))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(z), z)) | (~r(s(z), s(s(s(s(elem!1)))))) | (~r(s(s(s(s(elem!1)))), z)))),
% 0.75/0.92 inference(transitivity,[status(thm)],[3907, 3905])).
% 0.75/0.92 tff(3909,plain,
% 0.75/0.92 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(elem!1)))), z)) | (~r(s(z), z)) | (~r(s(z), s(s(s(s(elem!1)))))))),
% 0.75/0.92 inference(quant_inst,[status(thm)],[])).
% 0.75/0.92 tff(3910,plain,
% 0.75/0.92 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(z), z)) | (~r(s(z), s(s(s(s(elem!1)))))) | (~r(s(s(s(s(elem!1)))), z))),
% 0.75/0.92 inference(modus_ponens,[status(thm)],[3909, 3908])).
% 0.75/0.92 tff(3911,plain,
% 0.75/0.92 ($false),
% 0.75/0.92 inference(unit_resolution,[status(thm)],[3910, 14, 183, 3904, 1396])).
% 0.75/0.92 tff(3912,plain,((~r(s(z), z)) | (~r(s(z), s(s(s(s(elem!1)))))) | (~r(s(s(s(s(elem!1)))), z))), inference(lemma,lemma(discharge,[]))).
% 0.75/0.92 tff(3913,plain,
% 0.75/0.92 (~r(s(z), z)),
% 0.75/0.92 inference(unit_resolution,[status(thm)],[3912, 3903, 1396])).
% 0.75/0.92 tff(3914,plain,
% 0.75/0.92 (b(s(z), z)),
% 0.75/0.92 inference(unit_resolution,[status(thm)],[193, 3913])).
% 0.75/0.92 tff(3915,plain,
% 0.75/0.92 (~b(s(z), s(s(s(elem!1))))),
% 0.75/0.92 inference(unit_resolution,[status(thm)],[246, 3914, 157])).
% 0.75/0.92 tff(3916,plain,
% 0.75/0.92 (r(s(z), s(s(s(elem!1))))),
% 0.75/0.92 inference(unit_resolution,[status(thm)],[235, 3915])).
% 0.75/0.92 tff(3917,plain,
% 0.75/0.92 (~r(s(s(s(z))), z)),
% 0.75/0.92 inference(unit_resolution,[status(thm)],[1430, 3893, 1396, 1417, 182])).
% 0.75/0.92 tff(3918,plain,
% 0.75/0.92 (b(s(s(s(z))), z)),
% 0.75/0.92 inference(unit_resolution,[status(thm)],[823, 3917])).
% 0.75/0.92 tff(3919,plain,
% 0.75/0.92 (~b(s(z), s(s(s(z))))),
% 0.75/0.92 inference(unit_resolution,[status(thm)],[366, 117, 3914, 3918])).
% 0.75/0.92 tff(3920,plain,
% 0.75/0.92 (r(s(z), s(s(s(z))))),
% 0.75/0.92 inference(unit_resolution,[status(thm)],[376, 3919])).
% 0.75/0.92 tff(3921,plain,
% 0.75/0.92 (~r(s(s(s(elem!1))), s(s(s(z))))),
% 0.75/0.92 inference(unit_resolution,[status(thm)],[3121, 3920, 3916])).
% 0.75/0.92 tff(3922,plain,
% 0.75/0.92 (~b(s(s(s(elem!1))), s(s(s(z))))),
% 0.75/0.92 inference(unit_resolution,[status(thm)],[2967, 3918, 157])).
% 0.75/0.92 tff(3923,plain,
% 0.75/0.92 ((s(s(s(elem!1))) = s(s(s(z)))) | r(s(s(s(elem!1))), s(s(s(z))))),
% 0.75/0.92 inference(unit_resolution,[status(thm)],[2341, 46, 3922])).
% 0.75/0.92 tff(3924,plain,
% 0.75/0.92 (s(s(s(elem!1))) = s(s(s(z)))),
% 0.75/0.92 inference(unit_resolution,[status(thm)],[3923, 3921])).
% 0.75/0.92 tff(3925,plain,
% 0.75/0.92 (inj_0(s(s(s(elem!1)))) = inj_0(s(s(s(z))))),
% 0.75/0.92 inference(monotonicity,[status(thm)],[3924])).
% 0.75/0.92 tff(3926,plain,
% 0.75/0.92 (inj_0(s(s(s(z)))) = inj_0(s(s(s(elem!1))))),
% 0.75/0.92 inference(symmetry,[status(thm)],[3925])).
% 0.75/0.92 tff(3927,plain,
% 0.75/0.92 (s(s(z)) = s(s(elem!1))),
% 0.75/0.92 inference(transitivity,[status(thm)],[95, 3926, 151])).
% 0.75/0.92 tff(3928,plain,
% 0.75/0.92 (r(s(s(z)), z) <=> r(s(s(elem!1)), z)),
% 0.75/0.92 inference(monotonicity,[status(thm)],[3927])).
% 0.75/0.92 tff(3929,plain,
% 0.75/0.92 (r(s(s(elem!1)), z) <=> r(s(s(z)), z)),
% 0.75/0.92 inference(symmetry,[status(thm)],[3928])).
% 0.75/0.92 tff(3930,plain,
% 0.75/0.92 (r(s(s(z)), z)),
% 0.75/0.92 inference(modus_ponens,[status(thm)],[182, 3929])).
% 0.75/0.92 tff(3931,plain,
% 0.75/0.92 (s(s(elem!1)) = s(s(z))),
% 0.75/0.92 inference(transitivity,[status(thm)],[152, 3925, 94])).
% 0.75/0.92 tff(3932,plain,
% 0.75/0.92 (inj_0(s(s(elem!1))) = inj_0(s(s(z)))),
% 0.75/0.92 inference(monotonicity,[status(thm)],[3931])).
% 0.75/0.92 tff(3933,plain,
% 0.75/0.92 (s(elem!1) = s(z)),
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% 0.75/0.92 tff(3934,plain,
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% 0.75/0.92 (b(elem!1, s(s(s(z)))) <=> b(elem!1, s(s(elem!1)))),
% 0.75/0.92 inference(monotonicity,[status(thm)],[3976])).
% 0.75/0.92 tff(4030,plain,
% 0.75/0.92 (~r(z, s(s(s(elem!1))))),
% 0.75/0.92 inference(unit_resolution,[status(thm)],[1495, 1396, 1416, 145, 182])).
% 0.75/0.92 tff(4031,plain,
% 0.75/0.92 (b(z, s(s(s(elem!1))))),
% 0.75/0.92 inference(unit_resolution,[status(thm)],[692, 4030])).
% 0.75/0.92 tff(4032,plain,
% 0.75/0.92 (~b(s(z), s(s(s(elem!1))))),
% 0.75/0.92 inference(unit_resolution,[status(thm)],[682, 4031, 237])).
% 0.75/0.92 tff(4033,plain,
% 0.75/0.92 (r(s(z), s(s(s(elem!1))))),
% 0.75/0.92 inference(unit_resolution,[status(thm)],[235, 4032])).
% 0.75/0.92 tff(4034,plain,
% 0.75/0.92 (~r(s(s(s(s(elem!1)))), s(s(s(elem!1))))),
% 0.75/0.92 inference(unit_resolution,[status(thm)],[1342, 4033, 1336])).
% 0.75/0.92 tff(4035,plain,
% 0.75/0.92 (b(s(s(s(s(elem!1)))), s(s(s(elem!1))))),
% 0.75/0.92 inference(unit_resolution,[status(thm)],[1347, 4034, 156])).
% 0.75/0.92 tff(4036,plain,
% 0.75/0.92 (~b(s(s(elem!1)), s(s(s(elem!1))))),
% 0.75/0.92 inference(unit_resolution,[status(thm)],[1488, 4035, 1416])).
% 0.75/0.92 tff(4037,plain,
% 0.75/0.92 (r(s(s(elem!1)), s(s(s(elem!1))))),
% 0.75/0.92 inference(unit_resolution,[status(thm)],[253, 4036, 145])).
% 0.75/0.92 tff(4038,plain,
% 0.75/0.92 (~r(s(z), s(s(elem!1)))),
% 0.75/0.92 inference(unit_resolution,[status(thm)],[1479, 4037, 182])).
% 0.75/0.92 tff(4039,plain,
% 0.75/0.92 (b(s(z), s(s(elem!1)))),
% 0.75/0.92 inference(unit_resolution,[status(thm)],[416, 4038])).
% 0.75/0.92 tff(4040,plain,
% 0.75/0.92 (~(s(s(s(z))) = s(s(elem!1)))),
% 0.75/0.92 inference(unit_resolution,[status(thm)],[3742, 4039, 3738])).
% 0.75/0.92 tff(4041,plain,
% 0.75/0.92 (~r(s(s(s(z))), z)),
% 0.75/0.92 inference(unit_resolution,[status(thm)],[1430, 4040, 1416, 1396, 182])).
% 0.75/0.92 tff(4042,plain,
% 0.75/0.92 (b(s(s(s(z))), z)),
% 0.75/0.92 inference(unit_resolution,[status(thm)],[823, 4041])).
% 0.75/0.92 tff(4043,plain,
% 0.75/0.92 (~r(s(s(s(elem!1))), z)),
% 0.75/0.92 inference(unit_resolution,[status(thm)],[204, 4037, 182])).
% 0.75/0.92 tff(4044,plain,
% 0.75/0.92 (b(s(s(s(elem!1))), z)),
% 0.75/0.92 inference(unit_resolution,[status(thm)],[211, 4043])).
% 0.75/0.92 tff(4045,plain,
% 0.75/0.92 (~b(s(s(s(z))), s(s(s(elem!1))))),
% 0.75/0.92 inference(unit_resolution,[status(thm)],[3023, 117, 4044, 4042])).
% 0.75/0.92 tff(4046,plain,
% 0.75/0.92 (~b(s(s(s(z))), s(z))),
% 0.75/0.92 inference(unit_resolution,[status(thm)],[1389, 4042, 237])).
% 0.75/0.92 tff(4047,plain,
% 0.75/0.92 (r(s(s(s(z))), s(z))),
% 0.75/0.92 inference(unit_resolution,[status(thm)],[347, 4046])).
% 0.75/0.92 tff(4048,plain,
% 0.75/0.92 (((~![X0: $i, X2: $i, X1: $i] : ((~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))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~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))))),
% 0.75/0.92 inference(rewrite,[status(thm)],[])).
% 0.75/0.92 tff(4049,plain,
% 0.75/0.92 ((~![X0: $i, X2: $i, X1: $i] : ((~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))))),
% 0.75/0.92 inference(quant_inst,[status(thm)],[])).
% 0.75/0.92 tff(4050,plain,
% 0.75/0.92 ((~![X0: $i, X2: $i, X1: $i] : ((~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)))),
% 0.75/0.92 inference(modus_ponens,[status(thm)],[4049, 4048])).
% 0.75/0.92 tff(4051,plain,
% 0.75/0.92 (~b(s(s(s(elem!1))), s(z))),
% 0.75/0.92 inference(unit_resolution,[status(thm)],[4050, 117, 4044, 237])).
% 0.75/0.92 tff(4052,plain,
% 0.75/0.92 (r(s(s(s(elem!1))), s(z))),
% 0.75/0.92 inference(unit_resolution,[status(thm)],[467, 4051])).
% 0.75/0.92 tff(4053,plain,
% 0.75/0.92 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~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, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~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))))))),
% 0.75/0.92 inference(rewrite,[status(thm)],[])).
% 0.75/0.92 tff(4054,plain,
% 0.75/0.92 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~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))))))),
% 0.75/0.92 inference(quant_inst,[status(thm)],[])).
% 0.75/0.92 tff(4055,plain,
% 0.75/0.92 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~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)))))),
% 0.75/0.92 inference(modus_ponens,[status(thm)],[4054, 4053])).
% 0.75/0.92 tff(4056,plain,
% 0.75/0.92 (~r(s(s(s(z))), s(s(s(elem!1))))),
% 0.75/0.92 inference(unit_resolution,[status(thm)],[4055, 14, 4052, 4047])).
% 0.75/0.92 tff(4057,plain,
% 0.75/0.92 (s(s(s(z))) = s(s(s(elem!1)))),
% 0.75/0.92 inference(unit_resolution,[status(thm)],[1717, 46, 4056, 4045])).
% 0.75/0.92 tff(4058,plain,
% 0.75/0.92 (inj_0(s(s(s(z)))) = inj_0(s(s(s(elem!1))))),
% 0.75/0.92 inference(monotonicity,[status(thm)],[4057])).
% 0.75/0.92 tff(4059,plain,
% 0.75/0.92 (s(s(z)) = s(s(elem!1))),
% 0.75/0.92 inference(transitivity,[status(thm)],[95, 4058, 151])).
% 0.75/0.92 tff(4060,plain,
% 0.75/0.92 (inj_0(s(s(z))) = inj_0(s(s(elem!1)))),
% 0.75/0.92 inference(monotonicity,[status(thm)],[4059])).
% 0.75/0.92 tff(4061,plain,
% 0.75/0.92 (s(z) = s(elem!1)),
% 0.75/0.92 inference(transitivity,[status(thm)],[131, 4060, 166])).
% 0.75/0.92 tff(4062,plain,
% 0.75/0.92 (inj_0(s(z)) = inj_0(s(elem!1))),
% 0.75/0.92 inference(monotonicity,[status(thm)],[4061])).
% 0.75/0.92 tff(4063,plain,
% 0.75/0.92 (z = elem!1),
% 0.75/0.92 inference(transitivity,[status(thm)],[1730, 4062, 257])).
% 0.75/0.92 tff(4064,plain,
% 0.75/0.92 (b(z, s(s(s(elem!1)))) <=> b(elem!1, s(s(s(elem!1))))),
% 0.75/0.92 inference(monotonicity,[status(thm)],[4063])).
% 0.75/0.92 tff(4065,plain,
% 0.75/0.92 (b(elem!1, s(s(s(elem!1)))) <=> b(z, s(s(s(elem!1))))),
% 0.75/0.92 inference(symmetry,[status(thm)],[4064])).
% 0.75/0.92 tff(4066,plain,
% 0.75/0.92 ((~b(elem!1, s(s(s(elem!1))))) <=> (~b(z, s(s(s(elem!1)))))),
% 0.75/0.92 inference(monotonicity,[status(thm)],[4065])).
% 0.75/0.92 tff(4067,plain,
% 0.75/0.92 (b(elem!1, s(s(s(z)))) <=> b(elem!1, s(s(s(elem!1))))),
% 0.75/0.92 inference(monotonicity,[status(thm)],[4057])).
% 0.75/0.92 tff(4068,plain,
% 0.75/0.92 ((~b(elem!1, s(s(s(z))))) <=> (~b(elem!1, s(s(s(elem!1)))))),
% 0.75/0.92 inference(monotonicity,[status(thm)],[4067])).
% 0.75/0.92 tff(4069,plain,
% 0.75/0.92 (~b(elem!1, s(s(s(elem!1))))),
% 0.75/0.92 inference(modus_ponens,[status(thm)],[3738, 4068])).
% 0.75/0.92 tff(4070,plain,
% 0.75/0.92 (~b(z, s(s(s(elem!1))))),
% 0.75/0.92 inference(modus_ponens,[status(thm)],[4069, 4066])).
% 0.75/0.92 tff(4071,plain,
% 0.75/0.93 ($false),
% 0.75/0.93 inference(unit_resolution,[status(thm)],[4031, 4070])).
% 0.75/0.93 tff(4072,plain,((~r(s(s(s(s(elem!1)))), z)) | b(elem!1, s(s(s(z)))) | (~b(s(z), z)) | (~b(s(s(s(s(elem!1)))), s(s(elem!1)))) | (~r(s(s(elem!1)), z)) | (s(s(elem!1)) = s(s(s(elem!1)))) | (~r(s(s(s(s(elem!1)))), s(z)))), inference(lemma,lemma(discharge,[]))).
% 0.75/0.93 tff(4073,plain,
% 0.75/0.93 (b(elem!1, s(s(s(z))))),
% 0.75/0.93 inference(unit_resolution,[status(thm)],[4072, 4013, 3822, 237, 4017, 145, 4028])).
% 0.75/0.93 tff(4074,plain,
% 0.75/0.93 (b(elem!1, s(s(elem!1)))),
% 0.75/0.93 inference(modus_ponens,[status(thm)],[4073, 4029])).
% 0.75/0.93 tff(4075,plain,
% 0.75/0.93 (((~![X0: $i, X2: $i, X1: $i] : ((~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(elem!1, s(s(s(s(elem!1)))))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~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(elem!1, s(s(s(s(elem!1)))))))),
% 0.75/0.93 inference(rewrite,[status(thm)],[])).
% 0.75/0.93 tff(4076,plain,
% 0.75/0.93 (((~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(elem!1, s(s(elem!1)))) | (~b(s(s(s(s(elem!1)))), s(s(elem!1)))) | (~b(elem!1, s(s(s(s(elem!1)))))))),
% 0.75/0.93 inference(rewrite,[status(thm)],[])).
% 0.75/0.93 tff(4077,plain,
% 0.75/0.93 (((~![X0: $i, X2: $i, X1: $i] : ((~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(elem!1, s(s(s(s(elem!1)))))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~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(elem!1, s(s(s(s(elem!1))))))))),
% 0.75/0.93 inference(monotonicity,[status(thm)],[4076])).
% 0.75/0.93 tff(4078,plain,
% 0.75/0.93 (((~![X0: $i, X2: $i, X1: $i] : ((~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(elem!1, s(s(s(s(elem!1)))))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~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(elem!1, s(s(s(s(elem!1)))))))),
% 0.75/0.93 inference(transitivity,[status(thm)],[4077, 4075])).
% 0.75/0.93 tff(4079,plain,
% 0.75/0.93 ((~![X0: $i, X2: $i, X1: $i] : ((~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(elem!1, s(s(s(s(elem!1)))))))),
% 0.75/0.93 inference(quant_inst,[status(thm)],[])).
% 0.75/0.93 tff(4080,plain,
% 0.75/0.93 ((~![X0: $i, X2: $i, X1: $i] : ((~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(elem!1, s(s(s(s(elem!1))))))),
% 0.75/0.93 inference(modus_ponens,[status(thm)],[4079, 4078])).
% 0.75/0.93 tff(4081,plain,
% 0.75/0.93 (~b(elem!1, s(s(s(s(elem!1)))))),
% 0.75/0.93 inference(unit_resolution,[status(thm)],[4080, 117, 4074, 4028])).
% 0.75/0.93 tff(4082,plain,
% 0.75/0.93 (r(elem!1, s(s(s(s(elem!1)))))),
% 0.75/0.93 inference(unit_resolution,[status(thm)],[2907, 4081, 4026])).
% 0.75/0.93 tff(4083,plain,
% 0.75/0.93 (~r(z, elem!1)),
% 0.75/0.93 inference(unit_resolution,[status(thm)],[3483, 14, 4082, 4024])).
% 0.75/0.93 tff(4084,plain,
% 0.75/0.93 (~r(z, s(z))),
% 0.75/0.93 inference(modus_ponens,[status(thm)],[4083, 4004])).
% 0.75/0.93 tff(4085,plain,
% 0.75/0.93 (b(z, s(z))),
% 0.75/0.93 inference(unit_resolution,[status(thm)],[599, 4084])).
% 0.75/0.93 tff(4086,plain,
% 0.75/0.93 (b(z, elem!1)),
% 0.75/0.93 inference(modus_ponens,[status(thm)],[4085, 4001])).
% 0.75/0.93 tff(4087,plain,
% 0.75/0.93 ((s(z) = s(s(s(elem!1)))) <=> (elem!1 = s(s(s(elem!1))))),
% 0.75/0.93 inference(monotonicity,[status(thm)],[3983])).
% 0.75/0.93 tff(4088,plain,
% 0.75/0.93 ((s(z) = s(s(s(elem!1)))) <=> (s(s(s(elem!1))) = elem!1)),
% 0.75/0.93 inference(transitivity,[status(thm)],[4087, 1512])).
% 0.75/0.93 tff(4089,plain,
% 0.75/0.93 ((~(s(z) = s(s(s(elem!1))))) <=> (~(s(s(s(elem!1))) = elem!1))),
% 0.75/0.93 inference(monotonicity,[status(thm)],[4088])).
% 0.75/0.93 tff(4090,plain,
% 0.75/0.93 (~(s(s(s(elem!1))) = elem!1)),
% 0.75/0.93 inference(modus_ponens,[status(thm)],[230, 4089])).
% 0.75/0.93 tff(4091,plain,
% 0.75/0.93 (b(s(z), z) <=> b(elem!1, z)),
% 0.75/0.93 inference(monotonicity,[status(thm)],[3983])).
% 0.75/0.93 tff(4092,plain,
% 0.75/0.93 (b(elem!1, z)),
% 0.75/0.93 inference(modus_ponens,[status(thm)],[237, 4091])).
% 0.75/0.93 tff(4093,plain,
% 0.75/0.93 (~b(s(s(s(elem!1))), elem!1)),
% 0.75/0.93 inference(unit_resolution,[status(thm)],[1533, 117, 157, 4092])).
% 0.75/0.93 tff(4094,plain,
% 0.75/0.93 (r(s(s(s(elem!1))), elem!1)),
% 0.75/0.93 inference(unit_resolution,[status(thm)],[1235, 4093, 4090])).
% 0.75/0.93 tff(4095,plain,
% 0.75/0.93 (r(s(s(s(s(elem!1)))), s(z)) <=> r(s(s(s(s(elem!1)))), elem!1)),
% 0.75/0.93 inference(monotonicity,[status(thm)],[3983])).
% 0.75/0.93 tff(4096,plain,
% 0.75/0.93 (r(s(s(s(s(elem!1)))), elem!1)),
% 0.75/0.93 inference(modus_ponens,[status(thm)],[4013, 4095])).
% 0.75/0.93 tff(4097,plain,
% 0.75/0.93 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), elem!1)) | (~r(s(s(s(elem!1))), s(s(s(s(elem!1)))))) | (~r(s(s(s(s(elem!1)))), elem!1)))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(elem!1))), elem!1)) | (~r(s(s(s(elem!1))), s(s(s(s(elem!1)))))) | (~r(s(s(s(s(elem!1)))), elem!1)))),
% 0.75/0.93 inference(rewrite,[status(thm)],[])).
% 0.75/0.93 tff(4098,plain,
% 0.75/0.93 (((~r(s(s(s(s(elem!1)))), elem!1)) | (~r(s(s(s(elem!1))), elem!1)) | (~r(s(s(s(elem!1))), s(s(s(s(elem!1))))))) <=> ((~r(s(s(s(elem!1))), elem!1)) | (~r(s(s(s(elem!1))), s(s(s(s(elem!1)))))) | (~r(s(s(s(s(elem!1)))), elem!1)))),
% 0.75/0.93 inference(rewrite,[status(thm)],[])).
% 0.75/0.93 tff(4099,plain,
% 0.75/0.93 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(elem!1)))), elem!1)) | (~r(s(s(s(elem!1))), elem!1)) | (~r(s(s(s(elem!1))), s(s(s(s(elem!1)))))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), elem!1)) | (~r(s(s(s(elem!1))), s(s(s(s(elem!1)))))) | (~r(s(s(s(s(elem!1)))), elem!1))))),
% 0.75/0.93 inference(monotonicity,[status(thm)],[4098])).
% 0.75/0.93 tff(4100,plain,
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% 0.75/0.93 inference(transitivity,[status(thm)],[4099, 4097])).
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% 0.75/0.93 inference(quant_inst,[status(thm)],[])).
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% 0.75/0.93 inference(modus_ponens,[status(thm)],[4101, 4100])).
% 0.75/0.93 tff(4103,plain,
% 0.75/0.93 (~r(s(s(s(elem!1))), s(s(s(s(elem!1)))))),
% 0.75/0.93 inference(unit_resolution,[status(thm)],[4102, 14, 4094, 4096])).
% 0.75/0.93 tff(4104,plain,
% 0.75/0.93 (b(s(s(s(elem!1))), s(s(s(s(elem!1)))))),
% 0.75/0.93 inference(unit_resolution,[status(thm)],[448, 4103, 290])).
% 0.75/0.93 tff(4105,assumption,(r(s(s(s(s(elem!1)))), elem!1)), introduced(assumption)).
% 0.75/0.93 tff(4106,plain,
% 0.75/0.93 (~r(s(s(s(s(s(s(elem!1)))))), s(s(s(s(elem!1)))))),
% 0.75/0.93 inference(unit_resolution,[status(thm)],[1822, 14, 4105, 1555])).
% 0.75/0.93 tff(4107,plain,
% 0.75/0.93 (b(s(s(s(s(s(s(elem!1)))))), s(s(s(s(elem!1)))))),
% 0.75/0.93 inference(unit_resolution,[status(thm)],[1619, 46, 1919, 4106])).
% 0.75/0.93 tff(4108,assumption,(b(s(s(s(elem!1))), s(s(s(s(elem!1)))))), introduced(assumption)).
% 0.75/0.93 tff(4109,plain,
% 0.75/0.93 (~b(s(s(s(s(s(s(elem!1)))))), s(s(s(elem!1))))),
% 0.75/0.93 inference(unit_resolution,[status(thm)],[1830, 117, 4108, 4107])).
% 0.75/0.93 tff(4110,plain,
% 0.75/0.93 ($false),
% 0.75/0.93 inference(unit_resolution,[status(thm)],[1564, 4109, 1554])).
% 0.75/0.93 tff(4111,plain,((~r(s(s(s(s(s(s(elem!1)))))), elem!1)) | (~b(s(s(s(elem!1))), s(s(s(s(elem!1)))))) | (~(s(s(s(z))) = s(s(elem!1)))) | (s(s(s(s(s(s(elem!1)))))) = s(s(s(s(elem!1))))) | (~r(s(s(s(s(elem!1)))), elem!1)) | (~r(s(s(s(elem!1))), elem!1))), inference(lemma,lemma(discharge,[]))).
% 0.75/0.93 tff(4112,plain,
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% 0.75/0.93 inference(unit_resolution,[status(thm)],[4111, 4104, 3976, 2024, 4096, 4094])).
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% 0.75/0.93 inference(unit_resolution,[status(thm)],[1599, 4112, 3979])).
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% 0.75/0.93 inference(unit_resolution,[status(thm)],[1659, 117, 4113, 4086])).
% 0.75/0.93 tff(4115,plain,
% 0.75/0.93 (r(s(s(s(s(s(s(elem!1)))))), z)),
% 0.75/0.93 inference(unit_resolution,[status(thm)],[1666, 46, 1663, 4114])).
% 0.75/0.93 tff(4116,plain,
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% 0.75/0.93 inference(rewrite,[status(thm)],[])).
% 0.75/0.93 tff(4117,plain,
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% 0.75/0.93 inference(quant_inst,[status(thm)],[])).
% 0.75/0.93 tff(4118,plain,
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% 0.75/0.93 inference(modus_ponens,[status(thm)],[4117, 4116])).
% 0.75/0.93 tff(4119,plain,
% 0.75/0.93 (~r(s(s(s(s(s(s(elem!1)))))), s(s(elem!1)))),
% 0.75/0.93 inference(unit_resolution,[status(thm)],[4118, 14, 4017, 4115])).
% 0.75/0.93 tff(4120,plain,
% 0.75/0.93 (~b(s(s(s(s(s(s(elem!1)))))), s(s(elem!1)))),
% 0.75/0.93 inference(unit_resolution,[status(thm)],[1792, 117, 3985, 4113])).
% 0.75/0.93 tff(4121,plain,
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% 0.75/0.93 inference(unit_resolution,[status(thm)],[1586, 46, 4120])).
% 0.75/0.93 tff(4122,plain,
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% 0.75/0.93 inference(unit_resolution,[status(thm)],[4121, 4119, 3997])).
% 0.75/0.93 tff(4123,plain,((~b(s(z), z)) | (~b(s(s(s(elem!1))), z)) | (s(s(elem!1)) = s(s(s(elem!1)))) | (s(s(s(s(elem!1)))) = s(s(elem!1)))), inference(lemma,lemma(discharge,[]))).
% 0.75/0.93 tff(4124,plain,
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% 0.75/0.93 inference(unit_resolution,[status(thm)],[4123, 157, 145, 146])).
% 0.75/0.93 tff(4125,plain,
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% 0.75/0.93 inference(unit_resolution,[status(thm)],[193, 4124])).
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% 0.75/0.93 inference(modus_ponens,[status(thm)],[4125, 3992])).
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% 0.75/0.93 inference(rewrite,[status(thm)],[])).
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% 0.75/0.93 inference(quant_inst,[status(thm)],[])).
% 0.75/0.93 tff(4129,plain,
% 0.75/0.93 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(elem!1, z)) | (~r(s(s(s(s(elem!1)))), z)) | (~r(s(s(s(s(elem!1)))), elem!1))),
% 0.75/0.93 inference(modus_ponens,[status(thm)],[4128, 4127])).
% 0.75/0.93 tff(4130,plain,
% 0.75/0.93 (~r(s(s(s(s(elem!1)))), elem!1)),
% 0.75/0.93 inference(unit_resolution,[status(thm)],[4129, 14, 4126, 3822])).
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% 0.75/0.93 inference(rewrite,[status(thm)],[])).
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% 0.75/0.93 ((~![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))),
% 0.75/0.93 inference(quant_inst,[status(thm)],[])).
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% 0.75/0.93 ((~![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)),
% 0.75/0.93 inference(modus_ponens,[status(thm)],[4132, 4131])).
% 0.75/0.93 tff(4134,plain,
% 0.75/0.93 ((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)),
% 0.75/0.93 inference(unit_resolution,[status(thm)],[4133, 46])).
% 0.75/0.93 tff(4135,plain,
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% 0.75/0.93 inference(rewrite,[status(thm)],[])).
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% 0.75/0.93 inference(rewrite,[status(thm)],[])).
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% 0.75/0.93 inference(monotonicity,[status(thm)],[4137])).
% 0.75/0.93 tff(4139,plain,
% 0.75/0.93 (((~![X0: $i, X2: $i, X1: $i] : ((~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~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, X2: $i, X1: $i] : ((~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(elem!1)), s(s(s(s(elem!1)))))))),
% 0.75/0.93 inference(transitivity,[status(thm)],[4138, 4136])).
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% 0.75/0.93 inference(modus_ponens,[status(thm)],[4140, 4139])).
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% 0.75/0.93 tff(4143,plain,
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% 0.75/0.93 tff(4144,plain,
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% 0.75/0.93 tff(4145,plain,
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% 0.75/0.93 inference(unit_resolution,[status(thm)],[1599, 4144, 3979])).
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% 0.75/0.93 ((~![X0: $i, X2: $i, X1: $i] : ((~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(s(elem!1)))), s(s(elem!1)))))),
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% 0.75/0.93 inference(rewrite,[status(thm)],[])).
% 0.75/0.93 tff(4158,plain,
% 0.75/0.93 (((~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(s(s(elem!1)))), s(s(elem!1)))) | (~r(s(s(s(elem!1))), s(s(s(s(elem!1)))))))),
% 0.75/0.93 inference(rewrite,[status(thm)],[])).
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% 0.75/0.94 tff(4231,plain,
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% 0.75/0.94 inference(monotonicity,[status(thm)],[4231])).
% 0.75/0.94 tff(4233,plain,
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% 0.75/0.94 inference(transitivity,[status(thm)],[1730, 4232, 257])).
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% 0.75/0.94 (b(s(s(s(s(elem!1)))), z) <=> b(s(s(s(s(elem!1)))), elem!1)),
% 0.75/0.94 inference(monotonicity,[status(thm)],[4233])).
% 0.75/0.94 tff(4235,plain,
% 0.75/0.94 (b(s(s(s(s(elem!1)))), elem!1)),
% 0.75/0.94 inference(modus_ponens,[status(thm)],[1310, 4234])).
% 0.75/0.94 tff(4236,plain,
% 0.75/0.94 (r(s(s(s(s(elem!1)))), s(z))),
% 0.75/0.94 inference(unit_resolution,[status(thm)],[1327, 2484])).
% 0.75/0.94 tff(4237,plain,
% 0.75/0.94 (~r(s(s(elem!1)), s(s(s(elem!1))))),
% 0.75/0.94 inference(unit_resolution,[status(thm)],[204, 4213, 4183])).
% 0.75/0.94 tff(4238,plain,
% 0.75/0.94 (b(s(s(elem!1)), s(s(s(elem!1))))),
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% 0.75/0.94 tff(4239,plain,
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% 0.75/0.94 (r(s(z), s(s(s(elem!1))))),
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% 0.75/0.94 (~r(s(s(s(s(elem!1)))), s(s(s(elem!1))))),
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% 0.75/0.94 tff(4242,plain,
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% 0.75/0.94 tff(4243,plain,
% 0.75/0.94 (b(elem!1, s(s(s(z)))) <=> b(elem!1, s(s(s(elem!1))))),
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% 0.75/0.94 tff(4245,plain,
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% 0.75/0.94 tff(4246,plain,
% 0.75/0.94 (~r(s(s(elem!1)), s(z))),
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% 0.75/0.94 inference(unit_resolution,[status(thm)],[2544, 1036, 4247])).
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% 0.75/0.94 tff(4251,plain,
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% 0.75/0.94 inference(unit_resolution,[status(thm)],[1644, 46, 4250])).
% 0.75/0.94 tff(4252,plain,
% 0.75/0.94 (b(z, s(s(s(s(elem!1)))))),
% 0.75/0.94 inference(unit_resolution,[status(thm)],[4251, 1626])).
% 0.75/0.94 tff(4253,assumption,(s(s(elem!1)) = s(s(s(elem!1)))), introduced(assumption)).
% 0.75/0.94 tff(4254,plain,
% 0.75/0.94 ((s(s(s(s(elem!1)))) = s(s(elem!1))) <=> (s(s(s(s(elem!1)))) = s(s(s(elem!1))))),
% 0.75/0.94 inference(monotonicity,[status(thm)],[4253])).
% 0.75/0.94 tff(4255,plain,
% 0.75/0.94 ((s(s(s(s(elem!1)))) = s(s(s(elem!1)))) <=> (s(s(s(s(elem!1)))) = s(s(elem!1)))),
% 0.75/0.94 inference(symmetry,[status(thm)],[4254])).
% 0.75/0.94 tff(4256,plain,
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% 0.75/0.94 (s(s(s(s(elem!1)))) = s(s(s(elem!1)))),
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% 0.75/0.94 tff(4259,plain,((~(s(s(elem!1)) = s(s(s(elem!1))))) | (s(s(s(s(elem!1)))) = s(s(s(elem!1))))), inference(lemma,lemma(discharge,[]))).
% 0.75/0.94 tff(4260,plain,
% 0.75/0.94 (s(s(s(s(elem!1)))) = s(s(s(elem!1)))),
% 0.75/0.94 inference(unit_resolution,[status(thm)],[4259, 4253])).
% 0.75/0.94 tff(4261,plain,
% 0.75/0.94 (s(s(s(s(elem!1)))) = s(s(elem!1))),
% 0.75/0.94 inference(modus_ponens,[status(thm)],[4260, 4255])).
% 0.75/0.94 tff(4262,plain,
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% 0.75/0.94 inference(unit_resolution,[status(thm)],[146, 4261])).
% 0.75/0.94 tff(4263,plain,((~(s(s(elem!1)) = s(s(s(elem!1))))) | (s(s(s(s(elem!1)))) = s(s(elem!1)))), inference(lemma,lemma(discharge,[]))).
% 0.75/0.94 tff(4264,plain,
% 0.75/0.94 (~(s(s(elem!1)) = s(s(s(elem!1))))),
% 0.75/0.94 inference(unit_resolution,[status(thm)],[4263, 146])).
% 0.75/0.94 tff(4265,plain,
% 0.75/0.94 (~(s(s(s(s(elem!1)))) = s(s(s(elem!1))))),
% 0.75/0.94 inference(unit_resolution,[status(thm)],[155, 4264])).
% 0.75/0.94 tff(4266,plain,
% 0.75/0.94 (~r(s(s(elem!1)), z)),
% 0.75/0.94 inference(unit_resolution,[status(thm)],[1402, 1396, 1397])).
% 0.75/0.94 tff(4267,plain,
% 0.75/0.94 (b(s(s(elem!1)), z)),
% 0.75/0.94 inference(unit_resolution,[status(thm)],[1025, 4266])).
% 0.75/0.94 tff(4268,plain,
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% 0.75/0.94 inference(unit_resolution,[status(thm)],[2544, 4267, 4247])).
% 0.75/0.94 tff(4269,plain,
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% 0.75/0.94 inference(unit_resolution,[status(thm)],[599, 4268])).
% 0.75/0.94 tff(4270,plain,
% 0.75/0.94 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(z))) | (~r(s(s(s(s(elem!1)))), z)) | (~r(s(s(s(s(elem!1)))), s(z))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, s(z))) | (~r(s(s(s(s(elem!1)))), z)) | (~r(s(s(s(s(elem!1)))), s(z))))),
% 0.75/0.94 inference(rewrite,[status(thm)],[])).
% 0.75/0.94 tff(4271,plain,
% 0.75/0.94 (((~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(s(s(s(elem!1)))), z)) | (~r(s(s(s(s(elem!1)))), s(z))))),
% 0.75/0.94 inference(rewrite,[status(thm)],[])).
% 0.75/0.94 tff(4272,plain,
% 0.75/0.94 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(z))) | (~r(s(s(s(s(elem!1)))), s(z))) | (~r(s(s(s(s(elem!1)))), z)))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(z))) | (~r(s(s(s(s(elem!1)))), z)) | (~r(s(s(s(s(elem!1)))), s(z)))))),
% 0.75/0.94 inference(monotonicity,[status(thm)],[4271])).
% 0.75/0.94 tff(4273,plain,
% 0.75/0.94 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(z))) | (~r(s(s(s(s(elem!1)))), s(z))) | (~r(s(s(s(s(elem!1)))), z)))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, s(z))) | (~r(s(s(s(s(elem!1)))), z)) | (~r(s(s(s(s(elem!1)))), s(z))))),
% 0.75/0.94 inference(transitivity,[status(thm)],[4272, 4270])).
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% 0.75/0.94 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(z))) | (~r(s(s(s(s(elem!1)))), s(z))) | (~r(s(s(s(s(elem!1)))), z)))),
% 0.75/0.94 inference(quant_inst,[status(thm)],[])).
% 0.75/0.94 tff(4275,plain,
% 0.75/0.94 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, s(z))) | (~r(s(s(s(s(elem!1)))), z)) | (~r(s(s(s(s(elem!1)))), s(z)))),
% 0.75/0.94 inference(modus_ponens,[status(thm)],[4274, 4273])).
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% 0.75/0.94 tff(4277,plain,((~r(s(s(s(s(elem!1)))), z)) | (~r(s(s(s(s(elem!1)))), s(z))) | (~r(s(s(s(s(elem!1)))), s(s(elem!1))))), inference(lemma,lemma(discharge,[]))).
% 0.75/0.94 tff(4278,plain,
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% 0.75/0.94 (((~![X0: $i, X2: $i, X1: $i] : ((~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), z)) | (~b(s(s(s(s(elem!1)))), z)) | (~b(s(s(elem!1)), s(s(s(s(elem!1)))))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(elem!1)), z)) | (~b(s(s(s(s(elem!1)))), z)) | (~b(s(s(elem!1)), s(s(s(s(elem!1)))))))),
% 0.75/0.94 inference(rewrite,[status(thm)],[])).
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% 0.75/0.94 (((~b(s(s(s(s(elem!1)))), z)) | (~b(s(s(elem!1)), z)) | (~b(s(s(elem!1)), s(s(s(s(elem!1))))))) <=> ((~b(s(s(elem!1)), z)) | (~b(s(s(s(s(elem!1)))), z)) | (~b(s(s(elem!1)), s(s(s(s(elem!1)))))))),
% 0.75/0.94 inference(rewrite,[status(thm)],[])).
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% 0.75/0.94 (((~![X0: $i, X2: $i, X1: $i] : ((~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(elem!1)))), z)) | (~b(s(s(elem!1)), z)) | (~b(s(s(elem!1)), s(s(s(s(elem!1)))))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), z)) | (~b(s(s(s(s(elem!1)))), z)) | (~b(s(s(elem!1)), s(s(s(s(elem!1))))))))),
% 0.75/0.94 inference(monotonicity,[status(thm)],[4281])).
% 0.75/0.94 tff(4283,plain,
% 0.75/0.94 (((~![X0: $i, X2: $i, X1: $i] : ((~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(elem!1)))), z)) | (~b(s(s(elem!1)), z)) | (~b(s(s(elem!1)), s(s(s(s(elem!1)))))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(elem!1)), z)) | (~b(s(s(s(s(elem!1)))), z)) | (~b(s(s(elem!1)), s(s(s(s(elem!1)))))))),
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% 0.75/0.94 inference(modus_ponens,[status(thm)],[4284, 4283])).
% 0.75/0.94 tff(4286,plain,
% 0.75/0.94 (~b(s(s(elem!1)), s(s(s(s(elem!1)))))),
% 0.75/0.94 inference(unit_resolution,[status(thm)],[4285, 117, 1036, 4279])).
% 0.75/0.94 tff(4287,plain,
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% 0.75/0.94 tff(4288,plain,
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% 0.75/0.94 tff(4289,plain,
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% 0.75/0.94 inference(unit_resolution,[status(thm)],[193, 4288])).
% 0.75/0.94 tff(4290,plain,
% 0.75/0.94 (~r(s(s(s(s(elem!1)))), s(s(s(elem!1))))),
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% 0.75/0.94 tff(4291,plain,
% 0.75/0.94 (b(s(s(s(s(elem!1)))), s(s(s(elem!1))))),
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% 0.75/0.94 tff(4292,plain,
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% 0.75/0.94 inference(rewrite,[status(thm)],[])).
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% 0.75/0.94 (((~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)))))))),
% 0.75/0.94 inference(rewrite,[status(thm)],[])).
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% 0.75/0.94 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(elem!1)), s(s(s(s(elem!1)))))) | (~r(s(z), s(s(s(s(elem!1)))))) | (~r(s(z), s(s(elem!1)))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(s(elem!1)))) | (~r(s(z), s(s(s(s(elem!1)))))) | (~r(s(s(elem!1)), s(s(s(s(elem!1))))))))),
% 0.75/0.94 inference(monotonicity,[status(thm)],[4297])).
% 0.75/0.94 tff(4299,plain,
% 0.75/0.94 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(elem!1)), s(s(s(s(elem!1)))))) | (~r(s(z), s(s(s(s(elem!1)))))) | (~r(s(z), s(s(elem!1)))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(z), s(s(elem!1)))) | (~r(s(z), s(s(s(s(elem!1)))))) | (~r(s(s(elem!1)), s(s(s(s(elem!1)))))))),
% 0.75/0.94 inference(transitivity,[status(thm)],[4298, 4296])).
% 0.75/0.94 tff(4300,plain,
% 0.75/0.94 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(elem!1)), s(s(s(s(elem!1)))))) | (~r(s(z), s(s(s(s(elem!1)))))) | (~r(s(z), s(s(elem!1)))))),
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% 0.75/0.95 inference(rewrite,[status(thm)],[])).
% 0.75/0.95 tff(4375,plain,
% 0.75/0.95 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(elem!1)))), s(z))) | (~r(s(s(s(elem!1))), s(z))) | (~r(s(s(s(elem!1))), s(s(s(s(elem!1)))))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), s(z))) | (~r(s(s(s(s(elem!1)))), s(z))) | (~r(s(s(s(elem!1))), s(s(s(s(elem!1))))))))),
% 0.75/0.95 inference(monotonicity,[status(thm)],[4374])).
% 0.75/0.95 tff(4376,plain,
% 0.75/0.95 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(elem!1)))), s(z))) | (~r(s(s(s(elem!1))), s(z))) | (~r(s(s(s(elem!1))), s(s(s(s(elem!1)))))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(elem!1))), s(z))) | (~r(s(s(s(s(elem!1)))), s(z))) | (~r(s(s(s(elem!1))), s(s(s(s(elem!1)))))))),
% 0.75/0.95 inference(transitivity,[status(thm)],[4375, 4373])).
% 0.75/0.95 tff(4377,plain,
% 0.75/0.95 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(elem!1)))), s(z))) | (~r(s(s(s(elem!1))), s(z))) | (~r(s(s(s(elem!1))), s(s(s(s(elem!1)))))))),
% 0.75/0.95 inference(quant_inst,[status(thm)],[])).
% 0.75/0.95 tff(4378,plain,
% 0.75/0.95 ((~![X0: $i, X2: $i, X1: $i] : ((~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(z))) | (~r(s(s(s(elem!1))), s(s(s(s(elem!1))))))),
% 0.75/0.95 inference(modus_ponens,[status(thm)],[4377, 4376])).
% 0.75/0.95 tff(4379,plain,
% 0.75/0.95 (~r(s(s(s(elem!1))), s(s(s(s(elem!1)))))),
% 0.75/0.95 inference(unit_resolution,[status(thm)],[4378, 14, 1336, 4372])).
% 0.75/0.95 tff(4380,plain,
% 0.75/0.95 (b(s(s(s(elem!1))), s(s(s(s(elem!1)))))),
% 0.75/0.95 inference(unit_resolution,[status(thm)],[448, 4379, 323])).
% 0.75/0.95 tff(4381,plain,
% 0.75/0.95 (((~![X0: $i, X2: $i, X1: $i] : ((~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), s(s(s(s(elem!1)))))) | (~b(s(s(s(elem!1))), s(s(s(s(elem!1)))))) | (~b(s(s(s(elem!1))), s(s(s(z))))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(z))), s(s(s(s(elem!1)))))) | (~b(s(s(s(elem!1))), s(s(s(s(elem!1)))))) | (~b(s(s(s(elem!1))), s(s(s(z))))))),
% 0.75/0.95 inference(rewrite,[status(thm)],[])).
% 0.75/0.95 tff(4382,plain,
% 0.75/0.95 ((~![X0: $i, X2: $i, X1: $i] : ((~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), s(s(s(s(elem!1)))))) | (~b(s(s(s(elem!1))), s(s(s(s(elem!1)))))) | (~b(s(s(s(elem!1))), s(s(s(z))))))),
% 0.75/0.95 inference(quant_inst,[status(thm)],[])).
% 0.75/0.95 tff(4383,plain,
% 0.75/0.95 ((~![X0: $i, X2: $i, X1: $i] : ((~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(z))), s(s(s(s(elem!1)))))) | (~b(s(s(s(elem!1))), s(s(s(s(elem!1)))))) | (~b(s(s(s(elem!1))), s(s(s(z)))))),
% 0.75/0.95 inference(modus_ponens,[status(thm)],[4382, 4381])).
% 0.75/0.95 tff(4384,plain,
% 0.75/0.95 (~b(s(s(s(elem!1))), s(s(s(z))))),
% 0.75/0.95 inference(unit_resolution,[status(thm)],[4383, 117, 4380, 2177])).
% 0.75/0.95 tff(4385,assumption,(~r(s(s(s(elem!1))), s(s(s(z))))), introduced(assumption)).
% 0.75/0.95 tff(4386,plain,
% 0.75/0.95 ((s(s(s(elem!1))) = s(s(s(z)))) | b(s(s(s(elem!1))), s(s(s(z))))),
% 0.75/0.95 inference(unit_resolution,[status(thm)],[2341, 46, 4385])).
% 0.75/0.95 tff(4387,plain,
% 0.75/0.95 (s(s(s(elem!1))) = s(s(s(z)))),
% 0.75/0.95 inference(unit_resolution,[status(thm)],[4386, 4384])).
% 0.75/0.95 tff(4388,plain,
% 0.75/0.95 (b(s(s(s(elem!1))), z) <=> b(s(s(s(z))), z)),
% 0.75/0.95 inference(monotonicity,[status(thm)],[4387])).
% 0.75/0.95 tff(4389,plain,
% 0.75/0.95 (b(s(s(s(z))), z) <=> b(s(s(s(elem!1))), z)),
% 0.75/0.95 inference(symmetry,[status(thm)],[4388])).
% 0.75/0.95 tff(4390,plain,
% 0.75/0.95 (b(s(s(s(elem!1))), z)),
% 0.75/0.95 inference(modus_ponens,[status(thm)],[338, 4389])).
% 0.75/0.95 tff(4391,plain,
% 0.75/0.95 ($false),
% 0.75/0.95 inference(unit_resolution,[status(thm)],[1188, 4390])).
% 0.75/0.95 tff(4392,plain,(b(s(s(s(elem!1))), z) | (~b(s(s(s(z))), z)) | r(s(s(s(elem!1))), s(s(s(z)))) | (~b(s(s(s(z))), s(s(s(s(elem!1)))))) | (s(s(s(elem!1))) = s(s(s(s(elem!1))))) | (~r(s(s(s(s(elem!1)))), s(z))) | (~b(s(z), s(s(elem!1)))) | (s(s(s(elem!1))) = s(s(elem!1))) | (~r(s(s(elem!1)), z))), inference(lemma,lemma(discharge,[]))).
% 0.75/0.95 tff(4393,plain,
% 0.75/0.95 (b(s(s(s(elem!1))), z)),
% 0.75/0.95 inference(unit_resolution,[status(thm)],[4392, 4362, 338, 4361, 4359, 1336, 4358, 4356, 4355])).
% 0.75/0.95 tff(4394,plain,
% 0.75/0.95 (~b(s(s(s(elem!1))), s(s(s(z))))),
% 0.75/0.95 inference(unit_resolution,[status(thm)],[2967, 4393, 338])).
% 0.75/0.95 tff(4395,plain,
% 0.75/0.95 (s(s(s(elem!1))) = s(s(s(z)))),
% 0.75/0.95 inference(unit_resolution,[status(thm)],[2341, 46, 4362, 4394])).
% 0.75/0.95 tff(4396,plain,
% 0.75/0.95 (inj_0(s(s(s(elem!1)))) = inj_0(s(s(s(z))))),
% 0.75/0.95 inference(monotonicity,[status(thm)],[4395])).
% 0.75/0.95 tff(4397,plain,
% 0.75/0.95 (s(s(elem!1)) = s(s(z))),
% 0.75/0.95 inference(transitivity,[status(thm)],[152, 4396, 94])).
% 0.75/0.95 tff(4398,plain,
% 0.75/0.95 (inj_0(s(s(elem!1))) = inj_0(s(s(z)))),
% 0.75/0.95 inference(monotonicity,[status(thm)],[4397])).
% 0.75/0.95 tff(4399,plain,
% 0.75/0.95 (s(elem!1) = s(z)),
% 0.75/0.95 inference(transitivity,[status(thm)],[167, 4398, 82])).
% 0.75/0.95 tff(4400,plain,
% 0.75/0.95 (inj_0(s(elem!1)) = inj_0(s(z))),
% 0.75/0.95 inference(monotonicity,[status(thm)],[4399])).
% 0.75/0.95 tff(4401,plain,
% 0.75/0.95 (elem!1 = z),
% 0.75/0.95 inference(transitivity,[status(thm)],[1652, 4400, 90])).
% 0.75/0.95 tff(4402,plain,
% 0.75/0.95 (b(elem!1, s(s(s(z)))) <=> b(z, s(s(s(z))))),
% 0.75/0.95 inference(monotonicity,[status(thm)],[4401])).
% 0.75/0.95 tff(4403,plain,
% 0.75/0.95 (b(z, s(s(s(z)))) <=> b(elem!1, s(s(s(z))))),
% 0.75/0.95 inference(symmetry,[status(thm)],[4402])).
% 0.75/0.95 tff(4404,plain,
% 0.75/0.95 (b(z, s(s(s(elem!1)))) <=> b(z, s(s(s(z))))),
% 0.75/0.95 inference(monotonicity,[status(thm)],[4395])).
% 0.75/0.95 tff(4405,plain,
% 0.75/0.95 (~r(s(s(s(s(elem!1)))), s(s(s(elem!1))))),
% 0.75/0.95 inference(unit_resolution,[status(thm)],[3665, 913, 974])).
% 0.75/0.95 tff(4406,plain,
% 0.75/0.95 (b(s(s(s(s(elem!1)))), s(s(s(elem!1))))),
% 0.75/0.95 inference(unit_resolution,[status(thm)],[1347, 4405, 287])).
% 0.75/0.95 tff(4407,plain,
% 0.75/0.95 (~b(s(s(s(s(elem!1)))), s(s(elem!1)))),
% 0.75/0.95 inference(unit_resolution,[status(thm)],[1486, 117, 324, 4406])).
% 0.75/0.95 tff(4408,plain,
% 0.75/0.95 (r(s(s(s(s(elem!1)))), s(s(elem!1)))),
% 0.75/0.95 inference(unit_resolution,[status(thm)],[1690, 4407, 146])).
% 0.75/0.95 tff(4409,plain,
% 0.75/0.95 (~b(s(s(elem!1)), z)),
% 0.75/0.95 inference(unit_resolution,[status(thm)],[1046, 157, 324])).
% 0.75/0.95 tff(4410,plain,
% 0.75/0.95 (r(s(s(elem!1)), z)),
% 0.75/0.95 inference(unit_resolution,[status(thm)],[1025, 4409])).
% 0.75/0.95 tff(4411,plain,
% 0.75/0.95 (~r(s(s(s(s(elem!1)))), z)),
% 0.75/0.95 inference(unit_resolution,[status(thm)],[1402, 4410, 4408])).
% 0.75/0.95 tff(4412,plain,
% 0.75/0.95 (b(s(s(s(s(elem!1)))), z)),
% 0.75/0.95 inference(unit_resolution,[status(thm)],[1853, 46, 1625, 4411])).
% 0.75/0.95 tff(4413,plain,
% 0.75/0.95 ($false),
% 0.75/0.95 inference(unit_resolution,[status(thm)],[2986, 117, 157, 4406, 4412])).
% 0.75/0.95 tff(4414,plain,((~b(s(s(s(elem!1))), z)) | (s(s(s(s(elem!1)))) = s(s(elem!1))) | (~b(s(s(elem!1)), s(s(s(elem!1))))) | (s(s(s(s(elem!1)))) = s(s(s(elem!1)))) | (~r(z, s(s(s(elem!1))))) | (~b(s(z), z))), inference(lemma,lemma(discharge,[]))).
% 0.75/0.95 tff(4415,plain,
% 0.75/0.95 (~r(z, s(s(s(elem!1))))),
% 0.75/0.95 inference(unit_resolution,[status(thm)],[4414, 4393, 146, 4265, 237, 324])).
% 0.75/0.95 tff(4416,plain,
% 0.75/0.95 (b(z, s(s(s(elem!1))))),
% 0.75/0.95 inference(unit_resolution,[status(thm)],[692, 4415])).
% 0.75/0.95 tff(4417,plain,
% 0.75/0.95 (b(z, s(s(s(z))))),
% 0.75/0.95 inference(modus_ponens,[status(thm)],[4416, 4404])).
% 0.75/0.95 tff(4418,plain,
% 0.75/0.95 (b(elem!1, s(s(s(z))))),
% 0.75/0.95 inference(modus_ponens,[status(thm)],[4417, 4403])).
% 0.75/0.95 tff(4419,plain,
% 0.75/0.95 ($false),
% 0.75/0.95 inference(unit_resolution,[status(thm)],[3738, 4418])).
% 0.75/0.95 tff(4420,plain,((~b(s(z), z)) | b(elem!1, s(s(s(z)))) | (~b(s(s(s(z))), z)) | (s(s(s(s(elem!1)))) = s(s(elem!1))) | (~b(s(s(elem!1)), 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(s(elem!1)))), s(s(elem!1))))), inference(lemma,lemma(discharge,[]))).
% 0.75/0.95 tff(4421,plain,
% 0.75/0.95 (~b(s(z), z)),
% 0.75/0.95 inference(unit_resolution,[status(thm)],[4420, 324, 338, 146, 3738, 1336, 213, 1397])).
% 0.75/0.95 tff(4422,plain,
% 0.75/0.95 (r(s(z), z)),
% 0.75/0.95 inference(unit_resolution,[status(thm)],[193, 4421])).
% 0.75/0.95 tff(4423,plain,
% 0.75/0.95 (~r(z, s(s(s(elem!1))))),
% 0.75/0.95 inference(unit_resolution,[status(thm)],[4321, 4422, 213])).
% 0.75/0.95 tff(4424,plain,
% 0.75/0.95 (b(z, s(s(s(elem!1))))),
% 0.75/0.95 inference(unit_resolution,[status(thm)],[692, 4423])).
% 0.75/0.95 tff(4425,plain,
% 0.75/0.95 (((~![X0: $i, X2: $i, X1: $i] : ((~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(s(elem!1))))) | (~b(s(s(s(s(elem!1)))), z)) | (~b(s(s(s(s(elem!1)))), s(s(s(elem!1))))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(s(s(elem!1))))) | (~b(s(s(s(s(elem!1)))), z)) | (~b(s(s(s(s(elem!1)))), s(s(s(elem!1))))))),
% 0.75/0.95 inference(rewrite,[status(thm)],[])).
% 0.75/0.95 tff(4426,plain,
% 0.75/0.95 (((~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(s(elem!1)))), z)) | (~b(s(s(s(s(elem!1)))), s(s(s(elem!1))))))),
% 0.75/0.95 inference(rewrite,[status(thm)],[])).
% 0.75/0.95 tff(4427,plain,
% 0.75/0.95 (((~![X0: $i, X2: $i, X1: $i] : ((~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(s(elem!1)))), z)))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(s(elem!1))))) | (~b(s(s(s(s(elem!1)))), z)) | (~b(s(s(s(s(elem!1)))), s(s(s(elem!1)))))))),
% 0.75/0.95 inference(monotonicity,[status(thm)],[4426])).
% 0.75/0.95 tff(4428,plain,
% 0.75/0.95 (((~![X0: $i, X2: $i, X1: $i] : ((~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(s(elem!1)))), z)))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(s(s(elem!1))))) | (~b(s(s(s(s(elem!1)))), z)) | (~b(s(s(s(s(elem!1)))), s(s(s(elem!1))))))),
% 0.75/0.95 inference(transitivity,[status(thm)],[4427, 4425])).
% 0.75/0.95 tff(4429,plain,
% 0.75/0.95 ((~![X0: $i, X2: $i, X1: $i] : ((~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(s(elem!1)))), z)))),
% 0.75/0.95 inference(quant_inst,[status(thm)],[])).
% 0.75/0.95 tff(4430,plain,
% 0.75/0.95 ((~![X0: $i, X2: $i, X1: $i] : ((~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(s(s(elem!1))))) | (~b(s(s(s(s(elem!1)))), z)) | (~b(s(s(s(s(elem!1)))), s(s(s(elem!1)))))),
% 0.75/0.95 inference(modus_ponens,[status(thm)],[4429, 4428])).
% 0.75/0.95 tff(4431,plain,
% 0.75/0.95 (~b(s(s(s(s(elem!1)))), z)),
% 0.75/0.95 inference(unit_resolution,[status(thm)],[4430, 117, 4424, 4347])).
% 0.75/0.95 tff(4432,plain,
% 0.75/0.95 (~r(s(s(s(s(elem!1)))), z)),
% 0.75/0.95 inference(unit_resolution,[status(thm)],[1402, 4355, 1397])).
% 0.75/0.95 tff(4433,plain,
% 0.75/0.95 ($false),
% 0.75/0.95 inference(unit_resolution,[status(thm)],[1853, 46, 1625, 4432, 4431])).
% 0.75/0.95 tff(4434,plain,((~b(s(s(elem!1)), s(s(s(elem!1))))) | (~r(s(z), s(s(s(elem!1))))) | (~b(s(s(s(z))), z)) | (s(s(s(s(elem!1)))) = s(s(elem!1))) | b(elem!1, s(s(s(z)))) | (~r(s(s(s(s(elem!1)))), s(z))) | (~r(s(s(s(s(elem!1)))), s(s(elem!1))))), inference(lemma,lemma(discharge,[]))).
% 0.75/0.95 tff(4435,plain,
% 0.75/0.95 (~b(s(s(s(z))), z)),
% 0.75/0.95 inference(unit_resolution,[status(thm)],[4434, 4341, 4339, 146, 3738, 1336, 1397])).
% 0.75/0.95 tff(4436,plain,
% 0.75/0.95 (r(s(s(s(z))), z)),
% 0.75/0.95 inference(unit_resolution,[status(thm)],[823, 4435])).
% 0.75/0.95 tff(4437,plain,
% 0.75/0.95 (~r(s(s(s(z))), s(s(elem!1)))),
% 0.75/0.95 inference(unit_resolution,[status(thm)],[827, 14, 4327, 4436])).
% 0.75/0.95 tff(4438,plain,
% 0.75/0.95 (b(s(s(s(z))), s(s(elem!1)))),
% 0.75/0.95 inference(unit_resolution,[status(thm)],[1421, 46, 4437, 4346])).
% 0.75/0.95 tff(4439,plain,
% 0.75/0.95 (~r(s(s(s(elem!1))), s(s(elem!1)))),
% 0.75/0.95 inference(unit_resolution,[status(thm)],[4218, 14, 4337, 4327])).
% 0.75/0.95 tff(4440,plain,
% 0.75/0.95 (b(s(s(s(elem!1))), s(s(elem!1)))),
% 0.75/0.95 inference(unit_resolution,[status(thm)],[1547, 4439, 4356])).
% 0.75/0.95 tff(4441,plain,
% 0.75/0.95 (~b(s(s(s(z))), s(s(s(elem!1))))),
% 0.75/0.95 inference(unit_resolution,[status(thm)],[4223, 117, 4440, 4438])).
% 0.75/0.95 tff(4442,plain,
% 0.75/0.95 (~r(s(s(s(z))), s(s(s(elem!1))))),
% 0.75/0.95 inference(unit_resolution,[status(thm)],[1713, 14, 4337, 4436])).
% 0.75/0.95 tff(4443,plain,
% 0.75/0.95 ((s(s(s(z))) = s(s(s(elem!1)))) | b(s(s(s(z))), s(s(s(elem!1))))),
% 0.75/0.95 inference(unit_resolution,[status(thm)],[1717, 46, 4442])).
% 0.75/0.95 tff(4444,plain,
% 0.75/0.95 (s(s(s(z))) = s(s(s(elem!1)))),
% 0.75/0.95 inference(unit_resolution,[status(thm)],[4443, 4441])).
% 0.75/0.95 tff(4445,plain,
% 0.75/0.95 (inj_0(s(s(s(z)))) = inj_0(s(s(s(elem!1))))),
% 0.75/0.95 inference(monotonicity,[status(thm)],[4444])).
% 0.75/0.95 tff(4446,plain,
% 0.75/0.95 (s(s(z)) = s(s(elem!1))),
% 0.75/0.95 inference(transitivity,[status(thm)],[95, 4445, 151])).
% 0.75/0.95 tff(4447,plain,
% 0.75/0.95 (inj_0(s(s(z))) = inj_0(s(s(elem!1)))),
% 0.75/0.95 inference(monotonicity,[status(thm)],[4446])).
% 0.75/0.95 tff(4448,plain,
% 0.75/0.95 (inj_0(s(s(elem!1))) = inj_0(s(s(z)))),
% 0.75/0.95 inference(symmetry,[status(thm)],[4447])).
% 0.75/0.95 tff(4449,plain,
% 0.75/0.95 (s(elem!1) = s(z)),
% 0.75/0.95 inference(transitivity,[status(thm)],[167, 4448, 82])).
% 0.75/0.95 tff(4450,plain,
% 0.75/0.95 (r(s(elem!1), s(s(s(s(elem!1))))) <=> r(s(z), s(s(s(s(elem!1)))))),
% 0.75/0.95 inference(monotonicity,[status(thm)],[4449])).
% 0.75/0.95 tff(4451,plain,
% 0.75/0.95 (r(s(z), s(s(s(s(elem!1))))) <=> r(s(elem!1), s(s(s(s(elem!1)))))),
% 0.75/0.95 inference(symmetry,[status(thm)],[4450])).
% 0.75/0.95 tff(4452,plain,
% 0.75/0.95 (~b(s(z), s(s(s(s(elem!1)))))),
% 0.75/0.95 inference(unit_resolution,[status(thm)],[1928, 117, 4343, 4279])).
% 0.75/0.95 tff(4453,plain,
% 0.75/0.95 (r(s(z), s(s(s(s(elem!1)))))),
% 0.75/0.95 inference(unit_resolution,[status(thm)],[1938, 4452])).
% 0.75/0.95 tff(4454,plain,
% 0.75/0.95 (r(s(elem!1), s(s(s(s(elem!1)))))),
% 0.75/0.95 inference(modus_ponens,[status(thm)],[4453, 4451])).
% 0.75/0.95 tff(4455,plain,
% 0.75/0.95 (s(s(s(s(z)))) = s(s(s(s(elem!1))))),
% 0.75/0.95 inference(monotonicity,[status(thm)],[4444])).
% 0.75/0.95 tff(4456,plain,
% 0.75/0.95 (s(s(s(s(s(z))))) = s(s(s(s(s(elem!1)))))),
% 0.75/0.95 inference(monotonicity,[status(thm)],[4455])).
% 0.75/0.95 tff(4457,plain,
% 0.75/0.95 (s(s(s(s(s(s(z)))))) = s(s(s(s(s(s(elem!1))))))),
% 0.75/0.95 inference(monotonicity,[status(thm)],[4456])).
% 0.75/0.95 tff(4458,plain,
% 0.75/0.95 (s(s(s(s(s(s(elem!1)))))) = s(s(s(s(s(s(z))))))),
% 0.75/0.95 inference(symmetry,[status(thm)],[4457])).
% 0.75/0.95 tff(4459,plain,
% 0.75/0.95 ((s(s(s(s(s(s(elem!1)))))) = s(elem!1)) <=> (s(s(s(s(s(s(z)))))) = s(z))),
% 0.75/0.95 inference(monotonicity,[status(thm)],[4458, 4449])).
% 0.75/0.95 tff(4460,plain,
% 0.75/0.95 ((s(s(s(s(s(s(z)))))) = s(z)) <=> (s(s(s(s(s(s(elem!1)))))) = s(elem!1))),
% 0.75/0.95 inference(symmetry,[status(thm)],[4459])).
% 0.75/0.95 tff(4461,plain,
% 0.75/0.95 ((~(s(s(s(s(s(s(z)))))) = s(z))) <=> (~(s(s(s(s(s(s(elem!1)))))) = s(elem!1)))),
% 0.75/0.95 inference(monotonicity,[status(thm)],[4460])).
% 0.75/0.95 tff(4462,plain,
% 0.75/0.95 (~(s(s(s(s(s(s(elem!1)))))) = s(elem!1))),
% 0.75/0.95 inference(modus_ponens,[status(thm)],[1770, 4461])).
% 0.75/0.95 tff(4463,plain,
% 0.75/0.95 (b(s(elem!1), elem!1) <=> b(s(z), elem!1)),
% 0.75/0.95 inference(monotonicity,[status(thm)],[4449])).
% 0.75/0.95 tff(4464,plain,
% 0.75/0.95 (b(s(z), elem!1) <=> b(s(elem!1), elem!1)),
% 0.75/0.95 inference(symmetry,[status(thm)],[4463])).
% 0.75/0.95 tff(4465,plain,
% 0.75/0.95 (s(z) = s(elem!1)),
% 0.75/0.95 inference(transitivity,[status(thm)],[131, 4447, 166])).
% 0.75/0.95 tff(4466,plain,
% 0.75/0.95 (inj_0(s(z)) = inj_0(s(elem!1))),
% 0.75/0.95 inference(monotonicity,[status(thm)],[4465])).
% 0.75/0.95 tff(4467,plain,
% 0.75/0.95 (z = elem!1),
% 0.75/0.95 inference(transitivity,[status(thm)],[1730, 4466, 257])).
% 0.75/0.95 tff(4468,plain,
% 0.75/0.95 (b(s(z), z) <=> b(s(z), elem!1)),
% 0.75/0.95 inference(monotonicity,[status(thm)],[4467])).
% 0.75/0.95 tff(4469,plain,
% 0.75/0.95 (b(s(z), elem!1)),
% 0.75/0.95 inference(modus_ponens,[status(thm)],[4343, 4468])).
% 0.75/0.95 tff(4470,plain,
% 0.75/0.95 (b(s(elem!1), elem!1)),
% 0.75/0.95 inference(modus_ponens,[status(thm)],[4469, 4464])).
% 0.75/0.95 tff(4471,plain,
% 0.75/0.95 ((s(s(s(s(s(s(elem!1)))))) = z) <=> (s(s(s(s(s(s(elem!1)))))) = elem!1)),
% 0.75/0.95 inference(monotonicity,[status(thm)],[4467])).
% 0.75/0.95 tff(4472,plain,
% 0.75/0.95 ((~(s(s(s(s(s(s(elem!1)))))) = z)) <=> (~(s(s(s(s(s(s(elem!1)))))) = elem!1))),
% 0.75/0.95 inference(monotonicity,[status(thm)],[4471])).
% 0.75/0.95 tff(4473,plain,
% 0.75/0.95 (~(s(s(s(s(s(s(elem!1)))))) = elem!1)),
% 0.75/0.95 inference(modus_ponens,[status(thm)],[1663, 4472])).
% 0.75/0.95 tff(4474,plain,
% 0.75/0.95 (r(s(s(elem!1)), z) <=> r(s(s(elem!1)), elem!1)),
% 0.75/0.95 inference(monotonicity,[status(thm)],[4467])).
% 0.75/0.95 tff(4475,plain,
% 0.75/0.95 (r(s(s(elem!1)), elem!1)),
% 0.75/0.95 inference(modus_ponens,[status(thm)],[4327, 4474])).
% 0.75/0.95 tff(4476,plain,
% 0.75/0.95 (r(s(s(s(elem!1))), z) <=> r(s(s(s(elem!1))), elem!1)),
% 0.75/0.95 inference(monotonicity,[status(thm)],[4467])).
% 0.75/0.95 tff(4477,plain,
% 0.75/0.95 (r(s(s(s(elem!1))), elem!1)),
% 0.75/0.95 inference(modus_ponens,[status(thm)],[4337, 4476])).
% 0.75/0.95 tff(4478,plain,
% 0.75/0.95 (~r(s(s(s(s(s(s(elem!1)))))), elem!1)),
% 0.75/0.95 inference(unit_resolution,[status(thm)],[2102, 4440, 4444, 4477, 4475])).
% 0.75/0.95 tff(4479,plain,
% 0.75/0.95 (b(s(s(s(s(s(s(elem!1)))))), elem!1)),
% 0.75/0.95 inference(unit_resolution,[status(thm)],[1599, 4478, 4473])).
% 0.75/0.95 tff(4480,plain,
% 0.75/0.95 ((~b(s(elem!1), elem!1)) | (~b(s(s(s(s(s(s(elem!1)))))), s(elem!1)))),
% 0.75/0.95 inference(unit_resolution,[status(thm)],[1807, 117, 4479])).
% 0.75/0.95 tff(4481,plain,
% 0.75/0.95 (~b(s(s(s(s(s(s(elem!1)))))), s(elem!1))),
% 0.75/0.95 inference(unit_resolution,[status(thm)],[4480, 4470])).
% 0.75/0.95 tff(4482,plain,
% 0.75/0.95 ((s(s(s(s(s(s(elem!1)))))) = s(elem!1)) | r(s(s(s(s(s(s(elem!1)))))), s(elem!1))),
% 0.75/0.95 inference(unit_resolution,[status(thm)],[1812, 46, 4481])).
% 0.75/0.95 tff(4483,plain,
% 0.75/0.95 (r(s(s(s(s(s(s(elem!1)))))), s(elem!1))),
% 0.75/0.95 inference(unit_resolution,[status(thm)],[4482, 4462])).
% 0.75/0.95 tff(4484,plain,
% 0.75/0.95 (s(s(s(s(elem!1)))) = s(s(s(s(z))))),
% 0.75/0.95 inference(symmetry,[status(thm)],[4455])).
% 0.75/0.95 tff(4485,plain,
% 0.75/0.95 ((s(s(s(s(s(s(elem!1)))))) = s(s(s(s(elem!1))))) <=> (s(s(s(s(s(s(elem!1)))))) = s(s(s(s(z)))))),
% 0.75/0.95 inference(monotonicity,[status(thm)],[4484])).
% 0.75/0.95 tff(4486,plain,
% 0.75/0.95 ((s(s(s(s(s(s(elem!1)))))) = s(s(s(s(z))))) <=> (s(s(s(s(s(s(elem!1)))))) = s(s(s(s(elem!1)))))),
% 0.75/0.95 inference(symmetry,[status(thm)],[4485])).
% 0.75/0.95 tff(4487,plain,
% 0.75/0.95 ((~(s(s(s(s(s(s(elem!1)))))) = s(s(s(s(z)))))) <=> (~(s(s(s(s(s(s(elem!1)))))) = s(s(s(s(elem!1))))))),
% 0.75/0.95 inference(monotonicity,[status(thm)],[4486])).
% 0.75/0.95 tff(4488,plain,
% 0.75/0.95 (~(s(s(s(s(s(s(elem!1)))))) = s(s(s(s(elem!1)))))),
% 0.75/0.95 inference(modus_ponens,[status(thm)],[319, 4487])).
% 0.75/0.95 tff(4489,plain,
% 0.75/0.95 (b(s(s(s(s(elem!1)))), z) <=> b(s(s(s(s(elem!1)))), elem!1)),
% 0.75/0.95 inference(monotonicity,[status(thm)],[4467])).
% 0.75/0.95 tff(4490,plain,
% 0.75/0.95 (b(s(s(s(s(elem!1)))), elem!1)),
% 0.75/0.95 inference(modus_ponens,[status(thm)],[4279, 4489])).
% 0.75/0.95 tff(4491,plain,
% 0.75/0.95 (~b(s(s(s(s(s(s(elem!1)))))), s(s(s(s(elem!1)))))),
% 0.75/0.95 inference(unit_resolution,[status(thm)],[1605, 117, 4490, 4479])).
% 0.75/0.95 tff(4492,plain,
% 0.75/0.95 ((s(s(s(s(s(s(elem!1)))))) = s(s(s(s(elem!1))))) | r(s(s(s(s(s(s(elem!1)))))), s(s(s(s(elem!1)))))),
% 0.75/0.95 inference(unit_resolution,[status(thm)],[1619, 46, 4491])).
% 0.75/0.95 tff(4493,plain,
% 0.75/0.95 (r(s(s(s(s(s(s(elem!1)))))), s(s(s(s(elem!1)))))),
% 0.75/0.95 inference(unit_resolution,[status(thm)],[4492, 4488])).
% 0.75/0.95 tff(4494,plain,
% 0.75/0.95 ((~r(s(elem!1), s(s(s(s(elem!1)))))) | (~r(s(s(s(s(s(s(elem!1)))))), s(elem!1)))),
% 0.75/0.95 inference(unit_resolution,[status(thm)],[1957, 14, 4493])).
% 0.75/0.95 tff(4495,plain,
% 0.75/0.95 (~r(s(elem!1), s(s(s(s(elem!1)))))),
% 0.75/0.95 inference(unit_resolution,[status(thm)],[4494, 4483])).
% 0.75/0.95 tff(4496,plain,
% 0.75/0.95 ($false),
% 0.75/0.95 inference(unit_resolution,[status(thm)],[4495, 4454])).
% 0.75/0.95 tff(4497,plain,((~r(s(s(s(s(elem!1)))), s(s(elem!1)))) | b(elem!1, s(s(s(z)))) | (s(s(s(s(elem!1)))) = s(s(elem!1))) | (~r(s(s(s(s(elem!1)))), s(z)))), inference(lemma,lemma(discharge,[]))).
% 0.75/0.95 tff(4498,plain,
% 0.75/0.95 (b(elem!1, s(s(s(z))))),
% 0.75/0.95 inference(unit_resolution,[status(thm)],[4497, 4245, 146, 4236])).
% 0.75/0.95 tff(4499,plain,
% 0.75/0.95 (b(elem!1, s(s(s(elem!1))))),
% 0.75/0.95 inference(modus_ponens,[status(thm)],[4498, 4243])).
% 0.75/0.95 tff(4500,plain,
% 0.75/0.95 (((~![X0: $i, X2: $i, X1: $i] : ((~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(s(s(elem!1))))) | (~b(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~b(s(s(s(s(elem!1)))), elem!1)))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(s(s(elem!1))))) | (~b(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~b(s(s(s(s(elem!1)))), elem!1)))),
% 0.75/0.95 inference(rewrite,[status(thm)],[])).
% 0.75/0.95 tff(4501,plain,
% 0.75/0.95 ((~![X0: $i, X2: $i, X1: $i] : ((~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(s(s(elem!1))))) | (~b(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~b(s(s(s(s(elem!1)))), elem!1)))),
% 0.75/0.95 inference(quant_inst,[status(thm)],[])).
% 0.75/0.95 tff(4502,plain,
% 0.75/0.95 ((~![X0: $i, X2: $i, X1: $i] : ((~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(s(s(elem!1))))) | (~b(s(s(s(s(elem!1)))), s(s(s(elem!1))))) | (~b(s(s(s(s(elem!1)))), elem!1))),
% 0.75/0.95 inference(modus_ponens,[status(thm)],[4501, 4500])).
% 0.75/0.95 tff(4503,plain,
% 0.75/0.95 ($false),
% 0.75/0.95 inference(unit_resolution,[status(thm)],[4502, 117, 4499, 4242, 4235])).
% 0.75/0.95 tff(4504,plain,((~b(s(z), z)) | (~b(s(s(s(s(elem!1)))), z)) | (s(s(s(z))) = s(s(elem!1))) | (s(s(s(s(elem!1)))) = s(s(elem!1))) | (s(s(elem!1)) = s(s(s(elem!1))))), inference(lemma,lemma(discharge,[]))).
% 0.75/0.95 tff(4505,plain,
% 0.75/0.95 (~b(s(z), z)),
% 0.75/0.95 inference(unit_resolution,[status(thm)],[4504, 1310, 1417, 146, 145])).
% 0.75/0.95 tff(4506,plain,
% 0.75/0.95 (r(s(z), z)),
% 0.75/0.95 inference(unit_resolution,[status(thm)],[193, 4505])).
% 0.75/0.95 tff(4507,plain,
% 0.75/0.95 (~r(s(s(elem!1)), z)),
% 0.75/0.95 inference(unit_resolution,[status(thm)],[2734, 4506, 145, 4183])).
% 0.75/0.95 tff(4508,plain,
% 0.75/0.95 (b(s(s(elem!1)), z)),
% 0.75/0.95 inference(unit_resolution,[status(thm)],[1025, 4507])).
% 0.75/0.95 tff(4509,plain,
% 0.75/0.95 (~b(s(s(s(s(elem!1)))), s(s(elem!1)))),
% 0.75/0.95 inference(unit_resolution,[status(thm)],[2191, 4508, 1310])).
% 0.75/0.95 tff(4510,plain,
% 0.75/0.95 (s(s(s(elem!1))) = s(s(s(z)))),
% 0.75/0.95 inference(unit_resolution,[status(thm)],[2355, 4506, 4183, 3618])).
% 0.75/0.95 tff(4511,plain,
% 0.75/0.95 (~r(s(s(s(s(elem!1)))), s(s(elem!1)))),
% 0.75/0.95 inference(unit_resolution,[status(thm)],[2326, 4508, 1310, 4510, 4506, 3618])).
% 0.75/0.95 tff(4512,plain,
% 0.75/0.95 ($false),
% 0.75/0.95 inference(unit_resolution,[status(thm)],[1690, 4511, 4509, 146])).
% 0.75/0.95 tff(4513,plain,((~b(s(s(s(s(elem!1)))), z)) | (s(s(s(s(elem!1)))) = s(s(elem!1))) | (s(s(elem!1)) = s(s(s(elem!1)))) | (s(s(s(z))) = s(s(elem!1)))), inference(lemma,lemma(discharge,[]))).
% 0.75/0.95 tff(4514,plain,
% 0.75/0.95 (s(s(s(z))) = s(s(elem!1))),
% 0.75/0.95 inference(unit_resolution,[status(thm)],[4513, 4209, 145, 146])).
% 0.75/0.95 tff(4515,plain,
% 0.75/0.95 (inj_0(s(s(s(z)))) = inj_0(s(s(elem!1)))),
% 0.75/0.95 inference(monotonicity,[status(thm)],[4514])).
% 0.75/0.95 tff(4516,plain,
% 0.75/0.95 (s(s(z)) = s(elem!1)),
% 0.75/0.95 inference(transitivity,[status(thm)],[95, 4515, 166])).
% 0.75/0.95 tff(4517,plain,
% 0.75/0.95 (inj_0(s(s(z))) = inj_0(s(elem!1))),
% 0.75/0.95 inference(monotonicity,[status(thm)],[4516])).
% 0.75/0.95 tff(4518,plain,
% 0.75/0.95 (inj_0(s(elem!1)) = inj_0(s(s(z)))),
% 0.75/0.95 inference(symmetry,[status(thm)],[4517])).
% 0.75/0.95 tff(4519,plain,
% 0.75/0.95 (elem!1 = s(z)),
% 0.75/0.95 inference(transitivity,[status(thm)],[1652, 4518, 82])).
% 0.75/0.95 tff(4520,plain,
% 0.75/0.95 (b(z, elem!1) <=> b(z, s(z))),
% 0.75/0.95 inference(monotonicity,[status(thm)],[4519])).
% 0.75/0.95 tff(4521,plain,
% 0.75/0.95 (b(z, s(z)) <=> b(z, elem!1)),
% 0.75/0.95 inference(symmetry,[status(thm)],[4520])).
% 0.75/0.95 tff(4522,plain,
% 0.75/0.95 (s(z) = elem!1),
% 0.75/0.95 inference(transitivity,[status(thm)],[131, 4517, 257])).
% 0.75/0.95 tff(4523,plain,
% 0.75/0.95 (r(z, s(z)) <=> r(z, elem!1)),
% 0.75/0.95 inference(monotonicity,[status(thm)],[4522])).
% 0.75/0.95 tff(4524,plain,
% 0.75/0.95 (r(z, elem!1) <=> r(z, s(z))),
% 0.75/0.95 inference(symmetry,[status(thm)],[4523])).
% 0.75/0.95 tff(4525,plain,
% 0.75/0.95 ((~r(z, elem!1)) <=> (~r(z, s(z)))),
% 0.75/0.95 inference(monotonicity,[status(thm)],[4524])).
% 0.75/0.95 tff(4526,plain,
% 0.75/0.95 (r(s(s(s(elem!1))), s(z)) <=> r(s(s(s(elem!1))), elem!1)),
% 0.75/0.95 inference(monotonicity,[status(thm)],[4522])).
% 0.75/0.95 tff(4527,plain,
% 0.75/0.95 (~r(s(s(s(elem!1))), s(s(elem!1)))),
% 0.75/0.95 inference(unit_resolution,[status(thm)],[4218, 14, 4183, 182])).
% 0.75/0.95 tff(4528,plain,
% 0.75/0.95 (b(s(s(s(elem!1))), s(s(elem!1)))),
% 0.75/0.95 inference(unit_resolution,[status(thm)],[1547, 4527, 1539])).
% 0.75/0.95 tff(4529,plain,
% 0.75/0.95 (~r(s(z), z)),
% 0.75/0.95 inference(unit_resolution,[status(thm)],[2734, 182, 145, 4183])).
% 0.75/0.95 tff(4530,plain,
% 0.75/0.95 (b(s(z), z)),
% 0.75/0.95 inference(unit_resolution,[status(thm)],[193, 4529])).
% 0.75/0.95 tff(4531,plain,
% 0.75/0.95 (~b(s(z), s(s(s(elem!1))))),
% 0.75/0.95 inference(unit_resolution,[status(thm)],[2554, 4187, 3616])).
% 0.75/0.95 tff(4532,plain,
% 0.75/0.95 (r(s(z), s(s(s(elem!1))))),
% 0.75/0.95 inference(unit_resolution,[status(thm)],[235, 4531])).
% 0.75/0.95 tff(4533,plain,
% 0.75/0.95 (~b(s(s(s(s(elem!1)))), s(s(elem!1)))),
% 0.75/0.95 inference(unit_resolution,[status(thm)],[1508, 4532, 3616, 156, 4187])).
% 0.75/0.95 tff(4534,plain,
% 0.75/0.95 (r(s(s(s(s(elem!1)))), s(s(elem!1)))),
% 0.75/0.95 inference(unit_resolution,[status(thm)],[1690, 4533, 146])).
% 0.75/0.95 tff(4535,plain,
% 0.75/0.95 (~r(s(z), s(s(elem!1)))),
% 0.75/0.95 inference(unit_resolution,[status(thm)],[1890, 4534, 182, 4530])).
% 0.75/0.95 tff(4536,plain,
% 0.75/0.95 (b(s(z), s(s(elem!1)))),
% 0.75/0.95 inference(unit_resolution,[status(thm)],[416, 4535])).
% 0.75/0.95 tff(4537,plain,
% 0.75/0.95 (~b(s(s(s(elem!1))), s(z))),
% 0.75/0.95 inference(unit_resolution,[status(thm)],[4370, 117, 4536, 4528])).
% 0.75/0.95 tff(4538,plain,
% 0.75/0.95 (r(s(s(s(elem!1))), s(z))),
% 0.75/0.95 inference(unit_resolution,[status(thm)],[467, 4537])).
% 0.75/0.95 tff(4539,plain,
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% 0.75/0.95 inference(modus_ponens,[status(thm)],[4538, 4526])).
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% 0.75/0.95 inference(rewrite,[status(thm)],[])).
% 0.75/0.95 tff(4541,plain,
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% 0.75/0.95 inference(quant_inst,[status(thm)],[])).
% 0.75/0.95 tff(4542,plain,
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% 0.75/0.95 inference(modus_ponens,[status(thm)],[4541, 4540])).
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% 0.75/0.95 tff(4545,plain,
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% 0.75/0.95 inference(unit_resolution,[status(thm)],[4544, 4539, 4183])).
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% 0.75/0.95 (~r(z, s(z))),
% 0.75/0.95 inference(modus_ponens,[status(thm)],[4545, 4525])).
% 0.75/0.95 tff(4547,plain,
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% 0.75/0.95 inference(unit_resolution,[status(thm)],[599, 4546])).
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% 0.75/0.95 inference(modus_ponens,[status(thm)],[4547, 4521])).
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% 0.75/0.95 (~(s(s(s(s(s(s(elem!1)))))) = elem!1)),
% 0.75/0.95 inference(unit_resolution,[status(thm)],[1446, 4514])).
% 0.75/0.95 tff(4550,plain,
% 0.75/0.95 (r(s(s(s(s(elem!1)))), s(z)) <=> r(s(s(s(s(elem!1)))), elem!1)),
% 0.75/0.95 inference(monotonicity,[status(thm)],[4522])).
% 0.75/0.95 tff(4551,plain,
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% 0.75/0.95 inference(unit_resolution,[status(thm)],[1316, 4530, 4209])).
% 0.75/0.95 tff(4552,plain,
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% 0.75/0.95 inference(unit_resolution,[status(thm)],[1327, 4551])).
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% 0.75/0.95 inference(modus_ponens,[status(thm)],[4552, 4550])).
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% 0.75/0.95 inference(unit_resolution,[status(thm)],[4102, 14, 4539, 4553])).
% 0.75/0.95 tff(4555,plain,
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% 0.75/0.95 inference(unit_resolution,[status(thm)],[448, 4554, 290])).
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% 0.75/0.95 tff(4559,plain,
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% 0.75/0.95 inference(unit_resolution,[status(thm)],[1666, 46, 1663, 4558])).
% 0.75/0.95 tff(4560,plain,
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% 0.75/0.95 inference(monotonicity,[status(thm)],[4514])).
% 0.75/0.95 tff(4561,plain,
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% 0.75/0.95 inference(symmetry,[status(thm)],[4560])).
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% 0.75/0.95 inference(monotonicity,[status(thm)],[4561])).
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% 0.75/0.95 inference(symmetry,[status(thm)],[4562])).
% 0.75/0.95 tff(4564,plain,
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% 0.75/0.95 inference(monotonicity,[status(thm)],[4563])).
% 0.75/0.95 tff(4565,plain,
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% 0.75/0.95 inference(modus_ponens,[status(thm)],[319, 4564])).
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% 0.75/0.95 inference(monotonicity,[status(thm)],[4566])).
% 0.75/0.95 tff(4568,plain,
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% 0.75/0.95 inference(symmetry,[status(thm)],[4567])).
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% 0.75/0.96 inference(monotonicity,[status(thm)],[4568])).
% 0.75/0.96 tff(4570,plain,
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% 0.75/0.96 inference(modus_ponens,[status(thm)],[1577, 4569])).
% 0.75/0.96 tff(4571,plain,
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% 0.75/0.96 inference(monotonicity,[status(thm)],[4522])).
% 0.75/0.96 tff(4572,plain,
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% 0.75/0.96 inference(unit_resolution,[status(thm)],[1586, 46, 4573])).
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% 0.75/0.96 inference(unit_resolution,[status(thm)],[4578, 14, 4534, 4575])).
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% 0.75/0.96 tff(4594,plain,((s(s(s(s(elem!1)))) = s(s(elem!1))) | (s(s(elem!1)) = s(s(s(elem!1))))), inference(lemma,lemma(discharge,[]))).
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% 0.75/0.96 inference(rewrite,[status(thm)],[])).
% 0.75/0.96 tff(4698,plain,
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% 0.75/0.96 inference(rewrite,[status(thm)],[])).
% 0.75/0.96 tff(4699,plain,
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% 0.75/0.96 inference(monotonicity,[status(thm)],[4698])).
% 0.75/0.96 tff(4700,plain,
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% 0.75/0.96 inference(transitivity,[status(thm)],[4699, 4697])).
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% 0.75/0.96 inference(quant_inst,[status(thm)],[])).
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% 0.75/0.96 inference(modus_ponens,[status(thm)],[4701, 4700])).
% 0.75/0.96 tff(4703,plain,
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% 0.75/0.96 inference(unit_resolution,[status(thm)],[4702, 117, 4696, 4678])).
% 0.75/0.96 tff(4704,plain,
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% 0.75/0.96 inference(unit_resolution,[status(thm)],[599, 4703])).
% 0.75/0.96 tff(4705,plain,
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% 0.75/0.96 inference(unit_resolution,[status(thm)],[958, 14, 4704, 4671])).
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% 0.75/0.96 inference(unit_resolution,[status(thm)],[582, 4705])).
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% 0.75/0.96 tff(4708,plain,
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% 0.75/0.96 inference(rewrite,[status(thm)],[])).
% 0.75/0.96 tff(4709,plain,
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% 0.75/0.96 inference(monotonicity,[status(thm)],[4708])).
% 0.75/0.96 tff(4710,plain,
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% 0.75/0.96 inference(transitivity,[status(thm)],[4709, 4707])).
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% 0.75/0.96 inference(quant_inst,[status(thm)],[])).
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% 0.75/0.96 inference(modus_ponens,[status(thm)],[4711, 4710])).
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% 0.75/0.96 inference(unit_resolution,[status(thm)],[4712, 117, 4706, 4676, 4673])).
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% 0.75/0.96 tff(4715,plain,
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% 0.75/0.96 inference(unit_resolution,[status(thm)],[4714, 4641, 4595, 1539, 3616, 4639, 4626, 4607])).
% 0.75/0.96 tff(4716,plain,
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% 0.75/0.96 inference(unit_resolution,[status(thm)],[253, 4715, 145])).
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% 0.75/0.96 inference(unit_resolution,[status(thm)],[2401, 4722])).
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% 0.75/0.96 inference(monotonicity,[status(thm)],[4727])).
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% 0.75/0.97 inference(transitivity,[status(thm)],[4767, 295, 4596, 166])).
% 0.75/0.97 tff(4769,plain,
% 0.75/0.97 (s(s(s(s(s(s(elem!1)))))) = s(s(elem!1))),
% 0.75/0.97 inference(monotonicity,[status(thm)],[4768])).
% 0.75/0.97 tff(4770,plain,
% 0.75/0.97 ((s(s(s(s(s(s(elem!1)))))) = s(s(s(s(z))))) <=> (s(s(elem!1)) = s(s(s(s(z)))))),
% 0.75/0.97 inference(monotonicity,[status(thm)],[4769])).
% 0.75/0.97 tff(4771,plain,
% 0.75/0.97 ((s(s(s(s(s(s(elem!1)))))) = s(s(s(s(z))))) <=> (s(s(s(s(z)))) = s(s(elem!1)))),
% 0.75/0.97 inference(transitivity,[status(thm)],[4770, 2418])).
% 0.75/0.97 tff(4772,plain,
% 0.75/0.97 ((s(s(s(s(s(s(elem!1)))))) = s(s(s(s(z))))) <=> (s(s(s(s(z)))) = elem!1)),
% 0.75/0.97 inference(transitivity,[status(thm)],[4771, 4766, 294])).
% 0.75/0.97 tff(4773,plain,
% 0.75/0.97 ((~(s(s(s(s(s(s(elem!1)))))) = s(s(s(s(z)))))) <=> (~(s(s(s(s(z)))) = elem!1))),
% 0.75/0.97 inference(monotonicity,[status(thm)],[4772])).
% 0.75/0.97 tff(4774,plain,
% 0.75/0.97 (~(s(s(s(s(z)))) = elem!1)),
% 0.75/0.97 inference(modus_ponens,[status(thm)],[319, 4773])).
% 0.75/0.97 tff(4775,plain,
% 0.75/0.97 (~b(s(s(s(z))), s(s(elem!1)))),
% 0.75/0.97 inference(unit_resolution,[status(thm)],[853, 4762, 3616])).
% 0.75/0.97 tff(4776,plain,
% 0.75/0.97 (r(s(s(s(z))), s(s(elem!1)))),
% 0.75/0.97 inference(unit_resolution,[status(thm)],[1421, 46, 4775, 4614])).
% 0.75/0.97 tff(4777,plain,
% 0.75/0.97 (~b(s(s(s(s(z)))), s(z))),
% 0.75/0.97 inference(unit_resolution,[status(thm)],[948, 4776, 3616, 4722, 4774, 4762])).
% 0.75/0.97 tff(4778,plain,
% 0.75/0.97 (r(s(s(s(s(z)))), s(z))),
% 0.75/0.97 inference(unit_resolution,[status(thm)],[554, 4777])).
% 0.75/0.97 tff(4779,plain,
% 0.75/0.97 (~b(z, s(z))),
% 0.75/0.97 inference(unit_resolution,[status(thm)],[2544, 4754, 3616])).
% 0.75/0.97 tff(4780,plain,
% 0.75/0.97 (r(z, s(z))),
% 0.75/0.97 inference(unit_resolution,[status(thm)],[599, 4779])).
% 0.75/0.97 tff(4781,plain,
% 0.75/0.97 (~r(s(s(s(s(z)))), z)),
% 0.75/0.97 inference(unit_resolution,[status(thm)],[958, 14, 4780, 4778])).
% 0.75/0.97 tff(4782,plain,
% 0.75/0.97 (b(s(s(s(s(z)))), z)),
% 0.75/0.97 inference(unit_resolution,[status(thm)],[582, 4781])).
% 0.75/0.97 tff(4783,plain,
% 0.75/0.97 (~b(s(s(s(s(z)))), s(elem!1))),
% 0.75/0.97 inference(unit_resolution,[status(thm)],[908, 117, 4782, 4760])).
% 0.75/0.97 tff(4784,plain,
% 0.75/0.97 (~(s(s(s(s(z)))) = s(elem!1))),
% 0.75/0.97 inference(unit_resolution,[status(thm)],[476, 4595])).
% 0.75/0.97 tff(4785,plain,
% 0.75/0.97 (r(s(s(s(s(z)))), s(elem!1))),
% 0.75/0.97 inference(unit_resolution,[status(thm)],[504, 46, 4784, 4783])).
% 0.75/0.97 tff(4786,plain,
% 0.75/0.97 (r(s(elem!1), s(s(elem!1))) <=> r(s(s(s(elem!1))), s(s(elem!1)))),
% 0.75/0.97 inference(monotonicity,[status(thm)],[4598])).
% 0.75/0.97 tff(4787,plain,
% 0.75/0.97 (r(s(s(s(elem!1))), s(s(elem!1))) <=> r(s(elem!1), s(s(elem!1)))),
% 0.75/0.97 inference(symmetry,[status(thm)],[4786])).
% 0.75/0.97 tff(4788,plain,
% 0.75/0.97 (b(s(elem!1), s(s(elem!1))) <=> b(s(s(s(elem!1))), s(s(elem!1)))),
% 0.75/0.97 inference(monotonicity,[status(thm)],[4598])).
% 0.75/0.97 tff(4789,plain,
% 0.75/0.97 ((~b(s(elem!1), s(s(elem!1)))) <=> (~b(s(s(s(elem!1))), s(s(elem!1))))),
% 0.75/0.97 inference(monotonicity,[status(thm)],[4788])).
% 0.75/0.97 tff(4790,plain,
% 0.75/0.97 (((~![X0: $i, X2: $i, X1: $i] : ((~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), z)) | (~b(s(elem!1), z)) | (~b(s(elem!1), s(s(elem!1)))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(elem!1)), z)) | (~b(s(elem!1), z)) | (~b(s(elem!1), s(s(elem!1)))))),
% 0.75/0.97 inference(rewrite,[status(thm)],[])).
% 0.75/0.97 tff(4791,plain,
% 0.75/0.97 ((~![X0: $i, X2: $i, X1: $i] : ((~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), z)) | (~b(s(elem!1), z)) | (~b(s(elem!1), s(s(elem!1)))))),
% 0.75/0.97 inference(quant_inst,[status(thm)],[])).
% 0.75/0.97 tff(4792,plain,
% 0.75/0.97 ((~![X0: $i, X2: $i, X1: $i] : ((~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(elem!1)), z)) | (~b(s(elem!1), z)) | (~b(s(elem!1), s(s(elem!1))))),
% 0.75/0.97 inference(modus_ponens,[status(thm)],[4791, 4790])).
% 0.75/0.97 tff(4793,plain,
% 0.75/0.97 ((~b(s(elem!1), z)) | (~b(s(elem!1), s(s(elem!1))))),
% 0.75/0.97 inference(unit_resolution,[status(thm)],[4792, 117, 4754])).
% 0.75/0.97 tff(4794,plain,
% 0.75/0.97 (~b(s(elem!1), s(s(elem!1)))),
% 0.75/0.97 inference(unit_resolution,[status(thm)],[4793, 4760])).
% 0.75/0.97 tff(4795,plain,
% 0.75/0.97 (~b(s(s(s(elem!1))), s(s(elem!1)))),
% 0.75/0.97 inference(modus_ponens,[status(thm)],[4794, 4789])).
% 0.75/0.97 tff(4796,plain,
% 0.75/0.97 (r(s(s(s(elem!1))), s(s(elem!1)))),
% 0.75/0.97 inference(unit_resolution,[status(thm)],[1547, 4795, 1539])).
% 0.75/0.97 tff(4797,plain,
% 0.75/0.97 (r(s(elem!1), s(s(elem!1)))),
% 0.75/0.97 inference(modus_ponens,[status(thm)],[4796, 4787])).
% 0.75/0.97 tff(4798,plain,
% 0.75/0.97 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(z))), s(s(elem!1)))) | (~r(s(s(s(z))), s(elem!1))) | (~r(s(elem!1), s(s(elem!1)))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(z))), s(s(elem!1)))) | (~r(s(s(s(z))), s(elem!1))) | (~r(s(elem!1), s(s(elem!1)))))),
% 0.75/0.97 inference(rewrite,[status(thm)],[])).
% 0.75/0.97 tff(4799,plain,
% 0.75/0.97 (((~r(s(elem!1), s(s(elem!1)))) | (~r(s(s(s(z))), s(s(elem!1)))) | (~r(s(s(s(z))), s(elem!1)))) <=> ((~r(s(s(s(z))), s(s(elem!1)))) | (~r(s(s(s(z))), s(elem!1))) | (~r(s(elem!1), s(s(elem!1)))))),
% 0.75/0.97 inference(rewrite,[status(thm)],[])).
% 0.75/0.97 tff(4800,plain,
% 0.75/0.97 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(elem!1), s(s(elem!1)))) | (~r(s(s(s(z))), s(s(elem!1)))) | (~r(s(s(s(z))), s(elem!1))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(z))), s(s(elem!1)))) | (~r(s(s(s(z))), s(elem!1))) | (~r(s(elem!1), s(s(elem!1))))))),
% 0.75/0.97 inference(monotonicity,[status(thm)],[4799])).
% 0.75/0.97 tff(4801,plain,
% 0.75/0.97 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(elem!1), s(s(elem!1)))) | (~r(s(s(s(z))), s(s(elem!1)))) | (~r(s(s(s(z))), s(elem!1))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(z))), s(s(elem!1)))) | (~r(s(s(s(z))), s(elem!1))) | (~r(s(elem!1), s(s(elem!1)))))),
% 0.75/0.97 inference(transitivity,[status(thm)],[4800, 4798])).
% 0.75/0.97 tff(4802,plain,
% 0.75/0.97 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(elem!1), s(s(elem!1)))) | (~r(s(s(s(z))), s(s(elem!1)))) | (~r(s(s(s(z))), s(elem!1))))),
% 0.75/0.97 inference(quant_inst,[status(thm)],[])).
% 0.75/0.97 tff(4803,plain,
% 0.75/0.97 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(z))), s(s(elem!1)))) | (~r(s(s(s(z))), s(elem!1))) | (~r(s(elem!1), s(s(elem!1))))),
% 0.75/0.97 inference(modus_ponens,[status(thm)],[4802, 4801])).
% 0.75/0.97 tff(4804,plain,
% 0.75/0.97 (~r(s(s(s(z))), s(elem!1))),
% 0.75/0.97 inference(unit_resolution,[status(thm)],[4803, 14, 4776, 4797])).
% 0.75/0.97 tff(4805,plain,
% 0.75/0.97 (b(s(s(s(z))), s(elem!1))),
% 0.75/0.97 inference(unit_resolution,[status(thm)],[627, 46, 4604, 4804])).
% 0.75/0.97 tff(4806,plain,
% 0.75/0.97 (~b(s(z), s(s(s(elem!1))))),
% 0.75/0.97 inference(unit_resolution,[status(thm)],[1139, 4805, 4595, 4762])).
% 0.75/0.97 tff(4807,plain,
% 0.75/0.97 (r(s(z), s(s(s(elem!1))))),
% 0.75/0.97 inference(unit_resolution,[status(thm)],[235, 4806])).
% 0.75/0.97 tff(4808,plain,
% 0.75/0.97 (r(s(z), s(elem!1))),
% 0.75/0.97 inference(unit_resolution,[status(thm)],[642, 4807, 4595])).
% 0.75/0.97 tff(4809,plain,
% 0.75/0.97 ($false),
% 0.75/0.97 inference(unit_resolution,[status(thm)],[917, 14, 4778, 4808, 4785])).
% 0.75/0.97 tff(4810,plain,(s(s(elem!1)) = s(s(s(elem!1)))), inference(lemma,lemma(discharge,[]))).
% 0.75/0.97 tff(4811,plain,
% 0.75/0.97 (b(s(s(elem!1)), s(z)) <=> b(s(s(s(elem!1))), s(z))),
% 0.75/0.97 inference(monotonicity,[status(thm)],[4810])).
% 0.75/0.97 tff(4812,plain,
% 0.75/0.97 (inj_0(s(s(elem!1))) = inj_0(s(s(s(elem!1))))),
% 0.75/0.97 inference(monotonicity,[status(thm)],[4253])).
% 0.75/0.97 tff(4813,plain,
% 0.75/0.97 (s(elem!1) = s(s(s(elem!1)))),
% 0.75/0.97 inference(transitivity,[status(thm)],[167, 4812, 151, 4253])).
% 0.75/0.97 tff(4814,plain,
% 0.75/0.97 (inj_0(s(elem!1)) = inj_0(s(s(s(elem!1))))),
% 0.75/0.97 inference(monotonicity,[status(thm)],[4813])).
% 0.75/0.97 tff(4815,plain,
% 0.75/0.97 (elem!1 = s(s(s(elem!1)))),
% 0.75/0.97 inference(transitivity,[status(thm)],[1652, 4814, 151, 4253])).
% 0.75/0.97 tff(4816,plain,
% 0.75/0.97 ((s(s(elem!1)) = elem!1) <=> (s(s(s(elem!1))) = elem!1)),
% 0.75/0.97 inference(monotonicity,[status(thm)],[4253])).
% 0.75/0.97 tff(4817,plain,
% 0.75/0.97 ((s(s(elem!1)) = elem!1) <=> (elem!1 = s(s(s(elem!1))))),
% 0.75/0.97 inference(transitivity,[status(thm)],[4816, 1198])).
% 0.75/0.97 tff(4818,plain,
% 0.75/0.97 ((~(s(s(elem!1)) = elem!1)) <=> (~(elem!1 = s(s(s(elem!1)))))),
% 0.75/0.97 inference(monotonicity,[status(thm)],[4817])).
% 0.75/0.97 tff(4819,plain,
% 0.75/0.97 (~(elem!1 = s(s(s(elem!1))))),
% 0.75/0.97 inference(modus_ponens,[status(thm)],[264, 4818])).
% 0.75/0.97 tff(4820,plain,
% 0.75/0.97 ($false),
% 0.75/0.97 inference(unit_resolution,[status(thm)],[4819, 4815])).
% 0.75/0.97 tff(4821,plain,((~(s(s(elem!1)) = s(s(s(elem!1))))) | (s(s(elem!1)) = elem!1)), inference(lemma,lemma(discharge,[]))).
% 0.75/0.97 tff(4822,plain,
% 0.75/0.97 (s(s(elem!1)) = elem!1),
% 0.75/0.97 inference(unit_resolution,[status(thm)],[4821, 4810])).
% 0.75/0.97 tff(4823,plain,
% 0.75/0.97 (s(s(s(elem!1))) = s(s(elem!1))),
% 0.75/0.97 inference(symmetry,[status(thm)],[4810])).
% 0.75/0.97 tff(4824,plain,
% 0.75/0.97 (s(s(s(elem!1))) = elem!1),
% 0.75/0.97 inference(transitivity,[status(thm)],[4823, 4822])).
% 0.75/0.97 tff(4825,plain,
% 0.75/0.97 (b(s(s(z)), s(s(s(elem!1)))) <=> b(s(s(z)), elem!1)),
% 0.75/0.97 inference(monotonicity,[status(thm)],[4824])).
% 0.75/0.97 tff(4826,plain,
% 0.75/0.97 (b(s(s(z)), elem!1) <=> b(s(s(z)), s(s(s(elem!1))))),
% 0.75/0.97 inference(symmetry,[status(thm)],[4825])).
% 0.75/0.97 tff(4827,plain,
% 0.75/0.97 (r(s(s(z)), s(s(s(elem!1)))) <=> r(s(s(z)), elem!1)),
% 0.75/0.97 inference(monotonicity,[status(thm)],[4824])).
% 0.75/0.97 tff(4828,plain,
% 0.75/0.97 ((~r(s(s(z)), s(s(s(elem!1))))) <=> (~r(s(s(z)), elem!1))),
% 0.75/0.97 inference(monotonicity,[status(thm)],[4827])).
% 0.75/0.97 tff(4829,plain,
% 0.75/0.97 (r(s(s(z)), elem!1) <=> r(s(s(z)), s(s(s(elem!1))))),
% 0.75/0.97 inference(symmetry,[status(thm)],[4827])).
% 0.75/0.97 tff(4830,plain,
% 0.75/0.97 ((~b(s(s(z)), s(s(s(elem!1))))) <=> (~b(s(s(z)), elem!1))),
% 0.75/0.97 inference(monotonicity,[status(thm)],[4825])).
% 0.75/0.97 tff(4831,plain,
% 0.75/0.97 (r(s(s(elem!1)), z) <=> r(s(s(s(elem!1))), z)),
% 0.75/0.97 inference(monotonicity,[status(thm)],[4810])).
% 0.75/0.97 tff(4832,plain,
% 0.75/0.97 (r(s(s(s(elem!1))), z)),
% 0.75/0.97 inference(modus_ponens,[status(thm)],[182, 4831])).
% 0.75/0.97 tff(4833,plain,
% 0.75/0.97 (elem!1 = s(s(elem!1))),
% 0.75/0.97 inference(symmetry,[status(thm)],[4822])).
% 0.75/0.97 tff(4834,plain,
% 0.75/0.97 (elem!1 = s(s(s(elem!1)))),
% 0.75/0.97 inference(transitivity,[status(thm)],[4833, 4810])).
% 0.75/0.97 tff(4835,plain,
% 0.75/0.97 (b(elem!1, s(s(s(z)))) <=> b(s(s(s(elem!1))), s(s(s(z))))),
% 0.75/0.97 inference(monotonicity,[status(thm)],[4834])).
% 0.75/0.97 tff(4836,plain,
% 0.75/0.97 (~r(s(s(s(elem!1))), s(s(s(z))))),
% 0.75/0.97 inference(unit_resolution,[status(thm)],[2337, 180, 196])).
% 0.75/0.97 tff(4837,plain,
% 0.75/0.97 (s(s(elem!1)) = elem!1),
% 0.75/0.97 inference(unit_resolution,[status(thm)],[4821, 4253])).
% 0.75/0.97 tff(4838,plain,
% 0.75/0.97 (s(s(s(elem!1))) = elem!1),
% 0.75/0.97 inference(transitivity,[status(thm)],[4256, 4837])).
% 0.75/0.97 tff(4839,plain,
% 0.75/0.97 (r(s(s(s(elem!1))), s(s(s(z)))) <=> r(elem!1, s(s(s(z))))),
% 0.75/0.97 inference(monotonicity,[status(thm)],[4838])).
% 0.75/0.97 tff(4840,plain,
% 0.75/0.97 (r(elem!1, s(s(s(z)))) <=> r(s(s(s(elem!1))), s(s(s(z))))),
% 0.75/0.97 inference(symmetry,[status(thm)],[4839])).
% 0.75/0.97 tff(4841,assumption,(r(elem!1, s(s(s(z))))), introduced(assumption)).
% 0.75/0.97 tff(4842,plain,
% 0.75/0.97 (r(s(s(s(elem!1))), s(s(s(z))))),
% 0.75/0.97 inference(modus_ponens,[status(thm)],[4841, 4840])).
% 0.75/0.97 tff(4843,plain,
% 0.75/0.97 ($false),
% 0.75/0.97 inference(unit_resolution,[status(thm)],[4385, 4842])).
% 0.75/0.97 tff(4844,plain,(r(s(s(s(elem!1))), s(s(s(z)))) | (~r(elem!1, s(s(s(z))))) | (~(s(s(elem!1)) = s(s(s(elem!1)))))), inference(lemma,lemma(discharge,[]))).
% 0.75/0.97 tff(4845,plain,
% 0.75/0.97 (r(s(s(s(elem!1))), s(s(s(z)))) | (~r(elem!1, s(s(s(z)))))),
% 0.75/0.97 inference(unit_resolution,[status(thm)],[4844, 4810])).
% 0.75/0.97 tff(4846,plain,
% 0.75/0.97 (~r(elem!1, s(s(s(z))))),
% 0.75/0.97 inference(unit_resolution,[status(thm)],[4845, 4836])).
% 0.75/0.97 tff(4847,plain,
% 0.75/0.97 ((s(s(s(z))) = elem!1) <=> (s(s(s(z))) = s(s(s(elem!1))))),
% 0.75/0.97 inference(monotonicity,[status(thm)],[4834])).
% 0.75/0.97 tff(4848,plain,
% 0.75/0.97 ((s(s(s(z))) = elem!1) <=> (s(s(s(elem!1))) = s(s(s(z))))),
% 0.75/0.97 inference(transitivity,[status(thm)],[4847, 2166])).
% 0.75/0.97 tff(4849,plain,
% 0.75/0.97 ((s(s(s(elem!1))) = s(s(s(z)))) <=> (s(s(s(z))) = elem!1)),
% 0.75/0.97 inference(symmetry,[status(thm)],[4848])).
% 0.75/0.97 tff(4850,plain,
% 0.75/0.97 (s(s(s(s(elem!1)))) = s(s(s(elem!1)))),
% 0.75/0.97 inference(unit_resolution,[status(thm)],[4259, 4810])).
% 0.75/0.97 tff(4851,plain,
% 0.75/0.97 ((s(s(s(z))) = s(s(s(s(elem!1))))) <=> (s(s(s(z))) = s(s(s(elem!1))))),
% 0.75/0.97 inference(monotonicity,[status(thm)],[4850])).
% 0.75/0.97 tff(4852,plain,
% 0.75/0.97 ((s(s(s(z))) = s(s(s(s(elem!1))))) <=> (s(s(s(elem!1))) = s(s(s(z))))),
% 0.75/0.97 inference(transitivity,[status(thm)],[4851, 2166])).
% 0.75/0.97 tff(4853,plain,
% 0.75/0.97 ((s(s(s(z))) = s(s(s(s(elem!1))))) <=> (elem!1 = s(s(s(z))))),
% 0.75/0.97 inference(transitivity,[status(thm)],[4852, 4849, 332])).
% 0.75/0.97 tff(4854,plain,
% 0.75/0.97 ((~(s(s(s(z))) = s(s(s(s(elem!1)))))) <=> (~(elem!1 = s(s(s(z)))))),
% 0.75/0.97 inference(monotonicity,[status(thm)],[4853])).
% 0.75/0.97 tff(4855,plain,
% 0.75/0.97 (~(elem!1 = s(s(s(z))))),
% 0.75/0.97 inference(modus_ponens,[status(thm)],[279, 4854])).
% 0.75/0.97 tff(4856,plain,
% 0.75/0.97 (b(elem!1, s(s(s(z)))) | r(elem!1, s(s(s(z))))),
% 0.75/0.97 inference(unit_resolution,[status(thm)],[400, 4855])).
% 0.75/0.97 tff(4857,plain,
% 0.75/0.97 (b(elem!1, s(s(s(z))))),
% 0.75/0.97 inference(unit_resolution,[status(thm)],[4856, 4846])).
% 0.75/0.97 tff(4858,plain,
% 0.75/0.97 (b(s(s(s(elem!1))), s(s(s(z))))),
% 0.75/0.97 inference(modus_ponens,[status(thm)],[4857, 4835])).
% 0.75/0.97 tff(4859,plain,
% 0.75/0.97 (~r(s(s(s(s(z)))), s(s(s(z))))),
% 0.75/0.97 inference(unit_resolution,[status(thm)],[895, 14, 180, 3860])).
% 0.75/0.97 tff(4860,plain,
% 0.75/0.97 (b(s(s(s(s(z)))), s(s(s(z))))),
% 0.75/0.97 inference(unit_resolution,[status(thm)],[529, 4859])).
% 0.75/0.97 tff(4861,plain,
% 0.75/0.97 (((~![X0: $i, X2: $i, X1: $i] : ((~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~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, X2: $i, X1: $i] : ((~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~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)))))))),
% 0.75/0.97 inference(rewrite,[status(thm)],[])).
% 0.75/0.97 tff(4862,plain,
% 0.75/0.97 ((~![X0: $i, X2: $i, X1: $i] : ((~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~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)))))))),
% 0.75/0.97 inference(quant_inst,[status(thm)],[])).
% 0.75/0.97 tff(4863,plain,
% 0.75/0.97 ((~![X0: $i, X2: $i, X1: $i] : ((~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(elem!1))), s(s(s(z))))) | (~b(s(s(s(elem!1))), s(s(s(s(z))))))),
% 0.75/0.97 inference(modus_ponens,[status(thm)],[4862, 4861])).
% 0.75/0.97 tff(4864,plain,
% 0.75/0.97 (~b(s(s(s(elem!1))), s(s(s(s(z)))))),
% 0.75/0.97 inference(unit_resolution,[status(thm)],[4863, 117, 4860, 4858])).
% 0.75/0.97 tff(4865,assumption,(s(s(s(elem!1))) = s(s(s(s(z))))), introduced(assumption)).
% 0.75/0.97 tff(4866,plain,
% 0.75/0.97 (s(s(s(s(z)))) = s(s(s(elem!1)))),
% 0.75/0.97 inference(symmetry,[status(thm)],[4865])).
% 0.75/0.97 tff(4867,plain,
% 0.75/0.97 (s(s(s(s(z)))) = s(s(elem!1))),
% 0.75/0.97 inference(transitivity,[status(thm)],[4866, 4823])).
% 0.75/0.97 tff(4868,plain,
% 0.75/0.97 (inj_0(s(s(elem!1))) = inj_0(s(s(s(elem!1))))),
% 0.75/0.97 inference(monotonicity,[status(thm)],[4810])).
% 0.75/0.97 tff(4869,plain,
% 0.75/0.97 (s(elem!1) = s(s(elem!1))),
% 0.75/0.97 inference(transitivity,[status(thm)],[167, 4868, 151])).
% 0.75/0.97 tff(4870,plain,
% 0.75/0.97 ((s(s(s(s(z)))) = s(elem!1)) <=> (s(s(s(s(z)))) = s(s(elem!1)))),
% 0.75/0.97 inference(monotonicity,[status(thm)],[4869])).
% 0.75/0.97 tff(4871,plain,
% 0.75/0.97 ((~(s(s(s(s(z)))) = s(elem!1))) <=> (~(s(s(s(s(z)))) = s(s(elem!1))))),
% 0.75/0.97 inference(monotonicity,[status(thm)],[4870])).
% 0.75/0.97 tff(4872,plain,
% 0.75/0.97 (s(s(s(s(elem!1)))) = s(s(elem!1))),
% 0.75/0.97 inference(unit_resolution,[status(thm)],[4263, 4810])).
% 0.75/0.97 tff(4873,plain,
% 0.75/0.97 (~(s(s(s(s(z)))) = s(elem!1))),
% 0.75/0.97 inference(unit_resolution,[status(thm)],[476, 4872])).
% 0.75/0.97 tff(4874,plain,
% 0.75/0.97 (~(s(s(s(s(z)))) = s(s(elem!1)))),
% 0.75/0.97 inference(modus_ponens,[status(thm)],[4873, 4871])).
% 0.75/0.97 tff(4875,plain,
% 0.75/0.97 ($false),
% 0.75/0.97 inference(unit_resolution,[status(thm)],[4874, 4867])).
% 0.75/0.97 tff(4876,plain,(~(s(s(s(elem!1))) = s(s(s(s(z)))))), inference(lemma,lemma(discharge,[]))).
% 0.75/0.97 tff(4877,plain,
% 0.75/0.97 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), z)) | (~r(s(s(s(elem!1))), s(s(s(s(z)))))) | (~r(s(s(s(s(z)))), z)))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(elem!1))), z)) | (~r(s(s(s(elem!1))), s(s(s(s(z)))))) | (~r(s(s(s(s(z)))), z)))),
% 0.75/0.97 inference(rewrite,[status(thm)],[])).
% 0.75/0.97 tff(4878,plain,
% 0.75/0.97 (((~r(s(s(s(s(z)))), z)) | (~r(s(s(s(elem!1))), z)) | (~r(s(s(s(elem!1))), s(s(s(s(z))))))) <=> ((~r(s(s(s(elem!1))), z)) | (~r(s(s(s(elem!1))), s(s(s(s(z)))))) | (~r(s(s(s(s(z)))), z)))),
% 0.75/0.97 inference(rewrite,[status(thm)],[])).
% 0.75/0.97 tff(4879,plain,
% 0.75/0.97 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(z)))), z)) | (~r(s(s(s(elem!1))), z)) | (~r(s(s(s(elem!1))), s(s(s(s(z)))))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), z)) | (~r(s(s(s(elem!1))), s(s(s(s(z)))))) | (~r(s(s(s(s(z)))), z))))),
% 0.75/0.97 inference(monotonicity,[status(thm)],[4878])).
% 0.75/0.97 tff(4880,plain,
% 0.75/0.97 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(z)))), z)) | (~r(s(s(s(elem!1))), z)) | (~r(s(s(s(elem!1))), s(s(s(s(z)))))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(elem!1))), z)) | (~r(s(s(s(elem!1))), s(s(s(s(z)))))) | (~r(s(s(s(s(z)))), z)))),
% 0.75/0.97 inference(transitivity,[status(thm)],[4879, 4877])).
% 0.75/0.97 tff(4881,plain,
% 0.75/0.97 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(z)))), z)) | (~r(s(s(s(elem!1))), z)) | (~r(s(s(s(elem!1))), s(s(s(s(z)))))))),
% 0.75/0.97 inference(quant_inst,[status(thm)],[])).
% 0.75/0.97 tff(4882,plain,
% 0.75/0.97 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(elem!1))), z)) | (~r(s(s(s(elem!1))), s(s(s(s(z)))))) | (~r(s(s(s(s(z)))), z))),
% 0.75/0.97 inference(modus_ponens,[status(thm)],[4881, 4880])).
% 0.75/0.97 tff(4883,plain,
% 0.75/0.97 (~r(s(s(s(elem!1))), s(s(s(s(z)))))),
% 0.75/0.97 inference(unit_resolution,[status(thm)],[4882, 14, 196, 3860])).
% 0.75/0.97 tff(4884,plain,
% 0.75/0.97 (((~![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))))))),
% 0.75/0.97 inference(rewrite,[status(thm)],[])).
% 0.75/0.97 tff(4885,plain,
% 0.75/0.97 ((~![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))))))),
% 0.75/0.97 inference(quant_inst,[status(thm)],[])).
% 0.75/0.97 tff(4886,plain,
% 0.75/0.97 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (s(s(s(elem!1))) = s(s(s(s(z))))) | b(s(s(s(elem!1))), s(s(s(s(z))))) | r(s(s(s(elem!1))), s(s(s(s(z)))))),
% 0.75/0.97 inference(modus_ponens,[status(thm)],[4885, 4884])).
% 0.75/0.97 tff(4887,plain,
% 0.75/0.97 ($false),
% 0.75/0.97 inference(unit_resolution,[status(thm)],[4886, 46, 4883, 4876, 4864])).
% 0.75/0.97 tff(4888,plain,((~r(s(s(s(s(z)))), z)) | (~r(s(s(s(elem!1))), z)) | (~r(s(s(s(z))), z))), inference(lemma,lemma(discharge,[]))).
% 0.75/0.97 tff(4889,plain,
% 0.75/0.97 (~r(s(s(s(s(z)))), z)),
% 0.75/0.97 inference(unit_resolution,[status(thm)],[4888, 180, 4832])).
% 0.75/0.97 tff(4890,plain,
% 0.75/0.97 (b(s(s(s(s(z)))), z)),
% 0.75/0.97 inference(unit_resolution,[status(thm)],[582, 4889])).
% 0.75/0.97 tff(4891,plain,
% 0.75/0.97 (((~![X0: $i, X2: $i, X1: $i] : ((~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), z)) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(s(z)))), s(z))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), z)) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(s(z)))), s(z))))),
% 0.75/0.97 inference(rewrite,[status(thm)],[])).
% 0.75/0.97 tff(4892,plain,
% 0.75/0.97 ((~![X0: $i, X2: $i, X1: $i] : ((~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(z), z)) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(s(z)))), s(z))))),
% 0.75/0.97 inference(quant_inst,[status(thm)],[])).
% 0.75/0.97 tff(4893,plain,
% 0.75/0.97 ((~![X0: $i, X2: $i, X1: $i] : ((~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(z), z)) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(s(z)))), s(z)))),
% 0.75/0.97 inference(modus_ponens,[status(thm)],[4892, 4891])).
% 0.75/0.97 tff(4894,plain,
% 0.75/0.97 ($false),
% 0.75/0.97 inference(unit_resolution,[status(thm)],[4893, 117, 237, 562, 905])).
% 0.75/0.97 tff(4895,plain,((~b(s(s(s(s(z)))), z)) | (~b(s(z), z)) | (~b(s(s(s(s(z)))), s(z)))), inference(lemma,lemma(discharge,[]))).
% 0.75/0.97 tff(4896,plain,
% 0.75/0.97 (~b(s(s(s(s(z)))), s(z))),
% 0.75/0.97 inference(unit_resolution,[status(thm)],[4895, 4890, 237])).
% 0.75/0.97 tff(4897,plain,
% 0.75/0.97 (r(s(s(s(s(z)))), s(z))),
% 0.75/0.97 inference(unit_resolution,[status(thm)],[554, 4896])).
% 0.75/0.97 tff(4898,plain,
% 0.75/0.97 (b(s(s(s(z))), elem!1) <=> b(s(s(s(z))), s(s(elem!1)))),
% 0.75/0.97 inference(monotonicity,[status(thm)],[4833])).
% 0.75/0.97 tff(4899,plain,
% 0.75/0.97 (r(s(s(s(z))), elem!1) <=> r(s(s(s(z))), s(s(s(elem!1))))),
% 0.75/0.97 inference(monotonicity,[status(thm)],[4834])).
% 0.75/0.97 tff(4900,plain,
% 0.75/0.97 (r(s(s(s(z))), s(s(s(elem!1)))) <=> r(s(s(s(z))), elem!1)),
% 0.75/0.97 inference(symmetry,[status(thm)],[4899])).
% 0.75/0.97 tff(4901,plain,
% 0.75/0.97 ((~r(s(s(s(z))), s(s(s(elem!1))))) <=> (~r(s(s(s(z))), elem!1))),
% 0.75/0.97 inference(monotonicity,[status(thm)],[4900])).
% 0.75/0.97 tff(4902,plain,
% 0.75/0.97 (~r(s(s(s(z))), s(s(s(elem!1))))),
% 0.75/0.97 inference(unit_resolution,[status(thm)],[1713, 14, 4832, 180])).
% 0.75/0.97 tff(4903,plain,
% 0.75/0.97 (~r(s(s(s(z))), elem!1)),
% 0.75/0.97 inference(modus_ponens,[status(thm)],[4902, 4901])).
% 0.75/0.97 tff(4904,plain,
% 0.75/0.97 ((s(s(s(z))) = s(s(s(s(elem!1))))) <=> (s(s(s(z))) = elem!1)),
% 0.75/0.97 inference(transitivity,[status(thm)],[4852, 4849])).
% 0.75/0.97 tff(4905,plain,
% 0.75/0.97 ((~(s(s(s(z))) = s(s(s(s(elem!1)))))) <=> (~(s(s(s(z))) = elem!1))),
% 0.75/0.97 inference(monotonicity,[status(thm)],[4904])).
% 0.75/0.97 tff(4906,plain,
% 0.75/0.97 (~(s(s(s(z))) = elem!1)),
% 0.75/0.97 inference(modus_ponens,[status(thm)],[279, 4905])).
% 0.75/0.97 tff(4907,plain,
% 0.75/0.97 (b(s(s(s(z))), elem!1) | r(s(s(s(z))), elem!1)),
% 0.75/0.97 inference(unit_resolution,[status(thm)],[756, 4906])).
% 0.75/0.97 tff(4908,plain,
% 0.75/0.97 (b(s(s(s(z))), elem!1)),
% 0.75/0.97 inference(unit_resolution,[status(thm)],[4907, 4903])).
% 0.75/0.97 tff(4909,plain,
% 0.75/0.97 (b(s(s(s(z))), s(s(elem!1)))),
% 0.75/0.97 inference(modus_ponens,[status(thm)],[4908, 4898])).
% 0.75/0.97 tff(4910,plain,
% 0.75/0.97 (~r(z, s(z))),
% 0.75/0.97 inference(unit_resolution,[status(thm)],[868, 181, 182])).
% 0.75/0.97 tff(4911,plain,
% 0.75/0.97 (b(z, s(z))),
% 0.75/0.97 inference(unit_resolution,[status(thm)],[599, 4910])).
% 0.75/0.97 tff(4912,plain,
% 0.75/0.97 ((elem!1 = s(s(s(s(z))))) <=> (s(s(elem!1)) = s(s(s(s(z)))))),
% 0.75/0.97 inference(monotonicity,[status(thm)],[4833])).
% 0.75/0.97 tff(4913,plain,
% 0.75/0.97 ((elem!1 = s(s(s(s(z))))) <=> (s(s(s(s(z)))) = s(s(elem!1)))),
% 0.75/0.97 inference(transitivity,[status(thm)],[4912, 2418])).
% 0.75/0.97 tff(4914,plain,
% 0.75/0.97 ((s(s(s(s(z)))) = s(s(elem!1))) <=> (elem!1 = s(s(s(s(z)))))),
% 0.75/0.97 inference(symmetry,[status(thm)],[4913])).
% 0.75/0.97 tff(4915,plain,
% 0.75/0.97 ((s(s(s(s(z)))) = s(elem!1)) <=> (s(s(s(s(z)))) = elem!1)),
% 0.75/0.98 inference(transitivity,[status(thm)],[4870, 4914, 294])).
% 0.75/0.98 tff(4916,plain,
% 0.75/0.98 ((~(s(s(s(s(z)))) = s(elem!1))) <=> (~(s(s(s(s(z)))) = elem!1))),
% 0.75/0.98 inference(monotonicity,[status(thm)],[4915])).
% 0.75/0.98 tff(4917,plain,
% 0.75/0.98 (~(s(s(s(s(z)))) = elem!1)),
% 0.75/0.98 inference(modus_ponens,[status(thm)],[4873, 4916])).
% 0.75/0.98 tff(4918,plain,
% 0.75/0.98 ((~r(s(s(s(s(z)))), s(z))) | (~b(s(s(s(z))), s(s(elem!1)))) | (~r(s(s(s(z))), s(z))) | (~r(s(s(elem!1)), s(z)))),
% 0.75/0.98 inference(unit_resolution,[status(thm)],[1071, 4822, 4917])).
% 0.75/0.98 tff(4919,plain,
% 0.75/0.98 (~r(s(s(s(z))), s(z))),
% 0.75/0.98 inference(unit_resolution,[status(thm)],[4918, 181, 837, 3])).
% 0.75/0.98 tff(4920,plain,
% 0.75/0.98 (b(s(s(s(z))), s(z))),
% 0.75/0.98 inference(unit_resolution,[status(thm)],[347, 4919])).
% 0.75/0.98 tff(4921,plain,
% 0.75/0.98 (((~![X0: $i, X2: $i, X1: $i] : ((~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(z))) | (~b(s(s(z)), s(z))) | (~b(s(s(z)), z)))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(z))) | (~b(s(s(z)), s(z))) | (~b(s(s(z)), z)))),
% 0.75/0.98 inference(rewrite,[status(thm)],[])).
% 0.75/0.98 tff(4922,plain,
% 0.75/0.98 ((~![X0: $i, X2: $i, X1: $i] : ((~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(z))) | (~b(s(s(z)), s(z))) | (~b(s(s(z)), z)))),
% 0.75/0.98 inference(quant_inst,[status(thm)],[])).
% 0.75/0.98 tff(4923,plain,
% 0.75/0.98 ((~![X0: $i, X2: $i, X1: $i] : ((~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(z))) | (~b(s(s(z)), s(z))) | (~b(s(s(z)), z))),
% 0.75/0.98 inference(modus_ponens,[status(thm)],[4922, 4921])).
% 0.75/0.98 tff(4924,plain,
% 0.75/0.98 (~b(s(s(z)), z)),
% 0.75/0.98 inference(unit_resolution,[status(thm)],[4923, 117, 574, 1])).
% 0.75/0.98 tff(4925,plain,
% 0.75/0.98 (r(s(s(z)), z)),
% 0.75/0.98 inference(unit_resolution,[status(thm)],[62, 46, 59, 4924])).
% 0.75/0.98 tff(4926,plain,
% 0.75/0.98 (((~![X0: $i, X2: $i, X1: $i] : ((~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), s(z))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(z)), s(s(s(z))))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(z)), s(z))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(z)), s(s(s(z))))))),
% 0.75/0.98 inference(rewrite,[status(thm)],[])).
% 0.75/0.98 tff(4927,plain,
% 0.75/0.98 (((~b(s(s(s(z))), s(z))) | (~b(s(s(z)), s(z))) | (~b(s(s(z)), s(s(s(z)))))) <=> ((~b(s(s(z)), s(z))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(z)), s(s(s(z))))))),
% 0.75/0.98 inference(rewrite,[status(thm)],[])).
% 0.75/0.98 tff(4928,plain,
% 0.75/0.98 (((~![X0: $i, X2: $i, X1: $i] : ((~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), s(z))) | (~b(s(s(z)), s(z))) | (~b(s(s(z)), s(s(s(z))))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), s(z))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(z)), s(s(s(z)))))))),
% 0.75/0.98 inference(monotonicity,[status(thm)],[4927])).
% 0.75/0.98 tff(4929,plain,
% 0.75/0.98 (((~![X0: $i, X2: $i, X1: $i] : ((~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), s(z))) | (~b(s(s(z)), s(z))) | (~b(s(s(z)), s(s(s(z))))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(z)), s(z))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(z)), s(s(s(z))))))),
% 0.75/0.98 inference(transitivity,[status(thm)],[4928, 4926])).
% 0.75/0.98 tff(4930,plain,
% 0.75/0.98 ((~![X0: $i, X2: $i, X1: $i] : ((~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), s(z))) | (~b(s(s(z)), s(z))) | (~b(s(s(z)), s(s(s(z))))))),
% 0.75/0.98 inference(quant_inst,[status(thm)],[])).
% 0.75/0.98 tff(4931,plain,
% 0.75/0.98 ((~![X0: $i, X2: $i, X1: $i] : ((~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(z)), s(z))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(z)), s(s(s(z)))))),
% 0.75/0.98 inference(modus_ponens,[status(thm)],[4930, 4929])).
% 0.75/0.98 tff(4932,plain,
% 0.75/0.98 (~b(s(s(z)), s(s(s(z))))),
% 0.75/0.98 inference(unit_resolution,[status(thm)],[4931, 117, 848, 1])).
% 0.75/0.98 tff(4933,plain,
% 0.75/0.98 ((s(s(s(z))) = s(s(z))) <=> (s(s(z)) = s(s(s(z))))),
% 0.75/0.98 inference(commutativity,[status(thm)],[])).
% 0.75/0.98 tff(4934,plain,
% 0.75/0.98 ((~(s(s(s(z))) = s(s(z)))) <=> (~(s(s(z)) = s(s(s(z)))))),
% 0.75/0.98 inference(monotonicity,[status(thm)],[4933])).
% 0.75/0.98 tff(4935,assumption,(s(s(s(z))) = s(s(z))), introduced(assumption)).
% 0.75/0.98 tff(4936,plain,
% 0.75/0.98 (s(s(z)) = s(s(s(z)))),
% 0.75/0.98 inference(symmetry,[status(thm)],[4935])).
% 0.75/0.98 tff(4937,plain,
% 0.75/0.98 (inj_0(s(s(z))) = inj_0(s(s(s(z))))),
% 0.75/0.98 inference(monotonicity,[status(thm)],[4936])).
% 0.75/0.98 tff(4938,plain,
% 0.75/0.98 (s(z) = s(s(z))),
% 0.75/0.98 inference(transitivity,[status(thm)],[131, 4937, 94])).
% 0.75/0.98 tff(4939,plain,
% 0.75/0.98 ((s(s(z)) = s(z)) <=> (s(z) = s(s(z)))),
% 0.75/0.98 inference(commutativity,[status(thm)],[])).
% 0.75/0.98 tff(4940,plain,
% 0.75/0.98 ((~(s(s(z)) = s(z))) <=> (~(s(z) = s(s(z))))),
% 0.75/0.98 inference(monotonicity,[status(thm)],[4939])).
% 0.75/0.98 tff(4941,plain,
% 0.75/0.98 (~(s(z) = s(s(z)))),
% 0.75/0.98 inference(modus_ponens,[status(thm)],[136, 4940])).
% 0.75/0.98 tff(4942,plain,
% 0.75/0.98 ($false),
% 0.75/0.98 inference(unit_resolution,[status(thm)],[4941, 4938])).
% 0.75/0.98 tff(4943,plain,(~(s(s(s(z))) = s(s(z)))), inference(lemma,lemma(discharge,[]))).
% 0.75/0.98 tff(4944,plain,
% 0.75/0.98 (~(s(s(z)) = s(s(s(z))))),
% 0.75/0.98 inference(modus_ponens,[status(thm)],[4943, 4934])).
% 0.75/0.98 tff(4945,plain,
% 0.75/0.98 (((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((s(s(z)) = s(s(s(z)))) | b(s(s(z)), s(s(s(z)))) | r(s(s(z)), s(s(s(z)))))) <=> ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (s(s(z)) = s(s(s(z)))) | b(s(s(z)), s(s(s(z)))) | r(s(s(z)), s(s(s(z)))))),
% 0.75/0.98 inference(rewrite,[status(thm)],[])).
% 0.75/0.98 tff(4946,plain,
% 0.75/0.98 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((s(s(z)) = s(s(s(z)))) | b(s(s(z)), s(s(s(z)))) | r(s(s(z)), s(s(s(z)))))),
% 0.75/0.98 inference(quant_inst,[status(thm)],[])).
% 0.75/0.98 tff(4947,plain,
% 0.75/0.98 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (s(s(z)) = s(s(s(z)))) | b(s(s(z)), s(s(s(z)))) | r(s(s(z)), s(s(s(z))))),
% 0.75/0.98 inference(modus_ponens,[status(thm)],[4946, 4945])).
% 0.75/0.98 tff(4948,plain,
% 0.75/0.98 ((s(s(z)) = s(s(s(z)))) | b(s(s(z)), s(s(s(z)))) | r(s(s(z)), s(s(s(z))))),
% 0.75/0.98 inference(unit_resolution,[status(thm)],[4947, 46])).
% 0.75/0.98 tff(4949,plain,
% 0.75/0.98 (b(s(s(z)), s(s(s(z)))) | r(s(s(z)), s(s(s(z))))),
% 0.75/0.98 inference(unit_resolution,[status(thm)],[4948, 4944])).
% 0.75/0.98 tff(4950,plain,
% 0.75/0.98 (r(s(s(z)), s(s(s(z))))),
% 0.75/0.98 inference(unit_resolution,[status(thm)],[4949, 4932])).
% 0.75/0.98 tff(4951,plain,
% 0.75/0.98 (((~![X0: $i, X2: $i, X1: $i] : ((~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(z))) | (~b(z, s(s(s(z))))) | (~b(s(s(s(z))), s(z))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(z))) | (~b(z, s(s(s(z))))) | (~b(s(s(s(z))), s(z))))),
% 0.75/0.98 inference(rewrite,[status(thm)],[])).
% 0.75/0.98 tff(4952,plain,
% 0.75/0.98 (((~b(s(s(s(z))), s(z))) | (~b(z, s(z))) | (~b(z, s(s(s(z)))))) <=> ((~b(z, s(z))) | (~b(z, s(s(s(z))))) | (~b(s(s(s(z))), s(z))))),
% 0.75/0.98 inference(rewrite,[status(thm)],[])).
% 0.75/0.98 tff(4953,plain,
% 0.75/0.98 (((~![X0: $i, X2: $i, X1: $i] : ((~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), s(z))) | (~b(z, s(z))) | (~b(z, s(s(s(z))))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(z))) | (~b(z, s(s(s(z))))) | (~b(s(s(s(z))), s(z)))))),
% 0.75/0.98 inference(monotonicity,[status(thm)],[4952])).
% 0.75/0.98 tff(4954,plain,
% 0.75/0.98 (((~![X0: $i, X2: $i, X1: $i] : ((~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), s(z))) | (~b(z, s(z))) | (~b(z, s(s(s(z))))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(z))) | (~b(z, s(s(s(z))))) | (~b(s(s(s(z))), s(z))))),
% 0.75/0.98 inference(transitivity,[status(thm)],[4953, 4951])).
% 0.75/0.98 tff(4955,plain,
% 0.75/0.98 ((~![X0: $i, X2: $i, X1: $i] : ((~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), s(z))) | (~b(z, s(z))) | (~b(z, s(s(s(z))))))),
% 0.75/0.98 inference(quant_inst,[status(thm)],[])).
% 0.75/0.98 tff(4956,plain,
% 0.75/0.98 ((~![X0: $i, X2: $i, X1: $i] : ((~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(z))) | (~b(z, s(s(s(z))))) | (~b(s(s(s(z))), s(z)))),
% 0.75/0.98 inference(modus_ponens,[status(thm)],[4955, 4954])).
% 0.75/0.98 tff(4957,plain,
% 0.75/0.98 (~b(z, s(s(s(z))))),
% 0.75/0.98 inference(unit_resolution,[status(thm)],[4956, 117, 574, 848])).
% 0.75/0.98 tff(4958,plain,
% 0.75/0.98 (r(z, s(s(s(z))))),
% 0.75/0.98 inference(unit_resolution,[status(thm)],[711, 4957])).
% 0.75/0.98 tff(4959,plain,
% 0.75/0.98 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(s(z))))) | (~r(s(s(z)), z)) | (~r(s(s(z)), s(s(s(z))))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, s(s(s(z))))) | (~r(s(s(z)), z)) | (~r(s(s(z)), s(s(s(z))))))),
% 0.75/0.98 inference(rewrite,[status(thm)],[])).
% 0.75/0.98 tff(4960,plain,
% 0.75/0.98 (((~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))))))),
% 0.75/0.98 inference(rewrite,[status(thm)],[])).
% 0.75/0.98 tff(4961,plain,
% 0.75/0.98 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(s(z))))) | (~r(s(s(z)), s(s(s(z))))) | (~r(s(s(z)), z)))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(s(z))))) | (~r(s(s(z)), z)) | (~r(s(s(z)), s(s(s(z)))))))),
% 0.75/0.98 inference(monotonicity,[status(thm)],[4960])).
% 0.75/0.98 tff(4962,plain,
% 0.75/0.98 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(s(z))))) | (~r(s(s(z)), s(s(s(z))))) | (~r(s(s(z)), z)))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, s(s(s(z))))) | (~r(s(s(z)), z)) | (~r(s(s(z)), s(s(s(z))))))),
% 0.75/0.98 inference(transitivity,[status(thm)],[4961, 4959])).
% 0.75/0.98 tff(4963,plain,
% 0.75/0.98 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(s(z))))) | (~r(s(s(z)), s(s(s(z))))) | (~r(s(s(z)), z)))),
% 0.75/0.98 inference(quant_inst,[status(thm)],[])).
% 0.75/0.98 tff(4964,plain,
% 0.75/0.98 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, s(s(s(z))))) | (~r(s(s(z)), z)) | (~r(s(s(z)), s(s(s(z)))))),
% 0.75/0.98 inference(modus_ponens,[status(thm)],[4963, 4962])).
% 0.75/0.98 tff(4965,plain,
% 0.75/0.98 ($false),
% 0.75/0.98 inference(unit_resolution,[status(thm)],[4964, 14, 4958, 4950, 4925])).
% 0.75/0.98 tff(4966,plain,((~b(s(s(z)), s(z))) | (~b(s(s(s(z))), s(z))) | (~b(z, s(z)))), inference(lemma,lemma(discharge,[]))).
% 0.75/0.98 tff(4967,plain,
% 0.75/0.98 (~b(s(s(z)), s(z))),
% 0.75/0.98 inference(unit_resolution,[status(thm)],[4966, 4920, 4911])).
% 0.75/0.98 tff(4968,plain,
% 0.75/0.98 (r(s(s(z)), s(z))),
% 0.75/0.98 inference(unit_resolution,[status(thm)],[141, 4967])).
% 0.75/0.98 tff(4969,plain,
% 0.75/0.98 (r(s(s(elem!1)), s(z)) <=> r(s(s(s(elem!1))), s(z))),
% 0.75/0.98 inference(monotonicity,[status(thm)],[4810])).
% 0.75/0.98 tff(4970,plain,
% 0.75/0.98 (r(s(s(s(elem!1))), s(z))),
% 0.75/0.98 inference(modus_ponens,[status(thm)],[181, 4969])).
% 0.75/0.98 tff(4971,plain,
% 0.75/0.98 (((~![X0: $i, X2: $i, X1: $i] : ((~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(z)), s(z))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~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(z)), s(z))))),
% 0.75/0.98 inference(rewrite,[status(thm)],[])).
% 0.75/0.98 tff(4972,plain,
% 0.75/0.98 (((~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(s(s(elem!1))))) | (~r(s(s(z)), s(z))))),
% 0.75/0.98 inference(rewrite,[status(thm)],[])).
% 0.75/0.98 tff(4973,plain,
% 0.75/0.98 (((~![X0: $i, X2: $i, X1: $i] : ((~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))))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~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(z)), s(z)))))),
% 0.75/0.98 inference(monotonicity,[status(thm)],[4972])).
% 0.75/0.98 tff(4974,plain,
% 0.75/0.98 (((~![X0: $i, X2: $i, X1: $i] : ((~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))))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~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(z)), s(z))))),
% 0.75/0.98 inference(transitivity,[status(thm)],[4973, 4971])).
% 0.75/0.98 tff(4975,plain,
% 0.75/0.98 ((~![X0: $i, X2: $i, X1: $i] : ((~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))))))),
% 0.75/0.98 inference(quant_inst,[status(thm)],[])).
% 0.75/0.98 tff(4976,plain,
% 0.75/0.98 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(elem!1))), s(z))) | (~r(s(s(z)), s(s(s(elem!1))))) | (~r(s(s(z)), s(z)))),
% 0.75/0.98 inference(modus_ponens,[status(thm)],[4975, 4974])).
% 0.75/0.98 tff(4977,plain,
% 0.75/0.98 (~r(s(s(z)), s(s(s(elem!1))))),
% 0.75/0.98 inference(unit_resolution,[status(thm)],[4976, 14, 4970, 4968])).
% 0.75/0.98 tff(4978,plain,
% 0.75/0.98 (~r(s(s(z)), elem!1)),
% 0.75/0.98 inference(modus_ponens,[status(thm)],[4977, 4828])).
% 0.75/0.98 tff(4979,plain,
% 0.75/0.98 ((elem!1 = s(s(z))) <=> (s(s(z)) = elem!1)),
% 0.75/0.98 inference(commutativity,[status(thm)],[])).
% 0.75/0.98 tff(4980,plain,
% 0.75/0.98 ((~(elem!1 = s(s(z)))) <=> (~(s(s(z)) = elem!1))),
% 0.75/0.98 inference(monotonicity,[status(thm)],[4979])).
% 0.75/0.98 tff(4981,assumption,(elem!1 = s(s(z))), introduced(assumption)).
% 0.75/0.98 tff(4982,plain,
% 0.75/0.98 (s(s(z)) = elem!1),
% 0.75/0.98 inference(symmetry,[status(thm)],[4981])).
% 0.75/0.98 tff(4983,plain,
% 0.75/0.98 (s(s(z)) = s(s(s(elem!1)))),
% 0.75/0.98 inference(transitivity,[status(thm)],[4982, 4833, 4810])).
% 0.75/0.98 tff(4984,plain,
% 0.75/0.98 (inj_0(s(s(z))) = inj_0(s(s(s(elem!1))))),
% 0.75/0.98 inference(monotonicity,[status(thm)],[4983])).
% 0.75/0.98 tff(4985,plain,
% 0.75/0.98 (s(z) = s(s(s(elem!1)))),
% 0.75/0.98 inference(transitivity,[status(thm)],[131, 4984, 151, 4810])).
% 0.75/0.98 tff(4986,plain,
% 0.75/0.98 ($false),
% 0.75/0.98 inference(unit_resolution,[status(thm)],[230, 4985])).
% 0.75/0.98 tff(4987,plain,(~(elem!1 = s(s(z)))), inference(lemma,lemma(discharge,[]))).
% 0.75/0.98 tff(4988,plain,
% 0.75/0.98 (~(s(s(z)) = elem!1)),
% 0.75/0.98 inference(modus_ponens,[status(thm)],[4987, 4980])).
% 0.75/0.98 tff(4989,plain,
% 0.75/0.98 (((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((s(s(z)) = elem!1) | b(s(s(z)), elem!1) | r(s(s(z)), elem!1))) <=> ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (s(s(z)) = elem!1) | b(s(s(z)), elem!1) | r(s(s(z)), elem!1))),
% 0.75/0.98 inference(rewrite,[status(thm)],[])).
% 0.75/0.98 tff(4990,plain,
% 0.75/0.98 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((s(s(z)) = elem!1) | b(s(s(z)), elem!1) | r(s(s(z)), elem!1))),
% 0.75/0.98 inference(quant_inst,[status(thm)],[])).
% 0.75/0.98 tff(4991,plain,
% 0.75/0.98 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (s(s(z)) = elem!1) | b(s(s(z)), elem!1) | r(s(s(z)), elem!1)),
% 0.75/0.98 inference(modus_ponens,[status(thm)],[4990, 4989])).
% 0.75/0.98 tff(4992,plain,
% 0.75/0.98 ((s(s(z)) = elem!1) | b(s(s(z)), elem!1) | r(s(s(z)), elem!1)),
% 0.75/0.98 inference(unit_resolution,[status(thm)],[4991, 46])).
% 0.75/0.98 tff(4993,plain,
% 0.75/0.98 (b(s(s(z)), elem!1) | r(s(s(z)), elem!1)),
% 0.75/0.98 inference(unit_resolution,[status(thm)],[4992, 4988])).
% 0.75/0.98 tff(4994,plain,
% 0.75/0.98 (b(s(s(z)), elem!1)),
% 0.75/0.98 inference(unit_resolution,[status(thm)],[4993, 4978])).
% 0.75/0.98 tff(4995,plain,
% 0.75/0.98 (b(s(s(z)), s(s(s(elem!1))))),
% 0.75/0.98 inference(modus_ponens,[status(thm)],[4994, 4826])).
% 0.75/0.98 tff(4996,plain,
% 0.75/0.98 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), s(z))) | (~r(s(s(s(elem!1))), s(s(s(s(z)))))) | (~r(s(s(s(s(z)))), s(z))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(elem!1))), s(z))) | (~r(s(s(s(elem!1))), s(s(s(s(z)))))) | (~r(s(s(s(s(z)))), s(z))))),
% 0.75/0.98 inference(rewrite,[status(thm)],[])).
% 0.75/0.98 tff(4997,plain,
% 0.75/0.98 (((~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(s(s(elem!1))), s(s(s(s(z)))))) | (~r(s(s(s(s(z)))), s(z))))),
% 0.75/0.98 inference(rewrite,[status(thm)],[])).
% 0.75/0.98 tff(4998,plain,
% 0.75/0.98 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(z)))), s(z))) | (~r(s(s(s(elem!1))), s(z))) | (~r(s(s(s(elem!1))), s(s(s(s(z)))))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), s(z))) | (~r(s(s(s(elem!1))), s(s(s(s(z)))))) | (~r(s(s(s(s(z)))), s(z)))))),
% 0.75/0.98 inference(monotonicity,[status(thm)],[4997])).
% 0.75/0.98 tff(4999,plain,
% 0.75/0.98 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(z)))), s(z))) | (~r(s(s(s(elem!1))), s(z))) | (~r(s(s(s(elem!1))), s(s(s(s(z)))))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(elem!1))), s(z))) | (~r(s(s(s(elem!1))), s(s(s(s(z)))))) | (~r(s(s(s(s(z)))), s(z))))),
% 0.75/0.98 inference(transitivity,[status(thm)],[4998, 4996])).
% 0.75/0.98 tff(5000,plain,
% 0.75/0.98 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(z)))), s(z))) | (~r(s(s(s(elem!1))), s(z))) | (~r(s(s(s(elem!1))), s(s(s(s(z)))))))),
% 0.75/0.98 inference(quant_inst,[status(thm)],[])).
% 0.75/0.98 tff(5001,plain,
% 0.75/0.98 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(elem!1))), s(z))) | (~r(s(s(s(elem!1))), s(s(s(s(z)))))) | (~r(s(s(s(s(z)))), s(z)))),
% 0.75/0.98 inference(modus_ponens,[status(thm)],[5000, 4999])).
% 0.75/0.98 tff(5002,plain,
% 0.75/0.98 (~r(s(s(s(elem!1))), s(s(s(s(z)))))),
% 0.75/0.98 inference(unit_resolution,[status(thm)],[5001, 14, 4970, 3])).
% 0.75/0.98 tff(5003,plain,
% 0.75/0.98 (b(s(s(s(elem!1))), s(s(s(s(z)))))),
% 0.75/0.98 inference(unit_resolution,[status(thm)],[4886, 46, 5002, 4876])).
% 0.75/0.98 tff(5004,plain,
% 0.75/0.98 (~r(s(s(z)), s(s(s(s(z)))))),
% 0.75/0.98 inference(unit_resolution,[status(thm)],[69, 14, 3, 4968])).
% 0.75/0.98 tff(5005,plain,
% 0.75/0.98 (b(s(s(z)), s(s(s(s(z)))))),
% 0.75/0.98 inference(unit_resolution,[status(thm)],[106, 5004])).
% 0.75/0.98 tff(5006,plain,
% 0.75/0.98 (((~![X0: $i, X2: $i, X1: $i] : ((~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), s(s(s(s(z)))))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(z)), s(s(s(elem!1))))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(elem!1))), s(s(s(s(z)))))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(z)), s(s(s(elem!1))))))),
% 0.75/0.98 inference(rewrite,[status(thm)],[])).
% 0.75/0.98 tff(5007,plain,
% 0.75/0.98 ((~![X0: $i, X2: $i, X1: $i] : ((~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), s(s(s(s(z)))))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(z)), s(s(s(elem!1))))))),
% 0.75/0.98 inference(quant_inst,[status(thm)],[])).
% 0.75/0.98 tff(5008,plain,
% 0.75/0.98 ((~![X0: $i, X2: $i, X1: $i] : ((~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(elem!1))), s(s(s(s(z)))))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(z)), s(s(s(elem!1)))))),
% 0.75/0.98 inference(modus_ponens,[status(thm)],[5007, 5006])).
% 0.75/0.98 tff(5009,plain,
% 0.75/0.98 (~b(s(s(z)), s(s(s(elem!1))))),
% 0.75/0.98 inference(unit_resolution,[status(thm)],[5008, 117, 5005, 5003])).
% 0.75/0.98 tff(5010,plain,
% 0.75/0.98 ($false),
% 0.75/0.98 inference(unit_resolution,[status(thm)],[5009, 4995])).
% 0.75/0.98 tff(5011,plain,((~r(s(s(elem!1)), s(z))) | (~r(s(s(s(s(z)))), s(z))) | (~b(s(s(s(z))), s(s(elem!1)))) | (~r(s(s(elem!1)), z))), inference(lemma,lemma(discharge,[]))).
% 0.75/0.98 tff(5012,plain,
% 0.75/0.98 (~r(s(s(elem!1)), s(z))),
% 0.75/0.98 inference(unit_resolution,[status(thm)],[5011, 4897, 4909, 182])).
% 0.75/0.98 tff(5013,plain,
% 0.75/0.98 (b(s(s(elem!1)), s(z))),
% 0.75/0.98 inference(unit_resolution,[status(thm)],[178, 5012])).
% 0.75/0.98 tff(5014,plain,
% 0.75/0.98 (~b(s(s(s(z))), s(z))),
% 0.75/0.98 inference(unit_resolution,[status(thm)],[853, 5013, 4909])).
% 0.75/0.98 tff(5015,plain,
% 0.75/0.98 (r(s(s(s(z))), s(z))),
% 0.75/0.98 inference(unit_resolution,[status(thm)],[347, 5014])).
% 0.75/0.98 tff(5016,plain,
% 0.75/0.98 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(z)), s(z))) | (~r(s(s(s(z))), s(z))) | (~r(s(s(z)), s(s(s(z))))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(z)), s(z))) | (~r(s(s(s(z))), s(z))) | (~r(s(s(z)), s(s(s(z))))))),
% 0.75/0.98 inference(rewrite,[status(thm)],[])).
% 0.75/0.98 tff(5017,plain,
% 0.75/0.98 (((~r(s(s(s(z))), s(z))) | (~r(s(s(z)), s(z))) | (~r(s(s(z)), s(s(s(z)))))) <=> ((~r(s(s(z)), s(z))) | (~r(s(s(s(z))), s(z))) | (~r(s(s(z)), s(s(s(z))))))),
% 0.75/0.98 inference(rewrite,[status(thm)],[])).
% 0.75/0.98 tff(5018,plain,
% 0.75/0.98 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(z))), s(z))) | (~r(s(s(z)), s(z))) | (~r(s(s(z)), s(s(s(z))))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(z)), s(z))) | (~r(s(s(s(z))), s(z))) | (~r(s(s(z)), s(s(s(z)))))))),
% 0.75/0.98 inference(monotonicity,[status(thm)],[5017])).
% 0.75/0.98 tff(5019,plain,
% 0.75/0.98 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(z))), s(z))) | (~r(s(s(z)), s(z))) | (~r(s(s(z)), s(s(s(z))))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(z)), s(z))) | (~r(s(s(s(z))), s(z))) | (~r(s(s(z)), s(s(s(z))))))),
% 0.75/0.98 inference(transitivity,[status(thm)],[5018, 5016])).
% 0.75/0.98 tff(5020,plain,
% 0.75/0.98 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(z))), s(z))) | (~r(s(s(z)), s(z))) | (~r(s(s(z)), s(s(s(z))))))),
% 0.75/0.98 inference(quant_inst,[status(thm)],[])).
% 0.75/0.99 tff(5021,plain,
% 0.75/0.99 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(z)), s(z))) | (~r(s(s(s(z))), s(z))) | (~r(s(s(z)), s(s(s(z)))))),
% 0.75/0.99 inference(modus_ponens,[status(thm)],[5020, 5019])).
% 0.75/0.99 tff(5022,plain,
% 0.75/0.99 (~r(s(s(z)), s(s(s(z))))),
% 0.75/0.99 inference(unit_resolution,[status(thm)],[5021, 14, 283, 53])).
% 0.75/0.99 tff(5023,plain,
% 0.75/0.99 (b(s(s(z)), s(s(s(z))))),
% 0.75/0.99 inference(unit_resolution,[status(thm)],[4949, 5022])).
% 0.75/0.99 tff(5024,assumption,(r(s(s(s(z))), s(s(s(s(z)))))), introduced(assumption)).
% 0.75/0.99 tff(5025,plain,
% 0.75/0.99 ($false),
% 0.75/0.99 inference(unit_resolution,[status(thm)],[2796, 14, 5024, 3, 283])).
% 0.75/0.99 tff(5026,plain,((~r(s(s(s(z))), s(z))) | (~r(s(s(s(z))), s(s(s(s(z)))))) | (~r(s(s(s(s(z)))), s(z)))), inference(lemma,lemma(discharge,[]))).
% 0.75/0.99 tff(5027,plain,
% 0.75/0.99 (~r(s(s(s(z))), s(s(s(s(z)))))),
% 0.75/0.99 inference(unit_resolution,[status(thm)],[5026, 283, 3])).
% 0.75/0.99 tff(5028,plain,
% 0.75/0.99 (b(s(s(s(z))), s(s(s(s(z)))))),
% 0.75/0.99 inference(unit_resolution,[status(thm)],[2685, 5027])).
% 0.75/0.99 tff(5029,plain,
% 0.75/0.99 (((~![X0: $i, X2: $i, X1: $i] : ((~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(z)), s(s(s(z))))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(z)), s(s(s(z))))))),
% 0.75/0.99 inference(rewrite,[status(thm)],[])).
% 0.75/0.99 tff(5030,plain,
% 0.75/0.99 ((~![X0: $i, X2: $i, X1: $i] : ((~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(z)), s(s(s(z))))))),
% 0.75/0.99 inference(quant_inst,[status(thm)],[])).
% 0.75/0.99 tff(5031,plain,
% 0.75/0.99 ((~![X0: $i, X2: $i, X1: $i] : ((~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(z)), s(s(s(z)))))),
% 0.75/0.99 inference(modus_ponens,[status(thm)],[5030, 5029])).
% 0.75/0.99 tff(5032,plain,
% 0.75/0.99 ($false),
% 0.75/0.99 inference(unit_resolution,[status(thm)],[5031, 117, 5028, 5023, 107])).
% 0.75/0.99 tff(5033,plain,((~r(s(s(z)), s(z))) | (~r(s(s(s(z))), s(z))) | (~r(s(s(s(s(z)))), s(z)))), inference(lemma,lemma(discharge,[]))).
% 0.75/0.99 tff(5034,plain,
% 0.75/0.99 (~r(s(s(z)), s(z))),
% 0.75/0.99 inference(unit_resolution,[status(thm)],[5033, 5015, 4897])).
% 0.75/0.99 tff(5035,plain,
% 0.75/0.99 (b(s(s(z)), s(z))),
% 0.75/0.99 inference(unit_resolution,[status(thm)],[141, 5034])).
% 0.75/0.99 tff(5036,plain,
% 0.75/0.99 (b(s(s(s(elem!1))), s(z))),
% 0.75/0.99 inference(modus_ponens,[status(thm)],[5013, 4811])).
% 0.75/0.99 tff(5037,plain,
% 0.75/0.99 (((~![X0: $i, X2: $i, X1: $i] : ((~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(s(z)), s(s(s(elem!1))))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~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(s(z)), s(s(s(elem!1))))))),
% 0.75/0.99 inference(rewrite,[status(thm)],[])).
% 0.75/0.99 tff(5038,plain,
% 0.75/0.99 ((~![X0: $i, X2: $i, X1: $i] : ((~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(s(z)), s(s(s(elem!1))))))),
% 0.75/0.99 inference(quant_inst,[status(thm)],[])).
% 0.75/0.99 tff(5039,plain,
% 0.75/0.99 ((~![X0: $i, X2: $i, X1: $i] : ((~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(s(z)), s(s(s(elem!1)))))),
% 0.75/0.99 inference(modus_ponens,[status(thm)],[5038, 5037])).
% 0.75/0.99 tff(5040,plain,
% 0.75/0.99 (~b(s(s(z)), s(s(s(elem!1))))),
% 0.75/0.99 inference(unit_resolution,[status(thm)],[5039, 117, 5036, 5035])).
% 0.75/0.99 tff(5041,plain,
% 0.75/0.99 (~b(s(s(z)), elem!1)),
% 0.75/0.99 inference(modus_ponens,[status(thm)],[5040, 4830])).
% 0.75/0.99 tff(5042,plain,
% 0.75/0.99 (r(s(s(z)), elem!1)),
% 0.75/0.99 inference(unit_resolution,[status(thm)],[4993, 5041])).
% 0.75/0.99 tff(5043,plain,
% 0.75/0.99 (r(s(s(z)), s(s(s(elem!1))))),
% 0.75/0.99 inference(modus_ponens,[status(thm)],[5042, 4829])).
% 0.75/0.99 tff(5044,plain,
% 0.75/0.99 (~r(z, s(z))),
% 0.75/0.99 inference(unit_resolution,[status(thm)],[3779, 5015, 180])).
% 0.75/0.99 tff(5045,plain,
% 0.75/0.99 (b(z, s(z))),
% 0.75/0.99 inference(unit_resolution,[status(thm)],[599, 5044])).
% 0.75/0.99 tff(5046,plain,
% 0.75/0.99 (~b(s(s(z)), z)),
% 0.75/0.99 inference(unit_resolution,[status(thm)],[4923, 117, 5045, 5035])).
% 0.75/0.99 tff(5047,plain,
% 0.75/0.99 (r(s(s(z)), z)),
% 0.75/0.99 inference(unit_resolution,[status(thm)],[62, 46, 59, 5046])).
% 0.75/0.99 tff(5048,plain,
% 0.75/0.99 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), z)) | (~r(s(s(z)), s(s(s(elem!1))))) | (~r(s(s(z)), z)))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(elem!1))), z)) | (~r(s(s(z)), s(s(s(elem!1))))) | (~r(s(s(z)), z)))),
% 0.75/0.99 inference(rewrite,[status(thm)],[])).
% 0.75/0.99 tff(5049,plain,
% 0.75/0.99 (((~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)), s(s(s(elem!1))))) | (~r(s(s(z)), z)))),
% 0.75/0.99 inference(rewrite,[status(thm)],[])).
% 0.75/0.99 tff(5050,plain,
% 0.75/0.99 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), z)) | (~r(s(s(z)), z)) | (~r(s(s(z)), s(s(s(elem!1))))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), z)) | (~r(s(s(z)), s(s(s(elem!1))))) | (~r(s(s(z)), z))))),
% 0.75/0.99 inference(monotonicity,[status(thm)],[5049])).
% 0.75/0.99 tff(5051,plain,
% 0.75/0.99 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), z)) | (~r(s(s(z)), z)) | (~r(s(s(z)), s(s(s(elem!1))))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(elem!1))), z)) | (~r(s(s(z)), s(s(s(elem!1))))) | (~r(s(s(z)), z)))),
% 0.75/0.99 inference(transitivity,[status(thm)],[5050, 5048])).
% 0.75/0.99 tff(5052,plain,
% 0.75/0.99 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), z)) | (~r(s(s(z)), z)) | (~r(s(s(z)), s(s(s(elem!1))))))),
% 0.75/0.99 inference(quant_inst,[status(thm)],[])).
% 0.75/0.99 tff(5053,plain,
% 0.75/0.99 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(elem!1))), z)) | (~r(s(s(z)), s(s(s(elem!1))))) | (~r(s(s(z)), z))),
% 0.75/0.99 inference(modus_ponens,[status(thm)],[5052, 5051])).
% 0.75/0.99 tff(5054,plain,
% 0.75/0.99 (~r(s(s(z)), s(s(s(elem!1))))),
% 0.75/0.99 inference(unit_resolution,[status(thm)],[5053, 14, 4832, 5047])).
% 0.75/0.99 tff(5055,plain,
% 0.75/0.99 ($false),
% 0.75/0.99 inference(unit_resolution,[status(thm)],[5054, 5043])).
% 0.75/0.99 tff(5056,plain,((~r(s(s(s(z))), z)) | (~r(s(s(elem!1)), z)) | (~b(s(z), z))), inference(lemma,lemma(discharge,[]))).
% 0.75/0.99 tff(5057,plain,
% 0.75/0.99 (~r(s(s(s(z))), z)),
% 0.75/0.99 inference(unit_resolution,[status(thm)],[5056, 182, 237])).
% 0.75/0.99 tff(5058,plain,
% 0.75/0.99 (b(s(s(s(z))), z)),
% 0.75/0.99 inference(unit_resolution,[status(thm)],[823, 5057])).
% 0.75/0.99 tff(5059,plain,
% 0.75/0.99 (~b(s(s(s(z))), s(z))),
% 0.75/0.99 inference(unit_resolution,[status(thm)],[1389, 5058, 237])).
% 0.75/0.99 tff(5060,plain,
% 0.75/0.99 (r(s(s(s(z))), s(z))),
% 0.75/0.99 inference(unit_resolution,[status(thm)],[347, 5059])).
% 0.75/0.99 tff(5061,plain,
% 0.75/0.99 (r(s(s(s(elem!1))), s(z)) <=> r(s(s(elem!1)), s(z))),
% 0.75/0.99 inference(symmetry,[status(thm)],[4969])).
% 0.75/0.99 tff(5062,plain,
% 0.75/0.99 (~b(s(s(s(s(z)))), z)),
% 0.75/0.99 inference(unit_resolution,[status(thm)],[4895, 562, 237])).
% 0.75/0.99 tff(5063,plain,
% 0.75/0.99 (r(s(s(s(s(z)))), z)),
% 0.75/0.99 inference(unit_resolution,[status(thm)],[582, 5062])).
% 0.75/0.99 tff(5064,plain,
% 0.75/0.99 (~r(s(s(s(elem!1))), s(s(s(s(z)))))),
% 0.75/0.99 inference(unit_resolution,[status(thm)],[4882, 14, 4832, 5063])).
% 0.75/0.99 tff(5065,plain,
% 0.75/0.99 (b(s(s(s(elem!1))), s(s(s(s(z)))))),
% 0.75/0.99 inference(unit_resolution,[status(thm)],[4886, 46, 5064, 4876])).
% 0.75/0.99 tff(5066,assumption,(b(s(s(s(elem!1))), s(s(s(s(z)))))), introduced(assumption)).
% 0.75/0.99 tff(5067,plain,
% 0.75/0.99 (((~![X0: $i, X2: $i, X1: $i] : ((~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), s(z))) | (~b(s(s(s(elem!1))), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(z))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(s(s(elem!1))), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(z))))),
% 0.75/0.99 inference(rewrite,[status(thm)],[])).
% 0.75/0.99 tff(5068,plain,
% 0.75/0.99 (((~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(s(s(elem!1))), s(z))) | (~b(s(s(s(elem!1))), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(z))))),
% 0.75/0.99 inference(rewrite,[status(thm)],[])).
% 0.75/0.99 tff(5069,plain,
% 0.75/0.99 (((~![X0: $i, X2: $i, X1: $i] : ((~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~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, X2: $i, X1: $i] : ((~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), s(z))) | (~b(s(s(s(elem!1))), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(z)))))),
% 0.75/0.99 inference(monotonicity,[status(thm)],[5068])).
% 0.75/0.99 tff(5070,plain,
% 0.75/0.99 (((~![X0: $i, X2: $i, X1: $i] : ((~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~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, X2: $i, X1: $i] : ((~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(s(s(elem!1))), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(z))))),
% 0.75/0.99 inference(transitivity,[status(thm)],[5069, 5067])).
% 0.75/0.99 tff(5071,plain,
% 0.75/0.99 ((~![X0: $i, X2: $i, X1: $i] : ((~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~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)))))))),
% 0.75/0.99 inference(quant_inst,[status(thm)],[])).
% 0.75/0.99 tff(5072,plain,
% 0.75/0.99 ((~![X0: $i, X2: $i, X1: $i] : ((~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(s(s(elem!1))), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(z)))),
% 0.75/0.99 inference(modus_ponens,[status(thm)],[5071, 5070])).
% 0.75/0.99 tff(5073,plain,
% 0.75/0.99 ($false),
% 0.75/0.99 inference(unit_resolution,[status(thm)],[5072, 117, 2010, 562, 5066])).
% 0.75/0.99 tff(5074,plain,((~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))))))), inference(lemma,lemma(discharge,[]))).
% 0.75/0.99 tff(5075,plain,
% 0.75/0.99 (~b(s(s(s(elem!1))), s(z))),
% 0.75/0.99 inference(unit_resolution,[status(thm)],[5074, 562, 5065])).
% 0.75/0.99 tff(5076,plain,
% 0.75/0.99 (r(s(s(s(elem!1))), s(z))),
% 0.75/0.99 inference(unit_resolution,[status(thm)],[467, 5075])).
% 0.75/0.99 tff(5077,plain,
% 0.75/0.99 (r(s(s(elem!1)), s(z))),
% 0.75/0.99 inference(modus_ponens,[status(thm)],[5076, 5061])).
% 0.75/0.99 tff(5078,plain,
% 0.75/0.99 (~r(z, s(z))),
% 0.75/0.99 inference(unit_resolution,[status(thm)],[868, 5077, 182])).
% 0.75/0.99 tff(5079,plain,
% 0.75/0.99 (b(z, s(z))),
% 0.75/0.99 inference(unit_resolution,[status(thm)],[599, 5078])).
% 0.75/0.99 tff(5080,plain,
% 0.75/0.99 (((~![X0: $i, X2: $i, X1: $i] : ((~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), s(z))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(z)), s(s(s(s(z)))))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(z)), s(z))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(z)), s(s(s(s(z)))))))),
% 0.75/0.99 inference(rewrite,[status(thm)],[])).
% 0.75/0.99 tff(5081,plain,
% 0.75/0.99 (((~b(s(s(s(s(z)))), s(z))) | (~b(s(s(z)), s(z))) | (~b(s(s(z)), s(s(s(s(z))))))) <=> ((~b(s(s(z)), s(z))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(z)), s(s(s(s(z)))))))),
% 0.75/0.99 inference(rewrite,[status(thm)],[])).
% 0.75/0.99 tff(5082,plain,
% 0.75/0.99 (((~![X0: $i, X2: $i, X1: $i] : ((~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(z)))), s(z))) | (~b(s(s(z)), s(z))) | (~b(s(s(z)), s(s(s(s(z)))))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), s(z))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(z)), s(s(s(s(z))))))))),
% 0.75/0.99 inference(monotonicity,[status(thm)],[5081])).
% 0.75/0.99 tff(5083,plain,
% 0.75/0.99 (((~![X0: $i, X2: $i, X1: $i] : ((~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(z)))), s(z))) | (~b(s(s(z)), s(z))) | (~b(s(s(z)), s(s(s(s(z)))))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(z)), s(z))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(z)), s(s(s(s(z)))))))),
% 0.75/0.99 inference(transitivity,[status(thm)],[5082, 5080])).
% 0.75/0.99 tff(5084,plain,
% 0.75/0.99 ((~![X0: $i, X2: $i, X1: $i] : ((~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(z)))), s(z))) | (~b(s(s(z)), s(z))) | (~b(s(s(z)), s(s(s(s(z)))))))),
% 0.75/0.99 inference(quant_inst,[status(thm)],[])).
% 0.75/0.99 tff(5085,plain,
% 0.75/0.99 ((~![X0: $i, X2: $i, X1: $i] : ((~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(z)), s(z))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(z)), s(s(s(s(z))))))),
% 0.75/0.99 inference(modus_ponens,[status(thm)],[5084, 5083])).
% 0.75/0.99 tff(5086,plain,
% 0.75/0.99 (~b(s(s(z)), s(s(s(s(z)))))),
% 0.75/0.99 inference(unit_resolution,[status(thm)],[5085, 117, 562, 1])).
% 0.75/0.99 tff(5087,plain,
% 0.75/0.99 (r(s(s(z)), s(s(s(s(z)))))),
% 0.75/0.99 inference(unit_resolution,[status(thm)],[106, 5086])).
% 0.75/0.99 tff(5088,plain,
% 0.75/0.99 (((~![X0: $i, X2: $i, X1: $i] : ((~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(z))) | (~b(z, s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(z))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(z))) | (~b(z, s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(z))))),
% 0.75/0.99 inference(rewrite,[status(thm)],[])).
% 0.75/0.99 tff(5089,plain,
% 0.75/0.99 (((~b(s(s(s(s(z)))), s(z))) | (~b(z, s(z))) | (~b(z, s(s(s(s(z))))))) <=> ((~b(z, s(z))) | (~b(z, s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(z))))),
% 0.75/0.99 inference(rewrite,[status(thm)],[])).
% 0.75/0.99 tff(5090,plain,
% 0.75/0.99 (((~![X0: $i, X2: $i, X1: $i] : ((~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(z)))), s(z))) | (~b(z, s(z))) | (~b(z, s(s(s(s(z)))))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(z))) | (~b(z, s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(z)))))),
% 0.75/0.99 inference(monotonicity,[status(thm)],[5089])).
% 0.75/0.99 tff(5091,plain,
% 0.75/0.99 (((~![X0: $i, X2: $i, X1: $i] : ((~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(z)))), s(z))) | (~b(z, s(z))) | (~b(z, s(s(s(s(z)))))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(z))) | (~b(z, s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(z))))),
% 0.75/0.99 inference(transitivity,[status(thm)],[5090, 5088])).
% 0.75/0.99 tff(5092,plain,
% 0.75/0.99 ((~![X0: $i, X2: $i, X1: $i] : ((~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(z)))), s(z))) | (~b(z, s(z))) | (~b(z, s(s(s(s(z)))))))),
% 0.75/0.99 inference(quant_inst,[status(thm)],[])).
% 0.75/0.99 tff(5093,plain,
% 0.75/0.99 ((~![X0: $i, X2: $i, X1: $i] : ((~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(z))) | (~b(z, s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(z)))),
% 0.75/0.99 inference(modus_ponens,[status(thm)],[5092, 5091])).
% 0.75/0.99 tff(5094,plain,
% 0.75/0.99 (~b(z, s(s(s(s(z)))))),
% 0.75/0.99 inference(unit_resolution,[status(thm)],[5093, 117, 574, 562])).
% 0.75/0.99 tff(5095,plain,
% 0.75/0.99 (r(z, s(s(s(s(z)))))),
% 0.75/0.99 inference(unit_resolution,[status(thm)],[51, 5094])).
% 0.75/0.99 tff(5096,plain,
% 0.75/0.99 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(s(s(z)))))) | (~r(s(s(z)), z)) | (~r(s(s(z)), s(s(s(s(z)))))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, s(s(s(s(z)))))) | (~r(s(s(z)), z)) | (~r(s(s(z)), s(s(s(s(z)))))))),
% 0.75/0.99 inference(rewrite,[status(thm)],[])).
% 0.75/0.99 tff(5097,plain,
% 0.75/0.99 (((~r(z, s(s(s(s(z)))))) | (~r(s(s(z)), s(s(s(s(z)))))) | (~r(s(s(z)), z))) <=> ((~r(z, s(s(s(s(z)))))) | (~r(s(s(z)), z)) | (~r(s(s(z)), s(s(s(s(z)))))))),
% 0.75/0.99 inference(rewrite,[status(thm)],[])).
% 0.75/0.99 tff(5098,plain,
% 0.75/0.99 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(s(s(z)))))) | (~r(s(s(z)), s(s(s(s(z)))))) | (~r(s(s(z)), z)))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(s(s(z)))))) | (~r(s(s(z)), z)) | (~r(s(s(z)), s(s(s(s(z))))))))),
% 0.75/0.99 inference(monotonicity,[status(thm)],[5097])).
% 0.75/0.99 tff(5099,plain,
% 0.75/0.99 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(s(s(z)))))) | (~r(s(s(z)), s(s(s(s(z)))))) | (~r(s(s(z)), z)))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, s(s(s(s(z)))))) | (~r(s(s(z)), z)) | (~r(s(s(z)), s(s(s(s(z)))))))),
% 0.75/0.99 inference(transitivity,[status(thm)],[5098, 5096])).
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% 0.75/1.00 tff(5179,plain,
% 0.75/1.00 (~b(s(s(s(s(z)))), s(s(s(z))))),
% 0.75/1.00 inference(unit_resolution,[status(thm)],[890, 117, 5163, 5178])).
% 0.75/1.00 tff(5180,plain,
% 0.75/1.00 (r(s(s(s(s(z)))), s(s(s(z))))),
% 0.75/1.00 inference(unit_resolution,[status(thm)],[529, 5179])).
% 0.75/1.00 tff(5181,plain,
% 0.75/1.00 ($false),
% 0.75/1.00 inference(unit_resolution,[status(thm)],[895, 14, 5180, 5176, 5165])).
% 0.75/1.00 tff(5182,plain,((~r(z, s(z))) | (~b(s(z), z)) | (~r(s(s(elem!1)), s(z))) | (~b(s(s(elem!1)), z))), inference(lemma,lemma(discharge,[]))).
% 0.75/1.00 tff(5183,plain,
% 0.75/1.00 (~r(z, s(z))),
% 0.75/1.00 inference(unit_resolution,[status(thm)],[5182, 5157, 5155, 237])).
% 0.75/1.00 tff(5184,plain,
% 0.75/1.00 (b(z, s(z))),
% 0.75/1.00 inference(unit_resolution,[status(thm)],[599, 5183])).
% 0.75/1.00 tff(5185,plain,
% 0.75/1.00 (r(s(s(s(s(elem!1)))), s(z))),
% 0.75/1.00 inference(modus_ponens,[status(thm)],[5157, 5168])).
% 0.75/1.00 tff(5186,plain,
% 0.75/1.00 (b(s(s(s(s(elem!1)))), z)),
% 0.75/1.00 inference(modus_ponens,[status(thm)],[5155, 5173])).
% 0.75/1.00 tff(5187,plain,
% 0.75/1.00 (~b(s(s(s(z))), z)),
% 0.75/1.00 inference(unit_resolution,[status(thm)],[2495, 5186, 5185, 237])).
% 0.75/1.00 tff(5188,plain,
% 0.75/1.00 (r(s(s(s(z))), z)),
% 0.75/1.00 inference(unit_resolution,[status(thm)],[823, 5187])).
% 0.75/1.00 tff(5189,plain,
% 0.75/1.00 (r(s(s(s(elem!1))), s(z))),
% 0.75/1.00 inference(modus_ponens,[status(thm)],[5157, 4969])).
% 0.75/1.00 tff(5190,plain,
% 0.75/1.00 (b(s(s(s(elem!1))), s(s(z))) <=> b(elem!1, s(s(z)))),
% 0.75/1.00 inference(monotonicity,[status(thm)],[4824])).
% 0.75/1.00 tff(5191,plain,
% 0.75/1.00 (b(elem!1, s(s(z))) <=> b(s(s(s(elem!1))), s(s(z)))),
% 0.75/1.00 inference(symmetry,[status(thm)],[5190])).
% 0.75/1.00 tff(5192,plain,
% 0.75/1.00 (r(s(s(s(elem!1))), s(s(z))) <=> r(elem!1, s(s(z)))),
% 0.75/1.00 inference(monotonicity,[status(thm)],[4824])).
% 0.75/1.00 tff(5193,plain,
% 0.75/1.00 ((~r(s(s(s(elem!1))), s(s(z)))) <=> (~r(elem!1, s(s(z))))),
% 0.75/1.00 inference(monotonicity,[status(thm)],[5192])).
% 0.75/1.00 tff(5194,plain,
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% 0.75/1.00 inference(unit_resolution,[status(thm)],[4966, 848, 574])).
% 0.75/1.00 tff(5195,plain,
% 0.75/1.00 (r(s(s(z)), s(z))),
% 0.75/1.00 inference(unit_resolution,[status(thm)],[141, 5194])).
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% 0.75/1.00 inference(rewrite,[status(thm)],[])).
% 0.75/1.00 tff(5197,plain,
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% 0.75/1.00 inference(quant_inst,[status(thm)],[])).
% 0.75/1.00 tff(5198,plain,
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% 0.75/1.00 inference(modus_ponens,[status(thm)],[5197, 5196])).
% 0.75/1.00 tff(5199,plain,
% 0.75/1.00 (~r(s(s(s(elem!1))), s(s(z)))),
% 0.75/1.00 inference(unit_resolution,[status(thm)],[5198, 14, 1911, 5195])).
% 0.75/1.00 tff(5200,plain,
% 0.75/1.00 (~r(elem!1, s(s(z)))),
% 0.75/1.00 inference(modus_ponens,[status(thm)],[5199, 5193])).
% 0.75/1.00 tff(5201,plain,
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% 0.75/1.00 inference(rewrite,[status(thm)],[])).
% 0.75/1.00 tff(5202,plain,
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% 0.75/1.00 inference(quant_inst,[status(thm)],[])).
% 0.75/1.00 tff(5203,plain,
% 0.75/1.00 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (elem!1 = s(s(z))) | b(elem!1, s(s(z))) | r(elem!1, s(s(z)))),
% 0.75/1.00 inference(modus_ponens,[status(thm)],[5202, 5201])).
% 0.75/1.00 tff(5204,plain,
% 0.75/1.00 ((elem!1 = s(s(z))) | b(elem!1, s(s(z))) | r(elem!1, s(s(z)))),
% 0.75/1.00 inference(unit_resolution,[status(thm)],[5203, 46])).
% 0.75/1.00 tff(5205,plain,
% 0.75/1.00 (b(elem!1, s(s(z))) | r(elem!1, s(s(z)))),
% 0.75/1.00 inference(unit_resolution,[status(thm)],[5204, 4987])).
% 0.75/1.00 tff(5206,plain,
% 0.75/1.00 (b(elem!1, s(s(z)))),
% 0.75/1.00 inference(unit_resolution,[status(thm)],[5205, 5200])).
% 0.75/1.00 tff(5207,plain,
% 0.75/1.00 (b(s(s(s(elem!1))), s(s(z)))),
% 0.75/1.00 inference(modus_ponens,[status(thm)],[5206, 5191])).
% 0.75/1.00 tff(5208,plain,
% 0.75/1.00 (~b(s(s(s(s(z)))), s(z))),
% 0.75/1.00 inference(unit_resolution,[status(thm)],[897, 848, 180, 574])).
% 0.75/1.00 tff(5209,plain,
% 0.75/1.00 (r(s(s(s(s(z)))), s(z))),
% 0.75/1.00 inference(unit_resolution,[status(thm)],[554, 5208])).
% 0.75/1.00 tff(5210,plain,
% 0.75/1.00 (~r(s(s(s(elem!1))), s(s(s(s(z)))))),
% 0.75/1.00 inference(unit_resolution,[status(thm)],[5001, 14, 1911, 5209])).
% 0.75/1.00 tff(5211,plain,
% 0.75/1.00 (b(s(s(s(elem!1))), s(s(s(s(z)))))),
% 0.75/1.00 inference(unit_resolution,[status(thm)],[4886, 46, 5210, 4876])).
% 0.75/1.00 tff(5212,plain,
% 0.75/1.00 (~r(s(s(z)), s(s(s(s(z)))))),
% 0.75/1.00 inference(unit_resolution,[status(thm)],[69, 14, 5209, 5195])).
% 0.75/1.00 tff(5213,plain,
% 0.75/1.00 (b(s(s(z)), s(s(s(s(z)))))),
% 0.75/1.00 inference(unit_resolution,[status(thm)],[106, 5212])).
% 0.75/1.00 tff(5214,plain,
% 0.75/1.00 (((~![X0: $i, X2: $i, X1: $i] : ((~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(s(s(z)))))) | (~b(s(s(z)), s(s(s(s(z)))))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~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(s(s(z)))))) | (~b(s(s(z)), s(s(s(s(z)))))))),
% 0.75/1.00 inference(rewrite,[status(thm)],[])).
% 0.75/1.00 tff(5215,plain,
% 0.75/1.00 (((~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(s(elem!1))), s(s(s(s(z)))))) | (~b(s(s(s(elem!1))), s(s(z))))) <=> ((~b(s(s(s(elem!1))), s(s(z)))) | (~b(s(s(s(elem!1))), s(s(s(s(z)))))) | (~b(s(s(z)), s(s(s(s(z)))))))),
% 0.75/1.00 inference(rewrite,[status(thm)],[])).
% 0.75/1.00 tff(5216,plain,
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% 0.75/1.00 inference(monotonicity,[status(thm)],[5215])).
% 0.75/1.00 tff(5217,plain,
% 0.75/1.00 (((~![X0: $i, X2: $i, X1: $i] : ((~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(s(elem!1))), s(s(s(s(z)))))) | (~b(s(s(s(elem!1))), s(s(z)))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~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(s(s(z)))))) | (~b(s(s(z)), s(s(s(s(z)))))))),
% 0.75/1.00 inference(transitivity,[status(thm)],[5216, 5214])).
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% 0.75/1.00 ((~![X0: $i, X2: $i, X1: $i] : ((~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(s(elem!1))), s(s(s(s(z)))))) | (~b(s(s(s(elem!1))), s(s(z)))))),
% 0.75/1.00 inference(quant_inst,[status(thm)],[])).
% 0.75/1.00 tff(5219,plain,
% 0.75/1.00 ((~![X0: $i, X2: $i, X1: $i] : ((~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(elem!1))), s(s(z)))) | (~b(s(s(s(elem!1))), s(s(s(s(z)))))) | (~b(s(s(z)), s(s(s(s(z))))))),
% 0.75/1.00 inference(modus_ponens,[status(thm)],[5218, 5217])).
% 0.75/1.00 tff(5220,plain,
% 0.75/1.00 (~b(s(s(s(elem!1))), s(s(z)))),
% 0.75/1.00 inference(unit_resolution,[status(thm)],[5219, 117, 5213, 5211])).
% 0.75/1.00 tff(5221,plain,
% 0.75/1.00 ($false),
% 0.75/1.00 inference(unit_resolution,[status(thm)],[5220, 5207])).
% 0.75/1.00 tff(5222,plain,((~b(s(s(s(z))), s(z))) | (~r(s(s(s(elem!1))), s(z))) | (~b(z, s(z))) | (~r(s(s(s(z))), z))), inference(lemma,lemma(discharge,[]))).
% 0.75/1.00 tff(5223,plain,
% 0.75/1.00 (~b(s(s(s(z))), s(z))),
% 0.75/1.00 inference(unit_resolution,[status(thm)],[5222, 5189, 5184, 5188])).
% 0.75/1.00 tff(5224,plain,
% 0.75/1.00 (r(s(s(s(z))), s(z))),
% 0.75/1.00 inference(unit_resolution,[status(thm)],[347, 5223])).
% 0.75/1.00 tff(5225,plain,
% 0.75/1.00 (~r(s(s(s(s(z)))), s(z))),
% 0.75/1.00 inference(unit_resolution,[status(thm)],[5135, 5224, 5157])).
% 0.75/1.00 tff(5226,plain,
% 0.75/1.00 (b(s(s(s(s(z)))), s(z))),
% 0.75/1.00 inference(unit_resolution,[status(thm)],[554, 5225])).
% 0.75/1.00 tff(5227,plain,
% 0.75/1.00 (~b(s(s(z)), s(z))),
% 0.75/1.00 inference(unit_resolution,[status(thm)],[5103, 5226, 5184])).
% 0.75/1.00 tff(5228,plain,
% 0.75/1.00 (r(s(s(z)), s(z))),
% 0.75/1.00 inference(unit_resolution,[status(thm)],[141, 5227])).
% 0.75/1.00 tff(5229,plain,
% 0.75/1.00 (~r(s(s(z)), s(s(s(elem!1))))),
% 0.75/1.00 inference(unit_resolution,[status(thm)],[4976, 14, 5189, 5228])).
% 0.75/1.00 tff(5230,plain,
% 0.75/1.00 (~r(s(s(z)), elem!1)),
% 0.75/1.00 inference(modus_ponens,[status(thm)],[5229, 4828])).
% 0.75/1.00 tff(5231,plain,
% 0.75/1.00 (b(s(s(z)), elem!1)),
% 0.75/1.00 inference(unit_resolution,[status(thm)],[4993, 5230])).
% 0.75/1.00 tff(5232,plain,
% 0.75/1.00 (b(s(s(z)), s(s(s(elem!1))))),
% 0.75/1.00 inference(modus_ponens,[status(thm)],[5231, 4826])).
% 0.75/1.00 tff(5233,plain,
% 0.75/1.00 (~r(s(s(z)), s(s(s(z))))),
% 0.75/1.00 inference(unit_resolution,[status(thm)],[5021, 14, 5224, 5228])).
% 0.75/1.00 tff(5234,plain,
% 0.75/1.00 (b(s(s(z)), s(s(s(z))))),
% 0.75/1.00 inference(unit_resolution,[status(thm)],[4949, 5233])).
% 0.75/1.00 tff(5235,plain,
% 0.75/1.00 (~r(s(s(s(elem!1))), s(s(s(z))))),
% 0.75/1.00 inference(unit_resolution,[status(thm)],[5117, 14, 5189, 5224])).
% 0.75/1.00 tff(5236,plain,
% 0.75/1.00 (~r(elem!1, s(s(s(z))))),
% 0.75/1.00 inference(unit_resolution,[status(thm)],[4845, 5235])).
% 0.75/1.00 tff(5237,plain,
% 0.75/1.00 (b(elem!1, s(s(s(z))))),
% 0.75/1.00 inference(unit_resolution,[status(thm)],[4856, 5236])).
% 0.75/1.00 tff(5238,plain,
% 0.75/1.00 (b(s(s(s(elem!1))), s(s(s(z))))),
% 0.75/1.00 inference(modus_ponens,[status(thm)],[5237, 4835])).
% 0.75/1.00 tff(5239,plain,
% 0.75/1.00 (~b(s(s(z)), s(s(s(elem!1))))),
% 0.75/1.00 inference(unit_resolution,[status(thm)],[5127, 117, 5238, 5234])).
% 0.75/1.00 tff(5240,plain,
% 0.75/1.00 ($false),
% 0.75/1.00 inference(unit_resolution,[status(thm)],[5239, 5232])).
% 0.75/1.00 tff(5241,plain,(~b(s(z), z)), inference(lemma,lemma(discharge,[]))).
% 0.75/1.00 tff(5242,plain,
% 0.75/1.00 (r(s(z), z)),
% 0.75/1.00 inference(unit_resolution,[status(thm)],[193, 5241])).
% 0.75/1.00 tff(5243,plain,
% 0.75/1.00 ((~r(s(s(elem!1)), s(z))) | (~r(s(s(elem!1)), z))),
% 0.75/1.00 inference(unit_resolution,[status(thm)],[188, 5242])).
% 0.75/1.00 tff(5244,plain,
% 0.75/1.00 (~r(s(s(elem!1)), z)),
% 0.75/1.00 inference(unit_resolution,[status(thm)],[5243, 181])).
% 0.75/1.00 tff(5245,plain,
% 0.75/1.00 (~b(s(s(elem!1)), z)),
% 0.75/1.00 inference(unit_resolution,[status(thm)],[5161, 181, 2, 3])).
% 0.75/1.00 tff(5246,plain,
% 0.75/1.00 ($false),
% 0.75/1.00 inference(unit_resolution,[status(thm)],[1025, 5245, 5244])).
% 0.75/1.00 tff(5247,plain,((~r(s(s(elem!1)), s(z))) | (~r(z, s(z))) | (~r(s(s(s(s(z)))), s(z)))), inference(lemma,lemma(discharge,[]))).
% 0.75/1.00 tff(5248,plain,
% 0.75/1.00 (~r(s(s(elem!1)), s(z))),
% 0.75/1.00 inference(unit_resolution,[status(thm)],[5247, 3, 2])).
% 0.75/1.00 tff(5249,plain,
% 0.75/1.00 (b(s(s(elem!1)), s(z))),
% 0.75/1.00 inference(unit_resolution,[status(thm)],[178, 5248])).
% 0.75/1.00 tff(5250,plain,
% 0.75/1.00 (b(s(s(s(elem!1))), s(z))),
% 0.75/1.00 inference(modus_ponens,[status(thm)],[5249, 4811])).
% 0.75/1.00 tff(5251,plain,
% 0.75/1.00 (r(elem!1, s(s(z))) <=> r(s(s(s(elem!1))), s(s(z)))),
% 0.75/1.00 inference(symmetry,[status(thm)],[5192])).
% 0.75/1.00 tff(5252,plain,
% 0.75/1.00 ((~b(s(s(s(elem!1))), s(s(z)))) <=> (~b(elem!1, s(s(z))))),
% 0.75/1.00 inference(monotonicity,[status(thm)],[5190])).
% 0.75/1.00 tff(5253,plain,
% 0.75/1.00 (((~![X0: $i, X2: $i, X1: $i] : ((~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(s(s(elem!1))), s(s(z)))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~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(s(s(elem!1))), s(s(z)))))),
% 0.75/1.00 inference(rewrite,[status(thm)],[])).
% 0.75/1.00 tff(5254,plain,
% 0.75/1.00 ((~![X0: $i, X2: $i, X1: $i] : ((~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(s(s(elem!1))), s(s(z)))))),
% 0.75/1.00 inference(quant_inst,[status(thm)],[])).
% 0.75/1.00 tff(5255,plain,
% 0.75/1.00 ((~![X0: $i, X2: $i, X1: $i] : ((~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(s(s(elem!1))), s(s(z))))),
% 0.75/1.00 inference(modus_ponens,[status(thm)],[5254, 5253])).
% 0.75/1.00 tff(5256,plain,
% 0.75/1.00 (~b(s(s(s(elem!1))), s(s(z)))),
% 0.75/1.00 inference(unit_resolution,[status(thm)],[5255, 117, 2010, 1])).
% 0.75/1.00 tff(5257,plain,
% 0.75/1.00 (~b(elem!1, s(s(z)))),
% 0.75/1.00 inference(modus_ponens,[status(thm)],[5256, 5252])).
% 0.75/1.00 tff(5258,plain,
% 0.75/1.00 (r(elem!1, s(s(z)))),
% 0.75/1.00 inference(unit_resolution,[status(thm)],[5205, 5257])).
% 0.75/1.00 tff(5259,plain,
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% 0.75/1.00 inference(modus_ponens,[status(thm)],[5258, 5251])).
% 0.75/1.00 tff(5260,plain,
% 0.75/1.00 (~b(s(s(s(elem!1))), s(s(s(z))))),
% 0.75/1.00 inference(unit_resolution,[status(thm)],[2353, 117, 2010, 848])).
% 0.75/1.00 tff(5261,plain,
% 0.75/1.00 ((~(s(s(s(z))) = s(s(s(s(elem!1)))))) <=> (~(s(s(s(elem!1))) = s(s(s(z)))))),
% 0.75/1.00 inference(monotonicity,[status(thm)],[4852])).
% 0.75/1.00 tff(5262,plain,
% 0.75/1.00 (~(s(s(s(elem!1))) = s(s(s(z))))),
% 0.75/1.00 inference(modus_ponens,[status(thm)],[279, 5261])).
% 0.75/1.00 tff(5263,plain,
% 0.75/1.00 (r(s(s(s(elem!1))), s(s(s(z))))),
% 0.75/1.00 inference(unit_resolution,[status(thm)],[2341, 46, 5262, 5260])).
% 0.75/1.00 tff(5264,plain,
% 0.75/1.00 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), s(s(z)))) | (~r(s(s(s(elem!1))), s(s(s(z))))) | (~r(s(s(z)), s(s(s(z))))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(elem!1))), s(s(z)))) | (~r(s(s(s(elem!1))), s(s(s(z))))) | (~r(s(s(z)), s(s(s(z))))))),
% 0.75/1.00 inference(rewrite,[status(thm)],[])).
% 0.75/1.00 tff(5265,plain,
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% 0.75/1.00 inference(rewrite,[status(thm)],[])).
% 0.75/1.00 tff(5266,plain,
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% 0.75/1.00 inference(monotonicity,[status(thm)],[5265])).
% 0.75/1.00 tff(5267,plain,
% 0.75/1.00 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(z)), s(s(s(z))))) | (~r(s(s(s(elem!1))), s(s(s(z))))) | (~r(s(s(s(elem!1))), s(s(z)))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(elem!1))), s(s(z)))) | (~r(s(s(s(elem!1))), s(s(s(z))))) | (~r(s(s(z)), s(s(s(z))))))),
% 0.75/1.00 inference(transitivity,[status(thm)],[5266, 5264])).
% 0.75/1.00 tff(5268,plain,
% 0.75/1.00 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(z)), s(s(s(z))))) | (~r(s(s(s(elem!1))), s(s(s(z))))) | (~r(s(s(s(elem!1))), s(s(z)))))),
% 0.75/1.00 inference(quant_inst,[status(thm)],[])).
% 0.75/1.00 tff(5269,plain,
% 0.75/1.00 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(elem!1))), s(s(z)))) | (~r(s(s(s(elem!1))), s(s(s(z))))) | (~r(s(s(z)), s(s(s(z)))))),
% 0.75/1.00 inference(modus_ponens,[status(thm)],[5268, 5267])).
% 0.75/1.00 tff(5270,plain,
% 0.75/1.00 (~r(s(s(s(elem!1))), s(s(z)))),
% 0.75/1.00 inference(unit_resolution,[status(thm)],[5269, 14, 5263, 4950])).
% 0.75/1.00 tff(5271,plain,
% 0.75/1.00 ($false),
% 0.75/1.00 inference(unit_resolution,[status(thm)],[5270, 5259])).
% 0.75/1.00 tff(5272,plain,((~b(s(s(s(elem!1))), s(z))) | (~b(s(s(z)), s(z))) | (~b(s(s(s(z))), s(z)))), inference(lemma,lemma(discharge,[]))).
% 0.75/1.00 tff(5273,plain,
% 0.75/1.00 (~b(s(s(s(z))), s(z))),
% 0.75/1.00 inference(unit_resolution,[status(thm)],[5272, 5250, 142])).
% 0.75/1.00 tff(5274,plain,
% 0.75/1.00 (r(s(s(s(z))), s(z))),
% 0.75/1.00 inference(unit_resolution,[status(thm)],[347, 5273])).
% 0.75/1.00 tff(5275,plain,
% 0.75/1.00 ((~r(s(s(s(z))), z)) | (~r(s(s(s(z))), s(z)))),
% 0.75/1.00 inference(unit_resolution,[status(thm)],[2173, 5242])).
% 0.75/1.00 tff(5276,plain,
% 0.75/1.00 (~r(s(s(s(z))), z)),
% 0.75/1.00 inference(unit_resolution,[status(thm)],[5275, 5274])).
% 0.75/1.00 tff(5277,plain,
% 0.75/1.00 (b(s(s(s(z))), z)),
% 0.75/1.00 inference(unit_resolution,[status(thm)],[823, 5276])).
% 0.75/1.00 tff(5278,plain,
% 0.75/1.00 (~r(s(s(s(z))), s(s(s(s(z)))))),
% 0.75/1.00 inference(unit_resolution,[status(thm)],[5026, 5274, 3])).
% 0.75/1.00 tff(5279,plain,
% 0.75/1.00 (b(s(s(s(z))), s(s(s(s(z)))))),
% 0.75/1.00 inference(unit_resolution,[status(thm)],[2685, 5278])).
% 0.75/1.00 tff(5280,plain,
% 0.75/1.00 ($false),
% 0.75/1.00 inference(unit_resolution,[status(thm)],[2788, 5279, 5277, 52])).
% 0.75/1.00 tff(5281,plain,((~r(s(s(s(s(z)))), s(z))) | (~r(z, s(z)))), inference(lemma,lemma(discharge,[]))).
% 0.75/1.00 tff(5282,plain,
% 0.75/1.00 (~r(s(s(s(s(z)))), s(z))),
% 0.75/1.00 inference(unit_resolution,[status(thm)],[5281, 2])).
% 0.75/1.00 tff(5283,plain,
% 0.75/1.00 (b(s(s(s(s(z)))), s(z))),
% 0.75/1.00 inference(unit_resolution,[status(thm)],[554, 5282])).
% 0.75/1.00 tff(5284,plain,
% 0.75/1.00 (~r(z, s(s(s(z))))),
% 0.75/1.00 inference(unit_resolution,[status(thm)],[1018, 14, 2, 283])).
% 0.75/1.00 tff(5285,plain,
% 0.75/1.00 (b(z, s(s(s(z))))),
% 0.75/1.00 inference(unit_resolution,[status(thm)],[711, 5284])).
% 0.75/1.00 tff(5286,plain,
% 0.75/1.00 (((~![X0: $i, X2: $i, X1: $i] : ((~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(s(z))))) | (~b(s(s(z)), z)) | (~b(s(s(z)), s(s(s(z))))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(s(s(z))))) | (~b(s(s(z)), z)) | (~b(s(s(z)), s(s(s(z))))))),
% 0.75/1.00 inference(rewrite,[status(thm)],[])).
% 0.75/1.00 tff(5287,plain,
% 0.75/1.00 (((~b(z, s(s(s(z))))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(z)), z))) <=> ((~b(z, s(s(s(z))))) | (~b(s(s(z)), z)) | (~b(s(s(z)), s(s(s(z))))))),
% 0.75/1.00 inference(rewrite,[status(thm)],[])).
% 0.75/1.00 tff(5288,plain,
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% 0.75/1.00 inference(monotonicity,[status(thm)],[5287])).
% 0.75/1.00 tff(5289,plain,
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% 0.75/1.00 inference(transitivity,[status(thm)],[5288, 5286])).
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% 0.75/1.00 inference(quant_inst,[status(thm)],[])).
% 0.75/1.00 tff(5291,plain,
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% 0.75/1.00 inference(modus_ponens,[status(thm)],[5290, 5289])).
% 0.75/1.00 tff(5292,plain,
% 0.75/1.00 ($false),
% 0.75/1.00 inference(unit_resolution,[status(thm)],[5291, 117, 5285, 5023, 63])).
% 0.75/1.00 tff(5293,plain,((~r(s(s(z)), s(z))) | (~r(s(s(s(z))), s(z))) | (~r(z, s(z)))), inference(lemma,lemma(discharge,[]))).
% 0.75/1.00 tff(5294,plain,
% 0.75/1.00 (~r(s(s(z)), s(z))),
% 0.75/1.00 inference(unit_resolution,[status(thm)],[5293, 283, 2])).
% 0.75/1.00 tff(5295,plain,
% 0.75/1.00 (b(s(s(z)), s(z))),
% 0.75/1.00 inference(unit_resolution,[status(thm)],[141, 5294])).
% 0.75/1.00 tff(5296,plain,
% 0.75/1.00 (~b(s(s(s(elem!1))), s(s(s(s(z)))))),
% 0.75/1.00 inference(unit_resolution,[status(thm)],[5072, 117, 2010, 562])).
% 0.75/1.00 tff(5297,plain,
% 0.75/1.00 (r(s(s(s(elem!1))), s(s(s(s(z)))))),
% 0.75/1.00 inference(unit_resolution,[status(thm)],[4886, 46, 4876, 5296])).
% 0.75/1.00 tff(5298,plain,
% 0.75/1.00 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), s(s(z)))) | (~r(s(s(s(elem!1))), s(s(s(s(z)))))) | (~r(s(s(z)), s(s(s(s(z)))))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(elem!1))), s(s(z)))) | (~r(s(s(s(elem!1))), s(s(s(s(z)))))) | (~r(s(s(z)), s(s(s(s(z)))))))),
% 0.75/1.00 inference(rewrite,[status(thm)],[])).
% 0.75/1.00 tff(5299,plain,
% 0.75/1.00 (((~r(s(s(z)), s(s(s(s(z)))))) | (~r(s(s(s(elem!1))), s(s(s(s(z)))))) | (~r(s(s(s(elem!1))), s(s(z))))) <=> ((~r(s(s(s(elem!1))), s(s(z)))) | (~r(s(s(s(elem!1))), s(s(s(s(z)))))) | (~r(s(s(z)), s(s(s(s(z)))))))),
% 0.75/1.00 inference(rewrite,[status(thm)],[])).
% 0.75/1.00 tff(5300,plain,
% 0.75/1.00 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(z)), s(s(s(s(z)))))) | (~r(s(s(s(elem!1))), s(s(s(s(z)))))) | (~r(s(s(s(elem!1))), s(s(z)))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), s(s(z)))) | (~r(s(s(s(elem!1))), s(s(s(s(z)))))) | (~r(s(s(z)), s(s(s(s(z))))))))),
% 0.75/1.00 inference(monotonicity,[status(thm)],[5299])).
% 0.75/1.00 tff(5301,plain,
% 0.75/1.00 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(z)), s(s(s(s(z)))))) | (~r(s(s(s(elem!1))), s(s(s(s(z)))))) | (~r(s(s(s(elem!1))), s(s(z)))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(elem!1))), s(s(z)))) | (~r(s(s(s(elem!1))), s(s(s(s(z)))))) | (~r(s(s(z)), s(s(s(s(z)))))))),
% 0.75/1.00 inference(transitivity,[status(thm)],[5300, 5298])).
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% 0.75/1.00 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(z)), s(s(s(s(z)))))) | (~r(s(s(s(elem!1))), s(s(s(s(z)))))) | (~r(s(s(s(elem!1))), s(s(z)))))),
% 0.75/1.00 inference(quant_inst,[status(thm)],[])).
% 0.75/1.00 tff(5303,plain,
% 0.75/1.00 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(elem!1))), s(s(z)))) | (~r(s(s(s(elem!1))), s(s(s(s(z)))))) | (~r(s(s(z)), s(s(s(s(z))))))),
% 0.75/1.00 inference(modus_ponens,[status(thm)],[5302, 5301])).
% 0.75/1.00 tff(5304,plain,
% 0.75/1.00 (~r(s(s(s(elem!1))), s(s(z)))),
% 0.75/1.00 inference(unit_resolution,[status(thm)],[5303, 14, 5297, 5087])).
% 0.75/1.00 tff(5305,plain,
% 0.75/1.00 ($false),
% 0.75/1.00 inference(unit_resolution,[status(thm)],[5304, 5259])).
% 0.75/1.00 tff(5306,plain,((~b(s(s(s(elem!1))), s(z))) | (~b(s(s(z)), s(z))) | (~b(s(s(s(s(z)))), s(z)))), inference(lemma,lemma(discharge,[]))).
% 0.75/1.00 tff(5307,plain,
% 0.75/1.00 (~b(s(s(s(elem!1))), s(z))),
% 0.75/1.00 inference(unit_resolution,[status(thm)],[5306, 5295, 5283])).
% 0.75/1.00 tff(5308,plain,
% 0.75/1.00 (r(s(s(s(elem!1))), s(z))),
% 0.75/1.00 inference(unit_resolution,[status(thm)],[467, 5307])).
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% 0.75/1.00 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(z))) | (~r(s(s(s(elem!1))), s(z))) | (~r(z, s(s(s(elem!1))))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, s(z))) | (~r(s(s(s(elem!1))), s(z))) | (~r(z, s(s(s(elem!1))))))),
% 0.75/1.01 inference(rewrite,[status(thm)],[])).
% 0.75/1.01 tff(5310,plain,
% 0.75/1.01 (((~r(s(s(s(elem!1))), s(z))) | (~r(z, s(z))) | (~r(z, s(s(s(elem!1)))))) <=> ((~r(z, s(z))) | (~r(s(s(s(elem!1))), s(z))) | (~r(z, s(s(s(elem!1))))))),
% 0.75/1.01 inference(rewrite,[status(thm)],[])).
% 0.75/1.01 tff(5311,plain,
% 0.75/1.01 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), s(z))) | (~r(z, s(z))) | (~r(z, s(s(s(elem!1))))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(z))) | (~r(s(s(s(elem!1))), s(z))) | (~r(z, s(s(s(elem!1)))))))),
% 0.75/1.01 inference(monotonicity,[status(thm)],[5310])).
% 0.75/1.01 tff(5312,plain,
% 0.75/1.01 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), s(z))) | (~r(z, s(z))) | (~r(z, s(s(s(elem!1))))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, s(z))) | (~r(s(s(s(elem!1))), s(z))) | (~r(z, s(s(s(elem!1))))))),
% 0.75/1.01 inference(transitivity,[status(thm)],[5311, 5309])).
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% 0.75/1.01 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), s(z))) | (~r(z, s(z))) | (~r(z, s(s(s(elem!1))))))),
% 0.75/1.01 inference(quant_inst,[status(thm)],[])).
% 0.75/1.01 tff(5314,plain,
% 0.75/1.01 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, s(z))) | (~r(s(s(s(elem!1))), s(z))) | (~r(z, s(s(s(elem!1)))))),
% 0.75/1.01 inference(modus_ponens,[status(thm)],[5313, 5312])).
% 0.75/1.01 tff(5315,plain,
% 0.75/1.01 (~r(z, s(s(s(elem!1))))),
% 0.75/1.01 inference(unit_resolution,[status(thm)],[5314, 14, 2, 5308])).
% 0.75/1.01 tff(5316,plain,
% 0.75/1.01 (b(z, s(s(s(elem!1))))),
% 0.75/1.01 inference(unit_resolution,[status(thm)],[692, 5315])).
% 0.75/1.01 tff(5317,plain,
% 0.75/1.01 (~r(s(s(s(elem!1))), s(s(s(z))))),
% 0.75/1.01 inference(unit_resolution,[status(thm)],[5117, 14, 5308, 283])).
% 0.75/1.01 tff(5318,plain,
% 0.75/1.01 (~r(elem!1, s(s(s(z))))),
% 0.75/1.01 inference(unit_resolution,[status(thm)],[4845, 5317])).
% 0.75/1.01 tff(5319,plain,
% 0.75/1.01 (b(elem!1, s(s(s(z))))),
% 0.75/1.01 inference(unit_resolution,[status(thm)],[4856, 5318])).
% 0.75/1.01 tff(5320,plain,
% 0.75/1.01 (b(s(s(s(elem!1))), s(s(s(z)))) <=> b(elem!1, s(s(s(z))))),
% 0.75/1.01 inference(monotonicity,[status(thm)],[4838])).
% 0.75/1.01 tff(5321,plain,
% 0.75/1.01 (b(elem!1, s(s(s(z)))) <=> b(s(s(s(elem!1))), s(s(s(z))))),
% 0.75/1.01 inference(symmetry,[status(thm)],[5320])).
% 0.75/1.01 tff(5322,plain,
% 0.75/1.01 (b(s(s(s(elem!1))), s(s(s(z))))),
% 0.75/1.01 inference(modus_ponens,[status(thm)],[1209, 5321])).
% 0.75/1.01 tff(5323,assumption,(b(z, s(s(s(z))))), introduced(assumption)).
% 0.75/1.01 tff(5324,plain,
% 0.75/1.01 (((~![X0: $i, X2: $i, X1: $i] : ((~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(s(elem!1))))) | (~b(z, s(s(s(z))))) | (~b(s(s(s(elem!1))), s(s(s(z))))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(s(s(elem!1))))) | (~b(z, s(s(s(z))))) | (~b(s(s(s(elem!1))), s(s(s(z))))))),
% 0.75/1.01 inference(rewrite,[status(thm)],[])).
% 0.75/1.01 tff(5325,plain,
% 0.75/1.01 (((~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(s(s(z))))) | (~b(s(s(s(elem!1))), s(s(s(z))))))),
% 0.75/1.01 inference(rewrite,[status(thm)],[])).
% 0.75/1.01 tff(5326,plain,
% 0.75/1.01 (((~![X0: $i, X2: $i, X1: $i] : ((~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~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, X2: $i, X1: $i] : ((~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(s(elem!1))))) | (~b(z, s(s(s(z))))) | (~b(s(s(s(elem!1))), s(s(s(z)))))))),
% 0.75/1.01 inference(monotonicity,[status(thm)],[5325])).
% 0.75/1.01 tff(5327,plain,
% 0.75/1.01 (((~![X0: $i, X2: $i, X1: $i] : ((~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~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, X2: $i, X1: $i] : ((~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(s(s(elem!1))))) | (~b(z, s(s(s(z))))) | (~b(s(s(s(elem!1))), s(s(s(z))))))),
% 0.75/1.01 inference(transitivity,[status(thm)],[5326, 5324])).
% 0.75/1.01 tff(5328,plain,
% 0.75/1.01 ((~![X0: $i, X2: $i, X1: $i] : ((~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), s(s(s(z))))) | (~b(z, s(s(s(z))))) | (~b(z, s(s(s(elem!1))))))),
% 0.75/1.01 inference(quant_inst,[status(thm)],[])).
% 0.75/1.01 tff(5329,plain,
% 0.75/1.01 ((~![X0: $i, X2: $i, X1: $i] : ((~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(z, s(s(s(elem!1))))) | (~b(z, s(s(s(z))))) | (~b(s(s(s(elem!1))), s(s(s(z)))))),
% 0.75/1.01 inference(modus_ponens,[status(thm)],[5328, 5327])).
% 0.75/1.01 tff(5330,plain,
% 0.75/1.01 (~b(s(s(s(elem!1))), s(s(s(z))))),
% 0.75/1.01 inference(unit_resolution,[status(thm)],[5329, 117, 674, 5323])).
% 0.75/1.01 tff(5331,plain,
% 0.75/1.01 ($false),
% 0.75/1.01 inference(unit_resolution,[status(thm)],[5330, 5322])).
% 0.75/1.01 tff(5332,plain,((~b(elem!1, s(s(s(z))))) | (~(s(s(elem!1)) = s(s(s(elem!1))))) | (~b(z, s(s(s(elem!1))))) | (~b(z, s(s(s(z)))))), inference(lemma,lemma(discharge,[]))).
% 0.75/1.01 tff(5333,plain,
% 0.75/1.01 ((~b(elem!1, s(s(s(z))))) | (~b(z, s(s(s(elem!1))))) | (~b(z, s(s(s(z)))))),
% 0.75/1.01 inference(unit_resolution,[status(thm)],[5332, 4810])).
% 0.75/1.01 tff(5334,plain,
% 0.75/1.01 ($false),
% 0.75/1.01 inference(unit_resolution,[status(thm)],[5333, 5319, 5316, 5285])).
% 0.75/1.01 tff(5335,plain,((~r(s(s(s(z))), s(z))) | (~r(z, s(z)))), inference(lemma,lemma(discharge,[]))).
% 0.75/1.01 tff(5336,plain,
% 0.75/1.01 (~r(s(s(s(z))), s(z))),
% 0.75/1.01 inference(unit_resolution,[status(thm)],[5335, 2])).
% 0.75/1.01 tff(5337,plain,
% 0.75/1.01 (b(s(s(s(z))), s(z))),
% 0.75/1.01 inference(unit_resolution,[status(thm)],[347, 5336])).
% 0.75/1.01 tff(5338,plain,
% 0.75/1.01 (~b(s(s(s(z))), s(s(s(s(z)))))),
% 0.75/1.01 inference(unit_resolution,[status(thm)],[2675, 117, 562, 848])).
% 0.75/1.01 tff(5339,plain,
% 0.75/1.01 (r(s(s(s(z))), s(s(s(s(z)))))),
% 0.75/1.01 inference(unit_resolution,[status(thm)],[2685, 5338])).
% 0.75/1.01 tff(5340,plain,
% 0.75/1.01 (~b(s(s(s(elem!1))), s(s(s(s(z)))))),
% 0.75/1.01 inference(unit_resolution,[status(thm)],[5074, 2010, 562])).
% 0.75/1.01 tff(5341,plain,
% 0.75/1.01 (r(s(s(s(elem!1))), s(s(s(s(z)))))),
% 0.75/1.01 inference(unit_resolution,[status(thm)],[4886, 46, 4876, 5340])).
% 0.75/1.01 tff(5342,plain,
% 0.75/1.01 (~b(s(s(s(z))), s(s(s(elem!1))))),
% 0.75/1.01 inference(unit_resolution,[status(thm)],[2078, 117, 2010, 848])).
% 0.75/1.01 tff(5343,plain,
% 0.75/1.01 ((s(s(s(elem!1))) = s(s(s(z)))) <=> (s(s(s(z))) = s(s(s(elem!1))))),
% 0.75/1.01 inference(symmetry,[status(thm)],[2166])).
% 0.75/1.01 tff(5344,plain,
% 0.75/1.01 ((s(s(s(z))) = s(s(s(s(elem!1))))) <=> (s(s(s(z))) = s(s(s(elem!1))))),
% 0.75/1.01 inference(transitivity,[status(thm)],[4852, 5343])).
% 0.75/1.01 tff(5345,plain,
% 0.75/1.01 ((~(s(s(s(z))) = s(s(s(s(elem!1)))))) <=> (~(s(s(s(z))) = s(s(s(elem!1)))))),
% 0.75/1.01 inference(monotonicity,[status(thm)],[5344])).
% 0.75/1.01 tff(5346,plain,
% 0.75/1.01 (~(s(s(s(z))) = s(s(s(elem!1))))),
% 0.75/1.01 inference(modus_ponens,[status(thm)],[279, 5345])).
% 0.75/1.01 tff(5347,plain,
% 0.75/1.01 (r(s(s(s(z))), s(s(s(elem!1))))),
% 0.75/1.01 inference(unit_resolution,[status(thm)],[1717, 46, 5346, 5342])).
% 0.75/1.01 tff(5348,assumption,(r(s(s(s(elem!1))), s(s(s(s(z)))))), introduced(assumption)).
% 0.75/1.01 tff(5349,assumption,(r(s(s(s(z))), s(s(s(elem!1))))), introduced(assumption)).
% 0.75/1.01 tff(5350,plain,
% 0.75/1.01 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(z))), s(s(s(elem!1))))) | (~r(s(s(s(z))), s(s(s(s(z)))))) | (~r(s(s(s(elem!1))), s(s(s(s(z)))))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(z))), s(s(s(elem!1))))) | (~r(s(s(s(z))), s(s(s(s(z)))))) | (~r(s(s(s(elem!1))), s(s(s(s(z)))))))),
% 0.75/1.01 inference(rewrite,[status(thm)],[])).
% 0.75/1.01 tff(5351,plain,
% 0.75/1.01 (((~r(s(s(s(elem!1))), s(s(s(s(z)))))) | (~r(s(s(s(z))), s(s(s(s(z)))))) | (~r(s(s(s(z))), s(s(s(elem!1)))))) <=> ((~r(s(s(s(z))), s(s(s(elem!1))))) | (~r(s(s(s(z))), s(s(s(s(z)))))) | (~r(s(s(s(elem!1))), s(s(s(s(z)))))))),
% 0.75/1.01 inference(rewrite,[status(thm)],[])).
% 0.75/1.01 tff(5352,plain,
% 0.75/1.01 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), s(s(s(s(z)))))) | (~r(s(s(s(z))), s(s(s(s(z)))))) | (~r(s(s(s(z))), s(s(s(elem!1))))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(z))), s(s(s(elem!1))))) | (~r(s(s(s(z))), s(s(s(s(z)))))) | (~r(s(s(s(elem!1))), s(s(s(s(z))))))))),
% 0.75/1.01 inference(monotonicity,[status(thm)],[5351])).
% 0.75/1.01 tff(5353,plain,
% 0.75/1.01 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), s(s(s(s(z)))))) | (~r(s(s(s(z))), s(s(s(s(z)))))) | (~r(s(s(s(z))), s(s(s(elem!1))))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(z))), s(s(s(elem!1))))) | (~r(s(s(s(z))), s(s(s(s(z)))))) | (~r(s(s(s(elem!1))), s(s(s(s(z)))))))),
% 0.75/1.01 inference(transitivity,[status(thm)],[5352, 5350])).
% 0.75/1.01 tff(5354,plain,
% 0.75/1.01 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), s(s(s(s(z)))))) | (~r(s(s(s(z))), s(s(s(s(z)))))) | (~r(s(s(s(z))), s(s(s(elem!1))))))),
% 0.75/1.01 inference(quant_inst,[status(thm)],[])).
% 0.75/1.01 tff(5355,plain,
% 0.75/1.01 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(z))), s(s(s(elem!1))))) | (~r(s(s(s(z))), s(s(s(s(z)))))) | (~r(s(s(s(elem!1))), s(s(s(s(z))))))),
% 0.75/1.01 inference(modus_ponens,[status(thm)],[5354, 5353])).
% 0.75/1.01 tff(5356,plain,
% 0.75/1.01 ($false),
% 0.75/1.01 inference(unit_resolution,[status(thm)],[5355, 14, 5024, 5349, 5348])).
% 0.75/1.01 tff(5357,plain,((~r(s(s(s(z))), s(s(s(s(z)))))) | (~r(s(s(s(z))), s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), s(s(s(s(z))))))), inference(lemma,lemma(discharge,[]))).
% 0.75/1.01 tff(5358,plain,
% 0.75/1.01 ($false),
% 0.75/1.01 inference(unit_resolution,[status(thm)],[5357, 5347, 5341, 5339])).
% 0.75/1.01 tff(5359,plain,((~b(s(s(s(elem!1))), s(z))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(s(z)))), s(z)))), inference(lemma,lemma(discharge,[]))).
% 0.75/1.01 tff(5360,plain,
% 0.75/1.01 (~b(s(s(s(elem!1))), s(z))),
% 0.75/1.01 inference(unit_resolution,[status(thm)],[5359, 5337, 5283])).
% 0.75/1.01 tff(5361,plain,
% 0.75/1.01 (r(s(s(s(elem!1))), s(z))),
% 0.75/1.01 inference(unit_resolution,[status(thm)],[467, 5360])).
% 0.75/1.01 tff(5362,plain,
% 0.75/1.01 (~r(s(s(s(elem!1))), s(s(z)))),
% 0.75/1.01 inference(unit_resolution,[status(thm)],[5198, 14, 1911, 53])).
% 0.75/1.01 tff(5363,plain,
% 0.75/1.01 (~r(elem!1, s(s(z)))),
% 0.75/1.01 inference(modus_ponens,[status(thm)],[5362, 5193])).
% 0.75/1.01 tff(5364,plain,
% 0.75/1.01 (b(elem!1, s(s(z)))),
% 0.75/1.01 inference(unit_resolution,[status(thm)],[5205, 5363])).
% 0.75/1.01 tff(5365,plain,
% 0.75/1.01 (b(s(s(s(elem!1))), s(s(z)))),
% 0.75/1.01 inference(modus_ponens,[status(thm)],[5364, 5191])).
% 0.75/1.01 tff(5366,plain,
% 0.75/1.01 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(z))) | (~r(s(s(s(elem!1))), s(z))) | (~r(s(s(s(elem!1))), z)))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, s(z))) | (~r(s(s(s(elem!1))), s(z))) | (~r(s(s(s(elem!1))), z)))),
% 0.75/1.01 inference(rewrite,[status(thm)],[])).
% 0.75/1.01 tff(5367,plain,
% 0.75/1.01 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(z))) | (~r(s(s(s(elem!1))), s(z))) | (~r(s(s(s(elem!1))), z)))),
% 0.75/1.01 inference(quant_inst,[status(thm)],[])).
% 0.75/1.01 tff(5368,plain,
% 0.75/1.01 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, s(z))) | (~r(s(s(s(elem!1))), s(z))) | (~r(s(s(s(elem!1))), z))),
% 0.75/1.01 inference(modus_ponens,[status(thm)],[5367, 5366])).
% 0.75/1.01 tff(5369,plain,
% 0.75/1.01 (~r(s(s(s(elem!1))), z)),
% 0.75/1.01 inference(unit_resolution,[status(thm)],[5368, 14, 2, 1911])).
% 0.75/1.01 tff(5370,plain,
% 0.75/1.01 (b(s(s(s(elem!1))), z)),
% 0.75/1.01 inference(unit_resolution,[status(thm)],[211, 5369])).
% 0.75/1.01 tff(5371,plain,
% 0.75/1.01 (((~![X0: $i, X2: $i, X1: $i] : ((~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), z)) | (~b(s(s(s(elem!1))), z)) | (~b(s(s(s(elem!1))), s(s(z)))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(z)), z)) | (~b(s(s(s(elem!1))), z)) | (~b(s(s(s(elem!1))), s(s(z)))))),
% 0.75/1.01 inference(rewrite,[status(thm)],[])).
% 0.75/1.01 tff(5372,plain,
% 0.75/1.01 ((~![X0: $i, X2: $i, X1: $i] : ((~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), z)) | (~b(s(s(s(elem!1))), z)) | (~b(s(s(s(elem!1))), s(s(z)))))),
% 0.75/1.01 inference(quant_inst,[status(thm)],[])).
% 0.75/1.01 tff(5373,plain,
% 0.75/1.01 ((~![X0: $i, X2: $i, X1: $i] : ((~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(z)), z)) | (~b(s(s(s(elem!1))), z)) | (~b(s(s(s(elem!1))), s(s(z))))),
% 0.75/1.01 inference(modus_ponens,[status(thm)],[5372, 5371])).
% 0.75/1.01 tff(5374,plain,
% 0.75/1.01 (~b(s(s(s(elem!1))), s(s(z)))),
% 0.75/1.01 inference(unit_resolution,[status(thm)],[5373, 117, 5370, 63])).
% 0.75/1.01 tff(5375,plain,
% 0.75/1.01 ($false),
% 0.75/1.01 inference(unit_resolution,[status(thm)],[5374, 5365])).
% 0.75/1.01 tff(5376,plain,((~r(s(s(s(elem!1))), s(z))) | (~r(s(s(z)), s(z))) | (~r(z, s(z)))), inference(lemma,lemma(discharge,[]))).
% 0.75/1.01 tff(5377,plain,
% 0.75/1.01 (~r(s(s(z)), s(z))),
% 0.75/1.01 inference(unit_resolution,[status(thm)],[5376, 5361, 2])).
% 0.75/1.01 tff(5378,plain,
% 0.75/1.01 (b(s(s(z)), s(z))),
% 0.75/1.01 inference(unit_resolution,[status(thm)],[141, 5377])).
% 0.75/1.01 tff(5379,plain,
% 0.75/1.01 (~b(s(s(z)), s(s(s(s(z)))))),
% 0.75/1.01 inference(unit_resolution,[status(thm)],[5085, 117, 5283, 5378])).
% 0.75/1.01 tff(5380,plain,
% 0.75/1.01 (r(s(s(z)), s(s(s(s(z)))))),
% 0.75/1.01 inference(unit_resolution,[status(thm)],[106, 5379])).
% 0.75/1.01 tff(5381,plain,
% 0.75/1.01 (~b(s(s(z)), s(s(s(z))))),
% 0.75/1.01 inference(unit_resolution,[status(thm)],[4931, 117, 5337, 5378])).
% 0.75/1.01 tff(5382,plain,
% 0.75/1.01 (r(s(s(z)), s(s(s(z))))),
% 0.75/1.01 inference(unit_resolution,[status(thm)],[4949, 5381])).
% 0.75/1.01 tff(5383,plain,
% 0.75/1.01 (~b(s(s(s(z))), s(s(s(s(z)))))),
% 0.75/1.01 inference(unit_resolution,[status(thm)],[2675, 117, 5283, 5337])).
% 0.75/1.01 tff(5384,plain,
% 0.75/1.01 (r(s(s(s(z))), s(s(s(s(z)))))),
% 0.75/1.01 inference(unit_resolution,[status(thm)],[2685, 5383])).
% 0.75/1.01 tff(5385,plain,
% 0.75/1.01 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(z))), s(s(s(s(z)))))) | (~r(s(s(z)), s(s(s(s(z)))))) | (~r(s(s(z)), s(s(s(z))))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(z))), s(s(s(s(z)))))) | (~r(s(s(z)), s(s(s(s(z)))))) | (~r(s(s(z)), s(s(s(z))))))),
% 0.75/1.01 inference(rewrite,[status(thm)],[])).
% 0.75/1.01 tff(5386,plain,
% 0.75/1.01 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(z))), s(s(s(s(z)))))) | (~r(s(s(z)), s(s(s(s(z)))))) | (~r(s(s(z)), s(s(s(z))))))),
% 0.75/1.01 inference(quant_inst,[status(thm)],[])).
% 0.75/1.01 tff(5387,plain,
% 0.75/1.01 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(z))), s(s(s(s(z)))))) | (~r(s(s(z)), s(s(s(s(z)))))) | (~r(s(s(z)), s(s(s(z)))))),
% 0.75/1.01 inference(modus_ponens,[status(thm)],[5386, 5385])).
% 0.75/1.01 tff(5388,plain,
% 0.75/1.01 ($false),
% 0.75/1.01 inference(unit_resolution,[status(thm)],[5387, 14, 5384, 5382, 5380])).
% 0.75/1.01 tff(5389,plain,(~r(z, s(z))), inference(lemma,lemma(discharge,[]))).
% 0.75/1.01 tff(5390,plain,
% 0.75/1.01 (b(z, s(z))),
% 0.75/1.01 inference(unit_resolution,[status(thm)],[599, 5389])).
% 0.75/1.01 tff(5391,plain,
% 0.75/1.01 ((~b(s(s(z)), s(z))) | (~b(s(s(s(s(z)))), s(z)))),
% 0.75/1.01 inference(unit_resolution,[status(thm)],[5103, 5390])).
% 0.75/1.01 tff(5392,plain,
% 0.75/1.01 (~b(s(s(s(s(z)))), s(z))),
% 0.75/1.01 inference(unit_resolution,[status(thm)],[5391, 1])).
% 0.75/1.01 tff(5393,plain,
% 0.75/1.01 (r(s(s(s(s(z)))), s(z))),
% 0.75/1.01 inference(unit_resolution,[status(thm)],[554, 5392])).
% 0.75/1.01 tff(5394,plain,
% 0.75/1.01 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), z)) | (~r(s(s(s(s(z)))), z)) | (~r(s(s(s(s(z)))), s(z))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(z), z)) | (~r(s(s(s(s(z)))), z)) | (~r(s(s(s(s(z)))), s(z))))),
% 0.75/1.01 inference(rewrite,[status(thm)],[])).
% 0.75/1.01 tff(5395,plain,
% 0.75/1.01 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), z)) | (~r(s(s(s(s(z)))), z)) | (~r(s(s(s(s(z)))), s(z))))),
% 0.75/1.01 inference(quant_inst,[status(thm)],[])).
% 0.75/1.01 tff(5396,plain,
% 0.75/1.01 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(z), z)) | (~r(s(s(s(s(z)))), z)) | (~r(s(s(s(s(z)))), s(z)))),
% 0.75/1.01 inference(modus_ponens,[status(thm)],[5395, 5394])).
% 0.75/1.01 tff(5397,plain,
% 0.75/1.01 ($false),
% 0.75/1.01 inference(unit_resolution,[status(thm)],[5396, 14, 183, 3, 3860])).
% 0.75/1.01 tff(5398,plain,((~r(s(s(s(s(z)))), z)) | (~r(s(z), z)) | (~r(s(s(s(s(z)))), s(z)))), inference(lemma,lemma(discharge,[]))).
% 0.75/1.01 tff(5399,plain,
% 0.75/1.01 ((~r(s(s(s(s(z)))), z)) | (~r(s(s(s(s(z)))), s(z)))),
% 0.75/1.01 inference(unit_resolution,[status(thm)],[5398, 5242])).
% 0.75/1.01 tff(5400,plain,
% 0.75/1.01 (~r(s(s(s(s(z)))), z)),
% 0.75/1.01 inference(unit_resolution,[status(thm)],[5399, 5393])).
% 0.75/1.01 tff(5401,plain,
% 0.75/1.01 (b(s(s(s(s(z)))), z)),
% 0.75/1.01 inference(unit_resolution,[status(thm)],[582, 5400])).
% 0.75/1.01 tff(5402,plain,
% 0.75/1.01 ((~b(s(s(z)), s(z))) | (~b(s(s(s(z))), s(z)))),
% 0.75/1.01 inference(unit_resolution,[status(thm)],[4966, 5390])).
% 0.75/1.01 tff(5403,plain,
% 0.75/1.01 (~b(s(s(s(z))), s(z))),
% 0.75/1.01 inference(unit_resolution,[status(thm)],[5402, 1])).
% 0.75/1.01 tff(5404,plain,
% 0.75/1.01 (r(s(s(s(z))), s(z))),
% 0.75/1.01 inference(unit_resolution,[status(thm)],[347, 5403])).
% 0.75/1.01 tff(5405,plain,
% 0.75/1.01 (~r(s(s(s(z))), z)),
% 0.75/1.01 inference(unit_resolution,[status(thm)],[5275, 5404])).
% 0.75/1.01 tff(5406,plain,
% 0.75/1.01 (b(s(s(s(z))), z)),
% 0.75/1.01 inference(unit_resolution,[status(thm)],[823, 5405])).
% 0.75/1.01 tff(5407,plain,
% 0.75/1.01 (~r(s(s(s(z))), s(s(s(s(z)))))),
% 0.75/1.01 inference(unit_resolution,[status(thm)],[5026, 5393, 5404])).
% 0.75/1.01 tff(5408,plain,
% 0.75/1.01 (b(s(s(s(z))), s(s(s(s(z)))))),
% 0.75/1.01 inference(unit_resolution,[status(thm)],[2685, 5407])).
% 0.75/1.01 tff(5409,plain,
% 0.75/1.01 (((~![X0: $i, X2: $i, X1: $i] : ((~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(z))), z)) | (~b(s(s(s(s(z)))), z)))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(z))), z)) | (~b(s(s(s(s(z)))), z)))),
% 0.75/1.01 inference(rewrite,[status(thm)],[])).
% 0.75/1.01 tff(5410,plain,
% 0.75/1.01 (((~b(s(s(s(s(z)))), z)) | (~b(s(s(s(z))), z)) | (~b(s(s(s(z))), s(s(s(s(z))))))) <=> ((~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(z))), z)) | (~b(s(s(s(s(z)))), z)))),
% 0.75/1.01 inference(rewrite,[status(thm)],[])).
% 0.75/1.01 tff(5411,plain,
% 0.75/1.01 (((~![X0: $i, X2: $i, X1: $i] : ((~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(z)))), z)) | (~b(s(s(s(z))), z)) | (~b(s(s(s(z))), s(s(s(s(z)))))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(z))), z)) | (~b(s(s(s(s(z)))), z))))),
% 0.75/1.01 inference(monotonicity,[status(thm)],[5410])).
% 0.75/1.01 tff(5412,plain,
% 0.75/1.01 (((~![X0: $i, X2: $i, X1: $i] : ((~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(z)))), z)) | (~b(s(s(s(z))), z)) | (~b(s(s(s(z))), s(s(s(s(z)))))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(z))), z)) | (~b(s(s(s(s(z)))), z)))),
% 0.75/1.01 inference(transitivity,[status(thm)],[5411, 5409])).
% 0.75/1.01 tff(5413,plain,
% 0.75/1.01 ((~![X0: $i, X2: $i, X1: $i] : ((~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(z)))), z)) | (~b(s(s(s(z))), z)) | (~b(s(s(s(z))), s(s(s(s(z)))))))),
% 0.75/1.01 inference(quant_inst,[status(thm)],[])).
% 0.75/1.01 tff(5414,plain,
% 0.75/1.01 ((~![X0: $i, X2: $i, X1: $i] : ((~b(X1, X2)) | (~b(X0, X2)) | (~b(X0, X1)))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(z))), z)) | (~b(s(s(s(s(z)))), z))),
% 0.75/1.01 inference(modus_ponens,[status(thm)],[5413, 5412])).
% 0.75/1.01 tff(5415,plain,
% 0.75/1.01 ($false),
% 0.75/1.01 inference(unit_resolution,[status(thm)],[5414, 117, 5408, 5406, 5401])).
% 0.75/1.01 tff(5416,plain,(~b(s(s(z)), s(z))), inference(lemma,lemma(discharge,[]))).
% 0.75/1.01 tff(5417,plain,
% 0.75/1.01 (r(s(s(z)), s(z))),
% 0.75/1.01 inference(unit_resolution,[status(thm)],[141, 5416])).
% 0.75/1.01 tff(5418,plain,
% 0.75/1.01 (~b(s(s(s(z))), z)),
% 0.75/1.01 inference(unit_resolution,[status(thm)],[965, 117, 5390, 848])).
% 0.75/1.01 tff(5419,plain,
% 0.75/1.01 (r(s(s(s(z))), z)),
% 0.75/1.01 inference(unit_resolution,[status(thm)],[823, 5418])).
% 0.75/1.01 tff(5420,plain,
% 0.75/1.01 ((~b(s(s(s(z))), s(z))) | (~r(s(s(s(elem!1))), s(z))) | (~r(s(s(s(z))), z))),
% 0.75/1.01 inference(unit_resolution,[status(thm)],[5222, 5390])).
% 0.75/1.01 tff(5421,plain,
% 0.75/1.01 (~r(s(s(s(elem!1))), s(z))),
% 0.75/1.01 inference(unit_resolution,[status(thm)],[5420, 5419, 848])).
% 0.75/1.01 tff(5422,plain,
% 0.75/1.01 (b(s(s(s(elem!1))), s(z))),
% 0.75/1.01 inference(unit_resolution,[status(thm)],[467, 5421])).
% 0.75/1.01 tff(5423,plain,
% 0.75/1.01 (b(s(s(s(z))), s(s(s(elem!1)))) <=> b(s(s(s(z))), elem!1)),
% 0.75/1.01 inference(monotonicity,[status(thm)],[4838])).
% 0.75/1.01 tff(5424,plain,
% 0.75/1.01 (b(s(s(s(z))), elem!1) <=> b(s(s(s(z))), s(s(s(elem!1))))),
% 0.75/1.01 inference(symmetry,[status(thm)],[5423])).
% 0.75/1.01 tff(5425,plain,
% 0.75/1.01 (s(s(s(s(s(elem!1))))) = s(s(s(s(elem!1))))),
% 0.75/1.01 inference(monotonicity,[status(thm)],[4260])).
% 0.75/1.01 tff(5426,plain,
% 0.75/1.01 (s(s(s(s(s(elem!1))))) = elem!1),
% 0.75/1.01 inference(transitivity,[status(thm)],[5425, 4260, 4256, 4837])).
% 0.75/1.01 tff(5427,plain,
% 0.75/1.01 ((s(s(s(z))) = s(s(s(s(s(elem!1)))))) <=> (s(s(s(z))) = elem!1)),
% 0.75/1.01 inference(monotonicity,[status(thm)],[5426])).
% 0.75/1.01 tff(5428,plain,
% 0.75/1.01 ((~(s(s(s(z))) = s(s(s(s(s(elem!1))))))) <=> (~(s(s(s(z))) = elem!1))),
% 0.75/1.01 inference(monotonicity,[status(thm)],[5427])).
% 0.75/1.01 tff(5429,plain,
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% 0.75/1.01 inference(modus_ponens,[status(thm)],[317, 5428])).
% 0.75/1.01 tff(5430,plain,
% 0.75/1.01 (r(s(s(s(z))), s(s(s(elem!1)))) <=> r(s(s(s(z))), elem!1)),
% 0.75/1.01 inference(monotonicity,[status(thm)],[4838])).
% 0.75/1.01 tff(5431,plain,
% 0.75/1.01 ((~r(s(s(s(z))), s(s(s(elem!1))))) <=> (~r(s(s(s(z))), elem!1))),
% 0.75/1.01 inference(monotonicity,[status(thm)],[5430])).
% 0.75/1.01 tff(5432,plain,
% 0.75/1.01 (~r(s(s(s(z))), s(s(s(elem!1))))),
% 0.75/1.01 inference(unit_resolution,[status(thm)],[1713, 14, 196, 180])).
% 0.75/1.01 tff(5433,plain,
% 0.75/1.01 (~r(s(s(s(z))), elem!1)),
% 0.75/1.01 inference(modus_ponens,[status(thm)],[5432, 5431])).
% 0.75/1.01 tff(5434,plain,
% 0.75/1.01 (b(s(s(s(z))), elem!1)),
% 0.75/1.01 inference(unit_resolution,[status(thm)],[756, 5433, 5429])).
% 0.75/1.01 tff(5435,plain,
% 0.75/1.01 (b(s(s(s(z))), s(s(s(elem!1))))),
% 0.75/1.01 inference(modus_ponens,[status(thm)],[5434, 5424])).
% 0.75/1.01 tff(5436,plain,
% 0.75/1.01 (~r(s(s(s(z))), s(z))),
% 0.75/1.01 inference(unit_resolution,[status(thm)],[2171, 14, 183, 180])).
% 0.75/1.01 tff(5437,plain,
% 0.75/1.01 (b(s(s(s(z))), s(z))),
% 0.75/1.01 inference(unit_resolution,[status(thm)],[347, 5436])).
% 0.75/1.01 tff(5438,plain,
% 0.75/1.01 (~b(s(s(s(z))), s(s(s(elem!1))))),
% 0.75/1.01 inference(unit_resolution,[status(thm)],[2078, 117, 2347, 5437])).
% 0.75/1.01 tff(5439,plain,
% 0.75/1.01 ($false),
% 0.75/1.01 inference(unit_resolution,[status(thm)],[5438, 5435])).
% 0.75/1.01 tff(5440,plain,((~r(s(s(s(z))), z)) | (~(s(s(elem!1)) = s(s(s(elem!1))))) | (~r(s(z), z)) | (~r(s(s(s(elem!1))), z))), inference(lemma,lemma(discharge,[]))).
% 0.75/1.01 tff(5441,plain,
% 0.75/1.01 ((~r(s(s(s(z))), z)) | (~r(s(z), z)) | (~r(s(s(s(elem!1))), z))),
% 0.75/1.01 inference(unit_resolution,[status(thm)],[5440, 4810])).
% 0.75/1.01 tff(5442,plain,
% 0.75/1.01 ((~r(s(s(s(z))), z)) | (~r(s(s(s(elem!1))), z))),
% 0.75/1.01 inference(unit_resolution,[status(thm)],[5441, 5242])).
% 0.75/1.01 tff(5443,plain,
% 0.75/1.01 (~r(s(s(s(elem!1))), z)),
% 0.75/1.01 inference(unit_resolution,[status(thm)],[5442, 5419])).
% 0.75/1.01 tff(5444,plain,
% 0.75/1.01 (b(s(s(s(elem!1))), z)),
% 0.75/1.01 inference(unit_resolution,[status(thm)],[211, 5443])).
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% 0.75/1.01 (((~![X0: $i, X2: $i, X1: $i] : ((~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(elem!1))), z)))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~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(elem!1))), z)))),
% 0.75/1.02 inference(rewrite,[status(thm)],[])).
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% 0.75/1.02 inference(rewrite,[status(thm)],[])).
% 0.75/1.02 tff(5447,plain,
% 0.75/1.02 (((~![X0: $i, X2: $i, X1: $i] : ((~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(elem!1))), z)))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~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(elem!1))), z))))),
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% 0.75/1.02 tff(5448,plain,
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% 0.75/1.02 inference(transitivity,[status(thm)],[5447, 5445])).
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% 0.75/1.02 inference(quant_inst,[status(thm)],[])).
% 0.75/1.02 tff(5450,plain,
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% 0.75/1.02 inference(modus_ponens,[status(thm)],[5449, 5448])).
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% 0.75/1.02 tff(5452,plain,(~b(s(s(s(z))), s(z))), inference(lemma,lemma(discharge,[]))).
% 0.75/1.02 tff(5453,plain,
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% 0.75/1.02 inference(unit_resolution,[status(thm)],[347, 5452])).
% 0.75/1.02 tff(5454,plain,
% 0.75/1.02 (~r(s(s(s(s(z)))), s(z))),
% 0.75/1.02 inference(unit_resolution,[status(thm)],[5033, 5453, 5417])).
% 0.75/1.02 tff(5455,plain,
% 0.75/1.02 (b(s(s(s(s(z)))), s(z))),
% 0.75/1.02 inference(unit_resolution,[status(thm)],[554, 5454])).
% 0.75/1.02 tff(5456,plain,
% 0.75/1.02 (s(elem!1) = s(s(s(elem!1)))),
% 0.75/1.02 inference(transitivity,[status(thm)],[167, 4868, 151, 4810])).
% 0.75/1.02 tff(5457,plain,
% 0.75/1.02 (b(s(elem!1), s(z)) <=> b(s(s(s(elem!1))), s(z))),
% 0.75/1.02 inference(monotonicity,[status(thm)],[5456])).
% 0.75/1.02 tff(5458,plain,
% 0.75/1.02 (b(s(s(s(elem!1))), s(z)) <=> b(s(elem!1), s(z))),
% 0.75/1.02 inference(symmetry,[status(thm)],[5457])).
% 0.75/1.02 tff(5459,plain,
% 0.75/1.02 (~r(s(s(s(elem!1))), s(s(s(z))))),
% 0.75/1.02 inference(unit_resolution,[status(thm)],[5117, 14, 1911, 5453])).
% 0.75/1.02 tff(5460,plain,
% 0.75/1.02 (~r(elem!1, s(s(s(z))))),
% 0.75/1.02 inference(unit_resolution,[status(thm)],[4845, 5459])).
% 0.75/1.02 tff(5461,plain,
% 0.75/1.02 (b(elem!1, s(s(s(z))))),
% 0.75/1.02 inference(unit_resolution,[status(thm)],[4856, 5460])).
% 0.75/1.02 tff(5462,plain,
% 0.75/1.02 (b(s(s(s(elem!1))), s(s(s(z))))),
% 0.75/1.02 inference(modus_ponens,[status(thm)],[5461, 4835])).
% 0.75/1.02 tff(5463,plain,
% 0.75/1.02 (~r(s(s(s(z))), z)),
% 0.75/1.02 inference(unit_resolution,[status(thm)],[5275, 5453])).
% 0.75/1.02 tff(5464,plain,
% 0.75/1.02 (b(s(s(s(z))), z)),
% 0.75/1.02 inference(unit_resolution,[status(thm)],[823, 5463])).
% 0.75/1.02 tff(5465,plain,
% 0.75/1.02 (r(s(s(elem!1)), s(z))),
% 0.75/1.02 inference(modus_ponens,[status(thm)],[1911, 5061])).
% 0.75/1.02 tff(5466,plain,
% 0.75/1.02 (~r(s(s(elem!1)), z)),
% 0.75/1.02 inference(unit_resolution,[status(thm)],[5243, 5465])).
% 0.75/1.02 tff(5467,plain,
% 0.75/1.02 (b(s(s(elem!1)), z)),
% 0.75/1.02 inference(unit_resolution,[status(thm)],[1025, 5466])).
% 0.75/1.02 tff(5468,plain,
% 0.75/1.02 (b(s(s(s(elem!1))), z)),
% 0.75/1.02 inference(modus_ponens,[status(thm)],[5467, 5172])).
% 0.75/1.02 tff(5469,plain,
% 0.75/1.02 ($false),
% 0.75/1.02 inference(unit_resolution,[status(thm)],[2965, 117, 5468, 5464, 5462])).
% 0.75/1.02 tff(5470,plain,(~r(s(s(s(elem!1))), s(z))), inference(lemma,lemma(discharge,[]))).
% 0.75/1.02 tff(5471,plain,
% 0.75/1.02 (b(s(s(s(elem!1))), s(z))),
% 0.75/1.02 inference(unit_resolution,[status(thm)],[467, 5470])).
% 0.75/1.02 tff(5472,plain,
% 0.75/1.02 (b(s(elem!1), s(z))),
% 0.75/1.02 inference(modus_ponens,[status(thm)],[5471, 5458])).
% 0.75/1.02 tff(5473,plain,
% 0.75/1.02 ((~b(s(s(s(s(z)))), s(z))) | (~r(s(elem!1), z)) | (~b(s(elem!1), s(z))) | (~b(z, s(z)))),
% 0.75/1.02 inference(unit_resolution,[status(thm)],[798, 4873])).
% 0.75/1.02 tff(5474,plain,
% 0.75/1.02 ((~b(s(s(s(s(z)))), s(z))) | (~r(s(elem!1), z)) | (~b(s(elem!1), s(z)))),
% 0.75/1.02 inference(unit_resolution,[status(thm)],[5473, 5390])).
% 0.75/1.02 tff(5475,plain,
% 0.75/1.02 (~r(s(elem!1), z)),
% 0.75/1.02 inference(unit_resolution,[status(thm)],[5474, 5472, 5455])).
% 0.75/1.02 tff(5476,plain,
% 0.75/1.02 (~b(s(s(s(elem!1))), z)),
% 0.75/1.02 inference(unit_resolution,[status(thm)],[5450, 117, 5390, 5471])).
% 0.75/1.02 tff(5477,plain,
% 0.75/1.02 (r(s(s(s(elem!1))), z)),
% 0.75/1.02 inference(unit_resolution,[status(thm)],[211, 5476])).
% 0.75/1.02 tff(5478,plain,
% 0.75/1.02 ((~r(s(s(s(elem!1))), z)) | r(s(elem!1), z)),
% 0.75/1.02 inference(unit_resolution,[status(thm)],[880, 4872])).
% 0.75/1.02 tff(5479,plain,
% 0.75/1.02 ($false),
% 0.75/1.02 inference(unit_resolution,[status(thm)],[5478, 5477, 5475])).
% 0.75/1.02 % SZS output end Proof
% 0.75/1.02 % E exiting
%------------------------------------------------------------------------------